Algas marinas Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣼⣿⡆⠀⠀⠀⠀⠀⣿⣿⣼⣿⣫⣤⡄⠀⠀⠀⠀⠀⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣦⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣀⠹⣿⣿⣿⣿⣿⣷⠀⢠⣦⣸⣿⣧⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣷⣶⠀⠀⠀⠀⢸⣿⣷⣼⣿⣿⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⢻⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠁⢀⣶⣶⢸⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⣀⠀⠀⠀⣠⡀⢻⣿⢁⣀⠀⠸⣿⣿⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⡇⠀⢰⣿⣿⣼⣿⣾⣿⠀⠀⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⠏⠀⠀⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⠟⠁⠀⣼⣿⣾⣏⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⣠⣦⡄⣠⣿⣯⣤⡄⠀⢹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢹⣧⣿⣿⡟⣿⣿⣿⡿⠁⣠⡘⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣿⣿⡟⠀⣿⣿⠋⠀⢸⣿⣿⣿⣿⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠃⠀⣿⡇⠀⠀⠸⣿⣿⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢻⣿⠀⠀⠸⣧⣾⣦⠀⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣤⣶⣿⣿⡇⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⢻⣿⣿⡇⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠙⣿⡇⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠃⠋


⣿⣿⣿⣻⣛⣟⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣟⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⣠⠖⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡞⢩⠟⠀⠀⠀⢠⠞⠁⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⠀⠀⣰⠋⢠⡏⠀⠀⠀⢠⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢀⡇⠀⢸⡇⠀⠀⠀⠀⢠⠏⠄⢸⠀⠀⢀⡴⡋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡳⣄⠀⢸⡇⠀⢸⡇⠀⠀⠀⢠⠏⠀⠀⣼⢀⡴⠋⠈⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣤⠶⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣆⠸⡇⠀⠈⣇⠀⠀⠀⡟⠀⠀⣰⠃⡞⠀⠀⠀⡼⠃⠀⠀⢀⣀⣀⣴⣞⢉⣱⠏⠥⠄⠀⠀⠀⢀⣴⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⡀⢷⠀⠀⢻⠀⠀⢰⡇⠀⣴⠃⣸⠀⠀⢀⡼⠁⣠⠖⠋⠁⠀⠀⠀⣀⣠⡤⠤⠴⠶⠖⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⣧⠸⡆⠀⢸⡇⢀⡾⠀⠀⡇⢀⣟⠀⣠⠎⡠⠞⠁⠀⣀⡤⠴⠚⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠸⡆⢿⠀⣸⠇⡼⠀⠀⡀⣧⣾⠃⣰⣣⠎⠀⠀⡴⢁⡟⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣇⠀⠀⣷⢸⠀⣿⢰⡇⠀⠀⠁⣿⢇⣶⣿⠃⠀⢠⠞⢠⡞⢑⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⢸⡄⠀⣼⠈⡇⢹⣸⡇⠀⠀⢸⣿⣿⣿⠇⢀⣴⢋⡴⠋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⠀⠈⡇⠀⠘⣆⡇⢸⣿⡇⠀⠀⢺⣿⣿⠏⣠⢞⡵⠋⢀⡴⠋⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣇⠀⠹⡀⠘⣿⡇⢸⣿⡇⠀⠀⢸⣿⣿⣾⡷⠋⣠⡴⠋⣠⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⠜⠦⡄⠹⣄⢹⣷⣸⣿⡇⠀⠀⣼⣿⣿⡟⡄⣰⣿⣴⢞⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⣦⠈⠳⣽⣿⣿⣇⠀⠀⣿⣿⣿⣼⡴⡫⢐⣿⡯⠴⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠘⢧⡀⠘⣿⣿⣿⠀⠀⢻⣿⣿⣏⡎⡄⣼⠋⣠⠶⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⡙⠷⣾⣿⣿⣧⣤⣆⢿⣿⣿⣼⡼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠉⡇⠀⠀⠀⠀⠀⢀⠔⣃⣿⣠⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡀⣇⠀⠀⠀⠀⠀⢸⠀⢼⠄⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣒⣶⡯⠄⡒⡜⠙⣆⠀⠀⡠⠏⢀⣎⠈⡌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢗⠊⠰⢾⣡⠘⢄⣸⡈⢡⡞⢐⢖⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢀⢅⠙⢿⡁⠹⢆⡞⠠⠰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠗⡀⢻⡄⣼⠁⢄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣣⣾⠹⡇⢰⠋⠀⠀⢀⠎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⡗⠌⡇⠀⢀⡜⢀⣓⠊⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠔⣷⠐⡇⢼⢹⡄⠃⢨⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣽⠔⠷⢣⠟⠄⠢⠊⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡏⣳⠏⠀⣰⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣸⡴⢛⡉⢕⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣿⣡⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠉⠀⠀⠀⠀⠀⢠⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢆⡇⢡⡂⠀⠀⠀⠀⠀⠰⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠙⠎⠃⡄⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣄⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠠⣠⠀⠀⠀⠀⠀⠀⠀⢈⣇⡃
⠀⠀⠀⠀⢨⣟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⣾⡥⠃⠀⠀⠀⠀⠀⠀⠈⢸⡁⡀
⠀⠀⠀⠀⠈⠫⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠁⠄
⠀⠀⠀⠀⠀⡆⠀⠀⠰⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⣿⠟⠆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀
⠀⠀⠀⠀⠀⠱⡄⠀⢆⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢻⡇⠸
⠀⠀⠀⠀⠀⠀⠸⡆⠈⠳⣀⡴⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⣠⠀⢸⡁⡐⠀⠀⠀⠀⠀⠀⡇⢸⠀⡧
⠀⠀⢂⠀⡄⠀⠀⠈⡖⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠲⣿⣧⠍⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣧⡞⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠰⠁⠀⠀⣤⠀⠀⠀⢨⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡆⠀⠀⠀⢿⠀⠀⠀⠈⠇⠀⠀⠀⠀⣀⣙⣆⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠳⡀⠀⠀⠈⢷⡄⠀⠀⢸⠆⠀⠀⠀⠁⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⢀⡹⠀⠀⠀⠀⠀⠀⠢⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠉⠀⢀⠀⡀
⠀⠀⠀⠀⠈⠓⢢⡀⠀⠙⡆⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⡐⠀⢨⣑⠀⢀⠀⠀⠀⠀⠀⠀⠘⠣⢤⡇⠀⢠⠀⠀⠀⠘⢤⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠞⠁⠀⠀⠀⠔⠈⠙⡅⠢⡀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠈⠶⠋⡴⠀⠀⠀⠀⠀⠀⠐⠂⠻⣀⣼⣀⣀⣀⣰⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠊⠀⠀⠀⠈⠀⠑⢤⠀⠀⠀⠀⢀⠈⡱⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣄⠀⠀⣆⠀⡆⠀⠀⠀⠀⠘⢤⣀⡿⣠⢄⠋⠀⠀⠀⡠⠊⠀⠀⠈⠉⠉⠑⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⢘⠀⢡⠀⠀⠀⠀⠀⠀⠚⠷⠛⠁⠀⠀⠀⡘⠀⢀⣀⡤⠤⠤⠤⠄⠀⠒⠚⡆⠀⠀⠀⡀⠀⠁⢂⡀
⠀⠀⠋⠑⠂⠤⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠃⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠲⡏⠘⠁
⠀⠀⡄⠀⠀⠀⢀⠑⠒⠤⡀⠀⠈⠓⠤⣄⣀⠀⡀⠀⠧⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⠔⠁⠀⢰⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡼
⠀⠀⠀⠄⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠄⠀⠀⠀⣀⣀⠐⠒⡄⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⠤⠀⠀⠀⠀⠀⠰⠃⠐⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⢰⠄⠈⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠈⠂⡀⠀⠀⡇⠀⠋⠀⠀⢽⠀⢀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⡈⠀⠘⠄⠀⠀⡨
⠀⠀⠀⠀⠸⠄⠤⢤⡀⡘⠦⠄⠤⠤⠄⠤⠤⠄⢀⠃⠀⠀⠀⠀⠀⠑⢤⣄⠀⠠⣀⣀⡤⠉⠀⣀⡀⢀⣀⠀⠀⠀⠀⠀⣀⠆⢀⠜⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⡀⢀⠀⠀⠀⠀⠿⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢴⣃⣀⣠⣀⣄⣠⠼

⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⡀⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠸⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣷⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣇⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠙⠁⠀⣤⡄⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡀⠀⠀⠀⠸⣿⣾⣿⠈⣷⡀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣄⠀⠀⠀⢹⣿⣿⠀⢻⣧⠀⠀⢸⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⠀⠀⢸⣿⡏⠀⠀⢿⣇⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⢸⡿⣿⠀⠀⠈⣿⡀⠸⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⠀⠀⣿⡅⣿⡄⠀⠀⢸⡇⢰⠀⣿⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⢿⠇⠀⠀⣿⣿⠙⣿⠀⠀⠀⢃⡜⢰⡟⠁⢀⡄⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⠀⠀⣿⣿⡃⢸⣇⠀⠀⠘⢇⣾⡇⠀⢸⡿⠀⠀⠀⢸⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣤⠀⠀⠀⠀⣿⣿⡇⠘⣿⠀⠀⠀⢸⣿⡇⢀⢻⡇⠀⢠⡆⢸⠀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⠀⠀⠀⠀⢿⣿⡇⠀⣿⡆⠀⠀⢀⣿⠀⢸⣿⠃⠀⠀⠁⣠⡄⠉⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⣸⡏⠀⣸⡟⠹⠀⠀⠀⠙⠀⠀⠦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣇⠀⠘⣧⠀⠀⣿⠇⠀⡿⠀⠀⣠⠀⢰⡀⠀⠀⣤⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠘⣿⣿⠀⠀⢿⠀⢠⡟⠀⢰⡇⠀⠀⠙⡀⠘⠃⢀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠏⣿⠀⠀⢸⡆⢸⡇⠀⢸⡇⠀⠀⠀⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⣿⣷⡄⠀⠀⢀⣦⣿⠀⠀⠀⣷⣾⠁⠀⣼⠀⣿⠀⠀⠙⢶⡶⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⠀⠀⡇⠀⠸⡆⠀⠀⣬⠇⠀⠀⢀⢹⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⢰⣿⣿⡇⠀⠀⣾⣿⣿⠀⠀⠀⠈⣿⠀⢸⡇⢀⠙⡀⣠⡄⢸⠀⢀⠀⣼⠛⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⣿⠀⣿⠀⠀⠸⣿⣿⠃⢸⠀⢨⡖⢯⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⢯⣴⠏⢠⡄⠀⠀⢻⠀⠀⠀⠟⠀⢸⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⡟⠀⠀⠱⣀⠀⢰⡄⢰⣧⠀⠀⢸⡇⠀⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⢸⡇⢰⡆⠀⠈⢧⡿⠁⠘⠁⠀⠀⠘⡇⠀⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡄⢀⠀⢸⡇⢸⡇⠀⠀⢀⠀⢴⡀⠀⠀⠀⠀⠀⣸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣿⣿⣿⣿⡀⠀⠀⢰⡇⢘⠀⢸⡇⣸⡇⠀⢦⠀⠐⠻⡇⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢻⣿⣿⣿⡇⠀⠀⢸⡆⣸⡆⢸⣧⣿⠀⠀⠈⡇⠀⠀⣷⠀⢰⡇⢰⣸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⢴⡿⠀⢸⡿⠃⠀⠀⠀⢰⠀⠀⠛⠀⠸⠃⢸⡟⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡾⠀⠈⢧⠀⡇⠀⠀⣴⣾⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣹⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠈⣶⡇⠀⢰⣿⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠏⣽⡇⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⡞⠁⠀⠀⠀⠈⡇⠀⢸⣿⠋⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡇⠀⠀⠀⠀⠀⡇⠀⣿⡟⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⡘⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠚⠀⠀⠀⠀⢸⣟⣷⣾⠃⠀⠶⠀⠀⠀⠀⡇⠀⣿⡏⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡏⣿⠏⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣀⡿⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣠⠞⠉⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡐⠉⠂⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⢳⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢦⠟⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠉⢀⡇⠀⠀⡀⠀⠀⠀⣀⠀⠀⠹⡀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢸⠀⠀⡎⢹⠆⢀⣸⠀⠱⣀⣠⠇⠘⠦⠴⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡄⠰⣍⠁⠀⠈⠲⠞⢁⡞⠀⠙⠲⢤⡀⠈⡀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⢠⠶⠤⠼⠀⡇⠀⠈⣆⠈⠠⠀⢠⠎⠀⣀⠀⠀⠀⠘⡆⠈⠀⠀⠀⠘⠦⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠘⠦⣀⠠⢸⡁⠀⠀⡸⠐⠀⢠⣇⢀⡞⠁⡇⠀⠀⠀⣽⠔⢦⠀⠀⣠⠴⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠑⠒⠚⠁⠀⡀⢸⠁⠛⠀⡜⠀⠀⠀⠀⡏⠀⡞⠀⡜⠁
⠀⠀⠀⠀⠀⠀⢰⠒⢦⣀⠇⠐⠀⠀⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⢸⠁⠀⠑⠒⠛⡆⢀⡔⠓⡆
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣞⢳⢀⢤⡁⠸⡇⠀⠳⠤⢄⠀⠀⢸⠀⢀⠀⠀⢸⠁⣸⠀⡰⠁
⠀⠀⠀⠀⢀⠤⠤⣤⠼⠐⠀⠀⠸⡌⠋⢰⠃⢀⡇⠀⠀⠀⡼⠀⢀⡏⠀⠀⠀⠀⡈⠉⠁⠀⠳⣄
⠀⠀⠀⠀⠻⣄⣀⠀⠀⠀⠀⠐⠀⢳⠀⠘⠲⠚⠀⠂⠀⠀⠧⠤⠞⠀⠀⠀⠀⠀⠁⠀⡤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠓⢬⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠐⠀⠈⠀⣠⠞⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡁⠀⢀⡀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⢮⣿⠃⠀⠀⠀⠀⡈⠓⠀⢈⠃⠀⠀⠀⢀⠀⠀⠀⠀⢰⣄⡀⣼⣾⣥⠄⠀⠀⠀⢹⣦
⠀⠀⠀⠀⢹⣿⣄⠀⡷⠀⠀⠀⠀⠀⠀⢹⣷⡆⠀⢀⣿⣤⠄⠀⠀⠀⠷⠄⠞⠈⢥⠄⠀⠀⢳⣤⠊⠀⣀⣬⣿⣷⣿⡟⠞⣀⠀⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⣯⢸⣗⠀⠀⠀⠀⠀⠘⠛⢛⣷⣄⣹⣿⡅⠀⠀⣀⣀⠘⡄⠀⠀⠀⠀⠄⠀⠀⢻⣤⠃⠉⠹⠿⠿⡿⠿⠿⠍⢰⠇⠀⢸⣿⡇
⠀⠀⠀⠀⣴⣿⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣌⣻⣿⡏⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢦⣃⣇⠘⠃⠀⠀⠀⢠⣄⠀⠀⠀⠀⢿⣧⠀⣾⣿⠀⣷
⠀⠀⠀⣴⣿⣿⡏⢾⡿⣠⣠⣤⠀⠀⠀⠀⠀⠙⣿⣿⠟⠉⠀⠀⠀⣴⣈⣈⣱⠆⠀⠀⠀⠙⡷⢠⠇⣄⡄⠀⢈⣿⡀⢀⠀⠀⠸⣿⣇⢻⣏⣼⠙
⠀⠀⠀⢺⡇⠹⠆⣹⡿⠏⠁⠐⢇⡀⠀⠀⠀⠀⠻⠟⠀⠀⣠⣀⣤⣿⣿⣿⣿⡀⠀⠀⢦⢠⠈⡌⣼⠋⠀⠀⢀⣽⠃⣸⠀⠀⠀⠘⠻⠎⠋⠁
⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⢀⣀⢫⡄⠀⠀⡾⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠀⠺⠛⠁⠀⢀⡟⢘⣏⠇⣸⠇⢰⡆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⣍⠘⠀⠇⠰⠦⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣵⡘⡜⡆⣻⠃⢼⡇⠀⣤⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣭⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣈⡞⣧⡧⣿⢠⣾⠀⠀⢹⡄⢸⡇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⢤⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⢫⠆⠿⢎⠋⠀⢀⠀⣿⢸⣇⣿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣦⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⢸⡟⣿⡞
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⣇⣿⠁
⠀⠀⠀⠀⠠⣬⣧⣧⣞⡤⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⠾⣿⠱⣾⠱⠎⡉⣿⣿⣹⠱⣿⠡⢾⡏⣮⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣿⡿
⠀⠀⠀⠈⣓⣾⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣫⣾⣙⣻⣼⣧⣷⣴⣤⣿⣘⣻⣌⣻⣇⣫⣼⣿⡟⠀⠀⠀⠈⠋⠉⢠⠄⠀⠘⠇⠿⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⣤⣾⣄⠄⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠈⠒⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⢁⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠙⢃⣤⡆⠀⠀⢻⡦
⠀⠀⠀⠀⠀⠀⣿⣿⡟⣼⣿⡟⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢰⠃⠋⢠⡀⠀⠀⠀⢀⣤⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠉⠀⠀⠀⠶⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣼⠃⠈⠳⣽⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⢄⡠⠄⠠⠀⠀⣀⣀⠀⠻⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠹⣆⢩⡀⠀⠀⣏⣾⠁⡀⢠⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠻⢃⠀⠰⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢉⡳⣬⡿⡏⠀⢀⣷⠟⠀⠀⠀⠀⢀⠀⢦⡀⢠⠀⠀⠀⠀⠀⠈⠲⠀⢠⠂
⠀⠀⠀⠀⠀⠀⣆⡠⣝⠧⠀⠀⠠⡆⠹⣧⠀⡴⠀⠰⠀⠀⠀⠀⠀⠀⠠⠽⠶⢿⣧⣧⠼⠋⠀⠀⠀⠀⠠⡈⢧⡄⣷⣿⣄⣤⣀⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢀⡿⣒⢲⣞⢆⡀⢠⡄⣰⢧⣠⣁⡾⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡧⠤⠄⠀⢀⠀⣼⠁⣷
⠀⠀⠀⠀⠀⢠⣛⣋⣰⡖⣊⠄⠀⠀⠀⠀⠉⠀⠁⠐⢌⡇⠈⢠⡉⠀⡀⢠⠄⠈⠋⠀⢀⢀⣴⣷⠂⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢺⣀⣿⠀⣸⡇
⠀⠀⠀⣸⡄⣝⡰⠀⣿⣏⠐⣾⠥⠀⠀⠀⠀⠀⠀⠀⠄⢉⠦⣉⡁⡈⣡⢊⠁⠀⠀⢀⣘⣿⣿⣿⣷⣦⣴⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣴⢻⡇
⠀⠀⠀⠹⣿⠚⠀⠠⣓⠖⠀⢈⣈⠵⠀⠀⠀⠀⠀⠈⢃⡹⣦⣿⡩⢅⡞⠉⠀⠀⠀⢸⣿⣿⣵⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢺⣇⣿⡇⢿⡀
⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠿⠓⠁⠀⠀⠀⠀⠀⠀⠛⠛⠿⠛⠟⠛⠉⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠛⠘⠃

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣤⣽⣥⣮⣭⣿⣵⣿⣹⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠠⠀⣿⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⠇⠀⣸⠀⠀⠀⠀⢰⡇⠀⠀⡀⠀⠀⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⠀⠀⡿⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⡾⠁⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⡇⢰⠇⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⣿⡇⠀⠀⠀⣰⢿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⠷⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⡇⠀⠀⢰⠇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢇⠙⢦⣄⡀⠀⠀⠘⣇⠀⠀⢀⠀⠀⡇⣧⠀⠀⣾⠀⢿
⠀⠀⣰⡆⠀⠀⠀⣿⠀⠀⠠⠄⠘⢦⠀⠈⠙⠓⠶⠦⢿⣄⣀⠘⡄⢸⡇⠹⡄⠀⢹⡀⠈⢷⡀
⢀⡾⣿⠀⠀⠀⠀⢸⡄⠀⠀⢇⠀⠀⢳⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠚⢧⡀⢻⡄⠘⣧⠀⠀⠹⣆
⣸⠁⡟⠀⠀⠀⠀⠀⢷⡀⠀⠘⡄⠀⠈⢻⣟⠷⢶⣤⣤⣀⣀⣀⠀⠀⠀⠈⢆⠹⣄⠘⣧⠀⠀⠸⡆
⡏⠀⣷⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⢆⠀⠀⠙⢦⡀⠀⠀⢹⡇⠉⢻⣦⠀⠀⠈⡆⠘⢷⣹⡆⠀⠀⢿
⣇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠣⡀⠀⠀⠻⣄⠀⠀⣧⠀⠘⢸⡆⠀⠀⣇⠀⠀⠙⢷⠀⠀⣿
⠸⡄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠈⢦⠀⠀⠹⡆⠀⣿⠀⠀⣸⠃⠀⢰⡿⣧⡀⢀⠎⠀⢠⠿⣆
⠀⠹⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡁⠀⠀⢻⡀⡏⠀⣰⠏⠀⢠⡟⣀⣼⠿⠋⠀⣠⠋⠀⠈⣧
⠀⠀⠈⠳⣄⡀⠀⠉⠓⠤⣄⣀⣀⣀⣀⠀⠀⠙⣆⠀⠸⣿⣣⡾⠋⣀⡴⠿⠛⠋⠁⢀⣠⣞⠁⠄⠀⢀⡟
⠀⠀⠀⠀⠈⠙⠶⣤⣀⡀⠀⠀⠉⠉⠉⠉⠛⠲⣿⣤⡾⠛⢁⡠⠊⠁⢀⣠⡤⠶⠾⠯⠶⠋⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⣤⣀⠀⢀⠀⢸⠏⠀⢠⡞⣡⠶⠛⠉⠀⠀⣀⡀⠀⣀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣭⣷⣄⣢⣸⡄⠀⣿⠞⣁⣤⣀⡤⠞⠉⠀⠉⢿⡉⠁
⠀⠀⠀⠀⠀⠀⢠⡾⠯⢍⡀⠀⠀⠀⠀⠀⠀⠈⢻⣧⢀⡿⠮⠭⠤⢤⣀⡀⠀⠠⠄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⠀⠀⢹⣀⣀⣤⣤⡼⣧⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⡇⠀⠉⠻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠘⢦⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠣⡀⠀⠉⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢠⡐⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⢄⠀⠀⢀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⢦⣤⣬⣤⣄⣀⣤⣿⠿⠋⠀⠙⠳⠶⠶⠤⢤⣤⣤⣄⣀⣀⡀⠀⠀⣠⡤⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⢘⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠇⠀⢸⡇⠀⠀⠀⠀⢸⠃⠀⠀⢸⠀⠀⢸⡇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⡀⠀⣸⠃⠀⠀⠀⠀⣾⠀⠀⠀⣾⠀⠀⢸⣷⡏⠀⠀⠀⠀⢀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇⢀⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⣰⢿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠸⡿⣼⠃⠀⠀⠀⠀⠀⢿⠀⠀⠀⢨⠀⠀⢸⣿⠀⠀⠀⢰⠇⣾
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠘⢧⣄⠀⠀⠀⠀⠸⡆⠀⠀⢸⠀⠀⣸⢹⡆⠀⠀⣿⠀⢿
⠀⠀⢀⣤⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣆⠀⠉⠛⠶⢦⣤⣄⣿⡀⠀⠀⡆⠀⣿⠀⣧⠀⠀⢿⠀⠈⢧⡀
⠀⣠⣾⡏⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠈⢳⣄⠀⠀⠀⠀⠈⠉⠉⠛⠒⠳⠦⣿⡀⠘⣆⠀⠸⡆⠀⠈⠻⣄
⢰⠏⣼⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⡀⠀⠀⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⣧⠀⢹⡄⠀⠀⠙⣆
⣾⠀⣿⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠱⡄⠀⠀⠻⣦⡉⠉⠛⠛⢲⡖⠲⢦⣀⠀⠀⠀⢳⠈⢳⡄⢻⡄⠀⠀⢹⡄
⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠙⢆⠀⠀⠈⠻⣄⠀⠀⠈⣇⠀⠘⠻⣆⠀⠂⠘⡆⠀⠙⢦⣧⠀⠀⢸⡇
⢷⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠲⡀⠀⠀⠙⣦⠀⠀⣿⠀⠀⠀⣿⠀⠀⢰⣧⠀⠀⠀⢹⠀⠀⢸⡇
⠘⣇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠘⢦⠀⠀⠘⣇⠀⣿⠀⠀⢠⡟⠀⠀⣼⠛⢷⣄⣠⠆⠀⢠⡏⠻⣦
⠀⠘⢧⡀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⢹⡄⡟⠀⣠⡟⠀⢀⣼⢃⣠⡾⠟⠁⠀⣠⠏⠀⠀⢸⡇
⠀⠀⠀⠙⢦⣄⠀⠀⠈⠓⠶⢤⣤⣀⣀⣀⣀⡀⠀⠹⡆⠀⢸⣿⣡⡾⠋⢀⡴⠿⠛⠋⠉⠀⣀⡤⣾⠁⠄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠦⣿⣠⡾⠛⠁⣠⠞⠉⠀⢀⣠⠤⠶⠿⠧⠶⠛⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⣤⣀⠀⢀⡀⠀⣸⠋⠀⢀⡾⢃⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣙⣳⣄⡙⣄⢿⠀⠀⣾⡵⠋⣀⡄⣀⡤⠖⠉⠉⠙⢿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⡋⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣆⠀⣿⣴⣚⣋⣉⣉⠀⠀⠀⣀⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠘⢿⡞⠉⠉⠉⠉⠉⠉⠙⣆⠀⠀⢀⣀⣈⣧⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⢀⣿⠶⠛⠉⠉⠉⠉⠉⠛⢻⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠆⠀⠀⠀⠀⠈⢆⠀⠀⢤⣀⠀⠀⠀⠹⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢿⣄⣀⡀⠀⠀⠀⠀⢰⠇⠀⠀⠙⢦⣀⣀⣠⡴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠶⠶⠶⠶⢤⣤⣤⣾⠿⠛⠁⠀⠈⠛⠛⠛⠶⠶⠶⠶⠶⢤⣤⣤⣀⣀⣀⣠⣴⠞⠉
⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣠⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠖⠒⢆⠀⠀⠣⣀⠴⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠃⠀⠀⠀⡜⠁⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⢄⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠒⢄⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⠅⠉⠀⠀⣸⠀⠀⠀⠀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠰⡞⠀⠀⠀⠀⠀⠉⢱⡾⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⡀⠀⠀⢱⣄⣀⣴⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠘⠤⢞⡁⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢣⠀⠀⠀⡌⠇⡏⠓⠒⢊⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠤⣀⢁⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡆⠀⢸⠃⠘⣷⠀⠀⡜⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡅⠀⠀⠀⣱⢩
⠀⠀⠀⠀⣤⠀⠀⢲⡅⢠⠀⠰⠀⡞⠀⠀⠍⠆⢰⠁⠀⠀⣣⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⡴⠓⠒⠃⢸
⠀⠀⠀⠀⠘⢳⠀⢸⡇⠀⠀⠠⣰⠀⢰⣰⠀⠸⡼⠀⠀⠀⣿⠀⢠⡞⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⠀⠈⡄
⠀⠀⠀⠀⡜⢸⠀⡜⡇⣀⡠⠦⡇⠀⠘⡑⢄⣀⡙⡀⠀⠀⡷⠀⡎⢃⠀⠀⢱⡄⠀⣿⠀⠀⠀⠀⠀⣦⠄⠸
⠀⠀⠀⠎⢀⠎⡜⠀⠉⣼⣁⣀⣵⠀⠀⠐⣄⡀⠉⠁⠀⠒⠇⢃⠰⡀⠣⡀⡘⠰⠀⢧⠀⢀⣄⠠⠔⠉⠀⠀⡇⠀⡀
⠀⠀⠰⠀⡸⠋⢈⠀⣼⢸⡏⢀⠞⢦⠀⠀⠘⢯⡉⠳⠒⢦⠀⢀⠳⣧⠀⠟⢀⢃⠆⠈⠀⣀⣀⣤⡶⠀⠀⠰⠀⠀⠛
⠀⢀⠞⢀⠀⢴⡛⡀⢹⡀⠣⡎⠀⡪⠷⢄⡀⠀⠱⡌⡇⢈⠀⡸⣄⠈⢀⠀⠾⠁⡀⢰⠃⡈⢠⠊⠀⢀⡐⠁⠀⢀⠂
⠀⠈⣄⠀⢵⣤⣉⠙⠂⢑⢄⡈⠊⠤⣤⣀⡛⢢⡀⣷⡡⢊⡴⠷⠊⣠⡎⠀⡀⠮⣡⡘⢄⢡⠇⡠⠖⠉⠀⢀⠔⢁⡐
⠀⠀⠈⠓⠦⡤⠤⢄⠉⠺⣧⠙⠒⢦⣤⣀⠈⠉⡷⢉⣔⠥⠐⠈⠙⢋⡡⣀⠙⠒⠀⠉⣠⡝⢦⠗⠚⢀⡀⠤⠒⠉
⠀⠀⠀⢀⣰⣁⠀⠀⠄⠁⠺⣼⡯⡖⠒⠊⠛⠲⣇⣸⣥⢒⡊⠀⠈⢇⠀⠀⢩⠃⠀⠂⠨⣽⣠⠆⠚⠁⠀⢤⡀
⢠⠊⠉⠉⠀⠈⠈⠓⢄⠀⡠⢹⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣨⠖⠒⡺⠒⠒⠛⠒⠲⠀⠀⠀⠋⠀⠀⠀⠀⠀⢹
⣆⠀⠰⠀⠀⠀⠀⠀⠀⠱⡀⣸⠀⠀⠀⠀⠀⠀⠀⠈⢠⠎⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢸
⠈⠑⠤⠀⠀⠤⠤⠤⠄⠒⠋⠻⠄⣀⣀⠀⠀⢀⣤⠴⢇⣀⣀⣀⠀⠑⠢⢄⡠⠤⠤⠤⠐⠋⠒⠦⠤⠤⠄⠒⠊

⠠⢂⡠⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⢀⡀⠀⠀⠀⠀⠀⠀⠒⠘⠒⢾⣸⣗⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⣷
⠈⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⣦⠀⣿⡟⠊⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢹⣿⣟⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢻⣿⣣⣾⡿⠖
⠀⠀⠀⠀⠀⠐⢾⣶⣾⣦⡀⠀⣿⣿⠇⠀⠀⠀⢀⣤⡿⣠⠄⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣤⣄⣿⠟⠉⠀⠀⢄
⠀⠀⠀⠀⢀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠀⢀⡀⠀⣴⣿⡿⠃⠀⠀⠀⠈⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠠⣐⡮⠂⠀⠀⠀⠀⠸⣿⡏⠀⣸⠃⢈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⢡⠂⠔⠂⠈⠀⠀⠂
⣦⣀⣀⡀⠀⠀⠀⠀⢰⣆⠀⢠⣿⠇⠸⣿⡾⣿⣿⣇⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⣋⣍⠉⠀⠀⠀⠀⠀⠺⠋⠀⠘⠋⣠⠀⠸⣧⣯⣿⠇⠀⠀⠀⣠⣶⣿⣿⣿⡿⠃⠀⠀⠀⠠⡆⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣠⣿⣯⣄⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠂⠀⠀⠑⠆⣠⣜⡡⠮⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⠉⠁⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣏⡀⠀⠀⠐⠟⣡⠟⠃⠰⡠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠰⠤⣄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⡖⠀⠀⠀⠁⠀⠙⠀⠀⠀⡌⠀⠁⡰⠁⠈⢀⠇⠨⢀
⢠⠀⠀⠀⠀⠀⠀⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⢠⠃⠀⣂⡼⣤⠆⠈
⠎⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣥⢒⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠟⣱⠁⠂⠐
⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣠⣦⣀⣠⣾⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠉⠀⡜⠘⢀⡇⡴⠋⢊⡴
⠀⠀⠀⠀⢐⣿⣿⣿⡀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⢿⣿⣿⣿⣿⡌⠁⠀⠀⠀⠀⠀⠀⠐⠳⡄⣶⠂⣸⣠⣧⡜⠋
⠀⣤⣄⠀⠈⢿⣿⣿⣇⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠂⡁⠄⢹⣾⡿⡁⠀⣀⡄
⠀⢻⣿⣷⣦⣸⣿⣿⣿⡇⣼⣿⣿⠃⠀⠲⢀⣂⠐⢂⡀⠀⠀⠀⠀⠄⠀⡄⠰⠆⠀⠀⠀⠀⠀⠂⠀⠘⠉⠑⢼⡇
⠀⠀⠙⣿⣿⣷⡙⣿⣿⣤⢸⣿⣿⡀⠐⠒⣨⢛⠃⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠺⢃⠠⢄
⠀⠀⠀⠈⠻⣿⣿⣿⣻⣷⡄⣿⣿⡇⠀⠪⠅⠈⠁⠈⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠁⠀⠐⠀⠸⠐
⠀⠀⢀⠀⠀⠉⠿⣿⣟⢻⡇⠘⣿⡁⠀⠀⠀⠀⠀⠀⠤⠂⠀⠨⢥⠀⠠⠀⠀⠀⠀⠀⠀⠀⢂⡠⠄
⣷⣾⣿⣿⣿⣷⣶⣌⠛⠌⠃⠀⢹⠀⠀⠀⠀⠀⣀⡀⠀⠳⣆⠀⡀⣢⠀⠐⠂⠀⠀⢀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠛⠋⠛⠉⠉⠉⠋⠉⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠑⢦⡀⡌⠓⢂⣟⣀⠀⡶⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣛⠒⠂⠀⠀⠀⠀⠁⡦⠀⠀⠙⣤⡀⠸⠘⠁⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣰⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠉⠂⠁⠀⠀⠀⠀⠀⠁⠀⠠⢙⣧⣴⡷⠃⣠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠈⣿⢙⣿⡇⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣰⠶⣒⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢀⠀⠈⠑⡍⠒⠀⠃⢰
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠠⡈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣉⡆⠀⠱⡀⢀⠇⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢸⠰⣅⡠⠜⠀⠀⠀⠀⠀⠀⣠⣤⣄⠤⠀⠀⠹⢌⣀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠾⡷⡢
⠀⠀⠀⠀⠀⠀⠈⡆⢄⠀⠀⠀⠀⢄⠀⠀⠀⢃⠑⠴⠃⡁⠀⠀⠀⠀⠀⠉⠑⢆⠀⠀⠀⡇⢀⠄⠀⠑⢊⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠊⣢⡀⠀⠀⠈⢦⠀⠀⢈⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢁⠠⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣒⢄⠀⠉⠒⠊⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⢐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⡠⠊⠀⠀⠀⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠜⢹⠫⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠃⠀⠀⠀⠐⡊⠅⠀⠡⢖⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠌⠀⠈⠐⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⢁⡀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠉⠉⠐⠢⡀⠀⠀⠀⠀⢸⠀⡠⠊⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⢄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠁⠀⠀⠠⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠣⡀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢷⢄⣀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⢀⡤⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠢⡀⠀⠀⠀⠀⠀⠁⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⡀⠀⠀⠀⣈⠵⢄⡀⠀⠀⢸⠀⠀⠀⠀⠈⠀⡀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠚⠂⠀⠅⣨⠋⠀⠀⠀⠀⠈⠉⠉⠐⢄⠀⠀⠚⠁⠀⠀⠀⠈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣗⠒⠒⠂⢄⣀⠠⠊⡓⠀⠤⠄⠒⢀⡐⠀⢉⣽⡤⠄⠋⠩⠷⠤⠤⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠚⠁⠂⠀⠀⠒⠉⠀⠀⠀⠈⠚⠥⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠘⣷⠀⠀⢀⣴⢶⣦⠀⠀⠀⠀⢠⡿⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣿⡀⠀⣾⠃⠀⣿⠆⠀⠀⠀⢸⡇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠹⣧⣼⠏⢀⣼⠏⠀⠀⠀⠀⢸⣇⠀⠀⣿⠀⣀⣴⠶⠶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠈⣿⠀⠀⠙⠛⠋⠁⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠐⣿⣀⣠⣄⣀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣦⠻⣆⠀⠈⠉⠉⠉⠹⣿⠻⣧⣀⠸⣧⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡇⣿⠀⠀⠀⠀⠀⢀⣿⡾⠛⠙⠻⣿⠀⠀⠀⢠⣿⠁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⢻⣆⠘⠿⠋⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⢹⡇⠀⠀⠀⠛⠷⠾⠛⠛⠉⢹⣧
⠀⠀⠀⠀⠀⢸⣟⠉⠉⠻⢶⣄⡀⠀⣿⡆⠀⠀⠀⠀⠀⣴⠟⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠉⠛⠻⠋⠀⠀⠀⠀⠀⣼⢯⣾⣿⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣽⣿⣶⣄⠀⠀⠀⠀⠻⣦⣴⣿⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⣴⠶⣮⣝⣻⡇⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⢸⡇⠀⠀⠀⣰⡿⠷⣦⠀⠀⠀⢀⣠⣴⠾⠛⠛⠉⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠈⢿⣄⣀⣼⠏⠀⣼⠿⠟⢻⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣏⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⡀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣈⠙⠻⣷⠀⠙⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠈⠙⠛⠿⠋⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣴⡶⠾⠛⣛⣻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠙⠻⣶⣄⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⠛⣛⣩⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣤⣤⣭⣿⣆⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠟⠋⠉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⣿⠛⠛⠷⣦⣄⠀⠀⠀⠀⢀⣴⠶⢿⡟⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠛⠃

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢦⡀
⠀⠀⠀⠀⠀⢤⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⡅⠀⠙⠂
⠀⠀⠀⠀⣇⣯⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣀⠂⣼⠟⠁
⠀⠀⠀⠀⣘⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡿⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠷⠀⢸⣦⣷⡖⠂
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣼⣶⢎⢠⣿⣋⣀⡀
⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠼⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠀⢀⠀⠀⠴⠀⠀⠀⠐⠀⠀⠀⠀⣄⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠘⢧⡀⢸⢿⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠄⠐⢶⠉
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠥⠀⠀⠀⠀⠀⠈⠛⠈⠸⣇⡼⠃⠂⠀⠀⠀⠀⠀⠀⠀⢌⡁⠈⠡⠀⠟⠠⠾⡆⢠⠀⡀
⠀⠀⠀⠀⠄⣠⣷⠒⠀⠀⠝⠁⡈⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⠁⠀⠀⠀⠈⠀⠀⠀⠉⠸⠃⣧⢀⣙⣀⣆⣀⠷⡆⠁⠈⡁
⠀⠀⠀⠀⢠⠠⡇⠀⠁⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢂⢠⠇⠀⠀⠀⠀⠀⢀⡀⢀⡀⣐⣰⣿⣿⣿⣿⡿⣷⣤⡅⢀⣦
⠀⠀⠀⠀⢈⡄⣷⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠀⠀⠀⠀⠀⠀⠈⣁⣘⣅⣸⣯⣿⣿⣷⣿⣼⠟⠙⠗⠘⠅
⠀⠀⠀⠀⠈⣷⣿⡗⡜⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣿⣼⠁⠀⠀⠀⠀⠀⠹⠛⢳⣼⣿⣿⣿⣿⣿⡏⡰⡄⠠⠖
⠀⠀⠀⠀⠀⢹⣿⣿⠃⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⠈⢀⠹⣿⣿⣿⣿⣿⡟⢱⡏
⠀⠀⠀⠀⠀⠀⠁⠻⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⠿⠛⠛⠛⠑⠇

⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠁⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠶⠀⠀⢨⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢡⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠁⠀⡀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠀⠀⠀⠀⠀⠙⠒⠀⢻⠂⠀⠸⢠⡀
⠀⠀⠀⠀⠀⡒⠠⠀⠈⡍⠹⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣹⡏⠀⠠⠖⢠⠇
⠀⠀⠀⠘⠀⠘⣆⡠⢀⠑⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⢀⡔⠀⢀
⠀⠀⠀⠐⠂⠀⠈⠢⢤⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠋⠠⢀⠉
⠀⠀⠀⠀⠀⣀⠀⢀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⣂⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠈⠀⠤⠵⠆⠀⠴⠶⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣵⣖⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⠔⠚⠋⢱⣄⣀⠀⠀⠀⠀⣀⣠⣤⢾⡑⠀⠀⠉⠉⠛⠓⠦⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠀⠀⠀⡶⠛⠉⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠙⠓⠞⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⡉⡛⢿⣙⣠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣠⠶⠛⠉⠀⠙⢀⣁⣒⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣿⠀⢠⠾⠋⠨⠛⣤⠀⠀⠀⠁⣸⠛⢻⢿⢿⣎⢥⢴⣶⣶⣦⣤⣀⠈⠛⢿⣿⢛⡟⠂⠔⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢰⣿⣉⣴⣿⠀⠀⢀⣤⠛⣷⠀⢻⡀⠛⣶⣿⣫⣬⠘⢾⡌⠉⠀⠀⠈⠙⢻⠒⣤⣽⣿⣿⡆⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣤⠴⣫⣀⣶⣼⠻⢮⠇⢈⣽⣿⣿⣷⡀⣨⡷⡀⠀⠀⠀⠓⢀⢤⡟⠈⠻⣿⣿⡄⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡬⣿⣿⠇⣄⣽⣿⣿⣿⢆⣈⣰⣦⠙⣿⣿⣿⠗⠎⠀⢨⣿⣧⡤⠀⠐⠮⡿⣴⠃⠈⠿⡧⠀⢀⡾⢘⠇
⠀⡤⠀⠀⠀⠀⢹⣧⡘⠷⢶⣾⣿⣿⣿⣧⣶⣿⠛⢀⣴⠟⠛⢿⣿⣄⣴⣿⣿⣿⡿⠀⠦⠀⠈⢫⠙⡋⠀⡰⢂⣾⢣⠈
⠀⢳⣾⣦⣤⣄⠀⠈⠻⡖⢶⣿⣿⣿⣿⣟⠛⠧⠸⠟⠁⡄⢠⣿⣿⠛⠙⣿⢿⣟⠛⢷⡀⠀⠀⠀⠀⠀⠀⣠⠾⠡⠎⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠹⣿⣿⣿⡷⠤⢠⣦⣀⣿⣿⣿⣿⣿⣞⠀⠀⠀⠀⠀⢸⣿⠘⠀⣾⢻⣼⡿⠀⠈⠀⠀⠀⠀⠁⢠⣄⠘⢂⣠⡔⠒⢈⣩⠄⠀⠀⠀⠁
⠀⠀⠀⠈⠛⠾⠿⣶⣤⣼⣿⠻⣶⣿⣛⠙⠇⢗⡤⠀⠀⠀⠛⢠⡄⠀⢸⠂⠙⡿⢶⡀⠀⠀⠀⢈⣡⢶⢿⡟⡋⠉⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⡟⠻⠿⠿⣿⣿⣦⡋⠁⠁⠀⠀⡀⣸⡇⠀⠾⠀⠀⠀⠁⠈⣀⣴⡾⠯⠄⡍⣌
⠀⠀⠀⠀⢠⠴⢋⣩⣤⡞⢡⣴⣦⣤⣄⣹⣿⣿⣄⣀⣠⠤⠉⠀⠀⠀⠄⢀⣀⣀⣠⣞⣋⣀⣴⡖⠚⠓⠛⢶⣌⠒⣄⡀
⠀⠀⠀⣴⠟⠚⠋⠁⠀⠀⣠⠰⠙⠉⠉⠛⢛⣏⣯⣻⠽⣿⣿⢿⣭⣿⣽⢿⣿⣾⣿⡀⠉⣩⣉⣛⣷⢆⠀⠀⠈⠓⠪⣱⣄
⠀⠀⠀⡷⠀⠀⠀⢀⣤⠾⠋⠛⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠓⠌⠉⠉⠛⢧⠱⠄⠀⠀⠀⠀⢬⣃
⠀⠀⠀⠀⠀⢀⢤⡿⠉⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡉⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⠿⠟⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣠⡄⣠⣀⡀⣀⣀⣀⢀⠀⠀⡀⢀⡀⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣷⣾⣦⣴⣶⣶⣾⣷⣾⣷⣾⣷⣿⣿⣶⣷⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡠⣤⣰⣄⣤⣀⣠⡀⡀
⠀⠀⠀⢀⣠⣴⣶⣶⣿⣾⣿⣿⣷⣿⣿⣿⣷⣦⣤⣶⣆⣶⣠⣤⣄⣤⣤⣠⡀⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣾⣿⣷⣶⣶⣴⣤⣤
⠀⠀⠸⠞⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠸⠆

⠀⠀⢀⣀⣀⣀⣠⣄⣄⣠⣤⣤⣄⣀⣄⣀⡀⣤⣦⣤⣦⣶⣤⣤⣤⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢤⣶⣦⣷⣿⣾⣦⣠⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡀⣀⢀
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶

⠀⠀⠀⠀⣄⣠⣀⣆⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⡀⠀⡀⢀⣀⠀⢀⠀⠀⠀⠀⢀⡀⣰⣄⣆⣴⡀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⢠⣴⣾⣿⣿⣿⣿⣿⣾⣷⣷⣾⣶⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣷⣧⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣾⣷⣾⣷⣾⣶⣷⣾⣷⣷⣾⣦⣰⣤
⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⣀⣠⣄⣄⣦⣠⣤⣤⣤⣤⣴⣀⣀⣤⣦⣤⠀⣀⣀⣠⣴⣦⣤⣀⣀⠀⣀⣠⣷⣿⣿⣤⣄⣄⠀⣀⢠⣀⡀⠀⣤⣤⣤⣀⠀⠀⠀⠀⡀⢀⢰⢠⡀⡀⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠃⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠃⠀⠀⠀⢈⠀⠀⠀⠀⢄⠎⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡐⡐
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠸⠀⠀⢰⠀⠀⠀⠘⡜⠀⡄⣼⡞⠀⠀⠀⠀⢰⠃⠀⠀⢰⢸⠀⠀⠇⠀⠀⡇⠀⡀⠀⢰⠁⠀⡰⡕⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⢃⠀⠀⡆⠀⠈⡇⡸⠀⣴⠃⠀⡷⡽⠀⠂⠀⡄⢀⢾⢀⠀⠀⠀⠀⡆⠀⠀⢀⠀⢻⢠⠀⢰⡎⠀⣶⢡⠁⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠁⡇⢸⠀⡄⢀⠇⠀⢣⠇⠀⣿⠀⢐⢣⣇⢀⠀⢰⠇⡜⣸⡼⣸⠁⢃⠀⡇⠰⢰⣤⠀⢸⡾⠀⣼⠁⠀⠃⣾⠀⡂⡘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣇⠈⣠⠀⣾⡀⠀⢸⠀⢀⡇⠀⠘⡼⢻⢸⠀⡼⣰⢁⡿⠃⢰⡄⢸⡇⠁⡄⢰⣯⠀⠀⡇⠀⣹⠀⢠⢹⢻⢀⢁⠇⡼⡇
⠀⠀⠀⠀⠀⠀⡇⢻⠀⡟⠀⡇⡇⠀⢸⠀⣼⡇⠀⣷⠇⣾⢸⢠⣧⠇⡜⣸⢠⡀⢸⠀⡇⢸⠇⢸⢹⠀⢀⡇⢸⣿⠀⣸⡏⢸⠐⡜⠰⢡⠃
⠀⠀⠀⠀⠀⠀⡇⢸⢰⡇⠀⡇⢣⠀⣿⠠⡟⡇⢠⡟⠀⡟⢸⣌⣿⡎⢠⡏⢀⢃⢸⡄⡇⢸⠀⢸⠸⡄⢸⠁⡼⣿⠀⣿⠁⡾⠀⣷⠁⡜
⠀⠀⠀⠀⠀⠀⢸⢸⣼⠇⢀⢷⢸⣦⣿⣸⢡⡇⢸⡇⢰⣧⣸⣿⡟⢠⢻⡇⢸⢸⡀⣇⢱⠹⡀⠸⣿⣧⣼⢠⡇⣿⢰⡏⢠⣧⣠⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠉⠈⠉⠉⠉⠈⠁⠁⠁⠈⠉⠉⠉⠁⠁⠈⠁⠈⠀⠁⠉⠈⠀⠁⠁⠉⠉⠉⠉⠁⠉⠈⠁⠈⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⢈⠉⠙⣳⣶⡤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠰⢿⣶⠶⠂⠀⠀⠀⠈⠓⠦⣄⡉⢣⡀⡤⠋⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠑⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡦⠊⠀⠀⠀⠀⠀⢀⡀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠶⠏⠀⠀⠀⠀⠀⠂⠀⢠⠄⠃⠘⠈⢳⣬⡆⠀⠀⠀⠀⠀⠀⡄⠈⠉⠁⠻⣧
⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⢠⣶⡆⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⣿⡧⠠⣄⡀⠁⢠⢶⠆⠀⠀⠀⣠⡇⢀
⠀⠀⠀⠀⢻⡄⠈⢆⡀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄⠈⡷⢀⣼⣿⠀⠀⣠⡾⠏⠀⡞
⠀⠀⠀⠀⠀⠡⣄⠀⠈⠀⠐⠯⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠛⠉⠉⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠤⣤⣀⡈⠩⢷⣄⣀⡀⣦⣄⣀⣦⣀⣤⣾⡿⠏⢀⣀⣐⡦⠀⠀⠋
⠀⠀⣠⣤⣤⣄⠀⣐⡀⠠⢧⠤⠤⠤⠄⢾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⣤⠤⠄⢠⡬⠁⢐⠂⠀⢠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⡠⠴⡂⢀⣀⠀⠗⠁⠀⠀⠈⠁⠀⠲⠀⣀⣀⢁⠶⠴⠆⠀⠲⠄
⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠼⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠦⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠒⢦⡀⠳⡀⠀⠀⢠⠀⢰⠁⠀⡀⠀⣰⠋⠀⠀⠀⡀⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⣠⠀⣸⡆⣿⠀⣼⠁⣰⣇⠀⠀⣶⡞⢠⣶⣫⠄⠀⣦⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⢠⠈⣧⣾⡇⡼⢹⣷⣿⢰⣿⣦⡟⣿⡆⣰⣿⣇⣿⡟⠁⡄⣸⣿⡤⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⢦⣌⢻⣎⣷⣿⣿⣿⣷⢺⣿⣿⣾⣿⣻⣇⣿⣿⣿⢹⣿⣿⣶⢠⣿⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣏⣼⣿⣿⣿⡇⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⣷⢠⡏⣸⢀⢰⠀⠀⠘⡄⡀⡆⢳⡀⡇⠀⠀⢰⣇⣠⠄⢸⠀⡾⢠⠇⣄⡆⠀⡀⣠⠖⠁
⠀⠀⠀⢦⣜⢆⢳⢸⡆⣿⢸⣷⣏⡌⣿⣾⣷⢲⣷⢇⣻⣼⡇⡇⢸⠁⣿⣼⣁⣇⢸⣸⣷⣿⣸⣹⡷⢰⣾⣃
⠀⠀⠀⠀⠙⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣾⣿⣶⣿⣾⣿⣿⣿⣷⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢲⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣧⣀⠙⢶⡀⠀⣠⡆⢻⣤⢸⣗⣿⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣿⣿⣮⣿⣶⣿⢃⣾⣿⣼⣿⣿⣿⡆⣴⣎⣴⣏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⢦⣠⠀⣲⣄⢧⣱⡄⡇⠀⣤⡆⠀⡀⣷⣰⣣⣇⣴⣂⣄⣰⣤⢳⣱⡄⡆⢠⢀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠋⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠈⢻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠃⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⣿⣿⣿⣟⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢘⣿⣿⣿⡟⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⢿⣿⣧⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⠿⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⣷⣶⣶⣶⢞⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢶⣶⣶⣶⣿⡿⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣄⣀⣉⣉⣭⣶⡿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠻⣷⣮⣭⣉⣁⣀⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠿⠿⣫⣴⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣬⡻⠿⢿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢛⣿⡿⠋⠁⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠈⠻⣿⣟⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠟



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⣋⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⠛⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀

⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣧⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡄
⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠰⣿⣟⣷⣼⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣠⣘⣿⣟⣃⢀⠄⠀⠀⠀⠀⠙⠿⠾⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⠗⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⡿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄
⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢺⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⣀
⠀⠀⢠⣴⣶⣷⣤⣀⣀⠀⠀⠀⠀⠀⣾⣿⣷⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⡞⣻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠉⠛⠿⣿⡿⠃⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠰⡿⠟⠛⠻⢿⣿⡿⠀⠀⠀⢷⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠻⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠰⣟⣿⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⠀⣾⢁⡴⠀⠀⢠⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⣴⠋⡜⣿⣿⠁⠀⠀⠀⣷⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢮⣷⡀⠀⠀⠀⠀⠀⠀⢹⣆⣼⠇⢰⢱⢏⠇⠀⢦⠀⠀⢻⡇⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠰⢼⣿⡜⠀⡏⡜⣸⠀⠀⠘⣧⠀⢸⢿⠟⠀⠀⠀⢠⡆⠀⠀⢀⡤⠂
⠀⠀⠀⠉⠳⣦⣌⡿⡕⡄⢰⡄⠀⡸⢱⣮⡑⠧⡇⡇⠠⣄⠀⢻⡷⣱⢇⢲⡀⠀⠀⣾⠀⣠⡴⠋⠀⠀⠀⢀
⠀⠀⢀⣀⠀⠈⠳⢽⡱⠸⡀⢷⢀⠇⣮⢸⢸⢳⣌⠣⡀⢹⢣⡜⡴⣿⢸⠀⢿⡄⠀⣿⢞⠟⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠈⠻⡦⣄⠈⢇⢇⢳⣸⣿⣴⢹⡘⣼⢸⠈⠧⡙⣄⡟⣰⢳⢹⢸⠀⣸⡘⡴⣳⣇⢠⡀⢠⢞⠝⠁
⠀⠀⠀⠀⠀⠈⢪⡳⣸⢾⡸⣽⣿⢸⣿⣿⣿⢸⢀⡶⠳⡘⣇⡏⣿⢸⢸⣰⡏⡿⣵⡇⣿⡘⡷⢡⠎
⠀⠀⠀⠀⠀⠀⢀⣱⡘⡎⡿⣿⣹⣼⢹⢹⡏⣿⠋⡇⠀⣷⢸⡇⢿⣿⢸⣿⡽⣱⠹⡇⢋⡿⢡⡇⢠⡖⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠻⣧⡸⣧⢹⢾⠿⢸⡈⡇⣸⣸⣳⣤⣿⣄⣇⣸⡟⢸⣸⠇⣿⡠⠧⢼⡇⡞⡗⢹⣁⡼⡇
⠀⠀⠀⢠⣄⣸⣧⣠⣣⢱⡿⠼⢾⠊⠐⠛⠛⠒⢂⡠⠤⠄⢠⠖⢉⡇⡜⠸⣼⡧⠘⠠⠁⠙⣟⠑⠛⠨⠟⡓⢤⢤⡀
⠀⠀⠀⢀⠜⠏⢉⡧⠾⠛⡓⠒⠚⠣⠭⠑⢀⣈⣁⡬⠓⡒⠣⢄⠡⠍⢁⠈⠘⠍⠩⢃⠀⢐⣒⠭⣍⣐⣂⣈⣀⢗⠁
⠀⢠⡔⣇⣐⣀⡁⠠⣄⣰⢀⡬⠖⢒⠒⡊⠁⠠⢀⡽⠿⢯⡉⠩⠩⠍⠉⢍⠉⠒⠲⠚⠉⠻⠶⠤⠤⠋⠰⣿⡵⠈
⠀⠀⠉⠀⣈⣩⡍⢉⡉⢉⡛⠾⢤⠤⠴⠤⠜⠒⠒⠒⠒⠚⠁⢀⣂⣠⡤⢤⡀⠀⣀⡤⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠙⠒⠒⠛⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠦⠤⠚⠉⠐⠂⠑⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡎⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠈⡆⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠼⠤⠚⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⠢⠼⠤⠼⡄
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡜⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠘⡄⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⢰⠁⠀⢀⠞⠀⠀⠀⠀⢶⠆⠀⣀⣀⣀⡀⠀⢶⠆⠀⠀⠀⠘⢆⠀⠀⢱⠀⠀⠀⠀⠀⣏⡇
⠀⠀⠀⠀⢻⡉⢢⡀⠀⠀⣏⢉⡶⠯⣄⠀⢀⡠⠔⡊⠉⠉⠀⠀⠀⠈⠉⠉⠒⠤⣀⠀⢀⡬⠷⣎⢉⡇⠀⠀⣠⠊⡹⠃
⠀⠀⠀⠀⠀⠙⢄⡱⢄⡀⠈⠫⣀⡁⢊⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⠀⣁⡨⠋⠀⣀⠴⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣹⠒⠒⠢⠽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠅⠒⠒⢺⡡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣓⣒⣒⣛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣓⣒⣒⣋⣉⣉⣀⡀
⠀⠀⠀⠀⠀⢀⠴⢺⡥⠼⠦⠤⠤⠤⣤⡤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⡤⠤⠤⠤⠾⠤⣽⠢⢄
⠀⠀⠀⠀⠀⣷⠞⠁⠀⣀⠴⣋⣉⣉⣁⣠⠤⢜⣲⣄⣀⠀⠀⠀⠀⠀⢄⣂⣴⣛⡤⢤⣀⣉⣉⣉⡳⢄⡀⠀⠙⢶⡇
⠀⠀⠀⠀⠀⢿⠀⠀⢰⢧⠞⠁⠀⠀⡶⢿⡭⠥⠬⠷⠚⠋⠉⠉⠉⠉⠛⠲⠯⠤⠬⣭⢷⡄⠀⠀⠑⢦⢷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠘⠇⠀⣼⢸⠀⠀⠀⠀⢱⠔⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠓⢴⠁⠀⠀⠀⢸⢸⡄⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣢⣄⠀⠀⠀⠑⠮⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠬⠖⠁⠀⠀⢀⣤⣪⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⠁⣤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣴⠋⡜⣇⣾⠃⠀⠀⠀⢷⡀
⠀⠀⠀⠀⢀⣳⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣾⠃⣸⢸⠏⡏⠀⡀⠀⠀⢸⣇⠀⠀⣠⠴⠂
⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⢀⢸⣿⢎⡏⢀⠇⡜⣸⠀⠀⢹⡄⠀⢸⢿⣴⡾⠁⠀⠀⢀⡀
⠀⠀⠀⠠⣄⡀⠈⢿⡷⡄⠀⢀⠀⠈⠙⣿⡺⢄⣸⢠⠃⡇⠀⠀⠀⢿⣆⡸⣫⢋⠀⠀⠀⠀⣼⠁⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠈⠛⢗⢼⡜⡜⣆⠘⣆⠀⣸⢠⢿⡲⣍⠻⣼⠁⠘⣦⡀⢸⠞⡴⡿⡈⢷⡄⠀⢠⣿⢀⣴⠟⠁⠀⠀⠀⢀⡄
⠀⠀⠀⢤⣄⠀⠀⠑⢷⢹⠸⡄⢻⡄⡇⣼⡀⡇⡏⡳⢌⠳⡄⠸⣱⠎⣼⢳⡇⡇⠘⡟⡄⢸⡼⡫⠋⠀⠀⠀⡠⣾⠋
⠀⠀⠀⠀⠉⠻⡢⡀⠈⡇⣇⢳⣼⣿⢷⡇⣇⣳⡇⡇⢸⢣⡘⢆⡟⢰⣹⠸⡇⡇⢀⣷⢸⢞⡼⣥⢰⡄⢠⠞⡔⠁
⠀⠀⠀⠀⠀⠀⠙⢎⠢⣸⢿⡘⣽⣿⢸⣿⢟⣿⣧⡇⣸⡞⠱⡈⣇⡇⣧⡇⡇⣇⣿⢸⢏⣾⠀⣿⡌⡿⢃⠞
⠀⠀⠀⠀⠀⠀⠀⣈⢧⠹⡸⡿⡿⣿⣾⠘⡌⣿⠹⡾⢱⠁⠀⣧⢸⣇⢸⣿⠃⣿⣯⡎⡜⢸⡆⢇⣷⢁⡎⢀⣴⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠈⢿⣆⢹⣧⢹⣿⡿⠤⡇⢹⠀⡇⣸⣧⣤⣿⣄⣿⢸⣿⠀⣇⣿⢰⣇⣸⠧⢼⡇⡼⣷⠋⡇⣠⢾
⠀⠀⠀⢀⣀⠈⣷⡀⡨⡎⢆⣿⣸⣽⠖⠂⠷⠿⠯⠭⠉⣉⣥⡀⢀⡬⡛⡻⢰⠁⣇⣸⡍⠒⣐⠋⠳⣷⡓⠾⠍⡹⠞⢤⣀⣀
⠀⠀⠀⠀⢙⢿⡛⠻⣉⣽⠾⠥⠤⠤⢇⣒⠂⠄⠀⠒⠉⣐⡦⠤⣎⡀⢊⣙⠺⠀⠎⠝⠒⣒⠆⠀⢠⠭⢔⡒⠂⠤⠈⠐⢹⡼⠂
⠀⠀⣀⣜⠁⡀⠐⠋⠁⠀⢀⠃⢀⣀⡠⠤⠤⠔⠋⡉⠛⢤⣬⡥⠤⠽⠒⠖⠲⠷⠶⠬⠤⢤⠬⠴⢶⣋⣉⣉⣳⠒⣻⡷⢏⠒
⠀⠀⠳⠚⠒⠲⠶⠤⠬⠖⠶⣶⣩⠀⠀⠠⠐⠀⣄⣀⣘⣁⣤⡨⠆⠈⣉⠁⠀⠈⠁⠀⠀⠁⠁⠀⠀⠉⠁⠐⠐⠀⠩⠍⠉
⠀⠀⠀⠀⠶⣒⣛⣻⣶⠀⠰⠦⠉⠹⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡴⡒⠒⠛⣭⠷⡀⠰⣞⣭⡩⠭⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⡏⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣇⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⣼
⠀⠀⠀⠀⠀⠀⠛⠿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡷⠞⠃

⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⠀⠀⢀⡾⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢸⡁⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠋⠀⣹
⠀⠀⠀⠀⠀⠈⢷⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠱⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠐⣇⢀⡎⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣄⣠⣸⣶⠞⡵
⠀⠀⠀⠀⢠⠃⠀⠈⠙⠓⣅⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠈⠀⠫⠇
⠀⠀⠀⢀⡇⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢈⣰
⠀⠀⠄⢸⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣺⣻⠿⠓⠐⠻⠚⠻⢟⣻⡀⠀⠀⠀⠀⠀⠹⠇⠀⢄⣘⣿
⠀⢠⠀⢿⣶⠔⢀⡛⠟⠁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢠⡇⠀⠐⠀⣬⡇⠀⠀⢰
⠀⢸⠆⢸⡇⠀⠀⠀⡴⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢡⠀⠸⡅⠀⠀⠀⢰⠀⠀⠀⠈
⠀⠘⡄⢻⡅⠀⠀⠉⡇⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⣷⠐⠀⢤⡞⠀⠀⠰⡞
⡇⠀⠘⣼⢿⣄⡀⢀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣴⣟⠀⠀⠀⣰⠃
⢧⡀⠀⠘⢜⢿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣭⠎⠀⢤⡴⠃
⠈⢇⠀⠀⠈⠢⡙⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⡁⠈⣠⠞
⠀⠈⢳⡴⠤⠀⠉⠻⢶⣶⣾⣷⢴⣶⡆⣄⡀⠀⣢⠀⣴⡤⢦⡀⠀⠀⡀⢀⣠⡂⣼⠖⢲⣮⠴⠋
⠀⠀⠀⠙⠒⠒⠒⠒⠛⠓⠶⠾⣿⣿⣿⣧⣦⡟⠁⠀⢻⠇⠀⠑⣰⣾⣿⢻⣷⠞⠛⠛⠋⣡⠀⠀⠀⠀⣠⣤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣧⣬⣄⣀⣀⣬⣿⣿⣿⡄⣀⣁⣈⣁⠀⣠⣾⡿⣳⣿⡛⠉⠉⠉⣛⡍⠛⠒⠛⠋⠁
⠀⠀⠀⠀⣰⣦⡴⠋⠀⣠⣄⠈⠉⣉⣙⣻⣿⣻⢿⣿⣿⡿⢿⣿⣻⣽⣿⠛⠋⠉⣙⣿⠛⠷⡀
⠀⠀⠀⢐⣨⡟⠀⢀⡞⢹⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠻⣆⠀⠈⣶⠆
⠀⠀⠐⣿⡋⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢶⠀⠹⣄⡀
⠀⠀⠀⠈⠳⡀⠀⠈⣇⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠙⠀⠀⠘⠿⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⢠⢤⣤⡤⡴⣄⣤⡤⡦⠀⠀⠀⠈⠙⠓⠒⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠛⠑⠓⠃⠃⠐⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠛⠁



⡿⠿⠿⠿⠿⣻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄
⠀⠀⠀⠠⠤⠤⢄⡀⠀⢸⠁⡜⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢢⣸⢰⠁⢠⡇⠀⠀⠀⠀⡠⠀⢀⠎⣠⠊⠀⠀⠀⠀⠀⠀⣠⠎⠀⡀⣠⠊⠀⣴⡶⠋⢀⡞
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡏⠀⢸⠁⡀⠀⠀⣰⠃⠀⣼⢊⠂⠀⢀⠀⢀⣠⢀⣴⠋⠀⠀⣿⠁⢠⡿⠋⠀⢠⠏
⠀⠀⠀⡀⢀⡇⢧⢢⠀⢸⡇⡀⢸⣴⠁⡰⣰⠃⠀⣸⠃⠎⡄⢠⠎⣠⢾⡗⣹⠃⠀⢀⣼⣹⣴⢻⠀⠀⢠⡏
⠀⠀⠀⠹⣼⢇⡘⡎⡇⢸⣷⠇⢸⡇⢰⢣⡟⠀⣰⡟⡸⣸⣱⢃⣾⢣⡏⢸⡇⢰⡴⡾⢇⣾⡏⢻⣦⣤⡟
⠀⠀⠀⠀⣿⠀⣇⢷⢻⣼⢿⣀⣼⡇⣾⣸⢃⣧⣿⣇⠇⣿⣏⣾⣷⣿⢰⣾⣷⣼⣿⢃⣾⣿⡇⢸⣷⡿⢷⣸⡀
⠀⠀⠀⠀⣿⣦⣿⣸⣸⣿⣼⣿⣿⣿⣿⣿⣼⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣧⣿⣿⣧⣤⣿⡇⡀⢰
⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⣿⣿⣿⣼⣿⣟⣿⣿⣿⣧⣧⣿
⠀⠀⠀⠀⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡇⢿⣿⣿⡿⣿⢿⢻⡿⢿⣿⣿⢾⣿⢹⣿⢿⡿⣿⢿⠹⣿⠿⠹⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡠⠚⠑⠦⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⢄⡀⠀⠀⠈⠲⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⡤⠊⡠⠢⣄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢈⡇⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠈⠳⠔⠋⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣉⠉⠁⠀⠀⠸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠈⠉⢢⡀⢀⠤⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠀⣾⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣀⡼⠙⢦⡀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢀⣠⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⣄⡀
⠀⠀⠀⢠⠞⠉⢀⡤⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢤⣀⠉⠳⣄
⠀⠀⣰⠁⢀⡴⠁⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠈⢣⡀⠘⣦
⠀⢠⡇⠀⢸⠁⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⡇⠀⠸⡄
⠀⢸⡀⠀⠸⣤⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⡇
⢀⡜⠁⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣸⠁⠀⠀⠈⢳
⣼⠀⢀⣴⢦⣀⣀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠛⡟⢻⠛⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣀⣀⡴⣦⡀
⡇⠀⢸⠇⣧⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣿⠀⡇⢸⠀⣿⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⠸⡇
⠙⠲⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠈⠉⠙⠓⠿⠀⡇⢸⠀⠿⠞⠋⠉⠁⠀⠀⠈⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡷⢺⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡗
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢚⣳⠶⠂⠀⠀⠀⠀⠐⠶⣟⡓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⢀⡴⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⢀⡴⠋⢀⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠙⢦⡀⠀⠀⠈⠳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢻⡁⠀⠀⠀⢀⡞⠀⣠⠟⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⣄⠀⢳⡀⠀⠀⠀⢀⠟⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠁⠀⠀⠘⠷⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠳⠾⠃⠀⠀⠈⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢯⡖⠒⢦⡀⠀⠀⠀⠀⢀⡴⠒⢲⡽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀
⠀⠀⠀⠀⠀⠀⡿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢸⠀⢀⣼⠃⠀⠀⠀⠀⠘⣧⡀⠀⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠒⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢸⡆⣸⠃⠀⠀⠀⠀⠀⠀⠘⣇⢰⡇⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠐⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾⠉⠁⠀⠀⠀⠀⣀⣀⣷⡼⠤⠶⠶⠶⠶⠶⠶⠦⠯⣾⣀⣀⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⠀⠀⡽⣄⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⣠⠏⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⢻⠏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⡟⠁⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠓⠒⠦⣤⣀
⠀⠀⠀⠀⣠⠞⢉⡴⠷⠶⢶⣶⣶⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣶⣶⡶⠶⠾⢦⡉⠳⣄
⠀⠀⢀⡞⢁⡴⠋⣀⡴⠚⠉⠁⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⠈⠉⠓⢦⣀⠙⢦⡈⢳⡀
⠀⠀⣿⣹⠋⢀⡾⢋⡾⠓⠛⣩⡽⠋⠉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠉⠙⢯⣍⠛⠒⢷⡙⢷⡀⠙⣏⣻
⠀⠀⢿⠏⢠⠟⢀⡞⠁⢠⠞⣁⣠⢴⡾⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠙⢷⡦⣄⣈⠳⡄⠈⢳⡄⢻⡄⠹⡿
⠀⠀⠀⠀⡾⣴⠏⠀⣴⠋⢠⡏⢠⡞⣥⠖⠋⠈⠳⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠞⠁⠙⠲⣬⠳⡄⢹⡄⠙⣦⠀⠹⣦⢷
⠀⠀⠀⠀⢷⣿⠀⡼⣃⡴⠋⢠⡏⢀⡟⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⢻⡀⢹⡄⠙⢦⡘⢧⠀⣿⡾
⠀⠀⠀⠀⠈⠃⠀⣧⣸⠀⠀⡾⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⢷⠀⠀⣇⣼⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆⠀⠀⠀⣠⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢠⡾⠛⠳⣄⠀⠘⣆⠀⠀⠈⢷⡀⠀⢠⡟⠙⣇⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣨⠇⠀⠀⢸⠁⠀⠀⢹⡄⠀⢸⡄⠀⠀⠸⡇⠀⣾⠀⠀⡿⠀⠀⢀⡴⠋⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⣧⠀⠀⢧⠀⠀⠀⣷⢀⡇⢀⡼⠁⠀⣰⠟⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢀⣴⠶⠶⢦⣤⣀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢹⠀⠀⠈⢧⡀⠀⠘⣿⠁⣼⠀⢀⡾⠁⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠉⠳⢦⣄⠀⠀⠈⢳⡄⠀⢸⡄⢀⣀⣈⣷⠀⠀⢸⣦⠇⠀⣸⠁⠀⠀⢠⠏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠉⠳⣦⡀⠀⢿⠀⢠⡿⠛⠁⠈⡟⣇⠀⢸⡏⠀⣰⠃⠀⠀⣠⠟⠋⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠙⢦⣸⡆⢸⡇⠀⠀⢠⡇⡟⢠⡟⠀⡾⠁⠀⢀⡼⠋⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠈⢻⣇⠀⢷⠀⢀⡾⢸⡇⡾⠀⢸⠃⠀⢠⠟⠀⣰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀⠀⢹⡄⠸⡇⠘⣧⢸⡆⣷⠀⣼⡄⢠⣯⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢻⡀⣷⠀⣸⢸⡇⢹⡾⠁⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⣇⣿⠀⡟⢸⠇⣸⠇⢀⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣾⠀⢿⣸⡇⡿⢰⣿⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣿⢀⡾⣹⣶⡇⢸⡿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⣿⣾⠖⠛⢻⣧⣏⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣿⣾⣿⡟⠀⠀⢸⣿⠁⢹⣿⠛⠛⠛⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠉⠀⠸⡟⠙⠁⠀⠀⠀⠏⠀⠀⠿⠀⠀⠀⠀⠀⠈⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠚⠛⠛⠛⠒⠶⠤⠤⠤⠤⠤⠶⠚⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⢀⠀⠄⡀⠀⡎⠀⠀⠀⢠⡇⣠⠀⡀⢂⠀⠀⠀⠀⠂⡤⠂⠁⢸⠁⠀⣼⠀⠀⠀⡄⠀⠀⣧⢀⠆⠠⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠃⣠⣆⣯⡖⢻⡗⡆⠁⣿⣴⡇⢀⣀⠄⣸⢿⡍⢰⡁⣸⡆⣀⣀⣠⣿⣧⠘⡆⣿⣄⡘⣯⡴⡀⢠⠀⡤⣸⢿⣽⢀⡇⢠⡇
⠀⠀⠒⢤⣵⣀⣤⡿⣿⣵⣾⣧⣸⣿⣿⣗⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣾⣾⣷⣾⢿⣿⣿⣿⣦⣿⣿⣽⣽⣯⡘⣾⣾⣯⣾⣿⣷⣏⣟⣴⢥⡗⠂
⠀⠀⠀⢈⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣏⡿⣿⣻⣷⣿⡇
⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠟⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡟⠟⢻⣷⣿⠃⠀⠀⣀⣀⣀⣀⣤⣤⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡉⠉⠉⠉⠁⠀⠀⠀⠺⠋⠉⠀⠀⠀⠀⣴⣶⣶⣶⠞⠁⠀⠙⠻⣋⣍⠁⢸⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣿⠓⠶⠂⠀⠀⠀⠀⠔⠀⠀⣠⣿⢀⡄⠀⣰⠟⠛⠉⢄⠀⠀⠀⠀⠁⠀⠶⠦⢷⡄⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠯⠽⠿⠿⢭⣟⣿⣿⣿⣿⢻⣷⣤⣤⣤⣤⣤⣊⣀⣴⣿⠿⣷⡿⠓⠉⢀⣀⣠⡴⠿⠤⠤⠤⢄⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⣔⣾⣁⠇⠀⠀⠀⠀⢀⣾⣿⣿⠿⢣⠿⠟⠈⠓⠂⣩⠇⣀⣀⣴⣇⣤⣠⣦⣠⠾⠋⠉⠁⠐⠒⠒⠛⠓⢺⣿
⠀⠀⠀⠀⢠⡟⢁⣿⡏⠀⠀⠀⠀⠀⢈⡿⠛⢹⣿⣷⣾⡻⢋⡽⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠈⠀⠸⣿⠁⠀⠀⠀⠀⣠⣿⡄⢰⣺⣿⣿⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⠛⣧⣸⠛⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠃⠀⠈⣻⡀⠀⡟⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠟⢆⠘⢦⡙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⠁⠒⠚⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⢛⣟⣋⡿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠤⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠢⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠂⠀⠀⡀⣀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⢀⡇⠀⠀⠀⠀⠀⠨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠐⠓
⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢀⠀⠑⠀⡴⠆⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠋⠀⠠⡀⠐⠀⠠⠂⠠
⠀⢁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠲⡄⠀⠀⢸⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⢣⡀⠀⠀⢁⠀⠀⠀⠠⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢡⠀⠀⠈⠲⣄⢀⠇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⣿⠀⠀⠀⠰⣼⡜⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠆⠀⠆⠀⠀⠀⡸
⠀⢿⠀⠀⠀⡆⢹⠃⠐⡆⠀⡆⠀⢸⠀⠀⣧⠀⣀⠀⠀⠀⡀⢠⡄⢸⡀⡇⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡟⠀⡘⠀⡀⠀⡷⠁
⠀⢸⡆⡆⠀⡇⣸⣇⠀⣷⢰⡇⠀⢸⣸⢼⣿⠀⡿⢀⡆⡀⣷⣼⠀⡯⢣⢡⣿⠀⡀⣸⢱⠀⡀⠀⠀⡆⢀⡇⢀⡇⢀⡇⢸⠁⠀⠀⡄
⢰⢸⡇⡇⢠⠃⣿⢹⡀⠘⣼⡇⡠⢺⢸⣾⣿⠀⡇⠈⡇⣿⢸⠛⣦⡇⢸⡼⡏⡇⠇⡏⢸⡆⡇⠠⠀⡇⢸⡇⠸⢷⢾⡇⣾⠀⢀⢀⣷
⢸⡌⣿⣧⢸⢸⢻⠘⡇⣇⣿⠀⡅⢸⢸⣿⣿⡆⣿⠀⣿⡏⣼⣘⣿⡇⢘⣿⣷⡇⣸⡗⢸⡇⡄⡇⠀⠇⡟⣷⡆⡺⣼⡇⣿⢰⠀⡏⡇
⠈⡇⢸⣿⣼⣾⢸⠀⣧⢘⢹⠀⠱⣼⣸⣿⣿⡇⣿⠀⡏⣿⣿⣿⢹⣇⢸⢹⣿⡇⣿⡇⢺⡇⡇⣾⢸⢸⠃⣿⣇⣇⢻⡇⣿⢸⢀⡧⣧
⠀⡇⠈⡇⢻⣿⣼⠀⢻⢸⢸⠀⢸⡟⣿⣿⢻⠀⣿⠀⡇⣿⣸⣿⣾⢻⢸⢸⡏⡇⡿⡇⠈⡇⡇⠘⣸⣿⠀⣿⡿⢸⢸⠃⣿⣼⢸⡇⡿
⠀⣿⠀⡇⠸⣿⢹⠀⠸⣾⢸⡆⢸⡇⣿⣿⢸⠀⣿⠀⡇⣿⣧⡏⣿⢸⢸⠈⡇⣰⡇⡇⠀⣇⡆⠀⢻⣿⠀⣿⡇⠸⢸⡀⢸⡇⢸⡇⡇
⠀⢸⠀⡇⡆⣿⣾⠀⠀⣿⢸⠇⢸⣧⣿⢸⢸⣨⣿⡀⡇⣿⣿⠁⡏⡞⣾⢨⡇⣿⡇⡇⠀⣿⢁⠀⢸⣿⠀⣿⡇⢠⢸⡇⢸⡇⡏⡇⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⢠⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⡿⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣧⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠸⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣦⣙⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠙⢦⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢄⣾⠟⠀⠀⠀⢀⣀⣠⣤⣤⡶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⡠⠄⠀⠀⣐⠟⠁⠀⠀⣠⢞⡿⠟⡩⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⡀⠔⠊⠀⢀⡠⠔⣩⣖⠭⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡿⣁⠄⠂⠁⣀⠄⠒⡈⠄⣂⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⡠⡊⢔⣽⠊⠀⡠⢐⠭⡠⠖⠋⠀⠉⠀⢀⡀⠤⠒⢒⡒⠀⡀⠀⠀⠀⠐⠒⠂⠀⠐⠶⢶⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠊⠔⢡⣿⢻⣠⢊⢖⠕⠁⠀⠀⠀⢀⡠⠒⡡⠔⡪⠍⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢰⡟⡟⢸⡧⠡⠁⠀⠀⠀⣠⡺⢋⡴⠋⣴⣿⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⡤⠤⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡀⡬⢡⡿⡱⠁⠀⠀⡠⢪⠟⢀⠎⢀⡾⢋⠉⠍⠉⣉⣉⣉⠀⣀⣀⣂⠀⠀⠉⠉⠁⠀⣒⣒⣈⣉⠭⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⡀⢠⢀⣷⢋⢁⠁⠀⠀⢠⣵⢋⠤⠃⢀⡾⠗⡡⠖⠺⢏⣉⣉⣉⠓⠤⢄⣀⠀⠀⠀⢉⣉⣡⣤⣴⣶⣶⡶⠶
⠀⠀⠀⠀⠰⢸⢸⣼⢃⠂⡜⠀⢀⢔⣿⠡⠂⢀⣴⠟⢀⠎⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⢄⣀⡉⠉⢉⣀⡠⠤⠚⠋⠁
⠀⠀⠀⢀⠇⡈⢸⡇⡄⡰⡠⠊⠁⣾⢣⠁⢠⣿⠃⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣬⣸⡠⠁⢧⠀⣏⡤⣢⠞⡱⢃⣠⣿⢃⡔⠁
⠀⠀⠀⣿⣷⠃⢠⣾⡆⣯⣾⣿⣾⢗⣭⣾⠇⢸
⠀⠀⠀⠹⣿⠀⣿⣿⣷⣿⣿⣿⣿⣿⡟⣃⡤⠃
⠀⠀⠀⠀⢻⠀⢸⡏⠀⠛⢹⠸⠏⠉⠉⠁


⠀⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠄⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠠⡀⢠⠊⢠⠊⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡎⠀⡇⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢁⠀⠱⡀⠀⠀⠀⠀⡇⡄⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠑⢄⠀⠀⠂⠀⠐⠀⠀⢀⡴⠜⠀⠀⠀⢀⠎⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠡⠖⠋⠀⡀⠄⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⠊⠢⡄⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠰⡀⠎⠁⠀⠀⢀⠁⠀⠀⠄⠀⠄⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠄⠀⠈⢲⢠⡜⠀⢸⠀⡠⢐⡃⠐⠒⠁⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠢⡀⠀⠀⠆⠀⢠⡶⠉⢃⠀⢸⣼⠃⠁⠄⠀⠀⠀⠠⠃⢀⡄⣀⠠⠐⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠂⠀⠘⡄⠘⠁⠀⠘⡀⠘⡃⠀⡘⣠⠊⠀⠀⠀⠀⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣑⡂⠀⣀⣈⡀⠀⡀⠀⢠⠀⠀⠀⠀⠡⠀⠐⣼⠞⠁⢀⠤⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠣⣀⠈⠒⠄⠀⠐⢢⡅⠀⣋⣴⠎⢂⠁⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠤⣄⠑⠄⠀⠀⠀⢀⠃⠀⠟⠁⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⡎⠀⡘⠀⢀⡄⢀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠐⢄⠀⠈⡄⢃⠀⢰⠀⢠⣥⠴⠍⠒⠁⢀⠴⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣄⢀⠈⠂⠵⢾⠀⠸⠁⠀⢀⠠⢂⣁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢹⠀⢠⠀⢸⡄⢠⢀⢔⡵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⢀⠈⠳⡀⣮⠋⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠭⠔⣺⣏⢀⣤⠔⠀⠭⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⢀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⠀⠀⡀⠀⠑⠂⠠⠤⠤⠀⠒⠋⠀⠥⣀⣀⡤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⠂⢀⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠐⣄⠀⠀⠀⠀⠰⠄⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⢳⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣌⠀⠀⠀⠠⠀⡇⠆⠀⠀⡆⠀⠘⠀⠀⠀⢀⠈⠰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⠱⠰⠀⠀⢡⠀⠂⠀⠀⠀⠈⢠⠇⠠
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠸⡄⢸⢂⠀⡠⠀⠀⠀⠰⣘⠀⣧⠀⠀⢀⢃⠇
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣧⡄⢸⡄⡏⠀⠀⠀⡄⠙⣄⠂⠠⠀⢘⡞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⡀⠀⠀⠘⡰⢠⡄⡀⡄⠇⠀⠈⢀⣿⣏⣾⣷⣿⠂⣀⣼⡁⠀⣽⣿⠀⢀⣸⣀⣀⡀⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢄⠈⢳⡠⡄⢀⢷⡎⣦⠀⢹⣶⣦⣀⢘⣿⣿⡏⣿⣿⣿⣿⣯⣧⣤⣿⣼⣅⣽⡿⣀⣠⠉⢻
⠀⠀⡆⢁⣾⠀⠀⠀⣰⡄⢠⠘⣷⡀⠀⡀⠀⡆⢰⠀⠀⠀⡀⠸⢆⣦⣿⣿⣸⣼⣷⣧⣾⢬⡏⢿⣽⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣾⣿⣷⠿⡥⣰⣫
⢠⣀⢱⣼⣿⣆⣀⣀⣹⣇⢾⣼⣿⣷⣿⣯⣿⣶⣾⣄⣀⣰⣰⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣧⣀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢼⣏⠀⠀⠀⠀⢀⣠⣾⣾⣿⣿⣶⡴⣖⣠⣴⣾⢧⣍⣩⣭⣿⡿⣿⣿⣦⣄⡀⠀⠈⠳⣦
⠀⠀⠀⣠⡼⢿⡆⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣝⢿⣷⣿⣿⣿⡿⠉⣹⣿⡟⣻⣿⣿⣿⣿⣷⡤⡔⣾⢤⡀
⠀⠀⠀⢹⣧⢞⢿⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⢿⣿⡞⣿⣿⣾⣿⣼⡅⣼⡟
⠀⠀⠀⠀⣽⣧⣃⡹⣿⣿⣿⣼⣿⣾⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣽⣿⣿⣇⣴⣯
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣟⣿⣞⠁
⠀⠀⠀⠀⢀⣀⣤⣤⣼⣯⣿⡧⣭⡲⣝⡻⣿⣷⡙⢟⣿⣟⡛⣣⣿⣿⡿⣋⢻⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⣴⣿⣿⡿⠻⠿⠛⠁⠀⠻⠿⢾⢶⣾⢿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣽⠿⠟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠟
⠀⠀⠰⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠤⡀⠀⠀⣖⣚⣻⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣰⣿⡿⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⠀⢀⠄⠀⠙⠿⣿⣯⣷⣷⡄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢿⣿⣳⣭⣥⢀⣤⣶⣾⣿⣿⣯⣿⣿⣿⣾⣦⣀⣤⣴⣶⡿⡿⠃⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡹⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣠⣶⠿⠋
⠀⢀⡴⠾⠿⠿⠒⠾⠷⠶⣭⣟⣷⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣟⣻⣥⣷⣶⠾⠗⠿⠷⠶⢦⡄
⠀⠈⠀⠀⠀⣀⣤⣤⣴⣶⠴⣦⣭⣽⣟⣛⡿⣿⣿⣻⣼⣿⣏⣿⣿⣿⣿⣯⣾⣿⣿⣿⡿⠶⠶⣦⣤⣄⡀⠀⠀⠙
⠀⠀⠀⠀⢸⠋⠉⠀⠀⣀⣤⢰⣶⣦⣿⣯⣥⣅⠾⠟⣿⡿⣿⡟⠩⢶⣿⣿⣿⡿⢿⣠⣴⣤⣀⠀⠙⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡿⠷⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⠿⣿⣿⣇⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⠀⡇⢠⢀⡀⡄
⠀⠀⠀⠀⢠⡄⠘⠳⢸⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣾⠀⣀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠠⣄⠐⡇⣿⠀⢿⣃⠏⠸⣳⠁⣰⡤⠆
⠀⠀⠰⠆⠀⡇⢠⠀⠹⡆⡜⠀⡤⢠⡾⠀⠀⠀⠀⠀⠀⠀⠰⣦⠼⠀⣧⣻⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣣⣇⢸⠞⠀⡏⡀⠀⡏⢠⡏⣠⠄
⠀⠀⠻⠷⣤⡟⠘⢧⡸⡟⠁⡞⠿⠛⠀⠀⠀⠀⠀⠘⣇⢠⡇⠸⢶⡀⣍⠉⠀⡰⠀⠀⠀⠀⠀⠀⢰⡄⢈⠻⣼⠀⣧⡇⣧⠏⣷⢏⠉⡀⣰⠂
⠀⠀⢀⡀⠒⢤⡀⠉⢰⢣⠾⢃⢶⠤⠆⠀⠀⠀⠀⠀⠹⠆⠱⡀⠘⣠⠇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠼⢧⣸⠆⢸⣠⢏⣀⡟⡖⣼⢃⡞⣠⣿⣋
⠀⠀⠀⠙⠛⠗⠳⣤⠱⠈⠋⠙⠋⠛⠀⠀⠀⠀⠀⠀⠀⠘⠓⠿⢴⣇⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣙⣎⡻⣄⠘⡇⠀⡿⢱⣷⠗⣺⢍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣯⣝⡻⣆⣇⡼⢓⣞⡉⠉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡃
⠀⠀⠀⢠⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣠⡶⠶⠆⠶⠛⠧⠶⠀⠴⠆⠺⠆⠫⠄⠹⠧⠙⠃⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⣾⠀⠀⡘⠸⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡇⢢
⠀⠀⠀⢉⣶⠀⠛⠀⠇⠀⠀⠀⠀⣾⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠂⡘
⠀⠀⠀⠀⠿⠀⣭⢴⡆⠀⠀⠀⢀⠟⣿⠀⠀⠀⠀⡀⠀⠠⠶⠒⢒⠂⠒⠒⠒⠒⠀⠀⠤⠈⢁⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣴⠀⠀⢸
⠀⠀⠀⢰⡆⠘⡏⣸⠃⠀⠀⢀⡾⢣⠏⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠤⠤⠽⠗⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⢀⠃⡀⠀⡸
⠀⠀⠀⢸⠇⢀⡷⣩⠀⠀⣠⣞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⡇⢠⠃
⠀⠀⠀⣴⡿⠈⣧⢿⠀⢰⢛⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠠⡶⠒⠀⠄⢀⣤⣤⡀⠀⠀⠀⢻⠀⡀⢻⠀⡇⢸
⠀⠀⠀⡩⠇⠀⣧⡎⠀⢻⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠉⠠⠤⠀⠒⠐⠀⠚⡉⢁⣂⡒⠒⠒⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⠀⠇⢸
⠀⠀⠀⣷⠆⠀⢹⠇⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠉⠋⠉⠉⠀⢀⣀⣶⣶⣒⡂⠤⢤⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢲⢸⠇⢸
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣄⠸⡄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀
⠀⠀⢠⣾⣿⣶⣴⣿⣿⣶⣶⣿⣿⣿⣿⣿⣶⣿⣾⣿⣷⣾⣷⣶⣦⣶⣦⠀⠀⠀⠀⠀⢠⣴⣤⣬⣿⣿⣱⣷⣷⣦⢾⣦⣴⣗⣼⣴⢶⣰⣷⣦⣷⣿⣿⣿⣾
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠙⠛⠙⠋⠉⠉⠉⠋⠛⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⣀⡀⠼⠃
⠀⠀⠀⠀⠀⠀⢈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢀⡀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠳⣶⡟⠀⠘⣷⠀⠀⠀⠀⢷⡼⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⢸⡄⠀⠙⢦⡼⠁⢀⣷⠘⠂⣶⠀⠀⣸⠟⠀⠀⠀⢠⡇
⠀⠀⠰⣾⣿⡖⠀⣦⣧⣶⡜⡛⠋⣀⣉⣰⣷⣇⣠⣶⡀⣀⣤⡴⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠀⠀⠀⠀⠀⡬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢠⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢇⠂⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⢰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⡀⠀⠀⣀⡀⠀⢸⠔⠂⠀⢄⠀⡿⠁
⠀⠀⠀⠀⠀⢀⠠⠀⢀⠀⠀⠀⣰⡀⠀⣄⠀⣤⠀⡄⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡈⠈⠂⠀⠀⠠⠀⡌⢠⠀⠀⠀⣜⠁⡠⠄
⠀⠀⢢⢸⣯⣿⡷⣷⣿⣙⣷⣼⣿⣽⣶⣿⢱⣿⣰⣷⣿⡇⣴⣡⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⢢⠀⠀⣸⠃⡚⢂⠱⢀⣧⠎
⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡟⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣿⠀⠀⠀⠀⢡⡀⡿⣠⢿⣞⣺⣞⠡⠒
⠀⠀⠀⠀⠻⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⡠⢀⣂⢳⣅⣠⡿⠿⣾⣿⣿⣧⠂⠄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠙⠉⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠘⠛⠁⠛⠁⠀⠘⠛⠋


⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⣀⡠⢤⣄⡴⣰⡏⢠⣀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠙⡆⠀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣆⣜⢀⡿⢧⣀⣼⣷⣽⣴⡿⢡⠞⣠⠖⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⢳⣸⣴⣾⣥⣂⣀⡠⠤⡀
⠀⠀⠀⠀⢴⣀⠠⣜⣿⣿⣿⣿⣽⣿⣿⣿⣯⡿⣿⣿⣜⡡⣲⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠲⢵⣷⣽⣿⣿⣯⣼⠭⠙⠒⠀⠈
⠀⠀⠀⢀⣠⠤⣝⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢨⣷⣿⣿⣿⣿⢋⡁⠈⠁
⠀⠀⠀⠉⠀⣠⠖⠻⡉⠈⠛⢻⡉⠈⠉⠉⠛⠋⠀⠙⠏⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠿⡿⠟⠉
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙

⣄⣄⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⢀⣀⣤⣠⡀⣀⣀⣀⣤⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣤⣀⢀⣀⣀⣀⣠⣀
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⠀⠀⢀⣀⠀⢀⠀⣀⣀⣤⣠⣄⣠⣤⣤⣤⣦⣄⣀⣠⣤⡀⣀⣀⣀⣀⣠⣀⣤⣀⣠⣤⣀⣄⣀⣀⡀⡀⠀⣤⠀⡀⡀
⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛


⡀⠀⣀⢀⡠⠀⡀⣀⡀⢠⣀⣀⠀⡀⣀⡠⢄⣀⢀⣀⢀⡠⠀⣀⢀⡠⠦⣀⠀⣀⢄⣀⠤⣀⡀⣀⢄⣀⠤⣀⡀⢠⣀
⠧⠾⠿⠾⠧⠾⠷⠾⠾⠿⠿⠧⠾⠷⠿⠦⠾⠷⠿⠿⠾⠧⠿⠿⠾⠧⠾⠿⠿⠿⠾⠷⠶⠿⠾⠽⠶⠷⠴⠿⠿⠿⠷


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡄⢤⢠⠀⡀⡄⣠⠀⠀⡆⣀⢀⢠⠆⡄⡀⢠⠀⡄⡀⢴⢠⢀⡀⡔⢠⠀⠐⡆⣀⢀⢠⠆⣄⣀⢠⠀⡄⣀⢤⢰⡀
⢳⣿⣼⢤⣷⣿⣿⡼⣿⣷⡧⡼⣾⣷⣧⣽⣾⣿⣧⣷⣿⣼⢨⣷⢷⣿⡜⣷⣿⡧⡼⣾⣷⣧⣹⡾⣼⣦⣷⣿⣼⣧⣾
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣾⠉⡧⢀⡴⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⣤⡇⠀⡿⢻⠃⠀⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢠⢃⡞⠁⣧⠀⡿⣿⠀⣰⠏⢿⡏⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡶⠦⠤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠉⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠿⠾⠷⣯⣼⠃⠀⣿⢦⣤⣤⡽⢦
⠀⠀⠀⠀⠀⠀⢀⣴⣋⣽⠦⠶⠚⠛⠲⢶⡏⠳⣄⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣧⢀⡞⠉⣷⣀⠙⢳⣄⣧
⠀⠀⠀⠀⣀⣤⡿⠭⣶⠶⠶⠦⠤⢤⣀⠀⢳⡀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⡏⢀⣰⢁⠈⠳⣟⠉⢻
⠀⠀⣠⠾⣇⣀⣀⣠⠼⠲⠶⠶⠶⢶⡏⠛⢦⡙⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡿⠋⠉⠉⠉⢻⣿⣄
⣠⢎⡴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⢀⡞⠀⠙⣿
⠿⠋⠀⠀⠀⠀⠀⣀⣤⢤⡶⠒⠒⠶⠶⠶⠮⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡈⠓⡾⠳⠶⠶⣶⠋⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡴⠋⠁⣠⠜⠓⠒⠒⣶⣶⣶⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢜⣭⣿⣿⣤⡠⣄⣉⡿⠁⠀⠀⢠⡟⠲⠶⠒⢺⡏
⠀⠀⣀⡴⠚⢓⡶⠋⠁⣠⡴⠚⠋⠉⣉⣉⣭⠏⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣽⣿⣥⣼⢿⣿⡿⠃⣷⡼⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠃
⠀⣴⠁⣠⡾⠋⠀⠀⣰⠋⠉⡟⠉⠉⠉⠀⣸⠷⣴⠋⠀⡴⠀⢀⠀⢀⠀⠀⡀⢠⡿⣿⣿⠟⢹⡧⣄⣠⡴⠋⠀⢀⣠⠴⠒⡻⠛⢤⣀⠀⣰⠏
⠀⡟⢹⡇⠀⠀⠀⢠⡇⢀⡼⠀⠀⠀⠀⢰⠃⠀⠈⠻⢾⣥⣴⣏⣀⣸⡀⣀⣇⣈⣳⣤⣀⣠⣾⣷⠶⢿⡷⣀⠴⣫⡤⠖⣾⠇⠀⠀⢩⠟⠁
⠀⡇⢸⡅⠀⠀⠀⢸⠛⠉⡇⠀⠀⠀⠀⢸⠀⠀⢀⣀⣼⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⠟⠀⠀⠴⠟⠋⠁⢀⡾⠃⠀⠀⣠⠏
⠀⠹⣜⡇⠀⠀⠀⠘⣆⢰⡇⠀⠀⠀⠀⠘⡟⠋⠉⠀⠈⢳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣛⣠⠤⠖⠋⠁
⠀⠀⠘⠧⠀⠀⠀⠀⠘⣏⠙⢆⠀⠀⠀⠀⢿⡀⠀⠀⢀⡼⠉⠉⠉⠛⠲⠦⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⣦⣀⠀⠀⠛⠒⢾⠉⠀⠀⠀⠀⠀⠀⠴⣶⣦⡤⣶⠾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⠤⣤⣄⣀⣀⣀⣀⣠⡤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡆⠀⢀⡤⡀
⠀⠀⠀⢀⠞⠳⣄⠀⢰⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠐⠲⢄⣠⠖⢉⣀⡀⠉⠓⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⡴⠋⠀⢱
⠀⠀⠀⢸⠀⠀⠈⠣⣸⠀⠀⠀⠈⢆⠀⠀⠀⠀⡘⠀⢀⣾⣿⣿⣦⢀⠃⢰⣿⡿⣿⣆⠀⠈⡆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠸⠊⠀⠀⠀⡸
⠀⠀⠀⠘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⠀⠘⣿⣧⣸⣿⠀⣆⢸⣿⣧⣼⡿⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠳⢄⡙⠻⠟⣋⠔⠉⠲⢝⡛⣛⡡⠔⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⣀⠀⠈⠣⣀⠀⠀⠀⠀⠀⢀⣈⠤⠏⠈⠒⠒⠒⠋⠀⠑⠒⠂⠤⢄⡀⠀⠀⡠⠃⠀⢀⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠈⠑⠦⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠀⠀⠀⠀⠀⢎⠀⠀⠀⢀⡤⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣈⠙⠲⠤⣀⡏⠀⠀⠀⠀⠀⢀⣀⢤⡤⡴⢶⠒⡏⢩⣈⡖⣯⠃⠀⠀⠀⠀⠀⠈⠦⠔⠊⣁⠤⢦⠀⠙⢄
⠀⠀⠀⠀⠀⢠⠎⠀⢠⠊⠀⠉⢲⣤⣄⠀⠀⠀⠀⠀⠀⠈⠻⡖⠧⢶⠴⡶⢺⠈⣇⡷⠁⠀⠀⠀⠀⠀⠀⢀⣤⠶⢯⡀⠀⠀⢣⡀⠈⢣
⠀⠀⠀⠀⢠⠃⠀⡰⠃⠀⢀⡔⠁⣠⣉⡛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠬⢦⣥⠴⠗⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⡀⠱⡄⠀⠀⢱⡀⣀⠇
⠀⠀⠀⠀⠈⠂⠜⠁⠀⢀⠎⠀⡸⠁⠀⢩⠵⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢧⠀⠀⠀⢣⠀⠘⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⡴⠁⠀⠀⡏⠀⡆⠐⠒⠒⠒⠂⠤⠤⠤⠄⠀⠤⠤⠤⠔⠒⠈⠉⠉⠉⡇⠈⡀⠀⠀⠀⠧⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⠃⡄⢀⠀⢠⢣⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⡄⠀⠸⡇⠀⠀⢇⠀⢀⠀⢸⢸⠀⢸⢀⢮⠏⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇⢠⠀⢸⠀⡌⠀⢤⡏⠀⢸⡞⡎⢰⠀⠀⣰⠀⡸⡃
⠀⠀⠀⠀⠀⠀⠀⠘⠂⡄⢸⠀⡄⠃⡴⠀⠘⣆⠇⠀⣺⠁⠀⡾⣸⡁⢠⠀⢀⡏⢠⢃⠇
⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⢸⢀⠇⢰⡇⠀⠀⣿⠀⠀⣾⠀⠀⠇⡿⡇⢸⠀⢸⠇⡎⢸⣾
⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⢸⣼⠀⢸⣇⠀⠀⡟⠀⢰⡏⠀⢸⣸⠃⡇⣼⠀⡿⣸⠀⡞⡽
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⢸⡏⠀⡘⢿⠀⠀⡇⠀⣿⡇⠀⣸⡏⢠⡇⢸⢸⣹⠇⡜⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⢸⡇⠀⡇⡏⡆⢠⡇⢠⡇⡇⠀⣿⠁⢸⠁⢸⣆⢿⡞⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡸⠇⠀⣿⡇⣿⣼⡇⣾⣇⡇⢸⣿⠀⣞⣄⣸⣿⡟⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠘⠈⠉⠃⠙⠉⠁⠙⠙⠃⠘⠀⠐⠛⠛⠛⠛⠃⠊


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⢀⡿⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢀⡴⢃⢎⣧⡿⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢬⣷⡀⠀⠀⠀⠀⠀⠀⠘⣧⢠⣾⠃⡜⢸⢳⠃⠠⡄⠀⠀⣿⡄⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠠⣤⣿⣏⠇⢠⠃⡏⡎⠀⠀⢻⡄⠀⢿⢷⡟⠁⠀⠀⢀⡆⠀⠀⠀⢀⡄
⠀⠀⠀⠐⢶⣄⡈⣿⡵⡄⠠⡄⠀⠈⡟⣯⡒⢼⣸⢠⠃⢀⠀⠀⣟⡤⣫⡏⢄⠀⠀⠀⣸⠃⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠉⠫⣻⡽⡘⡄⢻⡄⢸⢠⡋⡏⡶⣌⠺⡀⠈⣷⣄⡜⣱⣻⢡⠘⣷⡀⠀⡿⡤⡺⠋⠀⠀⠀⣠⡴⠂
⠀⠀⠈⠙⢦⣄⡀⠈⢧⢣⢱⡘⣇⣇⡼⡇⢇⡇⡎⢳⡘⢦⠸⡜⢰⡇⣿⢸⠀⢸⢱⣀⢟⡜⢁⠀⠀⡠⢪⠏
⠀⠀⠀⠀⠀⠑⢝⢦⡘⣼⡄⡿⣿⡏⣷⣷⣾⣇⡇⢸⡸⣄⢳⢃⠿⣰⢸⢸⢠⡟⣦⢫⡎⣿⡞⣧⠜⡱⠃
⠀⠀⠀⠀⠀⠀⠈⢣⠱⡏⣷⣿⡿⡇⡟⡽⣿⢻⣣⢾⠃⠘⡄⢿⡄⣿⣼⢸⣾⢣⢃⠿⡇⢿⢧⠏⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠐⢦⣧⠹⣽⢹⣷⣿⣇⡇⢻⠈⡏⢸⡄⢠⢷⢸⡇⣿⡇⢸⢹⡏⣾⠀⣇⢸⡞⢰⣇⠔⡏⢀⣶
⠀⠀⠀⠀⠀⠰⣄⠀⣫⢣⢻⡀⣇⣏⠄⣱⣼⣖⣓⠚⠛⠛⠩⢚⣳⠿⡇⡘⢺⢠⡟⢫⠉⠝⢧⣧⢏⣼⠓⢯⣇⡀
⠀⠀⠀⠈⢳⣶⠿⡞⢚⣮⣟⣉⣉⣣⠠⠤⣀⠀⠤⠒⢫⣙⣀⡟⠡⠖⠧⡇⠨⢻⠭⠤⣌⠁⢀⣛⡠⠤⠄⣁⠐⠌⢯⡳
⠀⠀⢀⡴⢃⠈⠴⠚⠉⠁⡐⠀⠄⢀⣉⣀⡤⠖⠒⠶⣉⣑⣄⣉⠶⠬⠥⠴⠤⣄⣂⣈⣑⡢⣬⠖⠊⠓⢦⠔⣲⣤⡊⠆
⠀⠐⠯⠕⠤⢴⠦⣀⡳⠴⢥⢖⡉⠁⢐⡂⠀⣀⠁⠐⢋⣉⣱⠀⠐⠒⠀⠀⠒⠀⠀⠊⠐⠀⠈⠉⠉⠩⠥⠀⢛⠒⠃
⠀⠀⠀⠀⣔⣒⣓⣒⡆⠀⠤⠉⠓⢖⠒⠒⠊⠉⠉⠉⠉⠁⠀⢀⠤⠥⠶⢯⡱⢄⠀⣖⣲⣒⡲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⣼⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠛⠳⢦⣄⠀⠀⠀⠀⠙⣾⡏⠀⠀⠀⢀⡴⢋⣥⣬⣝⢷⡄⠀⠰⠿⠋⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠺⠛⠻⠷⣦⣉⠳⣄⠀⠀⠀⠈⠁⠀⠀⢠⡟⣱⡟⠁⠉⠉⢸⡇⠀⠀⠀⢠⣾⣿⡯⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⡝⣧⡀⠀⠀⠀⠀⠀⣼⢁⡿⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠈⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⣧⡀⠀⠀⠀⠀⡟⠘⠃⠀⠀⠀⢀⡾⠀⠀⠀⣾⠁⣀⡴⠋⠀⠀⣠⢞⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡞⠁⠀⠀⢰⣿⡾⠋⠀⠀⠀⠼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣿⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⡀⠀⢹⡄⠀⠀⢸⡄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⣩⣥⠶⠶⠺⠿⡦⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⠛⠶⢦⣄⠀⠀⠀⠀⠀⠈⠻⢷⣬⣇⠀⠀⠈⣧⠀⣿⠀⠀⣼⢻⡆⠀⠀⠀⠀⢀⡼⠋⣴⠟⠉⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠶⠾⠿⠷⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠸⣶⣿⠀⠀⢻⣼⠃⠀⠀⠀⢠⡟⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢄⠀⠹⠏⠀⠀⠘⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠦⣤⣄⣀⠀⠀⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣉⣤⡶⠶⠛⠃⠀⠀⠀⠀⠈⠉⠛⢦⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣀⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡷⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⠀⣠⣶⣶⡶⢤⣀⠀⠀⠀⠀⠀⠀⢸⣧⠞⠋⠀⠀⠀⠀⣀⣤⠤⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⣤⣴⠶⠾⠛⠉⠁⠀⠀⠀⢸⣏⣛⣉⣋⣀⣈⣧⡀⠀⠀⠀⠀⠟⠋⠀⠀⠀⢀⣴⣞⣉⣀⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉






⣿⣿⡿⠿⣿⠿⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣷⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡧⡦⡤⣦⡆⡴⣶⣷⣶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⡁⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⣤⠀⠀⠉⠁⠀⠀⠀⠘⠀⡀⠀⢸⣇⠀⢸⠁⠀⡀⠀⠀⠀⡂
⠀⠀⠀⢲⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠚⠂⠀⡆⠀⠄⡀⢷⡀⠀⢻⡆⢸⡄⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠐⣄
⠀⠀⠀⣝⡑⢀⠀⠀⠀⠀⠂⠘⠂⠀⠴⠄⠀⠀⠐⠀⠀⠰⡧⠀⠈⣿⣿⠁⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⠀⠈⣦⠀⠀⠀⠀⠐
⠀⠀⠀⣿⠃⠾⢄⠀⠀⢀⠀⢀⣤⠀⠀⢀⠀⢘⠀⠠⠆⢀⢹⡀⠀⡟⣴⠀⠀⠀⠈⣀⠄⠀⢀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸
⠠⣤⠠⣧⠄⠯⠘⠀⠀⠈⠀⠀⠇⠂⡼⠋⠀⠨⠉⠀⠀⠼⠿⠁⢠⣷⣹⠀⢀⠀⠀⠐⣆⢀⡾⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢸
⠀⢹⣿⣶⠞⣤⠀⣀⡆⠄⠈⠀⠸⠀⠀⠃⠀⡘⠐⢀⠈⢨⣏⠀⢸⣼⣿⠋⠈⣴⡀⠀⢟⡸⠀⠐⢈⡤⠤⢤⡀⠀⠀⠀⢰⠏
⠀⠀⣏⡃⢠⠏⡦⠂⠀⠘⣇⠀⠐⠀⢐⡄⡉⠀⠀⠀⠀⠀⠙⡀⠄⣿⣧⠀⠀⠙⠷⠰⣾⡗⠘⢁⣇⡤⢀⠀⠙⣆⠀⢄⡁
⠀⠐⢼⢳⠈⠀⢹⠀⠄⠀⢹⠌⢣⢁⡁⠀⠀⠀⠀⠀⠀⢀⠀⢁⡽⣿⠃⠦⠄⢡⠸⣀⢻⡿⠐⢱⢾⣳⢚⠴⣊⣨⡦⠂⠰⠰
⢹⡷⠚⠊⠁⢀⠀⠈⠑⡘⠀⠂⠀⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣷⣶⠕⣄⠪⠂⢼⣼⣷⣡⠦⣟⣶⣾⣽⡗⢦⣯⡲⢦⣠⣠
⣰⣽⣾⣳⣄⠀⠇⠁⠀⠘⠴⢧⣾⣿⣠⢳⣄⡀⠀⠀⠀⢀⠀⣬⣤⣦⠅⢤⣦⣤⢼⢸⣿⣿⣨⡞⡟⣿⠽⡈⣛⣌⡋⣀⣏⣀⢾
⣿⣿⣿⣷⣻⡄⠘⣴⣀⠰⣿⣸⣜⡿⠉⠙⣿⡏⠀⠀⣿⣿⣞⠿⡿⠉⡁⣚⢻⢡⠘⠉⠉⠙⢹⣽⡃⣿⣹⣿⣿⠟⠃⢽⢿⠏⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠞⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⠳⡍⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠔⠋⡠⠶⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠕⠶⢄⠉⠢⡈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠞⡰⠚⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⢆⠳⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠓⠂⠀⠐⢖⠋⠁⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠈⠙⡳⠂⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣀⡠⠒⠜⠳⠞⠡⠐⢄⣀⣠⠛
⠀⠀⠀⠀⠀⠢⠀⠀⠂⠉⠙⠋⠢⠤⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⣀⠤⠔⠙⠋⠉⠐⠀⠀⠔
⠀⠀⠀⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⢀
⠀⠀⠉⠇⠀⠀⠀⠙⠢⢀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⡀⠔⠋⠀⠀⠀⠘⠉
⠀⠀⠀⣠⠦⠀⠀⠀⣀⡎⠁⠀⠀⠀⠀⢀⡠⠐⠒⢦⡀⠀⠀⠀⠀⠀⢀⡴⠒⠂⢄⠀⠀⠀⠀⠈⢱⣀⠀⠀⠀⠴⣄
⠀⠀⠀⠈⠁⠐⠠⢰⡅⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⢨⡆⠄⠀⠀⠁
⠀⠀⠀⢀⣀⣀⣠⠔⠀⠀⠢⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⠀⠢⢄⣀⣀⡀
⠀⠀⠀⠉⠛⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠉
⠀⠀⠑⠀⠀⠀⠠⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠄⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣨⡓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢚⣅⠀⠀⠀⢀⠔⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠂⠈⠉⠉⠉⠁⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠀⠉⠀⡄⠀⠀⠀⢀⠀⡀
⠀⠀⠀⢨⣠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢉⡝⠀⠀⠀⠂

⣶⣦⣴⣶⣶⣦⣤⣶⣶⣴⣶⣶⣦⣤⣶⣾⣶⣴⣶⣶⣦⣶⣶⣶⣤⣴⣶⣦⣶⣷⣶⣦⣶⣶⣷⣦⣶⣶⣤⣴⣶⣦⣶⣷⣶⣤⣴⣶⣷⣦⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⣄⡀⢀⢠⡄⣿⣸⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⣄⢰⢠⣇⡄⣄⡆⢸⡇⣠⢠⡄⣰⠤
⠀⠀⠀⢀⡸⡇⠸⡎⣧⡇⣿⢧⣾⢴⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⣹⠃⣠⢹⡇⡿⢡⠈⣇⡏⠈⣷⡥⠆
⠀⠀⠀⢸⡇⢹⣀⡇⢻⣧⡟⣸⡟⡼⣰⡗⠀⠀⠀⠀⠀⢤⣙⣎⣧⢠⣿⢸⡟⡁⡙⡆⣿⢸⣸⠟⣤⡴
⠀⠀⠀⢸⣷⠜⣿⣡⡈⣿⢷⣿⣷⢇⣿⡇⠀⠀⠀⠀⠀⠀⣌⠉⢿⡀⢻⣸⢾⡿⠁⢳⡟⣸⠏⡼⠋
⠀⠀⠀⠀⢿⣄⣿⣿⢠⡏⢸⡇⡏⣼⡟⠀⠀⠀⠀⠀⠀⠀⠮⠷⣌⣷⡀⣿⠛⢠⠀⣸⠷⢋⣼⠶⣃
⠀⠀⠀⠀⠀⠈⠹⣿⠀⣇⠘⣿⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⢿⣴⢋⣴⣫⡴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠧⣽⣾⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣷⠾⠛⠁


⠀⠀⠀⠀⠀⠀⠀⢀⣠⢠⣜⠾⣇⣼⢀⢲⣤⣦⠀⣀⠀⠀⠀⠀⠀⠀⢠⢸⠀⡆⠈⣇⡄⢰⡄⣤⠀⢠
⠀⠀⠀⠀⠀⢠⡄⢰⡝⣿⢃⣸⠹⣧⠏⠺⣿⢹⣧⢟⠃⠀⠀⠀⠀⠀⢸⣿⠘⣇⢠⣽⣇⢸⡇⢹⣆⣸
⠀⠀⠀⠀⡀⠀⠛⣛⠛⢿⣌⠙⢷⢏⠈⢻⣘⡟⡋⣩⠀⠀⠀⠀⠀⢀⠀⠹⣇⢻⡆⡟⢸⡀⢷⣸⣿⠟
⠀⠀⠀⠐⣿⣿⣷⠾⣧⡇⣌⢷⡮⣼⢻⣎⣿⣡⣟⡥⢀⠀⠀⠀⠀⠈⣿⡇⣹⣶⡇⡇⢸⡇⣸⡏⣿⡷
⠀⠀⠀⠀⠉⡩⣿⣧⣽⡇⣎⡟⢷⡹⣾⣉⣟⣉⠙⢰⣸⠖⠀⠀⠀⠀⠹⣇⡟⣿⢹⣷⣸⡇⢸⠇⣿⠃
⠀⠀⠀⠰⠦⠷⣤⣆⢶⣿⣬⢿⣾⡟⡑⣿⡏⠈⡿⣸⣏⣷⠀⠀⠀⠀⠀⠈⢳⢻⢸⡏⣿⡇⣿⢰⠇
⠀⠀⠀⠀⠀⣳⣬⣿⣜⣆⣹⠹⣧⡇⣧⢟⣼⣳⣷⣛⣭⠉⠀⠀⠀⠀⠀⠀⠈⢿⡘⡇⢻⡇⣿⡾
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢧⣸⣿⣡⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣧⣸⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠉⡀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠈⠉⠉⣓⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠉⢩⡝⢤⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣰⢪⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠷⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢠⡺⡀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠑⠄⠐⡀⠔⠻⠀⠙
⠀⠀⠀⠀⢡⢄⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⡶⠦⠀⠒⠀⠀⠀⠀⠉⠉⠁⠐⠂⠄⡀⠀⠀⠀⠀⠀⠰⠶⡞
⠀⠀⠀⠀⠇⠙⠗⠠⠬⠄⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣎⠀⠀⠀⡠⠊
⠀⠀⠀⠀⢢⡤⠦⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃⢀⣁⠤⠒⢒⡆
⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠠⠤⡶⠋
⠀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠤⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠗⠒⠒⠚⣚⠆
⠀⠀⠀⠀⠀⠉⠲⣦⠶⠂⠀⢉⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⡒⠪⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⣉⣠⣀⠽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠈⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣏⣁⡼⠋⠀⠉⠂⠤⢀⢀⣀⡀⡀⠠⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣠⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠚⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⣵⡿⠃
⠀⠀⠀⣠⠖⠋⢡⡄⠈⠉⠛⠉⠁⢠⡌⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⣤⠀⠉⠙⠋⠉⠀⣤⠉⠓⢦
⠀⠀⠀⠘⠲⠤⣄⣉⣓⣒⣒⣒⣚⣉⣠⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⢤⣈⣙⣒⣒⣒⣒⣋⣁⡤⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣝⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣶⣦⣶⣶⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠄⢠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠄⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⡄⠀⢀⠀⢀⣤
⠀⠀⠀⠀⢀⠀⢀⣴⣷⣆⢸⠞⠀⡀⡀⠀⠀⣼⠀⢀⠲⠀⠀⠀⢤⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⢴⡀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣬⢀⣡⣾⣿⣿⣿
⠀⠀⠀⠀⢸⠀⡄⣸⠈⣿⣿⠀⠀⣟⢀⠀⣸⣧⣠⣧⣔⣲⡄⢰⠀⠀⠀⢢⠌⣿⣇⠀⠀⢀⠀⠠⠀⠀⢠⠄⠀⠫⢅⠀⠀⠀⡀⢱⣶⣸⣧⣼⣿⣿⣿⣿⣿⣿⣿
⠀⡤⡀⠀⢠⡄⢠⡿⡻⣡⣿⣷⡆⣹⣾⢰⣿⣿⢇⣿⣸⣿⡭⢿⢤⣧⣠⢦⣄⣿⣷⣻⡗⣿⣀⣠⠋⣰⡏⡆⣰⣴⣿⣤⣧⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⣿⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣣⣾⡟⣼⣧⣼⣿⣿⣿⣿⣿⣷⣿⣾⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⠀⠈⢻⣷⢶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⣷⣬⡛⢿⣿⣟⡿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢰⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⠿⡛⢳⢝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⢾⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⣓⣭⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣞⣹⣷⣬⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⣩⣭⣭⣭⣥⣶⣶⣿⡿⠿⣛⣩⣴⣿⣿⣿⣿⣿⣿⣿⠿⢋⣼⡿⠟
⠈⠉⠉⠀⠉⠙⠲⠮⣭⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣯⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⡿⠿⣟⣛⣭⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠑⠀⠀⢸⠀⡆⠀⡇⣢⠀⢠⣊⡆⢀⠀⠀⠰⡀⢠⠜⠀⣄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⠀⣇⠀⠄⢸⡄⠀⠀⢳⢸⠀⠟⠉⠀⡜⠒⠂⠀⠁⠛⠀⣇⠘⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⢀⠀⢰⡇⠀⡀⢧⠀⢹⠀⠀⠘⡀⠄⠀⠘⣆⠁⡀⠰
⠀⠀⠀⠀⠀⢤⡀⠀⠃⠀⡆⠀⠀⠀⠀⢀⢛⠀⡀⠘⠀⣤⣿⠐⡁⢌⣀⠐⡆⠀⠀⠰⡀⠀⡀⢈⡼⠁⠀⡀⠀⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⡄⠀⢁⣦⠚⠀⠃⠐⢧⣸⡏⢠⠀⠊⠀⠨⠹⡇⠀⡆⠀⠀⠁⢸⡁⠀⠀⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⣷⣸⣿⡇⠀⢳⠀⣴⡜⣧⠳⡄⢰⠀⠀⢁⣱⠇⢸⠁⠀⠀⠆⣾⡇⠀⠀⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⢸⢽⣿⣷⡆⣸⣼⢿⠎⠘⠦⡘⠦⠄⠘⠿⠇⠇⠸⠀⠴⠼⡼⢸⡇⡿⠶⢼⣷⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⣤⠺⠖⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠔⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⢻⣷⠀⠀⠀⣴⡿⠻⣿⡆⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣴⡿⠁⠀⣾⡇⠀⠀⠀⠀⢠⣿⠟⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠈⣿⣤⣾⠟⠁⠀⣸⡿⠁⣀⣠⣤⣤⣿⠃⠀⣠⣿⠃
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠸⣿⡀⠀⠈⠉⠁⢠⣴⣾⣟⣡⣾⠟⠉⠉⢉⣡⣴⡿⠟⠁⠀⢀⣤⣴⣶⣶⣄
⠀⠀⢰⣿⠛⠛⠿⣷⣦⣀⠀⠙⠿⣶⣤⣀⠀⠀⠉⠙⠛⠻⠃⠀⣴⡾⠿⠛⠉⠀⢀⣤⣾⠟⠋⠁⢀⣼⣿
⠀⠀⠈⠻⣷⣄⡀⠀⠉⠻⢿⣦⡀⠈⠉⠛⠿⢷⣶⣤⠀⠀⠀⣼⡟⠁⠀⠀⢀⣴⡿⠋⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠈⠙⠿⣷⣦⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⡟⠀⠀⢰⣿⠁⠀⠀⢀⣾⠏⠀⣠⣶⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣧⣀⠀⠀⠸⣿⡀⠀⣿⡇⢀⣤⣾⠿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⢿⣶⣤⣀⠀⠀⠀⠻⣷⣤⣀⠀⠉⠛⢿⣦⡀⠙⢿⣦⡙⠿⠿⠛⣡⣤⣄⡀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠈⠙⠛⠿⣶⣤⣀⠀⠉⠻⢿⣦⠀⠀⢻⣷⠀⠀⠹⣷⡄⠀⢰⣿⠉⠛⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣀⠀⠀⠙⠻⢷⣦⠀⠈⣿⡇⠀⠀⣿⣧⣤⣤⣽⡿⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣤⣶⣤⣀⠀⠀⠀⠉⠛⠿⣶⡄⠀⠘⣿⡄⠀⣿⡇⠀⠀⠉⠉⠉⠉⠁⠀⢀⣸⡿
⠀⠀⠀⠀⠀⢿⣯⡀⠉⠻⣷⣤⣀⣀⣀⣀⣻⡇⠀⠀⣿⡇⠀⣿⡇⠀⢀⣤⣴⣶⣶⠾⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠈⠉⠛⠛⠛⠛⠛⠃⠀⠀⣿⡇⢸⣿⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣶⣦⣤⣤⣤⣤⡀⠀⢻⣷⡿⠃⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡇⠀⠀⠉⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⣧⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⣆⣰⠃⢛⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠳⢋⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠁⢰⠏⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣀⠀⠀⠀⣸⠃⠀⠀⠉⣉⣩⣭⡽⠀⠀⠀⠀⠀⠀⠀⠀⣶⢳⣠⠏⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠹⣧⡀⢰⡏⠀⠀⡼⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠋⠐⣛⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢷⣾⠁⢀⡜⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣠⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠘⠓⢚⣉⣩⠿⠁⠀⠀⠀⠀⠀⢠⡴⡄⢠⡟⣰⠏
⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⣾⠀⠀⠀⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠻⠏⠸⠧⠖⣺⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⣄⠀⠀⢿⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢻⡀⠀⣤⠶⠶⠃⠀⠀⢀⣀⠀⡞⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⠦⣄⣸⠀⠀⡟⠀⢀⣠⡴⢶⠀⠀⠀⠀⠘⣧⡹⣆⣼⠁⣸⠃⠀⠀⠀⢀⡾⠉⠉⠻⠇⠀⠰⣧⠴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠁⠀⠀⠛⠋⢉⣡⠶⠋⠀⠀⠀⠀⠀⠈⠻⣌⠁⠀⠙⢺⡆⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⣠⣄⡀⢀⡿⠀⢠⡶⠛⠁⠀⠀⢀⣘⣦⠀⠀⠠⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⡇⢀⠀⢺⡇⠀⠀⠀⠀⠀⠀⢸⡃⠀⢙⡟⠀⢀⣟⠀⠀⠀⠀⣼⠉⠉⠉⠁⠀⡀⠀⠀⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠈⠛⢯⣙⠲⢤⣀⡇⠀⠀⢸⡇⠀⢀⣤⣦⠀⣠⠤⠧⠀⢸⠃⠀⢸⠉⣳⠀⠀⠀⠸⡄⠀⠀⠀⢀⠃⠘⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣌⠁⠀⠀⢸⣧⠖⢋⣠⠿⢠⡏⠀⠀⠀⢸⡆⠀⠨⠠⣏⠀⠀⢀⣀⣽⡄⠀⠀⠌⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⡴⠋⠁⢀⣸⣇⠀⠀⠀⡀⢷⠀⠀⢃⢸⡇⠀⡟⠀⠀⠉⠀⡼⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⠁⠀⢠⣏⠉⠁⠀⠀⠀⡇⠘⡇⠀⠈⣾⠇⠀⢷⠀⠀⢀⡜⠀⠐⢂⣠⡾⠃
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⠀⣻⡄⠀⠀⠂⠀⠇⠀⢷⠀⠀⢸⣄⣤⢸⡆⠀⠜⠀⢠⡶⠛⠁
⢰⠏⠀⠙⢦⠀⣠⣤⡀⠀⠀⠀⠀⠀⡟⠀⠀⠘⢦⡀⢸⡏⠉⠀⠈⠀⠀⡀⠀⣼⠀⠀⢈⣡⢼⡿⠃⠀⠀⠀⠀⣽
⢸⡄⠀⠀⠈⡿⠃⠀⢻⡄⢀⣀⣀⠀⢧⡀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⢠⠃⢠⠏⢀⡴⠋⣠⠞⠀⡠⠂⣀⡴⠟⠁
⠀⣳⣄⠀⠀⠀⠀⠀⠀⣷⡟⠉⠙⣆⠀⠙⠦⣄⠀⠀⠀⠀⠈⢷⡄⠰⢃⡴⠋⢀⣾⣥⣼⠃⢀⠎⣠⠞⠉
⣼⠉⠀⠀⠀⠀⠀⠄⣀⠈⠀⠀⠀⢹⣀⡴⢶⡌⢳⡀⠀⢄⠀⠀⢻⣴⡟⠀⠂⡾⢻⠀⠁⠠⢁⡾⠁
⠙⢦⣄⣀⣀⣀⠀⠀⠀⠑⡀⠀⠀⠈⠛⠁⠈⡇⠀⢳⡀⠀⢡⠀⠀⡟⠀⠀⢸⠇⢸⠆⠀⡀⢸⡇
⠀⠀⠀⠉⠉⢹⡏⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⣧⠀⠈⣧⠀⠀⠆⠀⣧⠀⡆⢸⣤⠟⠀⡜⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠀⠈⠉⠒⠤⡀⠻⣄⠀⣿⠀⠀⠂⠀⢿⡀⠁⠘⣧⡠⠊⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣇⠀⠀⠀⠀⠀⠐⠌⠛⠛⠶⠦⢤⣀⠐⠓⡄⢀⡽⠀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢷⣀⡀⢈⣙⣒⣂⣤⣬⣽⣧⠤⠿⠛⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣿⣿⡿⠿⠷⠦⠄⠀⠀⠙⠻⣿⡅⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠺⢴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠄⠐⠃⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡈⣻⣿⣷⣶⡶⠂⠀⠻⢿⣿⣿⠿⠃⠀⢀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⠃⣠⣆⡄⠑⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠪⡾⣷⣷⣸⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢾⣿⠏⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢄⠠⢄⣀⡀⠀⠈⠻⢿⣿⠁⠐⣀⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⢀⡞⠁⠀⠀⠀⠀⡂⠉⡍⣿⡾⠉⠀⠁⢻⣿⠀⠲⠀⡄⢄⠀⠀⠀⢀⣿⡟⠀⢀⠆
⠀⠀⠀⠀⡇⠀⠀⢷⣾⣿⣾⠇⠀⡰⢠⠐⠁⠀⠀⣴⡅⠁⠀⠀⠀⠀⣿⡶⠀⠀⠀⠳⢔⣶⡲⣸⣿⠃⠀⢸⠆
⠀⠀⠀⠀⢸⡀⠀⠈⠛⢿⡛⣦⣤⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⣿⠟⠁⠠⣴⠋
⠀⠀⠀⠀⡀⠙⠶⣆⣀⡀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠁⢠⣴⠟⠁⠀⡴⠁
⠀⠀⠀⠀⠙⢤⠀⠙⠻⠿⠷⣴⣶⣦⡀⣄⠀⠀⠠⣄⣄⠀⠀⠀⠀⠀⢠⣤⣴⣦⣤⡀⣠⠿⠟⠛⢡⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠙⠛⠶⢤⣤⡴⢶⣤⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠛⠉⡿⠛⠿⠿⠿⠖⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣀⣤⣶⢦⣴⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⠾⠷⠶⠄⠒⠲⣤⣤⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣆⣦⣴⡮⣤⠀⡀⠀⠀⠀⠐⠿⠲⠦⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡄⣀⠀⠀⡀
⢠⣶⣶⣾⣿⣿⣿⣿⣿⣷⣿⣶⣦⣤⣴⣴⣦⣀⣠⣤⣄⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣤⣤⣤⣦⣦⣠⣤⣴⣴⣤
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣾⣿⣿⣿⣷⣾⣶⣷⣤⣴⣶⣦⣦⣦⣴⣶⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿


⠀⣀⣄⣤⣄⣶⣃⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⣠⠀⢀⣤
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣦⣤⣄⡀⢠⣠⣀⣀⡀⡀⣀⣄⣀⣀⣄⣀⠀⡀⢀⡀⠀⢀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⡀⣤⣴⣤⣾⣿⣿⣷⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣶⣿⣾⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀
⢀⣿⣶⣿⣿⣴⣦⣤⣠⡀⠀⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣰⣤⣦⣄
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⣶⣶⣿⣷⣶⣿⣄⣦⣷⣼⣷⣴⣾⣶⣴⣿⣤⣤⣄⣰⣄⡆⣀⢀⣦⣤⣤⣠⣶⣤⣤⣶⣤⣷⣦⣾⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿