Kirby Sitting Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠤⠤⠴⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⣄⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣾⣠⠎⠀⣸⠁⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⣿⡏⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠷⠻⠟⠀⠀⠸⣿⠏⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⢠⡴⢦⣤⣄⠀⡇⠀⠀⠀⢰⣶⣶⡄⠀⠀⠀⠈⠛⠛⠯⠿⠃⠀⠀⠀⠀⠀⠀⢸⡘⠀⠀ ⢸⣹⢿⣾⣹⢿⣿⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⣀⣶⣆⣀⠀⠀⠀⠀⠀⠀⣿⡀⠀ ⠘⣭⢷⣫⡽⣯⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣻⠽⣶⣫⣟⣷⡄⠀⠀⠀⠀⠘⢖⡀ ⠀⠘⣯⢷⣻⣽⣻⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⣳⣻⢞⣟⣳⡽⣞⣳⢿⡀⠀⠀⠀⠀⠘⣡ ⠀⠀⠈⢯⢷⣞⣷⣻⣿⣄⠀⠀⠀⠀⢠⣿⣳⡽⣳⣟⣾⡳⣿⠽⣯⣟⣧⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠙⢞⣾⣳⢿⣿⣷⢤⠀⠈⢿⣳⣳⢟⣳⡽⣶⣻⣽⡻⣗⣯⠷⡄⠀⠀⠀⠀⡬ ⠀⠀⠀⠀⠀⠀⠱⢏⣿⡿⠁⠀⠉⠶⣸⣷⢏⡿⣷⢿⢷⡿⣶⢿⣹⡎⠁⠈⠳⠶⠶⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣿⣝⡷⣯⠿⣝⣯⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠠⢤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡴⢋⣟⠄⠀⢠⣴⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠐⣀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⣼⢀⣼⠟⠀⠀⣼⡇⠀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⡈⠄⡈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣺⣿⣿⠇⠁⠀⢳⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠐⡈⡐⠠⠀⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣾⣿⣿⡟⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢈⠐⠠⠠⢁⠌⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⣠⠏⢿⡿⠀⠀⠀⠀⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢁⠂⡀⠌⡐⢁⢂⡐⠠⢹⡄⠀⠀⠀ ⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠉⠃⠘⠀⠉⢀⣀⣄⣐⡀⠁⠉⠀⠀⠀⠠⢀⠒⠢⢄⡀⠀⠀⢀⠀⠠⢈⠀⡐⢀⠢⠐⠢⢀⠄⠡⢈⡇⠀⠀⠀ ⢰⣿⢻⣯⣟⡿⣷⣶⣄⡀⢸⡀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠈⠀⠑⠂⠀⠀⠀⠀⠈⡐⢀⠂⠌⡠⢂⢁⠣⠌⠠⠁⡌⡇⠀⠀⠀ ⢸⣏⡿⣶⣏⡿⣷⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣶⣷⣆⡈⠀⠇⡰⠀⠆⠰⢀⠁⠆⡈⣷⠀⠀⠀ ⠸⣯⣟⡷⢯⣟⡷⣯⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡾⣟⣯⢷⡯⢿⡽⣿⣯⡱⢀⠉⠄⡁⠂⠌⡐⢀⠘⢧⡀⠀ ⠀⢹⣾⣽⣻⢾⡽⣯⢿⡽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠨⣠⣿⢿⡽⣽⣫⣞⣯⡽⣯⣟⣷⣻⢿⡄⡁⠂⠄⡁⢂⠐⡀⠂⡘⣧⠀ ⠀⠀⠻⣾⣽⣫⢿⡽⣯⣟⡿⣿⣷⠀⠀⠄⢀⠠⢀⠀⠄⠠⠐⢠⢈⣾⡿⣽⣳⣟⣳⣟⣾⣳⣟⣷⣻⢾⣽⣻⣿⡀⠌⡐⠠⠀⠂⠄⠐⠠⢸⡆ ⠀⠀⠀⠙⣾⡽⣯⣻⣗⣯⣟⣿⣿⣧⡌⠐⡂⠔⡠⠊⡄⢣⠉⢦⣿⠿⣽⣳⣟⣾⣳⣟⡾⣳⣟⡾⣽⣻⣞⣷⣻⡇⡐⠠⢁⠈⠄⠂⢁⠐⣘⣷ ⠀⠀⠀⠀⠈⢻⣷⣻⣞⣳⣟⡾⣿⣿⣷⣅⠘⢢⠁⣇⠸⣄⢫⣿⢯⣟⣷⡻⣾⣵⣻⢾⣽⣳⢯⣟⣷⣻⣞⡷⣯⡇⠰⢁⠂⠌⡐⢀⠂⠠⢐⣿ ⠀⠀⠀⠀⠀⠀⠙⢷⣯⢷⣯⢿⣽⣿⣿⣿⣾⣤⡉⢄⠓⡌⣾⣟⣿⡺⣗⣿⣳⡽⣯⣟⡾⣽⣻⣞⣷⣻⢾⣽⣳⡏⠱⢀⠌⠠⢀⠂⡈⠐⣺⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣞⡿⣞⣿⣿⣿⠏⠀⠻⢦⣌⡐⢻⣟⣶⣻⡽⣞⣷⣻⣗⣯⣟⣷⣻⣞⡷⣯⣟⣾⡟⠶⣁⡢⢈⠁⢂⠐⣀⣓⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⠼⠛⠀⠀⠀⠀⠘⠻⠿⣿⡼⣧⢿⣻⡼⣧⢿⣜⡿⣼⢧⣟⡿⣧⣟⡿⠀⠀⠻⣧⣄⣸⣄⣘⡿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡽⣯⢷⣻⣽⣻⢾⡽⣯⣟⡾⣽⡷⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣯⣟⣯⣟⣷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢉⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜🟥🟥🟥🟥🟥⬜⬜⬜️⬜️ ⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜ ⬜⬜🟫🟫🟫🟧🟧⬛️🟧⬜⬜⬜ ⬜🟫🟧🟫🟧🟧🟧⬛️🟧🟧🟧⬜ ⬜🟫🟧🟫🟫🟧🟧🟧⬛️🟧🟧🟧 ⬜🟫🟫🟧🟧🟧🟧⬛️⬛️⬛️⬛️⬜ ⬜⬜⬜🟧🟧🟧🟧🟧🟧🟧⬜⬜ ⬜⬜🟥🟥🟦🟥🟥🟥🟥⬜⬜⬜ ⬜🟥🟥🟥🟦🟥🟥🟦🟥🟥🟥⬜ 🟥🟥🟥🟥🟦🟦🟦🟦🟥🟥🟥🟥 🟧🟧🟥🟦🟨🟦🟦🟨🟦🟥🟧🟧 🟧🟧🟧🟦🟦🟦🟦🟦🟦🟧🟧🟧 🟧🟧🟦🟦🟦🟦🟦🟦🟦🟦🟧🟧 ⬜️⬜️🟦🟦🟦⬜️⬜️🟦🟦🟦⬜⬜ ⬜️🟫🟫🟫⬜️⬜️⬜️⬜️🟫🟫🟫⬜ 🟫🟫🟫🟫⬜️⬜️⬜️⬜️🟫🟫🟫🟫

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡶⠒⠒⠶⣄⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢱⠀⠀⢠⠉⢡⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠄⠀⢸⣦⣾⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠶⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷ ⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇ ⠀⠀⠀⣀⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⣿⡛⠁⠀ ⠀⣠⢾⣭⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⣝⣷⡀ ⢠⡏⠘⠋⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠈⠛⠃⢻ ⠈⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡽⠟⠛⠿⣭⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠞ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀

⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀ ⠀⣠⣾⡿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣷⡀⠀ ⢰⣿⡏⠀⠀⠀⣶⣶⣆⠀⠀⣶⣶⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄ ⣿⣿⠀⠀⠀⠀⣿⣿⢿⣧⡀⣿⣿⠀⢰⣶⡆⢰⣶⣦⠴⢶⣦⡄⠛⣿⣿⠛⢀⣤⡖⠒⣶⣄⠀⣴⣶⡦⠶⣶⣦⡀⢀⣴⡶⠶⣿⣿⠀⢠⣴⡖⠒⣦⡄⠀⠀⠸⣿⡇ ⣿⣿⠀⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⠀⢸⣿⡇⢸⣿⡏⠀⠈⣿⣿⠀⣿⣿⠀⢾⣿⡟⠛⠛⠛⠂⣿⣿⡇⠀⢸⣿⡇⢸⣿⡇⠀⣿⣿⠀⣿⣿⠀⠀⣿⣿⠀⠀⢠⣿⡇ ⠸⣿⣇⠀⠀⠀⠿⠿⠀⠀⠹⠿⠿⠀⠸⠿⠇⠸⠿⠇⠀⠠⠿⠿⠀⠿⠿⠀⠈⠻⠧⠤⠿⠟⠀⠿⠿⠇⠀⠸⠿⠇⠘⠿⣧⡤⠿⠿⠀⠘⠿⠧⠴⠿⠋⠀⢀⣾⣿⠃ ⠀⠙⢿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠁⠀ ⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠛⠛⠛⠿⣦⣄⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢙⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⢱⡀⠀⠀⠀⠀⡜⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢰⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⠀⢸⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢠⣶⣶⣶⣦⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⣴⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡛⠛⠉⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠋⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠙⠻⣶⣄⠀⠀⠀ ⠀⢀⣴⣿⣯⣴⡆⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢰⣶⣬⣻⣷⡀⠀ ⠀⣾⠏⢸⣿⠿⠃⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠈⠻⢿⡿⠹⣿⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇ ⠀⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⠟⠛⠻⣿⣯⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠃ ⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠛⠛⠋⠁⠀⠀

▒▒▒▒▒▒▒▒▒▄▄▄▄▒▒▒▒▒▒▒ ▒▒▒▒▒▒▄▀▀▓▓▓▀█▒▒▒▒▒▒ ▒▒▒▒▄▀▓▓▄██████▄▒▒▒▒ ▒▒▒▄█▄█▀░░▄░▄░█▀▒▒▒▒ ▒▒▄▀░██▄░░▀░▀░▀▄▒▒▒▒ ▒▒▀▄░░▀░▄█▄▄░░▄█▄▒▒▒ ▒▒▒▒▀█▄▄░░▀▀▀█▀▒▒▒▒▒ ▒▒▒▄▀▓▓▓▀██▀▀█▄▀▀▄▒▒ ▒▒█▓▓▄▀▀▀▄█▄▓▓▀█░█▒▒ ▒▒▀▄█░░░░░█▀▀▄▄▀█▒▒▒ ▒▒▒▄▀▀▄▄▄██▄▄█▀▓▓█▒▒ ▒▒█▀▓█████████▓▓▓█▒▒ ▒▒█▓▓██▀▀▀▒▒▒▀▄▄█▀▒▒ ▒▒▒▀▀▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⣀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠁⠀⠀⣴⠃⣼⠀⠀⣰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⡄⠀⠀⠀⢸⣿⣿⡿⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⡰⠁⠀⣀⡀⢸⣿⣿⠇⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣀⡀⡀⠀⢾⣯⣭⠟⠉⢋⣀⣀⣀⡨⠍⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠲⠯⢭⣅⣈⡀⠀⠀⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠀⠀⠒⢺⢀⡇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡄⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⢠⡞⠁⠀⢷⣄⠀⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠙⢶⣤⡀⠀⠀⠀⠀⠘⠀ ⠀⠀⣾⠃⠀⠀⣈⣻⣿⣿⠟⠁⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⢹⡏⢦⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⣰⣿⢠⣾⠟⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠋⠀⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⠀ ⠀⡼⠀⠀⢰⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⣿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠁⢸⡁⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀ ⢠⡇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⠶⣦⣤⣀⣀⣶⣤⠞⠋⠁⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣸⣿⢦⣤⡀⠀⠀ ⢸⣴⠀⣤⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⡆⠀⠀⠀⠀⠀⠈⣽⡟⠛⣧⡀⠀⠸⡄⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠹⣧⣴⠟⢇⢀⣀ ⠘⣯⣜⠁⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣿⣄⠀⠀⠀⠀⣠⡿⠀⠀⠘⣷⡄⠀⠹⡆⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠟ ⠀⠹⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣧⡄⠀⢰⡿⠁⠀⠀⠀⠘⣷⣀⣠⢷⣽⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠻⣿⣶⣿⠃⠀⠀⠀⠀⠀⠘⣿⣏⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡶⣮⣽⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡶⠟⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠛⠙⡄⠀⠀⠀⠀⠀⠀⣰⠿⣟⠉⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⢠⣼⠏⠀⠀⠀⠀⠀⠀⠈⢿⣄⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

(੭｡╹▿╹｡)੭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣻⣿⣿⣿⣿⣯⣍⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⣾⠟⠋⣁⣀⣤⡉⠻⣷⡀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⢸⣿⠀⠼⢋⣉⣈⡳⢀⣿⠃⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠿⣷⡀⠀⠀⠀⣼⣿⠃⠀⠀⣀⣤⡿⠟⠛⠋⠉⠉⠙⢛⣻⠶⣦⣄⡀⠀⠘⣿⣷⡀⠀⠀⠀ ⢠⣾⠟⠳⣦⣄⢸⡇⠀⠈⣷⡀⠀⣼⣿⡏⢀⣤⡾⢋⣵⠿⠻⢿⠋⠉⠉⢻⠟⠛⠻⣦⣝⠻⣷⣄⠸⣿⣿⠀⠀⠀ ⠘⣧⠀⠀⠀⠙⢿⣿⠀⠀⢸⣷⠀⣿⣿⣧⣾⣏⡴⠛⢡⠖⢛⣲⣅⠀⠀⣴⣋⡉⠳⡄⠈⠳⢬⣿⣿⣿⡿⠀⠀⠀ ⠀⠘⠷⣤⣀⣀⣀⣽⡶⠛⠛⠛⢷⣿⣿⣿⣿⣏⠀⠀⡏⢰⡿⢿⣿⠀⠀⣿⠻⣿⠀⡷⠀⣠⣾⣿⡿⠛⠷⣦⠀⠀ ⠀⠀⢀⣾⠟⠉⠙⣿⣤⣄⠀⢀⣾⠉⠀⢹⣿⣿⣷⠀⠹⡘⣷⠾⠛⠋⠉⠛⠻⢿⡴⢃⣄⣻⣿⣿⣷⠀⠀⢹⡇⠀ ⠀⠀⢸⡇⠈⠉⠛⢦⣿⡏⠀⢸⣧⠀⠈⠻⣿⡿⢣⣾⣦⣽⠃⠀⠀⠀⠀⠀⠀⠀⣷⣾⣿⡇⠉⢿⡇⠀⢀⣼⠇⠀ ⠀⠀⠘⣷⡠⣄⣀⣼⠇⠀⠀⠀⠻⣷⣤⣀⣸⡇⠀⠹⣿⣿⣦⣀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⢸⣷⣾⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⢦⣍⣀⣀⣀⡄⠀⣰⣿⡿⠿⢿⣇⠀⠀⠉⠛⠻⣿⣿⡷⠾⣿⣿⡿⠉⠁⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢿⣿⣇⠀⠀⠈⢿⣧⣄⠀⠀⠀⢹⣷⣶⣶⣾⣿⡇⠀⠀⣀⣴⡿⣧⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠙⢿⣿⣶⣤⡀⠻⢤⣀⡤⠞⢀⣴⣿⣿⠟⢷⡀⠙⠻⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢠⡟⠁⠙⢻⣿⠷⠶⣶⠶⠾⠛⠙⣿⠇⠀⠀⢻⡄⠀⠀⠙⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⣿⠁⣤⣤⡄⢻⡶⠶⠛⠛⠛⠛⠛⣿⢠⣾⣷⣆⢻⡀⠀⠀⠈⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⡈⢿⡀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⢸⡇⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠀⠁⠀⠀⠈⠁

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜🟥🟥⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥⬜🟥⬜⬜🟥⬜🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥⬜🟥🟥🟥🟥⬜🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬛⬛⬜⬛⬜⬜⬛🟥🟥⬛⬛⬛⬛⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜ ⬛⬜⬜⬛⬛⬜⬜⬛⬛⬛🟥🟥🟥🟥🟥🟥⬛⬛🟥🟥⬛⬜⬜⬜ ⬛⬜⬜⬜⬛⬜⬜⬛🟥🟥⬛⬛⬛⬛⬛⬛🟥🟥⬛🟥⬛⬜⬜⬜ ⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜🏻🏻⬜⬜⬛⬛🟫⬛⬛⬜⬜⬜ ⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛🏻🏻⬛⬜⬜🏻🟫🏻🏻⬛⬜⬜ ⬛⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬛🏻🏻⬛⬜⬜🏻⬛🏻🏻⬛⬜⬜ ⬛⬜⬜⬜🟦⬛⬛⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛🏻⬛⬜⬜ ⬜⬛⬛🟦🟦🟦🟦⬛🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻🏻⬛🏻⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛🟥⬛⬛⬛⬛🏻🏻⬛⬛⬛⬛🏻⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛🏻⬛⬛⬛⬛🏻🏻⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬛🏻🏻🏻🏻⬛⬛🟥🟥⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥🟦🟦⬛⬛⬛⬛🟥🟦⬛🟥🟥🟥⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟦🟦🟦🟦🟥🟥🟥🟥🟦⬛🟥🟥🟥🟥⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟨🟨🟦🟥🟥🟦🟨🟨⬛🟥🟥🟥⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟨🟨🟦🟦🟦🟦🟨🟨⬛🟥🟥🟥⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛🟥🟥⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟦🟦🟦🟦🟦⬛⬛⬛⬛🟦🟦🟦🟦🟦⬛⬜⬜⬜ ⬜⬜⬜⬛⬛⬛🟦🟦🟦🟦⬛⬛⬛⬛⬛⬛🟦🟦🟦🟦⬛⬛⬛⬜ ⬜⬜⬛⬛🏻🏻🟫🟫🟧🟧🟫⬛⬜⬜⬛🟫🟧🟧🟫🟫🏻🏻⬛⬛ ⬜⬜⬜⬛🟧🟧🟧🟧🟧🟧🟧⬛⬜⬜⬛🟧🟧🟧🟧🟧🟧🟧⬛⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠟⠻⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⣡⡀⠀⠀⣠⣄⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⢠⠋⠀⣸⣿⣿⣆⣰⣿⣿⣧⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⣿⣿⠻⣿⣿⠿⣿⣿⣧⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣿⣿⡟⠀⠘⠋⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣙⣛⣁⣠⡤⠤⠤⠤⣭⣥⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠴⠚⠋⠉⢁⣀⣤⣤⣤⣤⣤⣤⣤⣬⣍⣙⠓⠶⢤⡀⠀⠀⠙⣦⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⠏⠀⣠⠖⠉⣠⣶⣶⣾⣿⠋⠉⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣷⣦⣌⡓⠄⠀⠈⢷⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⡏⠀⠘⠁⣠⣾⣿⠿⠿⠿⢿⣷⡀⠀⠀⠀⠀⠀⢀⣿⠿⠛⠛⠛⠿⣧⠈⠻⣦⡀⠀⠸⡇⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣇⢀⣴⠟⠉⠽⠁⠀⣀⠤⠤⢌⠳⠀⠀⠀⠀⠀⠚⣡⠴⠦⣤⡀⠀⠙⠀⠀⠈⠻⣦⣠⡇⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠹⠻⡇⠀⠀⠀⠀⣰⠁⣠⡶⢦⣀⠀⠀⠀⠀⠀⢰⣵⢶⣦⡀⠹⡄⠀⠀⠀⠀⠀⢸⠉⢀⣤⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠈⠛⡆⠀⢇⠀⠀⠀⠀⡇⠀⣿⣄⣀⣿⡇⠀⠀⠀⠀⣿⣅⣀⣿⣧⠀⡇⠀⠀⠀⠀⢀⡏⠀⡟⠁⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠒⠙⢶⣧⠀⢸⡄⠀⠀⠀⢣⠀⣿⣿⣿⡿⠛⠋⠉⠉⠑⠻⢿⣿⣿⡟⠀⠃⠀⠀⠀⠀⡼⠀⠀⣧⡞⠉⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢀⡤⣿⡀⣀⣷⠀⠀⠀⠀⠣⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠁⠀⠀⠀⠀⠀⠀⠙⢶⠀⣿⠤⠄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣤⣤⣀⠀⠀⢻⣆⠀⠀⠘⣷⠟⠉⠀⣾⣦⣄⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⣠⣴⣾⣧⠀⠀⠈⢶⠇⠀⠀⢀⣿⢃⣶⠿⠛⠻⣶⡄⠀⠀⠀ ⠀⣰⡟⠁⠀⠈⢻⣧⠀⠀⢻⣦⡀⠀⣀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠄⠀⠀⢀⠀⠀⣠⣾⠃⣾⠇⠀⠀⠀⠈⣿⠀⠀⠀ ⠀⢻⡇⠀⠀⠀⠀⢿⡆⠀⠀⠙⠻⣶⣿⡆⠀⠀⠘⠿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⣿⣶⡾⠛⠁⢠⣿⠀⠀⠀⠀⠀⣿⠃⠀⠀ ⠀⠸⣷⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣤⣤⣀⣤⣤⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⣿⡆⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠸⡟⠛⠛⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⢸⣧⠀⠀⠀⠀⣿⣴⣶⣶⣤⠀⠀⠀⠀⠉⣻⣷⣦⣄⡀⠀⠀⠀⠈⠛⠲⠶⠶⠒⢋⡄⠀⠀⠀⢀⣠⣴⡾⠛⠁⠀⠀⢠⡾⠟⠛⢿⣿⠀⠀⠀⠀⣿⣧⡀⠀⠀ ⢀⣶⠟⠛⠀⠀⠀⠀⡟⠁⠀⠀⢹⣷⣦⣤⣶⠟⠛⡟⠉⠉⠛⢶⣤⡀⠀⠉⠒⠒⠒⠊⠁⠀⠀⣠⡾⠟⢻⡟⠻⠷⣦⣴⠿⢿⡇⠀⠀⠀⠹⠀⠀⠀⠀⠋⠉⠻⣦⠀ ⣾⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠁⠈⠻⡀⠀⠀⡇⠀⠀⠀⢸⠀⠙⠓⠦⢤⣀⣀⣤⠤⠶⣟⠁⠀⠀⠀⣇⠀⠀⢸⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣀⣀⡀⠀⠧⠤⢀⣀⣀⣀⣀⣀⡀⠤⠿⠀⢀⣤⣄⡀⣇⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢀⣿⠃ ⠀⠹⣷⡀⠀⢲⡀⢷⠘⣆⠀⠀⠀⠀⠀⠀⣾⠀⢸⣾⠉⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠻⣿⠀⠸⣆⠀⠀⠀⠀⠀⢀⡞⢀⡟⢠⠏⠀⢀⣾⠏⠀ ⠀⠀⠘⠿⣦⣀⠁⠀⠁⠈⠀⠀⠀⠀⣠⢾⣏⣠⡿⢿⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣰⣿⢷⣄⣿⡓⠄⡀⠀⠀⠈⠀⠈⠀⢀⣠⣴⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣄⣀⣀⣩⣴⠿⢻⡿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⢻⣏⠻⣶⣤⣤⣤⣤⣴⡶⠿⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢠⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣯⣟⡿⣾⡿⠋⠁⣿⣿⠀⢀⣿⣇⠈⠻⣿⣿⡾⣽⣻⣟⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢯⣟⡿⣾⣽⣿⡟⠁⠀⣼⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⣿⣟⣷⣻⢾⣽⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣽⣻⣞⣿⣳⣿⣿⡆⠀⣼⣿⡏⠙⠿⠿⠀⢻⣿⣧⠀⣼⣿⣿⢾⡽⣟⣾⡽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢯⡿⣽⣳⡿⣾⣽⣻⣿⣷⡈⢿⣿⠁⣀⠀⢀⣄⠀⣿⣿⣸⣿⣿⣟⣯⡿⣯⡷⣟⣿⣻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣯⢿⣽⣻⣷⣿⣷⣿⡽⣿⣿⣿⣶⣷⣴⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣻⣞⡷⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣞⣯⡷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣽⣻⣿⣿⣿⣽⣻⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣧⢿⣻⢷⣻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡐⣉⠛⣿⣍⠋⡍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣧⠄⠒⣈⠣⠘⢸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠈⠐⠀⠂⠁⠚⣿⣿⣿⣟⢻⣿⣭⠉⠁⠌⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⠏⠁⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣦⠹⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣾⡿⢉⡁⠀⠈⣿⣿⣇⠀⠀⠀⠈⠀⠀⣿⣿⣧⣼⣿⠀⠀⠀⠀⠰⢿⣿⣦⣿⣿⣿⠀⣿⡇⠀⠀⢪⣿⣿⡟⠋⢀⣈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣷⣾⣿⠷⠒⣿⣿⣿⡆⠀⠀⠀⠀⠀⢹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣯⠀⣿⠇⠀⠀⢸⣿⣿⣧⠐⡨⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⠀⣠⣤⡀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠛⠃⠀⠀⢀⣶⣴⣿⣿⣿⣿⣷⡄⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⣠⣿⣿⣿⣿⣿⣿⣾⣯⠛⣿⣿⣿⠀⢈⣿⣿⠀⢰⣿⣿⣷⣶⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣽⣿⣿⣿⣿⡇⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣟⣭⣽⣿⡿⠟⠁⢀⣾⣿⠃⠀⠀⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠉⠛⣿⣿⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠉⠀⠀⣠⣾⡟⠁⣾⣶⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣠⣾⡿⠋⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣠⣤⣤⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠋⠀⠀⢀⣼⣿⠏⠀⣀⣠⣿⣿⣦⣀⡈⢿⣧⡄⠀⠀⠀⠀⠈⠙⠛⠋⢿⣿⣿⣿⡿⣿⣿⣿⣿⠿⢹⡟⠉⠁⠀⠀⠀⡀⣤⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣰⣿⡿⠃⠀⠀⣿⣿⣿⣿⣯⡽⢿⣦⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣖⠉⠛⡉⠂⠀⠀⠀⠈⢠⠀⣀⣥⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣄⡈⢉⠿⣿⣿⣿⣤⣀⠄⠀⠀⠀⠀⠉⠀⠿⠏⠀⠀⠁⠀⠀⠁⡀⣀⣧⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⡏⠀⠀⠀⠀⣺⣿⣻⣿⣿⣿⣿⣿⣿⣼⢾⣿⣿⣿⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠐⣀⠠⣀⣶⣼⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⡇⠀⢠⣴⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢹⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠈⠉⠁⠙⢿⣿⣯⢿⣽⣻⣟⡿⣿⢿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⣟⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣷⣙⠿⣿⣿⣿⣿⣟⣡⣿⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠀⠀⢘⣿⣿⣿⣾⣷⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣻⢾⡽⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⣰⣿⡟⠻⢻⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣛⡟⣿⢻⣟⡿⣻⢟⡿⣽⣻⣿⣯⠀⠀⠀⠛⣿⣿⣿⣿⢯⣿⣳⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠁⠀⣼⣿⠉⠀⠠⠘⠷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡁⣹⣿⣿⣳⡝⣾⡱⢯⣞⡽⣳⢯⣛⣷⣻⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣳⣿⣟⣾⣻⢿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣤⡉⠿⣿⣿⡇⠀⣾⣿⣧⡀⠀⠀⠀⠀⠀⢿⡟⣿⣿⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣯⢳⡽⣲⡝⣯⢞⡵⣯⢏⡿⣞⣳⢿⣿⣿⣦⣤⣶⣿⣿⣿⣿⣿⣷⣻⢿⣿⡽⣯⡿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣾⣿⡿⣹⣿⣿⣿⣷⣀⣀⣷⣼⣿⣿⣅⠀⠀⠀⠀⢸⣿⣿⢻⡵⣞⢯⡳⣇⠿⣜⡯⣽⢞⣯⣟⣭⣟⣻⣞⢿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣻⣞⣿⣽⣻⣽⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣽⣿⣿⣼⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣷⣿⠟⠻⠿⢿⣿⡿⠿⢛⣯⠻⣿⣦⡀⠀⢀⣿⣿⢏⡷⣽⢮⢷⡹⣎⣿⡹⣞⣧⣟⡾⣞⡵⣯⢷⣞⡿⣞⣷⣻⢾⣟⡾⣿⣿⣿⣿⣿⣻⣞⣷⢯⣷⣿⣾⣿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠨⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠡⠁⠚⣿⣿⣿⣿⣿⣟⡯⣞⢧⡟⣧⢿⣱⡗⣯⡽⡶⣯⡽⣏⡿⣽⣻⢾⣽⣻⢾⣽⣻⣞⡿⣽⣿⣿⣿⣿⣳⣿⣾⣿⠿⠋⠁⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠃⣿⣿⣿⣯⣿⣟⣿⣿⣵⣿⣿⣿⡿⠋⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣟⣞⡷⣭⣟⡾⡽⣏⡾⣽⣳⣻⣽⣳⠿⣽⣻⢷⣯⣟⣾⣽⣻⣞⣷⣻⢿⣷⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠐⡀⠄⡀⢀⠈⡑⢶⡄⠀⠀⠀⢀⣠⣿⡟⣿⣿⢷⣻⢾⣽⣳⢯⣽⣻⣽⣻⣗⣯⢷⣯⣟⣿⣳⢯⣟⣾⡽⣞⣷⡿⣽⣾⣟⣿⣾⣿⣿⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣮⣴⣡⣒⣠⣀⣬⣤⣴⣾⡿⠛⠛⣷⣿⣿⡿⣽⣻⡾⣽⣯⢷⣟⣾⣳⣟⡾⣟⣾⣽⡾⣽⣟⣿⢾⣟⣿⣯⣿⢿⣳⣿⣿⣿⣿⡧⠀⢻⣿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢸⣿⣿⣿⣹⡟⣷⣿⢻⣾⡟⣿⣾⣏⣿⣿⡟⣿⣾⣿⡟⣿⣾⣿⣿⢻⣾⣿⣿⣿⣷⣿⣿⣿⠁⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣻⣽⣿⣻⣿⣯⣿⣿⢿⣾⣿⣾⣿⣟⣿⣾⣿⣿⣟⣿⣾⣿⣿⣯⣿⣾⣿⣿⣿⡟⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄ ⠀⠀⠀⠀⠹⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⡀⢆⠰⡀⠤⣠⠄⠀⠀⠀⠀⣴⣿⣿⡿⣾⣿⣟⣿⣿⣻⣽⣿⢿⣿⣿⣯⣷⣿⣿⣿⣿⣽⣾⣿⣿⣟⣿⣾⣿⣿⣽⣾⣿⣿⡇⠀⠀⢸⣿⠀⠀⠀⣰⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣦⣷⣼⣦⣴⣿⣶⠄⠀⢀⣿⣿⡿⣽⣳⣟⡾⣿⣽⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣾⣿⣟⣿⣿⣷⠀⠀⢸⣧⠀⠀⢸⡿⠀⠀⠛⠀⠀⠀⠀⣠⣶⡶⢾⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣍⠋⠙⠛⠛⠛⠛⠛⠙⠋⠉⠀⠀⣼⣿⣿⣿⡽⣳⡽⣺⣽⣳⢯⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡽⣾⢿⣿⣿⡄⠀⠘⢿⣄⡀⢸⣧⠀⠀⠀⠀⠀⣀⣼⣿⣿⣧⣿⣿⣿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡟⢤⠐⢶⣶⣤⡀⠄⡀⠀⠀⠀⣼⣿⣿⣿⡿⣼⡳⢿⣳⢧⣟⣻⣞⣷⣻⣽⣾⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⡿⢿⣽⡺⢯⣷⣻⡽⣯⢿⣿⣷⠀⠀⠈⠻⢿⣿⣿⣷⣄⣀⣀⣰⣿⣿⣻⣿⣿⣿⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠙⢿⣿⣿⣶⣭⣾⣿⣿⣷⣠⣴⣷⣶⣿⠿⠋⣿⣿⣟⣶⣻⣏⣷⢻⣞⣷⣻⢾⣽⣻⣿⣿⣿⡇⠁⠸⣿⣿⣿⣟⢷⣻⡟⣶⡻⣟⣾⣳⢿⣽⣻⣿⣿⡀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⣿⣿⣟⢶⣻⣼⡳⣟⣾⣳⢯⣿⡽⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣞⣯⢷⣹⢷⡻⣽⢾⣽⣻⢾⡽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣮⢳⣞⣽⢻⡼⣯⣟⣾⣟⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣞⣧⠿⣽⠾⣝⣷⡻⣾⡽⣯⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣹⢎⡿⣼⢞⣯⣟⣷⣻⣞⣯⣿⣿⣿⡧⠀⠀⠀⠀⣿⣿⣟⣾⢻⣭⢿⡽⣶⣻⢗⣿⣳⣟⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡞⣵⢯⡽⣞⣻⣞⣾⣳⣟⣾⣟⣿⣿⣿⠁⠀⠀⠀⠀⣻⣿⣿⡞⣟⡾⡽⣞⡷⢯⣟⣾⣳⢯⣷⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡽⣎⣷⣻⡽⣧⣟⣾⣳⣯⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⡿⣭⢿⣽⡳⣟⣟⡾⣳⢯⣟⣷⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣜⣳⡽⣶⣻⢷⣻⣞⡷⣯⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡿⣝⣯⢶⣻⡽⡾⣝⣯⢿⡾⣽⢯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣟⡷⣽⣲⢟⡵⣯⣟⣳⢯⣟⡿⣿⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡽⣞⣯⢷⣻⢽⣛⡾⣏⡿⣽⣻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⡝⠳⣭⠿⣽⢳⢯⡟⡿⣾⡽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⣾⢹⢻⢾⣭⢷⢹⠾⣽⢳⡟⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⡾⣽⣳⢯⣷⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢷⣫⢯⣛⣮⢿⣼⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠟⢫⠱⡘⢦⢫⠽⣹⢻⠿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡟⣭⣟⣷⣿⣿⠿⣟⠿⣫⠝⣍⡚⢴⠒⣌⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⡜⢀⠃⠜⠂⣇⢛⡬⢣⣟⣳⢯⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣺⣿⣷⣿⣿⣿⢿⣫⢞⡹⢎⠳⡡⠞⡰⣉⠦⡙⢤⣋⠜⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡧⣙⠤⢃⠌⡀⢂⠜⢮⡜⣳⢎⡷⢯⣟⣿⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣹⣿⣿⣛⠟⡼⣣⢳⡭⢞⣡⠃⡔⢁⠒⡤⢣⡙⠶⣌⡳⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⢩⢎⡕⣪⡔⣡⢞⡱⣎⡵⣯⣞⣿⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣷⣯⣛⢼⣱⢳⡚⣭⠲⣍⡔⣪⠜⡴⣣⡝⣧⣏⣷⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣎⡾⣜⣳⡿⣔⣫⢷⣭⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣾⣶⣧⣝⡎⣷⢚⡼⣳⣯⡳⢷⣻⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠛⢿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

𓀻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠃⠻⢿⣿⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢛⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣀⣀⣀⣀⡀⠀⠙⢿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣶⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⠹⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣥⣶⢶⣶⣦⡙⢦⡀⠙⢿⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣉⠁⠶⠀⠀⠉⠻⢦⡑⠄⠈⠻⣿⣿⡟⢡⣿⡇⣼⠏⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢡⡙⠀⠀⢀⠀⢀⣴⣦⠙⠀⠀⠀⠉⠙⢠⣿⡟⢰⣯⣼⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢶⡎⢹⣿⣧⣙⠲⠤⠤⣀⣛⣛⣉⣒⣓⡀⠀⣠⣾⣿⡟⠰⠿⠿⠿⠟⠛⠛⠉⠉⠀⣸⢀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣤⣾⣿⣦⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣿⣾⣧⠀⠀ ⠀⠀⠀⠀⣾⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣄⣸⠈⣿⣿⣿⣦⠀ ⠀⠀⠀⠀⣹⢰⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠟⢿⣿⣿⣿⣿⣿⡄⠀⢠⣄⣠⣾⣿⣿⣏⡀⢹⣿⣿⣿⡄ ⠀⠀⠀⠀⢹⢸⢹⡇⡇⣿⡟⣿⢸⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⢻⣿⣿⣿⣿⣿⡌⣆⡙⣿⣿⣿⡾⢿⡾⢨⣿⣿⣿⡁ ⠀⠀⠀⠀⠀⠙⠾⡇⡇⣽⡇⠟⠘⠃⠁⣤⣰⢉⡿⣿⣿⣿⣿⣿⣿⣟⣿⣶⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⢾⠿⠋⠁⠻⣿⣿⣿⣿⣿⡷⠋⣐⣿⣿⢇⡷⠟⣠⣿⣿⣿⣿⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢸⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡱⢙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣤⣄⣄⢈⠻⠿⠛⣁⣄⣾⣿⡿⠣⡩⢃⡼⣿⡿⡏⡅⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠙⣿⢰⢹⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⡰⠆⢻⣿⣿⣿⢃⠍⢰⣿⣧⣧⣷⢗⣡⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⠡⠐⠠⠐⡀⠈⢻⣸⠆⣼⢹⣿⣿⣿⣿⣿⣿⣴⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⢶⣾⠄⣿⣿⣟⡋⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⢂⠐⡈⠄⠂⡁⢂⠡⢀⠡⠀⠘⢱⣏⢸⢸⠛⢿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣩⣥⣶⣮⣄⣒⣊⡥⢶⣭⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡞⠃⠈⡄⠂⠐⠈⠐⠀⠂⠐⠀⠂⠁⠂⡄⠈⢻⣾⢸⢸⢹⢹⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⡟⠋⢡⠀⠙⠓⠛⠛⠋⠉⠉⠛⠉⠉⠛⠁⠀⠈⠐⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠋⠋⢀⠐⠠⠈⠄⡁⢂⠡⠈⠄⠡⢈⠐⠠⠐⠠⢀⠈⠺⢼⢸⢸⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⠲⣶⣾⣿⣿⣶⣶⡿⠟⠀⠠⠁⢂⠁⢂⠈⠄⠀⠀⠀⠀ ⠀⢀⠂⡀⠐⡀⠂⠌⠠⢁⠂⡐⢀⠂⠡⢈⠐⠠⠈⠄⡁⠂⠄⠂⠄⡀⠈⠐⠺⢦⠙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⣶⣶⣾⣿⣶⠀⠀⠄⡁⢂⠈⠄⠂⠌⡐⢀⠀⠀ ⠀⠀⠂⠄⠡⢀⠡⢈⠐⡀⢂⠐⠠⢈⠐⠠⠈⠄⡁⠂⠄⠡⢈⠐⠠⢀⠁⠂⠀⠀⠀⠈⠻⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠄⡐⠠⢈⠐⡈⠄⡐⠠⠀⠀ ⠀⠀⠁⠌⡐⢀⠂⠄⢂⠐⠠⢈⠐⠠⠈⠄⡁⠂⠄⠡⢈⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠸⡌⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠛⠉⠀⠠⢁⠂⠄⡁⢂⠐⡀⠂⠄⠡⠈⠀ ⠀⠀⠀⠀⠀⠀⠈⠐⠠⠈⠐⠠⠈⠀⠁⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠈⠐⠀⠂⠐⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠑⠦⠴⠚⠋⠉⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢘⡄⢷⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠈⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⡳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠢⣕⠢⢄⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠒⠦⣄⠀⠀⠀⠉⠉⠁⠀⠀⣀⡤⠤⢄⡀⠀⠀ ⢀⡞⠁⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠲⠏⠀⠀⠀⠘⢦⠀ ⢸⡇⠀⠀⠀⠀⢀⡖⢳⠀⣠⠺⡄⠀⠀⠀⠀⠀⠀⠀⢘⡆ ⠀⢻⠇⠀⠀⢀⣾⣶⡏⢀⣿⣴⠇⠀⠀⠀⠀⠀⠠⢀⡾⠀ ⠀⡏⢠⠖⠓⡾⢿⡿⠀⠸⣿⣿⢠⠀⠢⣄⠀⠀⠀⢻⠀⠀ ⢸⠀⠈⠛⠚⠁⠀⠀⠺⠃⠈⠁⠐⠦⣴⠿⠀⠀⠀⢸⡆⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡄⠀ ⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣧⠀ ⠀⠀⡯⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⡟⠀ ⠀⠀⢳⣤⢡⣤⠉⠛⣲⡶⠒⠲⣞⠛⢉⣀⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠙⠓⠧⠴⠚⠉⠀⠀⠀⠙⢦⣀⠈⠁⣀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠛⠶⣄⡤⠞⠻⠫⠙⠳⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⢰⡆⠀⠀⠐⡄⠻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⣤⣇⢀⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢈⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣎⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣝⠳⣄⡀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣉⣒⣖⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠶⠶⢦⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀ ⠀⢀⡾⠋⠀⠀⠀⠀⠉⠧⠶⠒⠛⠛⠛⠛⠓⠲⢤⣴⡟⠅⠀⠀⠈⠙⣦⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⣇ ⠀⣿⡀⠀⠀⠀⠀⠀⢀⡟⢁⣿⠀⢠⠎⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠈⢻⡇⠀⠀⠀⠀⣾⣧⣾⡃⠀⣾⣦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠰⠀⣼⠇ ⠀⢰⡟⠀⡤⠴⠦⣬⣿⣿⡏⠀⢰⣿⣿⡿⢀⡄⠤⣀⡀⠀⠀⠀⠰⢿⡁⠀ ⠀⡞⠀⢸⣇⣄⣤⡏⠙⠛⢁⣴⡈⠻⠿⠃⢚⡀⠀⣨⣿⠀⠀⠀⠀⢸⡇⠀ ⢰⡇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠈⠓⠲⠟⠋⠀⠀⠀⠀⢀⡇⠀ ⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀ ⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⣷⠀ ⠀⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⣿⡇ ⠀⠀⢸⡯⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠂⠀⠀⣿⠃ ⠀⠀⠈⣷⣄⡛⢠⣈⠉⠛⠶⢶⣶⠶⠶⢶⡶⠾⠛⠉⠀⠀⠀⠁⢠⣠⡏⠀ ⠀⠀⠀⠈⠳⣅⡺⠟⠀⣀⡶⠟⠁⠀⠀⠘⢷⡄⠀⠛⠻⠦⡄⢀⣒⡿⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠛⠁⠀⠀⠀⠀⠒⠂⠀⠙⠶⢬⣀⣀⣤⡶⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤ ⠘⣿⣿⣿⣷⣦⣄⣀⠀⢠⠔⠀⢀⡼⠿⠿⢆⠀⠀⠲⣄⠀⣀⣠⣴⣾⣿⣿⣿⠇ ⠀⠈⠉⠉⠛⠛⠻⠿⢿⣿⠀⢀⣾⣷⡀⢀⣾⣷⡀⠀⣿⡿⠿⠿⠛⠛⠉⠉⠁⠀ ⠀⠀⣤⣤⣶⣶⣶⣶⣶⣿⣆⠈⠉⠉⠉⠉⠉⠉⠉⢠⣿⣶⣶⣶⣶⣶⣤⣤⠀⠀ ⠀⠀⠘⣿⡿⠟⠛⠉⣡⣿⣿⣷⣤⠀⢠⣆⠀⣤⣶⣿⣿⣬⡉⠛⠻⠿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⢋⣿⣿⠛⢠⣿⣿⡄⠛⢿⣿⡘⢿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⠏⠀⣸⣿⡇⢀⠻⣿⣿⠟⣀⠸⣿⣇⠀⠙⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠁⣿⣿⠀⠻⣆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠉⠙⠓⠀⠘⠏⠀⠘⠟⠉⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⠛⠛⠋⢉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠀⠀⠀⠀⢰⣾⣂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠀⠀⠀⠄⠂⠀⢀⣶⡿⠛⢿⡿⠀⠀⠀⠈⠰⠁⡀⣤⣽⣶⡄⠂⠀⢀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠐⢀⠂⠐⠀⢈⠰⢀⢢⣿⠏⠀⠀⣼⡇⡃⠄⠂⠐⠠⢢⣿⠏⠀⠙⣿⠀⠀⠀⡀⠂⠀⠄⠀⠀⠀⠘⠻⣦ ⠀⠀⠀⠀⠀⢀⣴⠿⠃⠐⠀⠈⠂⠀⠠⠁⠀⠢⢰⣿⡏⠀⠀⢠⣿⠃⠁⠄⠂⠱⣰⣿⠇⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠄⠁⠀⠁⠠⠁⠈ ⠀⠀⠀⡀⣤⣿⠋⠠⠐⠀⡀⠂⠈⠀⠠⠀⢀⢡⣿⣿⣇⣀⣴⣿⡏⠀⢀⠂⠄⣧⣿⣿⠀⠀⢀⣾⣿⠁⠀⠀⡀⠂⠀⠠⠀⠂⠀⠀⠀⠀ ⠀⠀⢈⣼⡟⠁⠠⠁⠂⠀⠀⠐⠀⡁⠠⠂⡀⣾⣿⣿⣿⣿⣿⡟⣰⠀⠂⠀⢰⣻⣿⣷⣦⣤⣾⣿⡏⠀⠀⢀⠀⠀⡐⠀⠠⠐⠀⡀⠀⠀ ⣠⣄⣾⠃⡀⠀⠐⠀⢀⢠⣀⢄⡀⠀⠁⠀⢀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠐⠀⡁⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠄⠀⠀⠀ ⣿⣿⠃⠀⡀⠁⠈⠐⣬⢷⡹⢮⡝⣆⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠁⠀⠀⡡⣿⣿⣿⣿⣿⣿⠃⠀⠈⠠⠐⠀⠠⠀⠂⠀⠠⠀⠀⠀⠀ ⣾⣧⠀⠀⠐⠀⠀⠀⠈⠫⠝⠧⠛⠀⠀⠀⠀⠹⠿⠟⠁⡀⢤⣤⣤⣀⠠⠀⠑⢻⣿⣿⣿⡿⠁⠀⠀⠐⠀⡀⢀⡀⢀⠀⠀⠁⠠⠀⠀⠀ ⣿⡇⠀⠀⠀⠄⠂⠄⠀⡀⠀⠀⠠⠐⠀⡄⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣷⠆⠀⠈⠛⠿⠋⠀⠀⢀⠀⢂⡷⣹⢧⣛⢧⣖⡠⠀⠀⢀⠀⠀ ⡏⠁⠠⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣹⣿⡿⢻⡏⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠹⢜⡳⢮⡝⣾⢸⠓⡀⠁⠀⠀⠀ ⠃⠀⠐⠀⡀⣦⣬⣤⣤⣴⣄⣂⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢼⣏⢻⡿⠃⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠂⠙⠀⠁⡀⠀⠀⠁⠀⠀ ⠀⠀⢀⣂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣧⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠀⠄⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠻⣿⣿⣳⣯⢿⣽⣻⡽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⠀⠀⠀⡀⠀⠂⠀⠀⠀ ⠀⠀⠠⢀⠀⠀⠈⢿⣿⡾⣯⡷⣿⣽⣻⣾⡟⠁⢹⣿⡿⠻⢿⣿⣳⣯⢿⡽⣯⣟⣿⣻⣟⡿⣿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⢀⠀⠠⠀⠀⠈⢿⣿⣷⣻⣷⣿⣿⣿⡇⠀⢸⣿⣷⣄⣰⣿⣿⡽⣯⣟⣷⣻⣞⡷⣯⣿⣿⠟⠋⠉⠉⠉⠉⠉⠙⠓⠤⣄⡀⠀⠀⠀ ⠀⠀⠀⡀⠄⠀⠀⠀⢹⣿⣿⠋⠁⣠⣀⡀⠀⠀⣿⣿⠋⠉⣿⣿⣿⠿⠟⠛⠿⢿⣾⣿⣿⠟⠁⠀⠀⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠡⠀⢿⣿⡏⠀⣸⣿⣿⣷⠀⢠⣿⣿⠀⠀⣿⡿⠁⢀⣤⡤⠀⠀⢿⣿⠏⠀⠀⠀⠂⠀⠀⠀⠂⠀⠁⡀⢀⠀⠐⠀⠀⠀ ⠀⠀⠄⠀⠠⠁⢀⢩⣾⣿⣇⠀⠹⢿⣿⠿⠀⢸⣿⡗⠀⢰⣿⡃⠀⠀⠀⣀⣤⣶⣿⣿⠀⠀⠂⠐⠀⠀⡀⠂⠀⡀⠁⠀⠀⠀⠈⠀⠀⠀ ⡀⢀⠀⠁⢠⡐⣮⣾⣿⡿⣿⣷⣄⣈⣉⣀⣀⣸⣿⣇⠀⢸⣿⣧⡀⠈⠛⠿⠟⠉⢿⣿⡆⠀⠀⠁⠀⠀⠀⡀⢀⠀⠄⠁⡀⠈⠀⢁⠀⠀ ⣼⡢⢎⣷⣣⣾⣿⣿⣯⣟⣷⣻⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⣟⣿⣿⣶⣦⣴⣴⣶⣿⣿⣿⡠⢀⠈⠀⠐⠀⠀⠀⠠⠀⢂⠀⠄⠁⢂⠀⣀ ⣿⣿⣿⣿⢟⠫⣍⢛⡹⢛⡛⡟⠿⠿⠿⡿⣿⣿⣿⣿⣷⣿⣯⣷⣯⣿⣽⣻⣟⣿⣻⣟⣿⣷⡍⡖⢤⣈⠐⡈⠠⢁⠂⠄⢠⢀⣂⢦⢳⠰ ⣿⢯⡿⣿⣯⡖⣡⠏⣔⠫⠴⡙⡬⢃⡳⣘⡔⠲⡤⡩⢍⡍⢏⡛⣛⢛⠻⠟⡿⢿⣿⣿⣾⣿⣿⣜⠦⣌⠳⢥⡓⢮⡜⣎⠳⡜⣬⢳⢣⡙ ⣿⢯⣟⡿⣿⣿⣇⣞⣌⢣⠏⣜⡡⢏⠴⣡⠚⡥⢣⡱⢣⠜⣪⠱⡌⡎⣝⢪⢱⣒⢦⣲⠱⣬⢽⡻⢿⣮⣝⢦⡙⢣⡚⢬⢓⣙⢒⡫⢆⡹

⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⡐⠁⠀⠀⠉⢡⡀⢈⢂⠀ ⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠃⡜⠀ ⠀⠀⠀⠈⢒⢄⠀⠀⠀⢀⠔⠁⠀ ⠀⠀⡠⠄⡀⠈⠚⠒⠊⠀⣀⣀⠀ ⠠⡊⠀⠀⢈⠍⠀⣈⠉⠋⠀⠀⠱ ⠀⡳⠀⠀⣮⡎⣸⡼⠀⠀⠀⢀⡴ ⢠⠁⠧⠜⠙⢰⠙⠃⢅⡵⠀⠀⡇ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⢀⠜⢵ ⠀⠸⡄⣑⠢⢤⡤⢤⠤⣚⠁⠀⡎ ⠀⠀⠈⠐⠂⠁⠀⠀⠓⠤⠥⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠟⠛⠛⠛⠿⣦⣄⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢙⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⢱⡀⠀⠀⠀⠀⡜⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⢰⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇⠀⠀⠀⢸⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠹⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣠⠶⠶⠶⣦⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⠒⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀ ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡛⠛⠉⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠋⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠈⠙⠻⣶⣄⠀⠀⠀ ⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢻⣷⡀⠀ ⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣤⣀⣀⠀⢀⣀⣠⣤⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣬⣿⠟⠛⠻⣿⣯⣥⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀ ⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠛⠛⠓⢦⡀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣤⢦⢡⣷⣴⣛⠩⡙⠓⢦⡀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⠤⠑⠈⠉⣀⣤⣤⣭⢷⣀⠀⡇⠀ ⠀⠀⠀⠀⣀⡟⠀⠀⡠⠊⠁⣀⠤⠂⠁⣬⣟⣉⠀⠀⢀⡼⠃⠀ ⠀⠀⠀⡞⠉⠃⠀⣼⣇⠈⠁⠀⢿⠀⠀⠉⠉⠉⠙⣦⠾⠁⠀⠀ ⠀⠀⠀⢧⡔⠈⡉⠻⣿⡷⠀⣤⣄⣀⡀⠀⠀⠀⢀⡾⠀⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⠈⠀⠈⠁⠀⠙⢿⣿⣿⣷⣶⣶⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣶⣶⣦⣀⠀⠀⢈⠉⡹⡻⣩⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡤⠶⡋⠁⢀⡠⠜⢹⠒⠲⡓⢫⠻⣅⣀⡴⠶⠶⣤⡀⠀ ⠀⡴⠋⠀⠀⠀⢑⡏⠀⠀⡰⢠⠂⠈⠄⠀⠏⢻⠁⠀⠀⢸⢻⡆ ⢸⡃⠊⠰⠀⠀⠀⣏⠐⠈⠀⠈⠢⠤⠂⠀⠈⡟⠀⠀⢀⢢⡟⠀ ⠀⠳⣄⡀⠀⣲⠞⠉⠹⢦⡀⠀⠀⠀⠀⢀⣼⣇⡀⢀⢨⡟⠀⠀ ⠀⠀⠀⢹⠏⠇⠀⠀⠀⢸⠧⠤⠤⠶⠚⠋⠀⠈⠉⠙⠛⠁⠀⠀ ⠀⠀⠀⢼⢰⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⢿⣄⠀⠀⠀⠉⠙⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⣄⠀⠀⠀⠀⢸⠁⠈⢣⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡆⠀⠀⠀⠸⣇⠀⠈⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣠⣿⠀⠀⠀⠀⢻⣷⣾⣿⡆⠀⠀⠀⠀⠹⣆⠀⠀⢰⡿ ⠀⠀⠀⠀⢠⡿⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠘⡿⠿⠟⣇⠀⠀⠀⠀⠀⢹⡆⢀⣿⠃ ⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠀⡇⠀⠀⠀⠀⠹⡀⠀⡏⢀⣴⣿⣿⣿⠀⢿⡿⠁⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠳⣤⡼⠁⠀⠀⠀⠀⡀⠙⠚⠁⠈⠛⠟⠛⠉⠀⢸⣧⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠘⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⣿⣿⡛⠛⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠐⠛⠛⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⠀⠉⠛⠷⢶⣶⠶⠶⠶⠖⠛⠋⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡴⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣠⡴⠶⠛⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣤⣶⠆⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠙⣛⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⡀⠀⠀⡈⠙⢿⣆⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⡐⠁⡀⠀⣤⠀⠑⡌⣿⡆⢀⣤⣾⣿⣋⠙⠻⣿⣶⣦⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⣿⢾⠟⣷⠀⢸⣸⣿⣿⣯⣥⣀⣉⡙⣦⠀⠀⠈⠛⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢆⠀⢛⡠⠤⠚⠚⠉⠉⠉⠁⠀⠉⣉⣉⣛⣿⡄⠀⠀⠀⠘⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⠿⠷⠤⠤⠀⢠⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⣠⠴⠚⠉⢉⠹⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠤⢒⠉⠀⠀⠀⠀⣿⣧⣸⣇⣀⣀⡀⠀⠀⠤⠤⣴⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⡝⠀⠀⠀⢀⣼⣷⠖⠒⠒⠋⠉⠀⠀⣿⣷⠀⠀⠀⠀⡹⠛⠉⠉⠉⠙⠻⢷⣄⣀⣠⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠀⢀⣤⠖⠒⠒⠚⢿⣿⣿⣿⣶⣤⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣷⡟⠁⠀⠠⢄⡀⠈⠻⣿⣿⣿⠟⠀⠀⣾⣿⣷⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠻⡄⠀⠈⠙⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣄⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠟⠛⢿⡿⣿⠟⢩⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⣇⠀⣀⡴⢋⡴⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠁⠀⠀⠀⠀⢈⣿⠻⣶⢦⣤⣤⣨⣭⡥⢶⡻⣷⣿⠏⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⢠⣶⡿⠿⠿⠷⢤⣀⠀⠀⠀⣀⣤⠖⠋⠁⠀⢹⠀⠀⠀⠳⡄⢀⣀⣱⡌⠻⣿⣶⣤⣴⣿⠟⠋⠉⠙⠛⢿⣷⣄⠀⠀ ⠀⢀⣤⣿⠟⠀⠀⠀⠀⠀⠈⠑⢦⣾⠟⠁⠀⠀⠀⠀⢸⠀⠀⣠⠤⠬⢍⡁⠀⠀⠀⣟⠙⢿⣿⠃⠀⠀⠀⠀⠀⠀⢻⢿⣿⡄ ⢀⣾⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣠⠏⠀⣸⠃⠀⠀⠀⢱⠀⠀⠀⢻⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡞⢀⣿⡿ ⣼⡏⠀⢰⡏⠀⣠⡆⠀⠀⠀⠀⠘⡏⠲⠦⠤⠴⠚⠁⠀⠀⠸⡄⠀⠀⠀⡸⠀⠀⠀⠀⠱⣾⡿⠀⠀⠀⠀⠀⠀⡸⠁⣼⣿⠃ ⢿⡇⠀⠈⠀⠀⠟⠀⠀⠀⡀⠀⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢰⢁⣾⡿⠃⠀ ⠘⣿⣄⠀⠀⠀⠀⠀⠀⣰⣥⣤⡾⠟⠛⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠠⢃⣿⡿⠃⠀⠀ ⠀⠈⠻⢿⣦⣄⣀⣀⣀⣠⡾⠋⠀⠀⠀⢰⠏⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣦⣀⣀⣀⣴⢁⣼⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⢻⣿⠏⡟⠀⠀⠀⠀⠀⡜⠀⠀⣿⣇⣀⠀⠀⢀⣀⣀⣤⣴⣾⡿⠋⠁⠀⠈⠛⠛⠛⠻⠿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡏⢀⠇⠀⠀⠀⠀⠀⠃⠀⢸⣿⡟⠛⠿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡀⣾⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣿⣦⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚫⚫⚫⚫⚫⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸⚫⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚪⚪⚪⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚪⚪⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚪⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸⚫⚫🌸🌸🌸🌸🌸🌸🌸⚫⚫🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸⚫⚫⚫⚫🌸🌸🌸🌸🌸⚫⚫⚫⚫🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸⚫⚪⚪⚫🌸🌸🌸🌸🌸⚫⚪⚪⚫🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚫🌸🌸🌸🌸🌸⚫⚪⚪⚫🌸🌸🌸🌸🌸⚫⚪⚪⚫🌸🌸🌸🌸🌸🌸⚫⚫⚪⚪⚪⚪ ⚪⚪⚪⚪⚫🌸🌸🌸🌸🌸⚫⚫⚫⚫🌸🌸🌸🌸🌸⚫⚫⚫⚫🌸🌸🌸🌸🌸🌸⚫🌸⚫⚪⚪⚪ ⚪⚪⚪⚫⚫🌸🌸🌸🌸🌸⚫⚫🔵⚫🌸🌸🌸🌸🌸⚫⚫🔵⚫🌸🌸🌸🌸🌸🌸⚫🌸⚫⚫⚪⚪ ⚪⚪⚫🌸⚫🌸🌸🌸🌸🌸⚫🔵🔵⚫🌸🌸🌸🌸🌸⚫🔵🔵⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚪ ⚪⚪⚫🌸🌸🔴🔴🔴🔴🌸⚫🔵🔵⚫🌸🌸🌸🌸🌸⚫🔵🔵⚫🌸🔴🔴🔴🔴🌸🌸🌸🌸🌸⚫⚪ ⚪⚫🌸🌸🌸🔴🔴🔴🔴🌸🌸⚫⚫🌸🌸🌸🌸🌸🌸🌸⚫⚫🌸🌸🔴🔴🔴🔴🌸🌸🌸🌸🌸🌸⚫ ⚪⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫ ⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🌸⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫ ⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🌸🌸⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫ ⚫🌸🌸⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🌸⚫⚫⚪ ⚫⚫🌸🌸⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚫⚫⚪⚪ ⚪⚫⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚪⚪⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚪⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫⚫⚫⚪⚪⚪⚪ ⚪⚪⚪⚪⚪⚫⚫⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🔴🔴🔴⚫⚪⚪⚪ ⚪⚪⚪⚪⚫🔴🔴🔴⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🔴🔴🔴🔴🔴⚫⚪⚪ ⚪⚪⚪⚫🔴🔴🔴🔴🔴⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫🔴🔴🔴🔴🔴🔴🔴⚫⚪ ⚪⚪⚫🔴🔴🔴🔴🔴🔴🔴⚫🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸⚫⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫ ⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫ ⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚪⚪⚪⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫ ⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚪⚪⚪⚪⚪⚫⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫ ⚪⚫⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚫⚪⚪⚪⚪⚪⚪⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚪ ⚪⚪⚫🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪⚪⚫🔴🔴🔴🔴🔴🔴🔴⚫⚫⚪ ⚪⚪⚪⚫⚫⚫⚫⚫⚫⚫⚫⚫⚫⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚪⚫⚫⚫⚫⚫⚫⚪⚪⚪

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⢠⣾⠟⠁⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⢻⡿⠿⣿⣄⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⣴⣶⣶⣦⣤⣄⡀⠀⢀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⢦⡄⠀⠀⠸⣏⢳⣄⠉⠙⢷⣦⡀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠟⠁⠀⠀⠀⠈⠙⠻⣷⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⣿⣆⠀⠀⢿⣿⣿⣧⠀⠀⠈⠻⢶⣄⣰⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠙⣿⣏⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀ ⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠇⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀ ⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⠉⠲⣄⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢹⣾⠃⠀⠀⢻⣦⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠘⣿⡆⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⠷⠦ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠋⠉⠉⠉⠉⠉⠓⠶⣤⣘⣿⡀⠀⠀⢰⣿⣆⡀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⡄⠀⣾⡿⠿⢿⣦⡀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢠⡿⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣾⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀ ⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠙⠶⣄⡀⠀⠀⠀⣀⣴⠟⢀⣾⠃⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦ ⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⢠⣾⣇⣀⣀⣀⣤⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣤⣤⣄⣀⣀⣠⣤⣤⣴⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢿⣤⣀⣀⣠⣤⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣉⣉⣉⣉⡉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟨🟨🟨🟨🟨🟨🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟨🟨🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟨🟨⬜⬜⬜⬜🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜🟨🟨⬜⬜⬜ ⬜🟨🟨🟨🟨🟨🟨⬜🟩🟩🟩🟩🟩🟦🟦🟦🟦🟦⬜⬜⬜🟨🟨🟨🟨🟨🟨⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟦🟦🟦🟦🟦⬜⬜🟨🟨🟨🟨🟨🟨🟨🟨 🟩🟨🟨🟨🟨🟨🟨🟥🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦⬜⬜🟩🟨🟨🟨🟨🟨🟨🟦 🟩🟩🟩🟨🟨🟥🟥🟥🟥🟩🟩🟩🟦🟦🟦🟦🟦🟦⬜🟩🟩🟩🟩🟨🟨🟦🟦🟦 🟩🟩🟩🟩🟥🟥🟥🟥🟥🟩🟩🟦🟦🟨🟨🟦🟦🟦🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟩🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟥🟥🟥🟥🟥🟨🟨🟨🟨🟨🟨🟨🟨🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟨🟨🟨🟨🟨🟨🟦🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟨🟨🟦🟦🟦🟦🟩🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦🟩🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟩🟩🟩🟥🟥🟥🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦🟩🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟩🟩🟩🟥🟥🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟩🟩🟩🟥🟥🟩🟩🟩🟩🟦🟦🟦🟦🟦🟦🟦🟦🟩🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟦🟩🟩🟩🟥🟩🟩🟩🟩🟦🟦🟦🟦🟥🟦🟦🟦🟦🟩🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟦🟩🟩🟩🟥🟩🟩🟩🟩🟦🟦🟦🟦🟥🟥🟦🟦🟦🟦🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟦🟦🟩🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦🟥🟥🟥🟦🟦🟦🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟦🟦🟩🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜🟥🟥🟥🟦🟦🟦🟦🟦🟦 🟩🟩🟩🟩🟦🟦🟦⬜🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜🟥🟥🟦🟦🟦🟦⬜ ⬜🟩🟩🟩🟦🟦⬜⬜🟩🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜🟥🟦⬜⬜⬜ ⬜⬜⬜🟩🟦⬜⬜⬜⬜🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟩🟦🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩🟩🟦🟦🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟦⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣅⣨⣇⠀⠀⠀⣇⣀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡷⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀ ⢠⠒⠀⠒⢤⠘⢯⡽⠁⠀⠀⠀⢷⣭⠇⢀⠤⠀⠠⢄ ⠈⠒⠀⠘⠊⠀⠀⠀⠈⠒⠒⠊⠀⠀⠀⠈⠂⠭⠭⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⢻⡄⠀⠀⠀⠀⠀⣸⠋⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⣠⣾⡧⠀⠀⠀⠀⠀⣿⣦⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⡻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠖⠋⠉⠉⠓⢦⡀⠀⢿⣤⣴⡿⠀⠀⠀⠀⠀⠀⠸⣷⣤⣼⠇⠀⢀⣠⠤⠀⠠⠤⣄⡀ ⠷⣄⠘⠀⠀⣢⣠⠟⠀⠀⠉⠋⠀⠰⣦⣀⣀⣀⣶⠀⠉⠉⠉⠀⠀⠸⣄⠀⠠⠶⠤⣀⡷ ⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠂⠊⠌⠈⠈⠁⠁⠂⠢⠠⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀ ⠀⢀⠴⠣⠀⠀⠀⠀⠀⠈⠀⢄⣀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡠⠃ ⠑⢄⡀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠉⢦⠀⢰⠋⠀⠀⠀⠀⠀⠉⣷⠉⠉⠀⠀ ⠀⠀⠀⠉⢨⡃⠀⠀⠀⠀⠀⠀⠀⢀⣧⢇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⣀⠤⠊⠁⠈⠢⣀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⢿⣄⠀⠀⠀⠉⠙⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⣄⠀⠀⠀⠀⢸⠁⠈⢣⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠸⡆⠀⠀⠀⠸⣇⠀⠈⣧⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣠⣿⠀⠀⠀⠀⢻⣷⣾⣿⡆⠀⠀⠀⠀⠹⣆⠀⠀⢰⡿ ⠀⠀⠀⠀⢠⡿⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠘⡿⠿⠟⣇⠀⠀⠀⠀⠀⢹⡆⢀⣿⠃ ⠀⠀⠀⢠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠀⡇⠀⠀⠀⠀⠹⡀⠀⡏⢀⣴⣿⣿⣿⠀⢿⡿⠁⠀ ⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠳⣤⡼⠁⠀⠀⠀⠀⠀⠙⠚⠁⡈⣛⠟⠛⠉⠀⢸⣧⠀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠃⠀⠀⢀⢲⡦⡀⠀⠀⠀⣀⣠⣤⣾⡿⠏⠀⠀⠀⠀⠀⣿⠀⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡯⠭⣭⣿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢶⣿⣿⡛⠛⠛⠛⠾⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀ ⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠐⠛⠛⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀ ⠀⠀⠉⠛⠷⢶⣶⠶⠶⠶⠖⠛⠋⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠀⠲⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⡴⠋⣹⡏⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣠⡴⠶⠛⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠉⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣤⣶⠆⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠙⣛⣡⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔𝐏𝐈𝐂𝐊𝐀𝐂𝐇𝐔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠂⠉⠁⠀⠀⠀⠀⠀⠈⠨⠑⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠠⠘⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠬⢅⢠⡂⠁⠀⢰⠉⣳⡄⠀⠀⢠⡴⠒⣿⡍⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠀⠐⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠂⠉⣑⣠⡀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢠⡊⠀⠀⢠⣿⣤⡿⠀⠀⠀⢀⡄⢀⣿⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠄⠘⠤⠀⠀⠀⢀⢞⠀⠀⠀⠠⠈⡒⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀ ⠀⡜⠅⠌⠀⠀⠀⠀⠀⠒⠘⠓⠤⠤⢎⣄⠐⠒⢠⠀⢀⠇⠀⣀⡀⢻⣿⡿⢀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢄⠀⠀⠀ ⢈⡇⢠⠀⠀⠀⠀⠀⠀⠀⢀⠂⡟⣀⣀⠀⠑⠌⠁⠀⠈⡆⠀⢳⢎⡌⠋⡐⠉⠓⠋⠙⡈⠻⠿⢁⢦⡹⣍⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢄⠀ ⠈⡇⠀⠀⠀⠀⠀⠀⢀⣤⣫⠎⠁⠀⠠⠄⠀⠀⠀⠀⠀⢧⠀⠀⠉⠁⠀⠀⠐⡄⢦⠀⠃⠀⠀⠫⠶⠕⠚⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⣄⠀⠀⠘⡄ ⠀⢋⠀⠀⠀⠀⠀⠘⠩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠀⠀⠀⠀⢸ ⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⢈⡼⠦⠖⠐⠒⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠡⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘ ⠀⠀⠀⠀⠉⠒⠴⠂⢄⡤⡀⣀⠀⡂⠡⢀⢔⠓⠀⠀⠀⠀⠀⠀⠀⠈⣷⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⣿⣧⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣻⢷⣯⣶⣦⣤⣤⣤⣤⣶⢶⣷⣻⢯⣿⣿⣿⡇⣸⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣻⣞⣷⣻⢿⣯⢷⣻⣞⡿⣾⣽⣻⢾⣿⣿⠏⠘⡄⠀⠀⠀⠀⠐⣠⠋⠀⠀⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⢷⣻⡾⣽⣻⣿⣯⢷⣯⣟⡷⣯⣟⣯⣿⢿⠇⠀⠀⠀⠀⠀⠄⠚⠀⠀⢀⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣷⣻⢯⣿⣿⠿⣟⡾⣽⣻⢷⣻⠾⠍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣽⣿⣿⠟⠀⠙⢿⡷⣯⢿⣽⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠙⠛⠿⠟⠛⡉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⢠⠀⠀⡰⠀⡴⢀⠕⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠎⠠⠰⠁⠜⠁⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢉⡉⢙⣿⣋⣙⣳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⡰⠃⠀⠀⠈⢇⠀⡀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇⠀⡇⠀⠀⣼⣿⡜⢸⣿⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣠⠟⠁⠀⡇⠀⠀⠹⢿⣡⠞⠛⠉⠉⠉⠉⠛⠷⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠿⠀⠀⠀⠃⠠⠤⣠⠞⠁⠀⠀⠀⠀⠐⢦⠀⣴⠊⠻⣦⠀ ⠀⠀⠀⠀⠀⣠⣴⢾⣿⠕⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⠀⢹⣯⢸⡇⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷ ⠀⠀⠀⠀⠀⠀⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⡀⠀⠀⠀⠀⢀⣠⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣬⣻⣦⣄⡀⠀⠀⠀⠀⠉⠳⠶⣤⣤⣀⣀⣀⣤⡶⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⣭⡿⠛⣿⠛⢢⠀⠙⢲⣾⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⣼⡷⣦⣄⣀⣶⡟⠁⠀⢀⡿⠁⣴⣟⠀⡘⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⢹⡟⢹⣆⠀⣀⡾⠃⣸⡏⠙⣧⡇⠀⡀⠀⠈⣿⡴⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠈⢳⣄⡉⠉⠉⣠⡴⢻⡇⠀⠈⡷⠛⠉⠛⢦⣿⢰⡇⢀⡿⠶⣄⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠈⠉⠛⠋⠉⠀⠀⢷⡀⠀⠁⠀⠀⠀⠘⠻⣮⠷⣾⡁⠀⣹⡇⠀⠀⠀⠀ ⠀⠈⢿⣤⣀⠀⠀⠀⠀⢀⣀⠴⠊⠻⣆⠀⠀⠀⠀⢠⣴⠟⠀⠈⣹⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣶⣌⠉⠉⠉⠁⠀⢀⣀⣀⡙⠶⣤⣤⣴⣿⣉⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠟⠛⠛⣻⠿⠛⠉⠉⠙⢷⣴⠟⠋⠈⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠒⠂⠀⠃⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢯⣭⣭⣍⣒⣒⣒⣒⣪⣽⣯⣭⣭⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡠⠒⠉⢉⣑⠢⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠎⢦⠀⣨⠞⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀ ⠀⢸⠀⠀⠀⢂⠈⡟⢡⠎⣀⣤⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⡠⠊⢠⠞⢁⡽⡄⠀ ⠀⡇⠀⠀⠀⠀⣜⣤⡷⠉⠘⡠⠱⡴⠀⠀⠀⠀⠀⡏⠈⠳⠁⠀⠁⠠⠃⢀⠇⠀ ⠀⡇⠀⠀⠀⡸⢸⠁⠔⠒⣄⠃⢸⠜⠊⠉⠑⡄⠀⠈⡆⠀⡀⡀⠀⠀⠀⠎⠒⢢ ⠀⡼⠀⠀⠀⡗⠉⠀⠃⠀⢿⠄⠉⠀⠀⠀⠀⡸⠀⠀⣥⠀⠁⠡⠂⠀⢀⠤⠴⠊ ⢸⠀⠀⠀⢀⠑⠤⠤⢄⠀⢉⠀⢀⣀⣀⣀⣴⡇⠀⠘⣄⠀⠀⠀⢀⡤⠃⠀⠀⠀ ⠀⠣⢄⡰⠊⣑⠢⠄⠴⠁⢸⣿⣿⣿⣟⡛⡟⠀⢀⠎⠀⠑⠢⡤⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠊⠑⠀⣀⠀⠀⠈⢟⠁⠲⡇⣧⡔⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠒⠊⢣⠙⠦⡀⠀⠐⠂⡰⢻⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⡀⢸⣀⠦⢞⡖⠊⠹⠀⠸⡀⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠉⠉⠉⠐⠃⠀⢱⡀⡠⠔⢏⠱⡀⡇⠀⠀⠙⠦⣀⠀⡘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⡯⠀⠠⠇⠈⡽⠋⠀⠀⠈⢢⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⡼⠂⠀⠈⠀⠈⣄⠀⢀⡤⠊⢉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⢸⣀⡠⢄⡀⠀⠀⠀⢉⠥⠓⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠈⠉⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠊⢇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠸⡂⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢏⢆⠀⠑⠦⢀⣀⡀⠴⢻⠈⡇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⢕⡢⢤⣀⣀⣀⡠⡞⢠⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠔⠚⠁⡜⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⣁⣀⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠤⢄⡀⠉⠲⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠈⠑⢌⢢⠀⠈⢦⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⣇⢣⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢣⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡏⡆⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣴⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

___________________▄▄▄▀▀▀▀▀▀▀▄ _______________▄▀▀____▀▀▀▀▄____█ ___________▄▀▀__▀▀▀▀▀▀▄___▀▄___█ __________█▄▄▄▄▄▄_______▀▄__▀▄__█ _________█_________▀▄______█____█_█ ______▄█_____________▀▄_____▐___▐_▌ ______██_______________▀▄___▐_▄▀▀▀▄ ______█________██_______▌__▐▄▀______█ ______█_________█_______▌__▐▐________▐ _____▐__________▌_____▄▀▀▀__▌_______▐_____________▄▄▄▄▄▄ ______▌__________▀▀▀▀________▀▀▄▄▄▀______▄▄████▓▓▓▓▓▓▓███▄ ______▌____________________________▄▀__▄▄█▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▄ ______▐__________________________▄▀_▄█▓▓▓▓▓▓▓▓▓▓_____▓▓____▓▓█▄ _______▌______________________▄▀_▄█▓▓▓▓▓▓▓▓▓▓▓____▓▓_▓▓_▓▓__▓▓█ _____▄▀▄_________________▄▀▀▌██▓▓▓▓▓▓▓▓▓▓▓▓▓__▓▓▓___▓▓_▓▓__▓▓█ ____▌____▀▀▀▄▄▄▄▄▄▄▄▀▀___▌█▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓__▓________▓▓___▓▓▓█ _____▀▄_________________▄▀▀▓▓▓▓▓▓▓▓█████████████▄▄_____▓▓__▓▓▓█ _______█▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓█▓▓▓▓▓██▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓██▄▄___▓▓▓▓▓█ _______█▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓█▓▓███▓▓▓▓████▓▓▓▓▓▓▓▓▓▓▓▓▓██▓▓▓▓▓▓█ ________█▓▓▓▓▓▓▓▓▓▓▓▓▓▓█▓█▓▓██░░███████░██▓▓▓▓▓▓▓▓▓▓██▓▓▓▓▓█ ________█▓▓▓▓▓▓▓▓▓▓▓▓▓▓██▓░░░░░█░░░░░██░░░░██▓▓▓▓▓▓▓▓▓██▓▓▓▓▌ ________█▓▓▓▓▓▓▓▓▓▓▓▓▓▓███░░░░░░░░____░██░░░░░░░██▓▓▓▓▓▓▓██▓▓▌ ________▐▓▓▓▓▓▓▓▓▓▓▓▓▓▓██░░░░░░░________░░░░░░░░░██████▓▓▓▓▓█▓▌ ________▐▓▓▓▓▓▓▓▓▓▓▓▓▓▓██░░░░░░___▓▓▓▓▓░░░░░░░███░░███▓▓▓▓▓█▓▌ _________█▓▓▓▓▓▓▓▓▓▓▓▓▓██░░░░░___▓▓█▄▄▓░░░░░░░░___░░░░█▓▓▓▓▓█▓▌ _________█▓▓▓▓▓▓▓▓▓▓▓▓▓█░░█░░░___▓▓██░░░░░░░░▓▓▓▓__░░░░█▓▓▓▓██ _________█▓▓▓▓▓▓▓▓▓▓▓▓▓█░███░░____▓░░░░░░░░░░░█▄█▓__░░░░█▓▓█▓█ _________▐▓▓▓▓▓▓▓▓▓▓▓▓▓█░█████░░░░░░░░░░░░░░░░░█▓__░░░░███▓█ __________█▓▓▓▓▓▓▓▓▓▓▓▓█░░███████░░░░░░░░░░░░░░░▓_░░░░░██▓█ __________█▓▓▓▓▓▓▓▓▓▓▓▓█░░░███████░░░░░░░░░░░░░░_░░░░░██▓█ __________█▓▓▓▓▓▓▓▓▓▓▓▓█░░░███████░░░░░░░░░░░░░░░░░░░██▓█ ___________█▓▓▓▓▓▓▓▓▓▓▓▓█░░░░███████░░░░░░░░░░░█████░██░░░ ___________█▓▓▓▓▓▓▓▓▓▓▓▓█░░░░░░__███████░░░░░███████░░█░░░░ ___________█▓▓▓▓▓▓▓▓▓▓▓▓▓█░░░░░░█▄▄▄▀▀▀▀████████████░░█░░░░ ___________▐▓▓▓▓▓▓▓▓▓▓▓▓█░░░░░░██████▄__▀▀░░░███░░░░░█░░░ ___________▐▓▓▓▓▓▓▓▓▓▓▓█▒█░░░░░░▓▓▓▓▓███▄░░░░░░░░░░░░░░░______▄▄▄ ___________█▓▓▓▓▓▓▓▓▓█▒▒▒▒█░░░░░░▓▓▓▓▓█░░░░░░░░░░░░░░░▄▄▄_▄▀▀____▀▄ __________█▓▓▓▓▓▓▓▓▓█▒▒▒▒█▓▓░░░░░░░░░░░░░░░░░░░░░____▄▀____▀▄_________▀▄ _________█▓▓▓▓▓▓▓▓▓█▒▒▒▒█▓▓▓▓░░░░░░░░░░░░░░░░░______▐▄________█▄▄▀▀▀▄__█ ________█▓▓▓▓▓▓▓▓█▒▒▒▒▒▒█▓▓▓▓▓▓▓░░░░░░░░░____________█_█______▐_________▀▄▌ _______█▓▓▓▓▓▓▓▓█▒▒▒▒▒▒███▓▓▓▓▓▓▓▓▓▓▓█▒▒▄___________█__▀▄____█____▄▄▄____▐ ______█▓▓▓▓▓▓▓█_______▒▒█▒▒██▓▓▓▓▓▓▓▓▓▓█▒▒▒▄_________█____▀▀█▀▄▀▀▀___▀▀▄▄▐ _____█▓▓▓▓▓██▒_________▒█▒▒▒▒▒███▓▓▓▓▓▓█▒▒▒██________▐_______▀█_____________█ ____█▓▓████▒█▒_________▒█▒▒▒▒▒▒▒▒███████▒▒▒▒██_______█_______▐______▄▄▄_____█ __█▒██▒▒▒▒▒▒█▒▒____▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒____▒█▓█__▄█__█______▀▄▄▀▀____▀▀▄▄█ __█▒▒▒▒▒▒▒▒▒▒█▒▒▒████▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______█▓▓█▓▓▌_▐________▐____________▐ __█▒▒▒▒▒▒▒▒▒▒▒███▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒_______█▓▓▓█▓▌__▌_______▐_____▄▄____▐ _█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒_____█▓▓▓█▓▓▌__▌_______▀▄▄▀______▐ _█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒███████▓▓█▓▓▓▌__▀▄_______________▄▀ _█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒███▒▒▒▒▒▒▒██▓▓▓▓▓▌___▀▄_________▄▀▀ █▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒█▓▓▓▓▓▀▄__▀▄▄█▀▀▀ █▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▓▓▓▓██▄▄▄▀ █▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒████ █▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▄▄▄▄▄ _█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒███▒▒▒▒▒▒██▄▄ __█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒███▒▒▒▒▒▒▒▒▒▒▒▒▒█▄ __█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ __█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒▒▒▒██▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ ___█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒▒▒▒▒▌ ____█▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒▒▒▒█▒▒▒▒█▒▒▒▒▒▒█▒▒▒▒▒▒▒▒▒░░░░░░░░░░░░░▒▒▌ ____█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█████████████▒▒▒▒▒█▒▒▒▒▒▒▒▒░░░░▒▒▒▒▒▒▒▒▒▒▒░▒▌ _____█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______▐▒▒▒▒█▒▒▒▒▒▒▒░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▌ ______█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█________█▒▒█▒▒▒▒▒▒░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▌ _______█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█________█▒█▒▒▒▒▒▒░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▌ ________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█________█▒▒▒▒▒▒░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█________█▒▒▒▒░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█________█▒▒▒░░░░░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▀ __________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______█▒░░░▒▒▒▒▒░░░░░░░░▒▒▒█▀▀▀ ___________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______█░▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░█▀ ____________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█▀ _____________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______█▒▒▒▒▒▒▒▒▒▒▒▒█▀ _____________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█_______▀▀▀███████▀▀ ______________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _______________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ ________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ __________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒██▒█ ___________________█▒▒▒▒▒▒▒▒▒▒▒▒▒██▒▒▒▒█ ___________________█▒▒▒▒▒▒▒▒████▒▒▒▒▒▒▒█ ___________________█████████▒▒▒▒▒▒▒▒▒▒▒█ ____________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ ____________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒█ _____________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▌ _____________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▌ ______________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░▌ _______________________█▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░█ ________________________█▒▒▒▒▒▒▒▒▒▒▒░░░█ __________________________██▒▒▒▒▒▒░░░█▀ _____________________________█░░░░░█▀ _______________________________▀▀▀▀

╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

╱|、 =(˚˕ 。 7 |、 ~〵 じし ˍ,)づ

⬜⬜⬜🟥🟥🟥🟥🟥⬜⬜⬜⬜ ⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜ ⬜⬜🟩🟩🟩🟨🟨🟩🟨⬜⬜⬜ ⬜🟩🟨🟩🟨🟨🟨🟩🟨🟨🟨⬜ ⬜🟩🟨🟩🟩🟨🟨🟨🟩🟨🟨🟨 ⬜🟩🟩🟨🟨🟨🟨🟩🟩🟩🟩⬜ ⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜ ⬜⬜🟩🟩🟥🟩🟩🟩⬜⬜⬜⬜ ⬜🟩🟩🟩🟥🟩🟩🟥🟩🟩🟩⬜ 🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩 🟨🟨🟩🟥🟨🟥🟥🟨🟥🟩🟨🟨 🟨🟨🟨🟥🟥🟥🟥🟥🟥🟨🟨🟨 🟨🟨🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨 ⬜⬜🟥🟥🟥⬜⬜🟥🟥🟥⬜⬜ ⬜🟩🟩🟩⬜⬜⬜⬜🟩🟩🟩⬜ 🟩🟩🟩🟩⬜⬜⬜⬜🟩🟩🟩🟩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠙⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⢸⠁⠀⡴⢲⠀⠀⠀⠀⢸⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⠀⠀⢰⠃⠀⠀⣇⣼⡇⠀⠀⠀⢸⡿⠏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⡼⠀⠀⠀⣿⣟⣿⠀⠀⠀⠀⠇⠀⠀⡅⣞⣩⣭⣭⣇⠖⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇ ⠀⠀⡇⠀⠀⠀⣏⠀⢨⠀⠀⠀⠀⠘⠦⠶⠋⠙⠛⠋⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸ ⢠⠀⢷⣞⡇⠀⢇⣠⠏⢠⠖⢲⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸ ⢘⠀⢹⠉⠁⠀⠀⠀⠀⠀⣇⠀⣸⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡏ ⠀⠇⠈⢇⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠏⠀ ⠀⠸⡀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀ ⠀⠀⠑⠂⠈⢣⣀⠀⠀⠀⠀⠀⢀⡒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⢦⡀⠀⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡅⠀⠈⠉⡳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⡞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⢀⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⡰⠋⠁⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡁⠀⠀⠀⠀⠀⠀⢀⢉⣿⠀⠍⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⠉⠀⠀⡀⠀⠀⠀⢨⢿⡂⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣄⠐⣿⠀⠀⠀⠀⠁⠀⠙⣆⠀⠀⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠃⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇⠸⡄⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⢧⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⡇⠀⢸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠃⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡈⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠳⣽⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⢷⣆⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⠀⠀⠘⣧⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣷⠀⠀⠀⢸⠀⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢠⠃⠀⠀⠀⠘⠒⠚⠁⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡹⠃⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⡇⠀⠀⠀⠀⣀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡎⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠞⠀⠀⠀⢀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠃⡀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠂⠀⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠀⠀⡀⠄⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠁⠀⠠⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⠀⠂⡐⠀⣂⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢛⠅⣃⣶⣶⡲⠄⢀⠘⡇⡀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⣺⣿⡀⣶⣿⣿⣿⣿⠀⠀⠀⡒⢴⢸⡀⠈⠷⣄⣀⣀⣤⠤⠶⠶⠒⢶⣶⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⣟⣿⣿⣿⡏⣿⢿⣿⠟⠀⠀⠐⠀⠂⠀⣤⣽⣽⡂⠼⣧⠀⠀⠠⣤⠀⣠⣶⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⣿⡿⢻⣷⣆⠂⢃⠀⣀⣀⣂⡀⢀⣿⣿⣿⣿⣻⠂⠐⡂⠁⠰⠀⣓⡿⠛⠛⢿⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡷⠓⠿⣿⣁⢀⣀⠀⠀⠈⠉⠁⠙⣿⣾⣿⣿⠏⠁⠀⣶⡴⠖⠋⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠛⠛⠛⠻⣇⠀⠀⠀⠀⠀⣈⣙⡋⠀⠈⠙⣿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠛⠛⢷⣄⣀⣺⣿⣾⣿⠂⠀⣰⠇⠀⠀⠀⢀⣤⣶⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⢦⣄⡀⠀⠀⠈⠛⢿⣿⣻⠿⠋⠀⡰⠃⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠉⠳⠶⢤⣤⣤⢭⠥⠤⠴⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣁⣼⣠⣴⡴⡶⢶⣤⣤⡸⣇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠉⠁⢀⠀⠀⠀⡀⠀⠉⠛⠷⡀⠀⠀⠀⠹⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⣾⠀⠀⠀⣿⣤⠀⠀⠀⠙⡄⠀⠀⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⣿⡇⠀⠐⢹⠯⠀⠀⠀⠀⢳⠀⢾⣽⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣽⣿⣶⣦⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣑⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⠘⠋⠙⠦⠒⠉⠹⠟⠋⠒⠦⠔⠻⠿⠗⠒⠶⠤⢀⣟⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⡤⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢤ ⢣⡀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠀⢀⡜ ⢸⡉⠒⠄⠀⠀⠀⢉⡙⢢⠀⠀⡔⢋⡉⠀⠀⠀⠠⠒⢉⡇ ⠀⠉⢖⠒⠀⠀⠀⣇⠀⣸⠀⠀⣇⠀⣸⠀⠀⠀⠒⡲⠉⠀ ⠀⠀⠀⠉⠙⠫⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠝⠋⠉⠀⠀⠀

⣯⢽⣣⡜⣦⣶⣒⡦⣔⣾⣿⣿⣿⠿⣟⡯⣿⣼⣿⣾⣿⣿⡿⠿⠿⣛⣻⡭⠥⠶⠴⠾⠶⠽⠿⢿⣿⣿⡿⣟⢿⢫⠟⣭⠳⣭⢋⠷⣩⠳⣍⠞⣥⢫⡜⣱⢊⠴⡀⢆⠠⢄⡀⢿⣿ ⠠⢂⠤⢉⠌⣙⠻⢿⣿⢿⣭⣷⣯⣿⣿⠿⡿⠛⡏⣙⣰⠴⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠧⣻⣌⠟⡴⣋⠳⣥⢛⡬⢛⡴⢣⠞⣥⢋⡞⡱⢊⡕⢢⠜⣹⣿ ⣆⢣⢂⡥⢎⣤⢳⣞⣾⣿⣿⣏⣯⡙⠤⢡⣐⣡⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢵⣩⠳⣌⠳⣜⢣⠞⣡⢛⡴⢋⡴⣉⠧⣘⠥⣊⠽⣿ ⣿⣧⣿⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⡬⣓⠬⢎⡜⣡⠎⡴⣉⢆⣉⠚⡌⠲⢡⢚⣿ ⣿⢻⡻⣟⢿⡻⣟⡿⣟⣿⡻⣏⣿⣹⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡎⡖⣥⢚⡴⢡⠎⡔⢣⠜⡡⢣⡘⣿ ⣛⢮⠳⣝⡎⣷⣙⢧⣻⡭⢷⣻⡽⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢷⣩⢞⡱⢎⡖⡱⢎⡔⢣⡌⣳⡽ ⣯⣞⡽⣺⣜⡳⣎⡟⣶⢻⡽⡾⠁⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣖⣫⡝⣮⡜⢧⡳⣜⢣⡜⣧⣟ ⡷⣏⡾⡵⣎⠷⣍⠾⣥⢻⣼⠃⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣱⡝⣶⢹⣣⢳⢭⢣⠟⣶⣫ ⡿⣜⡳⡵⣭⢞⡭⣞⣥⢳⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡟⣼⢣⡗⢯⡞⣽⢺⡵⢯ ⡟⣼⣱⢳⡳⣎⢷⣹⣎⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢸⡝⣮⢳⡝⣧⢻⣬⢳⣻⢯ ⣟⡶⣭⣳⢽⣚⣯⣳⢾⣇⠐⡌⠉⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⣧⢞⡵⣫⢖⡯⢷⣯ ⡿⣼⣳⡽⡾⣽⢶⣯⠿⢻⡷⢿⣴⣼⣄⡠⢀⠀⡀⣌⢀⡀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢆⠢⠈⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢹⣾⡱⣏⢾⡱⣏⣾⢻⣼ ⣟⢧⣟⡾⣽⣳⠟⠁⠀⢸⡻⣿⣯⢾⣿⣿⣷⣾⣤⣋⠰⣜⣬⢲⣥⢦⡷⣬⠲⣔⡲⢅⠢⢄⣂⣦⡙⠦⡁⠱⡀⠐⡀⠂⠌⢀⠂⠀⡁⠀⠀⠠⠐⢠⢩⢾⢧⡝⣮⠳⣝⢾⣱⡟⣾ ⣟⡾⢮⣽⠗⠁⠀⢀⠀⠸⣷⣹⡾⣏⣿⣿⣿⡿⠡⢀⠘⣾⣿⣷⣾⡿⡾⣯⣷⣧⣾⣥⣻⣼⣻⠖⡍⢒⠄⠃⡄⠡⠀⠄⡐⠠⢀⠁⡠⠈⣐⡲⠥⠶⢼⣾⡳⣝⢮⡻⣜⣯⢷⣻⢷ ⡟⣞⢿⠎⠀⠀⠀⠀⠡⢸⢻⣿⠹⢷⣾⡿⠿⣃⢈⡀⢦⣾⡱⠙⢿⣷⡩⣝⣻⠿⣯⣟⣿⡷⢋⠜⡈⢆⠊⡡⠄⡡⠘⣀⢂⠡⢂⠔⣠⡼⠋⠀⠀⠀⠀⠙⠳⣝⢮⡳⣝⡾⢯⣟⣯ ⣳⣝⡞⠠⠄⢀⢀⡀⠀⢸⢮⣿⡄⠈⠉⠁⢀⡟⠘⠃⣼⡯⠁⠀⠈⠙⢧⣽⣯⣤⣽⠛⢋⡁⢎⠰⠡⢌⠢⡁⢆⠡⣂⠍⡘⢄⠊⣴⡿⢁⠀⠀⠀⠀⠀⠀⠀⠙⢮⣳⡽⣳⣞⡿⣽ ⣳⢾⡁⠀⢀⠀⠌⡈⠃⣼⡯⣗⣿⣢⢄⢠⠾⠁⠀⠸⠵⠛⢲⡄⠀⡠⣀⣈⡉⠉⠁⣈⢐⣌⢦⢣⡍⢆⡱⢈⠆⡱⢀⠎⡱⢈⠆⠁⠐⢄⠂⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⣫⢿⡽ ⣳⣻⢴⣅⢊⠤⢣⢌⡱⣿⣷⣚⣯⣿⣿⣿⢿⣦⣾⣶⣤⣤⣤⣿⣄⡁⠐⠒⠂⢀⠠⢆⣿⣚⢧⣳⢚⡔⢢⠱⢌⠰⡁⢎⠰⡁⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣯⣟ ⢧⣛⢶⣪⢷⣎⣳⣎⣵⣿⢿⣾⣹⣿⣿⠉⢞⡻⣿⣿⠿⠟⠋⠍⡙⠿⣷⣦⣬⢰⠡⢿⣳⡹⢎⠶⣩⠚⠄⠣⢌⠢⡑⢌⠒⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢯ ⡻⣜⢧⣛⢮⣳⢽⡺⣽⢯⣏⣿⡷⣏⡿⣿⢾⡿⠿⠶⣶⣤⣀⡀⠀⠠⢌⡹⢯⡧⡙⢞⡷⢻⣬⠳⢥⡉⢬⡑⢌⢢⡑⢎⡜⢄⠣⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟ ⡷⣹⢮⣝⡳⣽⣚⡷⣹⢿⡼⣷⣿⣿⣟⡽⣳⣾⣶⣶⣤⣌⣭⣽⡿⠟⠭⡩⢭⣹⢽⢣⡘⢥⢢⡙⢦⡙⢦⡙⡬⢦⡙⢦⣚⣼⢣⢅⠢⡐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⣟⣵⣫⢞⡵⣣⢯⡽⣛⣟⠻⣽⣹⣾⣿⣿⡵⣯⣤⣍⣍⣛⠛⣃⡐⠌⢢⡑⢦⡙⢮⡱⣚⢬⡣⣝⠶⣩⢧⡝⣧⢧⣽⣞⣿⢺⡭⣞⡵⣈⡌⢥⠘⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣛⡶⡽⣞⣳⣛⣮⠷⣯⣞⣿⢿⡹⢧⢻⡽⣽⣷⣏⡿⣹⡻⣟⡶⢮⡜⣦⣙⢦⣝⡲⡽⣱⢧⡻⣜⡏⡷⣋⢾⡱⣏⣞⣿⢾⣻⡼⣳⡝⣶⣘⠦⢭⡐⡩⠌⡁⢆⠠⢀⠀⡀⠀⠀⢼ ⣟⠾⣵⢯⣗⣻⣼⣻⣳⣾⠛⣧⡝⢮⣳⣼⢿⣿⣿⣼⣳⡽⣳⣻⢯⣟⣾⡽⣾⢼⣳⡝⣧⢏⡷⣣⢟⡵⣫⢞⣵⠯⣞⢾⣿⣿⣿⣵⣛⢶⣫⢟⣳⢼⡱⣊⡔⢪⠔⣢⠒⣌⡱⢌⣾ ⠾⣝⣯⣟⣾⣳⣏⣷⡟⠀⠀⠈⣿⣽⣇⣽⣾⣯⣟⣿⣿⣿⣿⣯⣿⣞⣷⡿⣽⣯⢷⣯⡳⣏⢾⡱⣏⢾⣱⣻⡾⠟⠚⡉⠛⢿⣿⣿⣿⣷⣯⣞⡽⣎⢷⣳⢞⣣⢯⡵⣫⢶⣹⡿⣯ ⣶⢯⡽⣹⢏⡿⣽⡟⠁⠀⠀⠀⢹⣿⡽⢏⣻⢯⣽⢻⣿⣿⣿⣿⣯⣿⣿⣷⣿⣿⣾⣯⣷⣻⣞⣷⣿⡾⠟⢋⠡⠐⠠⠁⠐⢈⠙⢻⣿⣿⣿⢿⣷⢻⡼⣏⡾⣻⡜⣧⣻⡼⣟⣧⢻ ⣟⣮⢷⣽⣫⢷⣿⠇⠀⠀⠀⠀⠀⠹⣞⠿⣝⢯⠾⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡥⠊⢁⠂⠄⠁⠀⢐⡚⡶⠈⠄⣘⠻⢿⣯⣟⣷⣿⣼⣳⣭⢿⡵⣯⣽⢻⡼⣻ ⣟⣮⢿⡼⣯⣟⣿⣎⠡⠄⡀⠄⣠⠂⢻⣿⡭⣯⣿⣻⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠞⡠⢁⠂⠄⠀⠀⣀⡬⡈⠁⠰⢤⡌⣎⢙⢛⣿⣾⣷⣻⣾⣽⣾⣽⣫⣞⢯⣷⢻ ⡟⡾⢧⣟⣶⣿⢯⣿⣾⣆⡱⣈⠤⡑⢌⢻⣷⡽⣮⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣧⢣⠂⠌⠀⠂⠀⢻⢐⢯⠀⢦⠁⠀⣹⡸⣀⢚⣿⣷⣿⣽⣻⣞⣿⣟⢾⣳⣞⢯ ⡾⡵⢯⣜⡮⣝⡻⣟⣿⣿⣿⣷⣟⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣧⢇⠣⠀⠄⠀⠀⠀⠁⠀⠙⣅⠀⡠⠟⡔⣉⢧⣿⣿⣯⣿⣷⣿⣽⣞⢯⣗⡯⣟⭐⭐⭐⭐

⠀⠀⣠⡴⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀ ⢀⡞⠁⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢙⡇ ⢸⡇⠀⠀⠀⠀⠀⣰⢳⠀⣴⢳⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⣻⠀⠀⠀⠀⠀⢿⡇⠀⢿⡾⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⢹⡄⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⠀⠀⢎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁ ⠀⠀⣾⠈⠣⣄⣀⡀⠀⠀⠀⠀⢀⣠⡠⠞⢹ ⠀⠀⢯⡁⠀⠀⠀⠈⢉⡏⠉⣯⡉⠁⠀⠀⢘⡅ ⠀⠀⠀⠘⠲⠤⠤⠴⠛⠀⠀⠈⠳⠤⠤⠒⠋

╱|、 (˚ˎ 。7 |、˜〵 じしˍ,)ノ

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣔⣦⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣠⣖⣆⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣀⠔⠚⠛⠿⠛⠻⢧⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠛⠺⢿⣷⣾⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡌⢀⡼⣄⣀⠴⣆⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⡀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⣼⣏⣷⠀⠫⣿⠇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣀⣠⣶⣾⠗⠻⣷⡄⠾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣷⡼⣎⠉⣦⠉⣽⡼⡇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡇⣟⣿⢿⣏⠆⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠯⣵⣿⣮⣿⡷⠷⢤⡈⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⡈⠉⣰⣿⣿⣄⣀⠶⣋⣽⣷⣳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⡴⣼⢿⡏⢹⠀⠀⢀⣹⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣴⡞⠉⣘⣿⣵⣺⠟⠋⠛⢿⠿⠀⠀⠀⠀⠀⠀ ⢀⣰⣦⡀⣠⠔⠚⣃⣺⡗⣧⢿⣾⠇⠈⡗⣶⣾⢷⠀⣀⣈⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⣿⣹⡽⢸⡀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀ ⠈⢹⣆⡭⠔⠒⠉⠀⠀⠀⣨⠦⣄⣠⠼⣓⡿⠧⢬⢥⡤⢲⡈⢻⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⣋⡥⣞⣿⡙⠛⠁⣠⠿⢿⠟⢿⣀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠟⠤⣼⡱⣊⡁⠤⠖⢋⡴⠛⠋⡱⡏⠉⣙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⣧⣞⣩⠶⢏⣉⡲⣈⠩⠭⠭⠟⠒⢭⡲⢯⣓⣤⣶⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠦⠖⣫⠟⠒⠒⠒⠒⠙⠧⠴⠎⡹⠃⠀⠀⠀⠉⠙⠻⢽⠷⣄⠀⠀⠀⠀⠀⢀⡴⠋⠀⢈⣦⡞⠷⠶⠖⠒⠉⠙⠦⣉⣑⣒⣒⣁⠽⢉⡽⠿⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠦⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⢈⡇⣸⠀⠀⢀⡤⣤⠋⠀⣀⡤⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⢀⡼⣠⠏⠀⠀⠘⣦⣽⡦⠚⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢶⠋⠀⣤⠶⣾⢿⠁⢷⡀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⢠⠇⢨⡇⠀⠙⢦⡼⣿⠓⠦⢍⣒⣶⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣠⠗⢦ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣴⠏⢀⡾⠁⠀⠀⠸⣧⡘⠷⣄⣀⣸⠘⢦⣀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣧⡖⣊⣁⣴⡋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠖⢋⣠⠴⠋⠀⠀⠀⠀⠀⠈⠙⠲⢤⢿⡟⢧⣄⡉⠛⠒⠒⠒⠒⢒⠳⢤⣄⣀⣤⡤⠴⠚⠉⣰⠏⣉⡴⠏⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⢦⣀⠉⠉⠛⠛⠛⠛⣹⢦⣤⣀⣀⣤⣤⠤⠖⣻⠟⣯⠥⠤⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠻⣄⣀⣻⣄⣀⣀⣀⣤⠴⠚⢉⣴⣞⣃⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⡈⠉⠙⠛⠓⠒⣿⠻⣤⣀⣀⣀⣤⠤⠖⢛⣡⠾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠴⠷⢭⣭⡥⠤⠶⠾⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⠳⢦⣄⣀⣀⣠⠤⠴⠶⠿⠿⠿⠿⠿⠓⠂⠀

⠀⠀⠀⢀⡴⠛⠉⠙⠲⣤⣤⠴⠖⠚⠋⠉⠉⠛⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⣠⠞⠉⢀⡷⡀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⣤⡤⠤⠤⣤⡀⠀ ⠀⠀⠀⣧⠀⢠⠞⠁⠀⠀⡎⣇⢿⠀⠀⣶⢊⡏⠁⠀⠀⠰⠟⠁⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⢸⣤⠏⡠⢤⡀⠀⡃⢀⠇⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢠⡏⠀⠘⠤⠽⠀⢣⣊⣀⠀⠸⣀⠜⣀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠀⠀⠉⠢⡀⠀⠧⠠⠜⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠸⠀⠀⢀⠔⠊⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⢀⠀⡰⠃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⣠⠞⢻⡀⠀⠀⠸⣰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⢳⡄⠀⠀⢳⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣠⠏⠈⠳⣄⠀⠀ ⢰⡇⠀⠀⠀⠀⠙⢦⣀⠀⠱⢄⡀⠀⠀⣠⠋⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠘⡆⠀ ⠈⣧⡀⠀⠀⠀⠀⠀⢉⣳⢦⣤⣈⣉⣉⣀⣠⣤⣶⠚⠋⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠈⠙⠓⠲⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀

￣￣￣￣＼／￣￣￣ ∧＿∧ ;;（´・ω・） ＿旦_(っ(,,■)＿＿ |l￣l||￣しﾞしﾞ￣|"

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⢉⣉⣉⣉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣤⣤⡤⠤⣤⠞⢡⠒⠉⣤⠼⠀⠀⠠⠤⠋⠒⢬⠑⢤⠤⠤⣤⣤⡤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⣻⠟⠁⠀⣜⣵⡤⢚⣠⠴⠶⠒⠛⠛⠛⡒⠶⢤⡘⠦⡰⣳⡀⠀⠙⣿⣂⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠀⠀⡜⡊⢠⡶⢻⠁⠀⠀⡇⠀⠀⠀⡇⠀⠀⢹⠳⣄⠈⣷⡀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢸⡵⣱⠋⠀⠸⡀⠀⠀⡇⠀⠀⠀⢇⠀⠀⡸⠀⠘⢦⢣⢇⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢰⠇⠀⠀⠀⢣⣀⡜⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⠈⣇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠖⠒⢄⠀⠀⠀⡰⠛⠚⠒⠂⠈⠉⠉⠉⠉⠉⠉⡉⠭⠭⠭⡭⢤⠀⡀⠀⠉⠉⠱⡀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢳⡀⢰⡑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⡇⡏⠉⠉⠙⢸⠉⢱⠀⠀⠀⢸⠀⠀⡰⠋⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⠀⠠⠜⠀⠀⠀⠀⢳⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡄⣀⡼⠀⠀⠀⡀⡇⡴⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠡⠭⠭⠭⠭⠐⠁⣀⡠⠔⠋⠹⣴⠁⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⢄ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠳⡤⠤⣤⣄⣀⣀⣠⣤⡤⠤⡤⠤⠤⠒⠒⢎⠻⡀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠹⡴⢄⠉⠒⠀⠤⠄⠐⠊⠀⠀⡠⢄⣀⠎⠀⠙⣄⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎ ⠀⠀⠈⠑⠲⠤⠤⠀⠤⠤⡴⢺⠃⠀⠀⠀⠑⢜⢄⣠⠤⡀⠀⡠⠤⡀⢈⡢⠀⠀⠀⠀⢀⠜⢆⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⢀⣀⠤⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡜⠀⠀⠀⠀⠀⠈⠑⢌⡀⠘⠒⠚⠀⠈⠁⠀⠀⠀⣀⠔⠁⠀⠈⢣⡄⠤⠤⠤⢏⠁⠒⠈⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⠤⠀⠒⠉⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡜⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠒⠒⠒⠒⠒⠒⢲⣿⣄⣤⣠⣧⢀⡀⠀⢀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠛⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⡤⠤⣄⣀⠙⠷⣄⢀⣀⣤⠴⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⢋⣤⡀⠀⠀⠈⠳⣤⡾⠛⡁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⡇⠀⠹⣿⣄⣀⣤⡞⠁⣠⠞⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⣄⣀⣠⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣇⠀⠀⠘⢿⡿⠋⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣠⠟⠋⠀⠈⣷⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠦⣀⣠⡟⠁⢀⡼⠁⣀⣤⣾⣿⣷⡄⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⣰⠟⠀⠀⢀⡞⠁⠀⠀⣤⠞⠛⢷⡀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⣀⣾⡷⠛⠉⠀⠿⠁⠀⠹⣦⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠉⠳⣤⠏⠀⠀⢠⠎⠀⠀⢠⠞⠁⠀⠀⣸⠇⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣿⡿⠿⠿⠦⠀⠀⠀⡜⠉⢑⣌⢿⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡾⠁⣿⡏⠀⣠⠔⠂⢤⡀⠀⢣⠀⡁⡟⣆⡿⠞⠛⠉⠙⠛⢦⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣫⣤⣤⣤⡀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠇⢀⣽⡇⠀⡇⠀⢰⢁⣾⣆⠈⢢⡐⣽⠏⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢻⡀⠀⠠⣶⠀⣤⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿ ⠀⠀⢈⣇⠀⠀⠀⠀⠀⠀⣿⠴⠛⠁⠀⠀⢳⠀⠸⠈⣧⣼⡆⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⢸⡇⠀⠀⠁⠀⠋⢠⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠃ ⠀⢠⡟⠹⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠱⢄⠑⠌⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠋⠉⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⣤⣀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠙⢳⡄⠀⢠⣤⣤⣄⣀⣾⣶⣶⣤⣤⣶⣾⣿⣿⡿⠀⠀⠀⠀⣰⠟⢦⣀⠀⠀⠀⠀⠀⠲⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣄⡀⠀⢀⣴⠞⠛⠛⠛⠶⣤⣀⠀⠀⣼⠇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⢿⡟⠁⠀⠀⢀⣼⠋⠀⠀⠙⠳⢦⣤⣀⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⣾⠁⠀⣠⠤⣤⣄⠈⠉⠛⠛⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠯⠤⣶⠂⢸⡇⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠔⠋⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠁⠤⠶⢶⣿⠀⢸⡇⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⣠⣾⠳⣤⡀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢈⡟⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠞⠋⠹⣆⠈⠛⢦⣄⠀⠀⠀⠀⠙⠲⠖⠊⢀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢷⣄⠀⠀⠀⣀⣠⣴⡟⠁⠸⣇⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣿⠀⠀⣴⣦⡴⠛⣷⡴⠛⠉⠁⡾⠀⠀⠀⢻⡀⠀⠀⠀⠀⠴⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣤⣤⣄⣀⡀⠀⢠⡟⠉⠉⢿⡀⠀⠙⠷⠞⠃⠀⣀⣼⡏⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠉⠀⠀⠀⠀⠀⠉⠉⠛⠻⠄⠀⠀⠸⣧⠀⠀⠀⣀⡴⠟⢿⡀⠙⢷⡄⠀⣾⠁⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢸⡏⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢶⣤⣀⣀⡤⠄⠀⠀⠀⣀⠀⠀⣠⣤⣼⣧⣤⠞⠋⠀⠀⠈⢷⡀⠀⠻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣸⠃⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢩⣟⡀⠀⠀⠀⣤⣙⠃⠀⠁⣤⡴⠋⠁⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠋⠀⠀⠀⢀⣬⡅⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣧⠖⠂⠀⠀⠀⠁⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣴⠟⢹⠇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⢀⣠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠛⠒⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠶⠞⠋⠁⠀⠙⠳⢦⣤⣀⣀⣸⡶⠦⣴⠋⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢳⡄⠀⠀⠘⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⡝⠄⠀⠀⠀⠀⠈⠉⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⡀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠛⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢷⣄⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣠⡴⠟⠁⢹⡆⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠙⢷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣾⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣈⠙⠳⢦⣤⣀⣀⡀⠀⠀⣀⣀⣴⢾⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣮⡉⠉⠉⠉⠉⣁⣠⠟⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠉⠁⠀⠈⠉⠛⠶⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠶⠖⠶⠶⣤⣀⠀⠀⠀⠈⠻⣦⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠾⠛⠛⠛⠶⣤⡉⢳⣄⠀⠀⠀⠈⢷⡄⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠈⠻⣆⠙⣧⡀⠀⠀⠀⢻⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⣧⠈⢷⡀⠀⠀⠀⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⣀⣀⡼⣦⠈⢷⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠒⠚⠉⠉⠁⠀⠀⠈⢷⡈⢷⡀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣸⠇⣸⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢤⣶⣾⠿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣠⡴⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡀ ⢀⡞⠁⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⡅ ⢸⡇⠀⠀⠀⠀⠀⣰⢳⠀⣴⢳⠀⠀⠀⠀⠀⠀⣾ ⠀⣻⠀⠀⠀⠀⠀⢿⡇⠀⢿⡾⠀⠀⠀⠀⠀⠀⢹ ⠀⢹⡄⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⠀⠀⢎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁ ⠀⠀⣾⠈⠣⣄⣀⡀⠀⠀⠀⠀⢀⣠⡠⠞⢹⠀⠀ ⠀⠀⢯⡁⠀⠀⠀⠈⢉⡏⠉⣯⡉⠁⠀⠀⢘⡅⠀ ⠀⠀⠀⠘⠲⠤⠤⠴⠛⠀⠀⠈⠳⠤⠤⠒⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⡈⠉⠁⠢⡀ ⠀⠄⠂⠈⠁⠐⠂⠴⠉⠀⠀⠀⠀⠀⡖⠒⡄⠀⠀⢎⠑⡄⠀⠈⠢⡀⠀⢸ ⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣿⠀⠀⢸⣶⣿⠀⠀⠀⠘⡄⡜ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⠆⠀⠀⢻⣻⠇⢀⠤⣀⠘⡅ ⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠉⢊⣠⣴⣶⣦⣥⡀⠘⠦⠈⠀⢡ ⠀⠀⠀⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠉⠀⠀⠀⠉⠻⣿⣿⡇⠀⠀⡆ ⠀⠀⠀⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⢘⣿⠇⠀⡜⠀ ⠀⠀⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⣼⡟⢀⠎⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⠀⠀⠀⠀⠘⢿⣦⣴⣤⣴⣿⡿⢋⣠⡏⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣤⠤⠄⠀⠉⠉⢍⣩⣴⣶⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡴⣖⢲⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣋⡉⠁⠙⠓⠒⠶⠦⣤⣤⣄⠀⠀⠀⠀⢀⡤⠴⠒⠚⠋⠛⠛⠛⠒⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢿⣟⣻⣿⣂⣶⣦⣤⣤⣀⡈⠃⣷⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⡟⣿⣿⣿⣮⠉⢩⡟⠳⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⠒⡎⢛⣿⣿⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⠠⣿⣿⣶⣿⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣾⢿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢀⣿⣦⡀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠐⢁⡀⣾⣿⠛⠀⠐⣿⡿⠃⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠸⠟⠹⣧⠀⠀⢀⣻⠇⠸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠳⢤⠴⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⣿⡀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣗⣀⠀⠀⠀⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⣇⠈⠛⠳⠶⠖⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣾⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡶⣄⣀⡀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠽⠟⠋⠀⠀⠀⠉⠉⠉⠋⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣴⣶⣿⡟⠋⢁⣨⣷⡏⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣾⠿⠛⢉⣙⣿⣷⣿⡿⠟⣿⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢹⣟⣿⣴⣾⡿⠿⠛⠉⠀⠀⠀⢸⣽⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡿⡇⢹⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⣷⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⢸⡄⢻⡇⠀⠀⠀⣀⣤⣴⣾⣏⣡⣼⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡇⣧⠸⣿⡴⠶⣿⣿⣿⣿⠿⠛⢋⣹⣿⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⢹⡆⢻⣴⡶⠟⠋⣉⣠⡴⠞⠉⢹⣼⣧⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⣷⣾⣿⣴⠶⠛⠉⣁⣿⣠⠴⠚⠉⠁⠀⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⢿⡋⢻⣀⣤⣶⠾⠟⠋⣤⣤⡀⠀⠀⠀⣰⣶⣾⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡻⣾⣣⡿⠟⠉⠁⠀⠀⠀⠛⠟⠁⠀⢀⣼⣿⢥⣿⠃⠙⢷⣄⠀⠀⠀⠀ ⠀⢸⣇⣿⣿⣿⣄⠀⠀⠀⢠⣾⣿⣍⣿⣦⡀⠸⣿⣭⣿⠃⠀⠀⠀⠙⢷⣄⠀⠀ ⠀⠀⠛⣧⣈⣿⣿⣷⣄⠀⣿⣼⣷⣽⣿⢙⡇⠀⠈⣩⣅⠀⠀⠀⠀⠀⠀⠙⢷⣄ ⠀⠀⠀⠈⠻⣿⣿⣿⣟⢷⣜⢯⣍⣙⣫⡾⠃⢶⣻⣵⣿⣆⠀⠀⠀⠀⠀⠀⣀⣿ ⠀⠀⠀⠀⠀⠈⠻⣟⠙⢷⣝⢷⣄⠀⠀⠀⠀⠀⠙⣿⠞⠋⣴⣦⠀⣀⡴⢞⣭⡟ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢷⣝⢧⡀⠀⠀⠀⠀⢰⣿⣿⣻⡿⣛⣽⡾⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢧⡙⣦⡀⠀⢀⣨⣽⣻⣿⢿⣻⡷⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⢦⣍⣛⣭⡷⣿⣿⠞⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣤⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⠶⠶⠶⢦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⡀⠀⠀⠀⢀⣤⠶⠛⠋⣁⣀⣤⣤⣤⣤⣤⣤⣤⣀⣈⠉⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⢁⣠⣤⣤⣤⣀⠙⠲⣤⠖⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⢠⣿⣿⣿⣿⣿⣿⣷⡦⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣶⡎⢿⣿⣿⣿⣿⢣⣾⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢦⡀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⣿⣿⣿⡏⢸⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⢹⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⢸⣿⣿⣿⡇⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⢿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠙⣆⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢦⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⡟⠉⠉⠉⠙⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢧⡀⠀ ⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⣿⡷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⡇⠀ ⠀⠀⠀⠀⠀⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀ ⠀⠀⠀⠀⠀⢻⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⡿⠀ ⠀⠀⠀⠀⠀⠈⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠿⠋⢀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⢤⣤⠶⠋⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⣴⣾⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣷⣦⣄⠉⠳⣄⠀⠀⠀ ⠀⠀⡴⠋⠀⠐⠋⢹⣿⣿⣿⣦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⡏⠉⠓⠄⠈⢧⡀⠀ ⠀⣼⠁⣰⡇⠀⣀⣼⣿⣿⣿⣿⣿⣦⣌⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣴⣿⣿⣿⣿⣿⣷⣄⡀⢀⣆⠀⢧⠀ ⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⡙⠛⠛⠿⠿⣿⡿⠿⠟⠛⠛⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⡆ ⠀⠻⣄⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠓⠀⣠⣤⣄⠀⠐⠚⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢀⡼⠁ ⠀⠀⠈⠛⠶⣤⣤⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣠⣤⣤⠴⠖⠋⠁⠀⠈⠙⠲⠶⣤⣤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣤⣤⠴⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬜⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛🟩🟩🟩⬛⬜⬜⬜⬜⬛🟧🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟩⬜⬜🟩🟩🟩🟩⬜⬜🟩⬛🟧🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬜⬛🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟩🟩🟩🟩⬛⬜🟩🟩🟩🟩🟩⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟩🟩🟩🟩⬛⬜🟩🟩🟩🟩⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟩🟩🟩🟩🟩⬛⬛⬜🟩🟩🟩⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟩🟩🟩⬛⬜⬜⬜⬜⬜🟩⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬜⬛⬜⬜🟩🟩⬛🟧⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬜🟩🟩⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩🟩🟩⬛⬛⬜⬛⬛⬛⬛⬜⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜🟩⬛⬜⬛⬜🟧🟧🟥⬛⬜⬛⬛⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬛🟧🟥🟥🟥⬛⬜⬛🟩⬛ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬛⬛⬛⬛⬜⬛⬜⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬛⬜⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟧⬛⬛⬛⬛⬛⬛⬜⬜⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟧⬛🟧🟧⬛🟩🟩🟩⬜⬛⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟧🟧🟧🟧⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🟧🟧⬛⬛🟥🟥🟥🟥🟥⬛⬜⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣀⣀⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⠮⠍⠛⠒⠒⠒⠚⠠⠽⣉⠙⠻⢿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡂⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⡹⠛⠋⠑⡄⠀⠀⠀ ⠀⣀⣀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠜⠑⣄⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣷⠀⠀⠀ ⣿⣿⣿⣿⡏⠀⠀⠀⢸⠉⢆⠀⠀⢸⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀ ⣿⣿⣿⣿⠃⠀⠀⠀⠸⣄⣸⡆⠀⠈⢿⣿⣿⠀⣠⣴⣶⣶⡄⠀⢀⣤⣾⣇⣀⣀⡀ ⣿⣿⣿⣿⣦⣄⠀⠀⠀⢻⣿⣿⠀⠀⠈⠻⡿⠀⠘⠛⠛⠋⠁⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢿⣿⣿⣷⢀⣀⠀⠻⠿⢀⣴⣶⣶⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⣤⠛⣿⣿⣿⡿⠃⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣦⡈⣿⣿⠇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠉⠻⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠛⢿⣿⣿⣿⣷⢦⣄⣀⡀⠤⣤⣤⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣦⣭⣷⣶⣿⣿⡿⠿⠟⠋⠁⠉⠛⠛⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠭⢛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠇⣄⣀⣤⣤⣤⣤⣤⣆⣀⣀⣠⢠⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣴⣀⠸⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⣰⣿⡿⠟⠛⡛⠛⠛⠛⠿⠿⡷⠂⠀⠀⠻⢿⠿⠟⠛⠛⠛⠛⢛⢿⣟⡠⠘⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⢾⡟⠘⠀⠡⠀⣤⠴⢯⣽⢽⡽⡭⢽⡆⠈⠀⠀⢰⡖⢭⡿⣿⣿⢿⠲⢄⠨⠞⠀⠀⢸⡟⢶⣄⠀⠀⠀ ⠀⢀⣴⠋⠁⠘⠁⠁⠀⠈⠘⠑⠲⠚⠟⠻⠒⠽⠀⠁⠁⠀⠀⠁⠃⠺⠂⠛⠛⠛⠒⠊⠙⠀⠀⠀⠀⠛⠀⡹⢷⡀⠀ ⢀⡾⠡⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⡌⢻⡄ ⣸⣇⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢠⠆⠀⠀⠀⡿⠀⠀⠸⡈⣷ ⢹⣏⠀⠀⠀⢀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣶⢋⠀⠄⠀⡸⢇⠀⠠⢐⣡⡿ ⠀⠻⣶⣩⠽⠌⢾⡱⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⠞⡑⢱⢏⠆⠈⠀⣰⣻⠧⢫⣙⣷⠟⠁ ⠀⠀⠀⠉⠛⠛⠛⢷⡹⢄⠀⠀⠀⠁⢸⡶⠶⠶⠶⠶⠶⠶⠖⣒⠛⠋⠉⠀⠀⠔⡿⠀⠀⣠⢞⣵⠟⠙⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣨⣿⣜⠵⣄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⣀⢼⢱⣾⣯⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣻⢿⣷⣌⡚⢲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡚⢥⣾⡿⣿⡽⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣻⢾⣽⣻⣞⡿⣿⣥⣚⠮⣙⢦⠰⡤⢄⠤⡄⡤⢢⡔⣪⠕⣊⣶⣽⣿⣻⣽⣳⢿⡽⣾⣿⡆⠀⠀⠀ ⠀⠀⠀⣾⣟⣷⣿⣿⣾⣷⣿⣿⣷⣿⣿⣿⣶⣿⣾⣧⣟⣞⣳⣧⣧⣿⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⢻⣿⡀⠀⠀ ⠀⠀⢠⣿⣯⣟⣾⣻⣽⣻⢾⣽⣳⣟⡷⣯⣟⣿⣻⣿⠿⠛⠛⢿⣿⡿⣽⣳⣟⡷⣯⣟⡷⣯⢿⣽⣻⣽⣞⣿⡇⠀⠀ ⠀⠀⠈⢿⣟⣾⣳⣟⡾⣽⣻⣞⡷⣯⣟⣷⣿⡿⠟⠁⠀⠀⠀⠈⠙⠿⣷⣿⣾⣽⣳⢯⡿⣽⣻⣞⣷⣻⣞⡿⠁⠀⠀ ⠀⠀⠀⠀⠉⠛⠷⠯⢿⣷⣿⡼⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠷⠿⠾⠟⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠾⠿⠿⠿⠷⠷⠶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠿⠛⠉⠉⠀⠀⠀⢀⠀⡐⠀⡐⠀⠂⠀⡀⠈⠉⠛⠻⢷⣶⣤⡀⢀⣠⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⢀⠀⠂⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠙⡿⠿⠋⠉⠀⠀⠀⠀⠈⠙⠻⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣀⠀⠀⠀⠀⢀⣴⣾⠟⠁⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡠⠄⠀⢀⠠⠙⠲⢤⡀⠀⠂⠐⠀⠁⠠⠈⢿⣧⠀ ⠀⠀⠀⣠⣴⡿⠟⠛⠉⠉⠉⠉⠛⠛⠻⢿⣶⣴⡿⠋⠄⡈⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣦⡀⠀⠀⠀⠀⠀⠠⣿⠋⠙⢷⣅⠀⠀⠄⠂⠄⠛⢦⣈⠐⠀⡁⢀⠂⠈⢿⡇ ⠀⢀⣼⡿⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⣿⡆⠀⠀⢿⡆⠀⠀⠁⠀⠌⢀⠁⢪⠐⡀⠂⠌⡐⢸⣷ ⢀⣾⢏⠀⠐⡀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣸⣷⠀⠀⠀⠀⠀⢿⣿⣄⣀⣼⣿⡀⠀⠀⠐⠈⠀⠈⠄⠓⡤⢁⠢⠐⣸⡟ ⣸⡿⢀⠘⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣴⣿⣿⡆⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠀⠡⢈⠐⢌⠣⢌⢡⣿⠇ ⣿⡇⠄⡘⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠘⡀⠛⡄⣼⡿⠀ ⢸⣿⢀⠘⡀⠁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⢂⠡⠈⢼⣿⠀⠀ ⠈⣿⣦⠘⠠⢁⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢿⣿⣽⡿⠀⠀⢀⡼⣟⣛⠳⢆⠠⠉⠄⢿⣇⠀ ⠀⠈⢿⣯⡔⡂⠡⠌⡐⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⢤⣀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⣀⣀⣀⣀⣀⣀⠈⠉⠀⠀⠀⠈⢷⡜⡬⣛⢬⠃⠌⡐⠸⣿⠀ ⠀⠀⠀⠹⣿⣶⣁⠒⡠⢁⠐⡠⠀⠄⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⡀⢎⠥⡘⡡⢊⠔⣨⡇⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠈⠉⠒⢉⠊⠌⡐⠠⢃⢿⡇ ⠀⠀⠀⠀⠀⠙⠿⣷⣴⡡⢆⠤⢑⡈⠄⡈⠄⠂⠀⠀⠀⠀⠀⠀⠜⣨⠒⣡⣣⣥⠞⠋⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠐⡀⢂⠡⠌⣺⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡎⠔⡈⠄⡁⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠌⠐⡀⠆⢂⠱⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠰⢈⠐⡀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⡿⣽⢯⡿⣽⣻⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢂⠐⠄⠌⢂⡑⢺⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢡⠂⠌⠠⢁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢷⣯⣟⣯⡿⣽⣻⢷⣯⣟⡷⣯⣟⡿⣿⣿⣿⣿⣿⣿⣇⠀⢂⠈⢄⠃⢢⠐⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠘⡈⠔⡀⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⢿⡾⣽⣞⡿⣽⢯⣟⣾⣽⣻⢷⣯⣟⣿⣻⣿⣿⣿⣿⣿⠀⠠⠘⡀⠎⡄⢃⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡁⠆⢂⢁⠂⡐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣞⣯⢿⣳⢯⡿⣽⣻⢞⡷⢯⣟⡿⣾⡽⣞⣷⢿⣿⣿⣿⣿⠀⡡⠘⢠⠑⡌⢼⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡐⠈⡄⠢⠐⢠⠁⢂⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢾⡽⣯⢟⣯⢳⡝⣮⢯⣝⡻⣼⢻⣵⣻⣟⡾⣟⣾⣿⣿⣿⠐⠠⣉⠢⡑⢬⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⡁⢂⠡⢁⠂⠌⣀⠂⠌⡀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣯⢿⣽⢳⣏⡞⢧⣙⢦⡓⣎⠷⣭⢟⣞⡷⣯⢿⣽⢾⣽⣿⣿⠈⡒⠤⡑⣌⣾⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣿⣷⡠⢈⢂⡘⠤⢀⠌⡐⠠⢁⠂⡈⠄⠀⢀⠀⠁⣿⣯⣟⡾⣏⣾⣹⣓⢮⢖⡹⣬⢻⣜⣯⢾⡽⣯⣟⡾⣯⣿⣿⢇⢂⠱⢂⣱⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣟⣷⡿⣷⡄⢂⠐⠌⢂⠜⠠⣁⠂⠔⡀⢂⠁⡀⠂⠈⣿⣷⢯⡿⣽⢶⣳⡽⣮⢏⡷⣭⢷⢯⣞⣯⣟⡷⣯⣟⣷⣿⡿⡀⢎⠢⢥⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣯⣷⣿⣟⣿⣦⡈⠜⢠⠊⢡⠐⠌⡂⠔⡈⡐⠠⢁⠂⢹⣿⣯⢿⡽⣯⢷⣻⡽⣯⢿⡽⣯⣟⣾⣳⢯⣟⣷⣿⣿⡿⢡⠘⠤⣻⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣷⢻⣿⣾⢻⣿⣷⣬⠀⠘⢠⠉⠂⢱⠈⡔⢡⠂⣥⠈⡌⣿⣿⣯⣿⣽⣯⣷⣿⣽⣯⡟⣷⢻⣾⣽⢻⣾⣿⣿⡏⠐⡆⢹⣾⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⣯⣟⣿⣿⣞⡿⣿⣮⡖⢈⠤⠉⡄⢣⠐⡡⢊⠄⡒⠤⡘⣿⣿⣾⣳⣯⢷⣯⢷⣯⢿⣽⣻⣾⣿⣿⣿⠿⢋⠔⣣⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣻⣽⢾⣻⣞⣿⣿⣽⣻⣿⣷⣦⣑⠠⢂⠱⣀⠣⡘⢄⠣⠔⣈⠻⢿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⠷⣛⠡⢎⣬⣾⣿⢿⡽⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣳⣯⢿⣳⡿⣞⣿⣻⣷⣟⣯⣿⣿⣷⣮⣴⣀⢂⠡⠌⢂⠍⡠⠒⠠⠌⡙⠛⠛⢛⠛⠛⢩⠉⣔⣢⣶⣿⣿⢿⣻⡽⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣾⣻⣽⣻⣽⣞⣯⣟⡿⣷⣻⣾⣻⣟⣿⣿⣿⣷⣾⣦⣦⣥⣬⣡⣆⣤⣭⣬⣦⣵⣾⣷⣿⡿⣿⣻⢷⣻⣟⣯⢿⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢯⡷⣯⡷⣯⣷⣻⣽⢯⣷⣟⡷⣿⣞⣷⣿⠏⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣾⡽⣷⣻⢯⣟⡾⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣟⡷⣿⡽⣾⣽⢾⣻⢷⣯⣟⣷⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢷⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣽⣳⣟⡷⣯⢿⣽⣻⢾⣽⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣾⠿⠟⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠾⠟⠛⠛⠛⠛⠻⠿⠿⢶⣿⢷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣠⣴⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢽⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣉⡏⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣷⣤⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠛⠉⠉⠁⠀⠉⠛⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣠⣄⣤⡈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⣀⣤⣤⣤⣄⠈⢳⡌⢿⣿⣦⡄⠀⠀⠀⠀⣰⡇⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡟⢹⣏⣰⣿⣿⣿⡿⣶⣿⣯⣿⣿⣿⣦⠀⠀⣼⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀ ⠠⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⢿⣿⠿⣿⠃⠈⠻⣿⣿⣿⣿⣿⣿⣾⡿⠁⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⠿⢷⣦⡀⠀⠀⢣⣈⠉⠛⠚⠿⠥⠤⠶⠾⠿⣿⣿⣿⣇⠈⣿⠃⣴⣿⣷⣠⣤⣀⣀⣄⣀⣠⣤⣶⣾⡿⠿⣆⠀⠀⠀⠀ ⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣻⠏⠉⠁⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠴⠛⠃⠀⠙⠿⠘⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠹⣦⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀⢿⣦⠀⠀ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠿⡻⠿⣻⣵⣭⡿⣿⣿⠀⠀⠀⠈⣿⡆⠀ ⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠘⠀⠀⠀⠁⢾⣿⡿⣷⡀⠀⠀⠀⢸⣿⡀ ⠛⠠⡉⠀⠀⠀⣁⠈⢠⠀⠤⠔⢒⣡⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢦⡀⠀⠀⠀⠀⠉⠟⣿⡿⠀⠀⠀⠀⣹⣇ ⣶⣤⣤⣁⡤⢤⡤⠤⠆⢐⣴⣾⡵⡿⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠛⢠⡿⠀⠀⢠⡔⢴⣾⠏⠀⠀⠀⠀⠂⢠⢻ ⠉⠛⠾⡿⢿⣿⠿⠻⠟⠛⠉⢹⣶⣷⡀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠰⠿⣿⣿⣷⡀⠀⠀⠀⢀⣠⣶⡟⠀⠀⣰⢟⣴⣿⠋⣀⡠⢄⠼⠁⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠋⢻⣿⣷⣷⠈⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣤⣾⡛⠋⠉⠀⢀⣼⢻⣾⡿⠽⣉⣭⡛⠘⠁⠀⠀⢀⡼ ⠀⠀⠀⣀⣠⣴⠟⠋⡀⠀⠀⠀⠸⣿⣿⣾⣦⡈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣛⣳⠀⠀⠀⡜⣵⣿⣏⡙⠓⠶⠤⣶⣤⢤⠤⠖⠋⠀ ⠀⣠⣶⠟⠩⢣⡀⠀⠙⣄⠀⠳⣀⡈⢺⡿⣷⣜⢆⡘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣅⡉⠓⠀⠳⣄⡸⢷⣿⣯⡿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣉⠁⠀⡠⠀⠳⡄⠀⠈⠲⡀⠁⠉⠀⠙⢾⣿⣷⣘⢆⡻⣷⢄⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠛⠛⠿⣿⣶⠾⣿⠿⣷⣿⣿⣄⣿⣝⠻⣿⣦⡀⠀⠀⠀⠀⠀ ⢀⡌⠀⠀⠀⢀⠀⠘⢦⠀⠀⠘⠲⣀⣀⠀⠀⡙⠿⣿⣧⣅⠺⣗⡙⠢⢄⡀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⢿⣿⣯⣍⣤⣀⣤⣤⣴⣦⣤⣴⣾⣿⣧⣼⣿⡿⣙⡇⢻⣶⡟⡿⣿⣶⡄⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠠⠀⠀⠣⡀⠀⠀⠻⣄⢄⠀⠘⢄⠘⢿⣿⣧⣀⠻⣄⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢘⡛⠛⠛⠀⠘⠀⢛⠛⠀⠀⣸⣧⣿⢃⡤⠼⡿⣸⡿⣇⠸⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠘⢦⠁⠀⢨⣎⡳⣀⠈⠱⢄⠈⠙⢿⣷⣮⣽⡢⢽⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣤⣀⣤⣤⠶⠒⠠⣾⣿⡿⢁⠘⠀⡴⡵⡽⣿⠏⡔⡸⡟⣿⡀⠀ ⠀⠀⠀⠀⠰⡀⢢⠀⠑⠘⢦⠀⠙⢦⠀⠑⣦⠉⣢⡀⠀⠳⢄⢠⠈⠙⡛⠻⢶⣼⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⢤⣿⡿⠃⡎⢀⠟⠰⢙⡵⢃⠜⡼⢃⡿⠙⣧⠀ ⠀⠀⠀⠀⠀⠈⠦⡑⣀⠀⠀⠱⠀⠀⠑⢆⡀⠑⣄⣘⣦⣖⣯⡵⠞⠋⠁⠀⠀⠈⠙⠻⣿⣮⡛⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⣻⢻⣿⠀⡌⢁⠏⢀⣬⣼⡿⠟⣻⠰⢫⢁⣼⡇⠀ ⣤⣤⣤⣤⣤⣀⣐⣈⣒⣐⣀⣠⣤⣤⣴⣾⡿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣾⣭⣭⣄⡈⠲⠢⠀⠀⠀⠀⠀⣠⣤⣾⣻⡽⠿⠛⠿⢾⣥⣤⣤⣀⣮⣤⣇⣤⣤⣴⠾⠛⠉⠀⠀ ⠀⠉⠉⡉⠉⠛⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠷⠞⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢉⠉⠁⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀

⢀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣄⠀ ⣾⠁⠀⣿⣦⢸⡇⣛⡀⣀⢀⡀⢴⡦⢀⡤⣀⢀⣀⢀⡀⢀⡀⣶⠀⡠⢄⠀⠘⣧ ⢿⡀⠀⣿⠈⢿⡇⢿⠇⣿⠀⣿⢸⡇⠻⣏⡭⠸⡇⠸⡇⠻⣄⣿⠸⢇⡸⠇⢠⡟ ⠈⠻⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠋⠀

⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢸⡇⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠢⣑⠢⢒⠤⢃⠜⣫⠐⢆⠲⣐⠢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠤⠄⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⡄⢋⠆⣎⠡⠚⣄⠋⢆⠓⡌⣢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣣⠶⠚⢋⡉⣍⣹⠟⠙⠙⣧⡀⢍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣐⠤⣉⠒⢆⡉⢆⢱⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠤⣃⢮⡙⣦⣝⡾⠁⠀⠀⠀⢀⠘⢮⢻⣔⡢⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡢⢘⠢⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡠⢠⣃⠞⣜⡲⣝⣶⠏⠀⠀⠀⠀⠀⢨⡘⠬⢷⡹⣷⢮⡅⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⢯⣷⢁⠒⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢌⡔⣣⢎⡿⣜⣳⣯⠏⠀⠀⠀⠀⠀⠀⠰⣌⢳⡩⢗⣜⣿⣽⣫⢬⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠾⠥⠮⠿⠿⠟ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡜⢢⡝⣧⣿⠚⠋⠉⣤⡆⠀⠀⠀⠀⠀⠀⢱⡌⣶⢩⡏⡞⡌⠙⠛⣷⣮⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣲⣙⣮⠗⠋⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⡈⢦⡱⢎⡻⣜⡳⡁⣶⡠⢬⣝⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⡵⠟⠁⠀⠀⣀⡤⠒⡺⣿⡀⢐⠠⡐⢌⠢⡜⢦⡹⣭⢳⡽⣸⠁⣿⣳⢏⡾⢧⡸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠥⠋⠀⠀⡀⢄⡤⣂⢶⣩⣷⣻⠧⣬⢱⡘⣬⠳⣜⡣⢷⣩⢷⡹⢥⣻⣿⣧⣏⠿⣭⢋⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡠⠊⢀⣜⣲⣽⣯⣾⣿⣿⠏⠀⠀⠀⠈⠓⠿⣴⣻⡜⣽⣣⣏⣾⠵⠋⠁⠉⢿⣿⣿⣷⣏⡇⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠳⠾⢽⡾⣟⢯⡻⣽⢳⡇⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⠉⠉⠀⠀⠀⠀⢀⢸⣿⢧⠏⡿⠷⣿⣟⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣾⠐⣎⢧⣛⣼⢻⠃⠀⢰⣏⣹⡄⠀⠀⠀⠈⣿⡯⠀⠀⠀⠀⠀⣼⣹⠟⣿⣏⠖⡇⠀⠸⣯⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⠟⣈⢖⣣⢞⡼⣻⡆⠀⠘⢿⣿⠃⠀⠀⠀⠐⠋⠩⠥⣄⡀⠀⢀⢿⡿⢸⣿⣎⢳⡇⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⢣⢋ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡐⢌⡞⣴⢫⣾⠵⠿⠤⠤⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⡑⠲⠿⠿⣮⣻⠇⠀⠀⠈⢿⣿⣿⣄⣀⣀⣀⣀⣾⣿⣮⣱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠈⣷⢪⡜⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣼⠋⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⡇⠀⠀⠀⠀⠀⢻⡧⢞⣵⠃⠀⢀⠠⣀⣤⣠⣤⣦⣤⡀⠀⠀⠀⠀⠀⡀⠄⣀⣠⣮⣔⣢⢒⡿⠀⠀⠀⠀⡾⢤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⡉⣤⣒⢧⢿⠀⠀⠀⠀⠀⠈⣟⡟⣾⡆⠀⢪⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣤⣧⣶⣶⣿⣿⣿⣿⣿⢸⠇⠀⠀⠀⢰⣿⣧⡹⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⢿⣻⢯⣟⡾⢁⣴⣛⢶⣹⣎⢿⡆⠀⠀⠀⠀⢰⣿⢿⣽⡇⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣽⣿⢿⣿⣿⣿⣿⡟⡼⠀⠀⠀⠀⣺⣟⣷⣻⢧⣟⣮⡹⣿⣿⣿⣿⣿⣿ ⣟⣞⣯⣽⣛⡾⣱⡛⣶⡹⣮⢷⣻⣞⡇⠀⠀⠀⠀⢸⠹⣯⠞⣧⠀⢸⣿⣿⣿⣿⣿⢿⣯⣷⣿⡿⣿⣯⣿⣟⡿⣻⣿⡟⠉⣿⠃⠀⠀⠀⢀⣿⣟⡾⣽⣻⢾⣜⣳⠌⣿⣿⣿⣿⣿ ⡿⣼⡼⣤⣿⠃⣧⢻⡤⣿⣛⡿⣧⢿⡇⠀⠀⠀⠀⢸⠀⠻⣟⣸⠀⢠⣿⣿⣿⣿⣛⡿⡼⢧⣟⡿⣿⣻⣼⣿⢧⣻⠟⠀⢃⡇⠀⠀⠀⠀⢸⣿⣼⣻⢧⣟⡿⣼⣛⢿⡘⣿⣿⣿⣿ ⣟⢧⣿⣽⡁⣸⣜⡳⣽⢞⣽⣻⣽⣻⡇⠀⠀⠀⠀⢸⠦⠀⠘⠮⡇⠀⣿⣿⣿⡷⣏⣷⢻⡟⣾⡽⣳⢿⣽⢾⣿⠃⣀⣈⣠⡇⢀⠀⠀⠀⣿⣟⡾⣽⣻⢾⡽⣳⢯⡷⣭⠽⣿⣿⣿ ⣿⣿⠋⣀⣤⠷⣎⣿⣞⣿⣞⡷⣯⣿⠆⠀⠀⠀⠀⡟⢦⠀⠀⠀⢇⠀⢹⣿⣿⣿⣽⡞⣯⠿⠓⠛⠋⠛⣻⠛⠉⠉⠉⠉⠀⠀⠀⠉⠒⢤⣿⣯⣟⡷⣯⢿⣹⢯⣷⢻⡼⣳⢻⣿⣿ ⠀⠀⠀⠀⠈⠙⠺⢼⣻⣿⣾⡿⣽⣿⠁⠀⠀⠀⢠⠇⠀⠙⠦⡀⠘⡀⠈⠙⠛⠉⠈⠉⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡾⣽⢯⣻⣭⢷⣞⣯⣳⢭⢏⠿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⠇⠀⠀⠀⠀⡼⠠⠂⠀⠀⠈⠲⢄⠀⠀⠀⠐⠲⢤⡄⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣟⣧⡟⣯⢾⡵⣫⢞⢮⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠀⠀⠀⠀⣸⣅⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⢀⡽⠋⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⢻⣭⢷⡻⣝⠾⣌⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⡞⠻⠿⠶⠶⢶⢤⣤⣀⣀⠀⠈⡙⠶⣋⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣎⣯⢳⣏⡟⡬⡄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⠛⠋⠉⠀⠉⠙⠛⠿⢿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣶⣦⣤⣀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠿⢿⣷⣶⣤⣄⡀⠀⠀⠀ ⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⠈⠙⠛⠿⢿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣴⣾⡿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⡆ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠠⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠿⣿⣶⣤⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣷⣶⣤⣄⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠉⠙⠻⢿⣷⣶⣤⣿⣿⣿⣿⠿⠟⠋⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠛⠻⠿⣿⣶⣮⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠋⠉⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣶⣤⣀⣸⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠦⡄⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⣀⠤⠖⠒⠋⡉⠙⢲⣺⢅⡀⠀⠹⡀⠀⠀⠀⢀⡜⠁⠀⠀⠀ ⣼⠉⠀⠉⠓⠏⠁⠀⠀⠀⠀⢯⣧⠈⢿⡆⠈⠓⢴⠇⠀⠀⣠⠊⠀⠀⠀⡀⠀ ⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠄⠠⢀⠈⢣⡀⠀⠁⠀⢀⡤⠊⠀⠀ ⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⠘⡇⠀⢧⠀⠐⠊⠁⠀⠀⠀⠀ ⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢀⣀⣀⡀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⠄⢀⡀⢇⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀ ⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⠙⠆⡼⠛⢦⡀⠑⠢⣄⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠢⣀⠀⢀⡴⡰⠁⠀⢀⡇⠀⠀⠈⠑⠀ ⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠒⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠀⠉⠢⢄⣀⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⣨⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠂⠴⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠈⠉⠛⢿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢀⣨⣷⠀⠀⠀⠀⢻⠟⠋⠉⠁⠀⠈⠉⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠙⠛⠛⠿⣿⣿⣿⣿⣿ ⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣅⣠⣴⣶⣾⡿⠿⠛⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⠿⣿⣿ ⣿⣿⣿⣦⡄⡀⠀⠀⠀⠠⢠⣼⣿⣿⠿⠿⠛⠋⠉⠓⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡈⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⢿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣤⠶⢻⣿⣿⣿⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⣿⣿⣿⣇⠉⠙⠻⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠣ ⣿⣿⣿⣿⣿⡇⠀⠀⣠⠟⠁⠀⢹⡇⠀⠸⣼⣿⣿⣿⠀⠉⣷⡀⠀⠀⠀⠀⢸⣟⠁⠀⢻⣿⣿⣿⡏⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⠐⠃⠀⠀⠀⠀⠹⢄⡀⠈⠉⠉⠁⠤⠐⠋⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⠈⠉⠁⠠⠴⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡇⠀⡄⠀⣴⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⣿⣷⠀⠁⠀⠹⣦⡀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⣾ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠉⠂⠀⠈⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⣤⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠛⢶⡀⠠⠤⠤⠤⢤⡤⠤⢤⣤⡾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣾⣿⠿⠟⢛⣉⣛⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠙⠓⠦⢤⣤⣤⣤⠴⠞⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠁⠀⠀⠀⠉⠙⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠛⠋⠉⡉⠉⠙⠛⢶⣦⣄⠀⠀⠐⠲⠶⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠠⢀ ⣿⣿⣿⣿⣿⣿⣿⣿⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⠘⣠ ⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⣀⣤⠀⠀⡀⣠⣾⣶⣴⣿ ⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣯⣽⣯⣶⣶⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣗⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⢀⣀⠀⣀⠀⢀⣀⣠⣐⠖⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⡦⣶⣶⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⠒⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⠒⠤⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠪⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⡀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠁⠀⠀⢀⢀⣀⣠⡠⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣀⡠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣧⡯⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠶⠒⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⠉⠉⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⢰⣾⣿⣶⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⣾⣿⣷⡄⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⠀⠸⣿⣿⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⢿⣿⡿⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡲⠤⣀⣀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣤⣀⣀⣠⣴⢶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣿⣿⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠄⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⣤⣖⣢⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠁⠙⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠉⠙⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠉⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⢀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⢠⣾⠟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡜⢿⣏⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠋⣰⡿⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠈⢻⣄⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⣰⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⣿⣿⣿⠀⠀⠹⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣎⣰⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠘⣿⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⣵⣾⡟⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⢀⠀⣠⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣾⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⢿⣿⣷⠀⠀⠀⠀⢻⠀⠀⢀⣀⣦⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⡻⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠉⠁⠀⠀⠀⠀⢸⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⣿⡿⠛⠛⠈⠉⠻⣿⡟⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣿⡿⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⢿⣄⠀⠀⠀⠀⠀⠀⢀⠞⠘⢻⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣾⣻⣿⣠⣾⣤⣘⡄⠀⠀⠀⠀⠀⣾⣶⣷⣼⣿⣾⣝⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠖⢉⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⢀⡤⡇⠣⣴⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢀⡏⢸⡇⠀⡎⡟⡆⠀⠀⠸⡒⠉⠉⢧⣸⣀⣘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠘⡗⠋⡇⠀⣯⣁⡇⠀⠀⠀⡃⠀⠀⡜⠉⠀⠀⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠛⡆⠀⠉⢉⡡⠤⢖⣇⠖⠉⠉⣆⣇⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠱⢄⡀⠈⠣⠤⠋⡎⢀⣀⠔⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡆⠀⠘⠦⠴⢒⡇⠈⠉⠉⢩⠋⢯⣉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀hiii!⠀⠀⠀ ⢤⡗⠑⡲⠆⠀⠀⢸⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠗⠉⠻⠆⠀⠀⠀⠉⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀search⠀Rainbowcat64 for more<3

⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀ ⠀⢀⣾⣿⡿⠛⠉⠉⠉⠉⠉⠉⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⢸⣿⡿⠀⠀⣠⣶⣿⣷⣦⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠙⠿⣿⡿⠟⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⠙⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣦⣀⣀⣠⣾⣿⣿⣿⡇ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠈⢿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

⠘⢀⠐⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⢈⡉⠉⠉⠉⠉⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀ ⠊⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⡰⠁⣉⠀⠀⢠⠋⣧⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢸⣷⣴⠏⠀⢐⣇⣠⡏⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣨⣽⠟⠀⠀⢸⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠉⢰⣶⡄⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀ ⠀⠀⠀⠸⠀⠀⣴⠤⣄⣀⣀⣀⢀⣸⣽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀ ⠀⠀⢠⠎⠈⠉⠹⣦⠀⠀⠀⠈⠉⠉⠁⠁⠉⠋⠷⣒⣾⣆⡀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠈⠉⠓⠀⠀⠀⠀⢸⠀ ⠀⠀⠰⡄⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⠀⢀⡼⠦⡴⠞⠓⠤⠤⠤⣀⣀⢀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀ ⠀⢠⠏⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢷⣄⠀⠀⠀⠀⣠⡞⢹⡀⠀ ⠀⡇⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠋⠀⠀⣇⠀ ⠀⢧⡀⠀⢀⣀⣤⣾⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⣀⣄⡤⠒⠋⠁⠀⠀⠀⠀⢹⠀ ⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠿⠿⠿⠿⠿⢿⣄⠀⠀⠀⠀⠀⠀⢀⡯⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣀⣀⣀⣠⡊⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠲⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⢀⣠⣴⣾⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⣠⣤⠶⠞⠛⠳⢦⣤⣰⠏⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⢀⣠⡴⠖⠛⠙⠓⠶⣤⣄ ⣿⠀⠀⠀⢀⣠⣴⣾⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠟⠁⠀⠀⢀⣠⣴⣶⣿⣿ ⣿⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⢰⠿⠛⠋⠙⠻⢿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⣀⣤⣶⣾⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⢸⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢸⣆⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢸⣿⣆⠀⠀⠀⠛⠀⠀⠀⢸⣿⣿⣿⣿⡇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣄⡀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣀⡀⠻⣿⣿⣿⣿⣿⡿ ⠀⠈⠙⠻⠾⠟⠛⠉⠙⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⠙⠛⠿⠿⠛⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢾⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⣿⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣿⣄⠀⣠⣾⣇⠀⠀⠀⣀⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⢰⠟⣿⠿⠋⠘⠿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⣼⡿⠿⢿⣷⣶⣴⣿⠏⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠈⢛⣿⡟⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⢻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⢹⣿⠀⠀⠀⣼⣿⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠛⠛⠻⣿⣆⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⣿⣿⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠟⠛⢩⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⢹⣿⡄⢰⣿⡇⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣾⡿⠟⢻⣿⠁⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣼⣿⡇⠀⠀⠀⢸⡇⠈⠉⢹⣇⠀⣸⣧⠀⣼⣿⡆⠀⠀⢠⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢸⣿⠀⠀⢸⣿⣄⣿⣿⣷⣿⠿⣿⡄⠀⣼⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⡆⠀⣿⣿⣿⡟⠋⠙⠁⠀⠙⢿⣶⣿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣶⣶⣤⣀ ⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠈⣹⣿ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⢀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠾⠿⠿⣾⢿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠀⠀⠀⠀⠻⢾⣹⣻⣿⠏⠙⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀ ⣗⣲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠃⠀⠀⡀⠠⠰⢶⣶⣟⠟⠈⢃⡀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠪⠛⠛⠋⠉ ⠈⡀⠉⠭⠭⠛⠊⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡀⣦⣶⣿⣿⣿⣧⣭⣧⣭⣽⣿⣿⣕⣄⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⢙⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢹⢧⠈⠛⠉⢸⣿⣬⣿⠻⠯⣿⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡾⠁⠀⣴⣿⣿⣿⣿⣦⢀⢘⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⡀⢋⡀⠐⠀⠈⡛⣼⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠳⠀⠀⠀⠀⡄⡴⢩⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣤⣄⢀⠀⠀⠀⠙⠲⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣶⣤⡤⠴⡶⢂⣼⣿⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣶⣤⣄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣶⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⢿⣿⡿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠸⢀⡀⢀⠠⠅⣧⡄⠇⢠⡁⣎⠻⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⣤⣽⣽⣬⣿⠂⠀⠠⣿⠀⠀⠉⠓⠂⢀⣿⣿⣿⣿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠉⠉⠛⠿⠘⠂⠀⢯⡄⠘⠀⠀⠈⠉⢻⠛⣿⡟⠛⠇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢲⡇⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⠄⠠⣴⠆⠀⠀⡔⡄⡠⠀⠛⢺⢛⠠⠀⡀⠀⣷⢤⡟⣤⣤⠀⢄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣧⠀⠀⠀⢐⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠐⠀⠐⠎⠓⠀⠀⠁⠁⠈⠀⠸⣝⣶⡄⠀⡐⠂⣸⢻⠓⣿⠀⢰⠸⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀ ⣥⣿⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠩⠁⠀⠀⠀⠈⠈⠀⢸⠀⢀⡀⠀⠹⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⢤⢀⣀⠂⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢳⣐⡀⡀⠀⠁⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡧⠰⡀⠀⠀⠀⠀⠀ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠈⠀⠀⠈⠀⠀⠈⠠⠀⡌⠃⠀⠒⠒⠐⠒⠀⠃⢀⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡀⠀⠀⠀⠀⠀ ⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢸⣿⣿⡟⠷⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀ ⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢸⣿⡏⠀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢼⣿⣿⣿⣿⣿⡷⢀⢀⣤⣤⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢲⣧⣄⡀⠀⠁⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢚⣿⣿⣿⣿⣷⡧⡾⣿⣿⠶⠂⠀⠐⠐⠀⠀⢶⣼⣷⠂⠂⠀⠀⠐⠒⠈⠆⢽⣿⣿⣧⣼⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⣸⣿⣿⣿⣿⣿⣟⡉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢠⡤⠠⠀⠀⠀⠀⠀⠀⠀⢹⡿⣏⠉⢻⣷⢸⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⠠⠀⠀⣿⣿⣷⣿⠝⣿⣿⣣⠀⡄⠁⠀⠀⠂⠀⠀⠀⠀⠒⠚⠃⠁⠀⠀⠀⠀⠀⠀⠂⠁⠈⠃⠀⢸⡟⢸⢸⠁⠈⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⢽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠈⠇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⣐⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⡇⢸⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⣿⡏⣿⣿⠛⠉⠀⠀⠀⠉⢇⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⣥⣀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣤⣿⣇⠀⢀⢀⣾⡿⠋⠁⠀⠀⠈⢻⣿⠁⠀⠀ ⣿⡇⢸⡧⡀⡄⡄⠀⠀⠀⠀⠱⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢋⣿⡙⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡉⢠⢸⢸⡏⠀⠀⠀⠂⠀⠀⢸⡟⠀⠀⠀ ⣿⡇⠘⢷⢹⡅⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⢿⠀⢸⠈⠘⠯⣦⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⡏⡇⠀⠈⠑⠥⠦⠼⠦⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣀⣀⣄⣀⣀⣄⢤⣴⡆⢤⡄⢀⣀⠠⢀⡀⣦⢀⣀⡀⠠⢺⠀⢸⠀⠀⠀⠛⠻⠷⠄⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢡⡄⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⠒⠉⠀⢰⣧⡇⠠⣧⡞⠀⠀⠀⠀⠀⠈⠉⠁⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠀⠈⢠⡤⣼⢿⠃⠐⡿⠃⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⢣⠀⠀⠀ ⠀⠀⠀⣠⠁⠐⠋⡆⠈⠉⠀⠈⠻⠟⠀⠀⠀⠁⠀⠀⠀⠀⣄⠉⠉⠀⠀⢣⠀⠀ ⠀⢀⠖⢡⡀⢀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠳⣄⡀⠀⠀⠱⠀ ⠀⡼⠀⢠⢝⣿⠉⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣧⡆⠀⠀⠀ ⢠⠁⢠⠿⠛⠁⠀⠀⠈⡷⠤⣀⠀⠀⠀⠀⢀⡠⠒⠊⠹⠁⠀⠀⠀⢀⡝⠀⠀⠀ ⢘⢀⣠⡇⠀⠀⠀⠀⠀⢧⠀⠀⠉⠓⡶⢿⡉⠠⡀⠀⠀⠇⠀⠀⠀⢨⣩⡷⢀⡀ ⠸⣮⠀⠃⠀⠀⠀⠀⠀⣾⣦⠀⠀⣴⠃⠀⢳⡀⢱⣀⡼⠀⠀⠀⠀⠀⠀⠸⠞⠁ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣟⠳⣶⠇⠀⠀⠀⢻⣇⢩⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⡄⠀⠀⠀⢠⢿⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡶⠀⠀⠀⠸⣄⠆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⡞⠀⠀⠀⠀⠀⢸⣅⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠒⠂⠀⠐⠶⠶⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠀⣀⣤⢶⡿⠿⠿⢿⢶⣤⡀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⣾⠋⠀⣸⣧⡀⣰⣾⡆⠉⢿⣶⣤⠤⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢀⣾⠇⠀⣼⡿⠻⣿⡿⢻⣿⣆⠀⢻⣿⣤⣀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⢀⣸⣿⡄⢸⣿⠇⠀⠈⠀⠀⢻⣿⡄⣾⣿⣿⣿⣶⣄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡀⠀⠀⢈⣸⣷⣽⣿⣦⣝⣀⣤⣤⣤⣤⣼⣭⣾⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⣤⣶⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣭⣛⣿⣿⣿⣿⣿⡄⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣆⠄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠁⠁⡿⢏⣺⣽⣷⣯⣿⡄⠀⡀⠀⠀⣼⣻⡿⠧⣤⡈⠛⠂⠀⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠉⡿⠋⢠⣶⣚⣿⡄⠀⠀⠀⢰⣿⣟⣳⣦⠀⢻⡀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢻⣿⡇⠀⠀⠀⡇⠀⣿⣿⣭⣿⣷⠀⠀⠀⢸⣿⣯⣿⡿⡇⠀⡇⠀⠀⠀⣿⣿⠋⠁⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⣸⣿⣿⠀⠀⠀⣧⠀⢻⣿⡿⠋⠁⠀⠀⠀⠀⠉⣻⣿⣿⣧⣀⠇⠀⠀⣴⣿⣿⡀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⣼⢻⣿⠃⢀⣶⣄⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⢀⣰⡇⠉⢻⣿⣷⡄⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠸⠟⠀⢸⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⡄⠈⣿⣿⣇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠃⠀⢸⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠈⠙⢿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠟⠉⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠙⠛⢿⡛⢿⣿⣿⡿⣿⣿⣿⠿⣻⠟⠛⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣤⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣰⣷⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⢿⡿⠉⠻⢿⣷⣦⣄⣀⣀⣀⣀⣀⣠⣤⣾⣿⣿⣿⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⢠⣿⠁⠀⠀⢸⣿⠋⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⢩⡀⠘⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⢀⣾⣷⣠⠤⣤⣸⡿⣿⣷⣶⣤⣤⣴⣶⣿⣿⢿⣿⣾⠿⠶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⣀⣿⣿⠉⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠏⠀⠀⠀⢀⣴⣿⡟⣧⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠿⣦⠀⠀⠀⠀⠀ ⠀⠀⣴⡿⠁⠀⠀⠀⣰⣾⣿⡿⠃⠘⣷⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣿⡶⣶⣿⡋⠘⣿⣿⣿⣿⣿⡇⠆⢽⣷⡀⠀⠀⠀ ⢠⣾⡛⠁⠀⠀⢠⣠⣿⣿⡿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠈⢿⣿⣿⣿⡿⠀⠆⠀⠙⣿⣧⡀⠀ ⠉⠉⠛⢶⣦⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣃⣀⣠⣶⠿⠛⠉⠉⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢻⣿⣷⡽⠋⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⢄⠀⣹⠟⠁⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡄⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⡾⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⠉⡇⠀⠀⢸⠆⠀⠀⢸⡿⠀⠀⠀⠀⠀⠂⣦⣶⣶⣶⣶⣤⠴⣶⣦⣹⣷⣾⣶⡶⠐⠒⠒⠲⠂⠸⣿⡀⠀⠀⣧⠀⠀⣸⠋⠉⠀⠀⠀ ⠀⠀⠀⣿⡀⢠⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣤⣬⣿⣿⣿⣿⣯⣤⠖⠂⠀⠀⠀⠀⢿⡇⠀⠀⠹⣆⠀⢿⠀⠀⠀⠀⠀ ⠀⠴⠚⠛⠛⠉⠁⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠉⠹⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠙⠚⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⠛⠀⠀⠈⠉⠉⠛⠻⣶⣤⣀⠀⠘⠛⣿⡀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⢀⣠⣴⠞⠛⠋⠉⠁⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣄⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀ ⠀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀ ⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀ ⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡤⢆⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⠏⠀⠀⠀ ⠀⠀⠀⠙⠛⠻⠿⠿⠿⠾⠿⠿⠿⠟⠋⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⡛⠁⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡾⢽⣯⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⢺⡇⠛⠚⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣀⣶⣷⣾⣿⣿⡶⢠⠎⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣚⠏⣴⢏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⡀⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡘⢉⣾⡍⣈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡟⢤⢿⣿⢿⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡰⠋⡼⢿⡷⠿⠿⡿⠛⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣢⣴⣤⣄⣹⣿⣤⣄⣤⣔⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠉⠉⠁⠀⠀⠀⣠⣀⣈⣉⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⢀⣴⠞⠋⣯⠈⠙⡿⢷⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢀⣾⠿⣷⣾⣷⡈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⡄⢿⠟⠀⠙⠁⣿⣇⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠻⠾⡴⠶⣤⣤⣿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⢀⡶⠖⠀⠉⢀⣀⣴⣶⣤⣴⣶⣶⣶⣶⣾⣿⣷⣮⣭⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠶⣤⣔⣲⣲⣾⡧⣴⡶⢛⣿⣿⣿⡿⡿⣿⣄⠘⠀⠈⠉⣽⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⣤⣤⡀⠙⣿⣽⣿⡀⠀⠈⠑⠛⢿⣿⣞⡳⣾⠙⠃⠀⠀⣴⣿⣿⠛⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⣀⣁⡀⣿⣿⣿⣧⠀⠀⠀⢠⣿⣟⣿⡇⠹⡀⠀⠀⣶⣿⣦⠹⡆⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠯⠄⠀⣿⣿⡿⠃⠀⠀⡀⠸⣿⣿⣿⠇⣼⠀⠀⠀⣿⣿⣿⣀⡇⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⠋⠀⠀⢀⢰⣿⣦⡈⠉⠑⠚⠁⠀⠀⠀⠀⠈⠉⠙⠻⢾⡇⠀⠀⠀⠀⠐⠒⠢⢤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣼⡀⠀⠀⠀⠈⢺⣿⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣥⡀⠀⠀⠀⠀⠀⠀⠘⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢹⣿⠿⣿⣿⣷⣤⣀⡤⠠⢀⣠⡿⢻⣿⣿⣿⡇⢸⡆⠀⠀⠀⢰⡾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠠⢀⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢿⣤⣈⡛⠛⠛⢻⡿⠛⠉⠉⣠⣿⣿⣿⢿⣡⣞⠀⠀⠀⠀⣀⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⣠⣴⠞⠛⠛⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠈⠻⣿⣿⣿⠿⠋⠀⣠⣴⣾⡿⠛⠉⠉⠉⠉⠈⠉⠛⠒⠒⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⣀⡀⢀⣄⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣾⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠈⢧⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡴⣾⣿⡿⣽⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢷⡀⠀⠈⢧⢀⣼⣿⣿⣿⡟⡻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣫⣾⡿⠋⣼⠟⠃⠙⣧⡀⠀⠀⠀⣀⠀⠀⠘⣆⠀⠀⢀⣧⡀⣤⠾⠟⢈⣿⣿⣿⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠀⠴⠇⠂⠀⢤⣾⣿⣷⣄⠀⠹⡄⠀⠀⣹⣖⣆⣨⣿⡇⠀⢀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣟⣿⣇⢀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣷⣬⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣯⣽⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⠃⣀⡀⢙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏⢿⣍⣈⣿⣿⣿⠋⠀⠀⠻⣶⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡈⢟⡾⣿⠟⢁⣠⣀⣀⣴⣿⣿⡿⠟⢛⣻⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⡿⡃⢻⣼⣋⣠⣼⣿⣿⣿⣿⠟⣡⡴⠟⠉⢁⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣶⣿⣿⣿⣿⣿⣿⡿⢋⣠⡾⠋⠀⠀⢀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣹⣿⣿⣿⡿⢋⣴⣟⣋⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢛⡿⠿⠛⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣵⣞⣉⣥⠴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣦⣶⣶⣶⣶⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⡿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠿⠿⢿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠻⠿⣷⣤⣀⠀⢀⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢻⡀⠀⠀⠀⠀⠀⣰⠋⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣠⣿⣿⠀⠀⠀⠀⠀⣿⣶⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⣤⣶⣶⣶⣄⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣄⣄⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣦⣤⣶⣶⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⡛⠉⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠙⠻⢿⣶⣄⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣯⣴⣶⡄⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢰⣶⣤⡙⢿⣧⡀⠀⠀ ⠀⠀⣸⣿⠋⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡎⢻⣿⡄⠀ ⠀⢰⣿⠇⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⢹⣷⡀ ⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⣶⣤⣤⣀⣀⣠⣤⣴⣶⠶⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇ ⠀⠈⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣿⡿⠛⠉⠻⢿⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⡿⠏⠀ ⠀⠀⠀⠈⠉⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠿⠛⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠉⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⢀⠀⠀⠀⠀⠀⣾⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣴⣾⠇⠀⠀⠀⠀⢰⣿⣿⣿ ⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣦⠘⣿⣿⣿⣦⣄⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣟⣳⣦⣬⣤⣤⣴⣶⣾⣿⣿⣿⣶⣦⣦⣤⣬⣝⢻⣄⡛⠷⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢃⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣷⣄⣀⣀⣀⣄⣀⣉⣙⡻⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣉⣉⣉⣙⣋⣁⡀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡀⠙⢿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⠛⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⠟⠿⢿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣯⡁⢹⣿⣿⣿⣿⣄⢠⡟⡁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⡟⠉⣴⣾⣿⣦⣍⠻⣿⣿⣿⣿⣿⣿⣿⣯⣙⡛⠷⠞⢛⣋⣿⣿⣿⣿⣿⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣇⠸⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡏⣰⣿⣿⣿⣿⡇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣦⡙⣿⣿⣿⣿⡎⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿⢠⣿⣿⣿⣿⣿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⢿⣶⣬⣉⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡿⢃⣾⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡌⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠉⣁⣬⣽⣶⡏⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠟⠉⠁⣶⣶⣬⣉⣛⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡍⠉⠁⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣿⠇⣄⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢻⣿⣿⣿⣿⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣦⠀⠀⠀⣰⣦⡀⠀⣼⣆⠀⢸⣿⠸⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢰⣾⣿⣿⣿⣿⣿⣧⡀⢀⣿⣿⣿⣾⣿⣯⣆⢸⣿⢣⣭⣭⣭⣭⣭⣭⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⠀⠀⠀⠀⠈⠻⠟⠛⠛⣛⣛⣛⠛⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣮⣽⣿⣛⠛⢛⣉⣭⣶⣾⣿⣿⣿⡿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣦⣙⠛⠿⠿⠟⠛⣛⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣛⢿⢿⣿⣿⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜🟥🟥🟥🟥🟥⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜🟥🟥🟥🟥🟥🟥🟥🟥🟥⬜⬜⬜ ⬜⬜⬜⬜🟩🟩🟩🟨🟨🟩🟨⬜⬜⬜⬜⬜ ⬜⬜⬜🟩🟨🟩🟨🟨🟨🟩🟨🟨🟨⬜⬜⬜ ⬜⬜⬜🟩🟨🟩🟩🟨🟨🟨🟩🟨🟨🟨⬜⬜ ⬜⬜⬜🟩🟩🟨🟨🟨🟨🟩🟩🟩🟩⬜⬜⬜ ⬜⬜⬜⬜⬜🟨🟨🟨🟨🟨🟨🟨⬜⬜⬜⬜ ⬜⬜⬜⬜🟩🟩🟥🟩🟩🟩⬜⬜⬜⬜⬜⬜ ⬜⬜⬜🟩🟩🟩🟥🟩🟩🟥🟩🟩🟩⬜⬜⬜ ⬜⬜🟩🟩🟩🟩🟥🟥🟥🟥🟩🟩🟩🟩⬜⬜ ⬜⬜🟨🟨🟩🟥🟨🟥🟥🟨🟥🟩🟨🟨⬜⬜ ⬜⬜🟨🟨🟨🟥🟥🟥🟥🟥🟥🟨🟨🟨⬜⬜ ⬜⬜🟨🟨🟥🟥🟥🟥🟥🟥🟥🟥🟨🟨⬜⬜ ⬜⬜⬜⬜🟥🟥🟥⬜⬜🟥🟥🟥⬜⬜⬜⬜ ⬜⬜⬜🟩🟩🟩⬜⬜⬜⬜🟩🟩🟩⬜⬜⬜ ⬜⬜🟩🟩🟩🟩⬜⬜⬜⬜🟩🟩🟩🟩⬜⬜

[+..••]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠛⠉⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡍⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⠀⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠒⠦⢤⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡀⠔⠋⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠰⣨⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢀⣀⣠⡤⠖⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡁⣀⡿⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢫⣿⣿⣿⣿⠃⠁⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⣤⡀⠀⠐⠀⠈⠀⠀⠀⢀⣤⢖⡛⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡘⣿⣿⣿⠃⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⡀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⢠⡞⣔⠪⢜⠱⣪⢵⣻⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡃⠀⠉⠀⠀⠻⠤⠤⠤⣾⣶⣶⣶⣶⣾⢿⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣰⣎⡑⢪⣵⣭⢳⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⣿⣆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣳⡽⣞⣯⣞⣿⣇⠀⠀⠀⠀⠀⠐⠈⣿⡼⢿⡷⣥⢻⡌⣟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠩⣽⣆⠀⠀⠀⠀⠀⠀⠐⢹⣾⣳⢿⣹⣞⣿⡾⣿⠆⠀⠀⠀⠀⠀⠀⠹⣯⠽⣿⣧⣳⢽⣺⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡱⣚⣿⡄⠀⠀⠀⠀⠀⠀⠐⠻⣯⣟⣿⡿⣧⡟⣿⡅⠀⠀⠀⠀⠀⠀⠀⠙⠿⣜⣻⣝⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡹⣞⣿⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⡉⠵⣖⡂⣿⡐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠘⠀⠀⠀⡄⢀⠃⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢥⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠄⠀⠀⠁⢲⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⣾⣿⡉⣹⣏⠙⠙⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠄⠀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡳⢿⡮⡿⣧⢹⣦⡄⠀⠀⠀⠀⠀⠀⣼⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠃⠠⠀⠄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠋⠉⠁⠀⠀⠹⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠿⡿⡏⠊⠉⢛⠻⣻⣬⡇⠀⠀⠀⠀⠀⠀⠘⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠄⡈⠄⢡⠈⠔⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠤⢤⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣴⢶⡄⠀⣲⡟⠀⢨⣸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⢠⠘⡀⢂⠐⡈⠄⡨⣐⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡶⠞⡧⠄⣜⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠉⠲⡿⣟⡤⠞⠁⠀⠀⠙⢢⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣠⠴⠋⣄⠒⡈⢄⠂⡐⠄⢃⢰⣬⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠮⠁⠸⢯⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠤⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⢧⡀⠀⠙⢦⣡⠀⠒⡐⠠⢒⣠⣬⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⣘⢀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠙⢧⡂⠅⢒⡌⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠯⠬⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠙⢮⡈⢷⣇⡸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠲⠦⠤⠤⠤⠤⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⡠⠛⣦⣿⠿⣽⣻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣆⣀⣴⡿⣟⢯⡟⣶⢏⣟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣧⢻⡞⣽⡺⣽⣺⠽⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣽⣳⡯⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠸⣯⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠂⠀⣿⣾⣱⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠂⠀⣿⠾⠷⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⠀⠀⡀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⠀⠐⡀⠀⠂⠀⠀⠀⠀⢰⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠠⠐⠈⠀⠀⠀⢀⠀⠀⠀⠀⠄⢀⠄⡀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠒⠀⠀⠀⠠⠀⠀⢂⠈⠐⠈⠀⣄⡤⠶⠒⠚⠛⠓⠒⠒⠮⢤⣀⡀⠀⠀⠐⠀⠁⠂⠄⠀⡄⢀⠁⡀⠂⠀⢀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠁⠀⠀⣀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⢤⣤⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡟⢻⡛⢫⠍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢹⡏⡡⣇⡘⣌⠡⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡇⢹⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⠀⠿⣇⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣧⠀⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣇⠀⠹⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠁⢀⢀⣠⣶⡋⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⣾⠃⠀⠹⣻⠁⢸⡇⠀⠀⢀⡏⠀⣿⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣿⣇⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⣿⣷⣿⡇⠀⠀⢸⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣿⣿⡀⠀⠀ ⢀⣾⢻⠇⠀⠀⠀⢿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀ ⣼⠃⢸⡄⠸⢆⠀⠘⢷⠏⢠⣤⣄⠀⢻⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣷⠀ ⢻⣄⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣿⡇ ⠈⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⠒⠶⠒⠛⠁⣀⣼⡿⠀ ⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣷⣶⣶⣾⣿⠿⠋⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀ ⠀⣰⡿⣻⣿⣿⣿⣿⣦⡉⠓⠦⠤⢄⣀⡀⣀⡠⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣻⣿⣧⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠛⠿⠟⠛⠛⠛⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⣀⡤⢍⡻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣴⡛⠁⠀⠀⠀⠀⠘⢰⣷⣾⡐⢸⡗⠶⣄⠀⠀⠀ ⠀⠀⣤⢶⡏⠀⠀⠈⢧⣀⠤⠔⠒⠚⠊⠘⠚⠓⠚⠧⢄⣸⠀⠀⠀ ⠀⢸⡇⠈⣧⠀⠀⠀⠈⡧⠤⠤⠤⠤⠄⠐⠒⠒⠒⣶⣶⣮⣷⠀⠀ ⠀⠀⢷⣀⡬⠳⢤⣤⠼⠁⠀⠀⢰⠛⡄⠀⡔⢳⠀⢸⡏⠉⠀⠀⠀ ⢀⡴⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡇⠀⣷⣼⠀⣸⠷⠚⠲⢦⠀ ⣿⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠹⢏⡾⠁⠀⠀⠀⢸⡇ ⢿⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡟⠀⠀⠀⠀⠀⢸⠇ ⠘⣧⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣼⡄⠀⠀⠀⠀⢠⡟⠀ ⠀⠈⢧⣄⣀⡴⠏⠈⠙⠛⠛⠒⠚⠛⠋⠉⠀⠙⠦⣤⣤⡴⠋⠀⠀