Are you an art enthusiast? 🎨✨ Whether you’re an aspiring artist or simply appreciate the beauty of creativity, we’ve got you covered. Our list of top art emojis is here to inspire and enhance your conversations. From paintbrushes 🖌️ to masterpieces 🖼️, these emojis will help you express your love for all things artistic. So get ready to unleash your inner Picasso and dive into the world of art emojis! 🎨✨
Emojis to represent Art Emojis – Usage, Copy & Paste
Emoji | Meaning | Copy |
🎨 | artist paletteSymbolizing art and creativity. | |
🖌 | paintbrushRepresenting painting and artistic expression. | |
🖼 | framed pictureAssociated with traditional art and gallery exhibits. | |
🎭 | performing artsRepresenting performing arts and theater. | |
🎵 | musical noteSymbolizing music and musical talents. | |
🎶 | musical notesAssociated with writing and composing music. | |
🎬 | clapper boardSymbolizing filmmaking and the art of cinema. | |
📷 | cameraAssociated with photography and capturing artistic moments. | |
📚 | booksRepresenting literature and the art of storytelling. | |
🖋 | fountain penSymbolizing writing and literary arts. | |
📝 | memoAssociated with note-taking and the art of communication. | |
🖍 | crayonRepresenting childhood art and coloring. | |
🎥 | movie cameraAssociated with filmmaking and cinematography. | |
🎤 | microphoneRepresenting the performing arts, particularly singing or public speaking. | |
🎧 | headphoneRepresenting audio technology and the art of sound. | |
🎸 | guitarAssociated with music and the art of playing instruments. | |
🎹 | musical keyboardSymbolizing music composition and piano playing. | |
📸 | camera with flashAssociated with photography and capturing moments. | |
🎼 | musical scoreRepresenting sheet music and the art of reading music. | |
📹 | video cameraAssociated with videography and the art of recording. | |
📖 | open bookSymbolizing reading and the art of storytelling. | |
✒ | black nibRepresenting calligraphy and the art of handwriting. | |
🎻 | violinDepicting classical music and musical instruments. | |
🖊 | penDepicting writing and calligraphy. | |
🗿 | moaiRepresenting ancient art and sculptures. | |
🛠 | hammer and wrenchDepicting a variety of artist's tools. | |
📔 | notebook with decorative coverSymbolizing sketching and jotting down ideas. | |
🖥 | desktop computerRepresenting digital art and design. | |
👨🎨 | man artistDepicting a person engaged in creating art. | |
✏ | pencilSymbolizing drawing and sketching. | |
🌆 | cityscape at duskSymbolizing urban art and city landscapes. | |
🏞 | national parkRepresenting landscapes and natural art. | |
✍ | writing handSymbolizing creative writing and storytelling. |
Related emojis
Emoji Combos for Art Emojis – Usage, Copy & Paste
🟪🟪🟪🟪🟪🟪🟥🟥🟪🟪🟪🟪🟪🟪
🟪🟪🟪🟪🟪🟪🟥🟥🟥🟪🟪🟪🟪🟪
🟪🟪🟪🟪🟪⬜⬜⬜⬜🟪🟪🟪🟪🟪
🟪🟪🟪🟪⬜⬛⬜🟨🟨⬛🟪🟪🟪🟪
🟪🟪🟪🟪⬜⬜⬜🟥🟥⬜🟪🟪🟪🟪
🟪🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪🟪
🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪
🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪
🟪🟪🟪⬜⬜⬜⬜⬜⬜⬜⬜🟪🟪🟪
🟪🟪🟫🟨🟨🟨🟨🟨🟨🟨🟨🟫🟪🟪
🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⡼⣷⠼⣆⣼⢇⣿⣄⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠙⠢⠐⠉⠉⣴⣾⣽⢟⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠤⢴⣿⠿⢋⣴⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⠻⣿⣶⣦⣭⣉⠁⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠉⠉⠉⠉⠇⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⣦⣀⠀⠀⣀⡴⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⠛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣶⣯⣟⡷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⢿⣿⣮⡻⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⢿⣿⣞⢷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣴⡄⠀⠀⠹⣿⣎⢿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⣿⣄⠀⠀⠹⣿⣏⣿⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⣤⣾⠟⠃⠀⠀⢹⣿⣼⣷⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠛⠀⠀⠀⠀⠀⣿⣷⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣴⣿⣿⣿⣶⣶⠀⠀⠀⣿⣿⢾⣏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣧⣻⣼⣿⠋⠀⠀⢠⣿⣿⣾⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠿⣿⡧⠀⢀⣾⣿⢧⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣠⣾⣿⢯⣿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠈⠁⠉⠉⠉⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣾⣿⣿⣿⣿⡽⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⣿⣟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣹⣟⣿⣶⡀⠀⠀⠀⣀⡀⢀⠀⠄⡀⠹⣿⣿⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡟⣾⣿⡇⠀⠠⠜⠁⠀⠄⡈⢀⠐⠀⣻⣿⣧⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠏⠀⣰⠃⠠⠈⠐⡀⠄⢢⡔⠀⢸⣿⡷⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢀⠁⣂⣤⠾⠋⠀⠀⣾⣿⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠁⢀⣤⣤⣾⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣽⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠛⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⢹⣿⣞⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⢻⣿⣹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣠⣴⡿⠋⠀⡀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⣀⠄⠁⠠⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⡇⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣁⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠠⣿⣿⣟⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠁⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢷⢹⣿⡾⣝⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⢶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠀⠻⣿⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣷⡄⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣽⣟⡿⢶⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣰⠎⠀⠂⢁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⡀⠄⠁⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡀⠐⠀⡈⠠⠁⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠱⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀
⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⡡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀
⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣐⢣⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⢣⡙⠦⡙⠦⣙⠰⣃⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠻⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡑⠎⡔⢢⡑⢎⡡⢓⠬⡑⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⡑⢎⡜⡱⡘⢥⠚⡤⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣎⢷⣣⢻⢮⡻⣵⣻⣾⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢞⡷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣷⣴⣶⣾⣿⡿⠋⠙⢿⣷⡀⠀⠀⠀⠠⣶⣶⣾⣿⣿⣿⠿⠿⡛⡍⢦⠑⣎⡱⢌⢆⢣⡱⢌⢎⡱⢊⡜⡡⢎⡱⢪⣴⣿⡿⣛⣼⣾⣿⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠹⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⢀⣼⣿⣿⠫⣌⢣⢣⠱⡘⢦⡩⢔⡡⢎⡜⢢⡑⢎⢢⡑⢣⠜⣑⣮⣽⣿⠟⣏⣶⣿⡿⣿⣵⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣻⣵⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣯⣽⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣀⣀⣴⣿⣿⡛⠥⣃⢆⢣⠎⡱⣉⢒⡌⢦⡑⣊⠌⢧⡘⡌⠦⣙⣢⣽⣿⡿⢫⢥⣿⣾⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⡿⢿⡿⢿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⡿⢛⡍⢳⡐⢆⡛⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⠿⡛⢤⡙⢢⡑⣊⠦⡙⠴⡡⢎⡘⠦⢱⡘⡜⢢⢱⣸⣵⣿⡿⢟⢣⣾⣿⣿⣿⣽⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⢫⠱⡌⢣⡘⢥⡘⠦⠱⣌⠹⢻⢿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⡿⡛⢥⠒⡔⢢⠜⣢⢙⠴⣈⠇⡜⠤⢣⡙⠦⡱⢎⠬⣑⢣⠒⣍⣶⣿⣿⢟⢫⣼⣾⣿⣿⣯⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⡿⢡⠎⡱⢌⠣⢍⠦⢱⠩⡱⢌⢣⢃⠎⡜⣩⠛⡟⣛⠻⡛⢭⡙⡔⢢⡙⢆⡹⢌⢣⠚⣄⢋⠦⡑⢎⡌⢣⠣⢜⡡⢓⡌⢲⣡⣾⣿⣿⠿⣋⣶⣾⣿⡿⣻⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣇⠣⢎⡑⢎⡱⢊⡜⡡⢎⠱⡌⢦⡉⠞⡰⢡⢋⠴⢡⢣⢙⠢⡜⢌⠣⡜⣡⠚⡌⢦⡙⠤⢋⠴⣉⠖⣌⢣⡙⢦⡘⣥⣾⣿⡿⢟⢫⣔⣿⣾⡿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢆⡍⠲⢌⠣⡜⡰⡉⢖⠱⣂⠭⡘⣅⠣⠎⡜⡡⢎⡌⡓⡌⢎⡱⡘⢤⡙⠜⡢⢅⠫⠜⣢⠑⡎⡔⣢⣵⣶⣿⡿⠟⡭⣮⣽⣾⢿⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣷⣌⠜⡱⢊⠵⣨⠑⡍⢎⠲⡡⢎⡱⢢⡙⡜⡰⡑⢎⠴⢱⡘⠦⣡⠙⡆⡜⣡⠓⣌⢣⡙⣤⣫⣴⣿⣿⠿⣛⣥⣽⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣛⣿⣿⣯⣖⡩⢒⡡⢍⡜⠬⣑⠱⣊⠔⡣⢜⡰⠱⣉⠎⡜⡡⢜⠢⣅⠳⣘⢰⣡⣯⣴⣷⣿⣿⠿⣟⣹⣦⣿⣿⠿⠋⠁⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣬⢛⣿⣿⣿⣷⣮⣶⣘⣦⢡⠓⡬⡘⢥⢢⡑⢣⠜⡘⠴⣑⣮⣵⣦⣷⣾⣿⣿⡿⢟⡻⣍⣶⣷⣿⣿⣿⣏⠀⠀⠀⠀⣼⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣍⣛⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⣏⣹⣔⣮⣷⣿⣿⣿⣿⣧⣳⣞⣿⣷⣦⣶⡾⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣭⣖⣦⣩⡍⢯⣙⣛⡛⣛⠻⡹⣍⣫⣕⣲⣬⣽⣶⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣯⣽⣽⣭⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⡿⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⡿⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛🟨🟨🟨⬛⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛🟨🟨⬛🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟫🟫⬛🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟫🟫🟫⬛🟨🟨⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟫⬛⬛🟨🟨🟨⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨⬛⬛⬜⬜⬜⬛
⬜⬛⬜⬜⬜⬛⬛⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬛
⬜⬛⬜⬜⬜⬜⬛⬜⬛🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜⬜⬛
⬜⬛⬜⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨🟨⬛⬜⬛⬛⬛⬛⬜
⬜⬜⬛⬛⬛⬜⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬜⬛🟨🟨🟨🟨🟨⬛⬜⬜⬛⬛⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬜⬛⬛⬛⬛🟨🟨⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⬜⬛⬛⬛⬛⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜
⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬜⬜⬜
⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜
⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ᶠYͧoͨᵏu
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀
⢠⠞⠁⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⠤⠤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠑⢤⠀⠀⠀⠀
⣣⠔⠚⠻⣄⣡⣞⣄⣠⣆⠀⢼⣼⣄⣀⣀⣠⣆⠜⡘⡻⠟⠙⣲⠦⣈⢳⡀⠀⠀
⡇⠒⢲⡤⡜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠤⣖⠬⠓⠂⠉⣿⠇⠀⠀
⠙⠲⠦⠬⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡄⠀⠀⠀⠀⠀⣞⠀⢀⣲⠖⠋⠀⠀⠀
⠀⠀⠀⠀⠘⣟⢢⠃⠀⠀⠀⠉⠙⠻⠛⠁⠀⠀⠀⢀⡜⠒⢋⡝⠁⢀⣀⣤⠂⠀
⠀⠀⠀⠀⠀⡇⠷⠆⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠤⠟⠉⠀⢰⠱⡾⣧⠀⠀
⠀⠀⠀⠀⠀⠹⢄⣀⣀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢠⣤⡀⣼⢾⠀⠀⡟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⡏⠀⡡⠣⢖⣯⠶⢄⣀⣿⡾⠋⢸⢀⡶⠿⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣹⠃⣀⣤⠞⠋⠀⠉⠢⣿⣿⡄⠀⣿⠏⠀⠀⠐⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢱⢡⡾⠋⠀⠀⢀⡐⣦⣀⠈⠻⣇⢸⢁⣤⡙⡆⠈⡏
⠀⠀⠀⠀⠀⠀⣠⠎⢁⠔⡳⡟⠀⠐⠒⠒⠋⠀⠠⡯⠙⢧⡈⠻⣮⠯⣥⠧⠞⠁
⠀⠀⠀⣀⠴⠋⠀⢶⠋⢸⡝⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⠀⠙⡆⠘⠦⢄⡀⠀⠀
⠀⠀⣸⠅⢀⡤⢺⢸⠀⢸⡃⠤⠀⠀⠀⠀⣀⡤⢚⣋⣿⢄⡀⢇⡀⠀⠀⣝⡶⠀
⠀⠀⢿⠀⡏⠀⠘⠞⠀⢸⡵⣦⠤⠤⠖⣿⠥⠞⠉⠀⢸⠖⠁⠀⠙⠢⣑⠶⣽⢂
⠀⠀⠸⠤⠃⠀⠀⠀⠀⠀⠉⢳⠂⠈⡽⠁⠀⠀⠀⢀⡼⠒⠓⢤⠀⠀⠀⠙⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡎⠀⠀⠀⠀⢠⠎⣠⠀⠀⠈⢳⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡶⠗⠋⣱⠄⠀⠀⠀⣧⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠦⣤⣷⠂⢀⡸⠁⠀⡼⠁⠀⠀⠀⠈⢺⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠋⢀⣀⡀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠢⠤⠤⣄⡤⠼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⢦⣄⣉⣑⠢⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠃⠀⠀⠀⠀🇹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⢀⣘⠿⠀⠀⢠⣀⢄⡦⠀⣛⣐⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠣⠤⠘⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀
⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀
⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀
⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀
⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀
⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀
⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀
⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀
⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀
⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀
⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠛⢯⣍⠁⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⡿⣯⣟⡿⣿⣦⠀⠀⠹⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡿⣧⣟⣿⣻⣿⣤⣀⡀⢻⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢿⣽⣿⣿⣿⣟⡿⣿⢿⣿⣿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⣠⡞⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⢯⣿⣿⣿⢷⣯⢿⣽⣻⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⣰⠏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣾⣻⣿⣿⣾⣯⣷⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⢰⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠈⠉⠛⢿⣿⣽⣷⡿⠁⠀⠀
⠀⠀⠀⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⡀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠘⠒⢿⠷⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢾⡗⠒⠒⠂
⠀⠀⢸⡆⠀⠀⠀⠈⠩⣏⡛⠲⠆⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠈⣷⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⡶⠀⠁⠀⣼⠇⠀⠀⠀
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠚⢛⡟⠛⠒⠀⠀
⠀⠀⠀⢹⣆⣀⣤⡤⠶⠞⠛⠻⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⢀⣀⣼⡁⠀⠀⠀⠀
⠀⢠⡴⠞⠻⣍⠀⠀⠀⠀⠀⠀⣹⣿⣧⡀⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣴⡶⣤⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠷⣦⡀⠀
⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⣀⡾⠁⠈⢿⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠀⠀⠀⠀⢀⣰⡿⠀⠀⠀⠀⠈⢿⠀
⠀⠀⠀⠀⠀⠀⠘⢳⣤⡾⠋⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⣨⡧
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⠶⣄⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠜⢀⡇
⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠈⠉⣳⡶⢦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⠁⠀⠀⠀⢀⠎⠀⣸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⢣⡟⣼⣛⣿⡀⠀⠀⠀⠀⡞⠀⣰⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢸⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡼⣓⢾⡱⢮⡽⣷⣄⣀⡀⣘⣥⢾⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣄⣀⣀⠀⢸⣟⡞⡼⣭⣛⠿⣹⢻⠽⣭⢳⡹⢶⣙⢮⡳⣝⣣⢞⣽⠏⠉⠉⡋⠀⡨⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠉⠛⠻⣿⣜⡳⢧⣝⣫⢗⣫⡝⣮⢳⡝⣣⢏⡾⣱⢧⣋⢾⡿⠀⠀⠠⠁⠀⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣝⡳⣎⡳⣎⢧⡻⡜⣧⡛⣵⢫⢞⡵⢮⣝⣾⠃⠀⠀⡈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣤⣶⠿⣎⡵⣫⢵⢫⣞⣱⢻⡴⣛⡼⣹⢞⡼⣳⣾⡇⠀⠀⠀⢐⡀⠈⠀⠀⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⣀⣤⡿⣏⣗⢻⣬⢳⡝⣮⢳⢎⣧⢳⡝⡮⣵⢣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⡄⢀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⡵⢫⣜⡳⣎⠷⣹⠖⣯⢺⣬⢳⣾⣵⣿⣿⣿⠟⠋⣽⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢣⡏⣷⡎⡟⣥⢻⡜⣷⣿⣿⣿⢹⡏⠁⠀⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⣝⣶⣭⢳⡝⣎⣷⣧⣷⢾⡏⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠉⠙⠛⠙⠉⠉⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠖⠚⠋⠁⠀
⠀⠀⠀⠀⢀⣴⣶⣶⣶⣖⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⡐⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣶⣄⡀⣀⣤⣶⣿⣿⣟⣛⡛⠛⠋⠙⢻⣿⣷⡖⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⠉⠉⠀⠉⠙⠲⢤⣀⣿⣿⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣝⡲⢤⣄⡀⠀⠀⠀⠈⠛⡏⠀⠀⠀⢘⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠊⠉⠊⠿⣆⢌⠙⠥⣷⣤⣀⠀⡇⠀⠀⠀⡌⢀⣿⣷⡀⢀⡠⠐⠂⠉⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣾⠃⢄⠀⢀⠐⡪⢓⢦⡙⠿⣿⣿⣿⡇⠀⠀⢀⠐⣿⡿⣿⠋⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⠃⠆⣿⠀⠨⢄⠀⠡⢈⢄⠣⡈⠳⣬⡙⠿⣷⣼⣿⣿⣷⣿⣣⣅⡗⠉⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠇⡌⠂⢀⢻⡰⠂⠁⢁⠀⠃⣆⠀⠐⢄⠙⣟⡷⣮⣙⡢⢌⠉⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠀⠀⢸⢀⢸⢣⠈⠄⠀⡈⢰⣉⠷⣔⠳⡈⢹⠀⡘⡟⡿⣷⣶⣤⣄⣉⡙⠛⠿⣮⣕⡢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣾⡀⡀⠈⣸⡧⠄⢫⣎⡂⠰⡏⠇⣄⣤⣽⣾⣾⡇⠇⡅⢡⡷⣥⣭⣻⣿⣿⣿⣷⣾⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠿⣧⠁⡘⢹⣇⣠⣶⣿⢿⠲⣵⢼⠋⢿⣿⣿⢫⡩⢺⠀⡜⠘⢹⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢸⣠⠉⣿⡉⢿⣿⠄⠉⠘⠇⠒⠒⠛⠛⠉⠀⣜⠎⠞⣢⡟⡌⡘⣿⣏⢟⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⢃⣾⣧⣷⣌⠯⣉⡁⠘⠀⠀⠀⠀⠀⠀⠀⠐⠉⣰⣶⣿⠇⠈⣠⣱⣿⣿⣷⡈⢟⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣿⣿⣿⣿⣿⣿⣇⠀⠀⢴⠞⠛⣉⠃⠀⠀⠀⠈⢀⠟⡫⣢⣾⣿⣿⣿⣿⡿⢹⠓⢮⢈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠖⠉⣉⠉⠙⢳⣦⡀⡾⣿⣿⣿⣿⣯⣿⣿⣿⣷⣤⣀⠉⠉⠁⢀⡠⠊⠀⡰⠕⣾⢡⣿⡿⣿⣿⠿⠟⠀⠊⠀⢀⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⡏⠀⠀⠒⠁⠀⣼⣿⣿⡷⣿⣿⠅⢛⢿⣿⠯⡁⠙⢿⣿⣿⣶⣾⠟⠀⠀⠀⡉⠀⢻⢼⣉⠁⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣷⣕⠤⣄⣄⣰⣿⣿⣿⣷⢨⣿⣮⣤⣤⣭⣿⣢⣴⣅⣁⣿⣏⣼⠀⠀⠀⠀⠈⠀⠈⢮⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣿⣿⣷⣤⣼⣶⣶⣾⣿⡿⠟⠋⠉⠉⣭⣿⣿⣟⣿⠟⣿⠿⠛⠉⠀⠀⠀⣀⠤⠐⠂⠉⠉⠉⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢴⣿⣿⣿⡿⢃⣼⡥⢀⡀⠀⡀⠔⠈⠀⠀⠀⢀⢠⢰⢞⡫⢭⠚⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢈⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣧⣿⡿⠑⣲⠝⠋⠀⠀⠀⡀⡄⡎⣟⠌⠞⣙⣶⠾⠟⢻⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡌⣾⣿⢟⡴⠋⠀⣠⣤⠤⡴⣽⠾⣳⣩⣴⡷⠟⠛⠁⠀⠀⠀⢿⣿⣿⣿⣯⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠿⣿⣿⣿⠥⠤⡤⠤⢴⢛⡒⠭⠚⠉⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠋⠁⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⣿⠋⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠰⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢸⣿⣇⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⢮⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢃⣀⡀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡷⠀⠀⡀⠀⢠⣿⣧⡠⣀⠀⠀⠀⠀⠀⠘⣄⣠⣴⣿⡇⠀⠀⠀⠀⠀⢀⠸⣿⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⢸⣿⣿⣷⠀⢀⠰⡀⠀⢿⣿⣷⡝⠷⡄⠀⠀⠀⠀⢰⣿⣿⣿⡛⠲⠒⢲⡉⣇⣇⣰⡿⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠈⣿⣟⡻⢇⠀⡔⣳⣄⢈⠻⣿⣿⣦⡈⠀⠀⠀⠠⣿⡿⣿⢫⣯⠀⣑⣊⠉⠬⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠉⢂⠸⣔⡉⠻⣷⣄⠉⠓⠑⠄⠀⠀⡿⡡⣾⠁⠀⠘⣶⣿⡗⠁⠀⣀⣀⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⢀⠀⠹⣞⡄⠀⠉⠑⢄⠀⠀⠀⣼⢗⣿⠋⠀⠀⠀⣾⣿⣵⣾⣿⠭⠀⠀⠈⡇⠀⠀⠀⠰⠯⠐⠁⠿⠧⠴⠼⠼⠧⠆
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡹⢿⣧⣢⢠⣽⣿⡄⠀⠀⠀⠀⠀⠀⣉⣶⣿⠇⠀⠀⠀⠘⣿⣍⠀⠀⠀⠀⠀⢀⣾⠂⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣿⣾⢿⣿⣿⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⡀⠂⠀⠈⠙⠻⢿⣿⣿⣿⣏⢿⣿⣷⣯⣟⡷⣯⣿⢿⣽⣾⣻⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣿⢣⢟⡻⣛⢟⡤⢧⡜⣇⠿⣇⠀⠀⠀⠀⠀⠀⠛⢿⣼⡟⣼⣿⣧⢻⣼⣻⣧⢟⡿⣼⢧⣟⣧⣿⣼⣟⣿⣿⣼⣟⣿⣿⣿⠟⠃⠀⠀⠀⠀⣼⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣗⡌⣣⠏⡜⡭⣚⡜⣣⠞⡼⡸⢻⡤⠀⠀⠀⠀⠀⠀⠈⠙⠾⠿⢿⠿⠁⠉⠙⠛⠛⠛⠓⠛⠛⠋⠉⠛⠋⠁⠉⠘⠙⠛⠋⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠘⡤⢩⡘⠰⡡⢊⡕⠪⢔⢣⡙⢷⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⡘⠤⣈⠣⡁⠧⡘⡑⢊⠔⠲⢈⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣿
⣿⣿⣟⣿⣿⣿⣿⡇⠑⠒⡁⠛⠛⠛⠛⠛⠋⠛⡛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣋⠭⣍⢭⡙
⣿⣿⡿⣿⣿⣿⣿⣷⠀⠡⠐⠤⠣⠌⢡⢉⠡⡁⠒⡐⠂⣺⡷⠀⠀⠀⠀⠐⠿⣯⣭⣻⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢯⠽⠟⠛⠈⠀⠀⠀⢿⣿⢾⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣽⢯⡟⡿⣿⣿⣿⣟⠛⡋⠿⣛⣌⣲⡉⢦⠘
⣿⣿⢿⣿⣿⣿⣿⣿⠀⠐⠠⠐⢀⠂⡐⢈⠂⡁⠂⠙⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠟⣻⡟⠾⣌⢳⣽⣾⣿⣥⣩⣴⣸⣿⣿⣿⡳⠌⡜
⣿⣿⡿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⢀⠀⠀⡐⣀⠠⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⣷⢿⡾⣿⣿⣿⣿⣿⣿⣿⣉⠆⠩⢾⣾⣿⣿⣷⡳⡴⣾⣿⢿⢫⡝⢆⠡
⣿⣿⣿⣿⣿⣿⣟⣿⡇⠀⠀⠐⠀⠀⠀⢀⠀⠀⢤⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣟⣈⣹⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣀⣤⣠⣿⡶⣶⣷⡶⣶⠶⣶⠶⡿⢿⢿⡅⣈⡡⠈⢸⣿⣿⣿⣷⣳⣿⣟⠢⡃⡜⢄⢫
⣿⡿⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⠟⠁⠀⠀⠀⠀⠂⣈⣀⣤⡴⠦⠦⢤⣄⣤⣻⣛⣛⣛⣟⡛⠿⠷⠿⡳⡹⠀⢿⡃⠜⣀⣽⣿⣿⣿⣿⣿⣿⣿⢌⠳⡥⣘⢆⢣
⡷⣿⠸⣿⣿⣿⣿⢿⣿⡀⠠⠀⢀⣀⠀⠀⠀⠘⠛⠉⠉⠄⢻⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠒⠒⠂⠒⠒⠒⢩⣿⡇⠐⠒⠒⢒⣺⡯⡍⠯⣉⠙⢶⡒⠦⣄⣀⣜⣿⡿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣯⣥⣔⣰⣿⣿⣿⣿⣿⣿⣿⣿⣎⣕⣒⣡⣚⠲
⣗⣿⡆⢿⣿⣿⣿⣿⣿⣇⣀⣠⣤⣤⣴⣶⣶⣶⣾⣷⠾⣻⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⣶⣶⠿⠿⠻⠛⠻⠿⠿⣿⣷⣦⠙⢦⡈⠳⢤⡉⠒⢦⣼⣿⣿⣿⣶⣯⣝⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡽⣟⣫⣵⡾⠛⣫⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣻⣧⠠⣙⣶⡀⠙⠲⣄⣹⡿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣝⡻⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⡽⣟⣧⣿⠟⣋⣥⣶⣿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢻⡱⢂⢿⣌⢳⡀⠘⢹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢟⣵⣿⡟⡏⣼⣾⣿⣿⠟⣭⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⡹⠥⡉⠚⠙⠀⠚⠂⠈⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣧⣿⡿⣫⣷⢿⣶⣿⣿⢟⣽⡾⣯⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡈⠀⠀⠀⠀⠴⡏⠰⡃⠅⠱⠀⠸⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣿⣿⣿⡳⠜⣦⢳⡝⡶⣱⢎⡷⢭⡜⣭⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⣷⣿⡟⣷⣿⣿⣽⣿⣿⣿⢱⣿⣯⣿⡟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⢠⠃⡆⠐⢨⢱⡌⠁⠈⡄⠁⡄⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣤⣯⡜⢳⣭⣾⣽⣮⣵⣾⠛⠃⠈⠙⠛⠛⢻⣿⣿⣿
⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣽⣿⣿⣿⢿⣼⣿⣳⡿⢿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⢈⠱⣈⠂⡄⠁⠂⠀⡁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣶⣿⣷⣶⣶⣶⣶⣤⣤⣤⣄⣀⡉
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⢿⣿⢿⣹⣾⣟⣶⡿⣿⢿⡱⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢆⠠⠃⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣶⣿⣿⣿⢯⣷⣿⣻⣞⡾⣽⡽⣯⡟⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢈⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣟⣷⣻⢾⡽⣞⣳⢯⣝⢮⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣷⣻⡾⣽⢯⡿⣽⣫⣟⣮⢯⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣯⣷⣿⡿⣟⣾⡿⣽⣯⢿⣽⣳⢿⡼⣞⣭⠷⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣽⣷⢯⣟⡾⣽⣛⡾⣝⡞⣿⡱⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣟⣿⡾⣯⢿⣽⣳⢯⡽⢯⡽⡶⢯⡅⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⡀⠀⠠⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⠿⠿⣽⣯⣿⣿⣿⣿⣽⣥⡿⠿⣿⡿⡗
⣿⣇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣨⡾⠃
⠀⠛⣿⣿⣿⣻⣿⣿⣿⣿⣟⣿⣿⣿⡋⠁⠀
⠀⠀⢻⣿⣿⣤⣽⡿⠿⣯⣤⣾⣿⣿⠃⠀⠀
⠀⠀⠀⢽⣿⣽⣿⣷⣸⣻⣯⣿⣿⠇⠀⠀⠀
⠀⠀⠀⣨⣿⣿⣾⣭⣯⣿⣿⣿⣧⡀⠀⠀⠀
⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢄⠀⠀
⠀⠀⣿⡿⢿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣏⠀⠀
⠀⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠻⣷⡂⠀
⠐⢇⠀⠀⠀⣼⣷⣿⣿⣿⣻⡃⠀⠀⢨⠇⠀
⠀⠈⠡⣤⢾⠟⠀⠀⠀⠀⠹⢷⡤⠴⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⡿⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠋⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢓⣛⣛⣾⣞⣩⠽⢿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣮⣍⣛⠿⢿⣷⣦⣄⡀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣿⣿⡏⠙⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⡉⠛⠾⣅⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣿⣿⡐⠓⠒⠒⣿⠘⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⣄⡀⠉⠢⢄⠀⠀⠀⠘⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⣿⣿ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⠢⠀⠀⠁⠀⠀⠀⠈⠣⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⢀⣰⣆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⠿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⠀⠀⠉⢿⣿⣿⡿⡿⡿⣿⢿⣿⣿⣿⣿⣿⠷⠒⠀⠈⠻⣿⣽⣦⡀⠀⠀⠀⠀⠀⠀⠑⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠙⠻⣿⣾⣵⣼⣾⣾⣿⠿⠛⠁⣿⣿⠀⢑⠴⡞⠀⠈⠸⠙⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠩⠉⠩⠀⠀⠀⠀⠠⠀⡀⠀⡀⠉⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⡦⠖⠛⠀
⠀⠀⣀⣴⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢷⣦⡀⠀⠀
⣴⣾⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠥⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠿⠿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⢉⠉⠛⠛⠿⢿⣿⣿⣷⣝⠻⣷⣦
⠈⠛⢿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣿⣶⣶⣦⣦⣶⣶⣶⣶⣶⣶⣴⣤⣤⣴⡆⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣭⣍⡈⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡟⠋⠁⣴⣿⣿⣿⣿⣿⣿⣭⣿⣿⡆⠹⣿⣍⠙⠛⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠘⠛⢫⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠿⠿⠻⢿⣧⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣈⣿⣦⡄⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠆⢀⣴⣿⣁⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣀⣠⣤⣾⠿⣿⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠉⠀⠀⠀⣶⣿⣯⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⡿⠿⠛⠁⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
👉🏿👍🏿👇🏾👇🏾👇🏾👇🏾👇🏾👇🏾👇🏾👍🏿👈🏿
👉🏿👉🏾👍🏾👇🏽👇🏽👇🏽👇🏽👇🏽👍🏾👈🏾👈🏿
👉🏿👉🏾👉🏽👍🏽👇🏼👇🏼👇🏼👍🏽👈🏽👈🏾👈🏿
👉🏿👉🏾👉🏽👉🏼👍🏼👇🏻👍🏼👈🏼👈🏽👈🏾👈🏿
👉🏿👉🏾👉🏽👉🏼👉🏻❤️👈🏻👈🏼👈🏽👈🏾👈🏿
👉🏿👉🏾👉🏽👉🏼👍🏼☝🏻👍🏼👈🏼👈🏽👈🏾👈🏿
👉🏿👉🏾👉🏽👍🏽☝🏼☝🏼☝🏼👍🏽👈🏽👈🏾👈🏿
👉🏿👉🏾👍🏾☝🏽☝🏽☝🏽☝🏽☝🏽👍🏾👈🏾👈🏿
👉🏿👍🏿☝🏾☝🏾☝🏾☝🏾☝🏾☝🏾☝🏾👍🏿👈🏿
✊🏿☝🏿☝🏿☝🏿☝🏿☝🏿☝🏿☝🏿☝🏿☝🏿✊🏿
♫₊˚.🎧 ✩。﷽
🟩⬛⬛🟩🟩⬛⬛🟩
🟩⬛⬛🟩🟩⬛⬛🟩
🟩🟩🟩⬛⬛🟩🟩🟩
🟩🟩⬛⬛⬛⬛🟩🟩
🟩🟩⬛🟩🟩⬛🟩🟩
🟩🟩🟩🟩🟩🟩🟩🟩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠋⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠻⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⣴⣶⣶⣶⣶⣶⣦⣤⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣿⣿⠁⠼⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠿⠛⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⢸⣿⡇⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⣠⣴⣶⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⠀⣾⣿⠁⣀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⡿⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣷⣄⡀⠹⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡇⢰⣿⠿⠋⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠉⠻⣿⣿⣦⡈⠳⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⡇⠘⠁⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀
⠀⠀⠀⡀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀
⠀⠀⣰⣿⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣷⡀⢻⣿⣧⠀⠀
⠀⢰⣿⡿⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⢴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⡗⠀⢻⣿⣇⠀
⢀⣿⣿⠃⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⣿⣿⡆
⢸⣿⡏⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⣀⣤⣶⣄⠙⠿⣿⣷⣦⣀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠸⣿⣧
⣾⣿⣷⣶⣤⣤⣤⣄⣠⣤⣤⣤⣴⣶⣿⣿⡿⠛⠉⠀⠀⠈⠛⠿⣿⠿⠂⢀⣴⣿⣿⠋⢀⣠⣤⣤⣶⣾⣿⣿
⠀⠈⠙⠛⠻⠿⠿⣿⣿⠿⠿⠿⠟⠛⢉⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠋⢀⣴⣿⠿⠿⠿⠛⠛⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣄⣤⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⡩⡙⢿⣧⣾⠟⠛⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠁⠀⠜⠑⠀⠁⠀⠢⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠁⠀⠀⠀⠀⡌⢨⠀⠀⠀⠀⣴⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡈⠢⠘⠢⣉⠂⠀⠐⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠙⠿⣶⣤⣁⡀⣄⣠⣿⠟⠁⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⢹⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣤⣴⣦⣤⣄⡀⠀⠀⠀⠀⣠⣾⠟⠿⠿⠿⣦⡀⠀⠀⠉⠛⠻⠿⠟⠁⠀⠀⠀⣼⡟⠈⠻⣷⣄⣤⣤⣶⠶⠿⠿⠟⠁⠀⠀⢸⣧⠀⠀⠀⠀
⠀⠀⢠⣾⠟⠁⠀⠀⠀⠉⣿⣆⣀⣠⣾⠟⠁⠀⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⡀⠀
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⣠⣾⠋⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡾⠿⣿⣶⣦⠀⠈⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠉⣿⡆⠀⠀⢰⡟⠁⣠⡶⣿⡟⠉⣹⣿⢿⣦⡀⠀⠀⠀⣰⣿⣿⣄⣀⣼⣯⣿⡇⠀⣿
⠀⢰⣏⠁⠀⢀⣴⣾⣿⣿⣷⣦⡀⠀⠀⠀⢀⣴⡿⠻⣿⠿⢿⣦⠀⠸⣿⠀⠀⣿⡇⢸⣿⣿⠻⣷⡶⠿⣷⣴⣿⡇⠀⠀⠀⢻⣧⣿⢛⡟⠉⣽⡟⠀⢰⣿
⢠⣿⠁⠀⢀⣾⣿⣤⣿⣅⢉⣿⣿⣦⠀⠀⢸⣿⣧⣴⣿⣦⣌⣿⡇⢠⣿⡃⠀⢿⡇⠘⣿⣇⣰⣿⣁⣀⣼⣿⠟⠀⠀⠀⠀⠈⠙⠿⠾⠿⠿⠟⢀⣰⡿⠁
⢸⣟⠀⠀⠈⣿⣿⠛⠛⢿⣾⠛⢻⣿⡀⠀⢸⣏⡙⣿⡛⣻⡟⣿⠇⢸⡿⠇⠀⠸⣷⡄⠻⢿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣟⠁⠀
⠘⣿⡀⠀⠀⠙⣷⣤⣤⣼⣿⣶⡿⠟⠀⠀⠈⠛⠛⠻⠿⠿⠛⠁⢠⡾⠃⠀⠀⠀⠙⣿⣦⣤⣍⣀⣠⣤⣤⠴⠶⣶⢶⣤⢤⣤⠶⠶⠶⠟⠋⠁⠀⠹⣶⣄
⠀⢹⣷⡀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣿⣅⣀⠀⠀⣠⡶⠟⠁⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿
⠀⠀⠙⢿⣦⣄⣀⣀⣠⣤⣴⠶⠿⠛⠛⠛⠛⠙⠋⠉⠉⠉⠁⠀⠈⠉⠻⢷⣼⡟⠀⠀⢀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠋⠉⠀
⠀⠀⢀⣼⠟⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⠿⠷⣶⠾⠟⠉⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⢠⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠉⠙⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣶⠀
⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣦⣀⣀⣠⣿⡗
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⣠⣿⠟⠛⠛⠛⠛⠛⠀⠀⠀⠀⠛⠻⠛⠛⠃⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⢶⣤⣀⣿⡇⠀⠀⠀⠀⠀⠀⠻⠷⠶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⡁⠀⠀⣀⣤⡶⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⣿⣿⣿⣽⣿⠉⣿⣽⣿⢻⣿⣿⡟⣿⣿⣯⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠉⠀⠉⠈⠀⠀⠁⠈⠈⠉⠙⠃⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠙⠉⠉⠉⠉⠛⠳⠆⢀⣀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠳⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠛⠷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣿⣆⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⠾⠛⠛⠛⠁⠀⠀⠀⢸⡏⠀⣠⣀⣀⣤⣤⣤⡴⠶⠷⡆⠀⠀⠀⠀⠀⢠⢀⣀⣀⣄⣤⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⠁⢽⠉⠁⠀⠁⣀⣤⣠⣤⣼⡄⠀⠀⠀⠈⠛⠋⠉⠻⣿⣿⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⠀⠺⠶⠖⠛⢿⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⣿⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⡴⠟⠋⣁⣤⠾⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢡⣤⠶⠛⠋⢀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⣧⠄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠿⠛⠋⠉⠉⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡳⣶⡶⠶⠶⠶⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⠀⢀⣤⡽⠶⣥⣀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⠀⠀⠀⠀⠀⢀⣿⡁⠀⣼⣇⡈⡀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠋⠛⠛⠛⠛⠛⠛⣿⠁⠀⣿⠉⠛⠶⣦⣤⣤⣤⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⣠⣤⢿⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⣿⠙⠛⠛⠛⠉⢀⣼⠃⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡤⢤⠴⠶⠋⢹⡇⢀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⣤⣤⣤⠶⠿⠶⠞⠉⠛⠷⠦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
♫₊˚.🎧 ✩。
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣶⣶⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢽⡾⠀⠀⠀⠀⠀⢀⡄
⠀⢰⡿⠿⠟⠖⣦⣀⠀⠀⠀⣜⠹⠴⠀⠉⠳⡆⠀⠀⠀⡓⡇⠀⠀⠀⣽⠀⠀⠀⠀⢠⣻⡃⠀⠀⠀⠀⠀⢿⠀⠀
⠀⢸⣿⠀⠀⠀⠘⠚⡇⠀⠀⠀⠀⢳⠄⠀⠀⣼⠇⠀⠀⠀⣿⠀⠀⠀⢘⡇⠀⠀⠀⠀⢿⣟⡤⡤⣤⣤⣤⣿⠀⠀
⠀⢸⣿⣠⣀⣀⣀⡟⠁⠀⠀⢴⣾⣷⡒⠋⠁⠀⠀⠀⠀⠺⡃⠀⠀⢸⠂⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠺⠀⠀
⠀⢸⣿⠙⠻⠛⠦⣖⠀⠀⠀⠀⣯⡯⢿⣦⠀⠀⠀⠀⠀⠐⢞⠀⠀⠀⠇⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠨⡇⠀
⠀⢸⣿⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⣿⠁⠀⢿⢿⡆⡀⠀⠀⡧⡃⠀⣸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠟⠀
⠀⢸⣿⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠓⠃⠀⠱⣻⣔⡝⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣤⣄⣠⣄⡯⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠄⠠⠀⠄⠠⠀⠄⠀⠄⠠⠀⠠⠀⠄⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠠⠀⠄⠀⠄⠠⢀⠠⠀⠄⠠⠀⠄⠀⠄⠠⠀
⠂⠐⠀⠂⡀⠂⠐⠀⠂⠁⡀⠂⢈⠀⡐⠀⡁⢀⠂⠐⢀⠐⠀⠂⡀⠂⠐⢀⠐⠀⠂⡀⠂⠐⢀⠐⠀⠂⡀⠂⠐⢀⠐⠀⠂⡀⠂⠐⢀⠐⠀⠂⡀⠂⠐⠈⢀⠐⠀⡁⢀⠂⠀⠄⠐⠀⡐⠀⠂⠁⡀⠂⠀
⠌⠀⡁⠐⠀⠄⠁⠂⢁⠠⠐⠀⠂⠀⠄⠐⠀⠠⠀⠌⠀⠠⠈⠀⠄⠠⠁⠠⠀⠌⠀⠄⠠⠁⠠⠀⠌⠀⠄⠠⠁⠠⠀⠌⠀⠄⠠⠁⠠⠀⠌⠀⠄⠠⠁⠐⡀⢀⠂⠀⠄⠐⠈⠀⠌⢀⠠⠀⢁⠐⠀⠄⠁
⡐⠀⠄⠂⢈⠀⠂⠁⡀⠄⠐⠈⢀⠁⠠⠈⢀⠁⡀⠂⢈⠀⠄⠁⡀⠂⠠⠁⢀⠂⠈⡀⠐⠀⡁⢀⠂⠈⡀⠐⠀⡁⢀⠂⠈⡀⠐⠀⡁⢀⠂⠈⡀⠐⠀⡁⠀⠄⠀⡁⠠⠈⢀⠁⡀⠂⠀⠌⠀⠠⠈⠀⠄
⡀⠐⢀⠈⠀⠄⢈⠀⠄⠠⠈⢀⠂⠀⡁⠐⠀⠠⠀⡐⠀⡀⠂⠐⠀⠄⠁⡀⠂⢀⠁⠠⠀⢁⠠⠀⠠⠁⢀⠂⠁⡀⠄⠀⡁⠀⠂⠁⡀⠄⠀⡁⠀⠂⠁⡀⠐⠈⠀⠄⠐⠀⠂⠀⠄⠠⠁⠠⠈⠀⠄⠁⡀
⠠⠈⢀⠠⠁⢀⠂⠠⣐⣤⣂⣀⡄⠁⡀⠄⠁⡐⠀⠠⠐⠀⠠⠁⠂⢀⠂⢀⠐⠀⡀⠂⠁⠠⠀⠂⠁⡀⠂⢀⠂⠀⠄⠂⢀⠁⠠⠁⠀⠄⠂⢀⠁⠠⠁⠀⠄⠁⣈⢀⣢⣥⣄⣁⠀⢂⠠⠁⠠⠁⡀⠂⠀
⡐⠀⠂⢀⠐⢠⣾⣿⣿⣿⣿⣿⣿⠿⠷⣦⣔⡀⠈⡀⠐⠈⡀⠐⠈⢀⠀⠂⢀⠂⠀⠄⠁⡐⠀⠁⠄⠐⠀⠄⠐⠈⢀⠐⠀⠠⠁⡀⢁⠀⠂⠠⠀⢁⠠⣡⣴⡾⠿⣿⣿⣿⣿⣿⣿⣶⡄⠀⡁⠠⠀⠄⠁
⠠⠀⢁⠠⢠⣿⡯⣼⣿⣿⣿⡿⠟⠲⢾⣿⣿⣿⣷⣄⡠⠁⠀⠄⠁⠠⢐⣈⡀⠠⠈⢀⠂⠀⠌⠀⠂⢈⠠⠐⠈⠀⠄⢂⣌⡀⠐⠀⠠⠐⠈⢀⣰⣶⣿⣿⣿⣷⠖⠛⢿⣿⣿⣿⣧⢽⣿⡄⠠⠐⠀⡐⠀
⠂⠁⠠⠀⣿⣿⣷⣿⣿⣿⣿⡿⠶⠤⠬⢽⣧⣍⠙⠻⢿⣶⣈⠀⠌⠀⢿⡿⢻⣧⠀⠂⠀⠌⠀⠂⢁⠠⠀⠐⠈⠠⣰⡿⢿⣿⠀⠁⠄⢂⣼⡿⠟⠋⣉⣼⡿⠤⠤⠶⢾⣿⣿⣿⣿⣾⣿⣇⠠⠐⠀⠠⠀
⠌⠀⡁⠠⢸⣿⣿⣿⣿⣿⡿⠷⠤⠤⢤⣀⣀⠉⠙⠢⣼⣿⣿⣷⣄⠈⢀⠠⠀⠻⣷⠀⠁⠠⠈⠀⠄⠀⠂⢁⠠⣹⠯⠀⠈⢀⠠⣈⣾⣿⣿⣧⠴⠚⠉⣀⣀⣤⠤⠤⠾⢿⣿⣿⣿⣿⣿⠏⠀⠠⠈⠀⠄
⡐⠀⠠⢀⠀⢻⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠉⠛⢷⣶⣿⣿⣿⣿⣿⣷⣄⠠⠐⠀⠹⣦⠈⠀⠄⠁⠠⠈⠀⠄⣼⡯⠁⠀⠌⣠⣾⣿⣿⣿⣿⣿⣶⡾⠛⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠠⠈⠀⠄⠁⡀
⡀⠌⢀⠠⠐⠈⢻⣿⣿⣿⠟⠛⠛⠓⠒⠒⠲⠶⣤⣿⠀⠀⠄⡛⢿⣿⣿⣷⣄⠈⡀⠙⣆⠁⠠⠈⠀⠄⠁⣸⠿⠁⠀⣌⣾⣿⣿⡿⢏⠡⠀⠀⣾⡷⠶⠒⠚⠓⠚⠛⠛⢻⣿⣿⣿⡿⠁⠀⠂⢁⠀⠂⠀
⠠⠀⠂⠀⠄⠂⠈⢻⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠐⡈⢜⣩⢛⣿⣿⣿⣷⡀⠄⠹⣆⠀⡁⠈⢀⢢⠏⠀⣀⣶⣿⣿⣿⡟⣱⠊⠤⠁⣸⡟⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡟⠀⠠⠁⠐⠀⠠⠁⠂
⠁⡐⠈⢀⠐⠈⡀⠌⣿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠛⠛⠻⣶⣌⠲⣌⢏⡾⣽⣿⣿⣿⣆⠀⠸⣇⠀⢈⣰⠋⠀⣤⣿⣿⣿⣿⡳⣝⢦⡙⢤⣱⠿⠛⠛⠉⠉⠉⠉⠉⠛⠻⣿⣿⣿⠁⠠⠁⠐⠈⡀⠁⡀⠂
⢁⠀⡐⠀⡀⠂⠀⠄⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣀⣄⣂⣁⣹⣧⣞⡼⣹⢾⣽⣿⣿⣿⣧⡀⠘⣧⣰⠃⠀⣼⣿⣿⣿⣿⣳⢿⡹⣦⣽⣋⣉⣀⣀⣄⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠐⠀⡁⠄⠐⢀⠠⠀
⠄⠠⠀⠐⠀⠄⠁⡀⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠈⠉⠉⠉⡍⡛⠿⣯⣿⣾⣟⣿⣿⣿⣷⣰⣿⣿⡇⣼⣿⣿⣿⣿⡿⣽⣯⠿⣋⠭⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⠀⠠⠁⠀⠄⠈⡀⠠⠀
⡐⠀⠌⠀⠌⠀⡐⠀⢻⣿⣿⣇⡀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣤⣴⡭⢮⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣷⣴⣬⣤⣤⣦⣄⣀⣀⣀⠀⠀⠀⢀⣰⣿⣿⡟⠀⡀⠂⠁⡀⠂⢀⠐⠀
⠠⠐⠀⡈⢀⠐⠀⡐⠈⢿⣿⣿⣿⠛⠋⠉⠉⢀⠠⠀⡀⣀⣀⣤⣴⣦⣼⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣤⣦⣤⣄⣀⡀⠀⠄⠈⠉⠉⠙⠛⣿⣿⣿⡿⠁⠀⠄⠠⠁⢀⠐⠀⡀⠂
⢁⠀⠂⠀⠄⢀⠂⠀⠄⠀⡙⠿⢿⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⡿⠿⠋⠀⠠⠈⢀⠐⠀⠂⢀⠂⠀⠄
⠄⠂⠁⡈⠀⠄⠐⠈⢀⠂⢀⠠⠀⡀⠈⣩⣿⣿⣿⣭⠷⠶⠖⠛⠛⠿⠿⠿⣛⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⡿⠿⠿⠿⠛⠓⠶⠶⠾⣭⣽⣿⣿⣍⠀⠄⠀⠄⡀⠡⠐⠀⠂⠠⠈⢀⠂⠀⡁⠀
⠄⠂⠁⡀⠐⠈⠀⠌⠀⡀⠂⢀⠐⢠⣾⠟⢋⣹⣟⣁⣀⣀⣄⣢⣤⢶⡶⠛⢋⠍⢲⣽⡟⣾⣿⣿⣿⣿⣯⢻⣷⡑⢮⠙⠿⣶⡶⣤⣦⣀⣄⣀⣌⣻⣏⡙⠻⣷⡄⢈⠀⠠⠀⡐⠈⢀⠐⠀⠂⢀⠁⠠⠀
⠄⠂⠁⡀⠄⠁⡈⢀⠐⠀⡐⠀⣴⣿⠟⠋⢡⠏⠀⠀⠀⣀⣀⣤⣶⠋⠀⡐⠈⣈⣾⡿⢘⣽⣿⣿⣿⣿⣷⢋⢿⣯⡄⠩⠐⠀⠹⣦⣤⣀⡀⠀⠀⠀⠹⡍⠉⠻⣿⡄⠐⠀⡁⢀⠐⠀⠠⠈⢀⠂⢀⠂⠄
⠐⡀⠁⡀⠄⠂⠀⠄⢀⠂⠀⢄⣿⣇⠀⣀⣸⡦⠖⠚⠋⢉⣩⣴⡇⠀⠂⣀⣴⣿⠟⢀⢣⣿⢻⣿⣿⡿⣿⣇⢂⠛⣷⣆⡁⠈⢀⢹⣦⣍⡉⠛⠓⠲⢶⣧⣀⠀⢸⣿⠀⠐⠀⠠⠀⠌⢀⠐⠀⡀⠂⠀⠄
⠁⡀⠐⠀⡀⠂⠁⡀⠂⠀⠌⠀⣿⡿⠋⠁⠀⠘⣀⣤⠾⠋⢁⣼⠷⢻⡟⠋⢹⡇⠀⢂⣿⡿⢸⣿⣿⡇⢿⣿⡀⠂⢹⡏⠙⢿⡷⠾⣧⣈⠙⢳⣤⣀⠎⠀⠈⠙⢿⣿⠀⢈⠀⢁⠀⠂⡀⠄⠂⠀⠄⠁⡀
⢁⠀⠂⠁⡀⠄⠁⠠⠀⡁⢀⠂⢹⣧⡀⠀⣠⠖⠻⡀⠀⣴⡿⠃⢰⡟⠀⠀⣿⠃⢈⣾⣿⡇⠀⢿⣿⠀⢸⣿⣷⡌⠈⣿⠀⠀⢹⣆⠙⢿⣶⡀⠀⡹⠲⣄⠀⠀⣼⡯⠀⢀⠐⠀⠠⠁⠀⠄⠂⠁⡀⠂⠀
⠂⠀⠌⢀⠠⠐⠈⢀⠐⠀⠠⠀⠂⢻⣿⣿⠁⠀⠀⣹⢾⠉⠀⣤⡟⠀⠀⢰⡟⢀⣾⣿⣿⠀⠐⠸⠇⠀⠂⣿⣿⣷⡄⢻⡆⠈⠀⢻⣄⠀⠈⠳⣎⠀⠀⠈⢿⣿⡟⠀⠐⠀⠠⠈⠀⠄⠁⡀⠂⠁⡀⠄⠁
⡈⠄⠂⠀⠄⠐⠈⢀⠠⠈⢀⠐⠠⠀⠻⣿⣄⣀⡼⠃⠈⠐⢴⢯⠁⠀⣠⣿⣡⣿⣿⣿⠃⠀⠂⠄⠐⠈⢀⠘⣿⣿⣿⣎⢿⡄⠀⠀⣻⡤⠒⠁⠘⢧⣀⣀⣾⠟⠁⡀⢁⠈⡀⠄⠁⡀⠂⠀⠄⠁⡀⠄⠂
⡀⠄⠂⠁⠠⠈⠀⠄⠀⢂⠠⠀⠂⠐⠀⠘⢻⣿⣧⠀⠀⢠⠏⠀⠈⢐⣾⣿⣿⣿⡿⠃⠀⠂⠁⠠⠈⢀⠂⢀⠘⢿⣿⣿⣿⣿⡂⠉⠀⠹⡄⠀⠀⣸⣿⡿⠋⠀⠄⠠⠀⠠⠀⠐⡀⠄⠂⠁⡀⠂⠀⠄⠂
⡀⠄⠂⠁⡀⠂⢁⠠⠁⡀⠠⠀⠁⠂⠁⡐⠀⢈⠻⢿⣶⣿⣦⣀⣠⣾⣿⣿⡿⠟⠁⠀⠌⠀⡁⠐⠀⠂⠠⠀⠠⠈⠻⢿⣿⣿⣷⣄⣀⣰⣿⣶⡾⠟⠉⠀⡀⠂⠐⠀⠌⠀⠄⠁⡀⠄⠂⠁⡀⠄⠁⡀⠂
⠠⠀⠂⠁⡀⠐⠀⠠⠐⠀⡐⠈⠀⠌⢀⠀⠌⠀⡀⢀⠈⠙⠛⠛⠛⠛⠋⠁⡀⠠⠐⠈⢀⠐⠀⠄⠁⠠⠁⡀⠁⠠⠀⠄⠈⠙⠛⠛⠛⠛⠉⢁⠀⠄⠂⠁⡀⠄⠁⡈⠀⠂⢈⠀⠄⠀⠂⠁⡀⠄⠂⠀⠄
⠂⠁⠠⠁⠀⠌⠀⡁⢀⠂⠀⠄⠁⡀⠂⠠⠐⠀⠠⠀⠄⠂⠠⠐⠀⠄⠂⠁⡀⠐⢀⠈⠀⠄⠈⡀⠌⠀⡐⠀⠈⠄⠐⠀⡁⠄⠂⢀⠂⠄⠈⡀⢀⠂⢀⠁⡀⠄⠂⠀⠄⠁⠠⠀⠂⢁⠠⠁⠀⠄⠂⠁⡀
⠂⠁⠄⠂⠁⡀⠂⠀⠄⠐⠈⢀⠐⠀⠄⠁⠠⠈⢀⠐⠀⠂⠁⠠⠈⠀⠄⠁⠠⠐⠀⠠⠁⡀⠂⠀⠄⠂⠀⠌⢀⠐⠈⢀⠠⠀⠂⡀⠄⠠⠁⠀⠄⠀⠂⡀⠄⠀⠂⢁⠠⠈⠀⠄⠁⠠⠀⠄⠁⡀⠂⠁⡀
⠌⠀⡐⠀⢁⠠⠀⡁⠠⠈⢀⠂⠠⠈⠀⠌⢀⠐⠀⠠⠈⠐⠈⠀⠄⠁⠠⠈⢀⠐⠈⡀⠐⠀⠄⠁⡀⠂⠁⡀⠂⠀⠌⠀⠠⠀⢁⠀⠄⠂⢀⠡⠀⠌⢀⠠⠐⠈⠀⠄⠀⠂⢁⠠⠈⢀⠐⠀⠂⠀⠄⠁⡀
⠐⡀⠄⠈⡀⠠⠐⠀⡐⠀⠂⠠⠐⠀⡁⢀⠂⠠⠈⠀⠄⠁⠠⠁⠠⠈⢀⠐⠀⡀⠂⠀⠄⠁⡀⠂⠀⠄⠁⠠⠀⡁⠠⠈⠀⠌⠀⡀⠂⢈⠀⠠⠐⠀⠠⠀⡐⠈⢀⠂⠁⡐⠀⡀⠂⠠⠀⠌⠀⡁⢀⠂⠀
⠂⠀⠄⠂⢀⠐⠀⠂⠀⠄⠁⡀⠂⠐⠀⠠⠀⠂⠠⠁⠠⠈⠀⠄⠁⡐⠀⡀⠂⠀⠄⠁⡀⠂⠀⠄⠁⠠⠈⢀⠐⠀⡐⠀⡁⢀⠂⢀⠐⠀⡀⠂⡀⠡⠐⠀⠠⠐⠀⡀⠂⢀⠐⠀⠄⠁⡀⠂⠐⠀⠠⠀⠁
⠌⢀⠂⠈⡀⠄⢈⠀⠡⠀⠂⠀⠄⠁⡈⠀⠄⠁⠄⠂⠁⠠⠁⡀⠂⢀⠐⠀⠄⠁⡐⠀⡐⠈⠀⠌⠀⡁⠐⠀⡀⠂⢀⠐⠀⠠⠀⠂⢀⠂⢀⠐⠀⠄⠂⠁⡀⠂⠁⡀⠐⢀⠠⠈⢀⠂⠀⠄⠁⡈⠀⠄⠁
⠀┃⠀┃┃⠀┃
⠀┃⠀┃┃⠀┃
⠀┃⠀┃┃⠀┃
⠀┃⠀┃┃⠀┃
┏┛⠀┗┛⠀┗┓
┃⠀ >┳<⠀ ┃
┃ ◎┗┻┛◎┃
┃┏┓⠀┏┓⠀ ┃
┗┫┣━┫┣━┛
⠀┗┫♥┗┫
⠀⠀┣┳┳〇゛
⠀⠀⠀⠀⢸⠳⢶⣦⣴⡿⠋⢸⣇⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣧⡀⠈⢿⣧⣤⠾⠛⠋⠉⠉⠉⠉⠛⠛⢷⣶⣤⡀⢀⣴⡿⣿⡀⠀⠀⠀⠀
⠀⠀⢀⣴⠿⠋⠙⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠿⣿⣿⠋⠀⣿⡇⠀⠀⠀⠀
⠀⢰⡿⠃⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣿⠷⠶⢿⣧⡀⠀⠀⠀
⠀⣾⡃⠀⣠⠏⠀⠀⡀⢀⣼⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠙⢿⣦⠀⠀
⠀⣿⣷⣴⡏⠀⢠⣾⡇⣼⣯⠀⠀⠀⠀⠀⠀⠀⣷⡀⢀⠀⠀⠀⢻⡄⢀⠀⠀⠈⢿⡆⠀
⣞⣻⠟⣿⠁⠀⣿⠃⣿⣇⣸⣗⠒⣀⠀⠀⢀⣼⠋⣇⣸⣤⠀⠀⠈⣧⠘⣧⠀⠀⢸⡇⠀
⠈⢿⡇⣧⡆⠀⣿⣼⣿⣿⣿⡿⢦⣼⠀⢀⣼⣇⣄⣽⠏⢿⡇⠀⢠⡿⣆⠸⡄⠀⣼⡇⠀
⠀⠘⢿⣿⣿⣄⣿⡟⢹⡾⢿⡗⢀⡧⠶⠋⣽⢿⣿⣿⣷⣸⡇⠀⢀⡗⠛⠓⠻⣼⣿⣷⡄
⠀⠀⠀⠉⣻⣿⣿⣗⠈⠛⠛⠁⠀⠀⠀⠀⢹⡟⢿⡿⣸⡿⠀⣼⣿⠇⢠⡆⣠⣿⠟⠛⠁
⠀⠀⢀⣤⣿⣿⠃⠙⢦⣀⠀⠀⢀⠀⠀⠀⠀⠉⠉⢴⣿⣷⣾⡿⠿⣶⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠘⠿⣿⣾⠀⠀⢀⣿⠛⢶⣶⣿⡷⢤⣤⣤⣶⠾⠛⡟⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣿⢿⠇⡄⣨⡿⣴⡿⣧⣿⣶⣞⣵⡿⢿⠀⣾⡇⠀⠀⠀⣦⡙⢿⣤⡀⠀⠀⠀
⠀⠀⢠⣿⢟⡀⢰⠁⢻⡿⢃⣷⣾⣿⣿⣿⠙⣆⠈⢧⣹⣿⠀⠀⢰⡘⣿⡿⠿⠃⠀⠀⠀
⠀⠀⠈⣿⣿⠁⣿⣠⠟⢄⣼⡛⠛⠋⠻⠿⠀⠘⣆⠈⢿⠛⠀⢰⠘⣇⠸⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠙⣿⡀⣿⣏⣹⡾⡿⠋⠀⣄⠀⠀⠰⠄⢹⣦⠈⢧⡀⢸⠀⣿⣄⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⣷⣿⣧⠀⢰⣧⣄⣚⣿⡀⠐⠒⣀⣨⣿⣧⣸⡇⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⣷⣬⣷⣦⣭⣍⣙⣏⣉⣭⣴⡟⠁⣉⣰⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢿⣀⠀⣽⡇⠀⠀⣿⣧⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣁⣽⣿⠁⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🦋🟧🦋✨🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
✨🦋🟨🦋✨🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸
🌺✨🦋🟩🦋✨🌸🌸🌸🌸🌸🌸🌸🌸🌸
🌺🌺✨🦋🟦🦋✨🌸🌸🌸🌸🌸🌸🌸🌸
🌺🌺🌺✨🦋🟪🦋✨🌸🌸🌸🌸🌸🌸🌸
🌺🌺🌺🌺✨🦋🟥🦋✨🌸🌸🌸🌸🌸🌸
🌺🌺🌺🌺🌺✨🦋🟧🦋✨🌸🌸🌸🌸🌸
🌺🌺🌺🌺🌺🌺✨🦋🟨🦋✨🌸🌸🌸🌸
🌺🌺🌺🌺🌺🌺🌺✨🦋🟩🦋✨🌸🌸🌸
🌺🌺🌺🌺🌺🌺🌺🌺✨🦋🟦🦋✨🌸🌸
🌺🌺🌺🌺🌺🌺🌺🌺🌺✨🦋🟪🦋✨🌸
🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺✨🦋🟥🦋✨
🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺✨🦋🟧🦋
🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺🌺✨🦋🟨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣷⣀⣴⣿⣿⢧⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⢿⡀⠀⠀⠀⠀⢀⡠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣽⠚⠀⠀⣀⣤⠊⠁⣰⠟⣽⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠞⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣣⡵⠖⠉⠁⠀⡽⣰⠋⣠⡤⣶⣿⣿⣽⣿⣶⣶⣤⣄⡀⠀⠀⠈⠉⠛⠿⣿⣿⣿
⠀⠀⠀⢀⡴⠛⠁⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣏⠇⠀⠀⢀⡜⠁⠃⣩⣶⠿⠛⠉⠀⠀⠀⠀⠀⠉⠙⠿⣶⡄⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠠⠋⢠⠐⣡⠂⠄⢹⠀⠀⠀⠀⠀⠀⣠⡾⢟⠾⠋⠀⢀⠔⠉⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⢤⠀⠙⣿⣆⠀⠀⠀⠀⠀⢹
⢀⠐⢠⠑⢢⠑⠤⣉⠐⠈⡆⠀⠀⠀⢠⣾⣉⡁⠀⠀⡠⠔⠁⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣠⢊⡤⣊⡉⢱⠀⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀
⠁⡌⢢⠙⠤⠉⣐⣠⠤⠶⠃⠀⠀⢀⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⢠⠣⢎⡜⠱⠃⡼⡼⠁⠀⣸⡿⠀⠀⠀⠀⠀⠀
⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡟⠛⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣀⣠⣽⣴⣾⣷⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣿⣳⡄⠀⠀⠀⠀⠀⠀⣾⣀⣤⡴⣶⠾⢛⣿⡿⣟⡿⣿⠙⠛⠻⢯⣍⡉⠙⠓⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣯⣻⡽⢯⣷⠀⠀⠀⠀⠀⠀⠻⠛⠛⠓⢋⣠⠾⣿⣳⢯⣗⣿⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣽⣳⢯⣟⡿⣾⡆⠀⠀⢀⣀⣤⣀⣀⢀⡴⠋⠁⠀⣿⣽⣻⣞⣿⠄⠀⠀⠀⠀⠀⠀⠙⢷⣴⣆⣠⣴⣶⣦
⣿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣟⣾⣽⡿⠞⠛⠻⢷⣤⠞⠋⠁⠀⠀⠉⠋⠀⠀⠀⠀⣿⣷⣻⣞⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿
⣿⡟⢷⣤⡀⠀⠀⠀⠀⣿⡾⠿⣁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣻⣞⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣆⠈⠙⠦⡀⠀⠀⠉⠀⠀⠈⠓⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢰⣿⣳⣟⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀
⣿⣿⠿⠶⠖⣶⣶⣟⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡽⠟⠛⠻⣯⠉⠉⢻⣿⣷⣯⣿⠷⠶⠶⢤⣤⣄⣀⡈⠛⠛⠛⠉⠀⠀⣀⣾
⣿⡇⢀⣴⡿⠃⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢹⣆⠀⣸⣿⢻⣿⡿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⣶⣾⣿⣿⣿
⣿⢠⣾⠏⢠⠐⡠⢸⡇⠀⣰⣶⣄⠀⠀⠀⠀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠈⣿⡀⠛⠁⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠛⣿⠻
⣿⣿⠋⡜⢠⠊⡔⢸⣿⠐⣿⣿⣿⠀⢀⢰⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⢸⡇
⣿⢇⡛⡸⢄⠻⣀⢛⣿⣘⣿⣿⠇⢀⢧⣿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⣿⡿⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⣼⠇
⣋⢦⡱⣑⢎⡱⢌⣲⡿⣿⣿⠁⠦⣼⡿⢻⣇⠀⠤⢁⣠⣠⣄⣤⣠⣀⣀⡈⣿⡄⠈⠻⠟⠁⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀
⠞⣦⢳⡩⢆⡳⣾⢏⡾⢡⣟⣼⣿⠛⣴⣿⣧⣾⠾⠟⠛⡉⣉⠉⣉⠉⠛⠛⢿⣷⣄⡀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀
⣻⣴⣧⣽⣧⡿⢃⣾⠁⣸⡿⣛⢤⣿⠃⣿⢍⡒⢬⡘⣡⠒⡄⢣⠐⡌⢢⢁⠂⠌⠛⣷⣶⣬⡿⠏⢁⠀⢂⠡⢈⠐⡈⢀⠐⡀⣼⡇⠀⠀
⣿⣿⣿⣿⣿⠃⣼⡇⠠⣽⣿⣿⣾⠃⣸⡟⣤⡙⢦⡑⢦⠱⡌⣅⢣⡘⣄⢃⢎⡘⣄⢂⢛⣿⣄⣂⡌⣈⠐⡂⢄⢂⡐⣀⠒⣰⡿⢀⠐⡀
★ * ° 🛰 °· 🪐
. • ° ★ • ☄
▁▂▃▄▅▆▇▇▆▅▄▃▁▂.
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠏⠁⠀⢣⠀⠀⠀⠀⠀⠀
⠀⣴⣿⢹⣉⣙⢻⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠰⠀⣾⡄⠀⠀⠀⠀⠀
⢸⣿⣿⠘⣷⢀⠈⠉⠛⢯⣗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀
⢸⣿⣿⠀⢽⠀⠀⠀⠀⠀⢹⣷⣝⣲⡤⣄⡀⣀⣠⣤⣖⣲⡶⠚⠛⠒⠋⠉⠲⣶⣿⣻⠋⠀⠀⠐⠀⠀⣹⡇⠀⠀⠀⠀⠀
⢸⣿⣿⡀⠈⠓⠳⢦⣄⠀⠈⢿⣟⢛⣷⣶⣾⣶⣾⣛⣻⣿⠷⠒⠂⠀⠀⠀⠀⠀⠉⠹⠖⠀⠀⠂⠀⢰⣿⠀⠀⠀⠀⠀⠀
⣘⣿⣿⣷⣀⠀⠀⠀⠹⡇⠀⠈⢿⡝⠻⡽⠛⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣗⠀⣤⣻⠀⠀⠀⠀⠀⠀
⠈⠸⣿⠙⢿⣆⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢸⠋⠀⣀⣤⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣗⠻⠻⡄⠀⠀⠀⠀⠀
⠀⠀⢈⡆⠘⠻⠿⣦⢄⠀⠀⠀⠀⠀⠀⠀⡎⠀⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠻⡿⠿⠟⠒⠀⢙⣦⡀⠀⠀⠀
⠀⠀⠈⢹⡀⠀⠀⠘⣾⠀⠀⠀⠀⠀⢀⣴⣟⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣠⣤⣤⡤⣄⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀
⠀⠀⠀⠀⢣⢀⣀⣀⠘⠂⠀⠀⢰⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣍⣹⠋⠀⢀⡀⢀⣀⣀⣈⠈⢻⣧⠀
⠀⠀⠀⠀⠸⡌⣿⣿⣷⣤⣶⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠭⠥⢤⣦⣾⠽⠗⠚⠋⠉⠉⠛⠶⠦⠴⠈⣻⡄
⠀⠀⠀⠀⠠⢧⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠴⠾⠛⠁⠀⠀⠀⢠⠂⣸⡇
⠀⠀⠀⠀⠀⠘⢶⣿⣿⣿⣿⣿⣿⣿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡔
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣰⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣾⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⢀⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡝⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⡼⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⢯⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢳⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆⠘⡄⠀⠀
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁⢰⡇⠀⠀
⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⡇⠀⠀
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢷⠀⠀
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢹⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⠀
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀
⠀⠀⠀⢀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀
⠀⠀⠀⢘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⣻⣿⣿⣿⣿⣿⡟⠻⠟⠛⠋⣀⡀⣀⡀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣤⣤⣤⣴⣶⣷⣿⣿⣿⣿⣿⣷⣷⣤⣀⠀⠀
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀
⠀⠀⠀⠀⠀⠀⠘⣛⣿⣿⣿⣿⠿⠿⠟⠉⠉⠁⠉⠻⢾⣿⣿⣿⣿⠆
⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣿⣦⣆⣤⣀⠀⠀⠀⣺⣿⣿⣿⣿⡃
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⠃
⠀⣼⣿⣿⣿⣿⣿⡿⠿⠟⠉⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠚⠀
⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠗⣻⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀
⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣾⡁⠀⠀⠀⠀⠀
⠈⢿⣿⣿⣿⣯⣠⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⠀⠀⠀⠀
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠓⣿⣿⣿⡷⠀⠀⠀⠀
⠀⠀⠀⠉⠹⠿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⣀⣤⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣥⣶⣷⣾⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠒⠒⠒⣉⣉⣉⣉⣉⣉⣉⢉⠉⠉⠈⠉⠈⠈⠁⠁⠈⠉⠉⠈⠉⠁⠀⠀⠀⠁⠈⠉⠉⠉⠒⠒⠂⠠⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠉⠉⠉⢉⠉⠩⠉⢍⣆⢲⠆⠲⢴⢢⡌⣭⢩⢏⡽⣩⠝⣭⢫⡝⡭⣍⠳⣔⢲⣒⢶⡲⢦⣤⣤⠀⠀⡤⠶⠚⠛⠛⢿⣻⣶⣶⣯⣄⣒⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠄⢂⠌⡡⢊⡾⣬⡟⠠⣷⣛⢦⡝⣦⢏⡾⣴⢣⡟⣼⢣⡞⣵⢫⡟⣼⢣⡟⣶⣹⢳⢾⠃⢀⡞⡱⣈⠱⡈⠄⡀⠳⣹⣿⣿⣿⣿⣿⣶⣤⣌⡑⠢⢤⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⢀⡠⠀⠀⠀⢀⠠⡈⢆⡡⢎⠱⣸⡟⡶⣭⢷⡻⣜⣧⢻⣜⢯⣞⡵⣻⣼⡳⣯⡽⣞⣷⣫⢯⣟⣾⣵⣯⣯⠃⢀⡞⡬⠱⣄⠣⡘⠤⠐⡀⠹⣿⣿⣿⠏⠉⠙⠛⠿⣿⡶⠀⠁⠀⠙⢄⡒⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⣁⠔⢋⠀⣄⢠⡖⠁⣀⠠⡐⢄⠊⣔⣑⣎⡴⢧⣳⢯⣽⣳⡽⣞⣳⢿⣼⣻⢞⣯⢾⣽⣳⢷⣻⢷⣻⣽⣶⣿⣿⣿⣿⣿⣿⠏⠀⡼⣿⣜⡱⢌⡓⠌⢆⡡⠴⠠⠸⠿⠏⡀⠀⠀⠀⠀⡰⢁⠊⠀⠀⠀⠀⠈⠒⢵⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⣤⣎⣱⣊⢥⣋⢖⣟⣠⢣⡤⢧⡞⣮⢻⡵⢯⣞⡽⣯⣟⡾⣧⣟⡾⣽⢯⣷⣻⣞⡿⣞⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⢳⡹⣷⡍⢦⡙⢼⠃⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⠔⡁⠂⠀⠀⠀⠀⠀⠀⢀⣀⣣⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠚⠁⠀⠀⠀⠀⠉⠉⠙⠚⠛⠺⠵⠿⠾⠷⠽⠽⠿⠾⠿⠾⠽⠷⠾⠽⠷⢯⣿⣽⣻⣞⣷⣯⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠛⠀⠀⡛⠧⣽⣹⣿⢢⣝⣾⣾⡟⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣾⣧⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠛⠋⠌⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⡙⠋⡉⢲⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠈⠁⢆⡎⠰⠈⠹⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⢀⣬⢦⠀⠀⠀⢠⠁⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⢠⢲⠃⣶⠡⡀⠀⡘⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢁⡀⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⢀⣀⡤⡴⠐⠁⠀⠀⠀⠀⠀⠀⣰⢻⣿⣿⣿⢿⣧⡀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⣿
⠀⠀⢀⠃⢞⠀⢋⢀⣓⢄⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠋⠀⢀⠠⠒⠉⢀⣀⡤⠔⣶⡾⠻⠟⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⣀⠐⠉⢸⣿⣿⣾⣿⣿⣿
⠀⠀⠎⠀⠀⠑⠻⠬⠑⠀⠈⠁⠐⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⣥⣶⠸⣏⡹⢋⣠⠀⠟⡋⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⣿⣿⣿⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⣿⣷⣦⣀⠈⢁⣾⣿⣿⢿⣝⣯⡏
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⢀⣶⡶⠂⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠈⠛⠯⠤⠅⠖⠛⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠏⢹⡿⣿⣿⣿⡿⣿⣿⣟⣿⣿⡇⠀⠀⠀⠀⢀⡠⠚⡀⠌⣿⣿⣿⡿⠛⠀⠁⢸⣿⣯⢇⣿⣹⠇
⠀⢸⣿⣷⣦⣤⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⣾⣯⣿⠟⣩⣾⣗⠀⠀⡀⢀⡭⠐⠉⠀⠈⢁⡭⠋⠀⠀⣀⣤⣿⣿⣿⣾⣩⡟⠀
⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣄⣠⣀⣄⠠⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣯⡻⣿⣖⡿⡿⢸⡇⢀⠠⠐⠁⠀⠂⠠⢐⡊⠥⠐⠐⠚⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣿⣿⣿⣿⣿⣞⣷⣞⣶⣶⣶⣶⣶⣻⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣿⣷⡿⣿⣷⣿⢇⠇⣼⠇⠁⠀⢈⡠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣽⣾⣿⡎⢰⡿⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠪⢕⣻⠻⢿⣿⣽⣿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣉⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣡⣿⣿⡿⣯⠋⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠑⠒⠚⠒⠫⠼⠭⠭⠯⠝⠫⣛⣝⣛⣛⣟⣻⣟⣿⣿⣿⣿⣦⣅⡫⢙⡻⢿⠿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣠⣼⣮⣜⣫⣙⣛⣉⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁⠉⠉⠉⠉⠀⠈⠙⠻⠿⠿⠿⠿⠿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠻⡿⢿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⠀⠀
⠈⢹⣿⣿⣿⣿⣿⣦⣼⣷⣦⣀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠀⠀⠀
⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⡿⠇⠀⠀⠀
⠀⠀⠀⠈⠘⠿⣿⣿⣿⣿⣿⣿⠛⢿⠛⠟⠛⠋⠋⠉⠋⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠻⡿⡇⢀⣤⣤⣶⣶⣶⣶⣏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⣄⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠻⡿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⢿⠟⠿⠛⠛⠛⠙⠿⣿⣿⣿⣿⣿⣾⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⣀⣀⣀⣿⠿⢿⣿⣿⣿⡿⠿⠟⠟⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣦⣬⣭⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⢿⣿⣿⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡏⠿⠙⠃⠋⠀⠀⠙⠛⠘⠟⠿⠻⠟⢿⠿⡿⠿⡿⢽⠿⡿⠻⠷⠆⠀⠁⠉⠀⠘⠋⠛⠘⠛⠿⠻⠿⠿⠿⣿⢶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠻⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Y
--------
/
/ • _____)
/ / /
)/ ⊂ / ⊃
⠀⠀⠀⢀⢤⣶⣶⣿⣿⣿⣿⣿⣷⣍⠉⠐⠒⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠂⢻⣿⣿⣿⣿⣉⡘⢿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀
⠀⢠⠃⠀⠀⠀⠉⠋⢿⣿⣿⠀⠛⠟⠃⠀⣀⣀⣀⣄⣀⣀⡀⠑⠠⡀⠀⠀⠀
⠀⠆⠀⠀⠀⠀⠀0⠀⠀⠉⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠐⢄⠀⠀
⠰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⠿⠿⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢁⠀
⠀⢂⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣶⣦⣄⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠣⡀⠀⢀⡴⠢⡌⠉⠛⠿⢿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠐⢄⠘⡦⡙⢼⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠁⡗⡘⡜⡒⢖⡒⢒⡂⢎⠭⣉⢏⠱⡌⠉⠛⠿⣿⣿⣿⡷⠀⡆
⠀⠀⠀⠀⠀⠸⣆⠱⡆⡉⠶⣈⢱⠸⡈⠶⠷⠾⠏⠀⠀⠀⠀⠀⠈⠉⢀⠎⠀
⠀⠀⠀⠀⠀⠀⠘⠡⢜⣌⣣⢆⡙⡆⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠊⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧
🟨⬜⬜⬜⬜🟨🟨⬜⬜⬜⬜🟨
🟩⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜🟩
🟦⬜🟨🟨⬛🟨🟨⬛🟨🟨⬜🟦
🟪⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜🟪
🟪⬜🟨🟨⬛🟨🟨⬛🟨🟨⬜🟪
🟦⬜🟨🟨🟨⬛⬛🟨🟨🟨⬜🟦
🟩⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜🟩
🟨⬜⬜⬜⬜🟨🟨⬜⬜⬜⬜🟨
🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟧
🟥🟧🟨🟩🟦🟪🟪🟦🟩🟨🟧🟥
⬜⬛⬜⬜⬛⬜⬛⬜⬜⬛⬜
⬛⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛
⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛
⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛
⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜
⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜
⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢻⠛⠭⠉⠍⠙⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⢉⣁⣤⣀⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣉⣠⣄⣉⠙⢻⣿⣿⡿⠟⠩⠃⠘⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠿⣿⣿⢏⣰⣾⣿⣿⣿⣿⣿⡷⣆⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⡷⢦⣽⢋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣽⣤⣀⡀⠀⠀⠀⢀⣿⣿⣿⡼⣿⣿⡿⣟⢿⣿⣿⣏⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣽⣏⣿⣿⣿⣿⣿⣿⣶⣤⠀⣀⣤⣶⣿⡿⠿⢿⣿⣿⣿⣿⣶⣀⠀⡂⢾⣿⣿⣿⢽⣿⣟⡼⣧⣿⣿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⣿⣷⣾⢫⡿⠛⣉⣤⣤⣌⠙⢻⡷⣺⠟⢉⣤⣤⣤⣤⣀⠈⠛⢳⣯⣟⣧⢨⡙⣿⣿⣿⣷⠻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠛⠋⣾⡇⣾⣿⣿⡟⣿⣷⠀⠙⠋⢠⣿⣿⣿⠛⠛⣿⣿⡄⠀⢹⣾⣽⣦⣽⣾⣿⣿⣿⣷⢩⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡟⢡⡤⢄⢸⣇⠀⠂⣾⣿⡟⣡⣦⣄⠀⠯⢿⡄⠨⣿⡽⣿⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⢸⣿⡟⡧⣿⠀⠀⣿⣿⡞⢿⣿⡿⠄⠀⣽⡆⢐⣿⣿⣿⠿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢯⣇⢻⣷⣀⠋⣈⣰⣿⣤⣤⣹⣿⣧⡐⠯⢼⣥⣴⣿⠁⡀⣿⢿⡀⠄⢂⠡⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣞⠿⠊⢹⣿⣿⣿⣿⣿⣷⠄⠀⠀⠈⠉⠘⠛⠻⢿⣯⡒⣼⡿⣯⣴⣭⣶⣯⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡟⠁⠀⠀⠈⠙⠻⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⢛⡛⢻⢛⣝⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⢺⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢯⣜⣵⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡆⠁⠀⠀⠀⠀⢸⡅⠀⠀⠀⠆⠀⠀⠀⠄⢀⣀⣲⣷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣔⡢⣄⡢⣜⣧⡀⡄⢠⣀⠠⣄⣐⣶⣎⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣻⣿⡿⣿⣯⣿⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣮⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⣣⢴⣻⣿⣿⡿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠟⠋⠉⠉⠉⠀⠀⠀⢀⠀⣉⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢀⣀⣠⡩⠟⠛⠉⣉⣉⢉⣿⣯⢿⣽⣟⣾⣽⢾⣻⣽⣻⡽⣯⢿⡽⣯⣿⠁⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⠿⣻⣵⣿⣽⣿⣿⡿⣿⣿⣟⣷⣿⣟⣿⣿⣟⣿⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⢁⢠⣴⣀⣀⣤⠉⠁⠦⣄⡀⠀⠀⢀⠠⣶⡏⢰⣿⣿⡟⠀⠀⠀⠀⠀⣠⣾⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⣞⣯⢿⣞⡿⣾⣟⣯⡷⣿⡽⣯⣟⣿⣿⣯⠀⠈⠉⡟⠛⠛⠛⠻⠿⣿⠿⠟⠛⠛⠉⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⠛⠻⣿⣿⡿⣿⡿⣿⣿⢿⣿⣾⣿⡿⣿⣾⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⠛⠚⠛⠫⣤⣄⣲⣴⣶⣾⣿⣷⣸⣮⣷⣿⣧⣿⣿⣿⣗⣀⢀⠀⡀⣾⣿⣿⣥⣞⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣟⣯⡿⣟⣷⢿⣳⣟⣷⣻⣿⣿⡟⢩⠜⣆⠀⠸⡇⠀⢂⠐⡀⢰⠣⠀⠀⠀⠀⢠⣞⣽⣿⣿⣿⣿⣿⡿⠻⣍⢲⡭⣷⣶⣿⣯⣿⡷⣿⡽⣾⣻⢷⣻⣾⡽⣟⣷⢯⣿⣳⣯⣿⣳⣟⣾⢯⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢟⠉⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢍⡞⡴⣻⣿⣿⣿⣿⣠⢂⠤⡀⡄⢠⠀⡠⢀⢻⣷⣯⡷⣟⣿⢾⣻⢷⣯⢯⣿⣿⡟⠀⠐⢬⣽⣷⣤⣷⣀⢂⠄⡐⠸⣇⢠⣀⢴⣸⣿⣿⣿⣿⣿⣿⡿⠑⡌⢣⡴⠋⠉⢹⣿⣯⣟⣷⣻⢷⣟⣯⢿⣻⣽⣾⣻⣟⣾⣟⣷⣟⡷⣯⡷⣿⣽⣻⢾⡏⢯⠉⠛⠙⠓⠻⠯⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢟⣣⣥⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣵⣳⣯⣿⣿⣿⣷⣯⣖⡱⢎⡱⢎⢥⢋⢦⢫⢿⣿⣽⡾⣟⣯⡿⣞⣿⣿⡟⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡔⢣⡼⢋⡉⡁⣀⢢⣿⣷⣻⢾⣽⣻⣞⣯⢿⣯⣷⣻⣿⣭⣿⣞⡷⣿⡽⣷⢿⣳⣯⣿⡟⠍⠘⠧⠄⠄⡀⢀⣀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣭⣮⣝⣎⡳⣎⢿⣷⣿⢯⣷⣟⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⢸⣿⡷⣯⣟⡷⣿⣽⣯⣟⡷⣯⢿⡾⣽⣳⡿⣽⣷⣻⢯⣟⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⡤⠔⠈⠙⢻⣽⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣿⣭⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠁⠀⢀⡠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⢯⣿⡽⣷⣿⣻⣽⣟⣯⢿⣻⣽⣻⣽⣞⣯⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠿⢿⣿⣦⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣰⠊⠀⠘⢿⣿⣿⣿⢿⠿⠟⠈⠉⠻⡝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⣄⠀⠀⠀⠀⠀⠀⠐⢿⣿⣯⢿⡾⣽⡷⣯⣟⣾⣽⢾⣟⣯⣷⣿⣳⣿⣿⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣦⠈⠽⣿⣿⣦⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⣸⠃⠀⠀⠀⠀⠉⣿⠋⠀⠠⠀⠌⠀⣤⠞⠙⣟⣿⣿⣿⣿⣿⣿⠃⠀⠈⠳⡄⠀⠀⠀⠀⠀⢻⣿⣿⣯⣿⣷⣻⣯⣿⣽⣾⣿⣿⣿⣿⣿⡿⣿⢋⠶⡡⢎⡰⡁⢆⡐⢠⠀⡄⢠⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⡀⢀⠀⣰⣿⣿⣀⣜⣻⣿⣿⣿⡀⠮⣉⠵⠀⠀⠀⠁⠠⠀⡀⢀⠂⠩⢼⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠀⡼⠁⠀⠄⠁⠠⢀⠖⠁⠀⠀⠁⠀⠸⠿⢿⠻⠁⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠠⢿⣿⣿⣷⣿⣻⣽⣯⣿⣿⣿⣿⣛⡿⣎⠷⣡⢏⢮⡱⢎⡴⣩⢒⡬⢣⡙⡔⡣⡜⣰⢃⣎⠴⣡⢆⡱⢌⡲⢌⣆⡳⣴⣿⣯⣿⣽⣿⣿⣿⣿⣷⡄⠤⡐⣈⠰⢈⠤⠁⢆⠰⡀⢎⡑⢎⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢀⠟⠀⠠⠈⠀⢌⡔⠃⠀⠀⠀⠀⠀⠇⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣿⣆⠐⡌⡑⢺⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣷⣯⣶⣝⡾⣴⣣⢯⣜⣣⠽⣜⣱⣙⢶⡻⢾⡳⣎⢮⡵⣫⣜⣧⣾⣽⣿⣿⣿⣽⣿⣿⣿⣿⣿⠧⣜⢲⡱⣂⠳⣌⠦⣙⠤⡣⢜⡢⡜⣭⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⠏⠀⠄⢁⠠⡡⠊⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⠤⣑⢣⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣷⣿⣾⣽⣷⣿⣽⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⡿⣜⣻⡜⣧⢳⣍⡷⣬⡳⣭⢞⣵⢫⡶⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠐⠧⢄⣐⠈⢀⠠⠑⠚⠐⠒⠤⠤⠤⣄⣀⣀⣀⣀⣀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠸⣿⡜⣰⣋⣾⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣽⣻⣞⡿⣏⣷⣻⡾⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠉⠒⠦⠤⣂⣀⠂⡀⠠⠀⢀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠐⣿⣇⢷⡹⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣻⠀⠄⠀⠠⣘⡠⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣿⣟⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⡴⠟⠉⣀⣠⠤⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⣁⠲⡰⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⢀⣤⣶⣿⡯⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡿⡛⣄⢣⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣉⡡⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣑⢮⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢿⣛⢛⠳⠶⣦⣤⣤⣀⠀⠀⠀⠀⠀⢀⠀⡔⢢⣝⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣷⣝⠻⢶⣵⣄⣦⣙⠳⣌⣲⣄⣲⢌⡴⢸⡜⡷⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⣌⠿⣾⣀⠎⠩⢍⢛⠛⡍⢯⡙⢯⡸⣘⢵⣺⣽⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠾⣿⣬⢳⡱⣛⢿⣷⣬⣦⣡⣋⣦⣝⣦⣷⣽⣾⣿⡟⣵⣫⢷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡳⣹⣿⣧⡳⢭⡺⣔⢯⣛⣟⣻⢻⣛⣟⡻⣟⡻⢧⣻⣜⣳⢯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢳⡱⢎⠿⣿⣷⣝⡞⣮⡵⣺⢵⡻⣜⣮⠷⣭⣛⡧⣗⣯⣯⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⢵⣫⢟⡶⣯⣟⣿⣶⣛⣧⣟⣷⣻⣼⣻⢷⣯⣽⣿⣾⣿⣿⢟⣵⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢮⣳⢯⣟⣾⡿⣿⣿⣿⣿⣿⣷⣿⣷⣯⢟⡿⣻⢿⡻⣝⢮⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣠⣶⣶⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣀⣶⣿⣿⣿⣿⣿⣆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⣤⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠙⠛⠛⠻⢿⣿⡿⠟⠁⠀⣀⣴⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣉⣡⠀⣠⣴⣶⣶⣦⠄⣀⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⢃⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣾⡟⢡⣾⣿⣿⣿⡿⢋⣴⣿⡿⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⢡⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⡟⣰⣿⣿⣿⣿⠏⣰⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢚⣛⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠸⣿⠟⢰⣿⣿⣿⣿⠃⣾⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠻⠃⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢉⣴⣿⣿⣿⣿⡇⠘⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠁⢀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌
⣿⣿⣿⣿⣿⣿⡿⠁⣀⣤⡀⠀⠈⠻⢿⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⠛⠙⠃⠀⣿⣿⣿⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿
⣿⠟⠁⢀⣴⣶⣶⣾⣿⣿⣿⣿⣶⡐⢦⣄⠀⠀⠈⠛⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣼⡿⢛⣩⣴⣶⣶⣶⣶⣶⣶⣭⣙⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿
⠁⠀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣦⡙⠻⣶⣄⡀⠀⠈⠙⢿⣿⣷⣦⣤⣤⣴⣿⡏⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⠋⣠⠔⠀⠀⠻⣿⣿⣿⣿⢉⡳⢦⣉⠛⢷⣤⣀⠀⠈⠙⠿⣿⣿⣿⣿⢸⣿⡄⠻⣿⣿⠟⡈⣿⣿⣿⣿⣿⢉⣿⣧⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⡇⠠⡇⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣷⣤⣙⠢⢌⡛⠷⣤⣄⠀⠈⠙⠿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣤⣙⣛⣛⣥⣾⣿⣿⡌⣿⣿⣿⣷⣤⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣷⡀⠡⠀⠀⠀⣰⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⣌⡓⠤⣙⣿⣦⡄⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⠀⣶⡄⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠟⠻⣿⣿⡏⣉⣭⣭⡘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⢠⡀⠈⠙⠋⠉⠉⠉⠉⠛⠫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⠛⣿⣿⣀⣀⣾⡿⢀⣿⣿⣿⢻⣷⣦⢈⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⢸⡇⢸⣿⠀⣦⠀⠀⠶⣶⣦⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣦⣈⡛⠿⠟⣋⣤⣾⣿⣿⣿⣸⣿⣿⢸⡇⢰⡆⢈⡙⠻⢿⣿⣿⣿⠀⢿⡇⢸⡇⢸⣿⢠⣿⡇⣿⡆⢈⡙⠻⠧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣝⠛⢿⣿⣿⣿⣿⣿⣿⠟⣁⠀⠀⢈⠛⠿⢸⣇⢸⡇⢸⡇⣶⣦⣌⡙⠻⢄⡀⠁⠘⠇⠘⣿⢸⣿⡇⣿⡇⢸⡛⠷⣦⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⠈⠳⢶⣤⣍⡉⠉⣩⣤⣤⡉⠻⢶⣤⣀⠂⠀⠉⠘⠇⢸⡇⣿⣿⣿⣿⣷⣦⣍⡑⠢⣄⠀⠈⠈⠻⠇⣿⡇⢸⣿⣷⣾⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣦⣄⡀⠈⠉⠛⠶⢄⡉⠻⠿⣷⣦⣌⡙⠷⢶⣄⡀⠀⠈⠁⠙⢿⣿⣿⣿⣿⣿⣿⣷⣦⣍⡒⠤⣀⠀⠈⠃⢸⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠈⠉⠂⠄⢙⣿⣿⣷⣦⣈⠙⠳⢦⣄⡀⠠⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⡐⠄⢸⣿⣿⣿⣿⣿⡇⠀⣿⠿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⡿⢰⣦⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠉⠛⠛⠛⠿⠷⣤⣈⠛⠷⢤⣈⡂⢄⡉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣌⡛⠿⣿⣿⡇⠀⢿⣷⣌⡛⠿⠿⠏⣼⣷⣤⣉⣉⣀⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢀⣤⣶⣦⣤⣤⣄⡈⠙⠻⠖⠀⣉⣩⣤⣤⣤⣤⣤⣤⣀⡈⠉⠙⠻⣿⣿⣿⣿⣶⡄⠉⠀⠀⣸⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⣿⠟⣩⣽⣿⣿⣿⣷⣦⣀⠀⠙⢻⣿⣿⠇⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠏⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠉⠻⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣦⡀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣙⣟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣛⣻⣦⢀⣀⣙⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠿⠛⠛⠋⠉⠉⠛⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀
⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀
⠀⢠⡿⠁⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀
⢀⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀
⣸⡏⠀⠀⠀⠀⠀⢯⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ 😐
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠈⣿⡄⠀⠀⠀⠀⢀⣤⣦⢤⣶⣴⣤⣦⣶⣴⣶⡶⣶⣦⡶⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀
⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢴⠲⢤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠐⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣸⡀⠀⠈⠳⣄⠀⡤⠚⠉⠉⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⡯⠛⠋⠉⠀⠙⣧⠀⠀⠠⣘⡾⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞⠁⢀⡀⠀⡄⠀⠀⠹⡗⢤⡤⣤⣷⣦⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡴⠓⠀⢠⠏⠀⣰⠁⠀⡆⢠⢹⡄⠀⠁⡟⠄⠑⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⢺⠃⠀⠀⡜⠀⠀⡟⠀⠀⡇⡜⡾⡷⠀⣰⣷⠀⠢⢄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡟⠀⡎⠀⡘⣰⣧⠄⢸⡇⢀⠀⣹⢇⣇⡇⠘⢧⢻⣦⠀⠀⢣⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢎⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢠⠃⣐⡇⣿⢻⠀⣼⡁⢸⢠⡟⣸⢿⠃⣠⠞⠘⢮⢇⢄⠀⢣⣸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠬⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢀⡜⣸⠀⣽⡇⡇⢸⣴⣿⣥⡇⣾⠃⠋⠈⢈⣽⣶⣤⣬⣿⡌⣧⢣⡹⣗⣯⣀⣀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⣄⠼⡐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⡟⣱⢻⠀⢸⣷⣙⣲⣿⣿⡛⡧⠀⠀⠀⠀⠘⣿⣷⡷⡿⢻⡇⢻⣧⠱⣿⡉⠉⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⣠⣶⣿⣟⣀⣀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⢊⣴⣟⢸⡆⢸⣻⡻⠏⠸⠟⠛⠇⠀⠀⠀⠀⠀⠈⠀⠁⠀⢸⣧⢸⣿⣆⠹⣷⡀⠀⠀⠀⠀⠄⠸⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣤⠀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣠⡶⡿⢽⣾⠏⣿⡳⠈⣧⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢨⣿⣿⠀⣹⣧⠀⠀⠀⠀⠐⢲⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⡠⢸⡏⠁⡄⢰⡿⢸⡟⣧⢀⢻⣆⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣿⣿⢸⣿⡏⡇⣾⣿⡀⠀⠈⢲⡄⠸⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠤⠤⠼⡏⠀⡿⠁⠐⠠⢸⡇⣿⣧⢸⡄⢻⣿⣆⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⣾⣿⡇⣇⡏⢸⡇⠀⠀⠀⣇⠀⣇⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⠃⠀⠀⠃⠘⣯⡗⢹⡞⣿⡌⢿⣿⣷⡘⢿⣿⣷⣦⣤⣀⡀⠀⢀⣤⠾⠻⠛⠃⡿⠿⣽⢠⡼⠁⠋⠁⠀⠀⠀⠀⠀⣹⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇
⠁⠀⠀⠀⠀⠀⠀⡀⠸⡎⠁⠀⠀⠀⠀⠀⠹⣧⠀⠹⣿⡿⣦⠻⣿⣿⣷⡿⢭⡉⣧⣬⡽⠽⣽⠲⣤⠀⢀⣀⣀⣀⣽⠋⠄⠀⠀⠐⠐⠂⠀⡁⠉⢸⡄⠀⠀⠀⢿⣿⠟⣩⣭⣭⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣤⣤⡬⢶⠴⠾⠳⣍⠳⢞⣽⣧⣄⣀⣠⡟⠀⢄⣂⡼⠖⠋⠉⠉⠛⠭⡁⠋⠑⠲⣄⠀⢲⠀⠀⠀⠙⡆⠀⡇⠀⠀⠀⢈⣷⣿⣿⣿⡿⠿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠲⠖⠛⢛⣋⣉⣉⣡⣼⠤⠤⡄⠙⡲⠾⠛⢿⠿⢿⡿⠷⠶⠚⠛⠁⢶⠀⠀⠀⠀⠀⠱⡄⠀⠀⠙⢆⠈⠦⠄⡀⠀⠧⠀⢷⠀⠀⠀⢈⣿⣿⡿⢋⣥⣴
⠀⠄⠀⠀⠀⠀⠀⠀⠠⢾⡘⠛⠉⠉⣉⡉⠀⣀⣠⣤⡄⣼⠊⠀⠀⠀⠀⠳⣾⠀⠀⠀⠀⠀⠀⡏⠑⢄⡀⠀⠀⠀⠈⠳⣄⢀⣀⣧⠖⠒⠛⠓⢤⣀⢸⠀⠀⠀⢺⣿⡟⣡⣿⠋⠀
⠀⢁⠀⠀⠀⠀⠀⠐⣄⠸⡇⠀⡟⠉⠉⡇⠠⠋⠀⢈⡷⠇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⣾⣀⣀⡀⠈⠑⠒⠒⢤⡏⠙⢻⡀⠀⠀⠀⠀⠀⠀⠙⡎⢹⠀⠀⠀⢻⣿⣿⡁⢀⠂
⠀⢈⠀⠀⠂⠀⠀⠀⢹⠀⣧⠀⠓⣒⠒⠛⠀⠀⢠⣽⡴⣗⠓⠶⡥⣄⠐⢾⣥⠸⣤⠴⢺⠉⠈⢿⣿⣿⣯⣎⣀⠀⠀⢣⣀⣀⣳⡄⡆⣧⣀⣰⣄⠀⢣⣼⠄⠀⠀⠀⠹⣿⣟⣧⡄
⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⠀⢐⣒⣋⣀⣠⡔⢿⣦⡀⠸⣶⡀⠘⣬⠽⣂⢧⡀⠀⠀⠀⢣⠀⠀⠉⢉⠘⠛⣧⠤⡖⢻⣿⣽⣻⣿⠜⠲⣽⣲⢞⣷⣦⣉⢀⣀⡀⠀⠀⠙⢿⣯⣿
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢘⡏⠉⠉⠉⢀⡼⣷⡀⠹⣿⣄⣈⣿⡊⡡⠀⠁⠟⣥⣀⣶⣶⣾⡟⡛⣍⣉⣒⣿⣥⣠⡏⢸⣿⣞⡷⣿⣤⣴⣿⡷⠚⢛⣻⠏⠙⣻⠁⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣰⣴⣶⣶⣿⡿⠿⠿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠛⠻⠿⠿⣷⣶⣶⣖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⣿⣯⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⣼⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⣼⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣶⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀
⠀⠀⠠⢰⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⡀⠀⠀⠀⠀
⠀⠀⢰⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣠⣶⣶⣶⣶⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣾⣶⣶⣶⣶⣶⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠐⣾⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠁⣶⣿⣿⣿⡟⠃⠀⠘⣿⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣬⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡷⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣥⣤⣥⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠘⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⠀⠸⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀
⡀⣠⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀
⠁⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠈⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⠀⠀⠀
⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣠⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠹⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢶⣿⣿⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣒⣂⣂⣀⣒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠉⠻⣿⣮⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠛⠛⠛⠻⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢤⣴⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠉⠻⣿⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣏⣠⣀⣤⣠⣄⣀⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣤⢤⣤⣤⣥⣤⣬⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣧⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣷⣶⣖⣲⣖⣒⣒⣲⣶⣶⣶⣶⣶⣿⡿⠿⣿⠟⠛⠛⠋⠉⠉⠙⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠟⠛⣿⡟⢿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣿⣸⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⠀⠀⠀⣿⡃⠘⢿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⣨⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣿⡇⠀⢨⣿⡀⠘⠀⠀⠀⠀⣿⡿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡧⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢹⣿⡆⠄⠀⠀⠀⢸⢸⣿⣿⣷⣶⣶⣾⡿⠃⠀⠈⢹⣿⡆⢄⢀⣰⣶⣿⡗⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⢿⣧⡄⠀⠀⠒⢠⣾⣿⠀⠈⠉⠈⠉⠀⠀⠀⠀⠈⢿⠿⠿⠿⠿⠻⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣐⣴⣿⡟⠋⠀⠀⠈⠻⣿⣿⣴⣤⣾⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠟⠋⠀⠀⡀⠀⠀⠀⠘⠋⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠀⠁⠁⠁⠀⠀⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡇⡏⠈⡇⠀⠀⢠⣠⡔⠋⠉⢣⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠓⠋⠃⠀⠀⠀⠀⢇⢸⠀⠀⠀⡼⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢀⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⢸⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠃⠡⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠧⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠤⠤⠴⠛⡆⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⠀⠀⡀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠶⠒⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠑⠤⣰⣀⠀⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠓⢋⠏⠀⠀⠜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠇⠀⠈⡹⠉⢹⠏⠉⠉⠈⠈⠀⠉⠈⠁⡲⠋⠀⠀⢘⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡃⠀⡎⠁⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠧⢤⡀⡐⠁⠀⠀⡂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠉⠦⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢰⡁⠀⠀⡎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠉⠓⠦⠇⠀⠀
⠀⠀⠀⠀⡔⢂⡄⠀⠀⠀⠀⠀⠀⠀⢰⢍⢸⣜⠀⠀⢸⢀⠃⠀⠀⠀⠙⢦⣀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠩⠊⠁⠀⠀⠀⠀⠀⠀⣼⠎⡆⣿⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⢉⡿⠋⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡴⢫⠋⡆⠀⠀⠀⠀⠀⠀⡇⠀⢇⢫⡠⠤⠒⠛⠉⠙⢦⠀⢀⡠⠎⣿⠀⠀⠀⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⡅⢸⡰⡇⠀⠀⠀⠀⠀⠀⣾⡴⠋⠁⠀⠀⠀⠀⠀⠀⡠⠕⢭⠀⠀⢳⣋⡖⠉⠳⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡌⡇⢸⢁⡇⠀⠀⠀⠀⠀⢸⣙⡇⠀⠀⠀⠀⢀⣴⣿⣿⣦⠀⠘⣆⣀⣼⢳⡀⠀⠀⣸⡷⡻⣟⣒⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⡇⢸⣼⡇⠀⠀⠀⠀⠀⠸⣼⣱⣶⣶⣦⡔⠚⢿⣷⠯⠞⣠⢗⣿⣿⡏⣸⣿⣷⣶⣿⡴⠿⢟⣉⢝⣒⣭⣷⡤⠶⠖⠶⡶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠇⡷⡟⠹⡇⠀⠀⠀⠀⠀⠀⢱⢷⠻⠿⠟⡟⣦⣀⠰⡀⢸⡟⠛⣿⣿⢡⣿⣿⣿⣿⣿⣾⣾⣿⣷⣄⠀⠀⡀⠈⠉⠒⠤⠬⣀⣀⢈⣿⣷⣄⡀⠀⠀⠀
⠀⠀⢸⢱⣿⡇⠁⡇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠮⣦⡻⠚⠋⠀⠡⣨⡇⢀⣿⡏⣾⣿⣿⠟⣻⣿⣿⣿⣿⢿⣿⣷⣶⣾⣿⣷⣦⣤⣶⠶⠋⠉⢉⣲⡭⠭⢷⣦⡀
⠀⠀⢸⣾⣹⣷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣤⣴⣾⠟⣡⣾⣿⣽⡿⠋⠁⢀⣵⣿⣿⡿⠋⠈⡃⣨⣿⣿⣿⣟⣯⣿⣿⣦⣀⣼⡿⠁⠐⠢⡄⠀⠂
⠀⠀⢸⣏⣟⣿⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣬⣭⣴⣾⣿⣿⠟⠉⠀⠀⣠⣾⣿⡿⠋⠀⣠⠞⢪⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠸⡀⠀
⠀⠀⣾⡼⣫⡾⢿⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣻⣿⣿⣿⠋⢀⣠⢴⣯⣾⣿⡿⠃⢀⠜⠁⣠⣾⡿⠁⠀⣿⣯⣟⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠸⠀
⠀⢸⠯⣽⢉⣾⡟⠉⢻⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⢿⣿⣿⣿⣓⣛⣭⣔⣽⣿⣿⡿⢋⡽⠁⣠⣾⣿⢟⡁⡠⠊⠸⣿⠙⠻⣯⡿⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢸⠀⢸⡟⠙⡇⠁⢸⠁⠀⠀⠀⠀⢀⣿⣉⣿⣿⣿⣯⣗⡪⠭⣉⣻⠛⣻⣾⣿⣿⣫⡶⠉⣠⣾⣿⠟⢁⣾⣿⠾⠛⣧⠘⣇⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢸⡠⢼⠃⠀⢹⣿⡞⠀⠀⠀⠀⠀⣼⣽⡏⠻⣍⡙⣿⢷⡛⢻⡿⣶⣽⣿⡿⣿⡿⠋⣠⣾⣿⡿⡡⢰⣿⠟⠀⠀⠀⠘⣧⠘⣷⠃⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⢸⠁⠀⠇⠀⣼⡿⠁⠀⠀⠀⠀⣼⣿⢏⡘⢦⡈⠛⠿⣮⣉⣡⡤⠺⣻⣯⡾⠋⣠⢺⣿⣿⠋⠀⠀⣀⠨⢧⣤⠀⠠⠄⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀
⠀⢸⠀⠀⡇⠀⡏⠀⠀⠀⠀⠀⣴⢿⢹⣿⡉⠑⠛⠂⠀⠀⠁⠐⠉⠉⢔⣉⣤⣾⣿⣿⣿⡁⠂⡤⠋⠀⠈⠈⣇⡀⣀⣰⣿⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀
⠀⠘⣷⢮⠶⠾⠟⢳⠀⠀⠀⠸⣿⢯⣑⣾⣯⣿⣒⡶⠤⡤⢤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣥⡾⢿⣿⣲⠦⣤⣽⣿⣿⠈⠻⣷⡄⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀
⠀⠰⣇⣠⡧⠤⠖⠺⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⢛⣿⣿⣿⢿⣿⣿⣿⡿⢻⣟⣅⣠⡀⠈⠉⠛⠚⠛⠁⠸⡇⠀⠀⠹⣄⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⢹⡀⠀⠀⠀⠀⢳⠀⠀⢨⠿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣶⠛⠉⠀⢀⣿⠟⠭⠭⠽⠶⣾⠷⣤⣀⣀⠀⣷⠀⢀⣐⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠈⢧⡴⠋⠀⣿⡈⢿⣿⣿⣿⣿⣿⣿⠛⠉⠘⣿⣿⣦⠀⢀⣾⡇⣿⠀⠀⠀⠀⠈⠉⢳⣿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⣶⠀⠀
⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⣿⣶⣤⣸⡇⠈⢿⣿⣿⣿⣿⣿⣧⡀⠀⣹⣿⣿⣷⣾⡏⠐⠛⠀⢠⠀⢠⣾⢀⠞⡏⠀⠈⡯⠙⣿⡿⣻⠁⠀⠹⣧⠈⠁⠀⢹⡄⠀
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⣿⣯⡙⠃⠀⠈⢿⣿⣿⡟⠘⣿⣿⣿⣿⣿⡿⢻⣿⡗⠄⠀⢰⡃⠀⠘⣣⢻⣼⠃⠀⢸⡇⡿⣿⣧⣽⣀⠀⠀⢹⡆⠰⣶⣦⣧⠀
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⠉⢷⡄⠀⠀⠘⢿⡟⠀⠀⠈⠛⠛⠻⡍⠀⢸⣿⠁⠀⠀⣆⠱⢄⣴⣥⣺⣟⠀⠀⡿⠉⢠⢻⠈⣿⣿⣷⣶⣶⣷⣖⣿⣿⣾⡀
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣠⢹⡿⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠄⠀⠀⢸⣴⣿⣿⣿⣿⣹⠀⣸⢣⡇⢈⡟⢠⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠬⡾⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢾⠆⡰⣿⣿⣿⣿⣿⣿⣾⣰⣯⣮⣄⣼⠃⣾⣿⠀⣼⡟⢿⣏⣿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣸⣰⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⡿⠈⢠⣿⢷⡄⠙⢿⣏⠀⠀⠀
⠀⠀⠀⢀⣀⣀⠀⠘⣷⡀⡀⠀⢀⣠⣾⠿⠿⣷⠶⢶⡿⠿⢷⣶⣀⣀⣻⣿⡟⢳⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⢠⠀⣼⡟⠀⠹⣦⠀⣾⠀⠀⠀
⠀⠀⡴⠫⣿⠏⣉⣹⠉⠻⠶⠚⠋⣹⠁⠀⢸⡇⠀⢸⣤⣤⣤⡟⠉⢉⣿⠋⢡⣀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣿⠁⠀⠀⠈⠀⢹⡄⠀⠀
⢀⢞⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⡇⠀⣾⣿⣿⣿⡇⠀⣸⡏⠀⢠⡾⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⢷⠀⠀
⢈⠎⡏⣿⣿⣾⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⢀⡿⠀⣠⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⢸⠀⠀
⢠⠀⣷⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⠃⣰⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⢸⠀⠀
⢸⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠀⠀
⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠤⠤⠤⢀⠀
⬛⬛🟥🟥🟥⬛⬛⬛⬛⬛🟥⬛⬛⬜⬜
⬛⬛🟥🟥⬛🟥⬛🟥⬛🟥⬛⬛⬛⬜⬜
⬜⬛⬛⬛🟥🟥⬛🟥⬛🟥⬛⬜⬛⬜⬜
⬜⬜⬛🟥⬛⬛⬛⬛🟥⬛⬜⬜⬛⬜⬜
⬜⬜⬜⬛🟥🟥⬛⬛⬛⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬛🟥🟥⬛⬜⬜⬜⬜⬛⬜⬜
⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬜⬜
⬜⬜⬜⬛⬛⬛🟥⬛⬛⬛⬛🟥⬛⬜⬜
⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥⬛⬛⬛⬜⬜
⬛⬛⬛⬛🟥🟥🟥🟥⬛⬛🟥⬛⬜⬜⬜
⬛⬛🟥⬛⬛⬛⬛⬛⬛🟥⬛⬜⬜⬜⬜
⬜⬛⬛⬛🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
┊ ┊ ┊ ┊ ┊ ┊
┊ ┊ ┊ ┊ ┊ ✡
┊ ┊ ┊ ┊ ✫
┊ ┊ ︎┊ ★
┊ ┊ ✰
┊ ✬
❄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠒⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣴⣿⠟⢻⡉⠛⠛⠛⠛⠿⠶⢦⣤⣤⣄⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⣸⣿⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢷⣤⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⡇⠀⠀⡟⠀⠀⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢰⣿⠀⠀⠀⡇⠀⠀⠻⢿⠟⠀⠀⠀⣶⣶⡄⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⣿⠀⠀⠀⠀⣿⣿⣷⣶⣤⣀⣀⠀⠙⠛⠁⠀⠀⠀⣸⢻⡇⠀⠀⠀⣴⣿⣷⣾⣷⠀⠀⢀⣼⣧⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⢻⣂⡙⢧⣤⣀⣀⠹⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⡿⣸⠁⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣀⠉⠁⠀⠈⠉⠉⠉⠉⠉⠛⢷⣶⣌⣻⣿⡿⠃⠀⠀⣸⠃⡿⠀⠀⠀⠀⢯⣿⣿⣯⣿⣠⣾⣿⣷⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡛⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠻⠦⣤⣤⣴⠟⣼⠁⠀⠀⠀⠀⠀⢹⣿⣿⣟⢿⣮⢿⣿⣿⣿⡿
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⢹⣿⣿⡶⠀⠈⠙⠛⠿⠶⣶⣤⣄⣸⠇⠀⠀⠀⠀⠉⠻⢶⣇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣝⠷⠿⣷⣿⣿⣿⠃
⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣀⣀⣤⣴⡿⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷⣶⡾⠿⠛⠁⠀
⠀⠀⠀⠀⣿⣼⣿⣿⡿⣿⣿⣯⡿⠿⠟⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠋⠀⠀⠀⠀⠀⣸⣿⣿⣭⣟⣛⡿⠿⣧⠀⠀⠀⠀
⠀⠀⢠⣾⣿⡶⠟⠛⠛⠛⠛⢿⣦⣄⠐⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠛⠛⠛⠛⠒⠲⠶⢤⣄⠀⠀⠀⣼⣿⣿⣿⢀⡉⠉⠛⣻⠇⠀⠀⠀⠀
⠀⢰⣿⣿⣷⣶⣾⣿⣶⣶⣶⣤⣼⣿⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣿⣿⣿⣿⣿⠸⠂⠀⢀⡿⠀⠀⠀⠀⠀
⠀⣾⣿⣿⣟⣭⠭⠈⠉⢉⣙⣻⣿⣿⠇⠀⠀⠀⠀⣠⣾⡿⠋⠙⠷⣤⡀⠀⢰⢿⣾⣿⣷⡄⠀⢿⣿⣿⣿⣿⡿⠎⠀⠀⣸⠁⠀⠀⠀⠀⠀
⠀⠻⣿⣿⡧⠖⣒⠒⡲⠦⠬⣝⣿⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣨⣷⣤⣺⣷⣶⣿⡿⠃⠀⢸⣿⣿⣿⣿⣷⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣟⡏⠉⠉⠉⠀⠀⠀⠙⢻⡆⠀⠀⣤⣾⣻⣇⣀⣴⣾⣿⣿⢿⣿⠛⠛⠙⠛⠁⠀⠀⠈⣿⣿⣿⣿⣿⠀⢰⡾⠁⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢿⣿⣼⣿⣻⡿⠿⢻⣡⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⢰⣿⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠁⠀⠙⠿⠾⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣿⣿⣾⣿⣿⡿⠿⠷⢶⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣿⣿⣿⣯⣴⠶⠚⠛⠳⠮⣽⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⡟⠀⠀⣀⣀⡀⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠹⣿⣿⣿⣾⣿⣿⠿⢿⣿⣶⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⣿⣿⣿⣿⣦⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣿⣧⢀⠀⠸⣿⣯⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢨⣿⢻⣿⡟⠛⡆⠈⢛⡟⠷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠃⠂⠐⠂⠀⠤⠤⠤⠤⠄⠀⣀⣀⡀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⠓⢭⡓⢦⡀⠀⠀⠀⠀⢀⣀⢀⢀⣀⣀⠀⠀⠀⠀⣀⠴⢚⡭⠊⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣸⠉⠒⠓⠤⠙⢦⢙⣶⡖⠒⠋⢉⡹⠟⠩⠤⠭⣉⡓⠲⢞⣡⠖⠉⠴⠒⠓⢉⡇⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⣿⣲⠀⡀⠀⣠⠜⠋⠁⠈⢂⡴⣍⡀⠠⡀⠀⠀⠀⠈⠑⠢⣍⠢⣀⠀⠀⢠⣚⡁⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠐⣅⡀⠐⡫⠋⠀⠀⠀⠀⡴⠋⠀⠀⠙⠢⡈⠳⡀⠀⠀⠀⠀⠀⠑⢌⠳⡘⠀⢀⡽⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣯⣅⠞⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⢦⠈⠢⡀⠀⠀⠀⠀⠈⢳⡌⢦⣨⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠏⠀⠀⠀⠀⠈⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠙⣄⠀⠀⠀⠀⠈⢟⣎⢿⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠘⢆⠈⢦⠀⠀⠀⠀⠘⡌⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⣷⠀⢇⠀⠀⠀⢀⠁⢸⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡞⠀⢀⠤⣶⠟⢹⢱⡀⢀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠉⢳⡈⢧⠀⠀⠘⡄⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡧⢀⣴⣿⠁⠀⠘⡄⢳⡀⢧⠀⠀⠀⣏⢆⠀⠀⠀⠀⠀⡌⢿⣌⢧⡀⠀⢱⡀⢸⣷⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡷⠋⢠⠇⠀⠀⠀⢱⡀⢹⣦⣳⠀⠀⠘⣎⢷⡀⠄⠀⠀⠸⡜⣿⣮⢳⡄⠀⠃⢸⡟⠀⠀⠀⡸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⣿⣁⡴⢻⠓⠖⠒⠒⠒⠿⣄⢳⡻⣷⢄⣀⠹⣦⣻⣮⠢⡀⠀⢻⣿⢻⡷⣿⢦⣀⡸⣏⣀⠴⠊⢀⣾⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣭⣒⣿⡏⢠⢿⠀⠀⠀⢰⢤⡤⢬⡓⠓⠈⠙⠚⠒⠛⠙⠛⣓⢾⣷⣿⠛⠋⠛⢸⡷⣬⣉⢉⠀⢀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⣸⢠⣸⡷⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⢺⣾⢿⣿⣿⡷⣮⣠⠈⣿⠈⣿⣧⣾⣿⣭⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⡿⣟⣷⣻⣞⡷⣟⣿⡟⢠⣿⠀⠘⠀⢷⣾⣿⣿⠈⠃⠀⠀⠀⠀⠀⠀⠋⢸⣾⣿⣿⠇⠙⠁⢰⣿⡀⢹⣿⢿⣻⣯⢷⣟⣯⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⣿⣺⢷⢯⣽⡾⡋⣠⣿⣿⣆⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⣾⣿⣷⡀⢻⣿⣗⣯⢿⣞⣷⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣿⣿⣿⡿⣯⠿⠋⣴⡗⣯⣿⣇⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⣸⣿⣼⣿⣳⣼⣸⠛⢿⣷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡿⣯⣾⢹⡀⠀⠸⣿⣿⣿⣿⣮⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠁⣰⣿⣿⣿⣿⣷⣽⠞⠀⣽⢸⣯⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣽⣻⣷⣷⡄⠀⠙⢿⣿⣿⡽⣿⣿⣦⡀⠀⠀⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⢀⣼⣿⢿⡽⣯⣿⠿⠁⠀⣸⣷⣿⢯⣻⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⣿⣿⣷⣏⣿⣿⣶⣤⣀⣉⣛⣿⣷⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣯⣥⣤⣴⣾⣿⣟⣮⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣻⣟⣾⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⠑⠦⢄⣀⣀⡠⠔⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣮⡿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣿⡾⣳⣟⣾⡽⣟⣽⣿⣿⣟⣯⣟⣷⣿⣿⡿⠁⠱⢄⠀⠀⠀⠀⠀⢀⡠⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣳⣟⡾⡽⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣞⣷⣻⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠙⢢⣄⣠⠖⠉⠀⠀⠀⢹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡿⣭⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⣯⣻⣿⣿⡿⠿⠛⢋⣽⣿⡿⠃⠀⠀⠀⠀⣞⠉⢪⠾⠉⣣⠀⠀⠀⡜⠂⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠿⠏⣁⣶⠶⢶⠾⠉⠁⠸⡆⠀⠀⠀⣸⣿⣷⢏⣰⣿⣿⡆⠀⢰⠁⢀⠁⢀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡤⠊⠁⠀⠀⢸⠀⠀⢀⠀⡇⠀⠀⢠⢷⣻⣁⢶⢶⢍⣭⣽⣤⡟⠀⢀⠀⣂⢤⡁⠸⣿⣿⣿⣿⣿⣿⣍⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⠀⠀⠈⢰⢱⠀⢀⣯⣾⣿⣿⠾⠿⣿⣿⣿⣿⠃⠀⠄⢀⠈⠲⠷⢄⡽⠁⡽⠋⠁⠀⠀⠀⢀⠀⠈⢹⣲⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⢸⢈⣆⣼⣿⠟⠉⠈⠲⠊⠉⢹⣭⣿⣤⣬⣴⣶⣶⣾⣷⣾⣷⣾⡍⠙⠓⢦⠁⠈⢀⠀⣲⣿⣿⣯⡇⢲⠀⠀⠀⠀⠀
⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⢘⣴⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠘⣿⡿⢟⣻⣽⣷⣿⣿⡿⢿⣿⣿⣿⣄⠠⠀⠐⠈⢠⢾⣿⣿⣿⣿⣿⣯⣦⡀⠀⠀⠀
⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡆⢀⣴⣿⣿⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⠃⠘⢿⣿⣯⣻⣷⣄⠈⠀⢬⣿⣿⣿⣿⣿⣿⣟⣿⣯⡂⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣵⣿⣿⣿⢞⣻⡵⣿⣳⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣻⣿⣿⠀⢸⠈⣿⣿⣷⣝⢿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⡀
⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⠏⢳⡿⣼⣻⣷⡀⠀⠀⠀⠀⢠⣿⣿⣟⣯⠟⢺⣿⡇⠀⠈⠀⠹⣿⡿⣿⣮⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⣦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣼⣟⡷⣯⣿⣿⣀⠀⢀⣠⣿⣿⣟⣾⣳⣦⣾⣿⠃⠀⡁⠐⠀⢿⣿⡙⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
♫₊˚.🎧 ✩。﷽👌★🎸🎧⋆。 °⋆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⠀⠉⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣄⣀⣀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⡿⣿⡿⣿⡿⣿⡿⣷⣾⣾⢿⣶⣿⣷⣶⣶⣶⣶⣶⣾⣿⢿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣏⣿⣷⣿⢷⣿⣷⡿⣿⣾⣹⣏⣷⡿⣾⣹⣏⣿⣹⢿⣾⣹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣯⢿⣞⣷⢯⣿⣳⣯⢿⣳⣯⡷⣿⣽⣻⣽⢷⣻⣞⣯⣿⣞⣿⣻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⡿⣽⡿⣽⡾⣟⣷⢿⣽⣻⢯⣷⣟⡿⣾⡽⣯⡿⣯⣟⣷⣻⢾⣷⣻⣽⡇⠀⣠⣴⣾⠷⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠷⣦⣄⣀⠀⠀⣿⣟⡷⣿⢯⣟⣿⢾⣯⡷⣿⣻⢷⣯⢿⡷⣟⣯⣿⣳⣯⢿⡽⣟⣾⡽⣷⡿⠿⠛⠉⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠉⠙⠻⢿⣿⢾⣻⣽⣟⡿⣾⢯⣷⢿⣯⣟⡿⣾⣻⣽⣟⡷⣯⣷⣟⣯⣿⣻⣽⣻⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡄⠀
⠀⠀⠀⠀⣠⡶⢟⢋⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣯⡿⣯⣷⣻⣽⣯⢿⣯⢿⡾⣽⣻⢷⣟⡷⣯⣿⣻⢾⣽⣳⣯⣿⣞⣿⣻⠷⣦⣴⣤⣤⣤⣤⣤⣄⣀⠀⠉⠁⠀
⠀⠀⠀⠘⠛⢀⣴⠿⠋⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣽⣷⢯⣟⣾⡽⣟⣾⢿⣽⢿⡽⣿⣞⣿⣽⢾⣻⣯⣟⣷⣿⣷⣻⣷⠇⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⣧⠀⠀⠀
⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠛⠿⣯⡿⣯⢿⣽⢿⣽⣻⡾⣟⣿⣳⢿⡾⣽⣻⣷⣻⢾⣻⢿⣿⡿⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀
⢀⣤⠾⠋⠀⠀⠀⠀⠀⢠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠚⠛⠋⠓⠛⠛⠓⠛⠛⠛⠛⠓⠛⠛⠛⠛⠋⠁⠀⠀⠀⠈⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠻⠋⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠀⠀⠀⠀⠀⠀⠀
🧡💛💚🩵💙💜🩷❤️
💛💚🩵💙💜🩷❤️🧡
💚🩵💙💜🩷❤️🧡💛
🩵💙💜🩷❤️🧡💛💚
💙💜🩷❤️🧡💛💚🩵
💜🩷❤️🧡💛💚🩵💙
🩷❤️🧡💛💚🩵💙💜
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡟⠿⣦⣌⠙⠿⣿⣿⣿⡿⠋⣉⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⡿⣿⣿⣇⠸⣷⡀⠈⠙⠿⣶⣤⣉⠛⣠⣾⠟⠿⢷⣦⣌⡙⠻⣿⠿⠋⣠⣾⣶⣦⡒⠶⠤⣤⣉⠛⠿⣿⣿⣿⣿⣿⡀⣀⣿⣿⣿⣿⣿⢯⣾⣭⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⠶⣌⠙⣿⣄⠹⣷⡀⠀⠀⠀⠉⠛⣻⠟⠡⠂⡐⠂⡌⠙⠿⣶⣤⣤⣼⡿⠁⠈⠙⠿⣶⣍⠑⠪⣕⠦⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⣣⡿⠁⠈⠛⠛⣻⣆⣿⣿⣿⣿⣻⡽⣾⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢹⡆⡈⢳⡌⠻⣆⠘⢿⣄⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠁⠂⣬⣿⠿⠋⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠙⢮⡳⣄⠹⣿⣿⣿⣿⣟⠱⣿⣉⠀⠀⠀⠀⠰⣯⢾⣿⣿⣳⢯⡷⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣿⣰⣄⣹⣆⠙⣷⡀⠻⣷⣄⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠙⠻⣧⡌⠻⣿⣿⣿⣷⣬⣹⣧⢀⣴⠶⣦⣿⠯⣿⢾⡽⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣯⢿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣿⠀⣿⡿⠛⠛⠿⣷⣼⡶⠾⠿⠟⠿⠿⣿⡆⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢀⣤⣤⡘⠿⣷⣤⡉⠻⣟⣿⣇⠿⣟⣵⣾⣶⣶⣶⡿⣯⣟⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣷⣦⣄⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⢿⠟⠋⢻⣇⠀⠀⠙⣾⢦⠈⢿⡋⣠⣄⠙⠷⠿⠾⠷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⡿⠃⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⣿⠏⢸⡇⠈⠙⠻⢷⣶⣄⠀⠀⠀⠀⢀⣴⠞⠛⠉⠙⣧⠀⠰⢀⠂⠄⢃⠸⣿⡄⠀⠀⠈⢿⣳⠈⣧⠌⣁⣤⡶⠖⢲⣦⣄⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⣯⣷⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣿⠏⣠⠘⣿⡀⠀⠀⠛⣉⠻⣷⡀⢀⡴⠟⠁⠀⠀⠀⠀⠸⣆⠙⣎⢳⡌⢀⠂⣿⣇⠀⠀⠀⠀⢿⣇⢠⣾⠋⠁⠀⠀⠀⠀⠉⠻⣶⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⢿⣧⠘⣧⡘⢷⣄⢐⡄⢻⡇⢹⣷⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠸⡆⢹⡀⠄⣿⡿⣦⠀⠀⠀⢸⣿⢘⡿⠀⠀⣀⣀⠀⠀⠀⠀⠙⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⢻⣧⠘⣿⣦⣌⣉⣀⣼⡇⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢳⠀⢧⠐⣿⡟⣼⡆⠀⠀⣸⡽⠀⣷⣴⡾⣿⡩⢷⣄⠀⠀⠀⠈⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣷⣤⡙⠿⣶⣤⠀⠀⠀⠀⣀⡴⠶⠒⠖⠲⠒⠋⠡⢈⠀⢻⣧⠸⣿⣿⣿⣿⠏⣰⣿⣁⣤⠴⠶⠶⠶⠖⠆⠠⠀⠠⣼⣆⣸⠀⠘⢸⣿⠟⣼⠃⠀⢠⣿⠇⣰⠎⣻⣤⣾⣿⠢⠽⣆⠀⠀⠀⠸⣿⣄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣟⣯⡿⣿⣶⠈⣿⡃⢀⡴⠚⠡⣀⣴⣾⣶⣶⣶⣶⣷⡾⡿⠿⠛⠀⠻⣿⡿⢃⣴⡿⠉⠁⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⠉⠳⢴⣿⡿⣹⠏⠀⠀⣿⣞⠀⢁⣶⢟⣱⡿⠃⢙⢧⢻⡶⣤⡀⠀⠈⠙⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⢿⣷⣿⣾⣟⣿⣽⣿⠀⣿⡇⠠⠐⣠⣷⡿⢟⡩⢌⡣⠍⣿⣄⠀⠂⠀⠈⠻⣦⣈⣴⡾⠋⠀⠄⠂⠀⠁⠐⠈⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢓⢯⣤⠀⠀⠘⣏⣴⣿⠿⠟⠋⠀⡀⢸⢎⡳⡜⢦⢻⡄⠀⠀⠈⢻⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣯⣿⡿⣿⣽⣷⣝⣻⢿⣿⣿⡇⢸⣷⣠⣷⡿⢫⠱⢎⠔⣣⣬⡱⣌⢻⣷⡆⣠⣤⢤⣽⣿⢻⡱⣭⣤⣶⣶⣶⣶⣶⣤⣤⣄⡈⠀⠀⠀⠀⠀⠀⢰⣿⢣⣋⣶⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⢀⠀⣏⠆⢱⡙⢮⣹⠃⠀⠀⠀⠀⢿⡇⢹⣿⣯⣿⣟⣿⣿⣿⣿⢿⣟⣿⣯⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣟⣿⡜⣿⣅⣀⣽⡏⣼⣿⣿⣷⡀⠻⠛⣿⡘⢥⢋⡜⣾⡏⠀⢹⣷⣣⣿⡟⠁⣴⣿⠟⣥⣷⣿⣿⡿⠟⠋⣹⠉⠉⠹⠟⠛⠿⣷⣦⣄⣀⣀⢠⡿⣮⡟⠉⠁⠀⢀⣴⠿⣴⣤⣤⣀⣀⠂⠀⡘⠘⣦⢣⢏⣳⠏⠀⠀⠀⠀⠀⢸⡗⢸⣿⣿⠋⣿⣿⣿⣾⢿⣿⡿⣿⣻⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣻⣯⢿⣇⠹⣻⣍⡛⢃⣿⣿⣿⣿⣿⣶⠀⣿⡘⢤⢣⢼⣿⠀⣀⣤⣿⣿⡿⠀⢠⡿⢣⡛⣾⣿⣿⠏⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢨⠻⣿⣿⡿⠋⠀⢹⡇⢀⣤⠾⠋⠀⠀⠀⠀⠉⠙⠛⠿⣶⣤⡐⡬⢓⢾⡇⠀⠀⠀⠀⠀⢠⣿⠇⣸⣿⣿⠷⢿⣿⣾⡿⣿⣯⡿⠟⠿⢿⣿⣿⣾⡿⣟⣿⣿⣿⣽⣿⢿⣻⢿⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣾⢿⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣋⣙⣀⡸⣷⣊⣇⣿⣷⠛⣭⠳⣌⠭⡐⠀⠀⢀⠁⠀⣿⣿⣿⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣿⠟⠁⠀⠀⣼⠁⣸⠃⠀⠀⠠⢀⠠⢀⠀⡀⠀⢀⠀⠙⠻⣷⣿⣾⣥⣄⣀⠀⠀⠀⠸⣿⠀⣿⠋⣠⡶⠦⣤⣉⠛⠿⣿⡀⠀⠀⢈⣿⣿⣷⣿⣿⣿⡷⣟⢯⣽⣣⣟⣯⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣽⡿⠻⢿⣿⣿⣿⠿⠋⣁⡤⣖⣫⠭⠭⠄⠠⠭⢤⣭⣭⣿⣿⠼⠶⠏⠀⠁⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⠀⠘⠁⡀⠀⠀⢀⣤⣀⣀⣴⠟⠁⠀⠀⠀⠐⠁⢀⣇⣤⣶⣬⣤⣤⣤⣤⣤⣀⡁⡤⢴⡚⣧⢻⡜⣧⣻⣽⣿⠗⠀⠀⠀⢹⣧⠈⠀⣿⣀⠀⠀⠙⠳⣦⡈⠳⣶⣾⣿⣿⣿⣽⡟⣯⢳⡽⣚⢯⢶⡳⢾⣽⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣄⣀⣼⣿⡿⠁⡴⣪⠵⠋⠁⠀⠀⠀⢀⣴⡞⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⢿⣿⣿⣷⣶⣦⣿⣤⣴⣿⡷⠿⠋⠁⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠈⠀⠀⠀⠀⠉⠛⢷⡧⠽⢎⠷⣹⣾⡟⠋⠁⠀⠀⠀⠀⣸⣏⣀⣤⡾⠟⢻⢦⠀⠀⠈⢿⣆⠙⣿⡿⠉⠉⣷⡝⣞⢧⡻⣭⣛⢾⣹⣛⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣻⣿⣿⣿⠟⢀⡞⡵⠃⠀⠀⠀⠀⠀⠀⠸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠈⠁⣠⠴⠖⢛⣛⠻⣆⣤⠴⣦⡄⠀⠀⠈⢳⣶⣮⣽⡿⠟⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠁⠀⡐⢈⡞⣧⠀⠀⠀⢻⣇⠸⣿⢶⡶⣟⡽⣎⢯⣳⡝⣾⡹⢶⣛⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⡀⠀⠘⠓⠈⠐⠉⠒⣽⠆⠀⠀⠀⠻⠿⠧⣤⣄⡀⠰⣶⠞⠛⠁⠀⠀⠐⠛⠒⠶⣤⡔⣣⣿⠀⠀⠀⠀⣿⢀⣿⢎⡷⣹⢮⡝⣮⢳⡝⣮⢽⡳⡽⣞⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⡤⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠁⠠⠐⠠⠈⢀⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠁⠀⠀⠀⣼⡟⣸⣯⣞⡵⣫⠶⣝⣾⡹⣞⡵⣫⠷⣝⣯⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠄⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠛⠋⠁⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠶⢶⡀⠀⠀⠀⠀⠀⠙⣷⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣠⠙⢷⣭⣻⠟⣋⣙⡻⠾⠷⢛⣋⣥⣄⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⠖⠶⠲⠖⠶⠶⠶⠶⠶⣶⣶⣶⠾⠿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣼⠃⢳⡈⣷⡟⢰⡿⠛⠻⢷⡿⠟⠋⢹⣿⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣞⡇⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⣀⣀⠀⠈⠀⠲⢤⡀⠀⠀⠀⠂⠁⠀⢷⡀⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣶⡿⠛⠁⠀⢸⡇⣽⠇⣾⡇⠀⠀⠀⠀⢰⠁⣸⣿⠠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⣽⡀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢟⠶⣄⡀⠀⠈⠳⡄⠀⠂⠈⡀⢈⡟⢶⡖⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢰⣿⢡⣏⣾⠟⠁⠀⠀⠀⠀⠘⣆⠘⢿⣆⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠳⣻⡄⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⣄⡀⠀⠀⠐⠀⠈⢳⡜⣳⡄⠀⠀⠙⣆⠁⡀⠄⡸⣼⠏⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢹⢻⣿⣏⠀⠀⠀⠀⠀⢠⠖⣊⣠⣀⣻⣧⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣦⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠠⠈⡀⢘⡖⣹⠃⠀⠀⠀⢸⡤⣄⣞⡱⣯⡀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠘⣷⣦⡴⠟⢀⣬⡛⠿⣶⡀⠀⠀⣼⡿⠛⠛⠛⠛⢉⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⡼⣸⡇⠀⠀⠀⣠⡾⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢰⣯⡓⣿⡆⢹⣧⣠⣾⠏⣴⢶⡿⣿⢿⣿⣿
⣿⣿⣿⡿⣩⣽⣿⣏⢹⣿⣿⣿⣿⣿⣦⡀⠛⢽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⣱⢒⣧⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⣷⡹⣖⣻⣄⠹⠟⣡⡾⢏⡾⣽⢯⣿⣿⣿
⣿⣿⡟⣳⡟⠈⢹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣦⣄⠉⠻⢷⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠛⠛⠳⢼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠘⣷⢣⢧⣛⠷⣞⢯⡞⣽⢺⡽⣯⣿⣿⣿
⣿⣿⣷⣌⢿⣶⣛⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡉⠛⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⡀⢻⡝⣮⡝⣻⡜⣣⢟⡼⣣⢿⣷⣻⣿⣿
⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡉⢶⣦⣄⡉⠛⠿⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣿⣤⣬⣉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢹⣇⠈⣿⢲⣝⣱⣾⣵⢫⡞⣵⣻⣞⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣏⣴⠟⢻⣆⠻⣿⡟⣡⣤⣄⠈⠉⠛⠻⠿⣶⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠀⣼⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡓⢦⣤⣤⣤⣴⢾⣯⣿⣻⢿⣾⣭⣝⣛⠷⢮⣿⡻⠶⣄⡀⠀⠀⠀⠀⠀⠀⠘⡌⣿⡀⢹⡗⣮⡝⡿⣏⡳⣝⢶⣻⣞⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣯⠉⠁⠀⠀⠙⢻⣶⠁⠻⢿⠟⢀⣤⣶⠶⠗⠦⣽⡶⣨⣭⣿⣖⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢿⣷⣽⣦⡀⠀⠀⠀⠀⣠⠴⣋⣿⡉⠛⠺⢟⡻⣝⡛⠶⣍⣛⣷⢮⣙⢦⣍⠛⠶⣦⣽⣷⣮⠙⠶⣄⡀⠀⠀⠀⠀⠄⢻⡇⠈⣟⢶⣹⢣⣝⡳⣭⢞⣳⣯⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡿⠁⢀⡀⠀⢰⡟⣡⣶⣿⠇⣰⡿⠋⠀⠀⠲⢶⣟⣱⡷⠃⠀⢈⣷⠞⠓⠀⠀⠠⠀⠀⠠⠀⠀⠀⡀⠙⡄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣷⣴⣾⣿⠗⣛⣉⡉⠁⠀⠀⠀⠉⠻⢽⣧⡹⣿⣏⢻⣭⣷⣬⡳⢦⡈⠙⢳⣝⢻⣦⣌⠻⣷⣄⠀⠀⠀⠸⣿⠀⣿⢎⣧⢻⣬⢳⡝⣮⣟⡾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠘⠿⢛⣟⠻⢶⣿⢱⣿⣳⡏⢠⣿⠁⠀⠀⠀⠀⠀⠈⠁⠀⢀⣠⣼⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⡀⠙⠻⠭⣉⣻⣿⣶⣶⢦⣤⣤⣈⡑⠞⠻⣧⣿⣿⣷⣦⣄⠛⢶⣄⣘⢷⣙⢿⣷⣌⠹⣿⣦⡀⠐⣿⠀⢹⡞⣼⣓⢮⣷⣿⣶⣯⣟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⢿⡷⣿⡿⣿⢿⣦⣤⣾⢷⣻⣗⠸⣿⡀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠈⠙⠂⠀⠀⠀⠀⢀⡶⠆⠀⠀⠤⠞⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣶⣦⣄⣀⠉⠛⠷⣌⣓⢦⡹⢿⣿⣿⣷⣶⣟⣛⣛⣛⣿⢿⣶⣿⣯⣌⣉⠀⠹⣿⡷⣿⣿⣿⣦⣿⠀⢸⡝⡶⣽⡿⢋⣸⠙⣿⣯⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣽⡾⣟⣿⣳⣿⣽⣻⡾⣽⢯⣟⣷⣻⣤⣽⠷⠶⣶⠶⠶⠶⠶⠿⠷⠶⠶⠤⣤⣄⣀⣀⣠⣤⣴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣶⣶⣶⣶⡶⠷⢶⣶⣤⣤⣤⣬⣭⣿⣿⣷⣶⣤⠉⠛⠿⠿⢿⣿⡿⣧⣻⡿⣿⣿⣿⣿⣿⣷⣿⣿⣽⢻⣄⢹⣿⣿⣌⠻⣿⣿⡿⢿⣿⣿⣟⡵⡏⣿⠀⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣻⣿⣽⡾⣟⣿⣾⣿⡿⠛⠛⠉⣉⣉⣉⠛⠛⠛⠛⠉⢁⣠⣴⣶⣷⣤⣱⣶⣶⣶⣤⡀⢺⣶⣶⣿⣿⡄⠀⣾⣿⡆⠀⣶⣶⣶⣶⣶⣶⣆⠀⠙⣶⡦⢹⣶⣾⣷⣄⠈⣴⣾⣿⣷⣆⢀⣴⣾⣯⣍⠁⠀⠀⠀⣀⣴⣶⣤⣄⡉⣿⣷⣿⣿⣿⠉⢁⣼⣮⣝⠻⣾⣶⣿⢾⣿⣧⠱⣯⣝⠶⢦⣤⠽⣺⢿⡇⢸⣿⣷⣻⣿⣿
⣿⣿⣿⣿⣿⢯⣿⣟⣾⢷⣿⣻⣿⡟⠉⣀⣤⠶⠟⡭⢽⣻⠻⠿⣿⣿⡟⣿⣿⣿⠛⢿⣿⣿⣿⣿⣹⣿⣿⢸⣿⣯⣩⣉⠀⣰⣿⣿⣿⡀⠉⢹⣿⡏⠉⣿⣯⠀⠀⣿⡇⢠⣿⣏⣹⣿⠂⣿⣿⣩⣩⡁⣿⣿⣝⣿⠛⠀⠀⢰⣿⡿⠛⠉⠻⣿⣿⣿⣿⣿⣛⣯⠀⠸⣯⡖⣾⣧⣹⣿⣻⣯⣿⣯⣧⠈⣙⠿⠷⠾⠟⣽⣫⣇⣼⣿⣞⣿⣿⣿
⣿⣿⣿⣿⣿⣻⢿⡾⣯⣿⢾⣻⣿⣧⣬⡟⠙⠋⡛⢚⣫⡵⢾⣿⡿⠟⠀⣿⣿⡏⠀⢀⡀⢸⣿⣿⣿⡿⠋⢸⣿⡿⠿⠿⢃⣿⣿⣿⣿⣧⠀⢸⣿⡇⠀⣿⣇⠀⢨⣿⡇⢰⣿⣿⣿⡏⠀⣿⣿⠿⠿⠇⢸⣿⣿⣿⣷⠄⠀⣾⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣀⣀⣸⢿⣿⡿⣿⢿⡟⢿⣧⡘⢯⣧⠹⠿⣿⣿⠿⠋⢁⣼⣿⡿⣽⣻⣿⣿
⣿⣿⣿⣿⣿⡽⣿⣻⣽⣿⡿⢛⣋⣩⣭⡴⣖⡿⢟⣯⣿⡿⠟⠛⠉⠙⠳⣝⣿⣿⣶⣿⣿⣿⣿⣿⢿⣿⣤⣸⣿⣷⣶⣶⣾⣿⡿⠛⢻⣿⡆⢸⣿⡇⠀⢿⣿⣶⣾⣿⡇⠰⣿⡿⣿⣷⣄⣿⣿⣶⣶⣶⣿⣿⣶⣿⡟⠀⠀⠹⣿⣿⣷⣶⣾⡿⠋⣽⣿⣿⢿⣯⠀⠈⢻⡎⢿⣧⢿⠀⠹⣆⣳⡷⠌⢻⣆⠀⣾⣿⣿⣿⣿⡿⣏⣿⣻⣽⣿⣿
⣿⣿⣿⣿⣟⣿⣟⣿⡿⠋⣰⢫⠭⣍⣴⡿⣩⣾⣿⣿⡟⠀⣠⣤⣤⣄⠀⠈⠹⣿⠛⠛⠛⠁⠛⣻⣤⣹⣿⣟⣟⡛⠛⠛⠘⠛⣁⣀⣀⡛⠛⠈⠛⠃⣀⣈⣻⡿⠟⠋⠀⠐⣿⣧⣙⡟⠛⠙⠛⠛⠛⣃⣘⣻⣿⣯⣄⣀⠀⠀⢈⣿⣿⣿⣏⠁⠀⠻⠿⢋⣿⠇⠀⣀⠈⣿⠈⢷⡟⣧⣼⠟⠻⠷⢶⣞⣹⣾⣿⡏⢿⣆⠀⢻⣧⢿⣯⢿⣿⣿
⣿⣿⣿⣿⣿⣽⣾⣿⢠⠞⢑⣣⣾⣿⣟⣽⣟⣷⣿⡟⠀⢰⣿⡟⠋⠈⢿⠂⠀⠛⣷⣆⠀⣠⡾⠋⠁⠀⠀⠀⠀⠉⢳⣄⠀⣸⣧⠀⠈⢳⡀⠀⢠⣾⣿⡍⠉⣟⠀⠀⣶⣿⣯⠀⠈⠹⣆⠀⠀⣶⣿⣯⠀⢀⣀⣌⡀⠉⣷⣼⣿⣿⡄⠀⣏⠀⠀⠀⢀⣾⡟⠀⣼⣿⡀⠸⣧⠸⣷⡿⢁⣴⣾⣿⡿⠿⠛⠛⢉⢀⠘⣿⣆⠈⢷⣻⣽⣿⣿⣿
⣿⣿⣿⣿⣿⣞⣿⣿⣽⡞⢋⡴⣻⢿⡾⣏⡾⣽⡿⣧⠀⠈⢿⣷⣀⡀⢸⣶⣾⣿⠿⠋⢸⡏⠀⢀⣶⣿⠟⠿⣆⠀⠀⢻⣧⠈⣧⠀⣀⠀⠙⣆⠀⢸⣿⠇⠀⡧⠀⠀⢰⣿⠏⢠⣦⠀⢹⡄⠀⢹⣿⣿⠀⢼⡟⣿⡿⠂⣸⡆⢸⣿⡄⠀⢧⠀⠀⠀⣾⡟⠀⣰⣿⣿⣧⠀⢹⡆⠹⣿⣿⣿⠋⠀⠐⢦⠀⠃⡄⠊⣀⠹⣿⡄⠘⣿⣟⣾⣿⣿
⣿⣿⣿⣿⣷⣻⣽⡾⣿⣽⢟⣽⢫⣿⣳⢏⣾⠟⠁⠹⣦⣄⣀⠀⠉⠻⠛⠿⣄⠀⠀⠀⢸⡇⠀⣼⣿⡇⠀⠀⣽⠀⠠⣿⣿⡀⣿⠀⣽⣷⣄⠈⠳⣼⣿⡄⠀⡗⠀⠀⣿⡏⠀⣾⣿⣆⠸⢻⠀⢸⣿⣿⠆⠈⠛⠉⣀⣴⠟⠀⣼⣿⡇⠀⣫⠀⠀⣼⡟⠀⠀⠋⠉⠉⠉⠀⠈⢻⡀⢿⡍⠀⠀⠀⠀⠈⢧⠒⢀⡵⠋⠀⢹⣷⠀⢹⣿⣻⣿⣿
⣿⣿⣿⡿⢿⣿⣧⡞⢯⣴⣿⢣⣿⣳⢯⣿⠋⠀⠀⠀⠈⠙⠛⠿⣷⣦⡀⠀⠈⣷⣄⡀⢹⡇⠀⢿⣿⡆⠀⠀⣿⠀⠀⣿⣿⠃⣧⠀⣿⣟⢻⣧⡀⠘⢿⠇⠀⡏⠀⢸⡿⠁⠘⠛⠛⠛⠀⠈⣧⠀⣿⣿⠀⢰⣦⠈⢻⡁⠀⠀⣼⣿⡇⠀⡷⠀⣸⣿⠁⠀⣼⣷⣶⣶⣶⣶⡀⠘⣷⠈⢿⣄⠀⠀⠀⠀⠈⣧⠛⠀⠀⠀⠈⣿⡆⠈⣿⢿⣿⣿
⣿⣿⣿⠁⣴⣿⣼⣶⣿⣿⣿⢼⣷⢯⣿⠁⠀⢴⡶⠖⢦⣤⣄⣀⡀⢉⡿⠀⠀⣿⣿⣧⢸⣇⠀⠈⢿⣷⣄⡴⠟⠀⢀⣿⣿⠐⣯⠀⢽⣿⠀⠹⢿⣦⡀⠀⠀⣇⠀⣿⠃⢠⣶⣾⣷⣶⣶⠀⠘⡆⣿⣿⠀⢸⣿⣷⡄⠙⣦⡀⢽⣿⡇⠀⣯⢠⣿⠋⠀⣾⠛⢹⣿⣿⣟⣿⣷⡀⠘⢧⠈⣿⣦⠀⠀⠀⠀⠸⡆⠀⢀⡤⠀⢻⣷⣀⡀⠉⠛⠻
⣿⣿⡇⢸⡟⠹⣿⠿⢻⡿⣿⢻⣿⢺⡏⠀⠀⠘⣧⠀⠀⠻⣿⣿⡧⠞⠋⠀⣼⣿⣿⠃⠀⠙⣦⡀⠀⠁⠀⠀⠀⢰⣿⣿⠟⠀⡇⠀⢸⣿⡀⠀⠈⢿⣷⡀⢀⣧⣾⠋⠀⢙⣿⡇⠉⠉⢿⠇⠀⠙⣿⣿⣀⣘⡏⢿⣿⣆⠈⠙⣾⣿⣇⣴⣿⣾⠃⠀⣼⣃⢀⣿⠏⠀⢻⡎⢿⣷⡀⠘⣧⡙⢿⣧⠀⠀⠀⠀⢳⡴⠋⠠⠌⠌⠛⠛⠿⠿⣷⣶
⣿⣿⠅⣾⡇⠀⠀⠀⣿⡇⢿⣏⣿⡟⡇⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠀⠀⠀⣈⣿⣷⣶⣶⣶⣶⣿⣿⠏⠀⠈⢻⣶⣾⣿⡆⠀⢀⣀⣻⣿⣿⣿⢿⣿⣿⣿⣿⣃⠀⠀⢸⣿⣿⣿⣿⠿⠿⣿⣷⠀⠻⣿⣿⣿⣿⣿⡿⢹⡏⠁⠀⠀⠉⣿⣹⣿⠀⠀⢸⡟⣼⡏⠁⠀⠀⢹⡏⣿⣧⠀⠀⠀⠘⡇⢈⡰⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠏⣠⣿⠇⠀⠀⠀⢿⣿⡈⢷⡹⣷⢻⡄⠀⠀⠀⠈⠹⣶⣶⢾⣛⣛⣻⣟⣽⠯⣶⣶⣻⠿⠋⠀⠙⠛⠛⠛⠛⡟⣃⣀⣀⣤⣤⣶⣾⠿⠟⣻⣿⠿⣿⡅⣼⡿⣷⣿⣿⣿⣿⣿⣷⣶⣶⣷⣦⣶⣤⣦⣴⣶⣿⣤⣶⣾⣿⣿⣿⣿⣿⠸⠿⠿⠿⠿⠿⠇⣿⣿⠀⠀⣿⡇⠹⣿⣿⣿⣿⡿⠀⣿⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢡⣾⠏⠁⠀⠀⠀⠀⠀⢻⣷⡈⢷⡹⣿⣟⣿⣶⢶⠶⠟⠉⢶⣶⣿⣽⣿⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣭⡭⢛⣿⣿⣿⢟⣣⣼⣿⣿⡿⠷⠞⣻⣿⣿⠁⠀⠉⠈⠉⠉⠉⠉⠉⠛⠙⠛⠛⠛⠛⠛⠛⢋⠉⢿⣏⠀⠈⢿⣾⣿⣷⣶⣶⣾⣿⣿⡿⠀⠀⠘⣿⣶⣤⣤⣤⣤⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣉⣙⡓⠾⠯⠭⠭⠬⠭⢟⣞⣯⣽⣿⣳⢷⣾⣶⣯⣭⣭⣛⡛⠻⣿⠿⠿⣻⣯⡷⣞⠛⠉⢩⠾⠟⣛⣉⣉⣠⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢈⡇⠈⣿⣆⠀⠀⠉⠛⠻⡟⠛⠛⠋⠉⠀⠀⠀⠀⠈⠛⠻⠟⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣌⡙⠻⢷⣦⡄⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣻⣽⣿⣷⣯⣝⡛⠿⠿⠿⣿⣛⣼⡿⢟⣉⣻⣯⣯⠭⠿⠛⠃⣰⣿⠿⠻⠟⠛⠋⠉⠀⡀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⣠⠞⢀⣼⡿⠃⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⡄⢹⣧⠀⠀⢀⣾⠟⢁⣤⣤⣤⣿⣿⣽⣯⣿⣟⣯⣿⣾⣷⣿⣻⣾⣿⣽⣿⣿⣷⣶⣦⣤⣤⣀⣀⣤⣶⣤⣤⣤⣤⣴⣶⣿⡿⠃⠀⠀⠀⣠⠖⢀⢂⡁⠆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⣿⣿⣥⣤⣶⣴⣦⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣷⡀⢿⣆⣠⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡙⣻⣿⣿⣟⣿⣻⣛⣛⣛⣛⣋⣁⣀⣀⣀⣀⣞⣁⣀⣂⣄⣐⣈⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠏⢀⣼⣿⣿⣛⣾⢳⣯⢾⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣷⡈⠛⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⣿⣿⡟⣾⣝⡾⣻⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠂⠀⢸⣷⠀⢸⡟⡟⣿⣿⣓⣦⣤⠶⠶⠶⠶⠆⠆⠀⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠂⠀⠰⠂⠀⠀⢸⠀⠀⠀⠰⠖⠀⠖⠀⠀⡇⠀⠀⠀⠀⠟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀
⣿⣿⡏⠀⠀⠀⢸⡇⠀⠀⠀⢐⣿⣿⠀⣿⠀⠂⣿⣿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠆⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡅⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀
⣿⣿⣷⠀⠀⠀⢸⠇⡀⠀⠀⣸⣿⡿⢸⡇⠀⢰⡿⣿⢸⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡏⠈⣿⠃⢹⡇⠀⠀⠀⠀⣰⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⠀
⣿⣿⣿⠀⠀⠀⣾⠀⠀⠀⢀⣿⣟⣇⣼⣃⡀⣸⠏⣿⡎⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⢸⣿⠃⢰⡏⠀⠸⣇⠀⠀⠀⠀⡇⠀⠀⢸⣿⡇⠀⠀⣠⠤⠒⠉⠀⢀⠎⠉⠙⠒⠂⣿⠀⢀⣀⣿⣄⠀⠀⢀⣿⢸⣿⠀
⣿⣿⣿⠀⠀⠀⣿⠠⢀⣤⢾⣿⠻⡏⣿⠉⠙⣿⣶⢹⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠰⢸⡏⠀⣼⠧⠀⠀⣿⠀⠀⠀⠀⠇⠀⠀⢸⣿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢻⣿⠻⣦⡀⢸⡟⢸⡿⠀
⡟⣿⣿⠀⠀⠀⡟⢀⠛⠃⡼⡿⢀⢸⡇⠀⢰⡿⠏⠈⣷⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⣾⠃⢀⡟⠀⠀⠀⢻⡆⠒⡛⡛⡏⠙⠛⢺⣿⣧⣅⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡿⠀⢻⡆⠀⠀⠘⢿⣿⠇⢸⡇⠀
⡇⢹⣿⠀⠀⠀⡇⠀⠀⠀⣷⠗⡀⢸⠇⠀⢸⠇⣰⡄⢹⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⣸⢇⣶⠀⠀⡘⣧⠀⡆⢸⡇⠀⠀⢸⣿⡇⠈⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢿⣄⠀⠀⠈⢿⡄⢸⠇⠀
⠀⠘⢻⡆⠀⢸⡇⠀⠀⠀⠸⠀⡇⣾⠀⠀⣿⣸⠋⢻⡘⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢀⣿⡾⠙⣇⠀⠀⢿⠀⡇⣸⡇⠀⠀⢸⡏⣧⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⠻⣷⣄⠀⠸⣇⢸⠀⠀
⠀⠀⠘⡇⠀⢸⡇⠀⠀⠄⠄⠀⠃⣿⠀⢸⣧⡏⠀⠈⢧⢹⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⡿⠁⠀⠹⡄⠀⣿⠀⣿⠀⡇⠀⠀⢸⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢈⣿⢷⣧⣿⣿⡀⠀
⠀⠀⠀⣿⠀⢸⣷⡀⠀⠀⠀⠀⣸⣿⣦⣾⣿⣥⣀⠀⠘⣯⣷⠀⢿⡄⠀⠀⠀⠀⠀⠀⢀⣇⡿⠁⠀⠀⠀⢻⡄⣿⢠⣿⠀⣿⠀⠀⢸⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣾⠋⢸⠃⠀⣿⡇⠀
⠀⠀⠀⢻⡄⢸⡏⢷⡀⣰⣴⣾⣿⣿⣿⣿⣿⣶⣌⠛⠦⠘⣿⣇⠈⢻⡄⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⢻⣽⣾⣿⣤⣿⠀⠀⢸⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡾⠁⠀⣾⠀⢀⣿⡇⠀
⠀⠀⠀⠸⡇⢸⣿⣨⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⡀⠈⢻⡆⠸⣿⣄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠴⠖⢻⣿⣻⣿⣿⣦⡀⣸⠃⠀⠸⣧⠀⢠⣄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡾⠁⠀⠀⡏⠀⢸⣿⣇⠀
⠀⠀⢀⠀⢿⣠⣿⣿⣿⠟⠉⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢻⡄⢿⣿⣄⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⡆⠈⣿⡇⠀⠀⠀⠀⣾⠀⠀⠀⡤⠟⢁⡄⠀⢸⠇⠀⣼⣿⣿⠀
⠀⠀⠘⡆⠸⣇⣿⣿⡏⢠⡴⠛⢩⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡄⠀⢻⣼⡏⠛⣦⡀⣤⣀⡇⠀⠀⠀⢀⣴⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣏⣿⡀⠀⠀⣸⠇⠀⠀⡘⠀⣠⠞⠁⠀⡾⠀⢠⣿⣿⣿⡆
⠀⠀⠀⢻⡀⢿⡼⣿⣷⡏⠀⠀⠈⣿⣿⣿⣿⢿⣿⡿⣿⣷⠀⠀⠀⠀⠹⣿⠀⠈⠛⠿⠻⠷⠀⠀⠘⠋⠛⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣧⡀⢠⡟⠀⠀⠀⣠⡾⠃⠀⠀⣰⠇⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠈⣧⠘⣿⡿⣿⣿⣆⠀⠀⠘⣿⣁⠙⠞⠛⠃⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣆⣀⡉⠛⣿⣿⣿⣿⠃⠀⠀⠞⠉⠀⠀⠀⢀⡿⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⡆⢻⣷⣿⣿⣷⡀⠀⠀⠙⣋⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⢿⡿⠉⠹⡟⠻⢿⣯⠈⠉⠳⣄⠙⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⣿⣿⣿⣿⣿
⣄⠀⠀⠀⠀⢿⡜⣿⣿⣿⣿⣷⠐⠶⢀⡙⢿⣄⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢶⡌⠀⠀⠀⠀⠁⠀⣸⡏⠀⠀⠀⢘⣧⣿⣿⣻⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣷⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⣾⠟⢋⡵⠋⠀⠀⠀⠀⠀⠀⡾⣀⠀⣸⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣆⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠶⠶⠟⠛⠉⠘⠋⠀⢀⣼⠋⣴⠟⠁⠀⠀⠀⠀⠀⣰⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣷⣄⠘⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢁⣼⠇⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣶⣋⡿⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢛⣭⣿⣿⣿⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠀⣿⣿⡏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢀⣤⣾⡟⠋⠉⢹⣷⠶⠶⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠏⠙⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣁⣤⣿⣿⠃⠀⣿⣿⣿⣿⡿⠟⢋⣽⡿⠋⠻⠿⣶⣾⠟⠁⠀⠀⠀⠀⠉⢷⠋⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⢻⣿⡃⠀⠀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⢉⣿⢟⣿⡏⠀⣰⡿⠛⠉⠀⢀⣵⣿⠟⠀⠀⠀⠀⢸⡇⣴⠶⢦⣀⠀⠀⠀⠘⢧⣀⣠⠇⣷⡀⣀⣀⣤⣤⠶⠾⠛⣿⣿⣿⣷⡿⠁⠀⠀⡾⠁⠀⢿⡏⠻⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡶⠟⠁⢸⡏⢡⣾⡟⠂⠀⢀⣤⣾⡿⠅⠠⣇⡀⠀⠀⢸⣷⣏⡆⠀⠙⢷⣄⠀⠀⠀⠉⠁⠀⢻⣿⠏⠉⠉⠀⠀⠀⠀⠻⢛⣿⣿⡄⠀⠀⡼⠃⠀⠀⠸⣇⣰⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠀⣸⣷⡿⠉⠀⠀⠴⠋⢱⣿⣄⣴⠶⢿⡁⠀⠐⢸⣿⣟⣦⡀⠀⠂⠘⠣⠄⠀⠀⠀⢸⣿⡙⠀⠀⠀⠀⢀⣤⠔⣠⡟⣽⡟⠀⠀⠐⠁⠀⠀⠀⢠⣿⣿⣿⠟⠛⠛⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⢠⣿⠟⠉⠀⠀⠈⢷⣤⣿⣿⠿⠿⣿⣿⣶⡤⠄⢤⠀⠠⠀⣠⣿⣭⣥⡄⢀⣠⠾⠋⢀⡴⣋⣴⣿⠇⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⢘⣿⢿⣹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡆⠀⣼⡇⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢠⣼⡿⠁⠀⠀⠀⠙⠛⠿⢿⣶⣶⡶⠶⠛⠉⠀⠀⠀⠐⠋⣁⣤⣄⡀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⢠⣾⣧⠞⠉⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⡟⣼⢿⠁⠀⠀⠀⠀⠀⠀⠀⣻⣷⠀⠀⠀⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⣀⣴⠾⠛⠉⠀⠈⣧⣸⡿⡋⠀⠀⣠⠀⡀⠀⣿⣿⠋⠀⠀⠀⠀⠀⣰⣿⡿⠗⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⣸⢃⠏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⢸⠀⡾⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣗⣠⠶⠟⠉⠀⠀⠀⠀⢀⣴⣷⡟⢀⣠⡴⠿⠛⠙⠷⣼⣿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣧⠶⠶⠶⠦⣦⣄⣤⣄⣀⠈⢿⣿⣿⣿⣿
⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⢸⣸⡇⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣿⡿⠛⠁⠀⠀⠀⠀⢠⣿⠟⠄⠀⠀⠀⣠⡟⣵⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⣦⡿⠿⠟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠈⢿⣇⠀⠀⠀⢿⣤⣄⡀⠀⠀⣰⣿⡇⠀⠀⠀⢀⣠⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⣰⠏⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠁⠀⠀⠀⢸
⠤⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣴⡶⠾⠻⠷⣶⣶⣤⡽⠬⢽⣠⣾⠟⠋⡇⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡛⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⡀⠀⠀⠀⢨⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠋⠀⣀⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢱⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢿⣿⣄⣤⡾⠛⡈
⠀⠀⠀⠀⣧⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣠⣤⣾⣟⠙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠃⠀⠀⠀⠀⠀⠀⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣉⣉⡉⠀⠀⠹
⡐⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂
⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡆⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣭⣽⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣷⣿⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠿⠛⠋⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠀⠂⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠻⠿⣿⣿⣷⣄⡀⠠⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠁⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⢠⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡁⠈⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⡀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⣠⣄⣤⣤⣤⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣔⠫⠍⡭⠹⢍⡓⢦⣸⣿⡷⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠘⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⣛⢛⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⣈⠖⡩⠔⠣⢎⢰⢧⣿⣿⠇⠀⠀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢠⠒⠯⠹⠭⠽⢩⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⢎⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠽⠴⠭⠭⢖⣷⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡂⣍⠒⡩⢜⡐⢣⠚⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢂⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠙⢿⣿⣦⣝⡠⠧⠬⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠈⠀⠀⠙⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣤⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⣿⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠁⠀⠀⠉⠻⢿⣿⠇⠀⠀⠀⠀⠀
⢡⠐⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⣄⡀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⡿⣿⠿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⢿⣿⣿⣿⠿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣥⣾⣿⣶⣄⡀⠀⠀⠀
⡡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢸⣿⣿⣁⡀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠃⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠻⣿⣿⡿⠿⣿⣿⡇⠀⠀⠀
⡁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⢸⣿⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣸⣿⡟⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣎⢏⣹⣾⣿⡿⠃⠀⠀⠀
⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠘⢿⣿⣦⣤⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢰⣦⣼⣿⡿⠃⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀
⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠉⠛⠛⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠘⠛⠛⠉⢴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣧⡀⠰⣿⣶⣶⣦⣤⣤⣤⣤⣤⣠⡀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠁⠀⠻⣿⣿⣤⣠⣿⣿⠛⠻⠿⣿⣿⡿⠿⢃⣤⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠃⠀⠀⠀⢹⣿⣷⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢌⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
◍ ◍
◍ ☽ ◍
◍ ︵︵‿ ︵‿︵‿︵‿︵◍
◍ .˚ ̥ 𓆞 ◍
◍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠑⣎⠉⠛⠿⣷⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣀⣘⢷⡄⢀⡀⠈⢩⠏⠛⠛⠛⢿⠿⢷⣶⣴⡿⠟⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠠⡼⣯⠷⠋⠀⢠⢣⣤⢠⡦⣴⠊⢀⣠⠞⠋⠀⣀⡤⠔⠚⠁⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠁⠀⠀⠀⣯⢯⣿⠏⡷⠁⠀⠉⠀⠀⠀⠘⣿⣤⣤⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠁⣼⡏⠘⠃⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⡟⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⢰⣧⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢁⡴⢃⣬⣇⡛⠒⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣼⡟⠀⣼⣱⠋⣥⠼⠳⣄⠀⠀⠹⡀⠀⠀⠀⡠⠒⠚⠋⠈⠉⠉⠛⠲⢦⣀⣀⣀⢄⡞⠀⠀⠀⠘⣄⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢀⡠⠤⠄⣉⠛⠁⠀⠹⣿⡞⢋⡤⠞⠊⢧⡜⠦⠙⣔⡲⠀⣠⣠⡄⠀⠀⠀⠛⠛⢛⣒⣨⣏⠀⠈⠛⢶⣄⡀⠀⠘⣆⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⡔⣗⠃⠀⠐⠒⠃⠀⠀⠀⠘⣧⠟⢀⣀⡤⠞⠳⣄⠀⡸⣄⠀⠀⠉⡀⠀⢀⡠⠖⠚⠿⢦⣍⠉⠙⣦⠀⠀⣷⠙⣦⢀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣷⠈⠀⣠⣄⡀⠀⠀⠀⠀⠀⢹⡛⠉⢡⣀⣠⡴⠋⠻⠬⡬⠭⠶⠊⢁⡴⠋⠙⠛⠶⣄⠀⠘⣧⠀⢸⡇⠀⠏⣀⣬⡾⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠐⣿⠉⠻⣦⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣀⣀⡞⠀⠀⠀⠀⠀⠘⠓⠂⣹⣠⣼⣴⣶⠿⠛⠁⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡆⠀⣿⡇⠀⠀⠀⠀⠘⢧⣸⡀⠀⣤⠀⠀⣹⠏⠉⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⢉⡉⠠⠤⣤⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠸⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠓⠷⠾⠶⠚⠁⠫⢉⡀⠀⡇⠀⠀⠀⠀⠀⣀⢀⡾⠉⠀⣀⠤⠒⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠹⣧⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢤⣜⣀⠀⣠⡾⠋⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠹⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡘⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠑⢷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰⠈⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣌⠃⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⡋⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠾⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⠀⠀⣼⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡼⠃⠉⠙⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡤⠴⠚⠋⠉⠀⠀⣀⡀⠤⠤⠐⢒⣂⠩⠝⠃⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⠀⢠⡤⣀⠀⠀⠈⠙⠓⠦⣤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡔⣂⡩⠤⠔⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠁⠈⠰⣒⠠⠄⣀⠀⠀⠉⠓⠦⣄⡀⠀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠦⣉⠒⠤⡀⠀⠀⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠬⠧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥⬛⬛⬛
⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜🟥🟥🟥🟥⬛
⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥⬛
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥⬛
⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜🟥🟥🟥
⬛⬛⬛⬜⬜⬛⬜⬜⬜⬛⬜⬛⬛⬛⬛
⬜⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜
⬛⬛⬛🟥🟥⬜⬜🟨⬜⬜🟥🟥⬛⬛⬛
⬜⬛⬜🟥🟥⬜⬜⬜⬜⬜🟥🟥⬛⬜⬜
⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛
⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣽⣾⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣾⣿⢟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣟⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⡟⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡿⡻⣿⣿⠋⠰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣇⣿⣿⠀⠀⡘⡘⢅⠘⠛⢋⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣻⣿⡀⠀⠜⡰⢈⠌⡱⣣⢙⡯⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣄⡘⠄⡓⠖⣢⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢋⠞⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⡵⠛⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⣾⣿⣿⠋⡄⡇⢰⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣾⣿⣿⣿⠇⠀⢘⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⠀⠀⢮⠘⠀⠡⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠦⣄⠄⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣿⣿⣿⠀⠜⣼⠀⠁⠀⢢⡠⣿⣿⠿⣿⡿⣿⣿⣿⡟⢬⠑⣜⣦⠢⠀⠀⠀⠀⠀
⠀⠈⠏⠉⡟⡛⢿⣮⠘⣼⠀⠀⠄⠀⠳⣩⡆⠚⡷⢮⡵⣛⡟⢾⣄⠣⢼⣇⢣⠐⡀⠀⠀⠀
⠀⠀⠁⡸⣍⠷⡾⡄⣷⡈⠀⠀⠘⠀⠀⢸⠇⢰⡹⢧⣻⣽⡸⣡⠯⣓⢞⡇⢎⠥⡁⠀⠀⠀
⠀⡈⢠⡛⣬⢻⠃⣷⣿⣟⡀⢀⠀⠡⠀⡌⡆⠲⣝⢯⡖⣿⡱⢆⠯⡽⣯⡼⣊⠾⠁⠀⠀⠀
⢀⠃⢬⢳⡹⣾⠀⣿⣿⣿⣧⠸⠀⠀⢆⢱⠃⢴⣛⡼⣳⣯⣳⡜⢦⡳⣟⠃⠙⠀⠀⠀⠀⠀
⠰⢀⡏⢶⣹⡇⠀⣿⣿⣿⣿⣷⡀⠀⢰⢘⡀⡗⣎⢷⣣⡷⢭⡻⣷⣿⣯⠢⣄⠀⠀⠀⠀⠀
⡂⢼⡘⣧⣿⢠⡀⣡⣿⣿⠟⠛⣆⠀⢤⢷⠀⣽⣚⡬⢧⡹⢶⡹⡜⡽⣌⢫⣎⠀⠀⠀⠀⠀
⡏⣶⠹⡜⣥⢫⢵⡳⣯⢿⠐⠔⠮⠗⢸⢂⢥⣞⣵⣻⣎⠳⢧⢻⣙⣩⡜⠉⠈⠣⡀⠀⠀⠀
⠹⠶⠯⠜⢶⣫⣾⣵⣻⣦⢔⡨⣿⢳⢧⢗⣠⡀⢰⢏⣾⣛⣷⣻⣽⣻⣴⣳⣤⣀⠘⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⢏⠐⢹⠋⠀⠃⠰⠀⠿⡚⠷⠫⡖⡽⣺⣷⣛⣮⣿⠾⢾⢶⣿⡌⡄⠀
⠀⠀⠀⠀⠀⠠⢐⠖⠁⡰⠅⠠⠄⠀⠤⡃⠀⠳⠒⠌⠓⡲⣏⡿⣽⢯⣿⢀⡒⠯⠀⠛⢠⠀
⠀⠀⠀⡀⠁⡠⠅⠠⠘⠄⠀⠀⠀⠀⠄⠣⢀⠀⢣⢀⠣⡕⢮⣝⣯⣗⣻⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐⠄⢠⠊⠀⠀⠀⠀⠈⠲⢀⠯⣜⢣⡞⡾⣵⢯⡄⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⠀⠀⠀⠀⠀⠀⠀⢎⡲⣍⠾⣩⡗⣯⢞⡷⡀⠀⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⣹⠀⠀⠀⠀⠀⠀⢠⢉⠶⡱⣎⢻⡵⣻⢼⣛⣞⢷⡀⠀⠀⠀⠀
⠐⡀⠀⠀⠀⠀⠀⢀⡐⣣⢟⣆⠰⣀⠆⡄⢃⠦⣙⠮⡵⣹⢺⡜⣧⢿⣹⡞⣧⠷⠀⠀⠀⠀
⠀⢣⢄⠠⡀⡄⡔⣦⣝⣳⢯⣿⣢⠑⡮⠜⣭⠲⣍⠾⣱⢣⡗⣯⡽⣞⣷⣻⣭⣛⢇⠀⠀⠀
⠀⠈⢮⣱⠳⣜⡳⣵⠾⣭⢷⣻⣷⣍⠲⡙⢦⠻⣬⢻⡵⣛⣾⢳⡯⣟⣶⣛⣮⡽⣾⠀⠀⠀
⠀⠀⠀⡍⢻⡓⠿⢾⢻⠽⣯⣟⣿⣿⣷⣭⣂⠟⣼⣣⠿⣽⣚⣯⢷⣻⢾⡽⣞⣷⣳⣆⠀⠀
⠀⠀⠀⢰⠀⠈⠙⢌⠣⣝⢲⢯⡿⣿⣿⣿⡉⢟⠲⣭⣟⣳⡟⣞⣯⢯⡿⣽⣻⣞⣿⣿⡄⠀
⠀⠀⠀⠀⢂⠀⠀⠀⠒⡈⢏⠾⣽⣿⣿⣿⣷⡀⠱⣔⢭⣳⢻⡽⣞⢯⣽⣳⣿⣿⣿⣿⣷⠀
⠀⠀⠀⠀⠈⢕⣢⢤⣀⣰⣌⣷⣯⣿⣿⣿⣻⡌⠒⢯⢷⣾⣧⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⢷⡽⣿⣿⣿⣿⣿⣿⣿⣿⡃⠟⠄⠈⢳⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⣲⣶⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⣾⣵⣶⣲⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣶⣾⣿⣿⣿⣿⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣽⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⡿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠟⠛⠻⣿⣿⣷⠀⠀⡀⣰⣿⣿⠟⠿⠟⠝⠛⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡆⠀⣰⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣴⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣴⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣾⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⢿⣿⣿⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⠟⠁⠄⡙⢿⣿⣿⢄⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⡁⠄⠂⡙⢿⣿⣞⣄⢀⣀⡤⢠⣤⣴⣠⣶⣶⣴⣶⣾⣷⣷⣶⣶⣶⣂⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⡈⠐⠠⠐⠠⠿⣿⣯⣧⣤⣤⣤⣤⣼⣿⣿⠋⠄⡐⢈⠐⠠⢈⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣯⣶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⡏⠐⠠⢁⠂⡁⢂⠐⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⡈⠐⡀⠂⠌⡐⢀⠂⢛⠛⡛⢉⠉⠄⠠⠹⣿⣿⣿⣿⣿⣿⠃⡈⠼⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣷⣷⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⡟⡠⢁⠂⠄⠂⠌⡁⠌⡘⢿⡿⠛⢿⡿⠛⢿⡿⠃⠄⠡⢀⠁⢂⠉⠄⡈⠄⢂⠐⠠⠈⢄⠁⡂⣌⣛⡛⠛⠋⠠⠐⡀⢂⠘⠻⠿⠿⠿⠋⢀⠂⠄⡈⠹⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⣤⣀⠀⠀⠀
⣴⣯⣴⣬⣵⣿⣿⣶⣶⣯⣿⣿⠁⠔⠠⠈⠄⡁⠂⠔⠠⠐⠠⠐⡈⣤⡄⠡⠀⠄⡈⠄⡁⣂⠌⠠⢈⠐⠠⠈⢄⣬⣶⣿⣿⣿⣿⣿⣿⣿⠇⡈⠄⡁⠢⢐⠨⠐⠄⢂⠐⡈⠄⡈⠔⠠⢁⠂⠌⣻⣿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣾⣢⠀
⠙⠿⠿⣿⡿⢿⣿⣿⣿⣿⣿⠇⡌⠠⠁⠌⣶⣿⣿⣮⠐⡁⢂⠡⢰⣿⣿⠂⡁⢂⠐⢠⣿⣿⣿⣧⠂⠌⡀⠃⠜⢿⠟⠛⢉⠡⢁⠠⠀⠄⢂⠐⠠⢀⠡⠂⠤⠡⠌⡀⠆⠰⠠⠐⡈⠔⠂⠌⡐⢀⠙⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢀⣤⣌⣾⣿⣿⣿⣵⣿⣿⡿⠀⠄⠡⢈⡐⢿⣿⣿⡿⠁⡐⢰⣿⣿⣿⣿⣿⣿⡆⠈⠌⢿⣿⣿⠟⢀⠂⠄⠡⢨⣶⣶⣿⣶⣶⣶⣶⣷⣮⡄⡈⠐⡀⢂⠑⠂⢃⠒⠐⢊⠐⡁⠒⡐⢈⠐⡈⡐⢀⠂⠌⢿⣿⣟⣆⠀⠀⠀⢀⣴⣿⣿⡟⠉⠻⣿⣿⣿⣿⣿⡿
⢺⣿⣿⡿⣿⣿⣿⣿⣿⣿⠇⡈⠄⡁⠂⡄⠂⠄⠠⠐⠠⢀⠡⢉⠩⢉⠉⢋⠁⢂⠡⠈⠄⠠⠀⠌⠠⠈⡄⠁⠆⠙⢋⠛⠙⠛⠛⠛⠛⢛⠃⠄⠡⢀⠡⣈⠡⣈⢈⠡⡈⢄⠡⡁⢌⡈⢄⡁⢌⠠⡈⠐⡈⢿⣿⣟⣄⣰⣶⣿⣿⣿⣿⣤⢈⠐⣀⢙⣿⣿⣷⠃
⠀⠉⠉⠀⠀⠀⢈⣽⣿⡿⢈⠐⠠⢀⠡⠄⠡⠈⠄⡁⢂⠰⢀⠂⡐⠠⠈⠄⡈⠄⢂⠡⠈⠄⠡⠈⠄⠡⠄⠩⠄⠃⠄⢂⠡⠈⠄⠃⠌⢠⠈⠄⠡⠂⠔⠠⠐⠄⠢⠐⠄⠢⠐⠄⠢⠄⠢⠄⠢⠠⠁⠆⡐⠘⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⠃⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠆⡈⠐⡀⠒⡈⠒⠑⢂⠒⠐⢂⠂⠒⡀⢃⠘⡀⢂⠘⡀⢂⠃⡘⠂⢃⠘⢂⠊⡐⢈⠂⡘⢀⠂⠡⢈⠂⠌⡀⠂⠌⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢂⠁⢂⠑⡀⢃⠒⠠⠁⢿⣿⣿⣿⠁⢂⠙⢿⣿⣿⣿⣿⣿⣿⠗⠁⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠂⠄⠡⡀⢡⠁⡉⢌⠠⡁⡉⠄⡉⢄⠡⡁⢌⠠⡁⢡⠈⡄⠡⢈⠌⡠⢉⠠⡁⢌⠠⡁⢉⡈⠡⢉⡈⡁⣉⢈⠡⡉⢠⠁⡌⢠⠁⡌⢠⠁⡌⢠⠁⡌⢐⠈⡌⢠⠁⢌⠠⢈⠡⢈⢸⣿⣿⣿⡇⠂⠌⣀⣽⣿⣿⣿⠟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡿⣿⣿⠀⠃⠌⡐⠠⠂⠔⠠⠂⠔⠠⠐⠰⢀⠢⠐⠄⠢⠐⠄⠂⠔⠠⢁⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠠⢁⠂⡐⠄⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠠⠂⠌⠠⠂⠄⡡⢈⠸⣿⣿⣿⣿⣶⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣧⣿⣿⠈⡐⢠⠀⡑⠌⢂⠡⠘⡀⢃⢉⠐⢂⡐⢁⠊⠄⡑⢈⠡⠘⠠⡁⢂⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠂⡘⠠⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⠈⡄⠃⠌⠡⠘⡈⠡⢈⠐⡐⠠⢌⣿⣿⣿⣿⡻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣣⣿⣿⠐⡀⢂⠐⠠⡁⢂⠡⠌⡐⠤⠈⠤⠁⠄⢂⠡⠌⡐⠠⠡⢈⠡⠐⡈⠄⢂⠡⢂⠡⠈⠄⡂⠡⢂⠡⠄⠡⢂⠡⠐⠄⡡⠐⠠⡁⠌⠠⡁⠌⡀⠆⣈⠡⠠⠡⢈⡁⠆⡁⢂⠁⠂⠄⠡⢸⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠐⠠⢈⠐⡁⢂⠂⠒⡀⢂⠑⡀⢃⠘⡀⢂⠒⡀⢃⠒⡀⢂⠑⡐⢈⠂⡐⠂⢂⠑⢂⠐⡁⢂⠂⡘⠐⢂⠂⡑⠂⠄⢃⠒⠐⡈⠒⡀⠒⡐⢂⠐⡀⢃⠒⠠⠐⢂⠐⡀⠊⠄⡁⠂⣽⣿⣿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠌⡐⠠⠈⠄⡃⣈⠡⢈⠄⡡⢈⠄⡡⢈⠄⡡⢈⠄⣂⠡⣈⠐⡈⢄⠡⣈⠡⡈⢌⠠⡁⢌⠠⡁⢌⡈⠄⡡⢈⠌⡈⢄⡈⢡⢈⠁⡌⢁⠄⡡⢈⠄⡡⢈⡁⢡⢈⠐⠠⢁⠂⠄⢡⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠠⠁⠌⠠⠡⠄⠢⠄⠆⠰⠀⠆⠰⠀⠆⠰⠀⠆⠤⠐⡀⠆⠰⠀⠆⠤⠐⠄⠢⠐⠄⠢⠐⠄⠢⠀⠆⠰⠀⠆⠰⠠⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠢⠐⠄⠂⠌⡐⠄⡈⠐⣸⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠡⠈⠄⡁⢂⠘⡐⢂⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⠒⠐⡈⠒⢁⠊⡐⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⢈⠂⡑⠂⡑⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢁⠊⡐⢂⠐⠠⢀⢱⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡁⢂⠐⠠⢈⠐⠠⡁⢌⠠⡁⣌⠠⡁⣌⠠⡁⢌⡈⢡⢈⢡⠈⡄⣉⠠⡁⢌⠠⡁⣌⠠⡁⣌⠠⡁⡌⢠⡁⢌⡁⡄⡡⢈⠄⡡⣈⠄⡡⣈⠄⡡⢈⠄⢂⠡⠀⠌⡐⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠌⡐⠠⢈⠐⡀⢂⠡⠐⠠⠐⢠⠠⠐⠄⢂⠰⢀⠢⠀⠆⡐⢀⠂⠔⠠⠂⠔⠠⠐⠠⠠⠐⠄⠰⠀⠄⠂⠤⠐⡀⠆⡐⠄⠠⢂⠐⠠⠐⣀⠂⠌⡀⢂⠁⢂⣰⣿⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣤⠁⠌⡐⢀⠂⠄⡁⢂⠁⡂⠄⠡⠈⠄⠂⠄⢂⠁⢂⡐⢠⠈⡂⠡⠈⠄⠡⢈⠂⢡⠈⠄⡡⠘⠠⢁⠂⠡⠐⡐⠠⡈⢐⠀⡊⠄⠡⢀⠂⡐⢀⠂⢌⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣦⡔⢂⠈⣐⣀⣆⣐⣠⣈⣄⣡⣈⣐⠈⠄⡈⣄⣐⣀⣂⣄⣡⣈⣄⣁⣂⣌⣀⣂⣐⣠⣁⣂⠄⡈⠄⣡⣀⣡⣐⣀⣂⣐⣈⣐⣀⠂⡐⣠⣾⣿⣿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡐⠸⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⡇⢠⢹⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣜⣴⣿⣿⡞⠈⠉⠉⠚⠛⣿⣿⣧⣒⣼⣿⣟⠏⠉⠈⠁⠈⠈⠁⠒⠉⠒⠓⠚⠚⣿⣿⣷⣌⣿⣿⣿⠟⠀⠀⠁⠁⢹⣿⣿⣧⣦⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⠻⡿⢿⣟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⣿⠛⡍⢻⣿⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⣿⠟⡡⢎⠰⡁⠞⣿⣎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠿⠛⢿⣷⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⡿⢋⠴⡁⠦⡑⢌⡘⠼⣿⣮⣶⣦⣄⣒⣤⣤⣤⡤⠤⣀⣠⣾⣿⠟⡡⢎⠱⡈⢿⣷⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢟⡡⢊⠔⡡⢚⡐⢢⠑⢆⢹⣿⣿⣿⠛⣿⣿⣿⡿⢿⣿⣿⣿⠟⡱⢌⡑⢢⠑⡌⠚⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣾⣵⣶⣽⣿⠋⢆⠰⢡⢊⡑⢢⠘⠤⡉⢆⢂⠛⠿⡋⢌⠹⢿⡿⢃⠎⢿⣿⠟⡘⠔⢢⠘⢆⡱⢈⡱⠸⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣯⣿⡿⢿⣿⣶⡥⢊⠔⣈⠆⣉⠦⡑⢌⢢⠉⢆⠱⡈⢆⠡⢂⢅⠊⡔⢢⠑⡌⠬⡁⢎⡐⢢⢁⡒⢡⢻⣿⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣯⣿⣿⣿⣟⣠⢃⠬⡙⢅⠣⡘⢄⡊⢔⣢⡑⣌⠢⡉⢆⠱⠸⣀⠣⢊⠤⡉⢆⡡⢊⠔⡡⡘⠰⡈⡅⢒⡘⢄⠢⢿⣿⢧⣴⣶⣿⣷⣾⣳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣾⣿⣿⢛⠻⠿⣿⣷⢌⠢⠱⡈⠆⣼⣿⣿⣿⡦⡑⢌⠢⢡⣷⡠⠇⣾⣆⡑⣢⣔⡉⢆⠱⣨⣵⣠⢑⠊⡔⢊⠔⡩⣿⣿⡿⠟⠒⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣾⡟⡡⢊⠆⣑⠢⡑⢌⢂⠣⡑⠬⡘⢻⠿⢟⠣⡑⣌⣲⣽⣿⣷⣿⣿⣿⣴⣿⣿⣐⡌⢺⣿⣿⣿⣇⠣⢌⠣⡘⠤⢹⣿⣝⣢⣤⣤⣠⣠⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣿⠏⡔⢡⢊⡒⢌⢒⡉⢆⡡⠓⡌⢒⢡⠊⡔⢡⣲⣿⡿⡟⢫⢩⣭⣍⠡⠛⢛⡙⠻⢿⣿⣿⡟⢟⡛⢄⠣⡌⡱⢌⠢⢡⢻⣿⣿⠛⠿⣿⠿⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣽⣿⠃⢎⠰⠡⢆⡘⢄⡊⠴⡈⡔⢩⠰⡁⠦⡑⢌⣵⣿⠏⣰⣄⣃⠜⢻⣣⣜⣀⣃⢄⠀⠀⡘⢻⣿⣦⠘⠤⢃⠴⡁⢎⠰⡁⢎⣿⣯⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣿⣿⡡⠚⣄⢋⡑⢢⠘⣄⠚⣄⠓⣘⠢⢱⢈⠱⢌⢾⣿⡏⡐⢧⡀⡸⢺⣿⣿⣻⠿⢿⣷⡆⠰⢈⠂⢿⣿⡇⡩⢌⠢⡑⣊⠱⡈⠆⠼⣿⡾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⣿⣿⡕⢂⠦⢉⠆⡩⠤⢩⠄⣋⠤⣉⠆⡡⠚⣎⣹⣿⡗⡘⢠⠉⡔⠉⠻⠿⠿⢿⡿⠟⣰⣿⣦⢉⢸⣿⡇⡇⠬⡑⢤⠡⢆⠱⡘⢂⢿⣿⣣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⣿⣿⣿⡇⢣⠘⡌⢢⡑⣑⢊⡜⢠⠓⡰⢨⢁⢃⠆⡜⣿⣷⣾⣶⣥⠀⠀⠠⢑⢸⡉⠙⡆⠰⣉⠁⣦⣾⣿⠇⣅⠣⡘⡄⠣⢌⠣⢌⠡⢊⣿⣿⡆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⡿⢈⠅⢎⠸⢄⠱⠌⠦⠌⡅⢎⡑⢢⠁⡎⠒⣌⣻⣿⡌⠙⣿⣧⣘⣄⣣⣌⣙⢚⣨⣷⣾⡿⣿⣿⣿⡌⢄⠣⠔⣨⠱⣈⠒⡌⢡⠃⡼⣿⣵⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡿⠛⠟⡛⣩⢐⠩⡘⢤⠩⢌⡒⣉⢚⡘⣐⠢⡘⢄⠣⢌⣷⣿⠿⢿⣿⣦⡈⠛⠛⠛⠛⠻⠿⠿⠿⠋⢁⣰⣿⡟⢿⣿⡄⢣⡉⢄⠃⢆⢩⡘⢢⠑⡰⢻⣷⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢡⠉⢆⡱⢠⠊⡔⡉⠦⡑⢢⠑⡌⠲⢨⠄⢣⢉⠆⣉⠆⡩⠑⣬⣾⣿⠻⠿⣿⣶⣶⣶⣶⣶⣶⣶⣾⡿⢿⣿⣇⠚⡿⠟⠤⡑⠬⡉⠆⡥⠘⡄⡃⢆⠹⣿⣞⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡉⢆⡑⢂⢣⠐⣑⠢⡙⣄⢋⡔⣩⠒⡌⢣⢘⡐⠢⢌⠱⡁⢎⠛⡅⢣⠑⡢⢉⠍⡩⠍⢭⠉⡍⢒⠌⡂⠿⡃⢎⠰⡉⢆⡑⢢⡑⡊⢔⠱⣈⠱⣈⠒⣻⣿⣧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢀⠎⡡⢎⡘⠤⢣⠱⡐⢎⠰⢄⠳⠨⠅⢦⠨⠱⢌⠢⡑⢊⢒⠸⢄⠃⠖⣉⠒⡑⢊⠆⡱⢘⠢⣉⠴⠡⠜⡠⢃⠕⢢⠘⠤⡑⠬⢌⠢⡅⠲⡈⢆⡙⣿⣿⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠌⡜⡐⢢⡘⢂⢇⠚⣌⢢⡙⢌⣊⠱⣉⢆⢃⡓⢌⢒⠡⢃⠎⡘⢄⠋⡜⢠⠃⣍⠒⡸⢀⠇⣘⠰⣈⠣⡑⡘⢤⠚⡄⢋⠴⣁⠓⣌⠒⡡⠓⡌⢢⡁⢿⣿⢣⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠟⣨⠘⠤⠱⠡⡌⠥⢊⠜⠤⢢⠜⡰⢄⠣⠌⠦⠱⢌⠪⠜⣈⠧⡘⠜⡨⠆⠥⠣⠜⡄⢣⠱⠌⡜⠤⢣⠰⡁⢇⠩⢢⠱⢌⠱⠢⢅⡚⠤⠩⠔⢣⠘⠤⡘⠸⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢐⢄⡓⠌⡤⢉⡒⡩⡑⢌⡱⢉⢎⡘⣡⠚⣐⢊⡱⡉⢎⡑⣊⡑⢪⡐⢆⡱⢉⢆⡙⡌⣓⡘⣌⡑⣊⠜⣐⢃⢎⢒⡉⢆⡙⣂⠓⣌⢣⢉⢆⡑⢪⡑⡊⢆⡙⠤⣉⠒⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡇⢎⠰⡈⡜⢠⠃⡜⠤⡉⠖⡌⠎⢤⠑⠦⠱⠌⢆⡱⠌⠦⡑⠦⢌⠱⠌⠦⢌⠱⢢⠱⠌⠴⡐⠦⡘⠤⠓⠬⢌⠲⠤⣉⠦⠱⢄⠫⡐⠦⠡⠎⠬⢡⠒⡩⡐⢌⡒⠤⣉⢺⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⡉⢆⡡⠓⡌⢢⡑⡌⡱⡘⣌⢒⡉⢦⢉⡒⡍⢚⡐⢢⡙⢢⡑⣊⠜⡘⣌⠓⡌⡓⣌⢒⣉⢒⣉⢒⡡⡙⣌⠓⣌⠚⣄⢣⡘⣑⢊⠥⣑⢊⡱⣉⠜⣡⢊⡱⢈⠒⡌⠒⠤⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠌⠢⠔⡩⠔⡡⢆⠱⢢⠱⡐⢎⠸⢄⠣⠜⡨⠱⠌⡥⠌⠥⢒⠡⢎⠱⢄⠫⠰⢡⠒⠬⢄⠣⠔⢣⠰⠱⢠⠋⠤⠓⢤⠢⠜⠤⢃⠎⠤⠣⠔⠬⡘⠤⢃⠴⡉⠜⡠⢋⠔⡡⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣈⠓⡌⠱⣘⠐⣊⢅⣃⠚⣌⢂⡓⣌⢊⡱⣁⢋⡜⡰⢉⡚⢌⡓⢌⡊⣌⠣⣙⢢⢉⡚⣄⢋⡌⢣⡑⣩⢂⡝⣨⠙⣂⢣⡙⡘⣌⢊⡱⣉⠎⡱⢑⡊⢥⠒⡡⠚⡄⢣⠘⡰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⢠⠃⡜⠡⢆⠩⠔⡊⢤⠩⠔⡊⠴⢠⠃⢖⠨⠒⠤⢃⠎⠴⠡⠜⢢⠱⢄⠣⠆⡜⠤⢣⠰⠌⡔⢣⠰⢡⠒⡔⠢⠍⡔⢢⠌⡱⢄⠣⠒⠤⢣⠑⢎⠸⠤⠩⠔⣡⠘⡤⠓⡰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢠⠓⡌⡑⣊⠒⣉⢒⡡⢎⡡⢃⡙⢢⡉⢆⡍⡙⣌⢃⢎⡱⢉⢎⡱⢘⡌⡱⣑⠸⣈⠱⣘⡘⢌⡂⢇⡃⢎⡔⣉⠚⣌⢡⢚⡐⣊⠱⣉⠚⣄⢋⢆⡩⢒⡉⢎⠄⡃⠦⣉⢼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠄⢣⠰⢡⠢⣉⠔⡣⠔⠢⡅⢣⢌⠱⠌⠦⢌⠱⡐⢎⠰⠌⠥⢢⠜⡰⠰⠡⢆⠱⢌⠱⠢⠜⠤⣉⠦⡘⠴⡈⠦⠩⠔⣊⠤⠱⢄⠣⡌⡱⢄⠋⠴⢨⠡⠜⡠⢎⠡⣃⠔⣸⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢰⢁⡃⢲⠐⣊⠱⡌⢓⢌⠣⣘⡘⡌⡓⡌⢣⡘⢢⡙⢌⣃⠣⡜⢰⡉⡓⡌⣃⠎⡱⣁⢋⢆⡑⢢⡙⣄⢣⡑⣩⢊⡔⣡⢋⢌⠓⡰⡑⡊⣍⢒⡡⢎⡑⠒⡌⠒⡄⣊⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠣⢂⠍⢢⠩⢄⠣⣌⠱⠌⠦⢡⠒⠥⡘⢤⠣⠜⡡⠜⡰⢄⠣⡌⢥⠒⠥⢢⠱⢌⠱⠨⠌⠆⡍⠦⢰⡐⠦⡘⠤⠒⢬⠰⠌⠦⣉⠦⡑⠥⢂⢎⠰⢂⠥⡉⠴⡉⢔⣰⣿⣯⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡕⡌⠚⡄⠓⡌⠒⡤⢋⡌⢣⡑⣊⢅⡓⢢⢉⡒⡡⢓⡘⡄⠓⣌⠢⡙⢢⢑⠪⢌⢣⡙⢌⡓⡌⡑⢦⢘⢢⡑⣉⠚⣄⠓⣌⢃⡒⡔⢩⡘⡡⢊⢒⠡⡒⢡⠚⢄⣣⣿⣿⠋⠀
⠀⠀⢀⣀⢤⣤⣴⣢⣴⣶⣶⣶⣶⣯⣭⣽⣿⣿⡔⡩⠐⡍⠔⡩⠰⢡⠌⡅⠦⡑⠢⢌⠣⡘⠤⡑⢢⠒⡌⠱⣀⠣⠌⣅⠪⠱⠌⢆⡸⠰⡐⢅⡚⠤⢃⠆⡜⣠⠙⡄⢫⠐⢆⠱⢨⠡⠆⡅⢣⠊⡔⢡⠣⡘⣲⣿⣿⠃⠀⠀
⣠⣮⣿⣿⣿⠿⡛⢿⣿⣿⣿⣿⠩⢩⠙⣿⣿⣿⣷⠡⢍⡘⠤⢃⠱⢂⠜⡠⢃⠜⡡⢊⠆⡑⢆⡑⠆⠣⢌⡑⢢⠑⡌⢢⢁⠓⡌⢢⠐⡱⢈⠆⣘⠰⡁⢎⠰⣀⢣⠘⡤⢉⠆⡃⢆⠱⡘⢄⠣⡘⢄⢃⣶⣿⣿⣟⠁⠀⠀⠀
⣿⣿⣿⣿⣿⡇⡘⠸⣿⣿⣿⣿⡇⠦⣉⢻⣿⣿⣿⣇⢆⡑⢊⠅⠪⠌⢆⠱⢌⠒⡡⢎⠰⡉⠔⡨⢌⡹⣿⣿⣶⣥⢘⠡⢎⡘⢄⠣⠱⡘⢄⡃⠦⡑⢌⠢⠱⣈⠆⡱⢠⢉⠆⡱⣈⠒⡅⢊⠴⢉⠆⡹⢛⠻⢿⣿⣣⠀⠀⠀
⢿⣿⣿⣿⣿⣧⣥⣧⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣶⣾⣷⣾⣷⣾⣦⣷⣬⣦⣵⣦⣵⣬⣵⣴⣦⣴⣦⣬⣿⣿⣥⣾⣤⣼⣤⣧⣵⣬⣦⣼⣤⣵⣬⣦⣧⣴⣬⣴⣥⣮⣴⣥⣦⣵⣬⣦⣼⣦⣼⣤⣧⣾⣾⣿⠏⠀⠀⠀
⠀⠉⠛⠛⠛⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠓⠋⠉⠉⠉⠉⠙⠊⠉⠛⠛⠛⠛⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠉⠙⠛⠛⠛⠛⠚⠁⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠛⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢿⣸⣿⣏⡎⡍⣆⣿⣿⣌⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠻⣿⣿⣿⠻⣏⢧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣄⣂⣂⣀⣿⣿⣿⣿⣨⡷⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠈⠀⢰⣿⣿⣿⣿⠀⢻⣿⠋⢡⣴⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⠉⠿⠿⠃⠀⠈⠸⡄⢻⣿⣯⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣶⠒⠀⠀⢠⣀⣠⣄⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⠳⠦⣄⣀⣬⣥⣤⡿⣤⡀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⡀⠈⠙⠛⠋⢭⢓⡍⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠿⣽⣻⢿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⢿⣿⣻⡟⣿⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣞⣳⢯⣽⣳⢯⣿⠛⠛⠻⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣏⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢯⣟⣿⡿⣽⢯⡇⠀⠀⠀⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡳⣯⣟⣾⣿⣟⣳⡿⠀⠀⣾⠀⠀⢻⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣿⠿⣬⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣽⣳⣟⣾⣿⢾⣽⠃⠀⠀⣿⡄⠀⠘⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⣆⣀⠿⣁⣠⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⣞⡷⣞⣿⣿⣿⠃⠀⠀⠐⠛⠃⠀⠀⢹⣿⣯⢿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡷⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠰⣮⢻⣿⣿⣿⡟⢭⣽⣿⢾⣽⣻⡽⣞⣿⡇⠀⠀⠀⢀⣀⣀⡀⠀⠸⣿⣿⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣮⣗⡞⣴⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣦⣠⠄⢸⣿⣿⣉⢞⣿⣿⣯⣞⣷⣻⡽⢯⣷⡄⠀⢀⣿⡿⣿⣿⣄⣸⣿⢯⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣱⣿⣿⣷⣸⣾⣿⣿⣷⢿⡾⣷⢿⣏⣿⣿⣿⣿⢿⣹⢷⣏⣿⣿⡿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡏⣿⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣯⣿⠾⣯⣿⡿⢭⣟⣙⠋⢭⣻⣿⣿⣇⣿⣿⣿⡿⣯⣿⢿⣿⣾⣟⣾⡿⣽⢯⣟⣻⣞⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡽⣳⢯⣻⣿⣿⣉⡉⢿⣿⣿⣿⣿
⣿⣿⣽⡿⣯⣷⣻⣿⣿⣮⣏⣱⠊⠤⢼⣿⣿⣿⠿⣯⣽⠠⠿⣿⣯⣟⡿⣿⣿⣻⣽⣻⢾⡽⣞⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⠟⢿⣿⣿⣷⣾⣿⣿⣿⣿
⣿⣳⢯⣟⡷⣏⣿⢻⣼⡛⣿⣦⣛⣤⣸⢿⢟⣿⣿⣿⠃⠀⠀⢚⣻⣿⣿⣿⣷⣿⣾⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠋⠛⢿⡁⣀⣈⣷⣧⣾⣿⣿⣿⣿⣿
⣯⢟⡻⣞⡽⣹⢞⡯⣿⣟⣿⣭⢽⣿⣰⣯⠫⡙⢿⣿⣷⣤⣤⣄⣻⡦⠿⠿⠿⣿⣿⣿⣿⡿⠟⢡⣿⣿⣯⣿⢿⡾⣹⢯⢿⣻⢿⣦⣸⣿⣷⣦⣼⣿⣍⣁⣈⣿⢿⣿⣿⣿⣿⣿⣿
⣧⣏⣷⣹⣞⣵⣫⣼⣿⣥⡄⠽⠋⠉⣛⣄⣤⣵⣿⣟⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠽⡆⠀⣐⣢⣿⣿⡉⠀⢨⡗⠡⢋⣼⠷⠿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣻⢿⣻⡿⣿
⡛⣛⠛⡛⢛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠉⠁⣈⣿⣿⣿⣿⣿⣿⣿⣿⠿⣧⣄⡀⠀⠀⣰⣧⣼⣿⣿⣿⣿⡧⣤⠾⢷⢷⡿⣷⣦⣤⣼⣿⣿⣿⣿⣿⠍⠈⠉⠙⢦⡰⣯⣳⣏⡷⣻⢽
⠀⠀⠃⠄⢃⠐⠀⠂⠁⠀⠐⠀⠀⠀⢀⣰⣿⣏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⣄⡀⠈⠁⠉⠉⠙⠉⠛⠙⠛⠿⠿⠿⠿⠶⡶⢿⡛⢧⠯⣝⠳⣏
⠀⠀⠠⠀⠄⢂⠐⡄⣊⠴⣐⢆⡒⡄⣾⣿⣷⡝⢿⣿⣶⣿⣹⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠦⢤⣄⡀⠀⠀⠀⠈⠀⠀⢀⠂⠁⠊⢄⠡⠜⢂⡓⢌⠳⢌
⠀⡤⢃⡜⣜⠮⡱⢏⡳⢯⡹⣎⡵⣾⠇⢿⣿⣿⣧⣀⣁⣿⠁⢻⣿⣿⣿⣿⣗⣻⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⡟⠀⠀⠀⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⡈⢄⢂⠢⠌⢂
⠘⠰⡉⠖⣌⠳⣙⢮⡝⣧⣻⣜⣳⣿⡄⠐⢋⡻⠿⠿⣿⡷⣶⣦⣿⣿⣻⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠿⢳⠀⠀⠀⠐⢈⠠⠀⠄⡐⠠⡀⢂⠰⠈⠄
⠈⢱⡈⠵⡈⢧⡙⣮⡝⣷⣻⣞⣷⢯⣿⣦⡀⠁⠤⠾⣟⣢⡿⣿⢹⣿⣳⡿⠟⠁⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣟⣬⣀⣀⣤⣶⡋⠀⣀⠂⢈⠀⢂⠐⡠⠠⠑⠀⠆⢂⠌⡐
⠀⢢⠘⡔⡉⢆⡹⢰⢫⢷⣻⣞⣯⣿⣿⣿⣿⣦⡀⠀⢙⠿⣷⣾⣿⣿⣁⣀⡀⠀⠀⠀⠀⠙⢷⣏⡞⡭⢏⡻⢝⡻⢻⠿⠿⠿⡿⠟⠯⢑⠂⡄⡈⠤⢈⠔⡠⠄⠑⡈⠡⠌⢄⠂⡐
⠀⠀⠈⡄⡘⠄⢣⠑⢎⢯⡳⢿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠁⠪⣝⠿⣿⣽⣿⣻⢿⣶⣤⣤⣀⣀⣹⣮⢕⠫⡜⢢⡑⢣⢚⡐⢣⡐⣉⠒⡠⢁⠒⡐⠢⣁⠒⠠⢌⠡⡘⢠⠉⠆⣂⠐
⠀⠀⠠⠀⠠⠘⠠⡘⡘⢤⠻⣇⣟⣻⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠛⠤⣛⠿⢿⣿⣼⣻⣟⡿⣿⣿⣿⡜⢣⡛⡄⠻⣀⠄⡃⢄⡀⢃⠄⡃⣘⠠⢃⠃⣀⠛⠤⡘⠠⢃⠄⡛⠤⡀⡘
⠀⠀⠀⠐⠀⠁⠂⠐⠀⠎⡱⢌⠲⡱⢏⡿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣉⣙⠒⠮⠭⠭⣛⠛⢋⣼⠏⠦⡑⠌⠱⡀⠆⡑⠢⡘⢄⠊⠔⡠⠑⢂⠌⡰⠈⢆⠱⢈⠒⢨⡐⢢⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠑⡘⣌⠲⢍⠟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⠌⡱⢈⠂⠡⢀⠃⡐⠡⠐⢨⠈⡐⢁⠊⡁⢆⠡⢉⢂⠑⡌⢈⠂⠤⡁⠌⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠂⠌⡘⢀⠣⢉⢋⠛⢻⠻⠟⡿⠿⠿⠿⠟⠟⡛⠍⠣⠜⡈⠆⡑⠀⠄⠒⢀⠂⠠⢁⠈⠄⠂⡐⢂⠐⠡⠀⢂⠐⠄⠂⡐⠂⠌⡐⢀⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠈⠠⠉⡐⠌⠒⠄⡈⠒⠄⢊⡐⠁⠎⠑⡂⠌⡐⠠⠈⠀⢈⠠⠀⠄⠠⠀⢈⠐⠀⠄⠈⠄⠁⠄⠈⠄⠡⢀⠡⠀⠐⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢈⠐⢀⠂⠰⢈⠒⡀⠆⢁⠊⠄⠠⢈⠐⠐⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠐⠀⠁⢀⠂⠐⠀⠀⢀⠐⠀⠀⠀⠀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠂⠀⠄⠂⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⡅⠀⠀⠀⠀⠀⢀⣾⣿⣶⣷⣾⢿⣶⣷⣏⣡⣶⣷⣌⣿⣿⣿⣷⡉⠛⠋⢁⠈⠠⠐⠠⠈⠙⠛⠻⣷⡌⠻⣷⣿⡇⠀⠀⠀⠀⠀⠿⣿⣿⣿⣟⠁⠄⠃⠤⠑⢂⠐⠠⢂⠡⢀⠂⡐⠠⠁⣼⣿⠁⢢⠈⠄⢠⠁⠂⣴⣧⠂⢄⡁⢂⠌⣀⢂⡐⢂⡐⢂⠸⣿⡶⠟⣛⣩⣭⡶⠾⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣩⣭⡶⠾⢛⣋⣭⣴⠶⠟⣛⣩⣼⣿⣿⣇⣣⣮⣵⣷⣷⣿⣿⣿⣷⣾⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⠀⠀⣾⣿⣷⣿⠿⢟⣘⠿⠿⢏⡸⢿⡿⢋⡹⢿⠿⢻⣿⡄⠐⢀⠂⠄⡐⢀⠂⡐⢀⠂⢹⣿⡀⠘⢿⣧⡀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠇⡘⠠⢂⢡⣾⡷⢀⠂⡐⠂⠤⢁⠃⣸⣿⠇⡈⠆⣈⠘⠠⠌⠡⢸⣿⠀⠂⠌⠄⠊⠄⠡⡈⠄⡐⠂⠄⠹⣿⣟⣯⣽⡷⠾⣛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⡶⠾⣛⣻⣭⣷⠶⢟⣛⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡃⠀⠀⠀⠀⣸⡿⢈⡙⠿⣷⣿⣿⡷⢸⣿⣿⡧⣼⣿⣿⡆⣾⣿⣿⣷⣶⣤⡀⠂⠄⠠⢀⠐⠀⢂⠈⠁⠠⠀⠄⠙⣿⣦⣀⠀⠀⣼⣟⠈⡁⣶⣇⠠⠁⠆⡈⢿⣧⣼⡿⠂⣉⠰⢀⣾⣿⠃⠰⢀⠜⠠⠈⠔⡈⠡⢸⣿⠠⠡⡈⠄⠃⠌⠡⢐⠠⣁⣬⣶⣷⠿⠿⠿⠷⣾⣿⣋⣿⣇⠀⠀⣴⣾⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣾⣛⣋⣭⣵⠶⢟⣛⣩⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⣾⡟⠁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡅⠀⠀⠀⢀⣿⠇⠤⠐⢠⠈⡙⠿⣷⣮⡛⢛⣥⣼⡛⢛⣥⣜⠛⣛⣤⣝⠻⣿⣆⠈⠄⡀⠂⡁⢀⠈⡀⢁⠈⡀⠂⠈⠻⣿⣷⣶⣿⡿⣷⣶⣿⠏⠠⠁⡌⢐⠈⣉⠉⠤⢁⠄⢢⣽⡿⠁⠌⡐⡈⠄⠡⠘⢠⢈⡁⢺⣿⢀⠡⢐⡈⢡⠊⠁⣦⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣟⡻⢿⣿⣷⡶⢟⣛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠆⠀⠀⠀⢸⣿⠂⡅⠌⣀⠒⡀⢂⠄⠛⢿⣿⣿⣿⡇⢿⣿⣿⠇⣿⣿⣿⠂⣿⣿⣦⣤⣄⡁⠐⡀⠂⢀⠂⣠⣄⣄⠁⠄⠈⢿⣿⣿⡅⠠⢄⠠⠌⡐⠡⠐⣈⠐⠠⠌⠒⡈⢰⣾⡿⠁⠌⡐⢀⠒⡈⠐⣁⠢⢀⠂⣹⣿⠀⣂⠡⠐⢂⠘⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡈⢿⣷⣄⠻⣿⣿⣿⠿⠁⠀⠀⠀⠀⢀⣰⣿⠿⡼⣙⢧⡏⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⡇⠀⠀⠀⢸⣿⣤⣴⣀⠄⢢⠐⡈⠄⠃⠌⠹⣿⣷⣾⣶⡍⣱⣶⣮⡉⣵⣶⣯⢛⣽⣿⣿⢿⣦⠀⠁⠂⢰⣿⣿⣿⣷⠈⠠⠀⢿⣿⣧⠐⢂⡐⠤⢀⠡⠌⠠⠈⠔⠨⠄⡑⣼⣿⠁⠌⡐⠠⢁⠂⠤⠁⢄⠒⠠⢁⣿⡇⠢⢀⠆⡉⠄⢺⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⢻⣿⣷⣤⣌⣀⠀⠀⠀⢀⣀⣴⣾⡿⣏⢟⣱⣏⣮⠵⡮⣝⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡿⠛⢿⣤
⣷⣶⣤⣀⣼⡿⣩⠛⣿⡷⢀⠂⠔⡈⢡⠘⢠⠈⣿⣿⣿⣃⣿⣿⣿⡋⢿⣿⠿⡉⢿⣿⠿⠘⣿⣷⣶⣶⣮⣿⠿⠟⠃⠠⢁⠈⠸⣿⣿⣦⠂⡐⡀⠆⡐⢈⠡⠡⠌⠰⠈⠄⣿⣧⢈⠐⠠⢁⠂⠌⠠⠉⡄⠌⠡⣸⣿⠡⡁⢊⠐⡠⠁⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠸⣿⣏⣟⡻⢿⢿⡿⣿⠿⣟⢯⡳⣝⢮⣿⣿⣿⣿⣿⣷⢭⢺⣿⣿⣿⣿⣯⣾⣿⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠈⠻⣿⣿⣿⣯⠀⠀⠀⣉
⣿⣿⣿⣿⣿⣇⡋⠖⣿⡷⠈⠰⢀⠡⠊⡐⠈⡄⠙⠿⠿⠿⠿⠿⠿⢷⣾⣭⣴⣷⣮⢉⣶⣶⣿⢻⣿⣿⣟⢿⣦⡀⠂⡀⠈⠐⡀⠙⢻⣿⣦⣁⠃⢄⣡⣬⣤⣦⡐⠠⠒⠠⠹⣿⣌⠐⠂⢌⡐⠄⠂⠤⢁⡐⢠⣿⡏⠠⠡⠘⢠⠁⠂⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠋⠀⢠⣿⡯⣝⡳⢞⡼⣣⡝⢶⡹⢎⡷⣹⢾⣿⣿⣿⣿⣿⣿⡜⣮⣿⣿⣿⣿⡍⢿⣿⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⣠⣿⣿⣿⣿⠀⢠⣴⡿
⣿⣿⣿⣿⣿⣄⠛⣼⣿⠇⡈⠁⠆⠠⢁⠰⠁⡄⢃⡐⢂⠰⢀⠂⠔⢂⠈⢻⣿⣿⠟⣘⠿⣿⠟⡘⢿⡿⢏⡸⣿⣿⣾⠿⣿⣷⣄⣐⣼⣿⡿⣿⣾⡿⠛⢋⠙⢋⠁⡘⠠⠃⡄⠙⠿⣿⣶⣤⣐⡈⢁⠂⣄⣴⣿⠟⡀⢃⠡⠉⠄⠌⠡⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢳⡭⣝⣫⢖⠧⣝⣣⡝⣏⢶⡹⣎⢿⣿⣿⣿⡿⣟⡼⣱⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣻⣵⣿⣿⠏⠀⠹⣿⣿
⡟⠛⢋⠁⠻⢿⣷⣿⠟⠀⠄⡑⠨⠐⣀⠢⠁⡔⠠⢐⠠⢂⠂⠌⠒⡈⣐⣼⣿⢰⣿⣿⣷⢴⣿⣿⣧⣴⣿⣿⡦⣽⣿⣿⡆⣾⣿⣿⣿⡿⢿⣿⠃⠤⢁⠂⠌⣀⠂⣁⠂⢡⠐⡁⢢⠈⡉⠛⠻⠿⠿⠿⠟⢋⡁⠂⠤⢁⢂⢉⠰⢈⠁⠆⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⢷⡹⣎⡵⣎⠿⣜⢶⣙⢮⣣⠟⣜⢧⣫⢞⣥⢻⣜⢺⣵⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣦⣿⣿⣿⡿⠋⠀⣀⡀⠀⢉
⡇⢈⠰⢈⠐⠄⡉⠄⢂⠁⢂⠤⠑⡈⠄⣂⠱⢀⠃⡄⢂⠡⡈⠄⢿⣿⣿⡛⣫⣬⡛⠟⣫⣬⡛⢟⣣⣌⣻⣿⣡⣙⠿⢛⣡⣽⣿⠟⠁⠀⠀⣿⣧⡐⠂⠌⡐⢀⠢⠀⠜⡀⠂⡔⢀⠂⢡⠘⡀⠆⡐⠠⠌⠠⠠⠑⢠⠊⡀⠂⠔⡈⠌⠰⢀⠛⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣟⡳⢎⡳⣇⢷⣺⣼⣷⣾⣮⡝⡶⣣⢟⡼⣣⢗⡾⣸⡓⣮⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⠿⣿⣶⠿⠿⣿⡿⠀⠙
⡇⠈⠆⡐⠨⠐⠠⠌⠠⡈⠄⢂⠡⡐⠌⡀⠆⡁⠎⡐⢈⡐⠄⠊⠄⡉⠻⣿⣿⣿⡿⢸⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⠀⠀⠀⠀⠈⠛⢿⣷⣦⣴⣤⣦⣥⣂⣌⣁⠐⡈⠌⢠⠂⠔⠠⠄⠡⡈⠔⠡⠈⠄⠂⠄⡁⢊⠐⡈⠡⢂⠢⢀⠙⠻⢿⣶⣶⣶⣶⣿⠿⣟⢯⡳⡼⢭⣏⠷⣭⣾⡿⠋⠉⠉⠛⣿⣷⡹⢮⡵⣋⠾⣜⣥⣿⣿⠿⠿⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⡧⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⡓⠴⣈⢏⠲⣿⣧⣶⡶
⡇⢉⠔⠈⡅⠨⠐⢌⠰⢀⠃⡌⡐⠰⢈⠤⠑⡠⠃⠤⢁⡐⠨⠌⡐⠄⢡⠈⢿⣿⣶⣶⣏⢩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣭⣝⣛⠛⠻⠿⣷⣮⣄⡈⠄⠃⠌⠡⢐⠈⠤⠑⡈⠌⡐⡁⢂⠌⠠⡑⠠⢂⡁⠎⡐⠰⣿⣟⡼⢳⢎⣿⣼⣷⣷⣭⢳⣎⢿⡰⣿⡇⠀⠀⠀⠀⠈⢿⣯⢳⣣⢯⣿⡿⠛⠉⢀⠀⠀⡀⡄⢤⠠⠄⠤⣀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡇⠙⠿⠛⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣼⣿⢛⠲⣉⠖⣩⢎⡱⢛⣿⣦⡀
⡇⠌⡂⢡⠂⠡⠘⡀⠆⡁⠆⡐⡈⠔⡁⠂⠅⡂⠅⠢⢁⠤⢁⠒⣀⠊⠄⡂⠄⢻⣿⡿⠟⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣷⣦⡄⠀⢻⣏⠙⠛⢿⣶⣤⣠⣿⣿⣿⣿⣶⣬⣥⣂⣌⠐⠡⠐⠂⠔⡐⠠⠘⢠⠐⡁⢂⠐⡐⢠⠁⣿⣿⡜⣏⣾⣿⣿⣿⣿⣿⣷⣚⢮⣓⢿⣷⡄⠀⠀⠀⠀⢸⣿⣧⣿⡟⠃⠀⠀⠀⠂⠃⠀⠀⠀⠀⠉⠉⠑⠂⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⣿⣿⣤⣋⣕⠪⡜⣡⠎⣴⣣⣼⣿⡷
⡇⠰⢁⠂⡅⢂⠑⡈⠤⢁⠂⡡⠐⡐⠈⠌⡐⠄⢊⢁⠢⠐⢂⡐⠠⠌⡐⠌⠰⠀⢻⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⠛⠿⣶⣶⣬⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣷⣾⣤⣆⣈⡐⢁⠂⠔⠠⣁⠂⠌⡀⠆⡘⢿⣿⣜⣻⣿⣿⣿⣿⣿⡗⣮⢳⡭⡞⡽⣿⣦⣤⣀⣴⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠉⠙⠛⢿⣷⣡⢣⣾⣿⣟⡉⠉⠀
⡇⠘⡄⠘⡄⠂⠌⡐⠰⠈⢄⢁⠂⠡⠘⢠⠐⡈⠄⠂⠤⠉⠤⠠⢁⠂⡐⠌⠡⠘⠠⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣥⣤⣈⡐⢁⠂⠔⡈⠿⣿⣼⣛⠿⡿⡟⢧⡻⣜⠳⡞⣭⣳⣭⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣶⣤⡀⠀⠀⠀⠀⠀⢻⣷⣿⠟⠈⠻⣷⣤⡾
⡇⢡⠂⢡⠂⡁⢂⡐⡁⠊⠄⢂⣬⣴⣥⡂⠰⠀⠌⣁⠂⡉⣄⣁⠊⡐⣀⠊⢡⠘⣠⣾⠟⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⢠⣾⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣭⣿⣿⣿⣷⣿⣧⣷⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣻⣿⡟⠿⠛⠻⣿⡉⠀⠀⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣿⣏⠀
⡇⠰⡈⠄⢃⡐⠠⠐⡈⡐⢨⣿⡟⠉⠿⠟⠠⢁⠒⡀⠆⢸⣿⣿⠀⠔⠠⠘⡀⣲⣿⠋⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⢿⡿⠟⣼⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣶⡹⢞⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⣀⠀⣠⣿⣿⣟⡷⣿⡇⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢿⣧
⡇⢡⠐⠨⠄⡠⢁⣶⣿⠿⢿⣿⣧⣐⡠⢈⠐⡀⠂⠌⡐⠂⠌⢠⠈⠌⡁⠆⢱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⡆⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣦⣝⣻⣿⣿⠿⣍⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⢿⣟⡿⣿⠿⣿⣷⣿⡿⣏⣯⣽⣿⣇⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣤⡀⣹
⡇⢂⠡⠘⢠⠐⡘⣿⣧⡔⠀⣿⣿⠿⠃⡀⠆⡐⢁⠢⠐⡉⡐⠂⢌⡐⠐⡈⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠛⠟⠛⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⡿⣜⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡻⣽⢞⣯⣞⡽⣞⣻⡵⣫⣏⡷⡽⣾⠛⣿⣿⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣍⣿⣿⣏⣿
⡇⠄⢃⠌⡀⠒⠠⡈⠁⠄⢂⠉⠄⢂⠐⣀⠒⡀⠆⢂⢁⠒⠠⠑⢠⠠⢁⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⢶⣱⣾⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣳⡗⣯⣗⡻⣶⣹⠾⣝⣧⢟⣷⣹⡞⣽⡟⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠙⠛⠻⣿
⡇⠨⢀⠂⠄⡑⠠⠄⡉⠰⢈⠐⠨⠄⠒⡀⠆⠰⠈⡄⠂⠌⢂⠉⣄⣴⣶⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⣣⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣰⣿⣿⣿⢿⣿⣷⣏⣾⢳⣝⣻⠶⣏⡿⣽⣾⣿⣾⣧⣿⣽⠃⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣸⡟
⡇⠐⡈⣴⣶⣤⠁⠂⠄⠃⠄⢊⠡⢈⠤⠁⡌⢁⠒⢠⣉⣴⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣦⠀⠀⠐⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢟⡰⡑⢎⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⢿⣹⣾⣿⣟⣾⣼⣿⣿⣯⢿⣹⣽⣿⢏⣿⣿⢿⣿⠏⢀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣧
⡇⠠⢁⠻⣿⠏⠐⠰⢀⠒⠠⠌⠂⠌⠄⢂⠡⢈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢌⢣⠓⡜⡰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣏⣿⣿⣾⣿⣻⣼⢻⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢿⡏
⡇⠐⣂⠐⡀⢂⢁⠢⠁⡌⠂⢌⠁⡊⠌⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡄⠀⠀⠀⠻⣿⣿⠃⠀⠀⠸⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣾⣵⣯⣿⣿⣧⣯⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠘⢿
⡇⢁⠂⠌⡐⠂⠄⣂⠡⡐⠉⡄⢈⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣟⡻⠿⠿⠟⢛⣉⣉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⡇⠐⠌⢂⠡⠌⡐⡀⢂⠤⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⢿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣧⡻⣯⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠫⡜⠦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠉⠙⢿⣦⠀⣴⡿⠛⠻⣷⠙⢿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛
⣷⣬⣌⠐⡠⠡⠐⣈⣄⣰⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢿⡝⢷⡜⣷⡹⣧⡻⣧⠻⣏⢿⡝⢿⡟⣿⣟⠋⠻⣿⣿⣷⣎⡱⣌⣓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⠀⣀⣨⣿⡾⠟⠀⠀⢘⣿⡀⠀⡙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣫⣤⣶
⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣛⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⠿⣷⡿⣷⡹⣧⢻⣮⢻⣎⢿⣷⡀⠈⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣿⣿⢿⣻⣿⣿⣿⠿⠿⠛⠛⠛⠛⠙⠋⠛⢛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⠇⠀⠀⠀⠀⣸⡿⠻⠟⠟⠻⣷⣦⣤⣤⣤⣦⣦⣴⣤⣤⣤⣀⣀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣽⣶⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣼⣿⡜⣷⡝⣧⡹⣷⡻⣦⢻⣿⣄⢀⣈⣿⡟⣱⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣤⣿⣿⣿⡍⣿⣿⣷⡼⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣀⣀⠀⠀⠀⠙⠻⣿⡄⠀⢈⣿⣯⠻⣯⣿⡏⢉⣽⣿⣿⣿⣿⣆⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⣧⢻⣎⢿⡜⢿⡜⣷⡹⣷⣿⡿⠿⣟⢫⡑⢦⠙⡬⣉⡛⡝⢻⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣴⡿⢁⣠⣶⣾⠿⢋⡹⠿⠟⣁⣙⠟⢫⣤⣝⠛⣭⣦⣝⠋⣵⣾⣝⢻⣿⣿⣿⣿⣿⣥
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⣶⡀⠀⢠⣹⣿⣆⣼⣿⡼⣷⡹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⣷⡹⣧⡻⣧⢻⣮⢿⣎⢿⣜⣿⣿⣷⣌⠲⣉⠦⡙⠴⡱⣘⣼⣿⣿⣿⡿⢋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⠀⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⣾⣿⣶⣿⣿⣿⣦⢼⣿⣿⡧⣿⣿⣿⡇⣿⣿⣿⠖⢿⣿⡿⠘⢿⣿⠿⡘⠿⠿⣿⣿⠿⢻
⣿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣽⣾⣿⣿⣿⣆⠀⠙⠿⠿⠇⠀⠈⠉⠙⣿⣿⣏⢿⣌⢿⡜⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⠀⢀⣄⣀⣼⣿⣿⣿⣿⣿⣿⢻⣞⢿⡜⣷⡽⣷⡹⣷⡻⣮⢻⣎⢿⣟⣿⡖⣡⢎⡱⢣⠱⣸⣿⣿⣿⡟⢀⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⢀⣴⣿⠻⠿⢋⣈⡛⠛⣣⣬⡛⢛⣥⣬⡍⣩⣶⣾⡍⣱⣾⣷⡌⣼⣿⣷⣤⣾⣿⣿⣰⣿⣿⡷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠸⣿⣹⣷⣿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣧⣻⣮⢻⣎⢿⡜⢷⣝⣷⡹⣷⡻⣧⢻⣿⡗⣌⣶⣿⣷⣷⣌⣿⣿⣿⠁⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠃⠀⠀⢀⣠⣶⡿⣿⣿⣿⠄⣿⣿⣿⠸⣿⣿⡿⠸⣿⣿⡟⠹⣿⡿⢏⡹⢿⠿⣋⣹⠿⢟⣡⣝⠻⣋⣤⣝⠋⣥⣶
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⢻⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣝⣷⡙⣷⣹⣿⣿⣯⣻⣮⣿⣿⢿⣜⣷⡙⣷⣿⣿⠿⣯⢻⣟⢿⣿⣿⣿⣿⡄⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⣤⣤⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⡟⠁⠀⣀⣴⣾⡿⢛⣥⣍⡛⣩⣤⣭⡉⣵⣶⣮⣉⣶⣷⣦⢠⣾⣿⣦⢸⣿⣿⣧⢸⣿⣿⡇⢾⣿⣿⡇⢿⣿⣿⠇⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣯⣿⡷⠀⣾⣿⡛⣷⡻⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⠿⡿⠿⠟⠋⡈⠛⢛⠛⠙⢿⣮⣿⣾⣿⣿⣷⡝⣷⡹⣿⣿⣦⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⢀⣨⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⠿⠛⣻⣿⡗⢿⣿⣿⠗⢿⣿⣿⠋⠿⣿⠿⢉⠿⠿⢟⣈⡻⠿⣋⣬⡛⠛⣥⣬⡟⢋⣵⣮⣍⣩⣶⣾⡍⣴⣾⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⢸⣿⢿⡜⣷⡙⣷⡹⣿⡿⠟⠛⠛⠛⠛⠉⠉⠁⢸⣿⠿⠋⢀⠐⠠⢈⠐⢠⣾⣿⣿⣧⡀⢈⠉⡉⠀⢘⣿⣿⣌⢿⣼⣿⡜⣷⣹⣾⣿⠿⢿⣿⣦⣤⣤⣼⡿⠋⠉⢻⣷⣾⣿⣿⣿⣿⣶⣿⠋⠀⠈⣽⣿⠟⠛⠉⠉⠀⠀⠀⢠⣿⢋⣴⣶⣍⢡⣶⣶⡆⣴⣿⣿⡄⣾⣿⣿⡆⣿⣿⣿⠶⣿⣿⣿⠽⣿⣿⡿⠻⣿⣿⠏⠹⣿⡿⢇⡹⠿⠿⣃
⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⡿⣿⣻⣽⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣿⡿⣮⢻⣎⢿⣜⢿⣿⣧⣀⠀⠀⠀⣀⣀⣤⣶⡿⠋⠠⠐⡀⠈⠄⠂⠠⠈⠻⣿⡿⠟⠀⠄⠂⣠⣴⣿⡿⣧⠻⣎⢿⣿⣿⣿⣿⣟⠃⠀⠀⠀⠉⣽⡟⢹⣷⣀⣀⣤⡋⠉⠛⣿⡏⠀⠀⠀⢀⣤⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢿⡿⠟⡘⠿⠿⣃⣙⠻⠟⣡⣝⡛⢫⣥⣭⡛⣩⣶⣭⡉⣵⣶⣮⣉⣶⣿⣦⢰⣿⣿⣧⢰⣿⣿⣧⢼⣿
⠇⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣷⡹⣷⡻⣦⢻⣮⢿⣝⢿⣿⠿⠿⠛⠛⠉⢁⠀⠄⠡⠐⠀⡁⠄⢈⠠⠐⠀⡀⠠⠐⢈⢀⣾⣿⢿⣍⣷⡝⣷⡹⣧⣿⣧⢻⣎⢿⣷⡀⠀⠀⠠⣿⠃⠀⠙⠛⢻⣿⣦⣀⠀⠙⣿⣶⣴⣾⠿⠋⠁⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⣿⣿⣷⢰⣿⣿⣷⣸⣿⣿⡷⢺⣿⣿⡇⢿⣿⣿⠇⢿⣿⡿⠃⢿⣿⠿⣉⡻⠿⢟⣈⡻⠟⣫⣬⡛⠛⣥⣤⡙
⡆⠀⠀⢸⣿⠙⠻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⣿⣧⡻⣧⢻⣮⢻⣎⢿⣾⡿⠀⠀⠄⡀⠂⠈⠄⠠⠀⠄⠂⠁⡐⠈⠠⠐⠠⠁⠂⠐⣨⣼⣿⢿⡜⢿⡝⣷⡹⣷⡻⣿⣿⣮⢻⣎⣿⡇⠀⠀⠠⣿⡆⠀⠀⠀⢸⡿⠛⠿⣶⣶⡿⠛⠉⠉⠀⠀⢰⣿⢯⡹⣝⡻⢿⣷⣄⠀⠀⠹⣿⣿⠘⠻⢿⣿⣏⡻⠟⣣⣬⡛⢛⣥⣬⡛⢩⣴⣮⡍⣱⣶⣾⡍⣴⣿⣷⣄⣾⣿⣷⣰⣿⣿⣷⢰⣿⣿⡗
⠆⠀⢠⣿⠃⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⢿⣾⢷⡽⣷⡹⣷⣿⡿⠟⢁⣰⣌⣀⠠⠁⢂⠈⢀⠁⠂⠡⠐⠀⣸⣿⠀⡁⣈⣴⣿⣿⣯⡻⣧⢻⣮⢿⣞⢿⣜⣷⣽⣿⡹⣧⣻⣿⠃⠀⠀⠀⢻⣧⡀⠀⠀⢸⣟⠀⠀⣀⣴⡄⠀⠀⠀⠀⢀⣿⡿⣣⣿⣶⣿⣷⣚⣿⣷⣄⣀⣸⣿⣿⣿⣿⠛⢿⣿⡰⣿⣿⣿⠸⣿⣿⡿⠹⣿⣿⠟⡹⢿⡿⣃⡻⠿⢟⣁⣛⠿⣛⣤⣝⠛⣫⣤⣝⣫⣿
⡃⠀⢺⣯⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⠿⣛⢋⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠘⣿⣎⢿⣜⣿⣝⣿⣷⠀⣾⣿⣿⣿⡆⠐⡀⠐⠠⠰⣶⣦⣴⣾⡿⢃⣴⣾⠟⠋⠉⠙⠛⠿⢿⣷⣿⣧⣿⣮⣿⣿⣿⢿⣿⣿⣿⣷⠾⠿⠿⠿⣶⣿⣷⣄⠀⢸⣿⡾⠿⠛⠉⠀⠀⠀⠀⣠⣾⣿⠳⣽⣿⣿⣿⣿⣿⣒⢿⣿⡿⢻⣿⣇⢸⣿⢀⠈⠻⢿⣾⣿⣿⣶⣮⢡⣾⣿⣦⢰⣿⣿⣧⢸⣿⣿⣇⣾⣿⣿⡇⣿⣿⣿⠇⣿⣿⣿⣿⣿
⡇⠀⢸⣿⣶⣤⡀⠀⢀⣤⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡛⢥⠓⣌⠣⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣿⣿⡿⠛⠛⣿⡇⢀⠘⠻⠿⠛⠀⡁⠀⠌⠐⠀⠈⢉⣉⣥⣶⡿⣿⣿⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠉⠉⣻⣿⠛⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣁⡀⠀⠀⠀⠀⣀⣤⣾⣿⢻⡜⣻⡜⣿⣿⣿⢟⣧⣛⢮⣿⣟⢧⣻⣿⣿⡟⠀⠌⢠⣶⣾⡄⠘⢿⣿⣬⣿⣿⣏⣈⡿⠛⣣⣬⣛⢛⣥⣬⡛⣩⣶⣮⣍⣡⣾⣿⣿⣿⣿⣿
⣇⣤⣸⡿⢿⣿⣿⣦⡀⠻⣷⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣆⠫⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣿⠇⡄⠈⠐⠀⠀⠁⣀⢡⣠⣤⣾⣿⠿⠿⣿⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⢿⣷⣼⡿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡦⠙⣿⣿⢿⡿⣿⢿⡿⢿⡻⣝⠮⢧⣛⣥⢻⡔⣮⢖⣫⠶⣹⢎⣿⣟⢮⡵⣿⡟⠀⠌⡀⠘⣿⣿⣿⠀⠂⢉⠉⠉⢻⣿⣿⣿⣼⣿⣿⡿⠸⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠁⠀⢻⣿⣿⣷⣾⡟⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⢿⡟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣦⣄⡈⣹⡿⠀⠀⠀⠀⠀⠀⠶⡿⠟⠛⠉⣻⡇⠀⢸⣿⣎⢷⡹⢮⣹⢣⡝⣮⢛⡧⡽⢬⢧⣿⣴⣏⡞⣭⢧⣻⣿⣿⣾⣿⣿⡇⠈⠄⠐⠀⠉⠛⠁⡀⠡⠀⠌⠐⡀⠉⠛⠛⠋⠉⣿⣿⣷⣦⢡⣾⣿⣶⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣏⣛⠁⠀⢾⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⠿⠛⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣍⢷⡜⣷⡙⣧⡹⣧⠻⣮⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⣏⢾⡱⣏⢶⣋⢾⡱⣏⢾⡱⣻⣿⠋⠉⠻⣿⣾⣒⣿⡟⢉⣴⣿⣿⣧⣀⣄⣲⣿⠇⢀⠠⠀⡐⠠⠈⡐⠀⠌⠠⠁⣂⢸⣿⢋⠻⣿⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⣹⣿⣿
⣿⣿⣿⣾⣷⣯⣙⠻⡿⠃⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠈⠉⢿⣧⠀⠀⢀⣤⣀⣀⡀⠀⢀⣾⡿⣧⣻⣮⢿⣞⢿⣜⣷⣽⣿⣿⢿⣹⢮⣳⡝⣾⢻⣿⣶⣄⠀⢀⣀⣠⣶⡿⢿⣷⣄⠀⠀⠀⠀⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇⠀⢨⣿⣏⢞⡱⣎⠗⣮⢣⠟⡼⣣⣝⣿⡏⠀⠀⠀⢸⣿⣿⡟⠀⠘⢿⣿⣿⢻⣿⣛⣛⡁⠀⠀⡀⠐⠀⠀⠡⠀⠈⠀⠂⣸⣿⣿⣿⡉⣇⠲⣹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢄⠀⠒⣂⡀⠐⠢⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⣿⣿⣷⣿⣿⣶⣶⣢⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡒⢺⣿⡿⠙⣾⠋⠩⣐⢻⡧⠄⠀⠀⠐⢿⢻⡿⣣⣾⡟⢷⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢺⡟⠀⠀⠙⢯⠉⠉⠁⠃⠀⠀⠀⠀⢰⠀⢰⢻⣿⣿⡘⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠿⠿⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⡄⢰⡿⣟⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠔⣰⣁⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢛⢭⠍⠛⠒⠀⠀⠀⠀⢀⣴⠟⢁⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⠋⠀⠀⠀⣀⢤⠖⠋⠑⡾⠟⠙⠧⡹⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣭⣥⣤⣤⣤⣤⣤⣤⠐⠉⠑⣄⠀⠀⣧⠞⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⡟⠉⠁⠀⠀⠀⣈⠦⠞⠁⢠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⣿⡇⠀⠀⡀⠔⠈⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠁⣀⣿⣿⣿⠉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣏⣴⣿⣿⣿⣿⡆⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⠿⠛⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⡿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠀
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⣿⣿⣿⠿⠛⠉⠀⠀⢠⠏⠱⡉⠚⠀⢠⠙⢲⣠⣿⣿⣿⣿⣿
⣟⣉⣥⣤⣤⣶⣶⣶⢏⣠⠤⣏⠣⣀⠃⢀⠞⠹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⢢⠘⠒⢅⡠⢼⣿⣿⣿⣿⣿
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artist palette
🎨 The artist palette emoji is a vibrant and colorful symbol of art and creativity. It represents the tools that artists use to mix and create beautiful works of art. Whether you’re a professional painter or just enjoy dabbling in art as a hobby, this emoji is a perfect way to express your love for all things creative. So grab your brushes and let your imagination run wild!
paintbrush
🖌️ The paintbrush emoji is a versatile tool that represents the art of painting and artistic expression. Whether you’re a professional artist or just enjoy painting as a hobby, this emoji is a perfect way to show off your love for the visual arts. So grab your paintbrush and let your creativity flow!
framed picture
🖼️ The framed picture emoji is a classic symbol of traditional art and gallery exhibits. It represents the beauty and elegance of framed artwork, whether it’s a painting, a photograph, or a print. So whether you’re a fan of Renaissance masterpieces or contemporary art, this emoji is a perfect way to show off your appreciation for the visual arts. So step into the gallery and let the framed picture emoji transport you to a world of beauty and creativity.
performing arts
🎭 The performing arts emoji is a symbol of the world of theater and performing arts. It represents the magic and excitement of live performances, whether it’s a play, a musical, or a dance recital. So whether you’re a seasoned actor or just enjoy watching performances, this emoji is a perfect way to show off your love for the stage. So grab your tickets and get ready for a night of drama, laughter, and applause!
musical note
🎵 The musical note emoji is a symbol of the universal language of music. It represents the joy and beauty of melodies, whether it’s a catchy pop song or a classical symphony. So whether you’re a musician or just enjoy listening to music, this emoji is a perfect way to show off your love for the musical arts. So grab your headphones and let the musical note emoji transport you to a world of rhythm and harmony.
musical notes
🎶 The musical notes emoji is a harmonious symbol of the art of writing and composing music. Whether you’re a talented musician or simply appreciate the beauty of melodies, this emoji adds a touch of rhythm and melody to your conversations. So, let the music play and let the emoji sing!
clapper board
🎬 Lights, camera, action! The clapper board emoji is a classic symbol of the art of filmmaking and the magic of cinema. From Hollywood blockbusters to indie films, this emoji captures the excitement and creativity of the movie-making process. So, whether you’re a film buff or just love a good movie night, the clapper board emoji is a must-have for any cinephile.
camera
📷 Say cheese! The camera emoji is a snapshot of the art of photography and the joy of capturing artistic moments. Whether you’re a professional photographer or just love taking selfies, this emoji adds a touch of creativity and nostalgia to your conversations. So, strike a pose and let the camera emoji capture your best side!
books
📚 The books emoji is an open invitation to the world of literature and the art of storytelling. From classic novels to modern bestsellers, this emoji represents the joy of getting lost in a good book and the power of words to transport us to different worlds. So, whether you’re a bookworm or just love a good story, the books emoji is a must-have for any lover of literature.
fountain pen
🖋️ The fountain pen emoji is a sophisticated symbol of the art of writing and the beauty of the written word. Whether you’re a poet, a novelist, or simply appreciate the elegance of calligraphy, this emoji adds a touch of class and creativity to your conversations. So, grab your pen and let your words flow like ink on paper!
memo
📝 The memo emoji is a perfect representation of the art of communication and note-taking. Whether you’re jotting down important information or leaving a reminder for yourself, this emoji adds a touch of professionalism and organization to your messages. So, grab your pen and paper and let the memo emoji help you express yourself in style.
crayon
🖍️ The crayon emoji is a nostalgic symbol of childhood art and coloring. From scribbling outside the lines to creating vibrant masterpieces, this emoji captures the joy and creativity of artistic expression. So, whether you’re reminiscing about your own childhood or embracing your inner child, the crayon emoji is a colorful addition to your messages.
movie camera
🎥 The movie camera emoji is a classic symbol of filmmaking and cinematography. Whether you’re a film buff or just love to capture life’s moments, this emoji adds a touch of Hollywood glamour to your messages. So, grab your popcorn and get ready for a cinematic experience with the movie camera emoji.
microphone
🎤 The microphone emoji is a powerful symbol of the performing arts, particularly singing or public speaking. Whether you’re belting out your favorite song or delivering a passionate speech, this emoji adds a touch of star power to your messages. So, grab the mic and let your voice be heard with the microphone emoji.
headphone
🎧 The headphone emoji is a stylish symbol of audio technology and the art of sound. Whether you’re jamming to your favorite tunes or immersing yourself in a podcast, this emoji adds a touch of musicality to your messages. So, put on your headphones and let the music take you on a sonic journey with the headphone emoji.
guitar
🎸 The guitar emoji is a rockin’ symbol of the art of playing instruments and the power of music. Whether you’re strumming some chords or shredding an epic solo, this emoji captures the passion and creativity that goes into making music. So, whether you’re a seasoned musician or just love to jam out, the guitar emoji is a must-have for any music lover.
musical keyboard
🎹 The musical keyboard emoji is a harmonious symbol of music composition and the art of playing the piano. Whether you’re composing a beautiful melody or tickling the ivories, this emoji captures the elegance and skill required to create music. So, whether you’re a classical pianist or just love to tinker with the keys, the musical keyboard emoji is a must-have for any music enthusiast.
camera with flash
📸 The camera with flash emoji is a snapshot of the art of photography and the magic of capturing moments. Whether you’re a professional photographer or just love to snap pics with your friends, this emoji captures the excitement and creativity that goes into taking photos. So, whether you’re capturing a stunning landscape or a silly selfie, the camera with flash emoji is a must-have for any photography enthusiast.
musical score
🎼 The musical score emoji is a melodic symbol of the art of reading and playing sheet music. Whether you’re a classically trained musician or just love to sing along to your favorite songs, this emoji captures the beauty and complexity of musical notation. So, whether you’re composing a symphony or just humming a tune, the musical score emoji is a must-have for any music lover.
video camera
📹 The video camera emoji is a cinematic symbol of the art of videography and the magic of capturing moving images. Whether you’re a filmmaker or just love to document your adventures, this emoji captures the creativity and storytelling that goes into making videos. So, whether you’re shooting a short film or just capturing a funny moment, the video camera emoji is a must-have for any aspiring filmmaker. Lights, camera, action!
open book
📖 The open book emoji is a delightful symbol of the joy of reading and the art of storytelling. Whether you’re diving into a thrilling novel or exploring the pages of a captivating non-fiction book, this emoji captures the magic and wonder of the written word. So, grab a cup of tea, find a cozy spot, and let the open book emoji transport you to new worlds and adventures.
black nib
✒️ The black nib emoji is a stylish representation of the art of calligraphy and the beauty of handwriting. Whether you’re creating elegant invitations, writing heartfelt letters, or simply doodling in your notebook, this emoji adds a touch of sophistication and artistry to your messages. So, grab your favorite pen and let the black nib emoji inspire your creative endeavors.
violin
🎻 The violin emoji is a graceful depiction of the classical music and the enchanting world of musical instruments. From the soaring melodies of Mozart to the passionate performances of Beethoven, this emoji captures the elegance and emotion of the violin. So, whether you’re a seasoned musician or simply appreciate the beauty of music, let the violin emoji serenade your conversations with its harmonious charm.
pen
🖊️ The pen emoji is a versatile symbol of the art of writing and the power of words. Whether you’re jotting down your thoughts, signing important documents, or creating beautiful calligraphy, this emoji embodies the creativity and expression that comes with wielding a pen. So, grab your favorite pen and let the words flow as you embrace the art of writing with the pen emoji.
moai
🗿 The moai emoji is a fascinating representation of ancient art and sculptures. Inspired by the famous Easter Island statues, this emoji captures the mystery and wonder of these ancient works of art. Whether you’re a history buff or simply appreciate the beauty of ancient civilizations, the moai emoji is a captivating symbol that will transport you to distant lands and times. So, let the moai emoji be your guide as you explore the rich history and artistry of the world.
hammer and wrench
🛠️ The hammer and wrench emoji is a versatile representation of the various tools used by artists to bring their creations to life. From paintbrushes and chisels to sculpting tools and palette knives, this emoji encompasses the wide range of instruments that artists use to shape and mold their masterpieces. So, whether you’re a painter, sculptor, or any type of creative genius, the hammer and wrench emoji is a must-have for expressing your artistic side.
notebook with decorative cover
📔 The notebook with decorative cover emoji is the perfect symbol for sketching and jotting down ideas. Whether you’re an aspiring artist or a seasoned pro, this emoji represents the creative process and the importance of capturing inspiration as it strikes. So, grab your favorite notebook and let your imagination run wild as you bring your artistic visions to life.
desktop computer
🖥️ The desktop computer emoji is a modern representation of the world of digital art and design. From graphic design and animation to digital painting and 3D modeling, this emoji encompasses the vast realm of creativity that can be achieved through technology. So, whether you’re a digital artist or simply appreciate the beauty of digital art, the desktop computer emoji is a must-have for expressing your love for this innovative form of artistic expression.
man artist
👨🎨 The man artist emoji is a delightful representation of someone engaged in the act of creating art. Whether he’s painting a masterpiece, sculpting a masterpiece, or expressing his creativity in any other form, this emoji captures the passion and dedication that artists bring to their craft. So, whether you’re a professional artist or simply enjoy dabbling in various artistic endeavors, the man artist emoji is a perfect way to showcase your love for the arts.
pencil
✏️ The pencil emoji is a timeless symbol of drawing and sketching. From quick doodles to detailed illustrations, this emoji represents the foundation of many artistic creations. So, whether you’re an aspiring artist or simply enjoy expressing yourself through drawing, the pencil emoji is a must-have for showcasing your artistic talents. Grab your pencil, let your imagination run wild, and create something amazing!
cityscape at dusk
🌆 The cityscape at dusk emoji captures the beauty and vibrancy of urban art and city landscapes. With its colorful lights and towering buildings, this emoji represents the hustle and bustle of city life. Whether you’re a fan of street art or simply appreciate the stunning views of a city skyline, the cityscape at dusk emoji is a perfect way to express your love for urban art and the energy of city landscapes.
national park
🏞️ The national park emoji is a symbol of the breathtaking landscapes and natural art found in these protected areas. From majestic mountains to serene lakes, national parks offer a glimpse into the beauty and wonder of the natural world. Whether you’re an avid hiker or simply enjoy the tranquility of nature, the national park emoji is a perfect way to express your love for outdoor adventures and the stunning landscapes that surround us.
writing hand
✍️ The writing hand emoji is a symbol of creative writing and storytelling. Whether you’re a professional writer or simply enjoy expressing yourself through words, this emoji represents the power of language and the art of storytelling. So, grab your pen or keyboard and let your imagination run wild. With the writing hand emoji by your side, you’re ready to create your own masterpiece. Happy writing!