Baleen whale Emojis & Symbols

⠀⠀⣴⡒⠶⢤⣀
⠀⢸⠁⣌⠑⠢⡉⠓⢦⡀
⠀⢸⣿⣸⡠⠄⠘⢶⡀⠉⠳⣄
⠀⠀⢻⣿⣿⡜⣥⠀⠈⢳⣠⡈⠳⣄
⠀⠀⠀⢻⡜⢷⠜⢷⣄⠘⣿⡻⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠻⣦⡣⢡⣻⢷⣎⠋⣦⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠙⢷⣸⣿⣷⠊⠳⡮⢻⠂⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⠳⣜⠢⡁⣇⠀⠀⠀⠈⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠻⣿⣯⠻⡄⠂⢹⠀⠀⢱⡄⠀⠀⠀⢉⠓⠶⠤⣄⣀⣀⣀⣨⠇⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠻⣝⢮⣂⢼⡇⠀⠀⢹⡄⠀⠀⠀⠈⠑⠒⠀⠬⠉⠉⠀⣀⣠⣤⣀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢰⡏⠳⢿⣽⡇⠀⠀⠀⢷⢠⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠈⠙⠲⠤⠤⠼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠈⣧⠀⠀⠀⢸⡆⠈⠳⠦⠤⢴⣒⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠈⡇⠀⠀⠀⠸⡆⠀⠀⠀⡷⠶⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢻⡀⠀⠀⠀⠹⣆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠙⣇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⣴⣦⠀⠑⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣄⣔⠲⠄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⣯⣦⣄
⠀⠀⠹⠙⠹⠟⠖⠠⢌⣉⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠉⠉⠹⢿⣤⣆⡀
⠀⠀⠀⠀⠀⠂⠀⠀⡀⠉⠁⠀⠙⠍⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⣀⠉⠀⠢⢤⠆⠁⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⣀⣀⣀⣠⣀⡀⢐⡶⠋⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢀⣹⣿⡆⠀⣤⠀⠁⢠⣧⣧⣿⣿⣿⣶⣼⣾⣿⣿⡿⢯⠟⠠⢋⣿⣾⣏⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⣒⠤⣻⣿⢿⠀⠻⣷⡒⠒⠛⠛⠙⠙⠻⠿⣿⠟⠋⠉⠀⠀⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⠒⠿⢦⡀⠀⠙⣿⣿⡀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠩⣄⡀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣭⣤⣮⣼⣦⣵⣿⣽⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⠀⠀⠀⢸⡿⠟⠻⠛⠻⠿⡿⣶⣶⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⢻⣿⣟⡿⠧⠶⠶⠶⡦⣄
⠀⠀⠀⠀⠳⣦⣀⠀⠀⠀⠀⠀⠀⠙⣿⣹⣿⣝⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠛⢷⣐⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⠿⡿⣿⣿⡳⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠷⣶⣤⡄⣀⣬⣄⡀⠀⠈⠀⢾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢟⣟⣻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⢥⣬⠄⠀⠰⠮⠁⠠⣤⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣵⣢⣤⣀⣀⠀⠀⣙⣿⠿⣿⣧⣬⣥⠉⠉⠛⠛⠛⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣿⡿⠀⠈⠙⠛⠻⠿⣷⣾⣿⣷⣌⠻⣿⣯⣶⣶⣀⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⣌⠛⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆

⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠁⢸
⠤⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠑⠒⠂⠀⠀⠀⡀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠒⠒⠒⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⢀⣉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠉⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠍⣀⡀⠀⠀⣀⠔⠁⡸⠠⠠⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⣠⠌
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣐⣺⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢒⣒⣯⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢀⣤⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠀⣄⠀⠀⢴⡜⠀⠀⠀⠀⠀⠀⡀
⡆⠈⠙⠢⣀⠀⠀⢀⣀⡤⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣹⣾⠿⠋
⢠⠀⠀⠀⠈⢑⠒⡇⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀
⠀⠁⠀⠀⠀⠘⠀⠁⡆⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣠⢾⠋⢻
⠀⠀⠀⠑⠂⠿⡄⠀⢱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⢠⢫⡞⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠈⠀⠀⢀⡀⠖⣡⣿⠃⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠹⡇⠄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣌⡒⠀⠤⢀⣤⡤⠄⠠⠖⠋⠁⠀⢀⣠⠴⢋⡴⠫⠇⡟⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠋⠴⠚⠁⠀⠒⢳⡇⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡰⢒⡲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠭⠁⣀⣠⣀⣀⣤⣤⡤⠤⠄⠂⠀⠀⢸⡁⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣮⡁⠒⠤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣆⣀⠀⠀⠈⠛⠲⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣄⣴⣿⣿⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⢻⣿⣿⣷⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⣷⢿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⢻⡇⣻⣏⠘⢿⣿⣿⣿⡉⣛⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠘⠛⠀⢸⣿⢿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠁⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣷⣝⣁⡀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣎⣰⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣼⣿⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠇⠀⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠈⠻⡿⠿⢿⣿⣿⡏
⠀⠀⠸⢗⠶⠰⢿⣟⣧⣕⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠘⣿⣿⡇
⠀⠀⠀⠀⠙⢦⣤⣙⠛⠿⠿⣿⣷⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⠀⢀⣸⡶⠂⠊
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣄⣈⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣶⢿⣽⠾⠗⠒⠒⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠤⠤⣴⣶⡾⢋⣿⣏⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣾⣤⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠛⣁⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⢿⡿⣷⣤⣶⣦⣆⡀⡄⠀⠀⢢⣀⠀⠀⠀⠀⠀⣶⣿⣴⡿⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡿⠙⢿⣄⠙⠂⠉⠛⢿⣿⣿⣾⣷⣖⣶⠿⣿⣷⣶⣶⣾⣿⠟⠋⠀⠀⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⢷⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠻⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣛⣉⣉⣭⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠉⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⣥⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠩⢿⣿⣿⠿⣛⣚⣋⠽⠿⠟⠋⠉
⠀⠐⢾⣿⡿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠐⠒⠒⠒⠒⠒⠛⠉⠉
⠀⠀⢸⡿⠃
⠀⠀⠈⠁



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

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣦⣤⣄⣬⡉⣉⣉⣙⣻⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀
⠀⠀⠀⠛⠟⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠿⣷⣿⣤⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⣿⣋⣀⣿⣽⣿⢷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣄⣀⣀⢘⣝⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠋⠁⠈⠉⠘⢿⣿⠁⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠐⠀⠁⠀⠀⠃
⠀⠀⠖⠒⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠂⠀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠂⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠀⠠⡀⢸⠀⠀⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠁⠀⠆⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠁⠀⠀⠀⠘⢣⡅⠸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠄⠀⠀⡤⠊⠀⠐⠀⠀⠀⡠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠂⠐⠒⢁⠈⠀⠀⠀⠀⠀⠰⠁⠀⠀⠊⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠁⠀⠀⠄⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⣠⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⣀⣉⡤⠄⠀⠀⠈⢐⡌⠀⠁⠀⠀⠀⠀⠀⢀⡴⠃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⡤⠀⢀⣠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣊⡄⠀⢀⠴⠂⠀⠁
⠀⠀⠀⠀⢀⠀⡀⠂⠵⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣥⣴⠝⠋
⠀⠀⠀⡰⢡⠠⠊⠀⠀⠈⠙⠢⢄⣀⠀⠀⡀⠀⡀⠀⠈⠁
⠀⠀⠈⢐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐
⠀⠈⣰⠁
⠀⡨⠁
⢀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣇⡀
⠀⠀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣾⣷⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣀⣀⣀⣠⣴⣾⣿⡿⠛⠛⠻⣿⣿⣿⣄
⠀⠐⢿⣿⣿⣿⣻⣟⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⢿⣿⣞⠿⠿⠻⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⠙⠻⠿⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠘⢿⣿⣿⢿⣷⣆⠀⢀⣀⣀⠀⣀⣀⣴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⡀⠀⠀⠈⠻⢿⣿⣿⣿⣴⣿⣿⣿⣿⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⡿⣿⡿⠿⠿⣿⣿⡷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣤⣭⣭⣶⣶⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣃⢀⣀⠀⠀⠀⣼⣿
⠀⠀⠀⢀⣄⡄⡀⢂⣄⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⣶⣴⣴⣿⣿⡟
⠀⠀⠀⢀⣛⣛⣛⠻⠿⢶⣾⣭⣽⣧⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣤⣦⣴⣿⣿⣿⣿⢟⠟
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡻⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⠁⠀⠀⠙⠛⠻⠿⠿⣿⣿⣯⡿⣿⣆⠂⣀⡻⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠛⠉⠉⢸⣿⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈

⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⢠⡀⠀⠀⡀⠈⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠈⠛⠻⣿⣿⣿⣾⡍⣉⣻⣦⣤⣤⣄⣀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠿⣿⣍⣿⣤⣼⣿⣿⡉⠙⠛⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠒⠻⠏⠙⢿⣿⣷⣤⣤⣿⣏⡨⠿⠷⠛⠛⠉⠓⠒⠒⠂⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣇⡀
⠀⠀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣶⣶⣀⣀⣀⣠⣴⣾⣿⡿⠛⠛⠻⣿⣿⣿⣄
⠀⠀⢿⣿⣿⣿⣻⣟⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠉⠻⠿⣿⣷⣿⣿⣿⣿⣶⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⢻⣛⣚⠛⠽⢻⣿⣿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠀⠀⠀⠉⠻⠿⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠶⠤⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣥⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡟⣱⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣾⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢟⣴⣿⣿⣿⣿⡿⣿⡿⣟⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡙⣿⣿⣿⣿⣿⣭⣭⣥⣶⣿⡿⣿⢟⡽⣫⡾⣫⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣛⣿⠽⡫⠖⣫⢞⡯⠞⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠙⠛⠿⣿⣿⣿⣯⣭⣭⣭⣴⣶⠖⠀⠀⠀⢰⣶⣿⣆
⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣷⡀
⠀⠀⠀⢠⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣀⠀⠀⢀⣀⡘⣿⣿⣷⣿⡄
⠀⠀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣿⡄
⢀⣾⡿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡍⠛⠛⠉⠁⠀⠀⠙⢿⣿⣽⡄
⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠤⠐⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠐⠀⠠⠀⠈⢠⠀⠉⠀⠀⢻⠻⣷⣖⠀⢄⡀⠀⠈⠃⠀⣄⢀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠒⠒⠚⢁⣹⣿⠀⠀⠈⠓⢄⠀⠀⠀⠙⠂⡄⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡴⠶⠝⠀⠀⠀⠀⠀⠀⢊⡉⠁⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠐⠂⡀⠀⠐⠂
⠀⠀⠀⠀⠀⣀⢤⡲⠝⠒⢈⣁⣠⡤⠠⣉⠻⣦⠀⡀⠈⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠄⠀⠠⠄⡙⠁
⠀⠀⢀⣴⠞⢋⣡⠴⠖⢛⣩⣭⠔⠉⠉⠻⣷⡙⣷⠀⠈⡩⠁⡀⠀⠀⠀⠀⠀⠀⠒⠉⢁⡄⠀⠐⠀⠀⠈⠳⡀
⠀⡔⢉⣴⣊⡽⠷⠞⠋⠉⠁⠀⠀⠀⠀⠀⠈⢷⣽⠁⢠⠆⠉⠀⠀⠀⠀⠀⢀⡠⠒⠊⠁⠀⠀⠀⠹⡳⢦⡀⠙⢆
⣬⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠚⠁⠀⠀⠠⡨⠒⠋⠀⠀⠀⠀⠀⠀⠈⠢⡱⣄⠀⠠⡀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⡞⠁⠀⣠⠀⠀⠀⠎⣠⠥⡞⣁⠀⠀⠠⡀⠀⠀⠀⠈⠈⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⡴⠊⠀⠀⠀⠀⠀⠁⢚⣝⣁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡈⡁⠀⠀⠀⠀⠀⠀⠀⠈⠺⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠠⣮⣑⡀⣠⠎⠀⠀⢄⠀⠙⠿⣷⡤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠾⠛⢑⠒⠀⠰⠀⠀⠑⢄⠀⠈⠛⠾⢿⣖⣖⢂⡖⣲⣋⠯⠛⢁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡘⠀⠸⢠⠀⠀⠀⠀⠁⠁⠀⠀⢀⠄⠀⠀⠉⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢒⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⢀⠀⠁⠀⣀⠈⠃⢀⠀⠈⠢⣄⠀⠐⠄⡰⢢⠄⣄⡀⣀⡀⠀⠀⠀⠀⠀⢀⠠⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣼⣄⡀⠀⠀⠉⠒⠶⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⡀⠀⠀⠀⡉⠀⠀⡠⠊⠀⠉⠻⢷⣦⣄⠀⠀⢀⣩⣭⣚⠁⢤⣤⠄⢀⣤⡦⣶⣿⡿⡋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠹⣿⠁⠀⡒⠀⠀⠊⠀⠀⠒⣀⢀⡀⠀⠙⠳⢦⣄⣀⠀⢐⣂⣩⡴⠞⠋⠉⠀⠻⠉⠂⠄⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠀⢠⠀⠀⠀⠀⠀⠀⠐⠁⠀⠤⢤⣈⠉⡫⠉⠉⠀⠀⠀⠀⠀⣠⠇⠊⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢄⠎⠋⠂⠀⠀⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡙⠁⠀⣀⠠⠀⣊⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⠀⠃⠀⡀⠃⢀⡉⠒⠂⠂⠉
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂
⠀⠀⠀⢀⣠⣶⣿⣿⣿⢷⣶⣶⣿⣷⣄⡀
⠀⠀⢰⣿⣿⣟⣻⢦⣷⣾⣿⠟⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⢸⣙⡛⡟⠛⢛⡛⠙⠿⣦⡻⣇⢠⠙⢻⡿⢹⠛⠛⠿⠻⢻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠈⢻⣿⣿⣷⣿⣿⣷⣷⣮⣷⡜⣷⢀⣼⢅⣁⠀⠀⠀⠀⠀⠙⠿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣟⠛⢿⣿⣿⣯⣼⣾⣿⡆⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⠁
⠀⠀⢿⣿⣿⣿⣿⣞⣻⣿⣿⣧⣌⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⠿⠿⢿⣿⣦⡀⠀⠀⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⢰⠀⠐⠂⢒⣶⣶⣾⣿⣿⣦⣤⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠋⡉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠷⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣬⡽⠿⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⢄⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠉⣆
⠀⠀⠀⠀⠀⠀⢀⡏⠿⠹⣽⣅⠓⠶⠆⠤⣀⡠⠄
⠀⠀⠀⠀⠀⠀⢀⡆⠀⠈⠙⠟⠤⢄⣀⠸⠏⢠⣾⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣠⢤⣤⡄
⠀⠀⠀⠀⠀⠀⣸⠐⠀⠀⠀⠀⠀⠈⠙⡀⢰⡄⠹⣿⢯⣟⡵⠟⠻⣷⡖⣶⣤⣶⢆⣉⠫⠻⠋⣹⣆⣭⣼⠾⣟⡏⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢽⣇⣌⣙⡇⣨⣞⢙⣻⣟⣿⣿⡟⠋⢀⣤⣸⡾⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠨⠿⢿⠟⠝⠱⢾⣿⣽⡿⣱⡼⣻⡿⠟⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡁⠤⡴⠢⠔⡾⢟⣻⠟⡯⠁⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣤⣤⣤⡌⠒⠀⠤⢀⣴⣿⣿⠟⣤⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⢋⣠⣼⣿⡿⠏⠀⠐⠉⠀⠀⠀⢀⣼⣿⡿⠇⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⣟⣭⠋⢀⣴⠂⠀⠀⠀⠀⣠⣶⣟⠟⠋⠁⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠂⣠⡟⠙⠁⠀⠠⠜⠋⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢇⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣝⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣶⣾⣿⣷⣶⡶⣦⣠⣄⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠟⣛⣹⣿⣿⣿⡿⣿⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⢣⠟⠛⡟⠛⠓⠰⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣾⢠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀
⠀⢀⠀⢠⡄⠀⠀⢠⣿⣿⡿⠁⣶⡿⣆⠀⠀⠀⠀⣶⡶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠐⠟⢼⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣥⠠⡄⠠⠚⢫⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⢸⠷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡶⣣⣴⣧⠈⡟⣿⡿⠟⢹⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⣿⣿⣿⣸⣀⠀⠀⠑⠘⠉⣛⠽⢟⣵⣦⠀⡀
⠘⠻⠯⢭⣷⡶⠿⠿⠿⠿⣿⠿⣿⣿⣿⣷⣿⢻⣤⣤⣶⣿⣧⣦⣿⣿⣷⣿⣷⣿⡷⢦
⠀⠀⣀⠀⠉⠙⠳⠷⠶⣶⣤⣤⣤⣭⡟⠟⣿⣿⣿⣿⡇⣿⣿⢟⣿⠯⣽⣿⡻⢷⣶⣿⣷⣄
⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⣶⡬⠿⣿⣿⣿⡿⣟⣿⣿⣿⣯⣽⣟⠓⢬⣙⣛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣥⣶⣄⣬⠤⠈⠉⠀⠀⠉⠛⢿⣿⣿⣿⠷⣮⣟⣛⠧
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡫⠭⠷⢶⠀⠤⠄⠒⣀⠄⠈⠈⠷⡏⣿⣐⣈⣽⠳⠇
⠀⠀⠀⠀⠀⠀⠈⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣬⣥⣤⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠉⠉⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠈⠀⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣀⣴⣶⣦⣤⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢈⠽⠖⠂⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣯⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣬⣭⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣤⡄⠀⢀⣰⣿⠇
⠀⠀⠀⠶⢦⣬⣴⣶⣒⡶⢶⠦⣶⣤⣤⣀⣤⣀⣄⣀⢀⣀⣻⣿⣿⣿⣿⠟
⠀⠀⠀⠲⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⠟⠿⠋
⠀⠀⠀⠀⠈⠛⠿⠟⠉⠉⠛⠛⠿⠿⣷⣿⣟⣿⣇⢺⣟⡛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠉⠁⣿⣿⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠀⠀⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⡄⡠⠀⣤⡤⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠩⠀⠀⠀⠀⣀⠀⠴⢋⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⡡⠀⠠⢀⠀⣠⣴⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣵⣶⣶⣶⡞⣁⠉⣠⣤⣴⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠟⣉⣭⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣴⣿⡿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⣿⡟⠋⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⢦⡠⠂⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠣⡹⡁⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⣙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠋⠉⠛⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠄⠠⠀⠆⠶⠤⠀⠤⠀⠶⠠⠄⠴⠀⠋⠀⠀⠀⠀⠀⠀⠈⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣀⣀⣀⣀⣀⡀⠀⠀⣠⡄
⠀⠀⠀⢠⣶⣶⣿⣿⣏⣁⡀⢈⣙⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣄⣠⣄⡀
⠀⠀⠀⠈⢧⣀⠈⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢦⣤⣴⣶⣾⠟⠋⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠈⢓⣦⣤⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣠⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⠛⣿⣿⣿⣿⣟⣛⣋⣉⣁⡰⠾⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣆⠀⣀⣀⣀⣀⣀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⣀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣾⣿⣿⣿⣿⢯⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⢀⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠟⣿⠿⠿⠿⠭⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲⣶⣶⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣧⣄⠄⠀⠀⣀⣾⣿
⠀⠀⠀⢰⣦⣠⣌⣠⣤⠤⠤⣤⣤⢤⣤⣄⣀⣀⠀⡀⠀⣀⠀⠀⠈⠹⢿⣿⣾⣾⣿⣿⠇
⠀⠀⠀⢤⣤⣬⣭⣭⣽⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠿⠋⠋
⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⣿⣛⡿⣿⣿⡟⠉⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣉⣉⣻⣿⣿⢶⠻⣿⣀⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠿⠿⠛⠉⠀⠀⠀⢿⣿⣥⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠟

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠤⠒⠚⠋⠉⠙⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⣿⣧⣤⣤⣶⣵⣶⣶⣶⣶⣶⣤⣄⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣁⠤⠤⠄⠝⣿⣿⣿⣟⣿⠿⠿⠿⠛⠿⢿⣿⣷⡄⠀⢘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⠂⠀⠒⠀⠀⣀⣬⣣⡌⢉⡙⢷⠶⣄⠀⠀⠀⠙⣿⣿⡀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⢀⢘⣄⠀⠀⠀⠀⡠⠔⠫⢠⣤⣶⡀⠈⢄⡤⠖⠻⠏⠉⠙⣲⣔⡄⠁⠈⢳⡄⠀⠀⣹⣿⡇⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢳⠻⠌⠛⠹⣇⣤⠁⠤⠔⡡⠈⠈⠩⡎⠒⠑⡄⡎⠉⡃⣉⠙⣆⠁⠀⠀⣷⠀⢀⣽⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⡄⠂⠋⠂⠐⢀⣠⣴⣾⠒⠄⣀⣐⣠⣌⣨⠐⠅⠃⢾⡁⠄⠀⡏⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠤⣾⣿⠿⢁⡢⢶⢊⣙⣁⡂⢩⡍⠳⣞⠀⢡⣗⠀⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠤⠔⣚⠿⣫⠟⢋⠔⠊⠁⠈⠈⠉⠳⢄⠟⠈⢣⠉⣯⣾⣿⣿⣿⣿⣿⣿⠏⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠴⢿⡽⠋⠁⣰⣷⠚⠙⠻⣿⠶⢦⡀⠈⢧⢉⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⢀⣤⠞⠛⣻⠗⠂⢀⣿⣀⣠⣿⣷⡘⣄⡟⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠉⠃⠀⠐⣲⣿⣿⣷⠖⣸⣧⣤⡾⠋⠡⠀⠀⠀⠙⣷⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠴⣚⡽⣿⢦⡾⣾⣿⣿⠏⢀⣤⣶⣶⡲⡶⣼⣿⣿⣿⣦⣀⠘⢻⣿⣿⣿⡿⠛⠛⠋⠈⠙⠋⠉⠉⠙⠻⠍⣙⠋⠙⠻⣿⣿⠋
⠀⠀⣀⣀⡀⠈⠻⢿⣖⣷⢈⣿⣴⡿⠋⠐⠁⢿⡿⣴⣟⣯⠧⠬⣍⣴⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⣩⡁
⠐⠈⠀⠠⢍⣓⠲⠦⣘⣋⡩⠕⠋⡠⠄⠀⢀⣿⣽⠯⣪⠵⠒⢦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠐⠒⠒⠒⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢨⡆⢦⣠⣾⢻⣿⣿⣧⠶⠾⠿⠿⠿⠿⢿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣝⡲⣚⣵⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣋⣁⣀⣀⣀⣉⣈⣉⣀⣀⣀⣒⣒⣀⣀⣀⣀⣸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠂⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣷⣦⣤⡀⠀⢉⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⢯⢿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡝⢿⢸⣾⡈⢿⣿⣿⣿⣙⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠇⠀⠀⠛⠀⢨⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⣤⢀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣼⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠉⠻⣿⣿⣿⣿⣿⣾⣿⡄
⠀⠀⢠⠈⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇
⠀⠀⢶⢤⡄⣿⣿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⠸⣿⣿⠃
⠀⠀⠀⠙⢦⣄⡙⠛⠿⡾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⡿⠀⢀⣦⠆⠐
⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣙⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡾⣻⡵⠗⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠴⠤⠶⠞⣩⡿⣯⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣶⣷⣤⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⡿⢋⣼⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠙⢟⡻⢾⣿⣿⣦⣰⣀⡀⠑⣦⣄⣀⣀⣀⣼⣿⡿⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠁⠹⢷⣄⠀⠀⠈⠛⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠉⠓⠄⠀⠀⠈⢻⣿⣿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⡴⠂⠀⠀⠀⠀⠃
⠀⠀⠰⠶⢤⣒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠁⠉⠄⠀⠀⠀⠀⠈⠑⠾⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢰⡀⠀⠉⡑⣤⡉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⣄⠐⢄⠈⠂⠈⠓⠢⡜⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⢀⡀⠀⠀⠀⡄⠀⠀⣄⡴⠁
⠀⠀⠀⠈⠳⢄⠂⠀⠡⠡⡀⠈⠢⡀⠑⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣐⠁⠀⡶⠋
⠀⠀⠀⠀⠀⠈⠃⠀⠐⡀⠈⢄⠀⠛⠲⠦⢄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠐⢄⠀⠢⠠⡀⠀⠀⠑⢄⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠑⢄⠢⡑⠀⠀⠀⠀⢣⡀⠀⣀⠀⠉⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠐⢌⠢⡀⠀⠀⠀⠑⡄⠛⠛⠲⠀⠀⠀⠀⠉⠙⠚⠲⠷⡶⡶⠶⠾⠿⠿⠟⠉⠁⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠳⣌⠢⡀⠀⠁⠈⠢⢄⡀⠀⢀⡶⠲⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠠⠈⠳⢌⠢⠈⠀⠌⠂⠬⠉⠩⢷⡀⠈⠢⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠑⠠⣁⠀⠀⠁⠀⠀⠌⢷⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⡀⠄⢀⠄⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⠳⣄⣀⡀⠄⠊⢀⠄⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢬⡀⡐⠒⠠⠤⠀⡉⢠⣸⣄⠀⠀⠀⠀⠀⠈⢧⠀⠐⢂⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠈⢹⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⢀⢷⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠎⢇
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡴⠀⠀⠢⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠛⠶⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠑⠾⠻⠗

⠀⠀⠀⠀⣤⣤⣶⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣴⣢⣤⣀⣀⣀⡀⣀
⠀⠀⠀⠀⢻⠟⠍⠹⠉⠍⠛⠻⠿⠿⢿⣿⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⡿⣿⡷⠟⠒⠛⠛⠛⠻⠷⣄
⠀⠀⠀⠀⠈⢿⣾⣠⡁⠀⠀⠀⠀⠀⠀⠙⢿⣍⣿⣷⣽⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣌⠢⡀⠀⠀⠄⠀⠀⠙⠛⠛⢯⣿⣿⣿⣿⣿⣿⣿⣿⡳⣶⣤⣤⣄⣀⣀⠀⠀⣀⣀⣀⣤⣾⣿⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣾⣦⣤⣀⣀⢀⣐⣂⡀⠀⠀⠉⠉⢵⣶⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣟⣏⢑⣍⠉⠉⢈⡲⠤⠀⡀⠠⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣭⣰⣦⣅⠀⠀⠈⢚⠁⠬⠻⣿⣿⣿⣿⡏⠙⣟⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣿⡟⠲⠭⣷⣶⣴⣦⣀⣒⣾⣿⡋⢻⣷⣿⣟⢷⠀⠀⡀⠀⠀⢉⡉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡿⠃⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⣿⣦⡈⠻⣿⣷⣷⣼⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣈⠻⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀



⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣦⣶⣶⣶⣷⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠉⢉⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⣯⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⡟⣯⣿⠏⠀⠈⠹⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⡿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⡀⠀⣠⠾⣿⣿⠃⠀⠀⠀⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣹⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣅⣽⣻⣿⣾⣟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠛⠛⠿⠿⠟⠋⠁⠀⠁⠈⠛⠿⢿⡿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠁




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

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⡀⠀⠙⠛⠛⠛⠻⠻⢿⣿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣄⣀⣀⠀⠈⠀⣀⡀⠀⣀⣤⣶⣿⡿⠿⣿⣿⣷⣦⡀
⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠁⠉⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⡻⠪⠟⠋⠁⠀⠈⠙⠛⠛⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡡⠀⢮⡙⠛⠛⠛⠿⠿⠿⠿⠿⠛⠉⡡⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⣧⠇⠀⠙⢦⡀⠀⣀⣀⡀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠁⡀⠈⠈⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣠⣶⣦⣤⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣀
⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠉⠙⠛⠛⠿⢷⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡎⠻⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⠀⠀⠉⠛⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣍⣹⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣏⣥⣤⣤⣤⣤
⣿⣯⣤⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿