Frying Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣄⣸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠙⡄⠀⢠⠤⠜⠁
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠸⡀⡏
⠀⠀⠀⠀⠀⠀⠈⢤⣈⣂⠜⢆⠀⢿⡇⢰⢁⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⡇⠸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎
⠀⠀⠀⠀⠀⠘⢠⡀⠀⠀⠀⢠⠇⠀⡜⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠸⡀⢰⠁⣀⠀⠀⢠⠎⠁⠀⠀⡔⠁⢨
⠀⠀⠀⢶⠒⠂⠤⢄⡀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠋⠀⠀⠀⢀⡇⠀⣸⠤⠤⢒⡰⠖
⠀⠀⠀⢳⠀⠀⠘⠁⠘⢤⠀⠐⢳⣹⠀⠀⠉⠉⠉⢉⡩⠚⠁⢀⡴⠡⠔⠚⠉
⡠⠐⠈⠉⠁⠀⠀⠀⠤⠋⠁⠒⠀⠋⡰⠆⠠⠆⠀⠈⢀⠀⢠⠋⠀⠈⡱⡶⠤⠤⠤⠤⠤⠀⠀⠀⠒⠒⠚⠋⠉⠉⠉⠉⠉⠑⠒
⠑⡄⠀⠠⡄⠐⠦⡁⠀⠠⠐⠁⠀⢀⠆⠀⠀⠀⠀⠀⡠⠖⠁⡠⠖⠁⢠⠣⢀⣀⡀⡀⠀⠀⠤⠤⠀⢀⣀⣀⣀⣀⣀⣀⡀⠠⠔
⠀⢱⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠐⠒⠀⠀⠀⠚⠤⠁⠐⠈⠀⠀⠀⢀⠴⠋⠁
⠀⠀⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⣀⣀⣀⣀⣈⣁⣒⣢⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣄⣒⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢠⣿⠃⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣾⡏⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡟⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠸⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⡀
⠀⢀⣤⣶⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣶⣤⣀
⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⢿⣷⣄⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⣀⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⠻⢷⣾⣿⣟⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣛⣿⣷⣾⠿⣿⡟⢹⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠈⣿⡆⠀⠈⠉⠛⠛⠻⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠿⠿⠛⠛⠉⠁⠀⢀⣿⣷⠿⠛⠁
⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠉⠛⠿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡿⢁⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠟⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢪⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠣⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡃⠄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣶⣶⣶⣮⣽⣿⣿⣿⣿⣿⣯⣭⣭⣝⣛⣘⠷⣀
⠀⠀⠀⠀⠀⠀⡀⣔⡮⠟⢚⠉⠭⠁⡄⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⢀⢮⣾⣫⠀⣠⠸⢀⣈⠁⢁⣛⠫⠭⠭⠭⠭⠭⠽⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣿⣿⣟⣡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠏⢻⣳
⠀⠀⠀⠀⠸⣟⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣔⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣾⣯⣶⣴⣠⣤⡀⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣽⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢿⣟⡿⣻⣿⣿⠿⠿⡿⡿⣻⣿⣿⣿⣿⣟⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣾⣷⣿⣿⣴⡾⠿⢶⣿⣻⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁

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

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠈⠁⠒⠂⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣄
⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⡀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡎⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⠒⠒⠂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⢧⠋
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⡀⠠⠄⠤⠀⠂⠈⠁⠠⠟⠁
⠀⠈⢦⡀
⠀⠀⠀⠙⠢⠤⣀⣀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠑⡀⠀⠀⠠⠖⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠒⠁

⠀⠀⢀⣀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠤⠄⣀
⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠤⠄⠀⠀⠀⠒⠀⠒⠂
⡀⠀⢃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠤⠐⠒
⢋⠢⠬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣁⠴⡀
⠈⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣪⠄⠈⠉⣠⡁
⢰⠀⣀⣀⠀⠖⠀⠀⠀⠐⠀⠀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠂⢂⡉⠅⠃
⠀⠁⠰⢁⠀⠀⠠⠤⠀⠀⠐⡀⠀⠀⢀⠀⠀⠀⢀⠀⣂⣰⠦⠔⠉⠁⠕
⣀⣀⣀⣀⣈⣒⣤⣔⣂⣀⣐⣒⣒⣒⣚⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢀⣀⣤⠴⠶⠚⠛⠛⠉⠉⠉⢿⣍⠉⠉⠉⠉⠛⠛⠳⠶⢦⣤⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢻⠀⠀⣀⣠⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠙⠉⠉⠉⠉⠛⠛⠳⠶⢦⣤⣀⠀⠀⢹⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⣠⣼⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢾⣅⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠾⠛⠁⠀⢀⣠⠄⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⣤⡴⠶⠛⠛⠛⠷⣦⡀⠀⠀⠙⠓⠶⣤⡀⠉⠛⢶⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⣠⠞⠁⠀⠀⢀⣴⠟⠁⣠⡴⠶⠾⠛⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⢦⣄⡀⠁⠀⠀⠀⠙⢷⡘⣧
⠀⠀⠀⠀⠀⠀⣿⣴⠋⠀⠀⠀⠔⠋⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⣀⣀⣀⣀⣢⣴⠏⠀⠀⠀⠀⠀⢀⣀⣤⠞⢁⡾⠁⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⢿⡘⢷⡀⠀⠀⠀⠸⣧⣐⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⡿⠋⣡⠶⠋⠁⠀⠀⢀⡼⠋⣾⠁
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠙⠷⣤⣀⠀⠈⠉⠙⡛⠳⢦⡀⠀⠀⠀⠠⣤⡤⠤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠈⠁⠀⠀⣀⣤⠾⠋⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠉⠛⠲⠶⣤⣬⣁⣀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⠾⠿⠶⠚⠋⠁⠀⠀⢀⣀⣤⡴⠞⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠲⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠟⠉⠉⢻⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠙⣿⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⡇⠀⠀⠀⠈⡷⠶⠖⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠞⠛⠓⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠛⠙⠛⠢⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡟⠁⠉⢻⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠿⠟⠋⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡴⠶⠶⠲⠶⢤⣄⣷
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣹⡟
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣤⠴⠞⠋
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⡾⠏⢶⠳⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⠤⠤⠤⠤⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⢀⣀⣤⡴⠾⠛
⠀⠀⢀⣠⣴⣶⣟⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⢿⡶⢦⣤⠶⠒⢋⣁⣤⡴⠶⠚⠛⠉⠁
⢠⣾⣿⣿⣿⠿⢟⣂⣤⠤⠶⠶⠖⠒⠚⠛⠛⠛⠛⠒⠒⠲⠦⠤⣄⠈⠳⢹⣿⡿⠛⠉⠁
⣿⣝⠿⠫⠕⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⡿⠁
⢹⣽⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠟⠉⡼⣽⠁
⠀⢿⣻⣿⣿⣿⣟⣓⡶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠁⠀⠀⠀⣊⡼⠁
⠀⠀⠙⠻⢿⣿⣻⣿⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠶⠶⠶⠶⠛⠛⠋⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢒⣁⡤⣠⣦⣤⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠛⢻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣤⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡲⣿⣿⡆⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣀⢰⣿⡄⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠟⠁⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⡀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠂⠀⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡻⣿⣿⣷⣄⡀⠶⣾⡁
⠀⠀⠀⠀⠀⢀⠖⠛⢢⡀⠙⢮⡛⠿⠿⢿⣿⣿⡻⡢⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⡄⠀⠱⡄⠀⢰⣿⣿⣿⣇⢡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⣄⠀⢹⣿⡿⣿⣿⣇⠀⠀⠀⠀⢾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠈⠉⠈⢿⣷⠘⠿⠸⡄⠀⠀⡰⠛
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢱⠀⡸⠁⠀⠘⢿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⠁⠀⣤⠀⢺⡏⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠀⢾⣣⡟⠀⠀⠀⢀⣀⣠⠀⠁⠀⠈⢁⡠⠂⠀⠙⠛⠛⠀⢀
⠀⠀⠀⢡⠀⠀⠀⡡⢖⢛⡷⠒⠘⠉⠉⠁⠀⢰⠀⠀⠀⠀⢸⣽⣇⠤
⠀⠀⠀⠘⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠒⠉⢸⠐⠄⣾⣛⠛⠛⠛⣛⠛⠃⡄
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠏⠀⢀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠆⠶⢶⠒⢚⠋⠍⠅⠤⢨⡧⠷⠶⠶⠾⠶⠶⠞⠣⠶⠀⠀⠀⠀⠀⠠⠀⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢦⡀⠀⠀⠀⣤⠶⠖⠛⢻⡆⣠⠴⠦⢤⣤⡄⠀⣴⠛⠛⠛⠛⣻
⠀⠀⠀⠀⠀⠀⠀⢾⡏⠁⠀⠈⢧⠀⠀⠀⡇⠀⠀⠀⢸⡇⡟⠀⠀⠀⠀⣧⣠⡏⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⣧⠀⠀⣿⣠⣤⣄⢸⣿⡇⣠⠴⠞⠋⠉⢿⡃⠀⠀⠀⢰⡇
⠀⠀⣠⡴⢶⣄⠀⠀⠀⢘⣧⣀⣀⣼⣇⢠⡟⠁⠀⠙⣾⣿⡇⠘⣧⠀⠀⠀⠘⣧⠀⠀⠀⢸⠇
⣴⠛⠁⠀⠀⠙⢧⡀⢐⡏⠉⠉⠀⢠⡿⠚⠛⢷⡀⠀⠘⢿⡇⠀⠘⣧⠀⠀⠀⠘⣇⠀⠀⣼
⠈⠳⣄⠀⠀⠀⠀⠻⣄⡇⠀⠀⠀⢸⡇⠀⠀⢸⠷⣄⠀⢈⣷⣤⠤⠾⣆⠀⠀⠀⢹⡄⠀⣿
⠀⠀⠈⣷⠶⢷⡀⠀⠙⣇⢀⣤⢤⣸⡇⠀⠀⢸⡇⠹⣆⢸⠇⠀⠀⠀⣿⡆⠀⠀⠀⢷⠀⣿
⠀⠀⢾⣅⠀⠀⠹⣦⠀⣿⣟⠁⠀⠙⠳⣄⠀⢸⡇⠀⠹⣿⠀⠀⠀⠀⣇⢻⡄⠀⠀⠘⣇⣿⢀
⠀⠀⠀⠙⢷⣄⠀⠈⠳⣼⡝⢷⣄⠀⠀⠈⢷⣜⡇⠀⠀⣿⠀⠀⠀⠀⣿⠈⢷⠀⢀⡾⠉⠉⠹⡇
⠀⠀⠀⠀⠀⠙⢷⡀⠀⠙⢧⡀⠙⢧⡀⠀⠀⠙⣿⠀⠀⢿⠀⠀⠀⠀⢹⡀⠘⣧⠞⠁⣄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⣈⢳⡄⠀⢹⣦⠀⠀⠘⢧⡀⢸⡀⠀⠀⠀⢘⣧⠞⠁⠀⢀⣒⡂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠛⠿⣤⣘⣏⢳⡄⠀⠈⢷⣸⣇⣠⡴⠞⠋⠁⠀⠀⠀⠀⢀⣠⡴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠖⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⢀⡠⠖⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠵⠒⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⠉⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠶⠶⠶⠒⠚⠛⠋⠉⠁⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⢄⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠶⠖⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠬⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⣁⡴⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠛⠉⠁⣀⣠⡤⠶⠛⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⡤⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠑⠣⠂⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠚⠋⠉

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⢀⡶⠛⠛⠛⠻⡷⠖⠛⠛⠛⣶⡴⠶⢶⡄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠁⠸⡆⠀⡶⠚⠛⢶⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻⠀⠀⠀⣿⠋⠉⠛⠳⡦⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣶⠟⠛⢳⡄⢷⠀⠀⠀⢹⡀⣧⠀⠀⠸⣿⠀⠀⠀⠀⡿⠖⠒⣶⠦⠾⢶⣤⡶⠿⠶⠦⠀⠀⡇⠀⡼⠋⠀⢸⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⣼⣇⠀⠀⠀⢷⣿⠀⠀⠀⡿⠶⠒⣆⠐⡄⠀⠀⢹⠀⠀⠘⣻⠀⠀⠀⢨⢠⠶⠿⢿⡇⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠞⠛⠉⠹⡄⠀⣈⣿⣄⠀⠀⡇⠀⠀⢻⠉⠉⠉⣷⠘⠀⠀⠀⣿⠀⠀⠀⠘⢸⠀⠀⠀⠁⠀⡿⠉⠛⢶⡄
⠀⠀⠀⠀⢀⣀⢻⡀⢨⠃⠀⠀⠀⣇⡟⠉⠉⢹⡇⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⡄⠀⠀⣿⠀⠀⠀⠀⣜⠀⠀⠀⠀⢰⡇⠀⠀⣸⠃
⠀⠀⢠⡾⠋⠹⣎⣧⢸⠀⠀⠀⠀⣿⠁⠀⠀⢸⣇⡴⠦⠴⡄⢸⡄⠀⠀⡇⠘⡇⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⢰⠀⠀⢠⡇
⠀⠀⠘⣇⠀⠀⢿⣿⣼⣦⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⣇⣸⣧⡄⠀⡇⠀⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⢀⠀⡟⠀⠀⣾
⠀⠀⠀⢻⡀⠀⢸⡆⠀⠈⡇⠀⡖⠛⠻⠀⠀⢸⡏⠀⠀⠀⡏⠀⢀⡇⠀⡇⠀⣇⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⢸⢰⡇⠀⢰⣇⣀⣀⣀
⠀⠀⠀⠘⣇⠀⠀⣧⠀⠀⢁⠀⡇⠀⠀⡀⠀⢸⡇⠀⠀⠀⠁⠀⢀⠀⠀⡇⠀⣿⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀⢸⣼⠀⠀⣞⣉⣩⠝⠛
⠀⠀⠀⠀⢹⡄⠀⢹⡄⠀⢸⠀⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⠀⠀⠘⠀⠀⡇⢀⣹⣀⣀⣀⣿⣀⣠⣤⣧⣤⣤⣼⡧⠶⠚⠉⠁⠀⠀⢀
⣤⠶⠶⠶⠾⠗⠒⠚⠓⡆⠈⡄⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⠀⠀⠀⡗⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢷⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡜
⠈⣧⠀⠀⠀⠄⠀⠀⠀⢹⠀⢸⡇⠀⠀⡇⠀⢸⡇⠀⠀⢸⡇⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢳⣈⡇⠀⠀⣧⠀⢸⡅⠀⠀⢸⡇⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣿⡀⢸⡇⢀⣀⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⣿
⠀⠀⣿⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡴⠋⠀⡿
⠀⠀⢻⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠞⠀⠀⣠⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢰⣇⠀⠀⡴⢻⡇
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠸⡟⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠁⢀⡾⠁⢸⠇
⠀⠀⠀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣿⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⢈⡇⠀⣸
⠀⠀⠀⢸⡆⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠀⣂⠈⠀⠀⢠⠟⠀⠀⣿
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⡏⠀⠀⠀⠁⠀⠀⢠⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⢠⠂⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⠀⢻⠈⠉⠛⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠏⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠇⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠀⠀⠀⡆⢠⠋⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣷⠁⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠶⠶⠶⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣾⠾⠋
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠐⠒⡄⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⢇⠀⣸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠔⠊⠉⢣⠀⠰⠊⠉⠀⠈⡄⠀⢠⠼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⠘⡄⠱⠀⠀⠀⠈⢆⠀⡇⠀⠀⠀⢃⢀⠇⠀⠀⠉⡑⠀⠖⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⣄⢧⠀⠀⠀⠘⡄⠅⠀⠀⠀⢸⡜⠀⠀⠀⢠⠁⡎⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⡁⠀⠈⡆⠀⠀⠀⢡⢰⠀⠀⠀⢸⠃⠀⠀⠀⡎⠘⠢⡄⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠱⠀⠀⢰⠀⠀⠀⠀⣾⠀⠀⠀⡌⠀⠀⠀⢸⠀⠀⢠⠁⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢃⠀⠀⠇⠀⠀⠀⢻⠀⠀⢀⠃⠀⠀⠀⡌⠀⠀⠃⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⡄⠀⢡⠀⠀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠃⠀⠰⠀⡰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠢⣁⠀⢸⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⢸⠀⠀⣧⠞⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢋⠑⠲⠤⣀⢀⡇⠀⠀⣈⣀⣀⣀⠼⠒⢺⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⡄⠀⠀⢱⠀⠀⠀⢹⠀⠀⠀⡆⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢃⠀⠀⢈⡀⠀⠀⠸⠀⠀⠀⡇⠀⢠⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⣀⠤⠒⠒⠂⠉⠐⠒⠒⠤⡀⢸⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⠑⠢⣤⢀⣀⣀⣀⡀⡤⠔⠚⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣀⣇⠀⠀⡇⠀⠀⣇⣀⠤⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀⠀⡴⠋⠑⢢⠀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠑⢢⡰⠁⠔⠰⠛⠑⢦⠀⡇⢸⡏⢀⣈⡦⠤⣠⠊⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⢸⠃⠀⠀⡇⠈⠁⡘⠀⡇⢸⠇⠀⢸⠐⠄⢸⡇⢨⠤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢉⠉⢆⡇⢀⠀⢠⠠⠤⣼⠇⠈⠲⡟⠒⢄⢸⠠⢄⡆⠀⠀⢸⠉⠁⠤⠈⣥⠂⠙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢇⢰⠀⡛⠐⠄⡾⠀⠈⢠⠃⠂⢸⡇⠠⠀⡙⠀⠀⡸⠚⠲⣄⠀⡇⠀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⢦⠀⠇⠠⢰⢃⡴⢄⡌⠀⠀⢸⠀⠈⠀⠗⠊⠓⡇⠐⠀⡾⡸⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣀⣄⣘⣼⠀⣀⡟⡇⢀⠀⠁⢨⠤⠾⣀⢀⡸⡀⠈⠀⠃⠁⠰⢱⠁⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣄⣀⣀⡉⢻⠁⡇⠠⠀⡆⡇⢐⠂⣸⠡⡀⠘⠇⢸⣀⣀⣇⣆⣀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠳⡅⠀⠀⣇⠁⠘⠀⡏⢀⠀⠸⢀⡜⠀⣄⣀⣈⣉⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⣄⠈⠲⢄⣿⡁⠀⢰⠀⢀⡠⠗⠋⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠈⠉⠉⠉⠉⠁⣀⠴⠃⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠦⠤⠤⢤⣄⣤⣀⣀⣀⣄⣠⠤⠤⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠲⠦⠤⣄⡀
⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠋⡿⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⢯⣁⠀⠀⠀⠀⠀⢀⡠⡿⠀⠀⣠⠞⠓⢦⡀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡼⠁⠀⠈⠳⣄⠀⠀⠀⠀⢀⣴⠇⣀⡄⢉⣑⠒⢲⠖⠉⢰⠇⢀⡞⡟⠀⠀⠀⠙⢦
⠀⠀⠀⡰⠃⢀⣠⡤⠖⠚⠣⡀⠀⠀⠀⠈⠳⡄⠀⠀⡟⣻⠀⡁⠀⠀⠉⠂⡼⠀⠀⡾⢀⡞⢰⣅⠀⠀⠀⠀⠈⡇
⠀⠀⠰⣗⠛⠉⠀⠀⠀⠠⠶⠾⢦⡀⠀⠀⠀⠹⡄⠀⡇⣿⠸⠇⠀⢾⠗⢀⠇⠀⢰⠇⡞⢠⠃⠈⠳⢄⡀⠀⢰⠃
⠀⠀⠀⠈⠳⣄⢠⠞⠀⠀⠀⣴⡄⠙⣄⠀⠀⠀⠘⣆⡇⣿⢜⠀⠀⠀⠀⢸⠀⠀⣼⡼⢡⠇⣤⠉⠀⠢⠉⣲⠏
⠀⠀⠀⠀⠀⠈⠻⣄⠸⠷⠀⠈⠁⠀⠈⢦⠀⠀⠀⠘⣟⣿⢌⣁⠀⠀⠀⡏⠀⢀⡇⠳⡞⢠⠈⠀⠛⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠠⠠⠜⠀⠀⠈⢧⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠹⡝⠤⠂⢠⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡀⠀⠃⠃⠀⠀⠈⣆⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⢻⡀⢠⠇⢠⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢱⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣇⠀⠀⠀⠀⡆⠀⢸⠘⡄⠀⠈⣧⣏⡴⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠓⠷⢤⣀⣀⠀⠀⠀⢱⠀⠀⠀⢻⠀⠀⠀⠀⡇⠀⢸⡀⣧⣠⠴⠛⠉⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠉⠉⠙⠓⠒⠲⠶⠤⠼⠧⣤⣤⣴⣷⣚⣋⣉⣁⣀⣀⣀⣀⣄⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠶⠶⠤⠤⠴⠶⠖⠒⠚⠋⠉
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣻⣻⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡅⠀⡈⢐⡆⡴⠺⡄⠇⡰⢂⡄⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⢤⣠⠆⢤⣳⡇⢰⠃⢸⡷⢀⡀⠀⡎⢀⣎⡈⢀⠋⢂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡬⢨⢋⡃⢸⠀⠃⣯⠀⡞⢀⡜⠃⠐⢣⠈⣀⠆⡌⠀⢊⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠳⡒⢸⢧⠁⠊⢠⠀⠿⠀⢣⠞⢶⠋⠹⠸⢈⡟⢉⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣁⡌⢛⢇⢡⠁⣁⢈⡆⠘⡤⠀⠐⠋⠇⡘⠑⡎⢰⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⣦⠉⠳⢱⠋⠈⢹⠀⣎⠜⢨⡀⠀⢑⠔⠊⡁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡆⠑⢄⡊⢠⡪⠳⡀⠮⢀⠋⢀⠂⢁⠄⠈⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠛⠿⢄⣘⣆⣻⡧⠴⠚⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⢀⣀⣀⣀⣀⠠⠤⠤⠤⠤⢄⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣀⡠⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⡒⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠾⠶⠭⢭⡀⠀⠮⢴⠄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠸⠉⠉⣁⢸⡏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣄⠀⢀⣎⠀⠀⣠⠏
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⠤⢤⠤⠇⠈⠀⣀⠀⠀⠀⠀⠀⠰⡯⠟⠀⠀⠠⡧⢤⠀⢹⡤⠚⠁
⣞⠉⠁⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⡰⡄⠀⢏⣳⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘⠚⠁
⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠑⢤⡀⠐⠠⢀⡀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠠⠤⠄⣀⣀
⠀⠀⠀⠀⠈⠑⠢⢤⣈⠁⠂⠠⠀⠀⠀⠀⠀⠉⠲⣄⣀⠤⠒⠊⠉⠀⠀⢰⡁⢢⣼⠧⠀⠒⠒⠀⠐⠂⠀⠒⠢⣎⠧⠤⢀⣀⠀⠉⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣀⡀⠀⠀⡠⢔⡍⠀⠀⣀⠤⠒⠈⠁⠀⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡱⠊⠀⠈⡡⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠘⠀⠀⢠⠔⠒⠒⠲⢄⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢣⠀⢠⣐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠒⠢⠤⠤⠤⠤⠤⠚⠂⠀⠀⠀⠩⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠈⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠁⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠀⠉⠁⠒⠀⠤⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠠⠀⠤⠄⠒⠈⠉⠀⠀⠀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣒⣒⣢⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣖⣒⣚⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⡏⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⣦⡄⠀⠀⠀⢀⡦⣤⣀⠀⠀⢸⠇⢸⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢸⡄⢹⣷⠀⠀⠀⢸⠃⠀⡟⡇⠀⢸⠀⣾⠀⢸⠁⢠⠤⢶⣆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢧⡈⠉⠳⣄⠀⣧⠈⣿⣆⠀⠀⢸⠀⢀⣿⡇⠀⡟⢀⡇⠀⡟⢀⡟⢀⡏⠘⣆⠀⣠⠞⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡀⠈⢦⡸⡄⠸⣿⡄⠀⢸⠀⢸⣿⡇⢰⡇⢸⠃⢸⠇⡼⠀⡾⠀⢠⣧⠞⠁⣀⢴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⠀⠹⣷⠀⢹⣷⡀⢸⠀⢸⣿⡇⣼⠀⡟⠀⡞⣸⠁⡼⠁⣠⠟⠁⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠒⣌⢣⡀⠳⣄⠈⣧⠀⢻⢷⣸⠀⢸⣿⣢⠇⢸⠃⣸⣵⠃⣸⣣⠞⠁⣠⢾⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠳⣌⠳⣝⣆⠘⢦⡘⡆⠈⢧⢻⡆⠘⣿⣟⢀⡏⢠⡿⠁⣼⡷⠁⣠⢞⡵⢋⣠⠴⠚⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⢦⡈⠻⣷⡀⠳⣽⡄⠈⢷⡗⠋⠉⠉⠉⠉⠉⠓⣾⠏⢀⡴⣷⣫⠖⠋⠀⣀⡤⠖⠋⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⣆⠈⢿⣄⠙⣿⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣯⡾⠋⢁⣠⠖⠋⣁⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⣷⠤⠽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠯⢤⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⡤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⢤⣀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠞⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠑


⠀⠀⠀⠀⣀⠠⠄⠐⠂⠀⠉⠉⠉⠀⠁⠈⠀⠈⠉⠉⠁⠒⠒⠠⠄⣠⡄
⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠴⡀
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠁⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠤⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠀⠒⠀⠁

⣶⡾⠳⠛⢷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣿⣶⣶⣷⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠰⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⠀⠀⢸⠉⠁⠡⢀⠀⡀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⠤⠼⡀⠀⢠⡆⠈⠉⡅⠘⠈⠉⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠘⡄⠀⠀⡇⠀⢸⠁⢀⣰⡁⣼⠉⠓⢰⡇⠈⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠋⠹⡆⢀⣀⡇⡀⠋⠓⢒⡇⠀⠈⠀⠇⠀⠁⡇⠀⠀⡞⠇⠀⣠⣇⡀⢠⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠲⡇⠀⠀⡄⠃⠈⠁⣧⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡇⠀⢰⠁⠀⠀⠀⠀⢠⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⣷⠀⠀⢁⠀⠀⢠⡏⠀⠀⠏⠁⠀⠀⢰⠆⠀⢸⠀⠀⡜⠀⠀⣸⠀⠀⣸⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡄⠀⢸⠀⠀⢸⣃⠠⠼⠦⠓⠒⠂⠚⠂⠀⠚⠀⠀⡇⠀⠀⠛⠀⠀⡏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⡆⠀⠸⠀⣰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⡇⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡀⣤⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⠔⢀⣀⠀⣀⣀⣀⡀⢀⣀⣀⢀⣀⣀⣀⢀⣀⢀⣀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠋⠉⠛⠉⠙⠛⠋⠉⠙⠋⠉⠛⠋⠙⠉⠙⠛⠛⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠲⡆⢀⣠⢄⣾⠉⠉⠉⡏⠉⠉⢹⡟⠛⢳⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⢦⢻⠀⠀⢡⢸⠀⠀⢿⠀⠀⢀⡧⠀⢤⠼⠧⣠⠼⠤⡄⠀⡇⣠⠎⠉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢘⣾⣧⡀⠀⢿⡇⠀⠸⠓⢹⣤⡄⣀⠀⠀⠀⡏⠀⠀⢀⡞⠛⠟⠀⡴⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⢡⡴⠚⢳⡄⠀⠀⠀⡇⠀⠘⢀⠀⠀⣧⠀⠀⢘⠁⠀⠀⢀⠃⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠋⢷⣇⠈⠀⠀⢸⠃⠀⠘⣧⠶⠴⡀⡇⠀⠀⠘⠀⠀⢻⠀⠀⢸⠀⠀⠀⠘⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡛⠛⡆⢀⡼⢤⠀⠀⡇⠀⠀⠗⠳⡆⢰⠀⡆⠀⢸⠀⠀⢸⠀⠀⡆⡏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣇⠀⠠⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⡆⠀⢸⠀⠀⣧⠃⢠⣛⡚⠿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣱⣀⣹⣀⠸⠐⠀⠀⠀⢰⡇⠀⢨⠀⠀⣀⣼⠤⠧⠤⠼⠧⠰⠾⠲⠶⡟⠒⠉⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⠁⢸⠀⣶⠀⠀⠀⢸⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⡆⢹⠀⠀⡆⢸⠃⠀⢸⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠘⠾⣀⠀⡇⢸⡄⠀⢸⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠓⠦⣀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠞⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡴⠃⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠉⠢⢄⡀⠠⠦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠃⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⣀⠀⠀⠀⠀⠀⠀⠈⠂⠇⠀⠀⠈⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⢸⠠⠂⠀⡹⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⣸⠀⠀⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠁⠢⢄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠇⠀⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣘⡄⠈⠉⠒⠢⢄⣀⠀⠀⠀⠀⢀⠀⡴⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⣸⡌⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⣼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢙⠀⢀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠛⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⠄⠀⢀⠀⠀⠀⠀⢀⠔⠈⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠛⠁
⠀⠀⠀⡀⠄⠈⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠁⠒⢅⠀⠠⠐⠈⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣴⣿⣿⠿⠛⠉
⠀⢀⠈⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠑⠄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢍⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢚⠏⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭
⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠄⠀⠀⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⢀⡤⢀⡀⢀⡀⠀⠀⠀⠀⠀⡀⢶⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣦⡙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠋⠁⠚⠁⠿⠁⡾⠃⠀⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⠀⠀⠀⠀⠀⢀⣤⠸⠗⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠐⠶⠝⠓⠉⠀⠀⠀⣤⢸⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠵⠖⣤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡹⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⣄⠀⣤⠐⣦⠰⣶⢰⡎⠷⠀⠀⠀⠀⠀⠈⠉⠺⠋⣰⡖⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣆⠹⠇⠉
⡌⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣠⡀⣀⡀⠀⠀⠀⠀⢀⡤⣦⠹⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⡀⠀⠀⠀⠀⡀⣴⡈⠿⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠐⠛⠰⠟⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⡀⢤⡄⠿⠌⠛⠈⠁⠀⠀⣰⡘⡷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠏⢸⡆⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢶⡘⠷⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠾⣃⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢰⣄⢰⣆⢰⣆⢷⡸⠆⠀⠀⠀⠀⠀⠈⠁⠚⢁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶⡈⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⢠⡤⢠⡄⢀⡀⠀⠀⠀⠀⠀⡄⢾⠹⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡐⣶⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠀⠋⠁⠛⠡⠿⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠀⠀⠀⢀⠠⣦⡘⠇⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⡘⠷⠜⠃⠀⠀⠀⠀⣶⠸⠇⠉⠀⠀⠀⠀⠀⠀⠀⠄⠺
⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⢏⣴⠄⣀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠙⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⣤⡐⣶⠀⣶⠸⣧⠹⠎⠷⠀⠀⠀⠀⠀⠀⠀⠘⠋⣼⡖⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣶
⢀⡀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⣦⠹⠃⠉
⡄⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⣤⠄⣀⠀⠀⠀⠀⠀⢠⡔⡧⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀⠀⠀⠀⠀⡀⢼⡌⠟⠀⠀⠀⠀⠀⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠐⠛⠰⠟⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⢀⡀⢴⣆⠻⠆⠉⠀⠀⠀⠀⣴⡈⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢼⡇⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠐⢶⡌⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠾⢡⡶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⣆⢸⣆⠹⠇⠿⠜⠇⠀⠀⠀⠀⠀⠀⠀⠛⠡⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢾⠌⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⡖⢠⡤⣠⡄⢀⡀⠀⠀⠀⣄⢻⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡘⠷⠌⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠁⠀⠉⠁⠛⠀⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⣤⠀⠀⠀⠀⢀⡠⣶⠘⠋⠈⠀⠀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢶⡈⠿⠈⠁⠀⠀⠀⠀⣶⠸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠚⢫⣶⢂⣤⠀⠀⠀⠀⠀⠀⠀⠐⢦⠜⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢦⡀⣶⠈⣷⠸⠷⠸⠇⠻⠀⠀⠀⠀⠀⠀⠀⠙⠃⠼⢏⣤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣶
⢀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣧⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢠⠶⠖⠒⢶⡴⠶⠶⠶⣤⡤⢤⡄⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣟⠉⠁⢻⠀⡴⠚⠛⣾⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⣿⠋⠉⠛⣦⠀⢀⣤⣤⡀
⠀⠀⠀⠀⣾⠉⠉⢷⢹⡄⠀⠀⢧⢻⠀⠀⢹⡇⠀⠀⢰⠓⠉⢻⠒⠛⢦⡖⠛⠚⠇⢀⣿⣠⠏⠀⢀⡇
⠀⠀⠀⠀⢸⡀⠀⢈⡷⠧⣤⠀⠘⣿⠀⠀⢸⠉⠉⣧⠼⠤⣤⢀⠀⠀⢸⡇⠀⠀⠀⡏⠉⢹⠀⢠⠾⢤⣀
⠀⠀⠀⠀⠀⢧⠀⡘⠀⠀⢸⣠⠖⠛⢳⠀⢸⠀⠀⢸⠀⠀⢸⠸⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⣸⠃
⠀⠀⣴⠞⢻⡾⡄⡇⠀⠀⠸⡟⠀⠀⢸⣠⡼⠤⡄⢸⠀⠀⢸⠀⡇⠀⠸⡇⠀⠀⢸⠀⠀⠀⠀⡆⠀⢠⡏
⠀⠀⢻⠀⠀⢷⠷⠷⡄⠀⢰⣇⠀⠀⢸⡇⠀⠀⣯⡼⢤⠀⢸⠀⡇⠀⠀⡇⠀⠀⢸⡆⠀⠀⢠⠃⠀⣼
⠀⠀⠈⡇⠀⢸⠀⠀⢃⠐⠋⠉⠃⠀⢸⡇⠀⠀⡇⠀⢸⠀⢸⠀⡇⠀⠀⣿⠀⠀⢸⡇⠀⢠⣸⠀⢠⣧⣤⣤⣤
⠀⠀⠀⢹⡀⠀⣇⠀⢸⢸⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⢸⠀⣾⠀⣿⠀⠀⢻⠀⠀⢸⡁⠀⢸⣇⣠⠾⠖⠂⠉⢸
⣠⣤⣤⡬⠧⠤⠿⢤⠀⡎⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⢸⠴⠛⠒⠛⠓⠛⠛⠉⠉⠉⠉⠉⣙⠉⠀⠀⠀⠀⠀⡾
⢻⠀⠀⠀⠀⠀⠀⢸⠀⢹⡄⠀⢸⠀⢸⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇
⠘⡇⠀⠀⠂⠀⠀⠘⡆⢸⡇⠀⢸⠀⢸⠀⠀⠀⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⢿⠀⠀⠀⠀⠀⠀⠙⢮⡇⠀⢸⠀⢸⠀⠀⠀⣧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡿
⠀⢸⡶⢄⡀⠀⠀⠀⠀⠀⠉⠙⠚⠶⠾⠦⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠁⡇
⠀⠈⡇⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠋⠀⢰⡇
⠀⠀⣷⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⡁⠀⡰⢻⠃
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠘⡍⠓⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⢀⠎⠀⡼⠁⢸
⠀⠀⠸⡗⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠉⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⢸⠁⠂⠀⢀⠟⠀⡾
⠀⠀⠀⣧⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⢸⠃⠀⢠⠋⠀⠀⡇
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡎⠀⢠⠀⠀⠀⢸⠃
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠘⡏⠉⠓⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠇⠀⠀⠀⣼
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⡀⠀⢸⢠⠋⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡾⠃⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠴⠃
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⠉⠉⡉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠀⠀⠀⠀⠀⠀⠘⡧⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⠀⠀⠀⢀⣀⡀⠀⢣⡈⠹⠂
⠀⠀⠀⢠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢼⡀⡠⠞⠛⠀⠀⠀⠀⢣⠠⣄
⠀⠀⠀⠀⢻⣦⣿⢿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢀⣤⣤⣤⣴⠷⠶⠶⠋
⠀⠀⠀⠀⠀⠉⠻⢿⣾⣽⣛⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠹⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠉⠉⠓⢦⠀⠀⠀⠀⠀⡜⠛⢳⠈⠁⠋⠔⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠀⠛⠃⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⢀⡴⠖⠛⢉⡿⠳⢦⡀⠰⣖⠢⣄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠀⢺⣀⣀⠴⠊⠀⠀⠀⠹⡄⠀⠉⠉⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠦⠤⠤⠤⠄⣀⣀⠀⢠⠇⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⢀⣀⣀⣀⣀⡈⠛⠠⣀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⠀⠀⠀⠀⠀⠀⢀⠤⠔⠢⢤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⣤⢤⠀⡠⢠⣄⢀⣄⢀⣀⠀⢠⣤⡀⣠⠄⡤
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠁⠉⠉⠉⠉⠈⠁⠁⠈⠉⠀⠉⠉⠁
⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠊⢳
⠀⠀⠈⠓⠒⢷⠒⠂⠸⠤⠖⠉⠛⣄⢀⡮⣀⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⢀⠎⠈⠙⠒⠒⠒⠒⠋⠁⢀⠀⠀⠀⠀⠀⠀⠘⢉⡆
⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠄⠀⠐⠠⠀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢳⠤⣀⣈⡠⢄⣀⠈⣀⣤⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠀⠈⠉⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠠⠤⣌⠢⡀
⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠉⠉⠉⢨⠀⡠⡖⠁⠀⠀⠀⠀⠀⠈⡖⢄
⠀⠀⠀⡇⢠⠀⠀⡆⠀⠀⡇⠀⠀⢀⡀⢀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡌⠉⠭⠭⠭⠭⠍⠋⠥⠎
⠀⠀⢴⠃⠠⠀⠀⠀⠀⢀⣇⣀⣀⠀⠈⣉⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡀⠀⠀⠉⠳⣄⣠⣄⡀⢸⠉⠙⢏⠙⠛⢡⡟⢦⡀⠀⣀⠄⢢⢧⠄⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⣤⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠘⡏⠉⠀⠰⠚⠂⠀⠀⢴⠋⠂⠄⡀⠀⠀⠐⠂⠤⠔⠒⣁⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠶⣼⣄⣀⠤⢞⡥⠒⡂⠉⠁⠙⠁⠀⠊⠓⠲⠦⣅⠀⠀⠁⠀⠀⠀⠈⠀⠈⠗⠀⣤⠀⠀⣸⡀⠀⠀⠀⠀⠀⢸⠗
⠇⠀⠀⠀⠀⠀⠈⠂⡤⠏⠡⡀⠈⠑⠨⠑⣒⠀⠀⠀⠀⠒⠒⠂⢁⠅⠀⠀⢠⣀⣀⣀⣠⠀⠰⡀⠀⠇⠀⡀⠩⣷⣦⣤⣤⣤⣶⡧
⡆⠀⠀⠀⠀⠀⠀⡔⢸⠁⠀⠘⠢⠄⡀⠀⠀⠰⢁⠀⠀⠀⢀⡠⠂
⠁⠀⠀⠀⠀⠀⠀⣗⠃⣀⠀⠀⠀⠀⠈⠐⠒⠚⡳⣶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡬⠤⠭⢭⡭⠄⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠙⢄⠀⢀⡾⠄⡀⢥
⠁⠀⠀⠀⠀⢀⠞⠁⠉⢦⠤⠉⣽⠂⠠⠐⠚⡦⡀
⠁⠀⠀⠀⠀⠘⡀⠀⠀⠘⢄⣀⠼⡄⠀⠉⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡳⠄⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁
⣶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⢶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠠⡈⢣⡀⠀⢀⣠⡤⠔⠒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣰⣤⣉⣽⣿⣷⠾⠛⠋⣁⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⣒⣒⣀⣙⣾⣿⣿⠛⠉⠉⢉⣁⣤⣴⣾⣏⣋⡉⠉⠙⠛⢶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁⠀⢰⠶⠶⣟⡹⠟⠛⢉⣭⣾⣛⠙⠻⠮⣝⣋⠉⠛⠛⢟⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠒⠈⢁⣠⡴⣮⣛⡛⠓⠛⠻⠶⣤⣀⠉⠛⢭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠤⠒⠉⡘⡝⣽⠁⣰⢯⠉⠓⠓⠓⠛⠛⠻⣦⣄⣉⢦
⠀⠀⠀⠀⠀⠀⡠⠚⠋⠓⠲⠖⠒⠀⢶⡞⠘⣰⢛⣁⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠉⠁⠐⠀⠀⠀⠀⠀⢸⢠⠀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠙⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⠯⠖⣤⣽⣤⣈⣳⣄⣠⣴⠾⠛⠉⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠤⠤⠤⠤⣐⣶⣿⣦⣤⡴⣾⣛⡿⠟⠛⠉⢀⣠⣴⣒⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠽⠒⣒⠀⠊⢉⣉⣉⣻⣿⠟⠋⠉⠉⠉⢀⣀⣠⣤⣶⣟⣛⡛⠉⠉⠉⠉⠛⢯⣭⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠒⠚⠉⠉⠉⣩⢩⣭⣵⡿⠻⢶⣶⠶⠒⠛⣉⣿⠿⠛⠿⣟⣩⠉⠭⠿⠷⠶⠶⢶⠦⢼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣀⠭⠗⠂⠁⢀⣠⣴⣾⣟⣒⠲⢦⣄⠀⠉⠙⠒⢶⡦⠤⠤⠤⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠉⠀⢀⢠⡴⣾⢻⡶⠤⣄⣀⡉⠉⠉⠙⠻⢷⣦⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣏⠴⠒⠋⢁⡜⡰⢡⣏⠠⢐⡶⡌⠉⠉⠉⠉⠉⠉⠉⠑⠿⣦⣄⣀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠿⢒⣶⡦⠤⠬⠤⠤⢤⣤⠎⡼⣁⡾⠗⠊⠀⡀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠥⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⣐⡀⠀⠀⠀⠀⠀⠉⠙⡟⢰⠁⣼⠵⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢉⠃⡎⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⢞⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣱⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣖⣒⣒⣒⣒⣒⣲⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣝⡲⢄⡀⠀⣠⡼⢋⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣚⣵⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⢛⣷⣭⡻⣅⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⢫⣾⣿⣿⣿⣿⣿⠿⢛⣩⣥⣴⠶⠶⠶⠶⠶⠶⣤⣄⣈⠉⠛⠈⢧⡿⠙⢮⡻⣇
⠀⠀⠀⠀⠀⠀⢀⡜⣵⣿⣿⣿⣿⡿⣫⣷⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄⠀⠀⠀⠀⠹⣞⢦
⠀⠀⠀⠀⠀⠀⡼⣹⣿⣿⣿⣿⣫⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠸⡞⣇
⠀⠀⠀⠀⠀⢠⣇⣿⣿⣿⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢻⢹
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢠⡀⢸⢸⠆
⠀⠀⠀⠀⠀⠈⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⣸
⠀⠀⠀⠀⠀⠀⢹⡼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⡏
⠀⠀⠀⠀⠀⠀⠀⠻⡝⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣝⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣫⢶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡙⠶⢭⣗⣲⠤⢤⣀⣀⣀⣀⣀⣀⣠⡤⢤⣒⣮⣵⠞⣋⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣌⡙⢿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣽⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣛⣿⡛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠺⠟⣉⠴⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⣀⠴⢊⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⢀⡴⢚⣡⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⠞⣉⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣀⣀⡀⠀⠀⣀⣠⣴⠾⠋⠀⠀⢀⡾⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⣚⣛⣭⡭⠶⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠲⠶⠭⣭⣛⣛⠿⢯⣄⡀⠀⠀⠀⣸⢃⣾⠁
⠀⠀⠀⢀⣠⡶⣛⣭⠶⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠦⣍⡳⢦⣤⡟⣸⡇
⠀⢀⣴⢟⣵⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣝⢷⣿
⢠⡟⣱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⣆
⣿⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⢿⣎⢷⡀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⣠⠟⣰⡏
⢸⣿⣷⣝⢦⣀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⠞⣫⣾⣿⠁
⠀⢿⣌⠙⠷⣯⣛⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⣫⣵⠞⢋⣼⠃
⠀⠈⢻⣦⠀⠈⠙⠻⢶⣯⣝⣒⡦⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤⠶⣒⣛⣭⡴⠾⠛⠉⠀⢀⡾⠃
⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠉⠙⠛⠛⠷⠶⠾⣿⣭⣭⣭⣭⣭⣭⣭⣭⣽⣶⠶⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠲⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⣋⣥⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣭⣉⣉⣛⣛⠓⠒⠒⠒⠒⠚⢛⣉⣉⣉⣥⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⠒⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣰⠋⠉⠉⠉⣗⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣧⣄⠀⢀⣀⡈⠲⣀⣤⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢘⡷⡆⠀⢠⣄⠁⠀⠋⠀⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⣄⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢰⡬⢤⡤⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⣆⠓⠊⠀⠀⣠⠔⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠒⠉⠀⠀⠹⣷⣄⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢧⡀⠀⠀⢀⡏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠢⠞⠀⠀⠀⠀⠀⠘⢆
⣠⠶⠿⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠦⣤⣀⣤⠖⣫⡥⢭⣑⣶⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠋⠀⠀⠀⢯⠙⢷⡄⠀⢧⡀⠀⠀⠀⠀⠀⠀⣸⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⣦⡀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠘⢾⣷⢄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⡓⠾⢦⣄⣀⣀⠀⣷⣄⠀⠀⠻⣮⠳⡄⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠈⠓⠒⢶⡙⠲⣝⢷⠈⠓⠦⣄⣹⡷⡈⠢⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠹⢤⣈⣻⡆⠀⢀⣀⣩⢃⣷⣄⣈⣳⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠛⠛⢻⠿⠆⠀⠀⠉⡿⠯⢭⣉⣽⣟⣋⣉⣉⣉⣉⣉⣉⣉⣩⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠒⢾⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠙⠲⢤⣄⡀⠀⠀⠉⠳⣶⣦⣤⣤⣤⡤⢤⣤⣤⡶⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠒⠤⢄⣉⠉⠉⠁⠀⠀⢀⣤⣤⣭⣭⣥⣤⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⡤⠶⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣼⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠉⠓⠲⢤⣉⡙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⣰⡄⣄⢠⡀⣼⡇⢸⡇⢢⣰⢠⢠⣠⠋⡿⡶⣤⣬⣙⡶⡦⣶⣀⣠⠂⣼⣦⣾⣾⢦⠀⠀⡀⠀⠀⢉⠧⡎⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠈⠀⠁⢹⠉⢹⡏⠉⠈⠈⠈⠈⠀⠁⠁⠋⠉⠉⠛⠧⢬⣉⠉⠛⠻⠇⢿⢹⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣦⣄⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠺⡆⠀⠀⢸⡀⠀⡆⠀⠀⠀⠀⠀⠀⡏⢹⣧⠀⠀⣠⠞⠋⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢿⠙⣆⢀⡧⣄⣻⡀⠀⢀⣀⠀⠀⣧⠀⡿⣠⡞⠁⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢡⠀⠸⡀⠘⡟⢢⡤⢿⣧⠀⣸⠀⠈⡆⡏⠀⣿⠏⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠻⣄⠄⣜⠓⢄⠸⡆⠀⣻⠾⡇⠀⢧⢸⡿⡄⡇⠀⢠⡇⡇⠀⣸⡶⣶⡀⢀⡟⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡧⢄⠙⢧⠈⡇⠀⠁⠀⢸⡘⡇⢿⠃⠀⣼⢠⡇⣴⠏⠀⣿⠇⣸⠃⣠⠖⣡⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⣾⡆⠹⡀⢸⠀⠘⡇⣿⣸⡇⡼⠹⡈⢻⠃⠀⣼⡟⢷⣿⡞⢁⡔⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣎⢿⠀⣇⠈⡇⠀⣇⢸⣯⣿⠇⠀⡷⣼⠀⣰⣿⠀⣿⡟⣠⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠻⢇⣹⡄⣷⠀⢹⠘⣧⡿⠀⢰⢃⡏⢠⣿⡇⠀⣿⣿⢃⡞⢙⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⣆⠀⠀⠈⠙⠻⢦⡘⡆⢻⡇⠀⡟⣸⠁⢸⣿⡇⢸⣿⣧⣾⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡟⠛⠷⣦⣤⣂⣄⣙⣧⣸⠇⢀⣇⡿⠀⣿⣹⣡⣾⡿⢻⣿⠴⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠶⠤⣽⣆⣈⠉⠙⢻⢿⠷⣾⣾⣷⣶⣿⡿⣫⡿⢿⣿⣿⣴⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠶⠤⣼⣏⡉⠙⠛⢺⡦⢷⣧⣼⣼⣿⣿⠋⣹⣷⣾⣿⣿⡤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠤⣤⣿⣉⠉⠑⠚⡷⠴⣧⣼⣿⣿⡟⢋⣿⡤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢄⣸⣍⠉⠛⠒⡷⠤⣼⣿⣿⡟⠓⠿⠿⠻⢿⣿⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣈⣏⠉⠓⠒⢷⠤⣄⣀⣹⡿⠗⠛⣃⣔⠛⣛⣻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢴⣬⣿⡙⢓⠲⢾⠤⣤⣈⣹⣏⠤⢺⣏⣝⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠿⢷⣤⣦⣼⣧⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⡠⠀⣤⢀⠀⡄⢀⡆⠀⠀⠀⢰⠀⡄⢨⠀⡠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠃⠑⠀⠋⠘⠊⠓⠈⠁⠓⠀⠀⠘⠀⠓⠀⠈⠃⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⣻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠊⠑⠀⢙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⣀⠄⡀⠀⠀⠀⠀⠀⠘⣰⣤⠔⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠋⠐⠲⠟⡩⢆⠈⠀⠀⠀⠀⠀⠀⢇⣀⠀⢠⡴⠂⠸⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣢⣬⣤⡀⠀⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡇⠀⠙⣄⠀⠀⢨⡛⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢣⡀⠀⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠱⣤⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠳⣄⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⣤⣤⣄⣀⠀⣀⣀⡄⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⣴⣻⠃
⠀⠀⠀⠀⢀⣠⣴⣶⣆⠈⣿⡟⢳⡄⠈⢹⣿⠿⠟⠋⢉⣭⣅⣀⡀⠀⠀⢰⢻⣆⡀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢀⣴⡾⢡⡏
⠀⠀⠀⠀⠈⢛⠻⣿⣿⣶⣿⣭⣬⠍⢠⡀⢲⣿⠻⠇⠈⠳⣮⣛⣄⡈⠀⣿⠘⠿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⣼
⠀⠀⠀⠀⠀⠈⢦⡹⣿⣿⣿⣿⣿⠦⣈⠁⣼⠿⠀⠀⠀⠀⠈⣿⣾⢁⣀⡏⠀⠀⣿⣿⣦⣄⠀⢀⣤⣶⣿⡿⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⠛⠛⠛⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⠇⠀⠀⠈⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣜⡻⢿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠒⢲⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⠀⠀⠀⢀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠓⡄⠀⠀⡠⠶⠶⠆⠀⠀⢸⠀⠀⢠⠁⠀⠀⠈⡆
⠀⠀⠀⡠⠒⠓⠘⢦⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣇⣀⣸⠀⠀⠀⠃⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⡇⢀⠴⠶⠦⣄
⠀⠀⠀⢇⠀⠀⠀⠸⠆⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⡄⠀⠀⠀⢸⠆
⠀⠀⠀⠘⡀⠀⠀⠀⢳⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⢰⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⡇⠀⠀⠀⡀⠀⠄⠀⠤⢄
⠀⠀⠀⠀⢃⠀⠀⠀⠘⡆⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⡀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⣷⠀⠀⠀⠀⣏⠼⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠲⣸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⡸⠆⠀⠀⠀⡘
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿⠀⠀⠀⢰⡇⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠸⠃⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⣚⠀⠀⣸⠀⠀⠀⢸⠀⠀⣂⠀⠀⢘⡀⠀⢀⡃⠀⠀⣸⠀⠀⠀⢀⡃⠀⠀⢀⡇⠀⠀⠀⣐⠁
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡄⠀⠠⠀⠄⠠⠠⠐⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠠⣄⠀⠀⠀⠀⠄⠄⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠎⡉⢢⣀⣸⠁⡀⢃⠤⠢⡄⠀⠀⣠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⢹⠎⠀⢀⠃⠄⢙⠀⠀⢸⠀⠒⡞⠉⢲⡅⠀⠸
⠀⠀⠀⠀⠀⠀⠀⡠⠂⢢⠸⠀⠀⢸⢀⡀⣼⠠⠦⣸⢤⡀⣸⢀⠀⠀⠀⢸⢧⠊⡙⢢⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢳⠀⠀⢸⠁⠈⡏⠐⠂⡇⠄⢡⠋⠀⠙⠄⠀⢸⠷⢄⡀⢸⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢣⡀⡆⠀⣸⢁⠄⣰⠀⠀⣼⠀⠀⠸⠒⠢⡇⠐⢀⡇⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣠⣀⣧⣁⣠⠏⠁⠄⢸⢠⠄⠫⣀⣀⢇⠈⠀⡂⠀⡘⡜⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠤⠤⠄⢹⠀⠀⠀⢸⡈⠀⠀⡟⢠⠄⡏⢠⡤⠤⣵⣁⣄⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⣄⠀⢸⡇⠀⢀⠃⠀⢠⣣⠞⠀⠢⠤⠤⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢦⡈⠑⠺⠧⠤⠼⠤⠔⠊⣁⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢳⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠺⡆⠀⠀⢸⡀⠀⡆⠀⠀⠀⠀⠀⠀⡏⢩⣷⠀⠀⣠⠾⠋⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢿⠉⣆⢀⡧⣄⢻⡀⠀⢀⣀⠀⠀⣷⠀⡟⣠⡞⠁⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⢱⠀⠸⡀⠘⡏⠢⡤⢿⣧⠀⣸⠁⠈⡆⡟⠀⢹⠏⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠻⣄⠄⣜⠓⢄⠸⡆⠀⣻⠶⡇⠀⢷⢸⡿⡄⡏⠀⢠⡇⡇⠀⣸⡦⡆⡀⢀⡟⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⡧⡄⠙⢧⠈⡇⠀⠁⠀⢸⡈⡇⢿⠃⠀⣼⢁⡇⣠⠏⠀⣽⠇⢸⠇⣠⠖⢡⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡑⣾⡆⠹⡀⢸⠀⠈⡇⢿⢸⡇⣼⠹⠀⢻⠃⠀⣴⡟⢳⣿⡴⢁⡴⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣎⢿⡀⣧⠈⡇⠀⣇⢸⣧⣿⠇⠀⡷⢼⠀⢰⣿⠀⣿⣟⣠⠏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠉⠻⢇⣹⡄⣷⠀⢸⠘⣧⡿⠀⢰⠃⡏⢠⣿⡏⠀⣿⣿⢋⡞⢛⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣽⣄⠀⠀⠈⠙⠻⢦⡘⡆⢻⡇⠀⡟⣸⠁⢸⣿⡇⢰⣿⣧⣾⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠟⠛⠷⣦⣤⣆⣄⣘⣧⣸⡇⢀⣇⣿⠀⣿⣻⣡⣾⡿⢻⣿⠤⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠶⠤⣼⣄⣈⠉⠙⢻⠿⠷⣾⢾⣷⣶⣿⣿⣫⣿⢿⣿⣿⣤⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⠤⣬⣏⣉⠉⠛⢺⡦⢷⣦⣼⣼⣿⣿⠋⣹⣧⣾⣿⣿⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠷⠤⣤⣿⣉⠉⠑⠺⡷⠴⣧⣼⣿⣿⡟⢊⣿⣤⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡦⢤⣸⣍⠉⠙⠒⣷⠤⣼⣿⣾⡿⢶⠞⣿⡲⠟⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣈⣏⠉⠓⠒⢿⠤⣄⣀⣹⣿⠷⠚⣏⣠⠴⣟⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⢴⣬⣿⡙⢓⠲⢾⠤⣤⣀⣹⣧⠤⢺⡏⣕⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠿⢷⣴⣆⣼⣧⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡀⠠⠀⣤⢀⠀⡄⠀⡆⠀⠀⠀⢰⠀⡄⢨⠀⡤⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠃⠓⠀⠋⠘⠊⠓⠈⠁⠒⠀⠀⠸⠀⠓⠀⠈⠃⠀⠋

⠀⠀⠀⠀⡀
⠀⠀⣠⠞⠛⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⢀⠂⠀⣀⡅
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⠐⠂⠤⠀⠀⠐⠀⠀⢠⠄⠡⠘⠆
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢿⠇⠁⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢠⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣬⣥⣤⣁⡀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⣤⣤⣤⠀⠀⠀⢀⠀⠐⠂⠂⠘⠁
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣶⣿⣿⣷⡰⢏⣿⣿⣷⠀⠀⠀⠀⠂
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣸⢿⣿⠏⠀⠀⡄⢠⡌⢀⠤⠈⡄⠤⠀⣀⢀⣀
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⣾⣿⣿⣿⣿⣿⣿⠁⢿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣳⣿⠂⢤⣀⠀⠒⠁⠄⠀⠒⠀⠀⠊⠁
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⣿⣿⣿⣿⣋⠇⢺⣿⣧⣾⣿⣿⣿⣿⣿⣿⣾⢟⣾⣿⣿⣿⣿⡿⠿⣟⠻⢷⣦⣼⠗⠛⣽⣿⡶
⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣓⡿⣿⣿⣯⣿⣿⠫⣶⣦⠩⠋⢀⠈⠉⠉⡉⠉⠉
⠀⠀⢀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣮⣼⣿⣿⣿⣿⣿⣿⣿⡿⣻⠟⣵⠏⠈⠉⠉⠙⠛⠑⣭⠁⠈⠩⠶⠈
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⣸⣿⡟⣽⣿⣿⣿⣿⣿⣏⣼⣏⣶⡃⠀⢿⣶⣶⣶⢷⣄⠈⠳⣴⡄⠉
⠀⠀⠀⣿⣿⣿⣿⣿⢏⠧⣿⣿⣿⣿⡟⣡⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⡄⢸⣿⣿⡧⠄⠻⣦⡀⠘⢆⠀⠀⡀⢀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⢹⠇⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣴⣿⣿⣇⡀⢓⠈⠻⣷⣈⣵⣤⣤⠀⠀⠠⠈⠁⠀⠀⠀⠀⠄
⠀⠀⠀⣿⣿⣿⣿⣧⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡿⠇⢀⣾⣿⣿⣿⡯⢹⠀⡀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⣸⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⠀⣿⣿⣿⣏⣷⣾⣿⣿⣿⣿⡿⠰⠀⠀⠔⠲⡾⠀⠀⠀⡀
⠀⠀⢠⣿⣿⣿⣟⣼⡿⣿⣿⣿⣿⣻⡿⣿⣿⣿⡟⢿⣿⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠱⠠⢌⠁⠲⠄⠃⡀⠐⠀⠀⠘
⠀⠀⢈⣿⡟⢸⢻⣿⣧⣿⣿⡿⣿⣿⣷⣿⣿⣿⠍⢼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣐⣲⣌⣱⣆⣐⡶⠦⠉⠈⠁⠀⠀⠀⠩
⠀⠀⠸⢻⠇⠳⣾⣇⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⡖⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣯⣽⣷⣶⣦⣤⣤⣤⣶⣶⣿⣿⡿⣿⣿⣷⣶⠄
⠀⠀⠀⡏⣰⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢐⠈⣿⡽⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠿⠿
⠀⠀⠀⠀⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣾⣄⣨⡗⢻⣿⣿⣾⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣒⠦
⠀⠀⠀⠘⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⣿⣿⠾⣯⠁⢿⣗⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢛⡋
⠀⠁⠀⠀⠀⡻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⡇⢀⠸⡇⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⣿⢡⡎⢰⣥⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡟⠛⠛⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠻⠿⠿⠿⠿⠿⢿⡿⣿⣶⢻⣿⠿⠟⡧⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠁⠀⠉⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠁⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣾⡟⠁⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⢾⣿⣥⣀⡀
⠀⠀⠀⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⡄
⠀⠀⢸⣿⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣄⣀⠀⠀⠀⠀⣸⣿
⠀⠀⠸⣿⣿⣦⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⣤⡾⣿⡟
⠀⠀⠀⢻⣧⠈⠉⠛⠻⠿⢶⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⠾⠿⠛⠋⠉⣠⣿⠁
⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⡄
⠀⠀⠀⠀⠀⣀⡀⠘⣿⠀⠀⠀⠀⢸⣿⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⣶⠟⠋⠉⠀⣺⡇
⠀⠀⠀⠀⢸⣿⠛⠻⣿⡆⠀⠀⠀⠈⣿⠀⠀⠀⠀⣽⡇⠀⢀⣀⠀⣿⠀⠀⠀⠀⣿⣷⣤⡀⣀⡀
⠀⠀⣠⣶⠟⣿⡀⠀⢸⣇⠀⠀⠀⠀⣿⡆⠀⢀⣤⣿⠷⠟⢛⣿⠷⣿⡀⠀⠀⠀⣾⡇⠉⢻⡿⠛⢷⣦⣀
⢰⡿⠋⠀⠀⢻⡇⠀⠈⣿⠀⠀⠀⠀⢸⡇⠀⢸⡏⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠈⢻
⢘⣿⣀⣀⣀⣸⣇⠀⠀⢻⡇⠀⠀⠀⠸⣿⠀⢸⡇⠀⠀⠀⢸⡇⠀⢻⡇⠀⠀⠀⣿⡇⠀⣿⣃⣀⣀⡀⣸
⣿⡟⠛⠛⠛⢻⣿⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⡇⢀⣿⡟⠛⠛⠛⣿
⢹⡇⠀⠀⠀⢸⣿⡄⠀⠀⣿⡄⠀⠀⠀⢻⡇⣿⡇⠀⠀⠀⣾⡇⠀⢸⡇⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⣿
⠘⣇⠀⠀⠀⠘⣿⡇⠀⠀⢸⡇⠀⠀⠀⢸⣇⣿⠇⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⡇⣼⣿⠀⠀⠀⢸⡟
⠀⣿⠀⠀⠀⠀⢹⣷⠀⠀⠘⣿⠀⠀⠀⠘⣿⣿⠀⠀⠀⢠⣿⠃⠀⢸⣿⠀⠀⠀⣿⡇⣿⠇⠀⠀⠀⣸⡇
⠀⣿⡆⠀⠀⠀⠀⠻⣧⡀⠀⢿⡆⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⣿⠃
⠀⢸⣧⣤⣤⣤⣤⣤⣽⣷⣄⢸⣧⠀⠀⠀⢻⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⢀⣴⣿⣥⣤⣤⣤⣤⣤⣿
⠀⠸⣿⠉⠉⠉⠉⠉⠈⠉⠙⠿⣿⣄⡀⠀⢸⣿⣀⣀⣀⣿⣿⠀⠀⢀⣿⣶⠟⠋⠉⠉⠉⠉⠉⠉⢹⡏
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⠿⠟⠛⠉⠉⠉⠙⠛⠻⢾⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⡆⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿
⠀⠀⠀⠸⣷⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢸⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⢸⣷⠶⠶⠶⠶⠶⠾⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠿⠶⠶⠶⠶⠶⢾⣿
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣶⣶⣶⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡀⠙⣦⡠⠄⠒⠒⠒⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⣀⠰⡟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⣼⠀⠀⠀⠀⠀⠙⠋⣀⠀⠉⠉⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠉⠲⠄⠒⠉⠀⠀⠀⠀⡄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⠋⠁⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠤⡱⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠹⣦⡈⠋⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣤⣤⣤⠤⠤⠐⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠠⠄⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠸⢡⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠢⠄⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠘⢆⠀⠀⠀⠀⠀⢀⡀⡤⢸⠇⠀⠂⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⣤⠠⠔⠒⠈⠁⠀⣸⢤⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡴⠁⠀⠀⢀⡠⠔⠋⠀⠀⠈⠉⠛⠲⠦⠴⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⡤⠤⠤⠤⠴⠀⠉⠳⢄⠀⠀⠀⠀⢀⡜⠛⠦⢤⡄⠉⠀⠀⢦⣤⣄
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⣠⠊⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠉⠑⠒⠒⠒⠀⠐⠒⠒⠢⣤⠔⠁⠈⠻⣦⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠾⠅⠴⠂⠀⠀⠀⠐⠀⠒⢾⣶⣦⣠⡄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠋⢉⣉⣉⡙⢛⣛⣛⡛⢛⣛⣋⡉⠉⠉⠉⠀⠉⠛⠛⣛⣛⣛⠛⣛⣛⣛⠁⣀⣦⣀⢰⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠿⠉⠉⠁⠘⢋⣉⡟⠸⣏⡉⠟⠀⠀⠀⠀⠀⠀⠸⣿⣩⣿⠺⣿⣭⣿⠺⣿⣭⣿⢿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠦⠤⠴⠦⠤⠬⣭⠤⢤⣤⢤⣤⠤⡤⢤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣭⣥⣤⣈⣉⣅⣸⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⣴⣀⣀⣂⣆⣀⣀⣀⣠⣀⣀⣒⣲⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣿⠍⢹⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⡤⠤⠄⣠⡀⣀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠂⢰⠒⠒⠒⠒⡖⠲⠒⠒⠒⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠧⢤⡤⢤⣤⣤⡤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠙⠲⠤⢧⡀⠘⠒⡤⢄⡀⠠⢄⡀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠛⠛⠋⠛⠓⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡿⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡇⢠⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢹⣷⠀⠀⠀⠀⣸⠉⠙⣶⡄⠀⢸⡇⢸⠇⠀⡟⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡒⠶⠦⣄⠀⠀⣧⠈⢿⣇⠀⠀⠀⣿⠀⢰⣷⡇⠀⣸⠀⣼⠀⢰⠇⢠⡟⢉⡟⢧⠀⠀⠀⣠⠴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⢦⡀⠈⢳⡄⢸⡄⠘⣿⡆⠀⠀⣿⠀⢸⣿⡇⠀⡟⠀⡏⠀⣼⠀⡾⠀⡼⠁⢈⡇⣠⠞⠁⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⣆⠀⠙⢦⣷⠀⢻⣿⡀⠀⣿⠀⢸⢻⠁⢸⠇⢸⠃⢠⡇⣼⠁⣸⠃⠀⣾⠟⠁⢀⡴⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡈⠳⣄⠈⠻⣇⠈⢿⣷⠀⣿⠀⢸⢸⠀⡾⠀⡟⠀⡾⣰⠃⣰⠃⣠⠞⠁⢀⣴⡫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣏⠙⢦⡹⣄⠘⢧⡀⢹⡄⠈⣯⢧⣿⠀⢸⣼⣴⠃⣸⠃⢸⣷⠃⣰⢏⡞⠁⢀⣾⡷⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠈⠳⣄⠙⢮⣳⡀⠻⣄⢳⡀⠘⣎⢿⠀⢸⣿⣏⣠⣏⣠⣿⠃⣰⡿⠋⢀⡴⣫⠏⣀⡴⠞⠋⠉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠈⠳⡄⠹⣿⣆⠘⢮⣷⡀⠘⣿⠋⠉⠁⠈⠀⠀⠉⠙⢳⡟⠀⣰⣫⣞⡵⠚⠁⢀⣠⠴⠚⠋⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡈⠻⣧⡈⢻⣧⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣵⠟⠉⢀⡤⠞⠉⣀⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣱⣤⡬⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⣯⣤⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⢤⣤⣤⣤⣄⣀⣀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣆⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣠⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉