Dyscalculia Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⣀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡶⠀⠨⣿⡇⡧⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠒⣄⡧⣔⡆⢠⡤⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡄⠶⠶⠋⣱⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣖⣢⣿⡟⣟⢺⣝⣋⣡⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢰⢆⡔⠀⠁⡇⣿⣿⡇
⠀⠀⠀⠀⠀⣤⡤⣬⣤⣻⠌⠈⠈⠉⠉⠉⠂⢬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣶⣶⡄⠀⡄⣿⣿⣿⡆
⠀⠀⠀⠀⢀⡤⠛⣹⡃⢧⢂⠙⠀⠈⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠟⢼⠀⠀⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠑⠑⠀⠁⠀⠀⢚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⢪⣰⣜⣦⠀⡇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠆⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⢹⠤⣿⡟⡧⠑⡞⣽⣿⣿⣿⣾⣿
⠀⠀⠀⠚⣎⠑⢀⠈⠲⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠈⢢⣿⢰⠃⠀⡏⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⠀⡄⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠘⠛⠃⠀⠀⠂⣿⣿⡿⣿⣿⣿
⠀⠀⠀⣠⠘⠀⣿⠀⢠⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠒⠫⠤⣀⠀⡱⣿⣿⡻⣿⣿⣿
⠀⠀⠀⢹⠀⢠⣻⠀⠸⡀⢠⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⠠⢰⣿⣿⡇⠀⠀⣀⠀⠀⠀⣠⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠸⡇⢸⡇⢆⠀⠙⠛⠋⣠⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠦⣤⡀⠙⠓⠦⣄⡀⠥⠄⣀⠀⢹⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⣧⢸⡇⠈⠑⠒⠲⡟⠉⠈⡷⠋⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡝⠓⠦⣄⡀⠉⠑⠂⠤⢈⠉⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⠈⣷⣶⣶⣶⣾⣷⣶⣾⣷⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠙⡷⠦⣀⠀⠀⠀⠘⢯⠟⠛⠋⠁
⠀⠀⠀⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠈⠑⠢⣄⢸⣁⣘⠟
⠀⠀⠀⠀⠸⢦⡌⣉⣉⣉⣉⣉⣉⣉⣍⢉⣹⠛⡋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣷⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⣾⢰⠀⠀⠀⠀⠉⠉⠉⢩⠁⠸⣿⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡒⠛⠃⠀⠄⣀
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠀⠀⠂⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠂⠁⠄⠊⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠠⠂⠄⠂⠘⠀⠁⠈⠘⠆⠀⠺⠠⠼⠈⠐⠀⠚
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠠⢀⠀⢀⢀⢀⠀⠀⠄⠀⠀⢀⣀⠀⢠⠀⠀⠀⠀⡀⠄⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⡀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠈⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠀⠤⠔⠒⠒⠠⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣀⠀⠀⢀⣀⠀⠀⢠⣤⠄⣤⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢠⣾⢹⢿⢠⣿⠸⠟⢈⣻⠆⣚⠁⢘
⠀⠀⠀⠀⠀⣀⣀⠠⠤⠀⠆⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠜
⠀⠀⠀⠀⠈⣿⣴⠂⠁⠈⣧⠀⠀⠀⠀⠉⠀⠉⠁⢉⣠⣌⡈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢘⠆⣠⡆⠀⠀⠀⠀⢠⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢻⣷⡈⠄⠈⡘⠛⠻⢦⣄⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠀⡶⠒⣄⢠⡀⢀⠀⡠⠄⢀⡤⠀⠠⢤⠀⢾⠀⣠⠄⢠⠀⣠⠀⡇⢸⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣷⡉⠀⠀⢸⡀⠀⠀⠙⠷⣼⣿⡿⣿⡉⢼⣿⡇⠀⠀⠯⠤⠏⠀⢳⠃⠀⠙⠆⠸⠤⠀⠦⠸⠁⠽⠈⠧⠄⠸⠤⠿⠀⠇⠸⠀⢾⠽⠇
⠀⠀⠀⠀⠀⠀⢸⡿⡷⠀⠀⡠⢁⣄⠀⠀⠀⠈⠉⠋⢉⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⣿⠙⣧⢓⣨⡾⢿⡁⠀⠀⠀⢀⡀⠉⣸⠀⠙⣧
⠀⠀⠀⠀⠀⠀⡟⠀⢻⡿⠋⠀⠘⡇⠀⠀⠀⠈⢩⡍⢹⡄⠀⣸⢧
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⠀⠀⠀⢻⠀⠀⠀⣂⠀⠀⠈⡇⠀⠙⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆⠀⠀⠸⡇⠀⠀⢸⡏⠀⢿⡁
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣷⠀⠀⠀⢿⠀⠀⣼⠃⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢸⡄⠀⠀⠈⠀⠀⠈⠀⠀⠈⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢽⡦⣄⡀⠀⠀⠀⠀⠀⢤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢴⣿⣯⣯⣽⣯⣿⣿⠧⣀⣀⢲⣿⣭⣹⡝⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡖⢱⣶⢨⣶⣖⡞⣷⡼⡦⡖⣻⡇⣖⣶⣦⣶⣶⣖⣶⡖⠒⠂⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣽⣿⣦⡾⣾⡦⠙⠉⠙⠃⠷⢶⣾⣧⠌⠉⠈⠉⠙⠹⠷⣷⣴⣿⡏⡿⠽⣽⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣯⡏⣿⣯⣹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣻⣧⠿⣿⣍⠹⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣻⣻⣟⣻⣟⣽⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⢼⣾⠿⢿⣿⣿⢻⣶⣆⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣸⡾⣿⣟⣻⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣿⣶⡾⢷⣿⣿⣿⣭⣻⣿⣦⡄
⠀⠀⠀⠀⣀⣶⣿⠿⢿⡿⣿⣿⣯⢷⣨⣿⣿⣿⣏⠹⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣯⣭⣽⣿⣭⣥⢸⣴⣾⣿⣯⣿⣿⣼⣿⣿⣿⢧⢤⣄⡀
⠀⢀⣴⣟⣿⡿⣿⣾⣿⣇⣻⢿⣿⣿⢏⣿⡿⣿⢘⣿⣿⢹⣿⣷⣦⠄⡀⠀⠀⠀⣀⡴⠔⣿⡷⠂⠇⠖⠿⠶⠶⡞⣾⡟⡟⢽⡟⣿⠍⣽⣯⡿⣿⠹⣼⡏⣻
⣸⣿⢻⡿⢿⣿⣹⣿⣟⣿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠘⠛⠻⠾⡿⣿⣦⣠⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣋⣾⣻⣽⣿⢹⣻⣿
⢐⡶⣲⣶⣶⣶⣶⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣽⣿⣿⣼⣿⣿
⣶⣶⣾⣾⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡿⣷
⣿⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣶⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⡉⠉⢉⡉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡁⢱⡎⢘⢠⠼⡀⡁⡼⢧⢸⠀⢎⢀⠠⡀⡼⣁⠀⢇⡼⢧


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠖⠀⠀⢛⣛⠂⠀⠚⣛⡋⠀⠘⢏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠀⢸⣆⢸⣶⠀⠠⠌⠀⠀⡈⠯⠉
⠀⠀⢀⡆⢐⢀⡄⠀⠀⠀⠀⠀⠀⠀⣱⡷⢿⡀⢸⠗⢺⡏⠂⢾⢒⠺⠄⣼⠷⡒⡆⠀⠀⡄⢸⠆⢀⠀⠀⠀⠀⢰
⠀⠀⠀⡆⣸⢨⡦⢿⠂⠀⠀⠀⠀⠀⢹⢶⣸⠀⠀⣆⣯⠁⠀⢸⠘⡆⠀⠸⢆⣽⡀⠀⠀⠓⠼⠇⠼⠤⠚⡆⠐⠸
⠀⠀⠶⠿⠟⠾⠛⠛⠛⠉⠀⣀⣀⣄⢀⣷⣿⠀⢀⣘⢣⣶⢠⡠⣶⡧⡄⣤⡧⢹⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠒⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠉⠀⠖⠠⠀⠑⠢⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠶⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡴⠠⣄⣤⢤⣴⠶⡆⡖⢶⣴⡆⣶⣖⠐⣿⣆⢠⣷⡘⢻⡛⢻⣏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠧⠐⠃⠉⠙⡉⣀⣉⣁⢉⣀⡁⣉⣉⣈⣉⣉⣉⡈⢁⣈⠁⠺⠷⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡯⣏⡹⡯⢉⡉⠻⣇⣼⠁⢹⡯⢛⠙⡷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠙⠛⠛⠃⠀⠙⠋⠀⠛⠛⠛⠘⠛⠊⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢒⢒⠀⠈⠁⠈⠁⠁⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⢁⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠡⠒⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠾⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢠⠏⢐⢐⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠡⠡
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢃
⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠸⠈
⠀⠀⠀⠀⡄⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⢄⣀⡀⠈⢀⡠⠦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⢸⢀⡈⢹⣿⢝⡻⢷⣦⣀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡴⢄⠠⠶⣀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⢰
⠀⠀⠀⢀⠌⠀⠀⢸⢿⡤⠬⠖⠞⠉⠁⠈⢀⠀⠀⠀⠀⠀⠀⡇⣏⠟⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠄⠐
⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⣀⢀⠀⠀⠀⠀⠀⠁⠀⠢⠀⢀⡀⢁⠳⡄⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡘
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠰⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⣈⡔
⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠤⠐⠁⠀⠔⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟
⡞⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⠄⠀⠁⠐⠐⠀⠀⠀⠀⠀⠁⠀⣠⠔⠁
⠉⠒⠲⠋⡆⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠰⠖⢒⠞⠉
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⡟⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣄⠀⠀⠀⠀⠻⠀⠈⠉⠁⠀⠀⠀⠀⢄⠢⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⠓⠦⣤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠒⢀⣠⣶⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡉⠒⠓⢰⣿⣿⣿⣾⣿⣿⣿⡟⢀⠀⠠⠀⠐⠴⠂⠀⠀⠀⠀⠀⠀⠀⡠⣄
⡞⢢⡀⡶⢦⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣰⣿⢿⡿⠋⠹⠿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡼
⢿⡀⢳⣇⠈⢻⡆⠘⠄⠈⠀⣀⣤⣶⠿⢿⣿⠀⢀⣿⣿⣀⢀⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠘⠚⠁⡼
⠈⠻⠆⠉⠀⠈⢁⣠⣴⣾⣿⠿⠟⠛⠛⠳⣾⣷⣿⣿⣿⣿⣾⣿⡟⠛⠉⠉⠛⠻⠿⣿⣶⣤⣀⠀⠀⠂⠁⠀⣇
⠀⠀⢀⣠⣤⣾⣿⣿⣿⣭⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠏⠁⠀⣀⣀⣀⣠⣤⣼⣿⣿⣿⣿⣶⣶⡅⠀⠉
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣻⡿⢿⡿⢿⡛⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢀⣴⠞
⠀⠀⠀⠀⠀⠈⣉⣙⣻⣿⣿⣿⣿⣿⡏⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⠿⡿⠟⠛⠋⠁⠀⣰⡆⠀⠈⢀⡼
⠀⠀⠀⠀⢀⡈⠛⠯⣭⣁⣀⣙⣷⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠻⠑⡶⠂⠈⡹⠀⠀⣰⡿⠁⠀⢰⣋⣠
⣶⣶⣶⣶⣿⡿⠂⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠁⠐⠈⠀⠀⢼⡿⠔⠀⠀⠀⠉⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢀⡄⠀⠀⢀⡴⠋
⠿⠶⠄⠀⠀⠀⠀⡔⠒⠢⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣴⣯⡤⢦⣄
⠀⠀⠀⡴⠒⠤⣀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⢀⣽⡁⠘⠉⣀⣠⣾⡿⠂⠀⡀⠀⠀⣀⠠

⠀⠀⠀⠀⠀⣀⠤⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣤⢤⡴⡄⣬⣤⢭⣧⢤⢤⣤⣤⡤⣤
⠀⠀⠢⠖⠡⠀⠀⢠⠀⠀⠐⠈⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡟⠉⠩⠉⠉⠨⠍⠛⠛⠋⠙⠉⠛⠙⠋⠙⠙⡟
⠀⡁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⣄⡀⠀⠀⠀⠀⡇⡇⠘⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠂⠀⠘⠀⠀⡧
⡟⢀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⡇⢀⣈⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⣿
⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠀⡏⠀⠀⠀⣿⢓⣶⣦⣐⣖⣀⣶⣆⣶⣶⣾⣆⣶⣶⣳⣶⣶⣷
⠰⡔⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠉⠈⠉⠈⠀⠀⠁
⠀⠙⢌⠢⠈⠀⠀⠀⠀⠀⠄⡀⢌⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠉⠒⠤⢭⣠⣤⠬⠅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡍⠉⢡⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠿⠿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⢔⡢⠖⠊⢹⡄⠉⠛⠷⣠
⠀⠀⠀⠀⠀⠀⢀⡆⠈⠈⢰⠄⠈⠉⣏⣉⠁⠀⢰⡂⠁⠠⡀⠀⠀⠠⡞⠛⠓⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⢺⠋⠀⠀⠀⢾⡗⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠘⢲⡀⠖⣠⠔⠉⠀⠠⠀⠀⢉⠂⡝⢶⢀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢈⠀⠀⣀⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⡼⠁⢠⣄⠀⠀⠀⢀⡀⠑⠘⡀⠁⠀⠀⠀⠀⣷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡈⠁⠀⠀⠀⠘⠁⠉⠋⠁⠀⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⠀⠉⠳⣦⡞⠋⠀⠠⠀⠁⠀⠀⠀⠀⠀⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠫⢄⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⣐⡅⣀⡀⣀⡠⢦⣔⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠠⠀⠀⠄⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠿⡟⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠒⠒⠂⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠙⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠛⠳⢶⣄⠀⠀⠀⠀⠀⢸⣻⠞⠁⠀⠀⠀⠀⢀⠀⠤⠀⠁⠼⠤⠥⢈⣀⣤⣀⡀
⠸⠧⠥⠴⠦⠤⠄⠄⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠀⠀⠀⠀⠙⢦⣀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠰⠾⠿⠾⠿⠿⠿⠷⠶⠶⠶⠶⠶⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⡄⠀⠀⠀⠀⠀⢻⡇⢀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠘⣇⣾⡿⠁⠀⠀⠀⠀⠀⠈⠉⠏⢈⠁⠁⠀⡀⢀⠀⠀⠀⠙⢏⠁
⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠻⣿⣶⠄⠀⠀⢠⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡅⠀⠈⠂⠀⢀⢸
⠀⠀⠈⠐⠄⠂⠂⠈⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡧⠐⠾⢿⡗⢦⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⡀⠀⠀⢀⡀⠀⣀⠀⠠⢸⠈
⠀⠀⠀⡀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⣰⠀⠠⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⢸⠸
⠀⠠⢁⠄⠀⠀⠀⠐⠀⠑⡄⠀⠀⠀⠀⠀⢀⡎⠀⠀⢀⣔⠁⠀⠼⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠠⠄⢀⠠⡀⠀⠀⡀
⠀⢃⠇⠀⠀⠀⠀⠀⠀⠱⢡⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⡏⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠂⠀⡞⢹⡏⠙⠂⠈⠀⠀⡀⡆
⠀⡀⠃⠀⠀⠀⠀⠀⠀⢈⢨⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠇⠉⣠⢂⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠇⡈⠡⠀⠀⠀⠀⠀⠀⠇
⢠⣗⣐⣒⣆⣓⡒⠚⠒⠒⠚⠆⠀⠀⠀⠀⠈⠠⣈⣀⣠⣤⣼⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠓⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⢀⣤⣞⠁⠀⠀⠀⠀⠈⣉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠿⠦⠴⠷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠻⣿⣶⣄
⠀⠀⠀⠀⢀⣾⣿⣿⣷⣀⣴⣄⠀⠈⠛⠁⠛⠀⠀⠀⠀⠀⠀⠀⢔⡡⢟⢽⣵⢿⡧⡳⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢋⣼⣷⣶⣎⢻⣿⡆
⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⠈⠁⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⠀⢐⡿⠿⢸⣿⠃⠘⢺⡇⠿⢽⡂⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠈⣻⣿⣿⠟⢻⣿⡇
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣾⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣮⡷⣿⡻⠧⡆⢠⠾⢟⣽⢾⣱⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⣭⣭⣴⣾⣿⠃
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⣟⢹⣽⣷⣿⣿⡏⣛⢋⡆⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣝⡾⠷⠟⠻⠶⢷⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠠⢱⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤
⠀⠀⠀⠀⢀⣴⡟⣱⣟⣛⣛⠦⠹⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡠⠘⠖⣸⣽⣭⣿⢽⣶⠀⠀⠀⠀⠀⠀⢸⡀⠀⣸⠀⢀⣠⢤⣶⣶⠤⣄⡀
⠀⠀⠀⠀⣿⡸⠟⡼⢛⠿⠛⠿⠶⠝⢿⢻⡄⠀⠀⠀⠀⠀⠀⠴⠊⠐⠈⢂⢸⢿⣟⣿⢾⣛⣇⠀⠀⠀⠀⠀⠀⠙⡏⠁⠰⡻⠇⣿⣭⣭⣕⡸⣿⣧⡀
⠀⠀⠀⠀⢿⣿⢃⡞⢉⡍⠳⡜⠿⣶⣬⡃⡇⠀⠀⠀⠀⠀⠀⠋⠘⢓⠁⠘⢸⣿⣿⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⢀⡞⣋⡰⣷⣮⣵⣯⣭⣈⠳⢻
⠀⠀⠀⠀⠀⠀⠸⣆⠈⠁⢠⡇⣾⡶⠍⠻⠂⠀⠀⠀⠀⠀⠀⠴⣐⢀⠅⣈⣸⣿⣶⣿⢾⣶⡿⠀⠀⠀⠀⠀⠀⠀⢧⣨⠇⠛⢥⡻⣿⣷⣨⣭⣝⠷⡎
⠀⠀⠀⠀⠀⣠⡾⠋⠛⠛⠋⠲⠶⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠳⡕⢌⠠⠄⢸⣻⡿⣟⢺⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠩⢿⣷⡆
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠶⢀⠙⢿⣿⠿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣻⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⢛⣺⠫⡤⢎⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡁⢈⠀⡰
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠉⢿⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣫⡔⣫⡺⣽⠃⡰⢠⠛⢝⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣡⣯⠀⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⣀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⡻⣸⡏⣾⠉⡂⠸⢠⠀⣕⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠁⠀⣀⠆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⡏⡼⣯⣻⣶⣹⠢⠁⠐⠀⠆⢈⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣾⣿⣼⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢲⡨⣍⢼⣭⣽⠃⡂⢰⢒⢆⡜⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⡳⢶⣻⠦⠬⣄⣈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠛⠋⠙⠛⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣀⠀⠀⠰⠆⠀⠀⢀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠈⠁⠀⢸⡇⠀⠀⠋⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠉⠀⢀⣴⠟⠁⠀⠀⠀⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣠⠈⠁⠀⠀⠀⠀⣀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠁⠀⠀⢰⡆⠀⠀⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⡴⠞⠋





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉⠀⠀⠀⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣷⡄⠀⢤⣤⣠⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠛⣁⣀⣸⣀⡙⠻⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⣩⣷⡾⠟⠛⠛⠛⠛⠛⠿⢶⣿⣙⠛⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡄⠀⠀⠈⠙⢢⣦⡄⠀⠤⠤⠄⢤⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠉⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⠷⣶⣶⣶⣶⡶⠿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣄⠀⠀⠀⣿⣿⣟⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣧⡄⠀⠘⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣷⣶⣝⡛⣿⣷⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠎⠉⠀⣤⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣽⣛⣿⣛⣥⣭⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡿⣿⢫⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡛⠁⢿⣏⡶⡟⣓⣭⢾⢿⣇⠀⠈⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠏⠀⠀⠘⣿⣷⡷⣝⣫⣜⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⢀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠠⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⢠⣤⢤⣤⠀⠀⠀⢀⣬⣿⢿⣿⡿⠿⠻⢿⣿⡿⢟⣯⡄⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣇⣛⣿⠀⠀⠀⢸⣿⣿⡷⠉⠀⠀⠀⠀⠉⢵⣿⣿⣿⠀⠀⠀⣿⢓⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠉⢩⡭⢤⣤⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⢀⣼⣿⣿⠏⢀⣀⣀⣛⠒⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⠀⠀⠈⢻⣿⣿⠀⠀⠀⠀⢾⣿⡿⠃⠀⢸⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠛⠛⠛

⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢿⣿⠇⠀⠀⡐⠀⠂⡀⠀⠀⣚⣿⡇⠀⠰⣿⣿⡷⠀⠀⢘⢤⠜⠀⠀⣿⣏⣽⡇⠀⠀⣺⣇⡀⠀⠀⢪⣥⡄
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠛⠋⠀⠀⠀⠘⠓⠂⠀⠀⠈⠛⠃
⠀⠀⡀⢄⡀⠀⠀⠀⡀⡀⠀⠀⠀⣤⣄⠀⠀⣠⣤⢠⣤⠀⠀⠠⣶⠄⠀⠀⣴⣾⣶⠀⠀⢠⣶⣶⡄⠀⠀⣶⣶⡄
⠀⠀⢷⣿⠇⠀⠀⢨⣥⡅⠀⠀⢖⡟⣟⡆⠀⠹⠟⠈⠁⠀⠀⣿⠀⣿⠀⠀⢹⣿⡿⠃⠀⠸⣯⣽⡇⠀⠀⢹⣿⠟
⠀⠀⠈⠁⠀⠀⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢠⣿⣿⣆⠀⠀⢺⣿⣿⠀⠀⠀⣆⠀⠀⠀⠀⣚⣛⠂⠀⠀⡈⢤⢁⠀⠀⠠⠈⠀⠀⠀⢠⣾⣄⡀⠀⠀⣴⠄
⠀⠀⠻⠿⠋⠀⠀⠸⠏⠁⠀⠀⠀⠀⠰⠄⠀⠀⠹⠟⠁⠀⠈⠃⠀⠘⠀⠀⠈⠈⠁⠀⠀⠈⠹⠀⠀⠀⠀⠿⠒
⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⡀⠀⠀⢀⣤⣄⠀⠀⠀⢠⣤⡀⠀⠀⢀⣤⣀⠀⠀⢀⣀⣀⡀
⠀⠀⢸⢛⠀⠀⠀⣸⣛⣇⠀⠀⠸⣼⣼⠀⠀⠘⣿⣟⣶⠀⠀⢸⣿⡇⠀⠀⢸⣵⣿⠀⠀⠈⠿⠿⠉⠀⢠⡄⠉⢠⡄
⠀⠀⠛⠛⠃⠀⠀⠛⠛⠛⠀⠀⠀⠙⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⠃⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠐⠒⠀⠀⠀⡀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢀⡶⢶⡄⠀⠀⠀⣀⠀⠀⠀⢠⣤⣤⠀⠀⠀⢀⡀⡀⠀⠀⢠⡶⡄
⠀⠀⠀⡂⠀⠀⠀⢽⠻⡣⠀⠀⢰⡦⣶⠄⠀⠈⣿⡿⠇⠀⠀⠘⠄⠆⠀⠀⠈⣿⠟⠀⠀⠨⠿⠻⠇⠀⠀⣵⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠒⠋⠉⠉⠉⠉⠉⠉⠑⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⣀⡤⠴⠒⢚⣉⣉⣉⣉⣉⣉⣉⡙⠒⠲⠤⣄⡈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⡠⠖⢋⡡⠔⠚⠉⠉⠀⠀⡄⠀⠤⣄⠀⠈⠉⠙⠒⠤⣉⠓⠦⣀⠉⠲⣄
⠀⠀⠀⠀⠀⢀⡴⠋⣀⠔⢉⡴⠊⡅⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⢠⡄⠉⠢⣌⠑⢤⡈⠳⣄
⠀⠀⠀⠀⣠⠋⢀⠜⢁⠔⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢄⠙⢆⠈⠣⡀
⠀⠀⠀⡼⠁⡰⠃⡴⠁⠀⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠱⣄⠳⡀⠙⡄
⠀⠀⡜⠀⡼⢁⠞⢠⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠈⢆⠹⡄⠘⡄
⠀⡼⠀⡼⢁⠎⠀⢸⠀⣯⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠹⡄⠸⡄
⢠⠃⢠⠃⡞⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⡆⢳⠀⢳
⡼⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢳⠘⡆⠸
⡇⠀⡇⢸⠀⢀⠄⢦⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⣀⣀⣤⠤⠤⠶⠒⠒⠻⠖⠉⠀⠐⠦⠀⢸⠀⡇
⡇⠀⡇⢸⠀⠈⢃⠟⠛⠧⠼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢄⡼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢘⠀⡇
⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⡇
⢫⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇⢰
⠘⡄⠘⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃⡼⠀⡜
⠀⢳⠀⢱⡈⢇⠀⠀⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠗⢀⠏⣰⠃⢰⠃
⠀⠀⢣⠀⠳⡈⢦⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⠃⢠⠃
⠀⠀⠀⢳⡀⠱⣄⠳⡄⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⡴⢃⡴⠁⣰⠃
⠀⠀⠀⠀⠙⣄⠈⠢⡈⠢⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢀⡠⠊⡠⠊⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠈⠢⣌⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡤⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠑⠢⣌⡑⠲⠤⣄⣀⡀⠀⠀⠣⠘⠀⠀⣀⣀⡤⠴⠒⣉⡤⠖⠉⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡉⠑⠒⠤⠤⣍⣉⣉⣉⣉⣉⣉⡥⠤⠔⠒⠉⢁⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⢤⣀⣀⣀⣀⣀⣀⠤⠤⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣠⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⢟⡛⣿⢿⣿⣿⣿⠖⣽⣿⡿⢿⣿⣿⣿⢛⣛⣛⣛⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢔⡶⣻⣟⢲⡇⣿⣿⣿⣾⣿⣿⡿⣡⣿⣿⡗⣽⡏⣵⡍⢿⣎⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣅⠻⡸⣿⣿⢗⡿⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⡏⡜⣿⣿⣶⢹⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣕⣛⢲⡾⣛⣃⣿⠿⣛⣭⣭⣭⣭⣝⡛⢿⣧⡑⢬⣭⣶⣶⡯⣺⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣫⢻⣿⣿⣷⣶⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣾⣿⣯⡍⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡜⣿⣿⣿⣭⢝⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣴⣿⣏⢿⡏⣾⣿⣶⣟⣛⡿⣟⣫⣶⡜⠇⣿⣿⣿⣧⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⢫⣬⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠳⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡘⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⡤⠄⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⢤⡙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⢰⣦⣭⣭⣭⣶⡆⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⣿⣿⣿⣿⣿⣿⣷⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣷⡹⣜⠿⣿⣿⣿⠿⣣⣯⣾⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣝⣒⣒⣒⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠛⢲⡀⠀⢸⡏⢹⡆⠀⠀⢠⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⠻⡄⠀⠘⣧⣼⡃⠀⢸⡷⠛⠀⠀⢠⡏⠀⡇⠀⠀⢀⡤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣌⠳⣼⠇⢻⡀⠀⢿⠀⢹⡄⠸⡟⣆⠀⠀⡾⠤⣼⠃⠀⢠⠏⠀⠀⠁⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠀⠘⢦⠀⠀⠀⢳⠀⠸⣇⡼⠃⠀⠇⠸⠆⠸⠃⠀⡾⠀⠀⡏⠀⠀⠀⠀⣰⠋⠀⠈
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠙⢦⡖⠀⠀⠈⠳⡄⠀⠈⠁⠀⣀⣤⠤⢤⣄⣠⠤⠤⣤⣀⠀⠀⠀⠧⠴⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣠⠞⢳⣄⠀⠀⠀⠙⢦⣄⡖⠀⠀⢀⡤⠖⠋⠁⠰⣆⠀⠟⠀⠀⢀⡴⠈⠙⠲⣄⡀⠀⠀⢿⣄⠀⠀⠀⠀⠀⢀⣠⠟⢧⡀
⠀⠀⠀⠀⠙⠳⡄⣠⠟⠁⡀⠀⠀⠀⠀⠀⣀⣤⠏⠑⠲⡄⠤⠴⠞⠒⢦⣀⣠⠾⠦⠀⢠⠖⠊⠱⣤⣀⠀⠀⠀⠀⠀⠀⡀⠙⢳⡄⣴⠛⠁
⠀⠀⠀⠀⠀⠀⢹⠇⢀⣰⠷⣄⠀⠀⡴⠋⢡⠞⠁⠀⢀⣷⢤⣤⣀⠀⡴⠋⠀⠀⣀⣠⣯⠀⠀⠈⢳⡈⠓⣄⠀⠀⢀⡴⢧⣀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⢀⡀⠈⠳⡶⠋⠀⡾⣡⠤⠾⠖⠀⢀⡞⠁⠀⠀⠈⠻⣇⢀⡴⠚⠉⠀⠈⢳⡀⠐⠶⠷⢤⡈⢧⠀⠈⠳⡾⠉⠀⢀
⠀⠀⠀⠀⠀⣀⡼⢧⡀⠀⠁⠀⢸⠛⠃⠀⣀⡀⠒⠋⠙⣦⠖⠀⠀⠀⢸⠟⠀⠀⠐⠲⡶⠋⠙⠂⢀⣀⠀⠙⢺⡆⠀⠀⠁⠀⣠⠿⢦⡀
⠀⠀⠀⠀⠀⠉⢳⡞⠁⠀⠀⢀⡼⣦⠤⢾⠡⣄⠀⠀⣀⣼⡀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣧⣀⠀⠀⣠⠜⡶⢤⡴⣇⠀⠀⠀⠀⠙⣶⠎⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡞⠁⢰⡀⠸⣆⠈⣿⠋⠉⠀⠉⠓⠶⠴⢿⡀⠀⠶⠚⠋⠀⠉⠙⣏⠁⣸⠃⢠⡄⠈⣧⠀⠀⠀⠀⠈
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣈⣉⣙⣆⣁⣀⣻⣄⣈⣳⣄⣀⣀⣀⣠⣷⣄⣀⣀⣠⣞⣁⣠⣏⣀⣀⣴⣋⣉⣡⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⣾⡆⢻⠀⡟⠙⠁⣴⠀⣶⠀⢸⠙⡆⠀⣼⠛⡆⠀⣿⠳⡄⠀⢻⠋⠀⡇⠀⡇⠀⡟⠙⠀⢰⠛⣆⠀⣼⠛⠂⠘⡟⠀⠐⢻⠛⠀⣷⢀⡇
⠀⠀⠀⡇⣧⢸⠀⣇⡀⠀⣿⠀⢸⠀⢺⡴⠃⠀⡇⠀⢻⠀⣿⠀⣿⠀⢸⠀⠀⡇⢸⡇⠀⣇⡀⠀⢸⣤⠟⠀⠸⡄⠀⠀⡇⠀⠀⢸⠀⠀⢹⣼⠃
⠀⠀⠀⡇⢹⣸⠀⡏⠀⠀⣿⠀⣸⠀⢸⢷⠀⠀⡇⠀⢸⠀⣿⠀⣿⠀⢸⠀⠀⢿⢸⠇⠀⡏⠀⠀⢸⣷⡀⠀⠀⢹⡄⠀⡇⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⢷⠸⣿⠀⢷⣀⡀⠸⣄⡟⠀⢸⠈⢧⠀⢳⣠⡏⠀⢿⣠⠇⠀⣸⣄⠀⢸⡾⠀⠀⣧⣀⠀⢸⡇⢧⠀⢦⣠⠇⢀⣧⠀⠀⢸⠀⠀⠀⡇





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠈⠀⠐⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣶⣿⣿⣿⣿⡿⠿⣿⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⢿⣿⡿⢻⣿⡇⠒⠈⣿⣿⠿⠿⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡎⣭⢡⣿⣿⡇⠿⠗⣸⣿⣿⠇⣼⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣛⡛⢿⣿⣿⣀⣾⣿⣿⣿⣶⣿⣿⣿⣧⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢣⣾⣿⣿⡿⠿⣿⣿⣿⠟⣋⣙⣻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠈⠙⢻⣿⣟⣿⣿⣿⣿⣷⠗⣸⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣷⣬⣥⣾⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣠⣶⣿⣿⣦⡉⠉⠁⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠀⠀⠀⠻⠿⠋⠉⠛⠿⠏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿⣿⣿⣿⣿⡿⢆⡀⠀⠀⠀⠀⢠⣿⣿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⣿⣯⡡⣿⣿⣦⣀⣀⣀⣛⡻⢃⡞
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⣿⣿⣿⣿⣿⠇⠈⠛⠿⠿⠿⠿⠿⠇⠼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡛⠿⠿⢿⣿⠿⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣶⣶⣶⣆⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⣶⡄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠘⣷⡀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠸⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠶⠶⠶⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀⣰⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⢠⣷⣶⣤⣤⠀⠀⠀⣀⣀⣠⡀⠀⠀⢠⣾⡿⠿⠿⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⡿⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⣉⣉⠁⠐⠒⠈⠉⠉⠁⠀⠒⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣒⣈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⠪⢭⣯⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡶⠤⠤⠤⠬⣥⠤⠔⠒⡶⠚⣁⣴⡠⠴⢠⠀⠀⠀⠀⠀⠈⡓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣹⠇⠀⠀⢀⡏⠀⠀⠀⠈⠉⠁⠀⠀⢀⠈⣆⠀⠀⠀⠀⠲⣌⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠸⢄⡀⣠⠊⠀⠈⠀⠀⠀⠀⠀⠀⠒⠁⠀⠘⢆⠀⠀⠀⣀⡏⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠉⠑⠦⠔⠀⠀⠀⠀⠀⠀⠀⡤⠴⠉⢹⠳⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⠒⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠊⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⢄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠤⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⢍⣙⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⠉⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠰⡪⠗⡋⠐⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⠿⡧⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠠⠼⠄⠐⠉⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠧⢄⣀⣀⣀⡠⠔⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⣉⣤⣴⣀⣀⣀⣀⣀⣀⣀⣐⡂⣄⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⠄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠃⡰⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠡⡘⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡿⠿⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠗

⠀⠀⠀⠀⠀⢀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⠀⠉⠒⠂⠀⣄⠀⠀⠀⢠⠂⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠢⢄⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠅⠠⠤⠄⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡀⠠⠀⠀⠀⡀⡀⢀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠤⠄⠄⠀⠀⠀⠀⠀⢠⡄⡘⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠤⡀⠒⠀⠀⠈⡀⢅⡀⣀⠀⡨⠂
⠀⠀⠀⠀⠀⢀⠎⢁⠟⠁⡰⠁⠏⠀⠑⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠂⡬⢄⠀⠀⣤⣭⣄⡀
⠀⠀⠀⠀⠀⡌⠀⡌⠀⠰⠁⠸⠐⠚⠁⠎⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠚⠶⠁⠣⡀⠀⠀⢀⢻
⠀⠀⠀⠀⠰⠀⢠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡠⠒⠶⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⠀⠰⢤⠤⡬⠆⠀⣐⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⣭⠍⠉⠀⠀⠀⡤⠀⠄⠤⠥⠤⠤⠼⠤⠀⠀⠀⠀⠀⠀⠄⠀⠤⠱⠫⠏⠅⠀⠁⠀⠐⠀⢰⢙⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠺⡉⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠤⠀⠀⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣇⡀⢠⠀⠘⡀
⠀⠀⣀⡀⠀⢀⠃⠀⠐⠣⢌⠁⠀⠀⢡⠀⢀⣀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠘⠂⢤⠤⠀⠐⠒⠖⢺⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣆⣀⣀⣀⣠⣻⣧⣽⡷⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠀⠒⠂⠙⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠃⠘⠛⠀⠋⠋⠒⠘⠘⠙⠛⠃⠘⠀⠃⠋⠃⠛⠀⠃⠘⠓⠛⠈⠛⠈⠳⠀⠛⠐⠓⠋⠒⠃⠈⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠸⠶⠴⡄⠲⠴⠀⠔⠤⠄⠰⠴⠤⠶⠀⠦⠐⠦⠆⠤⠰⠦⠴⣤⠀⡆⠤⢴⠴⠠⠠⠲⠄⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⣿⣦⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⢈⣍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢿⠺⠿⢃⣿⢟⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠻⢹⣿⣿⣇⠘⣫⣤
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠘⣛⣋⣘⡛⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠀⢸⣿⣿⣷⠀⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠷⠹⠿⠿⠡⠿⠿⠿⠷⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠜⠿⠿⠇⠾⠿⠿⠿⠆
⠀⠀⠀⠀⠈⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⠁⠈⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡤⠒⣶⠒⠦⣤⣀⠀⠀⢰⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⣀⡔⠾⣀⠀⠉⠀⠀⠀⠙⢷⣄⣈⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢤⣀⣬⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠹⣿⠂⠀⠀⡱⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⣸⣿⣿⣿⣿⡌⠉⠀⠀⠀⠀⠀⠀⠀⢡⢴⣿⣶⠐⠃⠱⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⣠⣠⣶⣿⢏⣿⣿⣿⡆⢀⡀⠀⢀⠠⠤⠾⣞⠁⠀⠀⢿⡅⠆⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡤⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣾⡓⠀⠀⠀⠀⠀⢫⠀⠀⠉⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⣀⣠⣿⣖⣻⣿⣾⣿⣟⣿⣿⣿⣿⣿⣶⡦⠀⠀⠀⠘⠄⠀⢢⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠸⣶⠀⢸⣦⡾⣿⣤⣔⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠛⠛⠋⠀⠈⠉⠉⠉⣉⣉⣭⣽⣿⣬⣽⠙⠓⠒⠒⠛⠛⠁⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⢿⣿⣿⣷⣦⡀⠀⠀⢀⣴⣾⣿⣿⡿⢿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀⣾⡿⡿⠋⠀⠀⠀⠀⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⢀⣤⣴⣦⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣦⣤⣤⣴⣿⣿⣿⠟⠀⠈⠻⣿⣿⣷⣦⣤⣤⣴⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢶⡶⢦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣶⣶⣶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣀⣭⣭⣚⠀⠈⠑⢦⡀⠀⣴⣾⣿⣿⣿⣿⣿⣟⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋⠁⠀⠀⠈⠙⢦⡀⠀⠙⣾⣿⣿⣿⡟⠉⠀⠀⠈⠹⣦⣀⣸⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⢸⡛⣻⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⡀⠀⠀⠀⠀⣠⠾⢾⣿⣧⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⡼⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠲⠶⢶⣚⡅⠀⢈⡿⠁⠙⢿⣿⣿⣿⣷⢶⣶⣶⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣥⣿⣯⣭⠵⠚⠉⠀⠀⠀⠀⠉⠻⠿⣯⣿⣿⣯⠤⠞⠋

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠤⠀⠀⠀⡤⡤⡄
⠀⠀⠀⠂⠀⠠⣰⠀⠁⡀⠀⠀⠀⠀⠚⣨⣷⡄⠀⠄⠀⠄⠀⠀⠀⠀⠐⡇⡂⢫⠙⢀⢤⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠁⠀⣴⡜⠁⠠⣶⡀⢤⣌⢸⡿⠂⠀⠀⠀⠀⢠⢠⠞⣿⣻⣖⡾⡵⡘⠀⠀⢀
⠀⠀⠀⠀⠀⡆⠀⠐⣇⠵⠂⠀⢰⠥⠬⠿⠞⢧⡰⠄⠀⠀⢀⣼⣸⣿⡿⠿⢿⠿⣦⡶⣞⠊⠍⠛⣷
⠀⠀⢸⣔⣼⠗⠰⣴⠜⠃⠀⢲⠞⢥⠳⠆⠀⠈⠟⣲⠤⠶⠿⠿⡟⣿⢧⠈⢲⠃⢹⡗⣤⢀⢀⣤⢸
⠀⠀⠀⠉⠁⢸⣮⣿⠣⠑⣀⣤⠤⠏⠀⠀⣀⣀⢸⢠⠄⠀⣾⣷⡐⢄⣨⡏⣁⡄⠘⠀⠀⠘⠂⠀⠈
⠀⠀⠀⠀⠀⠁⠉⢀⠑⠀⠚⠛⠂⢄⠃⠀⣿⢿⡿⣍⡑⡔⠿⣿⡵⣿⣿⣿⠇⠀⠀⡀⠀⠑⠀⠔⠀⡀
⠀⠀⣤⣴⠀⠀⠀⢢⠐⢀⣴⡖⢒⠻⢿⣿⡟⠂⣿⣿⢿⣷⣀⢡⢤⠈⢸⠟⠂⠀⣄⢁⠀⠀⠀⡀⡀⠁
⠀⠀⣿⡇⢀⠀⢰⣼⡧⣼⣿⡗⠉⠐⠆⣿⢿⠇⡜⠉⣾⡝⠀⠀⠎⠀⡌⢀⡠⠀⠙⠁⣴⠄⠠⠏⠁
⠀⠀⠹⣇⠐⠐⢢⡿⠁⠸⣿⣧⡴⠖⠀⠇⢸⣜⢀⣐⣛⣁⢀⡀⠀⠀⠃⡍⠃⠀⠐⡖⠑⢨⠅
⠀⠀⠀⠉⠙⠛⢉⠐⢲⠠⠉⢻⠀⢈⡝⠙⠘⢺⣾⣿⡟⢿⠛⠛⠋⠉⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠐⣀⢰⠸⢄⣼⡄⠀⠰⠂⠈⠀⠀⣀⠈⣿⣿⡀⠈⠁⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠛⠋⠀⠈⠛⡁⠀⠀⠀⠒⠈⢀⡇⠀⢻⣿⣷⣼⣀⡀⠀⠐⠃⠄⠀⠀⢰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⢀⣀
⠀⠀⢀⣝⡁⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄
⠀⢀⡞⠟⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⠀⢂⠀⣴⡀⠠⠀⣠
⠀⠀⡈⠀⠀⠀⠀⠘⡈⠢⠀⠀⠖⠜⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠼⠋⠀⠀⠀⢉⡔⠛⠓⢠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⣴⣤⣀
⠀⠀⠁⠀⠐⠄⣤⠀⡁⠀⣰⡄⠀⠀⠀⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠊⡠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠓⠒⠒⠂⠀⡟⢆⣿⠀⡯⠉⠀⢸⠀⢰⠄⣯⣤⠆⣰⠟⢦⢹⠉⢢⢰⡆⢰⡀⡆⣰⣒⠀⡏⢑⡄⠊⠁⢰⠀⠶⣶⠆⣄⠀⣤⠀⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠋⠀⠓⠒⠀⠈⠒⠚⠂⠻⠙⢦⠻⢤⠞⠸⠶⠞⠘⠃⠈⠿⠀⠯⠤⠀⠟⠛⠄⣤⡴⠸⠆⠀⢿⠀⠈⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⢰⠊⢰⠁⢣⢀⠄⡇⠀⢸⠀⡇⡞⠘⠀⠟⠀⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣎⠱⠈⡆⠘⡄⡆⠀⠆⠸⠈⠀⠃⠀⠈⢀⠀⠁⡘⠸⠀⠀⡌⠀⠁⠄⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠣⡹⡄⠰⠐⡀⠰⠰⠀⠘⠀⡄⡄⣀⠀⠀⡟⠀⢀⠁⠃⠀⠀⢣⠀⡜⠀⡜⠀⠘⢄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡑⢵⡘⢄⠇⠰⠠⠆⠃⠀⠉⠀⠈⢀⣀⠀⠀⢀⣁⣀⠀⠀⠂⠜⡜⠀⡜⢀⠄⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠳⠀⠉⢀⣀⣠⣤⣤⣮⣭⣷⢹⣿⣿⣾⣿⣿⣯⣝⣦⢀⣤⣀⠈⠀⢊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⢿⡟⣿⣿⣋⣼⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⣫⣿⣿⣿⣿⣏⡝⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣕⣮⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢿⡿⢑⣿⣿⡟⣽⣿⣯⣧⢻⣿⣿⣿⣿⢹⣿⣿⡿⣿⣿⣿⣿⡿⣱⣷⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣱⣿⣾⣿⣯⣾⣿⣟⣻⣿⣷⣝⢛⡟⢫⣶⣶⣶⣟⣿⣿⣟⣋⢹⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⢿⣿⢿⣿⣿⣿⣿⡿⢞⣻⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣾⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⢼⣿⠈⠿⢿⡿⣨⣾⣿⣿⣿⡿⡿⢿⣿⣧⣭⣽⣶⣿⣿⣿⢟⣽⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⢸⣿⣿⣸⣽⣧⣜⣷⣿⣿⣏⢻⣿⣿⣶⣦⣶⣿⣿⣿⣿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⢿⣿⠿⠛⠿⠿⠿⠿⢿⣛⣋⣽⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠁⠀⠀⠀⠀⢾⢿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢚⠭⡳⡴⠃⠀⠀⠀⠀⠠⠚⠙⠳⣄
⠀⠠⣒⣭⣭⣭⣝⡒⠄⠀⠀⠀⣾⣙⠀⠀⢘⣙⣦⠀⠀⠀⠀⠀⣨⠆⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⢞⡁⣿⣯⣻⡷⢈⡷⠀⠀⣟⢩⡍⢹⢶⡏⢽⠍⡇⠀⠀⢠⢞⠁⢘⠟⠀⠀⠀⠀⢀⠀⠀⡔⠢⣿⣯
⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠘⠒⠒⠋⠀⠙⠒⠚⠁⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣴⣤⡀⠀⠀⢀⢄⠀⠀⠀⢠⠉⠀⠀⠈⢢⠀⠀⠀⠀⠠⢬⣿⣁⢀⠀⠀⠀⠀⠀⢘⣯⣷⣿⡴⠃
⠀⣸⣿⠟⢧⡴⠲⣿⡦⠕⠀⠀⠸⣄⠀⢢⣶⣿⡄⠀⠀⠀⢀⣬⣿⣏⣹⡑⠀⠀⠈⠓⠛⣿⣿⡿⢐⣒⣂
⠊⡻⡟⠛⠃⢽⣾⣿⠇⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⢸⠀⠙⢛⡿⣇⠀⠀⠀⠀⢸⣿⠟⣿
⠀⠈⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣴⣯⠁⠐⠘⢢⠀⠀⠀⠀⠀⣈⣿⣔⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢷⡄
⠀⢸⣿⠙⠦⡆⠈⠁⠀⠀⠀⠀⢸⣛⣛⣿⣛⣻⠄⠀⠀⢰⣿⠛⡟⡟⢿⡿⡀⠀⠀⠀⣠⣴⣿⣾⣷⣄
⠀⢸⣿⡇⢸⡗⠀⠀⠀⠀⠀⠀⠘⣿⣇⣗⣽⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⣿⣹⡟⢹⣏⣿
⠀⠘⠛⠃⠘⠙⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠈⠛⠁⠀⠀⠛⠛⠃⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢠⣾⣷⠶⢤⣄⣀⠀⠀⠀⠀⢀⣤⢴⣷⡦⣄⡀⠀⠀⢀⣤⣤⠤⢸⣹⣝⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀
⠀⢈⠁⠁⠀⣸⣯⡁⠀⠀⠀⠀⠻⢷⣾⣿⣶⠿⠛⠀⠀⠺⣿⣿⣷⡎⢣⣮⠇⠀⠀⢠⣼⣿⣇⣴⣿⣷⣄
⠀⠀⠀⠠⢾⣿⣿⣿⠂⠀⠀⠀⡔⠈⠉⠉⠉⠀⠄⠀⠀⠀⠀⠙⠋⢰⡳⠓⠃⠀⠀⡏⠙⠛⠀⠀⠘⠋⢹
⠀⠀⠀⠀⠀⠙⠙⠋⠁⠀⠀⠘⠓⠓⠒⠛⠒⠚⠛⠀⠀⠀⠀⠀⠀⠘⠚⠒⠀⠀⠘⠓⠓⠒⠚⠓⠒⠚⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠿⠛⠉⠉⠀⠀⠀⡀⠀⠠⠄⠀⢀⠀⠀⠈⠉⠙⠛⠿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⡀⠄⠒⠀⠀⠀⠀⠠⣤⠀⠠⠄⢦⡄⠀⠈⠀⠃⠠⠀⠀⠉⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠀⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⠄⠈⠀⠀⢻⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⠀⢀⣀⣋⣀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⢤⠀⠙⢿⣷⡀
⠀⠀⠀⠀⢀⣼⡿⠋⠀⠄⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠄⠀⠙⣿⣦
⠀⠀⠀⢠⣾⡟⠁⠠⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⢿⣷⡀
⠀⠀⢠⣿⠏⠀⠦⠀⢠⣤⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠆⠀⢻⣷⡀
⠀⢀⣿⡏⠀⡠⠀⠀⢸⡏⠀⣸⡃⠀⢸⡇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠤⠀⢻⣷
⠀⣼⡟⠀⢠⠀⠀⠀⢸⣇⠀⢹⡇⠀⢸⠇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⡀⠈⣿⣇
⢰⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠛⠀⠀⠀⢀⠀⢸⣿
⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⣿⡇⠀⠀⠀⣠⠂⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠃⠀⢿
⣿⡇⠀⠆⠀⠙⠶⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⣬⡀⠀⠀⠶⠀⢹
⣿⡇⠀⢀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣕⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⡄⠀⣿
⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⠀⠐⣿⣿⣿⡟⠁⢀⠀⠀⣿
⠸⣿⡄⠀⠀⠀⠀⠀⢀⡀⢀⡐⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣤⣴⣶⣾⣿⣿⣿⣦⣈⠀⢸⣿
⠀⢻⣷⠀⠙⡀⠀⠀⠸⣆⣠⠃⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⡏
⠀⠈⢿⣇⠀⠐⠀⠀⣴⠉⠙⣷⣰⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠘⣿⣦⠀⠖⠀⠈⠓⠚⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠈⢿⣧⡀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠲⠀⠀⠀⠈⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡈⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠘⣿⡧
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠃⢀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⠠⣿⣿⣿⣿⣿⣿⣿⢠⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠁⢾⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⡇⠈⢻⡆⠀⠀⠀⠀⠀⠘⠂⠈⠁⢠⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣼⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠓⠀⠚⠁⠀⠀⠀⢀⠀⠤⠐⠈⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣧⠁⠉⠀⠘⠂⠀⠉⠀⠀⢀⣀⣠⣤⣶⡿⠟⠋⠁⣼⣿⣿⣿⢿⣿⣿⡏⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⡿⣷⣶⣶⣶⣶⣾⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣏⣻⣿⣦⣈⣏⣙⣿⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣑⣾⣿⣛⣿⣁⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠓⢌⠀⠀⠀⢩⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠲⣇⡄⠄⠀⠁
⠜⡑⠂⠀⠀⢰⠀⢋⠆⠀⢀⣸⠀⠀⠈⠁⠀⠁⠀⠀⠀⣄⡇
⠀⠀⠤⠀⠀⠈⠀⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⢀⠙⠀⠀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁⡞⢰⠀⠈⠀⢠⣶⡵
⠴⠂⠀⢀⠀⠀⠸⠻⠀⢠⢴⠘⢹⠀⠀⠀⠀⠈⠀⠁⠈⠀⠄⠂⠈⠚⠁⠀⠙⠀⢀⣴⠄
⠀⢀⠀⠈⣱⣀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠆⠠⢠⠀⠈⠒⠀⠀⠀⠀⣀⣀⢀
⣘⣉⣱⠀⠉⠠⣀⠎⠉⠀⠀⠀⠀⠈⡁⠀⠈⠀⢀⡈⡁⠀⠀⠀⠀⠐⠀⠚⠐⠀⠀⠤⠄⠐⠀⢻⠟⡑⢫⣍⠀⣄
⠱⠴⠄⠀⠀⠀⠃⠀⠐⢂⠰⡈⡇⠈⠁⠴⢲⡄⠐⠑⠂⠀⠈⠤⠀⠀⠐⠐⣧⠐⠈⠀⠀⡀⠸⡖⡄⠈⠅⣱⠎⣏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠃⠁⠀⠀⠀⠠⡯⠄⠀⠀⠈⠀⠀⠀⣰⠀⠘⠀⠉⠀⢰⠀⡆⢹⠀⠀⠀⠱⡤⡄⢲⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠀⠒⠄⠀⠀⠘⠂⢈⢌⡄⠀⢀⣰⠂⣼⡿⢿⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠸⠂⡘⠧⠀⣀⣹⠀⢰⠱⣐⡍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠀⢴⣿⡏⠲⠙⠻⣧⠈⡿⢿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⡄⠀⠈⢱⠞⠀⢂⠑⣿⣷⢖⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠀⣸⣄⡄⣇⣿⠉⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣉⠀⣔⣯⢴⣡⣿⣷⣟⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⣷⢢⣠⢦⢠⣭⡅⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣦⣙⣸⣉⣼⣎⣠⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣀⣀⣈⠐⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠙⠻⢷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⡟⠀⠀⠀⠀⠀⢤⣤⣤⣄⣀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡘⠀⠀⠀⡰⢻⣆⣌⢛⣦⠀⠘⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢰⣧⣶⣠⣦⣷⣿⣼⣿⣿⣿⠀⢈⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣿⣦⠀⢸⡏⠸⡏⠀⢹⣿⣿⡇⠐⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡇⠀⡇⠀⢸⣿⣿⣷⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣅⣤⣡⣤⣬⣭⣭⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠋⠻⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠾⠷⠒⠒⠛⠛⠛⠛⠿⠦⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠀⠒⠂⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠴⠊⠀⠀⠀⠀⣠⠔⠚⡛⠥⠐⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⢐⠵⠁⠀⠀⠀⡀⠐⢉⠤⠂⠁⠐⠂⠀⠀⠀⠀⡶⠀⡷⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣀⡀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⣠⡖⠡⠀⠐⣄⢳⡀⠀⠀⠀⠀⢠⡄⣿⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠙⢷⣝⢦⡀⠀⠀⠈⢿⣆
⠀⠀⠀⡰⠁⠀⠀⠀⣴⢃⡴⠃⠈⠀⠀⠀⠈⠳⣳⡀⠀⠀⠀⠘⠓⠛⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡙⢶⣿⣦⡀⠄⠈⢿⣆
⠀⠀⡴⠀⠀⠀⢀⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⠈⠀⠈⢻⣿⣿⣶⣆⠀⢿⣆
⠀⢠⠃⠀⠀⠀⠞⠠⠀⠀⠒⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣡⣴⠿⠛⠀⠀⢻⣿⣿⣿⣶⠘⣿⡄
⠀⡄⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⣠⠖⠉⠀⠘⠋⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⢻⣧
⡀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠸⣿
⠃⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣦⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⣿⡇⢿⡇⠐⣿
⠀⠀⠀⠐⣼⡇⠰⠀⠬⠍⠉⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠛⠿⢀⡀⣿⣟⢸⣷⡀⣿
⠀⠀⠀⠘⡎⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⡿⣌⠧⠀⣿
⢠⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣸⣿⡇⢟⠁⢀⣿
⠈⡤⠀⠀⢹⡿⢣⠀⠀⢀⣄⢖⣫⢱⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠠⣄⠀⠀⠀⠀⠀⠀⣾⣿⣶⣤⣦⡀⠀⢠⣿⡻⠼⠞⠀⣸⡏
⠀⠐⢀⠀⠘⣷⡉⣧⡀⡈⠻⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉⠛⠶⠙⠀⢠⡿⡷⢡⠚⠀⣸⡟
⠀⠀⠀⢂⠀⢻⣷⡹⢿⡇⠀⠋⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⠀⢘⣧⡀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣏⡟⣡⠎⠀⣰⡟⠁
⠀⠀⠀⠀⡣⡈⣿⣿⣌⠢⣾⣦⠀⠀⠀⢀⣤⠏⠗⠀⠀⠘⠃⠈⠛⠉⠀⠀⠀⠈⠀⠻⣄⠀⠀⠠⠄⣠⣾⣯⢏⣴⠁⠀⣰⠟
⠀⠀⠀⠀⠘⢷⠈⢿⣿⣷⣝⠿⣷⣄⠀⠈⡉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠈⠂⢀⣤⣾⣯⠟⣡⠟⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢂⠉⢿⣿⣿⣮⡝⢷⣦⢄⡀⡀⠀⠀⠀⠘⠂⠰⡆⡀⠀⠠⠀⡀⣠⡴⣞⠿⠟⢋⣴⡟⠉⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⢻⣿⣿⣿⣷⣮⣘⣤⠉⡀⠐⠒⠂⠤⣤⣤⣶⣶⣶⣿⣿⠿⢞⣋⣴⣶⡿⠗⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣭⣍⣉⣁⣀⣠⣤⣤⣶⣶⣿⢿⢛⣉⢤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠻⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣥⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⣿⣦⡀⡀⠀⠀⠀⣤⣴⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡹⣿⣟⡟⢿⣻⣳⡦⠴⣞⣋⣿⡿⣿⡟⡻⡶⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣏⣙⣇⣞⡿⠿⣼⣳⣛⣚⣳⡛⠛⠛⠯⢃⣗⣠⣘⣿⣿⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣏⣿⣿⢻⡟⠉⠀⠀⠀⠀⠉⠱⠏⠀⠀⠀⠀⠀⠉⠙⠿⠻⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⢻⡿⣯⣗⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⠻⣾⣷⣏⣦⣄
⠀⠀⠀⠀⠀⢀⣠⣿⣷⡷⣻⣶⣱⣦⣮⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣶⣿⣿⡎⣿⣿⣼⣿⣷⢦⡀
⠀⠀⠀⣠⣴⣿⣖⣹⡞⣣⣟⣿⣻⣯⣿⣿⣟⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⢻⣶⣄
⣠⣶⣿⢝⡇⢿⣿⣿⢋⣹⣿⣿⠻⠟⠟⠛⠓⠿⠏⣿⣿⢟⣤⡀⠀⣀⣶⣻⡽⠿⠀⠀⠉⠉⠙⠚⠚⠛⠛⠃⢿⢿⣷⣢⡺⡸⣿⣷⣿
⣼⣷⣯⣭⢿⡯⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⣾⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⣲⣿⣻⣿⣾
⢨⣿⣽⣯⠻⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣭
⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣾⠟⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠏⠀⠀⢠⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠸⠋⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠛⠀⠀⠛⠀⢀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⢀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⣏⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠒⠶⣾⣧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣿⣷⣾⣿⣿⣾⣭⣍⠛⣦⠰⣧⣤⣼⠇⢾⣁⣀⣴⣾⣿⣿⣿⣿⣿⣷⣄⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⡄⢀⡞⣽⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣀⣿⣄⣀⣀⣈⠙⠻⢿⣿⣿⣿⣿⣿⣿⡟⣧⠀⢿⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡿⠀⡾⠀⣿⣿⣿⣿⣿⡟⣉⣤⠶⣛⣫⣭⣭⣿⣿⣿⣿⣿⣷⣶⣿⡟⠻⣿⣿⣿⡇⢸⠄⢸⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⠀⢿⣿⡿⢋⡽⠛⣩⣶⣿⠿⠛⠛⢉⣉⠉⠉⠛⠻⠿⣿⣿⣿⣷⣄⠉⠛⠧⡿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠻⣤⠞⠁⣰⠋⣠⣾⡿⢋⡅⠀⠀⠀⢸⣿⠀⠀⠀⠀⠖⠈⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⣾⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣾⡿⢡⡄⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠴⠶⠀⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢿⣸⣿⡄⠛⠃⠀⠀⠀⠀⠀⠀⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢿⡀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡾⢸⣿⠁⢠⡏⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⣇⠀⠹⣿⣿⣧⠀⡤⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢡⣿⠏⢀⡾⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣦⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⠞⣱⣿⠋⢠⠞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢳⡀⠈⢻⣿⣿⣷⣤⣘⠃⠀⠀⠀⣿⠄⠀⠀⣀⣤⠞⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢻⣿⣿⣿⣿⣶⣶⣶⣶⠶⣖⣛⣭⣴⡿⢿⣯⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠋⠛⠻⠿⢿⣿⣿⠿⠿⠟⠛⠉⠀⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋

⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⣿⡿⠻⣿⠛⡿⢿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠿⠛⢩⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢅⡈⠁⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠘⢄⣋⠖⢠⣝⠁⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⣿⣿⠀⣴⡄⠐⠤⡸⢮⣃⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡟⠀⢹⠻⡟⠀⣜⠊⠀⠀⠀⣀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⢸⡇⠀⢈⣷⡌⣀⠀⠉⠃⢙⣻⣿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⢀⡴⠋⢲⡄⠀⠀⠧⣰⠏⠀⠀⠘⢦⢀⡞⠃⠈⢿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⡿⠉⠛⢿⣿⣿⡇
⠀⠀⠀⢀⡾⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢷⡀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠄⢻⣿⡇
⠀⠀⠀⣼⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢻⡄⠀⠀⣿⡇⠑⠙⢿⡟⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢼⠤⠁⢀⠜
⠀⠀⢠⡟⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⢀⣀⠀⠀⢻⡀⠀⢿⡇⢂⢀⠀⠀⡉⠉⠿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢀⡡⢻⣦⡀
⠀⠀⢸⡇⠀⠀⠀⢈⣗⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⣫⠷⠀⠀⣼⠃⠀⠀⢧⠀⢸⣀⠤⢀⡄⣰⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠦⠤⠾⠃⠙⠆
⢠⣄⠸⡇⠀⣠⠾⡛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠞⠁⠀⠀⢠⡏⠀⠀⠀⠈⠛⠦⣄⣉⣉⠴⠁⢳⣤⡤⢤⣀⠀⠀⠀⠀⠀⠀⡞⠸⡇⠀⠀⠀⢲⡀
⠀⣿⣷⡄⠀⢁⡾⢁⣤⠞⠙⠲⣤⣀⠀⠀⠀⠀⠚⢹⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⠖⠉⢹⠋⠀⢀⣾⠃⠀⠀⠉⠳⣄⠀⠀⠀⠰⡄⠀⠁⠀⠀⠀⠘⡇
⠀⣿⣿⣿⣆⣼⣡⣟⡁⠀⠀⠀⠀⣝⣳⠤⠀⣤⣀⢸⡇⠀⠀⠀⢹⠀⠀⠀⢀⠞⠁⣀⠀⠈⠓⠚⠟⠁⠀⠀⠀⠀⠀⠸⣏⠛⠛⠳⠶⣶⣤⠀⢀⣀⣀⡀
⠀⣿⣿⣿⣿⡄⠈⡌⠉⠙⠲⠦⢴⣿⡀⢠⠀⠀⠙⢦⡀⠀⠀⠀⢸⠀⠀⣶⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⠀⣻⡀⠀⠈⠁⣼⠇⠡⣼⣅⡀⡀
⠀⣿⣿⣿⣿⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⢳⠀⠀⠀⠉⢀⣴⡙⢧⣀⢠⡇⠀⢀⡄⠀⠀⠀⠀⠀⠸⡏⠒⣋⣩⠇⠀⠒⢀⡿⠠⠶⢬⣬⡤⠊
⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣃⡀⡼⠸⡼⡇⣠⠤⠄⠫⡀⠨⢏⠉⢹⡇⠀⡸⣇⡀⠀⠀⠀⢀⡠⠍⠋⠉⡇⠀⣿⣿⠉⣀⠀⠀⠤⢤⣀⣀⡠
⠀⣿⣿⣿⣿⣿⡇⢹⣶⣦⣀⡀⠀⠀⢀⣀⣤⠴⠖⠋⠈⢃⣠⣤⠶⢺⡇⣦⡀⠦⠀⢂⠴⠛⠁⠈⠀⠚⠉⠁⠀⣀⣀⡤⠇⢠⣿⡿⠀⣿⣿⣿⣷⣶⣶⣴⣾
⠀⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⡟⠉⣁⠀⠀⣤⣶⣾⣟⣉⡀⠀⠀⠈⣀⠀⠶⠆⠘⠓⠶⠤⠤⠒⠒⠛⠉⢉⠍⣁⠀⠀⢸⣿⠇⠀⠉⠉⠛⠿⠿⣿⡿⠛
⠀⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣷⣶⣤⣍⡒⠢⠬⣙⠛⠿⣿⣧⣽⣎⣈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣾⠟⠉⠀⠈⠉⠙⠓⢒⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣌⣑⠂⠬⢉⡛⠻⢿⣿⣿⣶⣤⡀⢀⣴⣷⣿⠟⠋⠀⠀⠀⠀⢀⡠⠔⣊⠥⠋
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣉⠒⠠⠍⣛⠻⠿⣿⠟⠋⠀⠀⠀⠀⣀⠤⠚⣡⣴⣾⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣈⣑⠂⠤⣀⠀⣠⠴⢊⣥⣶⣿⣿⣿⣿⠿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣴⣾⣿⣿⣿⣿⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣼⣷⡀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⢀⣾⣧⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣤⣿⠈⠛⠟⠘⠟⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠻⠃⠻⠛⠁⣿⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣛⠉⠀⠀⢠⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⡄⠀⠀⠉⣛⣿⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⡶⠀⠀⠙⠿⠛⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠛⠿⠋⠀⠀⢶⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠷⠀⠀⢀⣀⣀⣀⠀⠀⢀⣤⡶⠟⠛⠛⠻⢶⣤⡀⠀⠀⣀⣀⣀⡀⠀⠀⠾⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⡿⠋⠉⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠉⠛⢿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⢸⣧⠀⣠⣴⣦⣄⣠⣴⣦⣄⠀⣼⠇⠈⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⢹⣿⠋⠀⠀⣽⡏⠀⠀⠙⣿⡏⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣿⣧⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⣠⡿⠃⠙⢿⣄⠀⠀⠀⠉⢛⡂⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⠏⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠙⣷⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠁⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠈⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣿⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠀⠙⠛⠓⠶⣄⣠⠶⠚⠛⠙⠛⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣤⣤⣴⠋⠻⣤⡤⣄⠀⠀⠀⠀⣰⠟⠀⠀⠀⠴⢦⡀⠀⠀⠀⣴⠛⠓⠚⣛⠒⠲⢤⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢘⡧⢀⡴⠶⠶⣄⠀⣾⠁⠀⠀⠀⠰⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡿⠀⢰⡟⣉⢻⡄⠀⠹⣆⠈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡼⠇⠀⢰⡋⠁⣿⠀⠀⠀⠈⡃⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢸⠃⣠⠞⠁⠀⠈⢛⢳⡄⣿⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⢙⡧⠹⢦⣀⣀⠸⠃⣾⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣆⢻⣌⠓⣠⣤⣬⡼⢃⡟⠀⠀⠀⢷⡀
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠘⠷⠶⢶⡄⢠⠖⠶⠞⠁⣀⡴⠖⠛⠋⠉⠉⠉⠙⠛⠲⢦⡀⠀⠙⢦⣍⡉⠁⠀⣀⡀⢈⡇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⡏⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠉⠉⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠉⠙⠋⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢿⡀⠀⠀⠀⢠⡞⠀⠀⠀⣀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠈⢷⡀⠀⠀⡉⠀⠀⠀⠈⢉⡽⠀⠀⣼⠁⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣷⠀⠀⠀⠀⠈⢠⡟⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⣿⠀⢰⡏⠀⠀⠈⠉⠰⢤⣄⣀⣠⡤⠞⠁⠹⡆⣿⠀⠀⠀⠀⠀⠋⠀⠀⢀⡴⠛
⠀⠀⠀⠀⠀⠈⢧⣀⣀⡀⠀⠀⠀⠀⠈⠀⠀⢀⡼⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡀⠀⠀⠀⠀⠁⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣤⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠛⠃⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠚⠓⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢳⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠐⠋⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡀⠁⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠘⢧⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣴⠚⢂⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⣰⠞⢶⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀⠀⠀⠀⠀⡏⠉⠛⠓⠶⠖⠛⠋⠀⣇⠀⠀⠀⠀⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠤⠴⢶⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣷⠶⠦⢤⣤⣄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠻⣌⠳⣄⡀⠀⠀⠀⠀⣀⡴⠋⠸⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣙⣛⠒⢚⣛⣩⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁


⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣏⣈⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣏⣈

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⠁⢾⠉⢲⠐⠀⢹⠉⢀⢷⡀⢸⣉⡆⢰⠀⠠⡏⠁⠀⠰⣉⠀⠉⡏⢰⡉⡳⢰⠊⠑⡆⢲⡔⠀⣏⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣸⣀⣜⣰⣀⣘⣀⣚⣈⣃⣸⣀⣇⣸⣀⣐⣇⣀⣀⣀⣈⣃⣀⣇⣘⣉⣳⣘⣄⣠⣃⣉⣙⣄⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠶⣶⣒⠲⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠲⠶⠶⠶⠦⠤⣄⣀⣀⡀⠀⠤⣄⣀⡀⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⠁⠀⠀⢀⣀⠀⠠⠄⠽⠏⠉⠉⠙⠛⠛⠛⠓⠀⠀⠀⠀⠜⠀⠀⠀⠈⠉⠑⠚⠂⠈⠉⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠰⡊⠀⠀⠀⠀⠀⠀⠛⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡘⢧⠀⠀⠀⠀⣭⠷⠀⠀⠀⠀⣀⠤⠴⠖⠒⠒⠒⠒⠒⠤⢇⢀⣠⠴⠒⠚⠋⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢧⠈⠳⣄⠘⡷⣌⢷⡀⠀⠀⡞⠁⠀⠴⠄⠀⠀⠀⠀⠀⢀⣸⠏⡄⠀⠀⠀⣠⣾⣁⣠⣤⡤⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠈⣯⣷⠀⠀⠙⠒⠶⠶⠤⠤⠤⠄⠒⠚⠉⠙⠲⠶⠶⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠲⢶⣖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣁⠤⣤⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠚⠉⠉⠁⠈⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠒⠒⠚⢛⣻⠿⠓⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⣠⡤⠴⠚⠋⠁⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⣯⡽⠛⠉⠀⢀⣠⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠤⢴⡖⠠⡤⢤⣤⣀⣀⣈⣊⠥⠤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠲⣀⠀⠇⠀⣰⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠙⠳⢤⣸⠀⡤⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⢢⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠲⢤⡀⢀⡍⢹⡇⠀⡉⠑⠒⠒⠒⠒⠂⢸⠓⠃⠀⠀⢀⡀⠀⢰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡀⠀⢙⠛⠀⠘⢦⠀⠘⣦⣄⡀⠀⠀⠀⢺⢤⣄⠚⢳⡏⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢠⡁⠀⢸⡄⠀⠀⢸⠀⠀⠸⡄⠉⠛⠒⠤⢼⡿⠘⠦⡼⠁⠀⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠀⠈⡟⠀⠀⢳⠀⠀⠘⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢠⠋⠈⠉⠁⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠀⢰⠇⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⣧⣴⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣀⡀⣀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠠⣾⣿⣿⣿⣿⣿⠿⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣎⣡⣌⣠⠥⠀⠀⣼⡀⠀⢀⣀⣤⣴⠇⠀⠀⠙⢿⠿⠋⠁⠀⠀⢀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠓⠒⠲⠶⠶⠶⠖⡾⠉⢻⠋⠉⠁⢠⡏⠀⠀⠀⠀⠀⠱⣄⠀⣠⡔⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀⣇⣀⣾⣀⡀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠈⠛⡹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠧⣄⠀⠀⠀⠤⠬⠭⠕⣾⠉⢁⣀⣁⡬⠷⣠⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠈⠉⢓⡶⠶⠒⠒⠋⠙⠣⠍⢡⡀⠀⢐⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠂⠒⠀⠐⠀⠀⠆⠂⠂⠀⠀⠂⠀⠀⠐⠐⠐⠂⠀⠀⠀⠀⠘⠀⠃⠁⠐⠀⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠀⠀⣤⡴⠶⠔⠿⠃⡀⢠⢠⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⡀⠀⢠⡄⠀⢦⣠⣆⠀⠀⠰⠁⠀⠀⠶⠋⢁⡀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠸⠟⡃⠄⢰⣶⠿⢈⣉⣭⣤⣤⣦⣴⣤⣿⣧⣀⡺⠻⣦⣤⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡈⠁⢀⣠⣴⣾⠛⠛⣻⣿⣿⣿⣿⠛⠛⠛⣻⣿⣿⣦⣄⡀⢠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠶⠀⠈⣁⣿⣿⣿⣿⣧⣄⡨⣽⣿⣿⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⣠⡦⢀⣶⣿⣿⣿⣿⣿⣹⣿⡇⠋⠈⠛⠛⠋⠙⠛⠻⣿⣿⣼⣿⣿⣿⣿⣿⣷⣠⣬⠁⠀⠄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⢀⣾⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⣿⣿⣿⣿⣿⣿⡄⢘⡁⠀⠀⢾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠺⢦⣾⣿⣿⣿⣿⣿⣿⣿⢸⣟⠠⣠⣤⣤⣤⣤⣤⣤⣤⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣞⣁⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡄⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠀⠙⢿⣿⣿⣿⣿⡿⣽⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠁⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⡻⠇⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⡄⠀⠙⢿⠿⠉⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡎⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡹⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣙⣿⣿⠀⠀⠈⠀⠀⢠⣿⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⢠⠆⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣷⠀⠀⠀⠠⣾⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⣟⣈⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣞⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⡈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⢶⠄⠘⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⢀⣴⣦⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣿⣿⣿⢋⡄⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠐⢤⡄⠈⢻⣿⣿⣿⣿⣿⢿⣿⣧⣀⣴⣿⣿⡿⢿⣦⣠⣿⣿⢿⣿⣿⣿⣿⣿⡿⠋⢘⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡄⠙⠿⣿⣿⣿⣾⠟⠿⢧⣶⣿⣿⣷⠒⠿⠿⢿⣿⣾⣿⣿⣿⡿⠋⣄⡀⢊⡙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠟⢴⣌⣻⢿⣿⣤⣈⣿⣿⣿⣿⣿⣭⣥⣤⣿⣿⣿⡿⠟⠉⠠⣶⡈⡁⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢨⡿⠻⢂⣤⠉⡙⢻⢻⠿⠿⡿⡿⠟⠛⣛⠉⢡⡄⢀⠛⠀⠂⢀⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠀⠀⠀⠀⠀⠀⢰⣶⡄⠻⠆⠛⢃⣈⡁⠀⠀⣿⣿⠶⣿⠁⠈⠁⣿⠁⠛⠀⠙⠋
⠀⠀⠀⠀⠀⠐⠀⢱⡜⢂⣀⣀⣠⣄⠱⣆⠀⣄⠀⣰⠃⠀⡙⠁⠾⠂⠠⠚⠛⠋⢰⣿⠀⠁⢴⡷⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⢀⣡⣼⣿⣿⣿⡏⣩⣦⣦⣶⣿⣿⡟⠀⠢⠉⠀⠀⠀⠀⠀⡀⠀⠀⠁⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⠤⢴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢠⣶⣦⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣿⣿⡟⣋⠙⣿⣿⣿⠛⢿⣿⣶⡆⣸⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣌⠙⢉⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⡿⢁⣾⣿⣦⣀⣶⣿⡏⣰⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠹⠿⠿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⣿⣿⡄⠛⣋⣹⣿⣿⣿⣿⣦⣤⣬⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣶⡶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢠⣿⣦⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⢡⣤⣬⣤⣬⣤⠘⣿⣿⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⣉⣁⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢋⡀⣍⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠙⠋⠉⢋⣉⠋⠉⠋⠉⠛⠉⠛⠉⠙⠉⠙⠉⣙⣉⠙⠉⠙⠋⠙⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡘⠃⠛⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⡙⠻⠷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡦⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣉⣠⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡶⢛⣻⡟⠶⣷⢦⡀
⠀⠀⠀⣿⢀⣾⣿⣿⣧⣼⣷⢿⣦⡀
⠀⠀⠀⣿⢻⣿⣩⡿⣿⡿⣿⣾⡏⣷
⠀⠀⢰⡟⢿⡿⢷⣾⣿⣥⣿⣿⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠈⣷⠘⢿⣛⣒⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠉⠉⢉⠉⠉⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠈⠳⠶⠼⠿⣿⠋⠉⠉⠀⠀⠀⢀⡴⠟⠉⠀⣀⣤⣶⡿⠿⠛⣁⣬⢓⣴⡗⣀⠈⡁⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⢀⣴⠏⠀⣀⣶⣾⢟⠩⣀⠒⣢⠬⢐⣴⣿⢟⣐⠆⣼⣯⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠄⣶⡿⡋⢊⠀⠵⠔⣂⣥⣾⢟⡫⡀⠇⢆⣾⡟⡹⣿⣧⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⢪⣾⠏⡐⣎⣠⣴⣶⠿⢟⡋⠁⢈⠢⢈⣴⠟⢹⣦⡒⢊⢻⣧⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⢢⡿⢃⣵⡾⢟⣋⠁⠒⠔⣀⣁⣠⣴⠾⠛⠁⠀⠀⠙⢿⣮⠀⢻⣿⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠲⠋⣡⣿⢋⡰⣌⣥⡶⠿⠛⠛⠉⠉⠀⠀⠀⢀⡀⠀⠀⠀⠹⣷⡠⢻⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠋⣰⡿⠅⣣⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⠀⠀⠹⣷⡘⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⢰⡿⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⣱⠟⠀⠀⡦⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢠⡆⠀⠀⠘⣿⣿⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢸⡏⠀⠀⠀⢿⣀⣠⡿⠀⠀⢀⣴⠆⠀⠀⠀⠹⣄⣀⣼⠃⠀⠀⠀⣿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣼⡇⠀⠀⠀⠀⠉⠉⢀⡀⠀⠿⢧⡀⠀⠀⠀⣀⡈⠉⠁⠀⠀⠀⠀⣿⣀⣴⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⢀⣀⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⣿⣿⣶⣌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠐⡇⠀⠀⢠⡾⠋⠉⠙⢳⡄⠀⠀⢸⠇⠀⠀⠀⣰⣟⠰⣀⠽⢓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡼⣟⡻⠿⠾⣆⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠋⠀⠈⠙⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⠟⠛⠛⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⣛⠛⠛⠁⠀⠀⠉⠙⢋⡟⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⡿⠀⠔⠁⠙⠷⣦⡀⢀⣀⣴⡾⠋⠁⠒⡀⢹⡆⠀⠀⠀⢀⣤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢈⣿⠷⠆⠀⠉⢷⡀⠀⢸⡇⢘⣀⠀⠀⠀⣿⠉⠉⠉⣿⡇⠀⠀⠈⣕⠀⣷⠀⠀⣰⠏⠀⠀⠲⢾⣟⡀
⠀⠀⠀⠀⠀⣠⠞⠋⠁⣀⣤⣤⠶⠿⣧⠀⢸⡇⣸⡟⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠈⣿⡀⢻⠀⢠⣿⠷⢦⣤⣄⡀⠈⠛⢦⡀
⠀⠀⠀⠀⢸⣇⣤⠶⠛⠉⠀⠸⣆⠱⠹⣧⢸⡇⣿⡇⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⢸⢀⣾⢓⠀⣼⠁⠈⠙⠛⠶⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢃⢻⣿⡇⢻⣷⠀⠀⠀⣿⡆⠀⠀⢸⡇⠀⠀⠀⣿⡇⢸⣾⢇⠂⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⡆⢻⣇⢸⣿⠀⠀⠀⣿⠁⠀⠀⣼⡇⠀⠀⠀⣿⢃⣾⠃⡌⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⠈⢿⢾⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⢠⣸⣿⣿⠏⡳⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠉⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠀⡠⢀⠀⠄⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⠀⢀⠀⢀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠶⠶⢶⡠⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠳⠶⢶⡶⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠈⠂⠀⠈⠀⡆⠀⠀⠀⢠⠤⠠⠠⠤⠤⠠⠠⠄⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠄⠀⠀⠀⠴⠣⡀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠃⠀⠀⠀⠀⠀⢰⠈⠑⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡆⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁

⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣤⣄⡀⠀⠀⢠⣶⣶⡀⠀⢠⣶⣶⡀⠀⢀⣶
⢸⣿⣿⣧⠀⠀⠀⠀⠀⣴⣿⣿⣦⠷⣦⠄⠀⠀⢄⡄⢠⣿⣿⣿⡄⣿⣿⡿⢃⣀⣀⣘⣿⣿⡇⠀⢀⣿⡟⠁⢀⡸⢿
⢈⣿⣿⡿⠀⠒⢁⣦⠰⣿⣿⣿⠟⣶⣿⣷⡄⠀⠀⠀⢨⣿⡿⠋⠀⣸⣿⣷⣼⣿⣿⣿⣿⣯⣴⣤⣀⣸⣿⠤⠜⠁⢘
⢾⣿⣿⣦⣤⣬⣿⣏⣀⡉⣿⣿⣾⣿⣿⣿⠇⢠⣾⣿⡾⠿⣧⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣤⠀⠀⠉
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⣿⠑⠄⣰⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⣿⣿⠛⠀⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⡆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠠⣶⡆⣠⡆⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢰⡶⢀⣀
⠀⠀⠀⡴⠾⠿⡋⠀⠀⠀⠀⠀⢠⡶⠷⣦⠀⠀⠀⠀⠀⠀⣄⣾⣷⣠⠀⠀⠀⠀⠀⢀⠶⠿⠶⡀⠀⠀⠀⠀⢠⠾⠿⣛⣟⡀
⠀⠀⠀⠇⠀⠠⠇⠀⠀⠀⠀⠀⠰⠆⠀⠰⠆⠀⠀⠀⠀⠘⠋⠿⠿⠙⠃⠀⠀⠀⠀⠸⠆⠀⠰⠇⠀⠀⠀⠀⠈⠐⠘⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⣀⠀⢿⠀⣀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⢰⣿⣧⠐⠀⠄⠀⠀⠀⢀⣾⣿⣯⣿⠶⠆⠀⠀⠀⠀⣸⠉⢉⣇⠀⠀⠀⠀⠀⢻⠂⣿⠀⣿⠀⠀⠀⠀⠀⠀⣫⣿⠳⢆
⠀⠀⠈⠉⠙⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠙⠛⠻⠋⠀⠀⠀⠀⠀⠉⠁⠛⠀⠉⠀⠀⠀⠀⠈⠀⠈⠁⠐

⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠠⢾⡆⢾⡦⠀⠀⠀⠀⠀⢠⣯⣿⣿⡀⠀⠀⠀⠀⠀⣰⣍⡉⣆⠀⠀⠀⠀⠀⠀⣼⡷⠚⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⠗
⠀⠀⢄⣾⡀⣘⣇⠀⠀⠀⠀⢀⠊⣵⣶⡎⠁⡄⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣿⣶⣿⣶⠀⠀⠀⠀⢀⣴⣦⣍⡸
⠀⠀⠀⠁⠁⠉⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁⠉⠉⠉⠁⠀⠀⠀⠈⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄
⠀⠀⣰⣶⡎⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢀⣿⣽⣯⣿⡄⠀⠀⠀⠀⠀⡴⠿⢦⠀⠀⠀⠀⠀⠀⠡⣥⣬⣷⡄
⠀⠀⠙⠛⢻⣿⣿⡇⠀⠀⠀⠀⣠⢿⣿⣶⡄⠀⠀⠀⠀⠀⣏⠀⠀⢸⠃⠀⠀⠀⠀⢠⣗⣠⣼⡄⠀⠀⠀⠀⠀⣠⡾⠷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⢀⣤⣦⣀⠀⠀⠀⠀⠀⣤⣠⣦⣠⡄⠀⠀⠀⠀⠀⠠⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⣲⡀⠀⠀⠀⠀⠀⠀⡀⢠⣤⡄
⠀⠀⢸⣟⠿⢿⡻⠁⠀⠀⠀⢠⣾⣴⣛⣾⣷⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⣬⠉⣥⠀⠀⠀⠀⠀⠀⠄⠈⢻⣷⣄
⠀⠀⠘⠋⠛⠙⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠾⠷⠾⠷⠀⠀⠀⠀⠠⣿⠿⡿⠿⣿⠄⠀⠀⠀⠀⠀⠶⠾⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣶⣿⠆⣿⣿⣿⣿⡏⠉⠁⠉⠁⠈⠀⠉⠉⠉⠁⠉⠁⠉⢹⣷⣶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⢿⢧⣿⣟⣛⡿⣧⣤⡤⠤⠤⠤⠤⠤⠴⠤⣤⣄⣠⣤⣼⣿⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡇⢸⠷⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠿⠙⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⡈⠋⠀⠀⠀⠀⠀⢶⣾⠡⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢄⠀⠀⠀⠀⢀⡾⠁⠁⠀⢀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣾⣿⠀⠀⠀⠀⠀⢄⠀⢀⡮⠊⠀⠀⠀⠈⠷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⢿⣷⠀⠀⠀⠀⡀⠈⢸⠀⠑⠀⠀⠀⠀⠀⡾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠈⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⡀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠣⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠈⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⡃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠑⢾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡇⣸⣦⢤⣤⡤⠀⠀⠀⠀⠀⠠⠧⣴⣃⠐⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣾⣾⡞⣿⣯⣽⣷⡟⠛⠳⠒⠒⠒⠒⠲⠖⠒⠛⠋⠑⠛⢻⣷⣶⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠿⣿⢆⣿⣿⣿⣿⣇⡀⠀⠀⡀⢀⠀⠀⢀⡀⣀⣀⣀⣀⣸⣿⠿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛

⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⣼⣿⣿⢆
⠀⠀⠀⠀⠀⣾⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣾⣶⣦⣤⣀
⠀⠀⠀⠀⢠⣼⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠠⠤⠤⠅⠤⠬⠤⠬⠄⠀⠀⠀⠀⢸⣿⣿⡟⠉⢿⠟⠙⣿⣿⣿⣆
⠀⠀⠀⠀⣾⣿⣿⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⢐⡖⠐⡒⠐⠂⠒⡒⠒⠂⡂⠀⠀⠀⠀⠈⣻⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠹⣿⣿⣯⣭⠁⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠬⠠⡅⠅⣄⠤⠤⠄⠀⠀⠀⠀⠀⣿⣿⡏⠀⢠⡄⠀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠐⠒⠐⠂⠂⠛⠒⠒⠂⠂⠀⠀⠀⠀⣸⣿⢠⣄⣺⣷⠀⣿⡿⠟
⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⠠⠬⠤⠤⠅⠤⠤⠤⠄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⢰⡏
⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣿⡗⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛
⠀⠀⠀⠀⠀⣙⡔⠋⠁
⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣆
⠀⠀⠀⢀⣤⣰⣿⣶⡆⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⢀⣀⡀⡀⣀⢀⠀⡀
⠀⠀⠘⢿⡷⣿⣿⡛⠀⠀⠈⠁⠻⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠴⠶⠴⠦⠤⠶⠶⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⣘⡃⢒⣙⢘⢂⡂⡓⣉⠂⡀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠻⣿⣿⣿⢛⠛⠀⠀⠀⠀⠀⠀⠀⠤⡥⠠⠤⢨⠄⠄⡤⠤⠄⠀⠄
⠀⠀⠀⣰⣶⣦⣤⣤⣴⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣚⡃⢈⣃⢘⣂⡂⡃⣉⠂⡁⡀
⠀⠀⠀⠹⣿⡿⠋⠁⣷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠬⠅⠠⠤⠸⠀⠄⠅⠤⠄⠂⠄
⠀⠀⠀⠀⠈⠁⠀⠈⠃⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⠒⠘⠀⠂⠃⠂⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⣿⡀
⠀⠀⠀⠤⠤⠤⠤⢤⠤⠤⠤⠦⠤⠀⠄⠀⠀⠘⢿⣿⣿⡿⢿⣿⣿⡁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣥⡍
⠀⠀⠀⣓⠀⢀⡓⠐⡀⠀⠃⡀⠀⠀⡃⠀⠀⠀⢸⣿⣿⣿⣷⣌⢻⣷⡀⠀⣴⠇⠀⠀⠀⠀⠀⠀⣻⣿⣿⡟
⠀⠀⠀⠬⠄⠠⠤⠤⠤⠤⠤⠤⠤⠀⠄⠀⠀⠀⠸⣿⣿⣿⣟⠛⠀⣼⠟⠱⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟
⠀⠀⠀⣒⠃⢐⡒⢒⡒⢊⣛⡓⢂⠀⡀⠀⠀⠀⠸⣿⣿⣥⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿
⠀⠀⠀⠬⠇⠠⠤⠰⠤⠠⠦⠄⠤⠀⠄⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢺⣿
⠀⠀⠀⣒⠂⢘⡒⢘⡒⢀⣒⣓⢂⠀⡀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠚⠉
⠀⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣗⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣉⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢹⡍⣠⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⡗⠀⠀⢀⣠⣍⡉
⠀⠀⠀⠀⠀⠀⣰⡤⢀⣄⣈⣻⣧⣰⣏⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠸⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷
⠀⠀⠀⠀⠀⠀⠻⣆⡀⠻⣇⠀⠀⠙⠁⠀⠀⢀⡀⠀⢀⣀⠀⢸⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠁⠀⠈⠈⠀⠀⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠁


⡟⠉⣿⣛⢻⣛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣟⣻⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠿⠿⠿⠿⢿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠿⠛⠉⠀⠀⠀⠀⣿⢸⡀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⢦⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⡴⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡞⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠤⠴⠄⠀⠀⢀⣀⣤⣤⣤⣤⣴⡛⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡼⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⡜⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠋⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠁⣀⡴⣫⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⣀⠀⠀⠘⠃⠀⢀⣀⣠⣴⣾⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠿⠿⣿⡿⠿⢿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣄⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⣰⣿⠟⠉⠉⢻⣿⡄⠀⢀⣠⣿⣧⣀⠀⠀⣼⡿⠋⠉⠙⢿⣷⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⢿⣿⡀⠀⠀⠀⠻⠃⠀⣾⡟⠉⠙⣿⡇⠀⠻⠃⠀⠀⠀⣸⣿⠃⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠈⠻⣿⣶⡆⠀⠀⠀⠀⢻⣷⣤⣴⣿⠃⠀⠀⠀⠀⣶⣾⡿⠋⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢀⣀⣀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣷⡄⠀⣭⡁⠀⠀⠀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠛⠃⠰⣾⠆⢾⣿⣿⣷⡀⠀⠀⠀⣻⣿⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣚⡛⠙⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⢆⠊⣉⠷⠶⣟⢊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⡈⠉⠛⠶⢄⠈⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠠⠂⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠒⠦⢤⣀⠀⠀⠀⢠⠖⠁⠐⠦⣠⠖⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⣠⠄⠀⠀⠀⠀⠈⠙⠲⢴⢻⠀⠀⠀⠀⠈⠀⠀⠰⠊⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠴⢾⣞⡁⢙⠤⠤⠤⣀⣀⠀⢀⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⠀⢔⢥⠀⠀⣡⣠⣌⠚⢤⢀⡂⠀⠀⠀⠉⢰⠁⠀⠀⠀⠀⠀⠀⠀⡘⢢⠀⠀⠀⠘⢆
⠀⠀⢴⡞⠋⠀⠀⣌⠈⠙⣦⠀⠷⡕⢄⠀⠇⠀⠀⢀⡤⠈⠓⠄⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠙⢦⠀⠀⠈⠢⡀
⠀⠀⠀⣿⢶⣄⠀⠈⠁⠂⠁⠙⢄⠈⢢⣑⣄⡠⢚⡡⠃⢀⡤⠞⢋⡜⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠑⢄⠀⠀⠈⢆
⠀⠀⠀⢸⠀⠈⠳⢤⡀⠠⢠⠀⠈⠢⣀⠭⠐⠉⣁⡴⠞⠛⠋⠉⢉⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡱⠜⢆
⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⡈⠃⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⣠⠖⠁⠀⠀⠈⠙⠂⠤⠄⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡦⡀⠑⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⣦⣤⠞⢻⠁⠀⠀⢈⣦⡴⠊⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣈⠒⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢀⡏⠀⠀⠀⢀⢀⡠⣤⠶⠭⠤⡤⣤⠴⢾⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠭⠹⣆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠈⠘⡅⠀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⢰⠻⡀⠀⠀⠀⠸⡀⣿⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⢠⣴⡞⢻⠛⡟⠉⡟⢙⡟⣦
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢸⠀⠹⡄⠀⠀⠀⢣⣿⠀⠀⠀⠀⣿⠀⠈⣧⠀⠀⠀⠀⠀⢿⣿⡿⡟⠻⡞⢳⡞⣿⡏
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣿⠀⢀⣼⠧⠤⣤⠞⠀⠀⠹⡄⠀⠀⠈⣇⠀⠀⠀⠀⠻⠀⠀⣿⠀⠀⠀⠀⠀⠸⡟⠓⠷⠶⠷⠚⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣿⠛⠉⠀⣀⣀⣸⠀⠀⠀⠀⠹⡄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⣿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠹⣄⣀⠤⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⡗⠈⣇⡴⡄⡆⡴⠑⣤⢠⡦⡀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠠⡇⣦⢰⡻⣆⡇⠻⠎⠀⠀⠇⠀⠏⠋⠀⠃⠣⠐⠇⠻⠷⠒⠇⡏⡏⢸⠃⣠⣦⠰⣄⠀⠀⢀
⠀⠀⠀⠀⠘⣆⢰⡷⠸⡧⠃⠙⠀⠀⠀⠉⢀⡀⢀⣄⠀⠄⠀⠀⠀⠀⢀⣤⣤⣄⡀⣀⠀⠁⠀⠀⠁⠙⠁⢼⠃⣾⢠⢆⡴
⠀⡖⠀⠸⣽⠘⠦⠉⠀⠀⠀⠀⡠⠐⠀⠝⢁⠀⡀⠀⠓⠂⢴⠀⠀⢰⡟⠛⠋⠘⠀⢾⡟⣻⣶⣦⣄⠀⠀⠀⠈⠁⠹⡎⢠⠖⣠
⠀⠳⠄⠠⠆⠀⠀⠀⠀⠀⢠⠊⠅⠀⠀⡄⠀⠁⠁⠀⠀⠀⠀⠁⠀⡿⢦⡀⠀⠊⠀⠀⠈⠻⠟⣥⠿⢷⡄⠀⠀⠀⠀⠀⣠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⢄⠀⠀⢀⠄⠠⠄⢀⠀⠀⠀⠠⡄⠀⣧⡎⣁⠀⠀⠀⠀⠀⠀⠀⠺⠶⠿⢷⣦⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠿⣿⠟⠀⠀⠀⠀⠀⠀⢦⣀⣀⠑⢾⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠔⢆⠀⠀⠀⠓⠀⠀⠀⠀⠑⣄⡀⠀⠀⠈⠂⠀⣼⡟⣼⣷⡜⠃⠰⡄⣀⣈⠿⡛⠃⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⢀⡀⠸⣯⡼⠉⠉⠀⠀⠀⢀⣽⠍⠀⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠊⠑⠴⠂⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠈⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠹⣿
⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⠂⠤⠠⠄⠀⢀⠀⠀⠑⠆⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⢹⡅
⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⠀⠀⠀⠀⠀⠀⡙⠓⢀⡀⠀⠀⠀⠀⠀⠊⠉⠐⢦⡀⠠⣤⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠐⠉⠀⠀⠉⠳⠄⠀⠀⠀⠀⢀⠄⠀⢷⣤⣤⣠⣴⠄⠀⠀⠀⠀⠀⣤⡿⠟⢁⣴⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⢠⣶⡳⠶⠆⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠉⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⠁⠀⢀⠀⠈⢛⣧⠀⠀⡤⠀⣀⣠⠐⠏⠀⠀⠀⠠⣤⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠁⠢⠀⠀⠐⢄⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣾⣉⣷⠄⠀⠘⠋⠉⠅⠙⣦⣀⠀⠀⢁⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠠⠄⠀⠀⠈⠅⠀⠈⠀⠀⠉⠐⠇⠀⣿⠟⠁⠀⣀⠀⠀⠄⠀⠀⠈⣁⣤⣶⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡀⠀⠠⠴⠀⢊⡀⠌⠀⠀⠀⠸⡿⠀⠀⠘⠊⠁⠀⠀⢀⣴⣾⠿⠟⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠤⠨⠐⠀⠀⠙⠶⠦⡤⣤⣼⣷⣠⠼⠟⠋
⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠆⠀⠃⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⡀⠰⠀⠀⠀⠀⠀⠠⢐⠀⠰⠀⠀⠐⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⣀⣴⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣾⣿⡀⠀⢉⣿⣿⣿⣏⡀⠀⣹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⣉⣉⡉⠻⠿⠿⠿⠋⠁⠙⠻⢿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⢹⣿⠉⣿⣿⣾⡇⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢸⣿⡀⣿⣿⣿⡇⠀⠈⢿⣷⡀⠀⠀⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣀⠀⠙⢛⢿⣿⣿⣇⣀⣀⣀⣹⣿⣆⠀⠿⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡀⢰⣿⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⣿⣿⣿⣿⣿⣿⣿⣯⡉⠉⣹⡿⠃⠘⢿⣿⣦⡀⣴⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣾⡟⠁⠀⠀⠀⢙⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣀⣤⣤⡈⠛⢋⣤⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⣰⣿⡿⢻⣿⡁⢹⣿⢀⣾⠃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣿⣿⣷⡄⠀⢠⣶⣿⣿⣥⣤⠉⠛⠋⣡⡿⢡⣾⠋⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠀⠀⠰⠟⠁⠀⠻⠷⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣲⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⢦⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⣴⣿⣿⣿⣿⡏⠙⠿⡇⢸⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣅⣀⣰⣿⣿⣿⡟⠛⠁⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣀⣠⣴⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠲⠋⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡉⢹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⠎⠉⠉⠉⢹⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⡰⠂⠀⠀⣠⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠟⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣀⣼⣿⡿⠋⠉⣻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⡟⠀⠀⣰⣿⡿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣆⠰⠛⠋
⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠐⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⡠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⣶⠆⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠈⣿⡇⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠛⠁⣀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡠⢀⠐⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠟⠂⠀⠰⠟⠶⠲⠾⠋⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠠⡀⢄
⠀⠀⠀⠀⠀⠜⡠⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠣
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠
⠀⠀⠀⠄⡐⠀⠀⢀⡀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢂
⠀⠀⠀⠐⠀⠀⠀⢸⡇⠀⣠⣟⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠘⣿⠀⠀⠀⠂⠀⡀
⠀⡀⠀⠁⠀⠀⠀⢸⡇⠀⢸⡿⢿⣿⣎⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠞⠁
⢀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠈⠿⠄⠙⠿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣤⣄⡀⠀⠀⠀⠀⢸⣿
⡇⠀⠀⠀⢠⡄⠐⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⣤⣀⠀⢈⣿⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀
⡇⠀⠀⠀⣿⡀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⣷⣦⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠇
⡇⠀⠀⠀⢈⡝⠂⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠻⣿⣿⠟⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⣶
⠇⠀⠀⠀⠈⠃⠀⠚⠁⠀⠀⠀⠀⠀⠀⠠⠄⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠤⠼⠋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠀⠀⠀⠀⠀⠀⣠⠄⠀⢤⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠃⠀⡀⠀⠀⠀⢿⣦⣀⡘⠀⠀⠁⠂⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠠⠀⠀⢰⠃⠀⠈⢻⡆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⣿⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠃⠀⠈⠓⠀⠀⠛⠁⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⡈
⠀⠀⠀⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰
⠀⠀⠀⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣼⡟⣴⠶⠶⠶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡔
⠀⠀⠀⠀⠀⠀⠑⠀⠠⡀⠀⠀⠀⢸⣿⠃⢀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢦⣄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠢⡀⠀⢼⡿⠀⢈⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣰⣏⡀⢈⡉⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⢀⣽⠀⠀⠀⠀⠀⠐⢁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⠀⠀⢠⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⠛⠐⠋⠁⠀⠀⡠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢂⡁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⡿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣤⣤⣤⡄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠛⠛⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣘⣋⣁⣀⣀⣀⣀⣀⣈⣛⣂⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⣉⣉⢿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣧⣙⣋⣼⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡋⢙⣛⣼⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣾⡇⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⡟⣹⣏⢻⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⢸⣿⣿⣥⣨⣽⣿⣿⢡⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢨⣿⣿⣷⣍⣩⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⡏⡄⣦⢹⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣟⠻⢦⣴⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⠶⢈⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⡀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠹⣿⣉⣉⣉⣹⡿⠁⠀⠀⠀⠀⠘⢿⣍⣉⣉⣩⡿⠃⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣉⣀⣀⣉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠉⠙⠛⠷⢿⠆⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣤⣄⣀⣀⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠢⠐⡒⢤⣤⡀⢀⠐⠂⡐⢒⢠⣤⡀⠀⠀⠒⡀⢒⢠⣤⣄⠀⡀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢤⢿⡈⣿⣛⣿⢤⡀⠡⡼⡈⢷⣛⣻⢦⣄⠠⡼⡎⢽⣟⣻⡦⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⠄⢀⡀⣘⢡⡊⢜⣁⣾⣏⣳⣾⣿⣆⢴⢁⣼⣿⣻⣾⣿⣆⢴⡃⣶⣿⣙⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠄⠀⠸⠂⠀⢼⡗⠺⢆⠉⠺⣟⣩⢿⣿⣿⣿⡏⠺⢟⣫⣿⣿⣿⣿⡏⠳⢟⣋⡽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣠⣦⣴⠀⠀⠀⠀⣹⣦⣿⣷⡧⢭⢷⣾⣿⣿⣿⣷⡷⢬⣷⣾⣿⣿⣿⣷⣶⢬⣽⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠲⣶⠿⠛⠿⣿⣯⣘⣿⣾⣿⡿⠿⣿⣯⣌⣻⣾⣿⣿⠿⢿⣿⣄⣻⣿⣿⣿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⠟⠛⠋⠀⠀⠀⠁⠻⠿⠛⠋⠁⠀⠀⠁⠚⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠲⠶⣤⣀
⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠤⠄⡀⠀⠀⡀⣀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⣄⠀⠸⣿⣿⣿⣄⡀
⠀⣰⠏⠀⠀⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠂⠀⠈⢻⣷⣄⠉⠿⣿⣿⣿⣆
⢠⡏⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣿⣿⣿⣿⡀
⣾⠀⠠⢄⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠈⠞⢑⠀⠸⡇⠙⠿⠟⣿⣿⣿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣲⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣿⣿⣿⡀
⣿⠀⠀⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⠀⠀⢀⠠⠄⠀⢠⡇⠀⠀⣠⣾⣿⣿⣿⡇
⢸⡆⠀⠓⠒⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣸⠁⣰⣿⣿⣿⠿⣿⣿⣷
⠀⢻⡄⠀⠀⠀⠠⣄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⣰⠇⠸⣿⣿⠋⠀⠀⠹⣿⣿⣆
⠀⠀⠹⣄⠀⠘⠓⠲⠀⠀⣀⠀⠀⠀⢀⡀⡀⠀⠀⠁⠈⠡⢀⡼⠃⠀⠀⢻⣿⣇⠀⠀⠀⠙⢿⣿⣷⣦⡀
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠨⠬⠑⠀⠀⠐⠪⠍⠀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⣀⡀⠀⢀⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⢀⣹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢉⣿⠿
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠉⢿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢈⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠥⠀⠀⠠⠍⠀⠈⠿⠛⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠀⠀⠀⠀⠀⣀⡴⠀⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠋⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠻⠿⠁⠀⠭⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠠⠍⠀⠈⠡⠀⠀⠹⠟⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠤⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⢀⣠⠆⠘⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠙⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣲⡖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⣿⣂⠘⠁⡰⠷⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠟⠊⠀⠀⠀⠀⠀⠀⠻⣐⠒⢐⣗⠠⠿⠅⢰⡇⠀⠀⠀⠀⠀⠀⡔⠉⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣎⣡⣒⣁⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠅⠒⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠥⢬⠁⠀⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠈⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⣀⠀⢀⠀⠀⠀⠀⣀⠦⢒⣂⣠⣤⣤⣀⣒⠠⢇⡀⠀⠀⠀⠀⠀⠀⡯⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⠖⠋⠉⠀⠀⢰⠀⠀⠈⠉⠓⢮⡑⢄⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣡⠞⠁⠀⠙⠀⠀⠀⠘⠀⠀⠀⠘⠁⠀⠈⢢⡱⡀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠐⠂⡜⣴⠁⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢠⠄⢱⡜⡄⠒⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⢰⠃⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢳⢠⠀⠀⠀⠀⠀⢀⠔⡣⠎⣴⣉⠙⡦⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢸⠀⣀⡀⠀⠀⠀⠀⠈⠓⢤⠖⠁⠀⠀⠀⠀⠀⣀⡀⢸⠌⠀⠀⠀⠀⠀⡒⢰⠥⣰⡀⢸⠉⠓⢲
⠀⠀⠀⣸⣷⣶⣶⣶⣶⣶⣶⣶⣷⠀⠀⠀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠦⢼⢀⡇⢀⠋⢐⠗⡼
⠀⠀⢠⣉⣀⣀⣶⣶⣶⣶⣎⣁⣉⡆⠀⠀⠀⡈⣆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡎⡈⠀⠀⠀⠀⠀⠈⠲⣤⣁⣍⡱⣓⠔⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠒⠉⠑⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡐⠉⠑⠂⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⡳⣄⠀⠖⠀⠀⠀⢰⠀⠀⠀⠐⠆⢀⡴⡫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠢⢝⠲⠤⣤⣀⣈⣀⣀⡤⠴⣚⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠓⡽⡂⠀⠀⠀⠀⢀⠋⠁⠒⠂⠀⠀⠒⠂⠉⢃⠀⠀⠀⠀⠀⠀⠀⡠⡺⡉⢱⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣎⠵⣳⣚⠳⡲⠽⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⠅⠸⣗⠀⠇⢣⣬⠫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣄⠀⡈⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⣖⠒⢒⣶⣒⠀⠀⠀⠀⠀⠀⠀⢀⢖⡭⠚⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠣⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡆⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠃⠐⣶⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠶⠶⠴⠭⠯⠯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⡉⠀⠀⠉⠉⠙⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢀⣾⠟⠀⠀⢠⣾⠟⣷⡄⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠻⢿⣿⠗⠀⠈⠿⣶⠿⠃⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⡀⠀⠀⢰⠿⠁⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣠⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣧⣄⠀⣼⣿⣆⠀⠀⢀⣤⣄⠀⢀⣾⠏⠛⢷⣦⣴⡿⠋⠁⣿⡆
⠀⠀⠀⠀⠀⢸⣿⠈⠻⣿⠏⠈⢻⣦⣴⡿⠋⠻⣷⣿⠃⠀⠀⠀⠉⠁⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⠉⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠶⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣀⡀⠀⢸⡇⠀⣧⣠⢦⢰⢠⡆⠓⣦⢀⡴⡄⠀⣀⣸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢀⣲⢲⡄⣴⢻⡎⡇⠸⣿⠃⠀⠈⡇⠀⣿⠻⠁⠘⠞⢇⠰⡇⠺⣧⡧⢾⢱⡇⡟⣰⠇⢀⡤⡄⠦⡀
⠀⠀⠀⠀⠀⠀⢦⡀⢰⢦⠸⣇⡿⠘⡇⠉⠁⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠈⠃⠸⠛⠑⡴⠃⣾⢂⡈⢡⡆
⠀⠀⣀⠀⠀⡶⡄⢧⡸⠫⠀⠙⠀⠀⠀⢀⡠⠄⡴⠊⠉⠈⠉⠦⣈⢢⠀⠀⠀⢠⣾⢛⣻⠿⢶⣶⣤⣤⣤⣴⢶⣤⡀⠀⠀⠀⠁⠠⠟⢼⣱⠋⢀⡄
⠀⠐⣇⠀⠀⠙⠃⠀⠙⠀⠀⠀⠀⠀⠴⠋⠀⢰⠀⠐⠄⣆⣀⡀⠀⠙⠄⠀⠀⡿⠾⠬⣵⣒⣼⣿⣿⣿⡿⠛⠀⢙⣽⡆⠘⠗⠀⠀⠀⠈⠃⠀⠋⣰⠟
⠀⠀⠈⠳⠄⠋⠀⠀⠀⠀⠀⠀⠀⡎⠀⠆⠀⠀⣄⠀⠀⠀⠀⢈⣄⠀⠠⠀⠀⢷⠓⠶⢤⢠⣥⠟⠉⠀⣠⣤⣶⣬⣿⣿⣶⣄⠀⠂⠀⠀⠀⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠁⠘⠂⠀⡀⠀⠀⠀⠃⠀⢀⣼⣿⡖⢰⣷⡅⠀⢠⣸⣭⡥⣬⣉⣻⣁⣼⣿⣆⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠀⠈⢿⣉⡿⣿⣿⣷⠷⠾⣿⣿⣿⣿⣛⠻⣮⣿⣿⢿⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡀⠀⠀⠀⠑⠀⠊⠀⠀⠀⡀⠀⠀⠀⠈⠃⠀⢠⣿⠛⡃⠉⣡⣶⢾⣶⢮⠛⡋⠘⠿⣗⠛⠱⡟⢾⡧⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⠐⠂⠐⠒⢄⠀⠰⠀⠀⠠⡀⠀⠀⠘⣷⡜⣄⡺⢿⣿⣿⣿⣿⡇⠙⢿⣶⣿⣾⣿⣼⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢄⡠⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠿⠿⠧⢉⡒⠮⢉⣛⡛⠃⢹⢸⣿⡿⠿⢽⡟⡰⣿⣛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢘⣷⢇⡀⠈⠓⠒⠂⢤⣄⣶⠿⠧⣤⠠⠊⠁⠰⣯⣯⡀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠲⡂⠀⠀⠊⠉⠀⠈⠈⠒⢄⠀⠀⠈⠃⠀⡀⠀⠀⣦⠁⠈⠁⠦⠀⠀⠺⠖⠈⠀⠆⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠀⠀⠀⠀⣀⡀⢀⡀⠀⠁⠀⠀⠀⠈⠁⠀⠀⢸⣴⣦⣀⠀⠚⠀⠀⠀⠰⠂⠀⠀⠰⠷⠀⠀⠀⣾⣏⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⠐⠀⠀⠀⠠⠊⠁⠀⠀⠈⢲⠤⠀⠀⠀⡠⡄⠀⢰⣧⣿⢿⡿⠀⠀⠂⠀⣶⡀⠀⠀⠀⠀⠀⣤⠀⢰⣿⡟⠃⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠄⠀⠉⠀⠠⠀⠀⢻⡆⣀⣰⣬⣦⢿⣤⣤⢀⠀⠂⠀⠀⠀⠀⢠⡟⣻⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⢀⠀⠀⠀⠀⠁⣀⠉⠀⢀⠀⠐⠎⢦⡔⠀⠀⣾⣻⣧⠾⣾⣿⣶⣧⣼⠀⡀⠢⠄⠊⢀⣴⣿⣷⠏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠒⢄⠀⠀⠙⠃⠀⠀⠀⡀⠁⠀⠀⠀⠡⠀⠀⠟⠿⠃⠀⠀⠨⠦⣿⣿⡀⠁⡀⠂⣠⣄⣽⣿⡟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣄⣀⣀⡀⠄⠀⠁⠦⠀⠀⠀⠀⠠⠀⠀⠀⢀⢀⣀⠀⠀⢀⡤⠀⣸⣝⣁⠀⣀⣄⠙⣿⣮⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠁⠂⠀⠀⣨⢀⡠⠀⠀⠀⠀⠈⠀⢸⡌⠁⠀⠀⠀⠀⠻⣿⢿⣿⣿⣻⣿⠿⠛⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠂⠈⠉⠀⠀⢠⠔⡡⢀⠄⠀⠀⠻⣾⣿⣧⣠⣤⣾⣿⣿⣿⠿⠋⢀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠒⠛⠒⠁⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠗⢰⢠⢰⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⡈⠆⡆⠷⠄⠲⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠇⠄⠸⠀⢐⠐⠐⠀⠠⠀⡄⠰⠀⠠⠠⢠⠀⢠⠠⡀⠸⠀⡀⠀⡆⠁⠂⢀⢘⢡⠸⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠈⠁⠈⠁⠀⠀⠀⠀⠘⠀⠘⠀⠈⠂⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠁⠀⠀⠂⠁⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠲⠒⡃⢈⡂⢘⡁⢘⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄⠀⡀⢀⡁⢊⡀⠀⠀⢄⠐⠗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡄⡈⠉⢀⠄⠀⡁⠈⠀⠠⡀⠉⢠⢠⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠏⠀⠤⠃⠺⢠⡄⢢⠄⠖⠐⡄⠀⠣⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡡⠀⡄⠀⠸⢀⠌⠒⢂⠈⠚⢡⡠⠁⠀⣠⠀⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢰⠀⠠⣀⢀⠔⠒⠒⡄⢠⠒⠚⢢⡀⣈⠄⠀⡂⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠊⡒⠀⠀⢀⣠⣀⡉⠕⠨⢁⢀⡌⡀⠀⠀⢊⠕⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢅⠈⠒⠂⠀⢔⠂⠨⠀⠐⡆⠀⠒⠒⠁⡸⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢁⠀⢈⠥⡀⠀⡆⣴⠈⢀⠼⡁⢀⠉⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⠀⢡⠴⠌⠡⠇⠨⠈⠡⠦⡋⠐⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠂⠤⠔⠂⠐⠢⠄⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡕⡟⣤⠄⡄⣤⠠⡄⣠⣄⢠⢴⡏⡜⣤⣤⢠⡄⠠⡄⢠⡄⡼⣸⢣⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠸⠟⠇⠘⠗⠇⠐⠇⠫⠉⠛⠺⠘⠇⠷⠋⠻⠀⠘⠗⠻⠛⠇⠇⣻⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢬⣿⡛⠳⢿⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠛⠛⠀⠈⠁⠀⠀⠀⠀⠻⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣀⠤⠔⠒⠒⠀⠐⠒⠒⠠⢄⣀⠀⠀⠀⣴⡏⠤⠄⠒⠂⠀⠂⠤⠄⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⢀⣾⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠘⢁⣤⠴⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠙⠶⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢀⣀⠈⠳⡀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣼⣿⣿⣄⡄⢳⠀⠀⠀⠀⢰⡇⢰⣾⣿⣇⣀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢻⣄⡀
⠀⠀⣼⠁⢸⡇⠀⠀⠘⠉⠉⠛⠻⢤⡀⠀⠀⠻⣿⣿⡿⠃⣸⠀⠀⠀⠀⢸⡇⠹⣿⣿⣿⠏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣺⠉⣷
⠀⠀⢹⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢄⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠻⣄⣀⣉⣀⣠⣤⠖⠋⠉⠉⠛⠒⠀⠀⠀⣿⢀⣿
⠀⠀⠀⠙⠶⣿⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣄⣰⠟⠉⠱⡄⠀⠀⠉⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠾⠁
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠈⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣴⣟⣻⣄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⣼⠐⢻⣶⣈⢉⢩⡏⢹⡆⢀⣠⡤⠖⢳⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣷⣶⣿⣼⣼⣼⣿⣾⣼⣗⣺⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⣤⠶⠚⠋⣉⣀⠤⠤⠤⠤⠤⢄⣈⡉⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠾⠋⠁⠀⠊⠉⠀⠀⠀⠂⠀⠀⠀⢀⠆⠈⠉⠒⠄⠈⠛⢦⡀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡀⠀⠀⠀⠀⠲⣄⠙⢶⡾⢧⣄⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠋⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠚⠈⢢⡈⠻⣤⠿⠻⣷⣿⡿⣆
⠀⠀⠀⠀⣠⡾⢋⣾⠁⡰⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢹⣆⠀⢹⣿⢿⣿⡄
⠀⠀⣠⠞⠁⠀⣼⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⠀⢿⣄⣠⡿⠈⠉⠙⢦⡀
⢀⡾⠃⣴⠛⠛⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⣿⠷⢶⣄⠀⠀⠀⠻
⣾⠁⠘⣃⣀⣴⡋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⢹
⠹⢦⣀⢠⡟⠁⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣴⠟⠛⣿⠋⠀⠀⣠⡴
⠀⠀⠉⠛⢻⣤⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⣀⣀⣼⠷⠞⠛⠉
⠀⠀⠀⠀⢿⡀⠀⣿⠰⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣼⠋⠙⣧
⠀⠀⠀⠀⠈⠛⠛⢿⡀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠠⢄⢠⠃⣰⠿⠦⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠱⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡠⠊⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠑⠢⣄⣀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡤⠒⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣄⣀⡙⠀⠒⠂⠶⠆⠳⠀⠚⢉⣀⣤⣶⠛⠁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠈⠉⢻⡟⠓⠶⠶⠶⠶⠛⠛⠋⠉⠀⣿⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⠳⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⡶⠊⠁⠉⢦⡠⢀⣠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢰⡁⣢⠀⠀⢸⡛⠛⠃⠳⣿⢷⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠚⠀⢀⡴⠉⢉⢁⡄⠀⡼⠷⠿⠒⠛⠺⠟⠿⠳⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⢈⠀⠀⠀⠙⠀⠀⢹⡄⠄⠂⠐⠀⠘⡇⠀⣿⠯⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣏⡀⠀⢀⠞⠁⠀⠀⣀⠀⠀⣸⡣⣐⣀⢀⡑⣀⣀⣀⣿⣛⣷⢎⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⡞⢉⢁⡌⠀⠀⠈⠛⠇⠀⠘⣒⠋⠛⢷⣒⣓⢿⢹⣙⣏⠪⣼⣻⢽⣗⡄
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠹⡅⠈⡇⠘⣤⠀⠀⠒⠒⠄⠀⢘⣉⡇⡠⠟⠛⠛⠳⣿⣯⢙⡾⠟⡉⢳⣿⡄
⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠐⠃⢸⠁⠀⠀⠠⣄⣀⢀⣼⡀⣸⠀⠆⢀⡀⠀⠈⢻⣷⠈⠀⠀⠡⡝⣧
⠀⠀⠀⠀⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠤⠋⠀⠱⣄⢯⣿⡀⠀⠀⡅⠀⠀⣸⡗⠈⢄⠀⠠⣨⣾⡀
⠀⠀⠀⠀⢘⣄⣀⢀⣀⣀⢤⠖⠒⠒⠚⢆⡀⠀⠀⡀⠀⠀⡏⢋⣷⣿⣦⣤⣄⣠⣼⠟⠉⠀⢔⣡⡾⠿⡶⢱⡀
⠀⠀⠀⠀⠃⠀⠈⠉⠀⠀⢸⠤⡀⠀⠀⠀⠈⠉⠉⠈⠒⠚⢒⡏⠗⠫⢤⡠⠏⣄⡷⣄⣪⣴⢫⣴⣾⡶⠡⡼⠁
⠀⠀⠀⠀⠡⣄⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐⠂⠒⠞⠒⢱⡚⣗⠦⣁⢊⠝⢞⡺⢱⢟⡇⠷⣼⡕⢏⠀⢀⡷⠆
⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠀⠀⠈⠉⠙⠄⠀⠀⠀⠀⠀⠀⠹⡇⠀⡝⣮⡐⠿⠙⠛⠛⣋⣎⠹⣛⡠⢜⣅⣦⠋
⠀⠀⠀⠀⠈⣆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⢤⣀⡀⠀⠀⣠⣇⣀⣷⣤⡌⡗⠛⠚⢶⣯⠛⠉⡙⡍⠉⣫⢣⡷
⠀⠀⠀⠀⠀⡀⠉⠛⠊⠣⣀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠉⠙⢿⠿⠿⠭⢭⠗⠅⡒⣚⡤⣣⡗⠔⣁⠑⣞⢋⡃⠇
⠀⠀⠀⠀⠀⠱⣄⠀⣀⠀⠈⠉⠛⠉⠙⢤⣀⣀⣀⠀⠀⠀⠈⡇⠀⠀⢸⡗⠭⡵⢋⣷⠘⢟⠶⠟⢈⠞⡆⣿
⠀⠀⠀⠀⠀⠸⠀⠁⠈⠲⢤⣀⣠⠤⡀⠀⠀⠡⣏⠀⠀⠀⠀⡇⠀⠀⢸⡯⡂⠓⠓⠚⠘⣄⣀⣄⡻⢟⡰⡟
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣀⠀⠀⠈⠑⠢⠤⠤⣀⡀⢀⣠⠃⠀⢀⣸⡟⡎⣷⣶⣾⣿⣿⣲⣖⣞⣹⣾
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠉⠈⠢⣀⣀⡀⣄⠀⠀⢀⣉⠁⠀⣛⣛⣻⣯⣷⢢⢯⣨⠞⠉⣄⠂⠻⡏⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⣀⠀⠀⠀⠀⠀⠙⠋⠁⠐⠒⠲⣟⡯⠟⣫⢷⡯⠛⡁⢦⢀⡈⠛⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡉⠒⠒⠊⠒⠺⣄⠀⠀⠀⢀⣋⢶⢏⣓⣼⣷⡳⣤⠄⢉⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠄⠀⠁⠰⢆⣉⣉⣾⣷⡫⠟⡩⢷⣶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⣄⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣦⣾⠷⠀⠀⢠⣾⣿⣿⣿⣿⡿⠛⢻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠐⢿⣿⣿⣿⣿⣽⣯⣷⡀⠀⢠⣿⣿⣿⣿⠿⣿⣦⢀⣀⡉⢀⣬⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠉⣀⣸⣏⠉⠿⠟⠁⠀⣿⣿⣿⣿⣄⠀⣉⡁⠀⣠⠽⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠹⣿⠟⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡿⠇⠀⡇⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⣠⣶⣆⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡼⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠔⢲⠀⠀⠀⠀⠀⠉⡟⠀⠀⠀⠐⠀⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣿⠁⢁⢍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠇⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠳⡟⣇⣌⣿⠀⠈⢀⠀⠙⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡴⠃⠈⠃⠋⢱⠀⠘⠁⠄⠀⠀⠀⠀⠄⠘⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡂⠀⠀⠈⠀⠀⠂⠀⠠⠀⡄⣀⠀⠁⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠂⠐⠀⠀⠐⠠⠤⠤⠄⢀⡀⠀⠀⠰⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⡀
⠀⠀⡀⠐⠀⠀⠀⠀⣠⢊⠇⡀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⣠⠦⠀⠀⠀⠀⠀⢀⡀⠀⠈⠆⠀⠀⡝
⢠⠚⡀⠀⡀⠀⠀⠞⢵⢋⠖⣥⠀⠀⠠⠁⠀⣒⠀⠠⠀⠀⠊⠀⢀⡀⠀⠀⠀⠀⠶⢁⢄⠀⠀⠀⠀⡀
⢠⣤⣤⣄⣉⣀⣚⡴⣱⢋⡞⠁⠀⠒⠾⡛⠉⡩⠙⠉⠛⠋⠉⠉⠉⠛⡛⠁⠀⠀⠢⡣⡠⢃⣀⣀⠀⠀⠂
⢰⣉⠈⠉⠉⠓⠒⠺⢡⠏⢀⠂⠀⡀⠀⠈⠀⣀⣀⡀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠙⢝⠎⠰⠖⠚⠖⡂
⠀⠈⣟⡛⠻⠶⠦⠾⠯⡄⡌⠀⠀⠈⠓⠤⠈⠉⠁⠉⠙⠙⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⡈⠷⠶⢖⣒⡒⠁
⠀⠀⠈⠉⠉⠉⠓⠒⠒⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⣻⣇⡼⠃⠀⠀⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⢺⡷⠀⠀⠀⠀⠀⠀⣺⡗⠀⠀⠀⠀⠀⣘⣗⣤⡄
⠀⠀⢸⠉⠉⡄⠀⠀⠀⠀⢸⠉⠙⡃⠀⠀⠀⠀⡶⣾⣷⢶⠀⠀⠀⠀⢞⠙⢋⡇⠀⠀⠀⠀⠉⠹⠾⠶
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⣠⣶⡆⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⡄⢸⡇⣀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⣿⢿⣤⡄⠀⠀⠀⢠⣿⢿⠿⠟⠃⠀⠀⠀⢸⣅⣬⡇⠀⠀⠀⠀⣏⢸⡇⣿⠀⠀⠀⠠⠀⠽⠏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠰⡧⢼⠦⠀⠀⠀⠀⢰⣾⣷⡆⠀⠀⠀⠀⢠⣟⡓⡄⠀⠀⠀⠀⠀⣿⠜⠀⠀⠀⠀⠀⠀⠀⣽⡶
⠀⠀⣸⡇⢰⣇⠀⠀⠀⠀⠈⠶⠶⠁⠄⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⢀⣶⣷⣾⣷⡀⠀⠀⢀⣴⣶⣥⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⣄⢾⡷⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⣰⣾⣟⣦⠀⠀⠀⠀⢀⣽⣇⠀⠀⠀⠀⠀⢐⣂⣻⡄
⠀⠘⠻⢿⣿⣿⡄⠀⠀⠀⣠⣾⣶⣄⠀⠀⠀⠀⢹⠉⠉⡿⠀⠀⠀⠀⢸⣂⣰⡇⠀⠀⠀⠀⢠⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣤⣾⣿⣶⠀⠀⠀⠀⣾⣺⣗⣷⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⠀⠀⠀⠸⢿⣀
⠀⠀⠿⠻⠟⠋⠀⠀⠀⠸⣿⢷⣾⣿⠇⠀⠀⠀⢠⣮⣵⡄⠀⠀⠀⢀⣾⣷⣾⣶⠀⠀⠀⠀⠀⣤⡾⢿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠙⣎⢳⡄
⠀⠀⠀⠀⠀⠀⡠⠖⠉⠂⠀⠀⣊⠜⠋⣀⣤⣴⣶⣿⣿⣤⡶⠟⣛⣠⣤⡦⠀⣀⣀⣤⣄
⠀⠀⠀⢀⣔⠪⣤⡁⠀⣀⠔⠊⣡⣴⣿⣯⣵⣾⣿⠟⣛⣭⣶⢿⣛⣭⣶⣾⣿⣿⡿⣛⣁
⠀⠀⣴⣿⣿⣷⣹⠴⠊⢀⣤⣾⣿⣿⣿⡿⠟⣩⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣛⣋⣤⣴⣶⣆
⠀⠘⠛⠛⠋⠉⠁⠀⣴⣿⣿⣿⣿⢟⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢡⣤⢹⡿⠛⢿⢫⡙⣿⣿⣿⣿⣿⢩⡝⣿⡏⣬⢹⣿⣿⡏⣤⢠⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⢸⣿⢘⡃⠀⢈⢸⡇⣛⣩⣭⣭⣍⢸⣇⣭⡅⣿⢨⣯⣭⡄⢟⢸⣿⣯⣤⡦
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠸⣿⢸⣧⣤⣼⣬⣥⣿⣿⣿⣿⣿⣬⣴⣿⣷⣤⣞⣯⣵⡆⣿⢸⣯⣭⡶⠾⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡜⣿⢸⣿⣿⢟⡛⡟⠛⢻⣿⣿⡟⠛⣿⢛⡛⣿⣿⡟⠉⠁⣿⠘⣋⣥⣤
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⣿⢘⣛⣛⢸⡇⡁⠀⢈⣟⣛⡃⠀⣭⢸⡇⣿⣶⡆⠀⠀⣿⢸⣿⣿⣿⣤
⠀⠀⠀⠀⣨⣿⣿⣿⢿⣿⣿⡇⣿⢸⣿⣿⣜⣣⣇⣀⣸⣿⣿⣧⣤⣿⣬⣥⣿⣿⣷⣤⡄⣿⢸⣿⣿⣿⠇⣀⡀
⠀⠀⠀⠘⠛⠛⢉⣵⣿⣿⣿⡇⣿⢸⣿⠉⠉⣿⢫⡍⣿⡏⠀⢹⣿⣿⣿⣿⠏⣦⢹⣿⡇⣿⢸⣻⣭⡶⠟⠋⠁
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⣿⢨⣭⠀⠀⣤⢸⡇⣶⡆⠀⢲⣶⣶⣶⣶⡆⡇⣶⣶⡆⣿⢸⣿⡿⠆⠀⠀⢀⣤
⠀⠀⠀⠀⠸⢿⠿⢿⣿⣿⣿⡇⣿⠘⣿⣬⣤⣿⣌⣥⣿⣷⣴⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇⠟⠈⣁⡀⠀⠀⢀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣤⣶⠿⠋⠁⠀⠀⠟⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⣴⣿⣿⣽⣶⠗⠀⠀⠀⠸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⠟⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⡿⣟⣥⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡀⠀⠀⡘
⠀⠀⠀⣴⢒⠖⠢⠤⣀⣀⠘⠿⠟⠛⠉⠁⢰⣿⠾⠛⢡⣾⡿⠿⠿⠛⠋⠙⢿⣿⡿⠿⠃⠀⠀⠀⠀⢀⠃⠀⠀⡇
⠀⠀⠀⢯⣸⠀⠀⡀⠀⠀⠈⠁⣲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⢰
⠀⠀⠀⠀⠀⠉⠁⠒⠠⠤⢄⣀⣇⢸⣇⣙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁