Virology Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡤⠀⡀
⠀⠀⠀⠀⢀⣤⡀⢀⡼⢤⠖⢳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡟⢺⠚⢣⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣸⠞⠲⣎⡠⠆⡀
⠀⠀⠀⠀⠀⢀⡼⠋⢀⠔⠓⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⡷⢺⢲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠴⢚⣇⠯⠽⣈⡓⢯⡔⢃⡄
⠀⠀⠀⠋⠉⠹⡉⠉⡏⢀⡔⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡼⢢⣄⡣⢊⠤⡜⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠈⠒⡟⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⡟⠻⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⣸⢉⡦⣑⣡⠖⠦⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡇⠈⠦


⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⠀⠀⣀⡀
⠀⠀⠀⠀⡤⣤⠀⠘⡞⠁⠀⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣀⣼⣠⠇⠀⣀⡀⠀⠀⠀⠀⠀⢀⠖⠒⠦⠤⠴⠋⡉⠳
⠀⠀⠀⠀⠉⢙⠖⡊⠉⡓⢞⠉⠁⠀⠀⠀⠀⠀⠀⣞⠓⣤⠊⠀⢠⠶⡌⠱⣎⡀⣸⠀⠀⠀⠀⠀⠈⢦⠉⠀⢴⡢⠀⠁⠸⡀
⠀⠀⠰⣛⠦⢾⠀⢙⠦⡁⢨⠦⢾⡱⠀⠀⠀⠀⠀⠈⠉⡇⢠⣦⠈⣋⡀⠀⣏⠈⠀⠀⠀⠀⠀⠀⡰⠊⡤⡄⠠⠄⢠⠲⡄⣉⠲⡄
⠀⠀⠀⠀⢀⣈⠦⣅⣀⡡⢾⣀⡀⠀⠀⠀⠀⠀⠀⢞⢉⡹⣄⠁⠀⠓⢃⡰⠣⣍⡵⠀⠀⠀⠀⠀⠣⢄⠭⣁⠀⣀⠈⢉⣀⣉⠴⠃
⠀⠀⠀⠀⠣⠟⠀⢠⢧⡀⠀⠧⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⡸⢻⠓⢺⠋⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠈⠓⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⢔⡦⢷⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠦⠔⠤⢦⣀
⠀⠀⠀⠀⠀⠀⢔⡮⡋⠘⠇⠙⢧⣂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣩⡑⢆⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢴⠋⡠⠄⢠⡖⠢⡘⢲
⠀⠀⠀⠀⣐⡾⣋⠘⠛⠘⢟⡴⠟⠂⠀⠀⠀⠀⠀⡎⣭⡙⣞⣄⡳⢕⠊⠀⣀⠞⡸⠀⠀⠀⠀⠀⢐⡇⢀⣀⠰⢄⠉⢦⡹⠀⣟
⠀⠀⠀⠀⢚⢧⡛⠀⢛⡴⡟⠈⠀⠀⠀⠀⠀⠀⠀⠣⠭⣇⢳⡤⣭⣙⣒⡩⠥⠊⠀⠀⠀⠀⠀⠀⠈⡆⠫⠼⠂⢀⠀⡤⡀⠀⡎
⠀⠀⠀⠀⢀⡇⠚⠶⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠬⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⡐⠁⠀⡉⡠⠟
⠀⠀⠰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠛⠲⣄⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡠⠖⠛⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⣸⠇⠀⠀⠸⣇⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⢆⡀⠀⠀⠀⠑⠖⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⠋⠀⠀⠀⢀⡴⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⣠⠞⠉⠀⠀⠉⠓⢆⣀⣀⣀⣀⣰⠃⠀⠀⠀⠀⠀⣠⠚⠉⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⣀⡠⠚⠉⠀⠀⠉⠳⣄
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠙⢦⣀⡀⠀⣀⡴⠋⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⢠⠏⠉⠉⠉⠉⠙⢦⣀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠴⠊⠀⠀⠀⢀⡴⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠖⢦⡀⠀⠀⠀⠑⠦⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢹⡆⠀⠀⢰⡏⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⡤⠴⠋⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠙⠦⢤⣤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠒⠋

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⠴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣼⣿⠀⠀⠀⠀⠸⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⣀⣀⣀⣀⣹⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣤⣾⠿⠟⠛⣛⣛⡻⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠙⢿⣦⣄⣠⡾⠟⠉⠀⠀⠙⢿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣄⠀⢀⣤⣶⠿⠋⠉⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⣠⡞⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣴⣿⣿⣄⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⣦⣀⣀⣀⣼⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡿⠛⠛⠉⢻⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⢿⣯⣿⣿⣿⣿⣿⡿⠶⣶⣶⣶⣿⣿⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣤⣼⣿⣎⣿⣿⣿⣿⣿⣿⣟⢉⡿⢶⣿⣤⣾⣿⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣠⣤⣶⡾⠟⠛⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣻⡷⣿⣹⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣯⣤⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⠟⠛⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠙⠿⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠉⠙⠛⠛⠛⠛⠉⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣼⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠈⡒⠀⠉⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠣⠔⠀⠘⠄⠂⠀⠸⠀⢀
⠀⠀⠀⠀⠀⠀⠌⠄⠀⠘⠂⠀⢀⠄⢈⠁⠃⠦⣄⡀⠀⠰⠔
⠀⠀⠀⠀⠀⠸⠄⠰⠄⠀⠣⠐⠀⢢⣣⡀⢈⡀⡠⠙⠠⡀⠀⢆
⠀⠀⠀⠀⠀⠄⠄⡀⠀⠊⢁⢝⣦⠀⠈⠉⠳⣄⡨⠄⡔⠰⠢
⠀⠀⠀⠀⠀⠂⠀⠉⠀⣂⠈⡀⢈⣳⡄⠐⠤⠀⠙⢆⠁⠂⠀⠰⠄⢀
⠀⠀⠀⠀⠀⢰⢧⠢⠆⠀⢢⡁⠠⢄⢨⠲⣄⡀⠀⠀⠈⠀⠀⠀⠀⠄⠂⢠⠀⢀
⠀⠀⠀⠀⠀⠀⢣⢢⠀⢀⠀⠉⢢⠀⠰⠒⠄⠑⠀⠘⡂⠀⠈⢂⢌⠜⠙⠉⠀⠈⠀⠘⠃⠀⠆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠱⣕⢧⠐⠀⠀⠈⠈⠀⠀⠀⡀⠀⠦⠀⠠⡫⠊⠀⡎⠁⢀⠀⠀⢠⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠭⣒⠤⠉⣀⡀⠀⢀⠒⠀⡀⠄⠊⢀⡤⠀⠉⠃⠁⡠⠀⠘⢆⡀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢶⡒⠒⠒⢮⣀⠜⠀⠀⢀⣉⣁⣀⣀⣀⠑⠃⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⡖⢺⡋⠣⠈⠇⠸⠀⠇⠈⠃⠹⠉⡖⢲⠤⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡖⠔⠢⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡤⢤⣀
⠀⠀⠀⠀⠀⠆⢃⠖⠋⡙⠳⣈⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⢀⠈⠀⠀⠨⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡕⠀⠈⣤⠝⢧
⠀⠀⠀⠀⢘⠅⡂⠐⠈⠁⠂⢸⠠⡋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠐⠀⠤⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠐⣏⠊⡞⡇⢱⡀⠂⣸⡆
⠀⠀⠀⠀⠈⢄⡘⢄⣁⢈⡠⠃⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡐⠀⠀⠀⠡⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠋⡴⠳⡈⢁⡜
⠀⠀⠀⠀⠀⠀⠂⠆⢄⡡⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠴⠦⠜⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠄⢩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡋⢩⠳
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⡄⣄⡲⠃
⠀⠀⠀⠀⠀⠀⡀⠜⣌⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢄⣼⡶⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡄⢩⠀⡴⠊
⠀⠀⠀⠀⠀⠈⠀⢠⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⠂⠈⣷⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢂⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣐⢁⡀⠠⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⡞⢀⣠⠒⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⢀⠔⠈⣁⠀⢄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡋⢴⡄⢠⡅⡚⠂⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠝⢁⠔⠁⠌⢠⡑
⠀⠀⠀⠀⠀⡂⠠⠋⠀⠢⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢤⠀⠰⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠐⠀⡠⠊
⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠴⠤⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠠⠤⠊


⡿⢿⠿⢿⠿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠐⠀⡄⠀⠀⠀⠀⠀⢀⣠⣤⣠⡆
⠀⠀⠀⠀⠀⠰⣌⣢⠆⠀⠀⠀⠀⠀⠀⠈⢺⠏⠃⠀⠀⠀⠀⠀⢀⠁⣠⣶⣶⣦⠠⠖⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠁⠙⣇⢀⠀⢾⡇⠀⣰⠷⢀⠸⡆⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⡿⠐⠒⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⢰⠘⣧⣶⣷⣶⣷⣦⡟⢰⡄⠀⠀⠀⠀⠀⠀⠉⢠⠈⠙⠉⡀⠙⠂⠀⠀⠀⠀⠛⢿⠿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠸⠷⢾⣿⣿⣿⣾⣿⣾⣿⣿⡗⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⣠⣰⣦⣾⣖⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠀⠙⣿⣿⣿⣿⣿⠋⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠁⠸⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢼⡀⠀⢀⠇⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢠⣼⣿⣋⣛⣿⣾⡀⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⣧⣤⠼⣤⣄⡔⠁⠀⠀⠀⡀⠀⠀⠀⠠⣯⡤⠥⠸⢰⣿⠅⠀⠀⠀⠀⠀⠈⣇⣸⠃
⠀⠀⠀⢀⡀⠀⠀⠈⡳⠋⢀⡄⠉⡙⢿⣷⣀⡠⠴⠖⠃⠀⠀⠀⠀⠘⢳⠶⣶⠿⠋⠀⠀⠀⠀⠀⢀⠀⠈⠁
⠀⠀⠀⠁⠈⠒⠢⡴⢡⣴⣶⣤⠈⢁⡼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠡⣿⣿⢿⣿⣧⡄⢈⣿⠗⠒⠲⠤⠵
⠀⠀⠀⠀⣠⠴⠒⠙⢽⣻⣶⣿⣿⣿⣿⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄
⠀⠀⠀⠉⠁⠀⠀⢀⠎⠉⢲⠟⠛⢻⠁⠀⠈⠉⢓⡄⠀⠀⠀⠀⠀⠀⠁⠆⠰⠀⡃
⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⢸⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠸

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

⠀⡀⢠⠀⠄⡀⠀⠀⢀⠤⠤⢀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⠂⠀⠀⠐⠡⠀⠡⠤⠠⣀⠈⠁⠈⢀⡀⠀⢈⠂⠀⡚⠀⠀⠱⠆⠀⠀⠂⠀⠀⠁⠄⠀⠈⡰⠐⠅⠈
⠀⠄⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠁⠀⡀⢈⠀⠀⠀⠁⠦⠤⠘⠀⠀⠘⠀⠀⠀⢠⠆⠀⠀⠀⢶⠀⠐
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠐⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⢀⠤⠂⠄⠀⠈⠁⠉⠀⠀⠀⠂⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠈⠀⠸⢠⠤⠃⢠⡀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⡆⠀⠈⠣⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠂⢠⠞⠀⠱⠀⡏
⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠠⠠⠀⠀⠀⠁⠀⠀⠁⠀⠄⠤⠖⠁⠀⠀⡄⠀⠈⠋
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⣶⠾⢶⣦⣄⠀⠀⠁⡀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠁⣀⣀⠂⠠⠀⢀⡾⡟⡄⠀⠢⡌⢆⢢⠭⠙⣦⣬⡿⢿⡆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢣⡨⠁⠠⠀⢸⣧⣠⡷⣶⡶⠾⡖⢺⢛⣻⠩⢉⠃⣈⣇
⠀⠠⠤⠤⡀⠀⠀⠀⠐⠀⠄⠀⠂⠀⠘⣧⢊⠇⢠⠁⡻⢻⡞⣆⠲⢃⢈⣀⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⡅⠀⠀⡀⠀⠀⠐⢀⠐⠀⠀⠤⠀⠀⠈⠑⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⢄⠔⠂
⠀⠈⠂⠈⡁⠀⢀⠀⠀⠸⣉⡕⠐⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡮⠞⠚⠃
⠀⢁⠐⠐⠀⠀⠀⠁⠀⠀⠄⠐⠀⠀⠀⠀⡠⠤⠀⠀⠀⠰⠉⡡⠀⠀⠀⠚⠉⣀⢠⡠⡀⠠
⠀⠀⠀⠘⠄⣀⠠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠣⠠⠂⠀⠀⠀⠀⠀⠀⠐⢙⡯⣧⠿⠂⠇⠁⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠄⡀⡀⠐⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠠⠐⠄⠒⠚⠐⠀⠀⠂⠪⡄⠀⠀⡠⠔⠒⢢⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⢀⡒⠀⠀⢐⠀⠀⠁⠀⢀
⠀⠀⢄⡀⠀⠀⠀⠀⡀⠀⠁⢠⢊⠤⠐⠒⢁⠠⠐⠁⣀⠔⠀⠀⠀⠀⠀⠀⠲⢀⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠄⠄⠂⠊⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣆
⠀⠀⠀⣤⣤⣄⠀⠀⠈⢻⣿⠋⠀⠀⢀⣤⣤⡄
⠀⠀⠀⢿⣿⣿⡀⠀⠀⢸⣿⠀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠈⢻⣶⣾⣿⣿⣿⣶⣾⠋
⢠⣴⣦⣀⣀⣀⣞⣿⠏⠁⠀⠙⢿⣿⣆⣀⣀⣠⣖⣤
⠹⢿⡿⠛⠛⠛⣿⣿⣄⠀⠀⠀⣼⣿⡟⠛⠛⠻⣿⠿⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣶⣿⣿⣿⡀
⠀⠀⠀⣴⣶⣾⠋⠀⠈⢹⣿⠉⠀⠈⢻⣶⣦⡄
⠀⠀⠀⠿⠿⠟⠀⠀⠀⣸⣿⡀⠀⠀⠘⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢠⣾⣿⣷⠀⠀⠈⢿⣿⠋⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⢂⠀⠀⠠⠀⠠⠀⠀⠀⠈
⠀⠀⠘⠿⣿⣿⣦⡀⣀⣼⣿⣄⡀⣠⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠀⡀⠠⠀⠠⠀⡀⠈⠀⡀⠠
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠈
⣴⣿⣿⣦⣤⣴⣿⣿⡟⠁⠀⠙⣿⣿⣷⣤⣤⣾⣿⣷⡄⠀⠀⠠⠀⠀⠀⠂⠀⠂⠀⠀⠂⠀⠈⠀⠀⠀⠂
⠻⠿⠿⠛⠛⠻⣿⣿⣧⣀⣀⣠⣿⣿⡟⠛⠛⠻⠿⠿⠃⠀⠀⠈⠀⠀⠠⠒⠐⠆⠀⠀⠢⠀⠠⠂⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡀⠀⠀⠀⠀⡀⠈⠀⡀
⠀⠀⢰⣿⣿⣿⠏⠀⠈⢹⣿⠉⠀⠈⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠈⠀⠐⠀⠐⠀⠀⢠⠀⠀⠈
⠀⠀⠘⠿⠿⠟⠀⠀⢠⣾⣿⣦⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠈⠄⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠘⠉⠂⡀⠀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⢀⡠⠤⠆⠐⠐⠒⠒⠦⠁⣐⡀⠀⠈⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠐⠢⢔⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢆
⠀⠀⠀⠀⠀⠄⠀⡠⠃⠁⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠤⠄⠀⠀⠀⠠⠀⠀⠄⠀⠱⠀⠉
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢡⠄
⠀⠀⠀⠡⠤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠇⠀⡀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⡀⠂⠈⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠙⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠔⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⣁⠐⠂
⠀⠀⠀⣀⠀⢂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡸⠁
⠀⠀⠀⠀⠀⢘⣆⠀⣀⠀⠀⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠏
⠀⠀⠀⠀⠀⣄⠔⠈⠻⡦⣄⠘⠧⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠤⠕⠀⠀⠀⣠⠞⠁⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⣷⣄⣀⡐⠐⠆⠄⠀⠀⠢⠐⠀⠀⠀⠀⢀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⢈⠯⠜⡿⢤⣤⣀⣀⣄⡄⢠⢤⠶⠚⠻⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠁⠀⠮⠅⢨⠀⠉⠁⠈⢀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠈⢷⡞⠁⠀⠀⣾⣙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡀⠀⠀⠉⣷⣀⣺⣤⣼⣧⣴⣇⣀⣾⠋⠁⠀⢀⡴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⣧⡀⣻⡶⠟⠋⠉⠀⢠⡄⠀⠉⠙⠻⢶⣏⢀⣼⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⣄⣨⡟⠉⠀⢰⡟⣳⡄⠀⠀⠀⣾⣻⡆⠀⠉⢻⣅⣤⠄⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣼⢷⣤⣼⠏⠀⠘⠁⠀⠙⠋⠀⢀⡀⠀⠈⠉⠁⠐⠆⠀⠹⣧⣤⡼⣯⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡏⠀⣾⢛⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⠾⣦⠀⢹⣇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣄⣈⣿⠀⠀⠈⠛⠁⠀⠆⠀⢠⡞⢳⡄⠀⠤⠀⠘⠛⠋⠀⠀⣿⣁⣀⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠉⠉⣿⠀⠈⠁⣀⡀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠰⠆⠀⣿⡉⠉⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣇⠀⢸⣏⣿⠂⠀⠀⠰⠆⠀⠀⠀⢠⡾⢳⡄⠀⠀⣸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣻⡞⠛⢻⣆⠀⠈⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠛⠛⠁⠀⣰⡟⠛⢷⡟⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠛⢙⣧⠀⠈⠁⠀⠐⣯⣽⠇⠀⢠⡀⠀⠀⣀⣼⡋⠙⠂⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡟⠁⣰⠷⣦⣄⣀⠀⠀⠀⠀⣀⣠⣴⠾⣯⠈⢻⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠁⠀⢀⣠⡿⠉⢹⠟⢻⡟⠛⡯⠉⢿⣀⠀⠀⠈⠳⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣍⡿⠀⠀⢀⡼⢧⡀⠀⠀⣿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠉

⠀⢀⣠⣶⣾⡆⢠⣤⣼⣿⠋⣾⣴⣦⣄⡀⠀⠠⡀⠀⣀⣴⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠺⣿⡋⠉⠉⠁⠀⠉⠁⠀⠁⠈⠉⢿⣯⡁⢠⣄⣰⡿⠟⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭
⡧⠈⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⢠⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿
⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠻⣿⡿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵
⠀⠪⠁⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣽⣶⣀⣀⣀⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⣉⣉⣩⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣾⠞⠛⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣛⡛⠿⠿⠟
⢿⣿⣿⣿⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢦⣿⠿⢿⣥⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⡀⢠⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢆⠈⠇⠀⠄⠜⠀⢃

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⢄⠀⠀⠀⠀⣀⡀⠀⠀⢠⠖⠓⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⡆⠀⠀⠸⠀⠠⠀⠀⠘⡄⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡄⠙⠢⠠⡀⠳⡤⠴⠖⠚⠓⠒⠶⣤⠁⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⢆⠀⠒⢄⣤⠔⠋⠙⢄⠈⢀⠀⠀⠐⠂⢠⠃⢠⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠠⡘⠢⡴⠋⠀⠀⠀⠀⠀⠂⠀⢀⠄⢀⢀⠂⠀⠂⠀⠈⠓⡀⡰⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠳⢌⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠹⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣠⠊⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇
⠀⠀⠀⠀⣀⠤⢄⡀⠀⢠⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢐⣆⠉⠁⣰⡒⠀⠂⡤⠼
⠀⠀⠀⢸⠁⠀⠀⠑⠤⠮⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⣄⢀⡞⠘⡄⡰⠁⢱⠀⡴⠁⠀⣔⠋⠁⢰⠄
⠀⠀⠀⠈⠓⠂⠒⠉⢱⠂⠀⠤⢉⠀⠀⠀⠀⢀⠀⡰⠁⠀⠀⠈⠛⢀⣄⣘⣁⣀⡀⠛⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡧⠴⠒⠈⠀⠉⠁⠀⠀⠀⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡠⠤⠀⠠⠄⣤⠀⠀⢀⣠⠤⠞⠀⠀⠀⠲⡉⠉⢢
⠀⠀⠀⠀⠀⠀⢤⡠⠘⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠀⠀⠀⡰⡄⠀⢠⣍⠱⠜⠐⢦⣀⠠⢆⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⡤⠊⡠⠀⠀⠀⠦⠤⠀⠀⠊⠀⠸⡄⠐⠈⢢⣈⡠⠐⠁⠀⡛⢀⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡷⢋⡠⠊⠀⠀⠀⠀⠀⠸⡀⡈⠒⠃⠀⠙⠓⠚⠉⠁⠀⠡⠤⡀⠑⢌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢰⠻⣄⠀⠄⠀⠀⠀⠀⠐⠉⠀⠀⠸⡀⠀⠀⠀⢀⠁⠢⡙⠲⡑⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠞⠀⠀⠑⢤⣀⠀⠀⠀⠁⠀⠀⡄⠀⢸⠀⡀⡀⠐⢄⡠⠊⠳⡌⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⢨⠉⠒⠦⠤⣤⣀⡀⣀⡄⠀⢣⠴⡀⠀⢱⠀⠀⠑⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠀⠀⠀⠀⠀⡜⠁⠣⡘⠤⠊⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⢀⣤⣾⡇
⠀⠀⠀⠀⢠⣿⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⢸⣿⣄⣀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠁
⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⢠⠖⢸⣷⢿⡄⠀⠀⠀⡠⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡀⢨⣿⣦⡃⠀⠀⣸⠃⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠿⠙⡍⠁⢰⠞⠙⣻⣿⣆⠀⠀⢀⡀⠀⢀⠀⢤⠀⠀⠀⠀⠀⢘⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⣑⣄⡙⠦⠼⣷⣄⣿⣧⠙⠂⣠⣏⣀⠠⢤⣤⠞⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣶
⣿⣿⣿⣦⡀⣠⣿⣿⡇⠠⡶⠂⠁⠀⣼⣵⢦⣻⠄⠠⠶⠃⠈⠿⣄⡼⠋⠛⠉⠳⠀⢀⣐⡀⠀⠀⠀⠀⢸⣿⣧⣄⣀⡀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠳⢤⡄⠀⠞⣿⣇⢇⠀⡀⢀⣰⡶⢟⣉⣄⣈⣠⠀⢺⡫⢍⠉⠋⠉⠈⢁⠀⢸⣿⣿⣿⣿⣿⣶⣤⣄
⣿⣬⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⢷⡌⠓⠿⣿⣿⣧⠀⢚⣿⣿⣄⣓⣾⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⡄⠉⠉⠚⠻⢿⠿⠀⠙⠸⣿⣿⠉⠉⠉⠱⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠙⠛⠿⠿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⠀⣠⠤⢄⠀⠀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣭⡅⣀⠠⠘⡗⠀⢚⢲⡗⠂⡤⢤⠊⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣸⣄⢀⡤⠚⢟⠂⠀⠀⠀⠀⠀⡰⠟⣃⠀⡽⢍⠑⢠⡎⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡫⣁⢤⠀⠈⠀⡠⠤⢤⠀⠀⢱⢨⡊⠀⢣⡖⠀⠠⢚⡵⡜⠀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢡⡰⠋⠀⠘⠓⢬⠦⠀⠀⠑⢢⠡⠀⠀⠀⠛⠃⡔⠊⠳⠀⣠⠊⠅⠌⢈⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠵⡍⠂⠀⠀⠀⠐⠴⠀⠀⠀⠠⠀⢄⠁⡐⡆⠀⠎⣴⡊⢀⠊⢊⠊⢐⡢⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⡎⠡⠀⠀⠀⠀⠀⠀⠀⠀⢑⣘⡃⢀⠊⢻⡈⣐⠋⢱⠱⠐⠊⢙⡁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⢑⡓⣠⣄⠀⠀⠛⠉⣷⠀⠀⢰⠉⢂⠀⠠⠐⠢⣄⠐⡒⠚⢔⣒⢲⠌⢔⣱⢕⢈⠭⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠊⢃⠸⢡⠒⠄⠀⠀⠁⠀⠀⠈⠳⠿⠂⢱⡬⠒⠅⠖⣀⠂⠙⡈⡄⢤⡝⢳⣓⠴⠥⢄
⠀⠀⠀⠀⠀⠀⠀⡖⣲⢦⡀⠈⠂⠻⠿⠂⢠⠂⠔⣤⠀⡀⠐⢉⢄⣐⢈⣐⢄⠱⡪⢊⣔⢅⣙⡩⣁⠔⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⢇⡠⠀⠀⠀⠀⠀⢓⡷⢟⠌⣢⠃⣐⢐⠾⣩⡩⢅⣁⡪⣔⠅⣇⠤⠯⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡈⣶⡻⣃⣀⡰⣂⠌⢺⡾⠛⢕⠫⠚⢥⠚⡣⠧⢔⡁⣈⡲⠱⣞⢀⠖⠢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢘⡦⠴⠡⢩⠖⢠⢢⡴⢞⡡⠸⣥⢊⠡⣻⠋⠛⢉⠛⣳⠺⡙⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣉⡙⠉⣙⠞⣠⢭⡒⠂⣈⠸⡻⠓⠒⡪⢔⢇⣙⣏⣛⡉⣘⡁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠉⠪⢄⢅⡠⡄⠨⠀⢅⡢⠔⣩⡋⡽⠋⠹⡬⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠸⠈⡇⣘⡎⠙⠀⠉⠀⢸⣈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄⡀⠀⣀⠀⣀⠀⡀⠤⢀⠠⠀⡠⢀⡠⣄⠠⢄⠤⢄⡠⢀⠦⠐⡂⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠂⠁⠂⠁⠂⠁⠒⠁⠀⠈⠀⠁⠀⠈⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⡰⢒⠉⣱⠄⠀⠀⠀⠀⠀⠠⡶⠢⡶⠆⡶⠆⠀⠀⠀⠀⠀⠀⡠⣤⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠌⠐⠀⢀⠍⠀⠀⠀⠰⣶⢄⢴⣰⣶⣶⠘⠷⠀⠀⠀⡠⡦⠀⢸⢏⣉⠁⠙⣿⡆⠀⠀⠀⠀⡴⠛⠉⠙⠈⠐⠶⣄
⠀⠀⠀⠀⢀⡜⠀⣂⠔⠃⠀⠀⠀⠀⠰⡶⢲⣋⣟⣌⣿⣇⣀⣄⠀⠰⣛⡇⠀⠀⠉⠒⣳⡆⢸⡇⠀⠀⠀⠀⠓⠧⠖⠖⠶⠠⠤⠟
⠀⠀⢀⡴⢠⠈⢭⣁⠀⠀⠀⠀⠀⠀⠈⠻⠁⣨⠃⣎⠙⣤⠘⠋⠀⠀⠹⣵⣤⣤⢠⡾⠋⢀⣽⠇
⠀⠀⠐⠦⣀⠐⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠛⠛⠉⠀⠀⠀⠀⠀⣀⠀⠠⡄
⠀⠀⠀⠀⠈⠉⠶⠤⢀⣐⡂⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢚⡤⡤⡶⠶⣆⢠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢁⠤⡀⢱⡤⢤⡞⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡃⢀⠐⡀⠀⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⡰⠃⠈⢀⠉⢯⠌⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⠊⠀⠐⢿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣡⣠⠂⢤⢀⡿⠤⡀⠀⠀⠀⠀⢠⡙⢢⠀⠀⠈⠁⣡⢄⡀⢠⢰⡤⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠏⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠞⠛⠁⢁⠈⠀⠀⠀⠀⠀⠁⠨⡄⠀⠀⠘⠊⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣑⣿⣟⣷⡄⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠉⢓⢐⢀⣀
⠀⠀⠀⠀⠀⢀⡬⠿⠶⢿⡛⣯⣧⢬⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀⢈⡣⠤⢄⣙⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠸⢧⡄⢀⣴⢫⡝⡇⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⢀⡐⡤⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⡇⢷⣴⠃⡿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠳⣂⠦⡆⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣇⣸⢿⠸⠃⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡁⣀⠈⠈⠷⠈⡕⠺⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣦⡽⠾⢾⣇⣤⡤⡀⠀⠀⠀⢻⣆⠙⢋⡟⠈⠛⠋⠀⠀⠀⣀⣄⢰⢲⡄⠀⠀⠀⣧⠝⡢⠂⢦⡈⡀⡀⠄
⠀⠀⠀⠀⠀⠀⢐⣾⠏⠉⠀⠀⢀⣸⡿⠅⠀⠈⠢⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠀⣿⠳⠽⣜⣷⡼⠃⠀⠀⣔⠵⡇⠀⠀⠈⠃⠐⠧⠄
⠀⠀⠀⠀⠀⠀⠰⠛⡦⢤⡶⠻⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣹⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣏⣩⠹⣭⡹⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⣰⡶⠚⢉⣋⢹⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢰⠁⣀⢀⣠⠤⠤⠆⠀⠀⢀⡀⠀⠀⠀⠰⠟⢰⡷⠘⠛⠀⣦⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡕⠂⠀⠀⠀⠀⡠⠼⡟⠾⠉⢀⣀⣠⠤⠶⠋⠁⠀⠀⠀⠀⠀⢲⣦⠸⡷⠚⠟⡈⣡⣼⣀
⠀⠀⠀⠀⢎⡡⢼⣂⣤⢤⢤⡔⣁⠟⠃⠀⠀⠀⠀⠐⠮⠅⢺⡏⠀⢀⣉⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠿⠓⢄⣰⣿⠙⣁⠜⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠊⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡇⠀⠀⠀⣴⡄⠀⠀⠀⠀⢀⣴⣿⡿⠇⣿⣦⡀⠀⠀⣿⣿⣿⣏⣉⣉⣉⣹⠀⠀⢀⡀⠀⠀⢸⢹
⠀⠀⡇⠀⢠⡄⣿⡇⠀⠀⠀⠀⣾⣿⠁⠀⠀⠈⣿⣷⠀⠀⣴⣶⣶⣶⣶⠖⠒⢲⠀⠀⣿⢹⠀⠀⢸⢸⢸⣿⡇
⠀⠀⡇⣿⢸⡇⣿⡇⣤⠀⠀⠀⢻⣿⣄⠀⠀⢠⣿⡿⠀⠀⣛⣛⣛⣛⣛⣓⣒⣚⠀⠀⣿⢸⢸⣿⢸⢸⢸⣿⡇
⠀⠀⣇⣛⣘⣃⣛⣃⣛⣀⠀⠀⠀⠛⠿⣿⡿⠎⠛⠀⠀⠀⣿⣿⣇⣀⣀⣀⣀⣸⠀⠀⢙⣛⣘⣛⣘⣚⣘⣛⠁

⠀⠀⣠⡀⠀⠀⡾⢷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⡇⠀⢠⣧⠀⠀⠀⠀⠀⠀⣿⣉⣏⣛⣙⡉⣋⢹⡇
⠀⠀⣙⡓⡤⡞⣷⣦⠹⠟⠀⠀⡇⠀⠀⠀⠀⠈⣿⠀⠀⠀⡇⣼⡸⡿⢠⡄⣤⠀⠀⠀⣿⠠⠅⢽⠼⠥⡧⢼⡇
⠀⠀⣿⡇⣬⡅⣿⣿⢸⣿⠀⠀⡇⢀⣀⣸⡟⠛⠋⠀⠀⠀⡇⢿⠃⠁⢸⡇⠿⠀⠀⠀⣿⠒⡖⣛⢘⡃⣗⢺⠃
⠀⠀⣿⡇⣿⡇⣿⡿⢸⣿⠀⠀⣇⣈⣉⣉⣁⣀⣀⣀⠀⠀⣇⣈⣀⣀⣈⣁⣀⣀⠀⠀⣿⣨⣇⣭⣨⣅⣏⣹⡆

⠀⠀⡏⢹⣉⡏⣻⢙⡏⢻⠀⠀⠀⠀⠀⢀⣄⠀⢰⡳⠀⠀⡇⠀⠀⠀⠀⠀⣠⡄⠀⠀⣷⠀⢀⡀⠀⢰⠆
⠀⠀⡇⢼⠄⠧⣽⠌⣣⢸⠀⠀⢖⣦⣀⡼⡟⢖⡿⡇⠀⠀⡇⢀⣤⡀⣠⡾⢋⡁⠀⠀⡏⠀⠈⡇⣤⢸
⠀⠀⡇⣠⣾⣷⣤⣾⣿⢸⠀⠀⢸⠀⢳⠋⡇⢸⡇⡇⠀⠀⡇⠈⣠⡾⢫⣤⠟⠃⠀⠀⣷⢰⠀⡇⣿⢸⠀⡆
⠀⠀⣇⣟⣟⣛⣛⣛⣟⣸⠀⠀⣸⣀⣸⣀⣇⣸⣇⣇⠀⠀⣇⣀⣉⣀⣀⣁⣀⣀⠀⠀⣿⣸⣀⣇⣛⣸⣀⣇

⠀⠀⠀⠀⢀⣄⠀⠀⢀⡴⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠛⠛⠛⠛⠛⣛⢻⠀⠀⠀⢀⡀⠀⡆⠀⣀
⠀⠀⢀⡴⡋⣍⠳⡴⣋⣶⠀⠀⠸⣢⡾⠋⠙⠳⣄⠏⠀⠀⣿⠀⠀⣶⢠⡀⣿⢸⠀⠀⠀⠈⠿⠷⡗⠿⠏
⠀⠀⠋⡆⡇⣟⣷⣶⣿⣿⠀⠀⢰⡏⣤⣀⣀⣤⠽⡆⠀⠀⣿⣠⡄⣿⢸⡇⣿⢸⠀⠀⠈⠉⣩⡯⣯⣿⣍⠉
⠀⠀⣃⣃⣃⣓⣛⣛⣛⡛⠀⠀⣾⠀⠀⠉⠉⠁⠀⣿⠀⠀⣿⣛⣃⣛⣘⣃⣛⣸⠀⠀⠀⠘⠋⠀⡇⠙⠻⢆
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢤⠀⡀⠀⢀⠀⡀⡀⢠⠀⠀⢀⠀⡄⠀⡠⠀⡀⠀⠀⢀⠄⠀⠄⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠁⠀⠀⠑⠀⠈⠁⠉⠁⠉⠀⠂⠈⠀⠀⠀⠑⠂⠘⠀⠀⠀⠂⠁⠂⠁⠙⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢤⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣼⠀⠀⠀⠀⠀⠀⠺⠀⢠⣤⢠⣤⢤⡄⠀⠙⠀⠀⠀⠀⣴⣿⣿⣇⣸⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⡗⠒⠒⢲⠀⠀⠀⠀⠀⢠⣾⣻⣾⣷⣾⣷⡆⠀⠀⠀⠀⠐⣿⣿⣿⣿⡨⣵⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢹⠀⡟⠉⡇⢸⠉⢻⠀⠀⠀⢰⣀⠉⠙⠛⠛⠉⠈⣁⣰⠀⠀⠀⠀⠻⣿⣿⣿⣿⡌⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠋⠉⠉⣉⡉⣿⠀⠀⠀⠀⠀⢀⡀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠬⠤⠆⠀⠀⣿⠀⠀⠀⠀⠀⠿⠿⣄⣰⡁⠀⠀⣀⠀⠀⠀⠀⠀⠠⣮⣭⣉⣉⣭⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣈⡉⣉⣩⡀⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠒⠺⠿⠇⠀⠀⠀⠀⠰⣮⣭⣉⣉⣭⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠻⠟⠃⣿⠀⠀⠀⠀⠀⣾⡞⠁⢠⣧⡄⠀⠀⠀⠀⠀⠀⠀⠠⣮⣭⣉⣉⣭⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣖⡆⠀⠀⠀⠀⣴⢛⡉⢉⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠨⠅⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠤⠚⠜⠲⣑⢣⠤⠄⠀⠀⠀⠐⣇⢰⣬⣵⡆⣽⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⠒⠒⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣅⠈⢹⢠⠤⣼⠀⡁⠀⠀⠀⠀⠙⠶⣤⣤⠾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠠⠼⠸⠤⠿⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠆⠀⠀⠀⠀⠀⠀⠀⣗⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⠀⠀⣀⠀⠀⢀
⣿⣏⢽⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⣒⡒⠒⠒⠒⠀⠀⠀⠀⡖⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⡖⡺⠿⠒⡆⠀⠀⠀⠀⢀⣴⣿⡷⠁⢀
⠀⠀⢀⣻⣗⣀⣀⣀⠀⠀⠀⠀⡇⠠⠦⠾⣏⣹⠀⠀⠀⠀⠀⡟⠓⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⣵⣤⣤
⠀⠀⠾⠿⠏⠙⠿⠿⠆⠀⠀⠀⠉⠉⠛⠏⠉⠉⠁⠀⠀⠀⠀⣇⣶⣖⣃⡇⠀⠀⠀⠀⠈⠹⢿⣿⠿⠋


⠀⢀⡖⠒⠚⠳⠖⠲⡄⠀⠀⠀⢠⠞⣹⣙⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙
⠀⢀⡇⣀⣦⣼⣶⠀⡇⠀⠀⠀⠸⣍⣹⣁⡟⠀⠀⠀⠀⠀⠀⢸⣏⣁⣸⡇⠀⠀⠀⠀⠀⢀⣠⣀⣠⣴⡀
⠀⠈⠷⠿⢿⡿⠿⠶⠃⠀⠀⠀⠀⠈⠉⠁⠙⢦⠀⠀⠀⠀⠀⠘⠻⠟⠀⢆⠀⠀⠀⠀⠀⠈⣍⣈⣈⡬


⠀⠀⠀⢠⠖⢒⣦⣀⡀⠀⠀⠀⠀⣴⠞⠃⢿⣷⠀⠀⠀⠀⠀⠘⠉⠻⠋⠛⠀⠀⠀⠀⠀⠘⢉⣉⡉⠃
⠀⠀⠺⠻⣖⣋⣹⠋⠁⠀⠀⠀⢸⡇⣀⣀⣴⣼⡇⠀⠀⠀⠀⢀⣁⢨⢀⣀⠀⠀⠀⠀⠀⢰⣧⠴⣿⠆
⠀⠀⠀⠀⠀⠁⠀⠳⠄⠀⠀⠀⠈⠻⣬⣀⣭⠟⠁⠀⠀⠀⠀⠈⢩⣿⣭⠉⠀⠀⠀⠀⠀⢠⣈⣉⣉⣦


⠀⠀⣶⣶⣶⣶⡶⣶⡆⠀⠀⠀⣠⠞⢉⡳⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⢀⣔⠊⡏⢒⢄
⠀⠀⢀⣄⣄⣔⣉⣢⡇⠀⠀⠀⢻⣔⠿⣣⡏⠀⠀⠀⠀⠀⠀⣟⣀⣁⣈⡇⠀⠀⠀⠀⠀⠰⠀⡇⠠
⠀⠀⠤⠤⠤⠬⠶⠵⡇⠀⠀⠀⠀⠈⠉⠁⠹⣦⠀⠀⠀⠀⠀⣿⣿⣿⡟⠃⠀⠀⠀⠀⠈⠺⣄⣇⡤⡊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡺⠭⠉⠀⠈⠉⠉⠒⠚⠭⢗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠕⠊⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠫⣓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⢀⢤⠀⠀⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⠈⢪⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠱⡱⡀
⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠱⣱⡀
⠀⠀⠀⠀⠀⢀⢞⠔⠁⢠⠔⠉⠉⡐⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳
⠀⠀⠀⠀⢀⠃⠂⠀⠀⠁⡀⢨⠌⠐⠀⠀⠘⢷⣄⡀⠀⠀⠀⢀⢔⠐⠁⠀⠀⠀⠈⠉⠆⠀⠀⠀⢣⢧
⠀⠀⠀⠀⢸⠸⠀⠀⢸⠀⠈⠤⡀⠄⠀⠀⠀⠀⠙⠻⠧⠤⠖⠚⠁⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠘⡸⡄
⠀⠀⠀⠀⠀⢧⢇⠀⠈⢆⠉⠂⠤⠐⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠀⠀⠀⡠⠤⠤⠤⠀⠀⠀⠀⠀⢃⢇
⠀⠀⠀⠀⠀⠈⢏⢆⠀⠈⠓⠤⠤⠔⠀⠀⠀⠀⡠⠐⠈⠀⢀⠴⠃⠀⠔⠁⠀⢀⡠⠔⠀⢀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠈⢮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠔⠒⠉⠀⠀⠀⣄⣀⠤⠊⠁⠀⠀⠠⡠⡙⡆⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠐⠁⣆⢀⠀⡘⠀⡐⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⢄⠀⠀⠀⠀⠠⠀⠈⠢⠀⠀⠁⠀⠁⠀⠀⠀⠀⠆⡐⠀⠂⠀⡠⢁⠔⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣗⢄⠀⠀⠐⠄⠀⠁⠀⠀⠈⠒⠚⠀⠀⠈⠪⢄⣀⠠⠄⣊⠔⡡⠎
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠳⢵⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⣒⡨⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣆⣤⣶⠤⠭⠵⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠢⢈⠠⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠈⠁⡐⠀⠄⠀⢀⠀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⣀⣀⡈⠀⢠⠂⠀⡀⠈⠤⠀⠀⠀⠎⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠲⠀⢸⡆⠚⠒⠓⠂⠀⠈⠀⠂⠘⡀⡀⠂⠀⠠⠀⠐⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠸⠆⠭⠭⠅⠀⠀⠐⠀⠁⠈⠂⡀⠁⠈⠀⠆⠀⠢⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠊⠀⠀⠴⠄⠠⠤
⠀⠀⠀⠀⠀⠀⡄⠀⠨⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡍⠉⠉⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⡇⢈⣉⠀⢘⡁⣉⡁⠀⠐⠀⣀⢠⣄⠁⠀⠀⠀⠀⠣⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠐⠐⠀⠀⠀⠀⠀⠀⠂⡃⠀⠀⠰⠀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⢈⠑⠀⠀⠀⠀⠀⠀⠀⢠⠍⠈⢅⠀⠀⠀⠀⠀⠀⠄⢄⣀⠂⡀⠀⠃⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠌⠀⠠⠀⠆⠰⠀⠀⠰⠀⠀⠦⠆⠆⠆⠀⠠⠀⠐⠀⠈⠂⠠⠊⠊⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡆⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢀⠆⠐⠀⠀⡀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠄⠀⠉⠈⢀⣄⠀⣀⠀⢀⡀⠀⣀⡀⠠⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠖⠃⠒⠰⠀⠀⢠⣤⡀⠀⠀⠀⠤⠲⠔⠀⠀⠀⠈⡇⠀⠀⠈⠉⠉⠏⠁⠘⡐⠀⠀⠐⠋⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠂⠐⠀⠈⠈⠐⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠐⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠞⠛⠛⠲⢶⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⢠⡰⢦⡀⠀⠹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢎⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⠀⠁⡀⢀⠀⠀⠀⠉⠄⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⠀⠀⠠⢲⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠃⢪⣤⢀⠲⠦⢅⠀⠀⠀⡔⠂⠀⠈⢷⡀⠀⠂
⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠐⠀⠀⠐⢤⣰⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠉⠉⡉⠠⢁⠞⠤⠀⣈⠁⠀⠀⠀⠀⣙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠊⠀⠀⣀⠘⠋⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⡀⢀⡀⡀⢃⠄⠤⠂⠀⠢⠀⠀⠀⣼⣻⠂⢸⡀
⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠎⠁⢀⡠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⢢⡁⠀⢂⡀⠀⠀⠀⠀⠂⠀⠀⢈⠁⢀⡾
⠀⠀⠀⠀⠀⠄⠀⠈⡇⠀⠈⠲⣄⣀⡍⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠨⢐⠒⣶⠤⢰⠇⠤⠤⠤⠤⠤⣲⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢹⠀⠘⠂⠐⠀⠒⠉⠉⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣖⠒⠂⠒⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢰⡟⠀⠀⠀⠀⠀⠀⠀⣤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃⠀⠀⠀⠀⠀⠀⠀⣿⣇⢠⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⠆⣸⡀⠀⠀⢀⣠⣴⡶⠞⠻⠟⢛⣻⠶⢦⣄⡀⠀⢀⡏⠈⠦⣉⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠸⢋⣰⠟⣧⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⢁⣀⡀⠈⠙⠦⣼⣃⡴⠾⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⢶⡬⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡙⢦⡀⠀⠛⠻⣦⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⠛⢸⡇⠀⠀⠀⠈⣷⣀⣤⠚⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠀⠀⠀⢸⡟⠛⠳⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠙⣷⣄⡀⠠⣿⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⣿⡇⣿⠈⢙⣉⣿⡶⠀⠀⣠⡾⢋⣁⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣀⣤⣴⣶⠻⡆
⠀⠀⠀⠀⠀⠀⠘⢿⣅⣿⠞⠋⠁⠘⣧⠀⠀⣿⡀⠛⣋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢶⣦⡀⣼⢣⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⢷⣄⠈⠙⠛⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠘⢿⡏⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣠⢿⣇⡀⠀⠀⠀⠀⣄⢀⣠⡾⠋⠁⠀⠀⠀⠘⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⢸⡟⠻⠶⠶⠶⠶⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠷⠶⣶⣿⠀⠀⠀⠀⠀⣿⠈⠳⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣛⣃⣠⡽⠃⠀⠀⠀⠀⣿⡶⠛⣉⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠐⠿⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢎⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠲⢠⠶⣾⣧⣈⡦⠰⣉⣽⡄⣀⢷⠀⠀⠀⢀⣀⡀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢠⠀⠀⠀⠈⠻⠟⠛⠋⠀⢀⣘⣿⡿⡾⠋⠀⠀⣀⠀⠀⠁⠀⢺⣿⣎⣿⡰
⠀⠀⠀⠀⠐⣿⣿⣷⣦⠀⠈⠘⢄⠀⠀⢠⣶⣆⣀⠀⠈⡸⡗⡻⠯⠂⡄⠡⡹⡂⢀⠀⠀⣾⣫⣿⣿⠅
⠀⠀⠤⠀⣀⣐⣂⠊⠋⣠⣶⡈⡌⢂⠀⠸⣿⣿⣿⣿⡀⠉⢒⠁⠀⠀⠀⠨⠶⢡⠀⢱⣼⣿⡷⠶⡶⠀⢂
⠀⠀⠠⡁⠷⣥⣘⣴⢾⢿⣿⣷⡄⣀⡀⠀⠀⠛⠾⠛⠀⢀⡀⢐⡾⠁⡤⠠⢄⢾⠳⠆⢈⠀⠀⣀
⠀⠀⠀⢃⡠⠗⠈⠈⣾⢮⢿⠟⠰⣫⣿⣷⣦⠀⠄⢀⡠⠠⠁⢄⠀⣠⡵⡯⡉⢸⠗⠀⠀⠀⠀⠀⠇
⠀⠀⠂⠂⠀⠀⠀⠀⠊⠉⠉⠀⢸⣿⣿⢿⣇⠰⣶⡌⠍⠀⠖⢻⠐⣃⣭⠀⠰⡀⠈⠀⠤⠙⠂⠀⢀⠄⠤
⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠿⠻⠂⠐⠖⠀⠀⢁⣄⠉⠁⠟⠀⠀⠀⠀⢤⡈⠁⣑⠢⢀⠀⣠
⠈⠶⠲⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡙⠁⠀⠀⠀⠀⢠⡒⠈⡀⣴⡌⢆⡆⢬⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄⠠⠠⠤⠠⠄⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡄⠘⠛⠃⠀⠈⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡩⠀⠀⠀⢌⠰⣋⣀⠀⠀⠘⠀⠀⠀⠀⡟⣱⡄⣀⣀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠂⠀⠀⠈⠀⠀⠀⠈⠉⣈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢠⡙⢧⠻⠁⠀⠀⠀⠀⠉⠉⢀⡀⠀⠀⠀⠀⠀⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠂⠀⠀⠀⠀⠀⠀⣠⣦⠿⠗⠀⠀⢰⣷⣄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠉⠁⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠐⣒⣀⣀⣠⠀⠄⠀⠨⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠹⠏⡆⠠⠞⠉⡉⠁⠀⠈⠐⠄⢠⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠉⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢐⣆⣙⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣅⠀⢀⠀⠀⠀⠨⢨⡃⠀⠀⠀⡂⠢⠄⠠⠼⠄⠀⢠⠭⠴⠀⠀⠄⠀⠀⠠⠠⠤⠤⠤⠠⠄⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠒⠠⠀⠀⠠⠲⢂⣁⣃⠄⠀⠀⢡⠀⢰⡎⠗⡆⠀⠀⢠⣤⡄
⠂⠀⠤⠀⡄⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡀⠀⠀⣠⣄⠘⠊⠈⠀⠀⠀⢋⠀⠸⠇⡆⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠈⠁⠉⠈⠀⠁⠈
⠀⠀⠠⠤⠠⠀⠠⠠⠠⠀⠀⠀⠂⠀⠀⠀⠠⠇⡀⣇⡇⠀⠰⢧⣽⠇⠀⠀⡀⠈⢵⠂⠀⣤⠸⠁⢠⡤⡄
⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠁⣄⢙⠌⠁⠀⠀⠀⢬⡁⠀⢀⡄⠀⠰⠅⠀⠀⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⡈⠃⠐⠒⠢⢄⣀⠚⡄⢀⣰⠌⠡⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠰⠀⠠⠀⠀⠰⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣤⡄⠀⢘⠷⠬⠗⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⣧⠀⠀⠉⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⠀⠰⣉⠆⠀⢀⠴⡄
⠀⠀⠀⠀⠀⡀⠀⠈⢻⠢⠒⣚⠀⠓⠒⠚⡎⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⢩⠆⠀⠀⢀⡀
⠀⠀⠀⠀⠸⠭⡢⠔⠁⠀⠘⠘⠁⠠⣒⡄⠈⠢⢔⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠣⣀⠤⠜⠘⠢⢄⣠⣧⠽
⠀⠀⠀⠀⠀⠀⡜⠐⣯⠇⠀⢰⣲⠀⠀⡠⢄⠀⢇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠘⠙⠃⣠⢄⠐⢇
⠀⠀⠀⠺⡩⠶⡁⠀⠀⠀⠀⢠⢤⠀⠀⠙⠁⠀⢨⠾⠭⠇⠀⠀⠀⠀⠀⠀⠀⠀⢞⣙⣒⠃⢠⢄⠀⣀⠀⠉⠁⢀⠀⢓⡚⣉⠆
⠀⠀⠀⠀⠀⠀⣱⠀⢯⡆⠀⠈⣉⠀⠀⣮⠇⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠁⠀⠫⠇⠀⠸⠝⠀⡅
⠀⠀⠀⠀⢸⣩⠗⠑⢄⠀⠀⠘⠓⠃⠀⠀⡴⠋⠺⣍⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠧⡄⠀⣖⡄⠀⢠⣲⠀⡠⣣⠤⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠜⡖⠒⠲⣄⠔⠚⢢⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠈⢱⢀⢄⣀⣄⢰⠊⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠰⣉⠆⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡣⠀⠀⠠⣏⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⠒⢢⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⡇⠀⣀⣀⠇⣏⣀⡀⠀⡇⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡸⠙⠊⣁⣀⠀⠀⠀⠉⠊⠰⡁⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣈⡢⠤⠊⠀⠀⠀⠣⠔⠁⠀⢠⠒⢄⠀⠈⠦⠤⣊⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢠⠒⡆⠀⠀⡠⢤⡀⠀⠉⠁⢀⠀⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⢀⡼⠀⠈⠊⠁⠀⠀⠘⠒⠃⠀⠀⢸⣉⠇⠀⠸⣄⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠖⠒⠄⠀⠀⠀⠀⠀⠀⡠⠒⡄⠀⠀⠀⠀⠀⠀⢠⡖⠒⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⣍⡣⠀⠀⠈⠈⠀⠀⠀⣞⣹⠀⠀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⣪⠤⣄⠈⠁⠀⠀⠠⣊⣱⠀⠀⠈⠀⢀⠤⠬⡳⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠀⠈⢳⠄⣀⠀⠀⠀⠀⠀⢀⡀⢔⠁⠀⠀⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⡞⠀⠉⠙⡆⡖⠈⠁⠘⡎⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢠⠃⢣⠀⠀⠀⠑⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠦⠀⠒⡲⠶⣲⠒⡳⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠺⣻⡤⠉⣁⠀⠠⠬⠏⡘⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⡉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡥⠗⠀⡀⣀⣀⢀⣀⡀⢀⡖⠀⠀⠠⠄⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⡿⠛⠛⠻⣿⣿⣷⡄⠀⠀⠀⠀⢀⠀⠂⣖⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⠀⠀⠀⠐⠻⣿⣷⣤⣤⣴⣿⣿⡿⠇⡇⠀⠀⢦⠁⠀⠀⠘⢀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠀⠀⠀⠀⡀⠈⠋⠉⠙⠉⠙⠋⢀⠼⠃⠀⠀⠀⢀⣧⡄⠄⠀⠀⢁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠓⠀⠀⠀⠈⠀⠀⠀⠀⡂⠀⣠⠂⢀⡠⠖⢀⠷⢦⡄⡈⠂
⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠲⣏⠁⠈⡀⠀⡈⡑⠈⠉⠆
⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠁⢄⠀⢷⡀⠀⠀⠠⢔⡇⠀⠠⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠪⢁⡀⠀⠀⠊⠁⡀⠄⠈⠀⠄⠁⠄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⡛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠄⣭⣭⣭⠅⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣴⠞⠛⢻⡟⠛⠶⣤⡾⠋⠀⠀⠀⠀⠀⠐⣃⣐⣛⡂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⠀⠀⢸⡇⠀⠾⠋⢷⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠁⠀⠀⠀⢸⣧⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡆⠀⠀⢠⡄⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣦⡀⠀⠙⢦⣀⣀⡴⠏⠀⠀⠀⠀⣛⣛⣛⡃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠳⠚⠛⠿⠦⠶⠶⠶⠶⠆⠭⠉⠽⠅⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⡟⣆⠀⠀⠀⠀⠀⠀⢰⠛⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⢠⣶⣦⣦⣤⣄⠀⢻⣾⣟⣿⡿⡆⠀⠀⠀⠀⠀⢀⠐⠊⠀⠀⠀⠀⣠⠴⠛⠛⢿⣆⠀⠀⠀⢀⡤⣀⢜⠾⣲⠀⢰⣅⣠⠃⡤⠤⣴⠋⣳
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠟⠀⠀⢿⣽⡿⣿⢿⡀⠀⠀⠀⠀⠆⠐⡆⠀⠀⣠⠞⠁⠘⠁⠀⢸⡟⠀⠀⠀⠈⣒⡛⠒⠁⠀⣠⣯⣉⡇⠀⠳⠔⠋⠉⠁
⠀⠀⠀⣠⣶⣦⣀⠀⠀⠀⢴⣄⡀⠈⢿⣻⣿⡿⣷⠀⠀⠀⠀⠙⠚⠀⣠⠞⢡⡘⠃⠸⠇⣰⠟⠀⠀⠀⠀⠸⣇⡹⢀⡤⢼⣍⣹⠟⣴⣮⠲⣄⡀
⠀⠀⠀⢿⣿⣷⢿⣷⣦⡀⠀⠙⠃⠀⠘⢿⣽⣷⠟⠀⠀⠀⠀⠀⢀⡞⠷⢀⠛⣁⠃⣠⠞⠁⠀⠀⠀⠀⠀⠀⣯⢿⡿⣤⠔⠁⠀⠀⡷⢟⠺⣏⢉⡆
⠀⠀⠀⠀⠙⠺⣿⣿⣻⣿⡆⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠐⠶⠀⢈⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡟⢤⠀⢰⠒⡄⠓⠊⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⠁⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠝⠀⠀⢀⣠⠤⠦⢤⣄⡀⠀⠀⠈⠉⠀⠀⣱⣴⣾⢧⣄⣀⠴⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣻⣆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣘⠗⠁⠀⠀⠀⡞⢱⠚⠛⠲⠦⠟⠀⠀⠀⠰⠠⢴⣯⣀⣽⢿⣿⣧⡀⡀⠘⠿⠀⠀⠀⠀⠀⣤⣶⡄⠀⢻⣷⣾⣧⣽⡯⠃⢠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⣀⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣏⣿⣿⣹⣏⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠉⠈⠀⠀⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⣠⠴⢒⢒⣚⣛⣋⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠛⠛⠟⠁⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣦⡀⠀⢠⡿⢻⣭⣷⣖⠄
⠀⠀⠀⠀⣾⢱⡟⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢋⠀⠀⠸⠆⠀⠀⣴⣶⣷⣆⠠⠀⠀⠀⠀⣄⣿⣧⣼⡿⣾⠀⠀⢻⣿⣿⣶⠏
⠀⠀⠀⠀⠹⣌⡧⠀⠻⣝⡲⢖⣒⣫⠭⠭⢭⡷⠀⠀⠀⠀⠀⣿⣾⣿⠆⠀⠀⠀⠀⠁⠘⣯⣽⣿⣾⢀⡀⠀⠀⠀⣛⣿⣽⠛⢳⣿⡇⠀⠀⠁⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⣄⠀⠀⠀⠀⠀⠈⠫⠿⣿⣿⣟⡇

⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⡰⠋⠀⠠⠀⡷⠀⣰⠟⠉⠉⠉⠙⢷⣄⠀⠀⠀⠀⠀⢰⢿⠇⠀⠉⠻⢶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⡇⠀⠀⠀⡞⠁⠀⢻⣆⠀⠓⠀⠂⡀⠹⣧⠀⠀⠀⠀⣾⡿⠀⣀⣤⣤⣶⣦⠀⢁⣴⡿⠂⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠙⠿⢿⣿⠽⠃
⠀⠀⠀⠀⢳⡀⠀⠀⢱⠀⠀⢀⡿⠀⠃⠀⠀⠁⠀⣿⠀⠀⠀⠀⣠⣴⣿⠟⠛⠋⢉⣡⣴⡿⠋⠀⠀⠀⠀⢠⣶⢛⣿⣽⣿⢻⣷⣶⣤
⠀⠀⠀⠀⠀⠉⠓⠒⠉⢀⣴⠟⠁⠄⠀⠒⠀⠁⢠⣿⠀⠀⠀⠀⠻⠋⢱⣶⡾⠿⠟⠛⢩⣤⣤⣄⠀⠀⠀⢸⣿⣾⣾⣾⠿⣾⣿⣿⣿⣿⡆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠴⠀⠀⡄⠲⠀⣸⡏⠀⠀⠀⢠⡶⡦⣄⣀⠀⠀⠀⠀⠈⠉⠉⠋⠀⠀⠀⠈⠹⢿⣿⣮⣿⣿⣿⣿⣽⢿⡧⡀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠘⠁⠀⢀⣴⠟⠀⠀⠀⠀⠈⠛⠻⠷⣿⣫⣿⣻⣻⣹⣻⣹⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠿⠟⠛⠁⠀⠈⢀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⡀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡗⠋⠁⠀⠀⠀⠉⠏⠿⠋⠀⠀⢀⡄⢀⠄⠀⠐⢩⡅⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠬⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠘⠣⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⡢⠊⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠤⠀⠀⠀⠀⠀⠰⣇⡛⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⡿⠽⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠾⠁⠈⠀⠀⠠⠀⠀⠀⠀⠀⠿⣿⣳⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⡅⠀⠀⣠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⠀⠀⠀⠸⠀⡀⠀⠀⢀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⢠⠀⡄⠀⠀⠀⠙⠠⠄⠀⠀⠂⠄⠒⠈⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢸⠁⠀⠀⠀⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠄⠁⠀⠀⠐⠷⠜⣿⡧⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⣐⢀⠏⠀⠐⣴⠀⠴⠁⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⣰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠠⠄⠐⠡⠀⠀⢀⠂⠈⠈⠀⠒⢚⡟⢧⠀⠀⠀⠀⠀⠀⡠⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⢢⢀⠘⠲⠼⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠜⠀⠀⠂⢀⠔⠁⡙⢱⣿⠀⠠⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⡐⢸⣿⠆⣄⣠⣶⡄
⠀⠀⠀⡀⠀⢄⡠⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⢀⠔⠁⠀⠈⢉⣸⡗⠀⠠⠀⠠⠌⠀⠀⠀⠃⠀⠀⠀⠀⠼⠋⢯⣅⠊⠁⠀⠜⠛⠋⠙⠂
⠀⠀⠀⠀⢀⣴⡗⠀⡀⠀⠀⠀⠦⠙⠃⠀⠀⠀⠈⠠⠔⠀⠀⠠⠁⠀⢠⠙⠁⠀⠀⠀⢠⠀⠀⠀⣘⠂⠀⠀⠀⠀⠀⠀⠀⠚⠑
⠀⠀⠀⠀⠘⠁⠀⠀⠳⡄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⣞⠃⠀⠀⠈⠀⠀⠀⠀⠀⢀⠴⠟⠳⣦⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⠀⠀⣿⠀⠐⠺⠷⠶⠄⠀⢰⣀⡀⢀⣤⠀⠀⠀⠀⠀⠀⠖⠂⣠⠉⠀⠀⠀⠀⢶⣾⡿⣷⠆⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢤⡀⠐⠂⠓⠚⠓⠒⠀⠈⠝⠃⠈⠋⠀⠀⠀⠀⠀⠀⠆⢠⠇⠀⢀⠀⠀⠀⢺⣿⠆⠀⠸⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⡘⠛⠸⠉⠋⢋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠿⠋⠀⣴⠄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣃⠈⡳⠤⠈⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣐⣿⡟⢤⡇⢀⠀⠤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣾⡟⠉⠀⢺⡀⠉⢀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⠀⠀⠀⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⣬⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠉⠛⠐⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⢉⠉⠉⠉⠉⢉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣉⡄⠀⠀⠀⠀⠀⠀⠠⠞⠋⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠘⠀⠂⠐⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠄⠀⡀⢠⠀⣀⠀⠀⣀⢀⡀⠀⡀⢀⠀⣀⠀⡄⠀⡀⠀⡀⠀⠀⡀⡀⢀⠀⡀⡀⠀⡀
⠀⠀⠀⠘⠒⠑⠙⠐⠀⠉⠀⠐⠉⠘⠙⠐⠙⠘⠂⠁⠀⠃⠀⠑⠂⠘⠂⠀⠊⠒⠈⠒⠁⠉⠃⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠠⢜⡒⢎⡅⠀⢀⠈⡟⢀⠀⠀⠛⣬⡅⣤⠀⠀⢠⢀⣛⡃⠀⢠⠳⣄⡇⠀⠀⠯⠍⢉⡩⡇
⠀⠀⠀⠘⠛⠛⠛⠃⠀⠺⠐⠗⠸⠇⠀⠒⠨⠆⠀⠀⠰⠿⠿⠿⠷⠀⠈⠉⠀⠙⠆⠀⠚⠛⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡄⠀⠀⠀⢠⢒⣓⡅⠀⠰⡁⢈⡇⠀⠀⢸⢥⣠⠆⡇⠀⢸⢤⢤⢼⡇
⠀⠀⠀⠠⠠⠀⠄⠀⠀⠈⠀⠁⠈⠀⠀⠸⢼⡦⠃⠀⠀⠈⠉⠑⢦⠀⠀⠱⢤⠞⠁⠀⢸⣹⣽⣸⠇
⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢐⠃⣀⡃⠀⠀⢃⡑⠓⢢⡀⠀⢀⣄⠤⠚⠀⠀⠀⠀⠀⠀⠀⢠⣄⣶⣀⡀⠀⠀⣿⣿⣷
⠀⠀⠀⠐⠜⠧⢥⡀⠀⣸⠿⡿⠷⠆⠀⣤⣶⣾⣿⠀⠀⠀⠠⠀⠐⠀⠸⠯⠿⠽⠇⠀⠀⣗⣷⡿

⠀⠀⠀⠀⣀⣀⠰⠂⠀⡎⠹⠎⢢⠄⠀⣠⣶⣶⣦⠀⠀⠔⠒⢠⠀⠀⠀⠀⢀⢺⠂⠀⠀⠀⣾⣻
⠀⠀⠀⠸⣯⣽⠆⠀⠀⡇⠈⠁⡃⠀⠀⢿⣿⣾⠿⠀⠀⠀⢡⠀⠠⠀⢠⢼⢾⢹⠀⠀⠠⣏⣻
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⠂⠀⠀⠀⡴⢒⢦⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⣶⣤⡀⠀⢠⠖⠒⠢⡀
⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠁⠀⠀⠀⠀⠳⠭⢿⣄⠀⢀⣤⣶⣆⣀⠀⠘⢻⣟⡟⠃⠀⢓⠺⠿⢂⠇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠁⠉⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠤
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢤⢤⣀⣀⣀⣀⣀⣀⣀⣠⡽⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⢧⡀⠻⣤⣀⣀⠀⠀⠀⠁⢈⣀⣀⡴⠃
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣆⡧⢀⣈⡉⠉⠉⠉⠉⠁⠀⣶⣛⣉⢉⣙⣦
⠀⠀⠀⢠⣶⠋⠙⢫⡳⡀⠀⠀⠘⡇⠀⠀⢩⢭⠉⢹⠀⠀⢸⡷⠤⠤⠤⠤⢾⣀
⠀⠀⠀⠇⡇⠀⣠⠤⣷⢹⠀⠀⠀⣷⠀⠀⠘⡫⠆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠉⠓⠢⢄⡀
⠀⠀⠀⡇⢧⡠⠗⣶⣹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠑⠒⠲⠶⠒⠊⡇⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠘⢾⣤⣞⣡⡧⠏⠀⠀⠀⢸⠉⠒⠦⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡌⡀⡜⢰⠁⢩⣦
⠀⠀⠀⠀⠀⠈⢉⣈⣱⡦⠤⠤⠴⠚⠓⠤⣄⣀⣀⣀⡤⠔⢻⡄⣀⣀⢀⣀⣠⠏⠙⠓⠷⠞⠛⠛⠉⠑⠢⢄⡀
⠀⠀⡠⠤⢤⠴⢅⣀⡤⠟⠀⠀⠀⠀⠀⡴⠶⠶⣆⠀⠀⠀⠀⠉⠛⠛⠚⠛⠁⠀⢠⠤⠖⠢⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠑⠲⠦⠤⠤⠃⠀⠀⠀⡆⢉⠉⣹⡯⠭⢭⡿⠶⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⣤⡤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠭⠟⠁⠀⣎⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⡠⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⢰⡁⠀⠰⣶⣶⣾⡆⠀⠀⣴⣾⠈⣿⣿⣦⡄⠀⠀⣏⡑⠒⠒⠒⢋⡇⠀⠀⢰⣿⠛⣿⣿⣿⣦
⠀⠀⠸⣿⣶⣶⣾⡟⠛⠁⠀⠀⣇⣿⠀⡇⢸⣿⡇⠀⠀⡧⢌⣉⣉⣉⡡⡇⠀⠀⠈⠛⠀⢻⣿⠛⠋
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠓⠸⠛⠁⠀⠀⠑⠦⠤⠤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⢴⣦⢺⠇⣴⡄⠀⠀⠀⣿⣿⣿⣤⣤⣤⠀⠀⠀⣿⣛⣻⣿⣿⣿⣷⠀⠀⢸⡱⢸⢸⡱⢾⡷
⠀⠀⢰⣢⢽⠋⢙⡯⣖⡄⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣖⣒⣲⣶⣲⣶⣶⠀⠀⢰⡆⡆⣖⡄⡆⡆
⠀⠀⠀⢴⡺⣹⡏⣖⡆⠀⠀⠀⠈⣉⣉⣏⣉⡉⠀⠀⠀⠀⣁⣀⣇⣀⣀⠀⠀⠀⢠⢦⢤⡸⠄⡤⡄
⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠈⠉⠈⠈⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄
⠀⠀⢸⣶⠖⠃⠓⠲⣶⡃⠀⠀⡴⠛⠀⠀⠘⢦⡀⠀⠀⢨⣛⣛⣛⣛⣻⡅⠀⠀⠀⠀⣴⡄⠀⢠⣤
⠀⠀⠸⢯⣽⣿⣿⡯⡿⠇⠀⠀⠳⠤⠤⠤⠤⠴⠃⠀⠀⢸⣭⣿⣿⣯⣭⠆⠀⠀⣴⣾⠉⢹⣶⡏⠉
⠀⠀⠀⠀⠺⠿⠿⠇⠀⠀⠀⠀⠠⠤⢴⡧⠤⠄⠀⠀⠀⠰⢾⣯⣭⣿⡶⠆⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢠⡖⢶⡀⠀⠀⠀⢰⣿⣿⡏⠉⠉⠉⡆⠀⠀⣶⡶⣂⣀⣐⣶⣶⠀⠀⣶⠒⠒⢒⠒⠒⢶
⠀⠀⠀⠀⢨⡷⢾⡁⠀⠀⠀⢠⣿⣿⣿⣿⣿⠛⡇⠀⠀⣿⠇⣿⣿⣿⢹⣿⠀⠀⣿⢀⣴⣿⣠⣤⢸
⠀⠀⢰⠟⢻⣤⣤⡟⢳⡄⠀⢈⣿⣿⣿⡿⠿⠶⡇⠀⠀⠿⠆⣟⣛⣿⠼⠟⠀⠀⠿⠬⢭⣭⡭⠭⠾
⠀⠀⠈⠓⠋⠀⠀⠛⠛⠁⠀⠘⠿⠿⠿⠷⠤⠤⠃⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠐⠚⠛⠛⠒

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠋⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠐⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢀⢶⣠⣀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠓⣽⣿⣿⣿⣿⡥⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⡬⢿⣿⣿⣿⣿⢏⡐⢦⣷⣾⣾⣤⢖⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣙⡟⢻⢻⡙⢣⡭⣿⣿⣿⣿⣿⡏⣤⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⢐⣻⢿⣿⣿⣿⣙⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠈⠁⠈⠼⢌⣥⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⣄⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠚⣼⣶⣷⣧⣜⡂⠀⠀⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⣤⢽⣿⣿⣿⣿⣿⢥⡄⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣚⠿⣿⣿⣿⢏⣁⣀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠠⣄⣦⣭⣽⣠⠧⠧⠸⣜⣧⣧⣧⡴⠂⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣲⣾⣿⣿⣿⣿⣃⣤⢻⣿⣿⣿⣿⣿⢥⡄⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠈⠠⢿⣿⣿⣿⣿⡓⠁⢺⣿⣿⣿⣿⣟⣣⡄⣄⣿⣤⢠⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣀⢤⣹⣴⣜⣗⡛⣽⣹⣮⣯⣆⣸⠄⡻⣿⣟⣝⣷⣾⣿⣿⣿⣿⢲⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⡶⠛⢻⣿⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣼⡟⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡟⠀⠀⢸⣿⠀⠀⠘⣷⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⣸⣧⣀⣿⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢺⡇⠀⢀⣼⠿⠶⣤⣄⣿⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⠀⠀⣹⡷⢷⣦⠶⠛⠉⠉⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⢿⣤⡟⠁⠀⠀⢀⣽⠏⠀⠀⠀⠀⠀⣿⠀⢸⡏⠉⣿⠀⠀⠻⣧⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠻⠷⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢠⣴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡟⠙⣿⠆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠀⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠿⠶⠾⠷⠶⠿⠶⠾⠷⠶⠿⠶⠾⠿⠶⠿⠷⠶⠆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣻⡿⠛⠛⠛⠛⠛⠛⠛⠻⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃






⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠁⠣⣄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠱
⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠓⠂⠮⡁⠠⠀⠀⠀⠀⠀⠺⠒⠒⠁⠈⠀⠀⣑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣃
⠀⠀⠀⠀⠀⠘⣢⠃⢀⡀⠀⠀⠠⠈⣦⠠⠄⠀⠀⠀⠀⣀⠹⡦⣠⠠⡔⠂⠈⠋⠀⠀⠀⠀⠀⠀⠀⠁⠊⠑⠂⢰⢠⡄⡀⠙⠀⡄
⠀⠀⠀⠀⠐⠂⡇⠂⡀⠀⠠⠀⠀⠀⡗⢀⠀⠀⠀⠀⠀⠈⠀⢴⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢠⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠖⠸⣦⡀⠀⠀⠤⡠⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠂⡀⠀⠀⡠⠀⠚⠃⠢⠬⠠
⠀⠀⠀⠀⠀⠀⠚⠀⢉⡏⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢲⡀⠁⠎⡦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠖⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠂⢀⠤⠀⠚⠆⠊⠃⠠⣠⠄⡀⠀⢀⠀⠠⠄⠢⢂⠀⠀⡀⠀⢀⠄⠀⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⢀⠀⠀⠃⠀⠀⠬⠀⣐⡇⠘⠈⠀⡸⠀⠀⠀⢀⠉⠈⠠⢁⠀⢂⠀⢠⠈⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⡀⠰⠀⠘⠀⠂⠇⠀⠀⠀⠀⠘⢄⠀⠀⠠⠀⠀⠀⠠⡈⠀⣀⠑⡌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠆⡐⠁⠀⢠⡁⡠⠀⠸⠈⢁⠓⣈⠁⠁⠀⢇⡠⠈⠠⣰⠂⠀⢆⡈⢁⡐⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠁⠀⠀⠉⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⢀⠢⠀⠀⠊⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⠌⠂⠈⠁⡀⢪⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠐⠠⠀⠜⠀⡀⢀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢤⢼⡏⠐⠃⣘⠀⠀⠂⢻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣼⣁⣀⡉⠀⠀⠀⠀⠀⢈⣁⠉⠀⢀⠀⠀⢘⡿⠉
⠀⠀⠀⠀⠀⠰⠤⠴⠂⠀⠀⠁⢀⠀⠀⠀⠰⢂⠔⠀⠈⠉⠉⠀⠀⠀⠀⢀⡀⠈⠞⠃⠈⢀⠉⠉⠶⠊⡉⠀⠀⠀⠊⢋⠆⠄⢰⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠈⠀⡈⠀⠀⣁⢄⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠆⠀⢀⠐⢺⣁
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⡴⠃⠀⠀⠇⠀⠈⠑⠰⣤⠀⠀⠀⠀⠀⠀⠀⣀⠠⢦⡄⠀⠀⢄⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⠙⠱⠉⠀⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠃⣀⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠿⡋⠀⠈⠁⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠾⠿⠁⠀⠈⠀⢠⡀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠧⠀⠀⣀⠀⢀⣶⠀⠹⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⣠⡾⠛⠻⢿⣯⠀⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢾⡏⠀⠀⣠⣾⣿⣧⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠃⢸⡇⠀⠰⣿⣟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⡇⠀⢀⣾⣙⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⣾⣏⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠓⠲⠛⠿⠿⠿⣿⣿⣀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣤⣀⣴⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠗⠀⢠⡾⠉⠀⠈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢸⡇⢠⣶⠄⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠈⠛⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠏⠀⠀⠰⠂⠀⠀⠁⠀⠰⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⡀⠀⢀⡄⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠋⠁⠀⠈⠁⢀⣾⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠃⠀⠀⠀⢀⣴⣶⡞⢿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠸⠿⠀⠀⣿⠃⠈⠀⠀⢹⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⢱⣦⠀⢶⣶⣄⠀⢾⡇⢠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠃⢀⠁⠀⠀⠀⠙⣦⣄⣶⡿⠻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣀⣾⣶⡀⠙⢋⣠⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠒⠀⠸⢿⣿⣿⣷⣶⠟⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠀⠀⠀⠈⠉⣻⣿⣤⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣶⠄⠻⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⣽⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠀⢠⣿⡿⠉⠁⢈⣹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠴⣶⡟⠁⢰⣿⣏⠀⠀⠀⢿⡏⢹⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣼⣿⣦⠟⠁⠀⠈⣿⣿⠀⠀⠀⢀⣴⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠻⣿⣦⣤⣤⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠆⠀⢀⡀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠉⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠋⠀⠀⠀⣈⡁⠀⠀⠀⠉⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠠⣶⡆⠀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠰⠛⠃⡀⠀⠠⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⡀⠀⠀⡇⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠙⠃⢀⡄⠀⣴⡿⠃
⢀⣾⣿⠇⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⢀⡄⠀⠚⢠⣀⠀⠀⠀⠀⠿⠆⠀⠻⡿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣤⣾⡟⠀⠉
⠿⠿⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠋⠀⣀⣀⠀⠹⡇⢀⣄⠀⠀⠀⣴⣶⠄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏
⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⣿⠆⠀⢠⣾⠛⢁⣀⣴⣿⣷⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣸⣿⠀⠻⠿⠁⣸⣿⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡅
⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠈⢀⣄⠀⠀⠀⢀⣴⣿⡟⠐⠒⢶⣾⡿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣿⣟⠛⣷⣤⠄⢈⣿⣷⣼⣿⣿⣿
⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠦⠀⠀⠉⠀⠀⠙⠉⠰⣿⣧⠀⠘⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢸⣿⣤⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣈⣁⣠⠟⣻⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣤⠀⠀⢠⠄⠀⠀⠀⠠⠀⠈⠉⢻⣿⣶⣿⣿⣿⡿⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠉⣿⣷⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠘⢻⣷⣤⣄⠉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣈⡉⠰⣾⣏⠙⠛⣾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢀⣤⡼⠛⠃⠀⢿⣏⣰⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⣴⣶⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣦⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠈⠙⢿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢾⣿⠆⠈⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⠀⣤⣤⠀⠀⠀⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠁⠀⠀⠀⣀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠛⠉⠻⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣶⣾⣿⣿⣶⣆⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⠀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⣠⠀⢀⣤⠀⢠⣄⠀⠀⠀⠀⢀⠠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠤⠄⠤⣄
⠀⠀⡼⢛⡻⠆⡭⠂⠀⠀⠀⠰⡇⠀⠈⡴⠀⠀⠀⠀⠀⢠⡀⠿⢀⡄⠀⠀⠀⠀⠔⢡⠘⠀⠘⡀⡁⠀⠀⠀⠂⡀⠀⠆⢠⠀⠆
⠀⢀⣗⣛⣃⡄⠀⠁⠀⠀⠀⠀⠐⡤⠎⠀⠀⠀⠀⠀⠀⢻⡀⡞⢁⡟⠀⠀⠀⠀⠱⢸⡋⠛⢛⠞⠀⠀⠀⠀⢀⠖⠗⠾⡒⢎
⠰⠅⠩⠁⠁⠀⠩⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠤⠉⠀⠿⠀⠉⠤⠀⠀⠀⠐⠺⠉⠩⠭⠖⠀⠀⠀⠀⠇⠸⠀⠆⠰⠰⠆

⠀⠰⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⢠⢔⢤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠘⣀⠂⠤⠉⠲⡽⠀⠀⠀⠀⠀⠘⢬⠜⠀⠀⠀⠀⠀⠀⢰⣜⣉⢳⡄⠂⠀⠀⠀⠀⠮⠀⠀⠈⡇⠀⠀⠀⠀⠀⣐⣯⢙⢢⡀
⠈⢚⣆⣂⣀⠐⢠⠀⠀⠀⢰⡾⠷⠀⢴⠷⠦⠀⠀⠀⠒⣸⣀⣉⡬⠛⠀⠀⠀⠀⣄⠉⣆⠀⡎⠁⡆⠀⠀⠀⢀⣽⣈⣋⡉⠁
⠐⠔⠁⠐⠀⠐⠂⠀⠀⠀⠠⠀⠶⠂⠀⠰⠞⠀⠀⠀⠪⠊⠐⠀⠀⠀⠃⠀⠀⠀⠓⠀⠓⠀⠇⠀⠇⠀⠀⠐⠅⠃⠀⠀⠐⠁

⠀⠰⠀⢰⡀⠐⠂⠀⠀⠀⠀⡠⠐⠀⢐⢀⡀⠀⠀⠀⠰⠆⡲⣶⠂⡤⡄⠀⠀⠀⠂⠀⡀⠀⠂⠀⡀⠀⠀⠀⢀⢄⡐⢂⡀⡀
⠈⠁⣚⣋⣛⣓⠈⠀⠀⠀⠀⠈⢀⠞⢄⠐⠐⠀⠀⠀⠠⠎⠢⠉⠗⣉⡁⠀⠀⠀⠐⠠⠀⠀⠶⢰⠀⠀⠀⢀⠀⠆⢉⣭⠤⠄⡀
⠠⠀⠦⣦⡼⠴⠠⠀⠀⠀⠀⡠⡙⠒⠒⠀⡀⠀⠀⠀⣐⠀⢠⡔⠓⡃⡃⠀⠀⠀⠀⣀⣉⣐⣠⡄⠀⠀⠀⠀⢁⠒⡿⢻⡒⠄⠁
⠀⠐⠐⠐⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠊⠀⠀⠀⠀⠚⠐⠂⠃⠂⠂⠂⠀⠀⠀⠋⠉⠛⠛⠋⠉⠃⠀⠀⠀⠀⠁⠐⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠐⠂⠒⠒⠓⠂⠁⠒⠘⠈⠚⠀⠒⠈⠐⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⡄⡄⣠⢀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⢀⠠⡀⢂⣀⣸⣠⣤⡦⠴⠶⠞⡚⣛⠛⠉⠉⠛⢷⡡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⣆⣈⣤⡦⠼⠾⠞⠚⠛⢉⠉⡉⡰⢠⠄⠀⠰⠂⠡⠄⠀⠀⠀⡗⠀⢹⡷⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢌⣶⢟⡉⠉⠰⠀⠠⠤⠷⠶⣄⣄⢄⠀⢀⠀⠂⡄⠁⠀⠂⣠⠂⠀⠰⠄⠀⠒⢸⡯⠅⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠑⣾⠁⡄⠥⠀⠀⠀⠀⡌⢹⣆⣉⢹⢱⠀⠐⠀⡀⠀⠀⠀⢀⢀⡒⢀⠐⠀⠈⣠⢞⡋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠥⣿⠀⣄⠒⢀⠠⠄⠀⠙⠋⠙⠥⠒⠚⢤⠂⠄⠰⠀⢀⣀⣀⣤⡤⢶⢶⢶⠫⠫⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⢉⠜⢷⣀⠂⠀⠰⠆⢠⣀⣃⣀⣠⣤⡤⠶⠶⠒⢛⠻⠙⠙⠘⠀⠃⠈⢈⣤⡶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠑⠩⢛⠛⠛⡋⠏⠩⠙⠈⠀⠂⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡀⠀⠀⢰⡋⢉⣩⠗⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠖⢾⣇⠀⠀⢀⠁⠘⡓⠠⠤⣾⡆⣉⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠴⠊⠰⡉⢀⢀⠉⣉⢲⡁⣐⣼⡄⢆⡑⣀⣮⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠌⣂⣠⠗⣚⢌⣦⢸⣿⣘⠶⢛⡸⠷⣺⣭⡬⣦⠥⢋⡙⣣⣬⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠱⠧⣤⡄⢡⣊⣛⣮⣿⣿⣿⣧⣼⢽⣾⣾⣇⡛⣍⠒⠑⣋⡹⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠞⣈⠒⢤⡄⣸⣽⢿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠛⠯⣿⢈⢥⢤⡜⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠑⣿⣫⣿⣿⣿⡏⡖⠀⣦⢻⣿⣿⠿⡁⣇⢀⠘⡷⠷⡏⠉⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⡷⠫⡛⠟⠩⢿⣿⣇⡛⠾⣋⣼⣿⣿⣇⣳⣬⣩⣼⣱⢆⢿⣾⠠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣡⠰⣇⠀⡼⣸⣤⣾⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⡯⣿⠁⣚⣣⡇⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠑⢞⡿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⢛⠙⢻⡠⠃⠀⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣉⣦⣽⡼⢛⣛⠿⠿⠿⠿⣹⡅⠷⢴⣸⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⣏⠴⠤⡑⡏⢷⠙⣄⡤⡾⠑⢊⠿⠏⣁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠀⠀⠀⡛⠭⡝⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⡀⡀⡔⠂⡀⠰⠀⠰⠀⠀⠀⠒⡀⠀⠀⢀⡰⠀⠀⠀⣀⣀⠀⠀⡤⡀⠀⢀⢠⠀⠀⡒
⠈⠁⠀⡀⠀⠐⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠐⠰⠰⠘⠀⠀⡆⠉⠀⠀⠰⠀⠈⠀⠁⠃⠁⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠂⠀⠀⢈⡁⠀⠀⠀⠈⠂⠠⢠⣄⢀⡀⠀⠀⠀⠆⠀⠀⠀⡠⠃⠀⠀⠑⠀⠓⠀⠃⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠄⡡⠜⢠⡆⣠⠈⠀⡄⠺⠀⠀⠀⠁⡮⠀⠀⠀⠉⠠⠁⠈⠀⠀⠉⠁⠂⠀⠀⠢⠡⠔
⠀⠀⠀⠈⠐⠀⠆⠂⠀⠀⢠⡀⠱⠁⠀⠀⠀⠑⡤⠄⠀⠀⠗⡀⠀⠀⢠⡆⠀⠀⠀⡄⠤⠒⣄⠀⠀⢁⡤⠁⠄⠀⠂⠒⠤
⠘⣂⠀⢀⠀⠀⠀⠀⠀⠐⠀⠠⠺⠀⠀⠀⠀⢠⡑⠒⠀⠀⠀⠉⠀⠛⠀⠀⠐⢀⠨⡴⠋⠙⢎⢩⠀⠈⢀⠆⠀⠃⠘⠂
⢠⡉⠐⠀⠀⠂⢀⠀⡀⠀⠀⠐⠃⠜⢂⠐⡖⢡⡈⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠫⠳⢄⠤⠊⡄⠃⠀⠀⣀⠀⠀⠄⠀⣐
⠈⠀⠀⠈⢠⠊⠈⠀⠡⠓⡄⠀⠀⠀⠈⠀⢀⠤⠀⠀⠀⠁⠀⢀⢀⠀⠀⠠⡀⠀⠀⠉⠣⠒⠁⠑⠄⣸⢄⢀⣠⠂⢀⠀⢓
⠀⠂⠄⠐⡃⠀⠀⠀⠀⠀⣘⡂⠀⠀⠀⠀⠀⠐⠐⢄⡀⠆⠂⠆⠸⠄⡔⡐⠁⠀⠀⣄⠀⢀⠀⢳⠚⠀⠀⠀⠈⠠⣁⡀
⠀⠄⠐⠀⠡⠀⠀⠀⠀⢄⠌⢀⠀⠀⠀⠎⠀⢀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠑⠂⠁⠈⠀⠀⠈⢁⣰⠀⠀⠀⠀⠀⢀⠢⠤
⠀⠀⠀⠀⠀⡉⠐⠀⠃⠉⠀⠀⠀⡄⠀⣀⢀⡃⠀⠀⠈⠀⠀⠈⠠⠃⠀⠀⠈⠤⠀⠀⡆⠀⢀⠤⠱⣄⠀⣀⡄⡊⠢
⠠⡨⠁⠘⢀⡀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠐⠑⠀⠋⠀⠀⠬⠀⠀⠀⠀⠀⡀⠈⠀⠆⠘⠀⠘⠀⢀⠂
⠠⠀⠀⠀⢠⠀⠀⡜⠉⠀⠉⢆⠀⠀⠠⡒⠈⡄⠀⠘⠂⠠⠂⠀⢀⠤⠀⠀⠀⠖⠀⠀⠡⠇⠀⠄⠀⡈⢀⠀⠂⠀⠀⠸⢄
⠀⠈⠁⠘⠀⠀⠀⢰⣄⣀⡤⠃⠀⠀⠀⠀⢀⠜⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠑⠀⡀⠀⠠⠀⠀⠁⠀⠀⠈⠐⠀⠀⠀⠑
⠀⠀⠀⠤⠄⠠⣀⠀⡀⠈⠀⠀⠂⠀⠀⠆⠀⠀⠀⠑⠤⠦⠀⡤⡀⠴⠒⠈⠀⠀⠈⠁⠀⠀⠨⠁⠀⠀⠀⠀⠀⠅⠀⠈
⠀⠘⠋⠀⠀⠀⠀⢒⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⢢⡠⠀⠀⠀⠈⠀⠀⠄⡀⢀⠠⠈⠀⠁⠀⠗
⠀⠈⠇⠀⠀⠀⠀⡂⠀⠀⠠⢀⠀⣄⠀⢀⠂⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠑⠀⠠⠀⠀⠀⠀⠀⡦
⠀⠀⠈⢂⠐⠚⠀⠄⠀⠀⠒⡔⠈⠀⠀⠙⢢⢁⠀⠀⠠⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠆⠀⢀⠑⠕
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⢀⡄⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⣠⢂⠌⠀⠡⡒⣄⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠖
⠀⠀⠠⠔⠀⠀⠂⠀⠀⠀⢠⠁⡤⡀⣀⠄⡊⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠂⠀⠀⠈⢁⠠⠀⠀⠀⠀⡨⠁⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠘⠒
⠀⠈⠀⠀⠀⠀⢀⠂⠀⠀⠉⠀⠀⠀⠀⠀⡠⠄⠖⠆⢄⠀⠀⠀⠁⠐⠀⠂⠋⠀⠀⠀⠀⡀⠀⠀⠈⠀⡀⠀⠆⠀⠰⣄
⠀⠀⠀⠑⠀⠈⠀⠀⠠⠮⠊⠈⠚⠠⠀⠠⠃⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⠀⠁⠐⠐⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⢄⠐⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠟⠻⣿⣄⡀⢀⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⣿⣿⣿⣯⡇⠀⠀⢀⠀⠀⠀⠀⢾⣿⣀⣀⣼⣯⠁⠾⠿⠻⠃⠀⠀⠄⠀⣤⡀⢠⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣿⡿⡇⠀⠀⠀⠀⠸⠛⠻⠏⠉⠀⠀⠀⠀⠀⠀⡀⠀⢤⣯⡅⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠇⠰⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⠤⠙⠀⠀⠉⠛⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⣤⣴⣧⡄⣿⢠⡄⢸⡇⠀⢀⢀⠀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡇⠀⠀⠀⠐⠻⠿⠿⠿⠃⠛⠘⠇⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠣⣄⠀⠀⠙⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠂⠈⣦⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢿⣶⠿⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⠶⠵⠆⠘⠒⠖⠰⠆⠴⠾⠰⠖⠖

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠇⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠲⣄⣀⠀⠀⠀⠀⠀⠰⠆⢰⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⠾⠛⠿⣠⣶⡄⠀⢠⡀⠀⠈⣿⡏⠀⡄⠀⠀⢰⣾⣷⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣧⡀⠈⣧⣀⣠⣿⣧⣼⣇⡀⢀⣼⠋⠉⠀⠀⢠⠀⠀⣮⠁⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣄⠀⢀⠀⠀⢘⣷⠾⢛⡉⠉⠥⠈⠉⢉⣛⠿⣧⣀⣤⠂⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⣦⣌⣳⣶⠟⠁⣾⠏⠉⣷⡀⠀⠰⣏⢹⡇⠈⠻⣧⡄⠀⢀⣴⣷⡆
⠀⠀⠀⠀⡠⢄⡀⠀⠀⢀⡀⣀⠀⢉⡿⠁⠤⠀⢿⣄⣨⡿⠁⠀⠀⠉⠉⠀⢈⣃⡈⢿⡾⢋⠉⠉
⠀⠀⠀⠀⠷⠋⠁⠀⠐⣿⠀⠈⠙⣿⠃⣀⡤⣄⠀⠀⢠⡴⠲⣄⠀⠀⠀⠐⣟⠠⣿⠘⣿⠉⠀⠀⣀⠀⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢮⣿⠷⠶⠶⣿⢰⡟⠀⣼⡧⠀⢻⣁⣐⡿⠀⢀⣀⣀⠈⠉⠁⠀⣿⠶⠶⢾⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢿⡀⠙⠒⠛⠁⠀⠀⠉⠉⢀⣾⡟⠁⠉⢷⡄⠛⢀⣿⠶⠤⠄⠀⠀⠀⠀⢴⣱⠄
⠀⠀⠀⠀⠂⠀⠀⠸⡷⢀⣀⣀⣠⣼⣧⡘⠃⠀⡰⠖⠲⢦⡀⠸⣿⡁⠀⠶⣿⡇⢀⣼⣧⣀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠉⠤⠾⣷⣄⠀⢿⡄⢀⣼⠇⠀⠙⠳⠶⠞⠋⣠⡾⠛⢎⠉⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣶⡦⠞⠉⢙⣷⣬⣙⠛⠉⠀⠀⠰⢀⣀⣤⣾⠋⠙⠦⠈⠀⠈⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃⢈⡿⠛⠛⣿⡟⠻⣿⠉⠁⠹⣧⣀⠀⠀⠀⠈⡿⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠻⡿⠇⠀⠘⠁⠀⠀⣿⡇⠀⠸⠀⠀⠀⢿⡿⠇⠀⠀⠀⢿⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡷⠀⠀⠀⠀⠀⡀⠀⠀⢸⡿⣿⠄⢴⠆⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢯⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠊⠀⠑⠂⠁⠀⠤⠄⠀⠀⠐⠐⠒⠂⠀⣀⣀⣧⠀⠀⠈⠉⠈⠀⠀⠫⠀⠀⠀⠉⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢀⠂⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠋⠠⠀⠀⠀⠛⠛⢶⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠑⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠐⠀⢀⣀⡂⠀⠀⠀⢀⡀⠀⠸⡇⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠉⠀⢀⠨⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠚⠗⠂⡉⢩⣆⠀⠀⠏⠀⠀⠀⠛⠦⣄
⠀⠀⠀⠀⠀⠀⢀⠀⡠⠂⠀⠀⠠⠞⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠠⢀⢌⡀⠘⢠⠀⠀⠀⣰⣶⠉⣇
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⠰⠊⠁⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡡⣘⠊⠡⠁⠀⠀⠀⠀⠄⠀⠀⠙⠋⢀⡟
⠀⠀⠀⠀⠀⡀⠁⢢⠀⠀⢰⣄⢈⡑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣑⠂⢬⡄⠠⡆⣀⢀⡀⡀⠩⢴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠘⡇⠒⠃⠐⠂⠒⠀⠉⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠙⠛⠒⠒⠶⠦⠴⠤⠶⠶⠖⠚⠛⡃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠂⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣇⢸⡇⠀⢾⣁⣈⢿⡄⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⡇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢡⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡧⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⢴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠓⠶⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠻⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡛⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄
⡞⠋⠉⡛⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⢹⠉⠓⢦⡀
⠉⠒⠲⠧⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠉⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⡩⠇⠀⠀⡼⠁⠀⠀⣰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⠀⡀⠀⢀⡀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠉⠀⠃⠋⠙⠛⠃⠃⠈⠁⠓⠊⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠀⠀⠀⠀⢀⡀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣷⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠳⣶⣾⣁⣼⣧⣀⠘⣷⣶⡦⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢤⣀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣀⠀⢠⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣷⣄⣸⣮⣆⣀⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠳⣶⣿⣿⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣸⣿⣿⣿⣿⣽⠟⠋⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣴⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣰⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⣿⣿⣽⣥⣤⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣀⡀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣤⣴⣿⣿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⣿⣿⣤⣤⣿⣿⣿⣿⣿⣏⢈⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⣿⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⠟⠉⢁⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠻⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠁⠀⣹⠏⢻⣿⣿⣿⡏⠀⢙⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⠛⠓⠀⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⡽⠿⣟⠛⢿⣿⠟⣿⠿⠻⠍⢿⡄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠀⠀⠁⠀⠘⠀⢸⡇⠀⠙⠀⠀⠀⠀⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠛⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠈⠀⠁⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⢀⣤⣄⠀⠀⠀⠀⠸⡀
⣤⣤⠀⠀⠀⢀⡤⠊⠁⠀⠀⢀⣶⣿⣿⣿⣿⣶⣷⣿⣶⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠒
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⡿⠃⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠉⠁⣠⣤⡀⠀⠀⢸⡀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠰⡦⠐⠶⢤⣀⡀⠉⠉⠀⣀⣀⡤⠞⠁⠀⢠⣄⠀⠀⠀⠀⠀⠻⠿⠏⠀⠀⠈⡇
⠀⠀⠀⠀⢷⠀⠀⠀⠀⢠⠖⠒⠶⣄⠀⠀⠈⠙⢦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠈⢆⠀⠀⢠⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠃⠀⠚⠃⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢧⠀⠈⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⡀⠀⠀⠰⠶⠒⠛⠁⢀⡀⠀⠘⠋⠀⣦⠈⠉⠀⠀⠀⠘⡆
⣀⢄⣠⡤⣀⣄⣄⢳⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⡀⠀⠀⠀⠀⠈⢡⣄⢰⡘⢧⠘⣆⠀⠺⠆⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠻⠿⠟⠛⠛⠋⠉⣡⡴⠞⣋⣉⡁⠀⠀⠀⠀⡀⠀⠈⢷⡙⣎⠳⡌⢳⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣀⠀⠀⠚⣩⣿⣿⣿⣿⣿⣷⣶⣄⢀⡋⠀⠀⠈⢳⡌⢷⡹⣆⠹⡄⠀⠀⠀⣧⠀⠀⠀⠠⣀⣀⣠⣀⡀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡼⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⢹⡄⣧⠘⣆⠻⠀⢀⡀⠘⡄⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠃⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⠀⢸⡇⠘⢀⠈⠀⠀⠛⠁⠀⢱⡀
⢠⡄⠄⣠⣤⢤⢠⣠⣤⠀⢸⡀⢸⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢷⡀⠀⠀⠺⣝⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⡀⢠⡀⣄⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠃⠀⢀⡈⠙⠻⠭⠿⠉⠁⠀⠀⠈⣧⢹⡌⡇⠸⡆⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠈⠈⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠦⣤⣤⣤⠄⠀⠲⢤⣤⠟⢠⠇⡿⠀⣇⠀⠀⣸⠁⠀⢀⣴⣾⣿⡷⠀⢨⡇⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠰⣶⠀⠀⠀⢦⡀⠀⣝⠳⢤⣤⠴⠋⢠⡇⢀⡇⠀⢰⠇⠀⠀⠈⢻⣿⡿⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⠀⠀⣤⡀⠀⠈⡇⢳⡌⠳⢦⣀⣀⣠⠞⢀⡾⠁⢠⡟⠀⠀⢀⣴⣿⡟⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡙⣦⡀⠀⠀⠈⠀⠀⢠⠇⠀⠙⠳⢤⣬⣩⣤⠴⠛⠀⣠⠟⠀⠀⢰⣿⣿⡿⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⠃⣈⡉⠀⢀⣀⣤⠶⠋⠀⠐⢦⡀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⢤⢤⣴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢠⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⠿⠿⠿⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡷⢶⣦⢉⡉⡋⠉⠁⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠉⠓⢥⡀⠄⣪⣽⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠶⠴⡶⢶⠒⣻⠂⠀⠀⠀⢀⣹⡥⡀⠀⠀⠹⡿⠿⠿⠿⢿⣶⣶⡶⢶⣤⣤⣇⡀⢸⠉⠙⠓⠒⢲⠀⠀⢱⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠸⠀⠿⡂⠀⢠⣾⡿⠛⠿⣖⢄⠀⣠⣷⣄⠀⠀⠀⠀⠈⠉⠲⡄⠈⠙⣿⣿⡄⠀⠀⠀⢸⠀⠀⢸⢸⣿⣿⣇
⠀⠀⠀⠀⢀⣤⠟⢳⣯⡿⠯⢿⣄⣶⣛⣦⣼⣿⣦⣤⣤⣾⣿⣟⢋⣡⣾⡁⠀⢀⣹⣿⣿⣷⣷⣦⣶⣿⣿⠁⠀⠀⠀⢸⠀⠀⢸⣼⣿⣿⡟
⠀⠀⠀⠀⡿⢥⣀⣀⠈⠉⠉⠉⢡⣿⣤⣤⣠⡤⣼⣟⣭⢫⡉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣽⢫⣿⡏⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⡆⡇⠀⢸⡟⣸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡇⠸⠀⡀⠀⠀⢸⠀⠀⢸⡟⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡏⠓⠒⠒⠒⠒⠚⣿⢛⣿⠻⠛⣿⡇⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣠⣾⣛⠋⣘⣃⢨⡳⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠂⠉⠉⠉⠀⠒⣦⡀⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣞⣿⣿⣿⣾⣿⣿⣗⠙⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠛⠒⠚⠋⢹⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⠤⠤⢤⣤⠤⠴⠚⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢉⠉⠉⠉⢉⣉⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠛⠒⠤⠶⠶⠶⠖⠙⢙⣆⡠⠤⢤⣧⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠘⢒⡶⠻⣟⠛⠀⠀⣿⣝⡢⢤⣄⣀⣀⣀⣀⣀⡤⣿⣝⣲⠲⠤⠤⠤⠤⠒⣎⣭⡏⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⣧⠀⠓⠤⠤⠤⢤⡇⠀⢰⡋⠀⠀⠈⣱⠆⠀⣿⣿⡿⠋⠓⠓⠒⠒⠒⠒⣋⣿⠀⠉⠉⠛⠒⠛⠋⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠽
⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⢀⡇⠀⢀⠙⢦⣤⠞⢁⠀⠀⢿⣿⡇⠒⠢⢤⠖⠂⠛⢿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡇⠀⠈⠙⠋⠛⠋⠋⠀⠀⣸⠿⣇⣀⡀⢸⣶⣶⣲⠷⡳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⣀⠴⠊⠁⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⣶⣦⣤⣤⣴⣶⡆⢹⣿⠀⠀⠈⢉⡹⣻⡉⢈⠇⢱⣿⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡤⠞⠉
⠀⠀⠀⢠⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠉⠙⣿⣟⣛⣡⠴⠃⣴⣆⣢⠿⠿⣿⣏⣁⣠⣿⣽⠀⠉⠙⠛⠒⠒⠛⠋⠁⠀⣿⠉⠙⠻⠿⢿⣿⣿⣇⡤⠞⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠄⠀⡄⠀⡈⠉⠛⠂⠀⠼⠈⠉⠉⠀⠘⠧⣄⣀⣀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠺⢿⡶⠦⠛⠲⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠸⡧⠤⠤⠶⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⢻⠀⠈⠳⠖⠚⠉⠁
⠀⠀⠀⠀⣧⡤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠒⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠄⠁⠀⠀⠆⠁⠐⠀⠈⠀⠀⠂⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⡄⣛⠀⠀⣀⠄⠄⠤⣃⠀⠀⢨⣟⣛⣻⡇⠀⠀⣰⣾⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣥⣿⣶⡆⣿⠀⠀⠄⡆⡆⢢⠀⠀⠀⢘⣶⠿⣶⡃⠀⠀⢻⣿⣷⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡶⠀⠀⠀⠀⢀⠀⣒⠄⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⣠⡀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣧⠠⣦⠀⠀⠑⢳⣲⠤⣢⠀⠀⢰⣶⣶⣶⡆⠀⠀⣭⡉⠛⠁⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣷⠀⠀⠀⠀⠫⠃⢜⠆⠀⠀⠀⠰⠿⠿⠷⠆⠀⠀⣿⠇⣿⠇⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠇⠀⠀⠀⠀⠨⢭⠅⠀⠀⠀⢀⣤⢄⡔⠃⠀⠀⡞⣡⣌⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣬⢉⣯⢉⣥⠀⢠⠮⠀⠭⠈⠥⠀⠀⢿⣏⣽⡗⠀⠀⠀⠙⠯⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠀⠉⠀⠉⠀⠉⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠒⡂⠀⠀⠀⠀⢒⠒⡂⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠒⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⡶⠀⠀⠀⠐⡂⠀⢰⠀⠀⠀⡇⠆⠀⣀⡆⡇⠀⠀⣦⣤⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠈⡠⠁⠀⠀⠀⠛⠛⠃⠒⠒⠃⠀⠰⣥⣈⡈

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠰⠆⡈⠗⠀⠁⠒⣃⡠⠀⠀⢴⠋⠀⠀⠉⠑⠢⢄⡀⢀⡀⠆⠒⠒⠒⠶⣀⠀⠀⠀⣤⠻⠚⠸⠷⢄⠄⠀⠀⠘⡀⠢⠵⠀⠦⣆⠐⠀⠀⠀⡄⡈⠡⡰⠀⢠
⠀⠤⠤⠁⠀⠀⠀⠀⠈⠤⠆⠀⠘⠖⠦⠀⠦⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⡨⠀⠐⢘⡍⠀⠀⠂⠀⠻⠀⠀⡀⡐⠉⠀⠀⠂⠀⠐⡃⠀⠀⠀⢀⢿⠈⠃⡇
⠀⢀⡠⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠁⠓⠒⠒⠉⠉⠀⠀⠉⠉⠁⠁⠀⠀⠌⢫⣄⢁⣀⡰⠟⠈⠀⠀⢓⠄⠀⠀⠀⠀⢠⠬⠈⠀⠀⠈⠀⢤⡆⠀⠰⠂
⠀⠀⠀⠞⠐⣒⠀⠢⠄⠀⠀⢠⠀⠒⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠎⠉⠱⡂⠄⠀⠀⢀⠀⠀⠍⠈⠀⢀⠀⠀⠀⠔⠰⠲⢀⠄⢦⠋⡁⠀⠀⣀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡁⠘⠠⡈⠀⠀⠀⠀⠀⢰⠄⠀⠆⠈⠐⠀⠀⠀⢀⠀⠀⣀⠆⠞⠠⠆⠀⠀⠀⠐⠐⠈⠀⠀⠀⠠⠀⠁⠀⠄⠰⠟⠂⠂
⠀⠀⠀⡔⠒⢢⠀⠀⠀⠀⠀⠀⠦⠀⠘⠀⠀⡈⠀⠀⠠⠐⠆⠡⠂⠀⠆⠀⠁⠀⠠⠀⠈⠀⠀⣩⡄⢀⣠⠓⠠⣠⠀⠀⣀⣀⡀⠀⠀⠀⠁⠠⠂⡈⠀⠀⠠⠐
⠀⠀⠰⠀⠠⠀⠀⠀⠴⠀⠀⠁⢰⢐⠈⠥⠀⠁⢀⠈⠈⠀⠈⠀⠀⠠⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠀⠑⢵⣄⡈⠉⠛⠶⣤
⠀⠀⠇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠈⠀⠀⠀⣀⣀⡀⠀⠤⠤⠒⠉⡉⠃⡄⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠑⡧⠀⠀⠀⠂⡀⠀⠄⠂
⠀⢈⠀⠀⢀⠃⠀⡰⠋⠈⠱⠀⠀⠀⠀⠀⠒⠂⠀⠄⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⡰⠀⠀⣠⡮⠃⠈⣵⠀⠈⠗⠀⠀⠀⠀⠀⠀⠁⠀⢁⠂
⠀⠈⢲⠐⠁⠀⠀⡄⠀⠀⠌⠀⠀⠀⢀⠄⢀⠀⠂⠈⠀⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢁⡀⠠⠄⠖⠁⠀⠮⠋⠀⠀⠀⠀⠀⣬⠃⠀⠀⠀⡀⠈⠀⠄⣅⢦⠂
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠄⣠⠀⠈⠑⠐⠰⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠴⠔⠛⠋⠀⠰⠀⠠⢚⠀⢢⠀⠘⡀
⠀⠀⠂⠀⠀⠀⠀⡄⠀⡸⠀⠀⠀⠈⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⢀⢀⣀⣀⣤⣴⣶⣾⣶⣶⣤⡀⠀⠀⠀⠋⠀⠀⠀⠰⠓⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⣤⠀⠀⡖⢀⡀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠟⣛⠻⠻⡟⠟⠉⠹⠿⣿⣏⠉⣹⢿⣿⣿⡄⠀⠀⠀⠀⠣⠌⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡄⢀⠀⠢⣀⣄⡈⠁⠠⠆⠀⠠⣾⡏⢸⢰⡄⢀⠉⠰⢧⠙⡆⠹⡶⠳⠂⢹⣯⣤⣾⡟⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡄⠐⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢽⡁⠀⡯⠀⢀⡀⠀⢰⣿⡇⠈⣸⣇⣸⣤⣷⣴⣷⡦⢾⡿⠶⢾⡟⢛⠛⠙⡇⢀⢻⡇⠀⠀⢀⠔⠡⠂⠐⠄⠐⠌⠉⢤⡠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠋⠋⠑⢀⡀⠀⠀⠐⣿⠟⡛⢿⠉⡙⢿⠀⣦⣶⣶⠸⣇⠘⢛⣣⡈⠠⣆⠁⢸⣾⡷⠀⠀⠸⡀⠀⢀⠊⡀⠉⡡⢀⠀⢀⡀
⠀⠀⡴⠒⠒⠲⡄⠀⠀⠀⠀⠀⠈⠁⠀⠴⠀⠀⠀⠀⠀⠀⡹⣧⠡⣜⠃⠰⣄⠡⡙⠋⢹⣧⢹⡄⠙⠛⢃⢰⣈⣠⣼⣿⠃⠀⠀⠀⠀⠀⠀⢀⠐⢀⠘⠢⠌⠤⠃
⠀⢼⠀⠀⠀⠀⢘⡄⠀⣀⠀⠴⠀⠀⢤⠀⢠⠀⢀⡀⠀⠀⠀⠨⠛⠶⢾⢶⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠋⠁⠀⣀⠀⡔⠄⠀⠀⠀⠑⠊
⠀⠘⢦⣀⣀⣀⠜⠀⠀⠀⠀⠀⠀⠓⢠⠤⢤⡔⢁⡀⠀⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣬⢃⡟⠠⣌⢀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⠀⠀⠀⣀⠤⠤⢄⡀⠙⠀⠀⠹⢄⣠⠏⠀⣀⠀⢀⡄⠀⡀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⣖⣀⣸⠶⠛⠉⠉⠉⠀⠀⠠⡀⠐
⠀⣞⠁⢹⠆⡼⠁⠀⠀⠀⠘⡄⠀⠚⠀⡐⠀⠦⠀⠈⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠁⡰⠋⠙⡆⠀⠀⠀⠐⠢⠼⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠁⢀
⠀⠈⠋⠉⠀⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⢡⠐⠀⠀⠐⠘⠢⢔⠁⠀⠀⣠⢤⣤⣤⣤⠲⣶⣩⠻⡍⢣⠀⠉⠀⠀⡈⠀⠀⠠⠀⢠
⠀⠀⠆⠀⠀⠈⠓⠤⡤⠤⠚⠀⠀⠀⠀⠀⡄⠀⠀⠉⠀⠀⠀⠀⠑⠤⠔⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠐⣭⡆⣻⡾⠷⠍⠛⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠘⠂⢀⡀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⢀⡀⢀⡀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠈⠀⢈⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢀⠂⢒⡠⣀
⠀⠀⣐⠢⢘⠀⡀⡎⢃⠉⡉⠤⠼⢄⡱⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠄⠂⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⢀⠀⢀⡄⠲⠒⠠⡀⢀⠀⢀⠎⠄⠱⠀⠀⠼⢌⠆
⠀⠆⢨⠖⠉⠈⠉⠁⠈⠀⠀⠈⠉⠀⠳⢼⠀⠀⠀⣠⠴⠏⠉⠁⢹⡆⠀⠀⠀⣠⠖⠐⢠⠅⠂⠀⠀⠀⠁⠀⠈⢸⡠⠀⠀⠀⠀⣩⠀⠀⢸⢰⠀⡄⠀⡄⠀⠸
⠀⡌⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⢯⡉⠀⣠⠞⠁⣠⠤⠤⠶⠛⠀⣀⣠⠔⠁⠀⢀⡜⠀⠀⠀⠒⠀⠀⠀⠀⠪⢴⡄⠀⠀⣨⠘⠀⠀⠀⠣⡓⠄⢀⠀⢔⠡⠃
⠀⠀⣃⠘⡚⠄⠤⠄⢂⠱⡌⣈⠆⠈⠆⠀⠀⢯⡴⠊⠁⠀⠀⠀⢰⡋⠈⣀⣀⠤⠒⠉⠀⠀⠀⠠⠆⣀⠀⠀⠀⠀⢠⠂⠋⠳⠁⠀⠀⠀⢀⡀⠀⠁⠂⠈⠁
⠀⠀⠀⠈⠠⠆⠒⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠋⠀⣀⡀⠀⠹⣿⠟⠁⢀⣀⠀⠉⢿⣿
⣿⣿⣴⣶⡿⠃⠀⣠⣿⠀⠀⣿⣿⡇⠀⢸⣿
⣿⣿⠟⠉⠀⣠⣾⣿⣿⠀⠀⢿⣿⠇⠀⢸⣿
⣿⣇⣀⣀⣀⣀⣀⣀⣿⣧⣀⡀⠀⣀⣤⣿⣿
⣿⣿⣿⣿⣿⢻⣿⢉⠙⠉⡉⠉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣈⣩⣼⣴⣤⣧⣀⣿⣿⣿⣿⣿
⣿⣿⣿⡏⡟⣭⣛⢩⡙⡏⠛⢙⠩⢹⣿⣿⣿
⣿⣿⣽⣧⣧⣭⣴⣬⣴⣧⣧⣼⣭⣼⣿⣿⣿
⣿⣿⡟⠛⡟⠟⡻⡿⢛⢿⠻⡟⢛⠟⣿⣿⣿
⣿⣿⣧⣤⣧⣦⣴⣷⢬⣦⣦⣽⣼⣴⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣀⣹⣿⣿⣿⣿⣿⣿⣿
⣿⠏⠹⢉⠹⠋⠹⠹⡏⢩⡌⣬⠉⠬⠍⠈⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣍⣈⣉⣹⣽⣏⣟⣛⣟⣿⣯⣿⣿⣿⣿
⣿⣽⣿⣽⣿⣽⣭⣽⣽⣯⣽⣿⣽⣽⣽⣽⣿
⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣾⣾⣷⣿⣿⣿⣿
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢔⠀⡠⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠁⠀⢀⠀⠀⠀⠀⣬⢅⡧⠧⣌⠗⠒⠀⠀⠀⠀⠀⢄⠀⢰⠂⠀⡀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠁
⠀⠀⠀⠀⣒⠆⠉⠉⠀⠀⠁⣠⠀⠀⠀⠀⠀⢤⠞⠚⠚⢥⠂⠉⠂⠀⠒⡨⣿⠀⠀⠈⡇⠩⡀⠀⣀⣄⠀⠹⠂⠁⠁⠲⠇⣀⣔⡀⠀⡄⠄⠄⠄⠩⠂
⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠈⠒⠁⡀⠘⡀⣬⡇⠀⠀⠀⢀⡧⠄⠒⠀⠀⣕⣩⠳⠶⢚⠡⠳⠀⠀⢀⠀⠂⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠎⣀⠀⠀⠀⠀⢨⣪⠀⠀⠘⠀⠐⣳⣄⣀⣀⣰⡗⠄⡈⠀⠀⠀⠈⠙⠊⠋⠘⠀⠀⠀⠁⠉⡀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠂⠀⠧⠓⡀⠀⠀⠀⠀⠀⢡⠠⠊⠙⡉⠣⡁⠑⠁⠀⢠⡀⠠⡄⠀⠇⠀⡀⠀⠀⠀⠞⠁⢠⣀⠀⢀⣠⠀⠐⠆⠂⠀⠀⠈⠠⠄⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠒⡀⠀⠀⠁⠁⠀⠀⠀⠀⢀⡀⣁⠲⠋⠂⠐⠺⡀⠤⠆⠀⠀⠰⠍⠀⢱⠁⠀⠡⠀⠀⠀⠀⠀⠒⠀⠀⠈⠄
⠀⠀⣰⠚⠉⠓⢅⠀⠀⠀⠀⢠⡤⠙⠉⠈⠛⢀⡃⠀⠀⠀⠀⠀⣄⡀⠸⠁⠀⠀⠀⠀⠀⠘⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⢬⡇⠀⠀⠀⢨⠁⠀⠀⠁⣠⡀⠐⠀⠀⠀⠙⠃⡀⠀⠀⠂⡀⠀⣀⢔⠀⠀⠀⠀⠀⠀⢠⡅⠠⠤⠀⠀⠀⢄⣀⡇⠀⠔⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠭⠦⢤⠴⠛⠀⠀⠀⠀⠌⢡⣄⠁⣀⡀⠟⠊⠁⠀⡀⠀⠃⠀⣀⡤⠡⣄⡀⢀⢀⡀⠞⠳⠄⠀⠀⠰⢤⠀⠔⠂⠒⢄⠲⠉⡀⠀⠀⠀⣅⡆
⠀⠀⡀⠀⠀⡠⡤⢴⠄⣤⡀⠀⠀⠹⠌⠉⠐⠂⠀⣀⡀⠈⠀⠀⠀⠈⠀⠐⠃⣁⠉⠹⠀⠱⠆⠀⠀⠀⡤⢆⢸⠀⠀⠀⢸⢀⠋⠁⠀⠀⠈⢆⠂
⠀⠈⠁⠠⡎⡵⠢⠁⠉⠳⣏⣤⠀⠀⠀⠀⠀⠀⢸⡲⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠃⠑⢒⡒⢁⡈⠉⠃⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠰⢸⡁⠀⠀⠐⠀⣙⠼⠀⠀⠀⠒⠤⠄⠀⠀⠀⢠⣤⣤⣶⣶⣶⣘⣛⣓⣙⣛⣂⣃⣰⣶⣶⣶⣦⡀⠔⡇⠀⠷⠀⠩⠂⠀⠀⢀
⠀⠀⠀⠘⢃⡾⡄⡀⣄⠤⣊⠟⠀⢀⠀⠀⠐⠂⢀⠀⠀⣼⡏⢿⢉⡉⠏⡭⢙⢹⡏⡟⠩⣽⠉⣭⡟⠩⣽⡇⠀⠀⠀⠀⠐⠂⠐⡀⠀⡄⠁
⠀⠀⠀⢀⡀⠑⠓⠤⠔⠓⠉⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⢿⣧⡘⣸⣅⣆⣄⣻⡘⢃⣟⢓⣨⡀⢒⣟⢓⣸⡇⠀⠀⠀⢀⢀⣘⠢⠛⠂⠐⢾⠀⠄
⠀⠀⠈⠀⠀⢀⠀⠀⠤⢀⢀⠀⠀⠀⠀⠀⡹⣂⠀⠀⠀⠘⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⣛⣛⣛⡛⠛⠃⠀⠠⠒⣀⡀⠇⠀⠀⠀⠅⠀⠘⡤⠊⠂
⠀⠀⠀⠠⡒⠀⡀⣤⢠⡄⡀⠐⢂⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⢀⠼⡅⠀⠄⠀⠀⠄⢠⠑⠲⡉
⠀⠀⠐⠁⠠⢮⠕⠈⠈⠘⢌⠦⠀⢂⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢄⠀⠄⠀⠀⠀⠁⠀⠈⠀⡠⡠⠀⠀⠀⠃⠀⠀⠀⠄⠴⠀⣦⠄⢠⣠⠔⡋⠡⠄
⠀⠀⢐⠀⣻⠠⠀⠀⡀⠀⠈⠯⡃⢐⡂⠀⡀⠀⠘⢀⠀⠀⠀⠀⠠⠃⠀⠀⡇⠀⠀⢀⠀⢜⠎⡀⠀⡀⠀⠀⠊⠖⠀⠀⠀⠀⠀⠔⠀⠊⠄⠉⠩
⠀⠀⠰⡀⠩⣔⠀⠀⣀⠀⡌⡬⠁⣀⠀⠀⡁⠀⠀⠀⠷⠀⠀⠰⠁⠀⠀⠀⢐⠀⣀⡀⠀⠀⠈⠀⠸⠖⠂⢈⠀⠐⢀⡠
⠀⠀⠀⠰⠀⠈⠇⠺⠸⠂⠋⠀⠀⠀⠀⠈⠀⠀⠰⠂⠀⠀⠀⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⡒⠀⠁⢠⠀⠈⠄⢠⠀⠘⠁⠀⠀⢀⠔⡨⠀⠀⢅⠢
⠀⠀⣀⠀⠀⠈⠂⠐⠐⠈⠊⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣶⡶⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠘⢁⡀⢠⠀⢈⠀⢦⠀⢈⠂⠈⠁⠀⠈⢁⠁
⠀⠀⠉⣠⠀⠀⠀⠀⠀⠀⠀⣠⠄⠚⠁⠀⠀⡓⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⣄⠀⠀⠀⠤⠀⠀⠎⠑⢀⠀⠀⠀⡀⣄⠀⠀⠁⠀⢀⢆⠙⠀⠃⢀⠄⠅
⠀⠀⠆⠀⡠⢄⡀⠀⠀⠀⢎⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠎⠑⡀⠀⠀⢀⠀⠀⡀⠀⢀⡁⠀⠀⠉⠚⠀⠀⠀⠀⠀⠑⠡⠤⠤⠕
⠀⠀⠀⡜⠁⠀⠈⠑⠤⡀⠀⠣⣀⡠⠊⠀⠀⠀⢀⠬⢁⣞⣧⡈⢦⡀⠀⠀⠀⠁⢀⡄⠈⠀⠀⠁⡀⠀⠀⠀⢀⣄⠎⠉⠩⡐⡄⠀⠀⢔⠀⠒⠢⠄
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠱⡀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠋⠉⠀⡀⠀⢀⠀⠀⠀⢀⠁⠀⠀⠀⠄⢈⠁⠀⢠⠔⠰⠀⠰⠀⠈⠈⠀⣸⠂⠈⡀⠤⠰⢀
⠀⠀⠀⠀⠀⠉⠒⠢⠤⠠⠜⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠐⠉⢀⡀⠀⠐⠁⠃⠀⠘⡑⡀⠤⠀⢈⢄⠌⠀⠹⣦⠀⠆⢀⢼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠈⠒⠙⠋⠁⠁⠀⠀⠀⠁⠂⠉⠈⠁