Ducks Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣦⣀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣿⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠉⠀⠀⠀⠀⠈⠉⢑⡿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠴⣶⣤⣯⣙⣛⠿⢿⣦⡄⣸⣿⣶⣲⣾⣧⣤⣴⣤⣄⡀⣿⣿⠁⠀⠀⠀⠀⠀⡰⠒⠻⠧⣄⣀⣑⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣉⠉⣻⣿⣿⣿⣷⣮⣿⣿⡛⠛⠉⠉⠉⠛⠓⠾⢼⣿⣿⡄⠀⠀⢰⣶⣶⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⢚⣿⣿⣿⣿⣷⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠳⢭⣳⡆⢾⣿⣿⣇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⡇⠀⢸⠀⠉⠻⠿⠿⠿⠿⣿⣿⣿⣯⣴⣄⠀⠀⠀⠀⠀⠀⢻⣍⡈⣻⡈⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠘⣶⡀⠀⠀⠀⠀⠀⠀⠈⠛⠃⢿⣷⣤⣀⣀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⡄
⠀⠀⠈⠙⠓⠂⠲⠄⠀⠤⠄⣀⣀⡀⠀⠀⠀⠑⠀⠈⠳⣦⡀⠀⠀⠀⠀⠈⠳⠀⠘⣯⡙⣽⣿⣿⣳⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⢻⠶⢤⣤⣄⣀⣈⣉⣠⣤⣤⣶⠿⠿⠿⠿⠿⠿⠿⠟⠻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠲⠦⠄⠀⠀⠀⠀⠀⠌⠉⠉⢉⠉⠉⠀⠀⠀⠂⠀⡀⠠⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡒⠀⢀⣀⣀⡀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠛⢿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⢠⣤⡄⠀⠀⠀⠸⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣞⡇⠀⠀⠉⠀⠀⠀⠀⠀⠤⣿⣿⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⡇
⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠉⠛⠉⠉⠀⠀⠀⠀⠙⠪⣧⠀⠀⠀⠀⠀⠀⠀⢼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣸⣿⡿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⡶⠶⠶⠶⠶⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⢰⣿⡿⣽⢁⠀⣀⣠⣴⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⡷⠟⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠸⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢋⣼⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⠿⠛⣁⣴⣿⢿⡿⠀⠀⠀⠀⠀⠀⠈⢙⢶⣤⣄
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠉⢀⣠⣴⣾⠟⢉⣵⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⣿⣿⣿
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠲⠟⠛⠋⣁⣤⣶⠿⢻⣿⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⢿⣿⣤
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠿⠋⣀⣴⣿⡿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠟⠉⠉
⠀⠀⠀⡀⣿⣿⡀⠀⠀⠀⣾⣿⣿⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⣀⣠⣶⠿⠛⣡⡿⠁⠀⠀⣠⣴⡿⢛⠉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⠈⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣾⠟⠋⠉⠀⣀⠔⠋⠀⢀⣠⣾⠟⠉⠈
⠀⠀⠀⠀⠰⡻⣿⣿⣷⣥⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣁⣰⣶⡷⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⢉⣠⣴⣾⣿⣷⡾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣀⡀⠐⠖⠛⣋⣉⣠⣤⣶⣿⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠤⠀⠠⠂⠬⠦
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡄⡀⢀⠾⡧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⠾⢛⣛⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠩⠀⠀⠀⠘⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣭⣭⣵⣿⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⡀⠀⠐⣢⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠬⢄⣀⡉⠂
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⣯⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡸⠀⠐⠀⡀
⠀⠀⠀⠀⠀⢸⣇⠉⣒⡼⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠌⢀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⣧⣾⡁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡂
⠀⠀⠀⡀⠀⠠⢿⣿⣷⣦⡴⠛⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡐⣀⠀⠐⠑⠐⠀⠐⠁
⠀⠀⠀⠉⠀⠶⢀⠙⠛⠻⠶⠶⠖⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⠀⠀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⢀⡀⢀⡄⠀⠀⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠾⠛⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⣴⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣟⠙⠛⠋⠛⢉⠈⠋⡙⠋⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠿⢣⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⢦⣠⣤⣤⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢈⡿⠃⠊⠙⣷⠆⠲⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⢀⡟⠀⠀⢀⡀⠀⢀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⠀⠀⠀⠄⠹⠒⠀⠰⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣴⡄⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⣠⢀⠂⠀⢩⣄⠐⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣁⠙⢶⡈⠀⠙⢾⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢘⠀⢀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠠⠀⣀⣀⣈⠁⢩⢘⠡⢦⢀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠎⠈⠀⠃⠈⠀⠀⠀⠨⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡄⠀⠀⣀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡠⢰⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠩⢡⡜⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠛⢁⣼⠻⣛⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣍⣿⣍⠀⠀⢀⡀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠊⠉⡀⢈⠄⣁⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣣⣌⣧⣤⠀⠀⠀⢠⠼⠀⠀⠀⠠⢐⡛⢃⣭⣾⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣄⣶⣦⣽⣾⣿⣖⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠉⠉⠉⠉⢹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⢧⡁⠀⠀⠀⠀⢀⣴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣍⣡⣿⣿⠛⢁⣼⣿⣷⣆⣀⣠⣴⡿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣽⣿⡷⣾⣿⣿⡿⠿⣻⣿⣿⡿⢿⣿⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢿⣶⣯⣿⡿⢁⣤⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⢄⡄⢀⡀
⠀⠀⠀⠀⠀⢀⠀⣎⠛⢟⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⣬⡻⣵⣺⡭⣞⣻⡥⢶⣶⣄
⠀⠀⠀⠈⠛⠉⠉⠛⠛⠛⠿⠿⣯⣭⣳⣶⢤⣴⣾⣧⣿⣿⣾⡪⠯⣕⣲⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠲⠂⠀⠐⣶⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣭⣯⣭⣭⣙⣛⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣻⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⡇⠀⠻⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣇⠀⠀⠀⠀⠀⠀⠻⢤⣀⣀⠀⠀⢀⣀⣠⠖⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣀⣤⣤⣀⣉⠉⠉⠉⣁⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⠞⠁⠀⠀⠀⠉⠉⠉⠉⠉⢹⠀⠀⠀⡾⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⠈⣩⠏⠀⠀⢠⠇⠀⠀⠀⠈⠀⢔⡢
⠀⠀⠀⠀⠰⡱⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⠧⣄⡀⠀⠀⣀⣒⡶⠞⠁⠀⠀⢠⠟⠀⠀⠀⢰⡋⡢
⠀⠀⠀⠀⠀⠀⢐⠙⡆⠀⣀⡘⢦⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⡴⠯⢄⣀⡠⠤⠤⢌⣀
⠀⠀⠀⠀⠀⠀⣀⠭⠤⠾⣅⠀⠀⠙⠲⢤⣄⣀⡀⠀⠀⣀⣀⣠⡤⠞⠋⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡷⡙
⠀⠀⠀⠀⠀⠀⡀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⣀⣀⣀⠘⣿⣿⣿⣿⣷⡌⢑⡀
⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢀⣀⣠⣤⣴⣶⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣴⣿⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠛⠉⠁⠀⢀⡐⠐⠒⠻⡿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠁⢀⣀⣻⣷⣶⣾⣿⣷⣿⣿⣿⠿⠟⣋⣭⣿⣿⣿⣿⣿⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣠⣾⣿⣶⣶⡞⣿⣭⣍⣉⣉⣛⣿⣛⣛⠑⢄⠙⣿⡿⠟⠛⠁⢹⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⣻⣽⣿⣿⢰⡟⠋⠉⠉⠉⠉⠛⠻⠿⠿⠿⠂⠁⠀⠀⢀⣠⣿⣿⠟⠋
⠀⠀⠀⢀⠀⠀⠀⠉⠛⠛⠿⠿⢿⣿⣇⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠈⠙⠿⢿⣦⣄⡀⠀⠀⠀⢀⣠⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣾⠀⡄⣨⣄⠨⠉⠛⢿⠞⣿⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣓⠷⣸⣇⣿⣯⣶⢛⣆⡘⢀⠋⠸⠠⠆⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⡾⣿⣿⣿⡿⠽⠻⠛⠻⣿⣿⡛⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠻⢿⣿⣿⣾⣿⢷⣿⣿⣾⣮⣛⣦⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⡠⠒⠉⠉⠉⠉⠐⠒⠒⠲⣦
⠀⠀⠀⠀⢠⠊⠀⠀⢠⡦⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⣟⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⣴⢋⠈⣧⣀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⣰⣃⠻⠆⢈⣭⠗⠒⠒⣶⠶⡄⠀⠀⠀⠀⠀⢈⡄
⢀⠜⡵⠑⣀⠜⠉⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣰⠁
⣎⣨⠴⠛⠁⠀⠀⠀⠀⣠⠊⡀⠈⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠓⠒⠲⠤⠤⣤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠤⣀
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠄⠠⢀⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⡀
⠀⠀⠀⠀⢸⠀⢄⠂⠐⠀⠄⢀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢐⣶⣄⣀⡀
⠀⠀⠀⠀⢸⠀⠄⠄⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠦⠤⣶⣦⣾
⠀⠀⠀⠀⢸⠁⠜⠀⠀⠀⠀⠂⠀⣀⠂⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠂⠧⣄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⣄⣿⠟⠁
⠀⠀⠀⠀⠈⢇⠚⡀⠀⠀⢀⠠⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡂⠔⠲⠶⠄⠀⢀⡤⠄⠀⠀⠀⠜⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠁⠓⠈⠀⢄⠀⢁⡐⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⢤⡉⠓⢦⡤⠄⣀⠝⠀⠨⠔⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠐⠀⠀⠂⡀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⢀⠀⠀⢀⣤⣔⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣶⣷⣤⣁⠄⠠⠁⠀⠌⠀⠀⣠⠀⠀⡄⠀⠀⠀⣀⡀⠀⠀⠸⢏⡀⠑⡂⠈⢱⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⢴⣦⣆⣠⡤⠈⠁⠀⠈⢀⡀⠐⠀⠙⢦⣀⢐⣀⣷⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠻⣶⢶⣮⣤⣀⣀⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⡟⠃⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⢼⣿⡏⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢹⡿⣿⣾⣿⣵⣾⣿⣿⡿⣽⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣽⣿⣿⣿⣭⣿⣿⠿⠒⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⢹⠆⠀⠠⠖⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡠⠔⠋⣀⡠⠘⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠰⣥⠶⠞⠛⠋⠉⢉⠳⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢄⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⠀⢹⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⢀⣤⡤⣴⡠⠋⠀⠀⢀⠜⢩⠇
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⢀⠔⠋⡹⠀⠀⠀⢁⣠⠏
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠴⣦⣠⠞⠁⠀⠀⠠⠴⣾
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠈⠉⣩⠃⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⣄⠀⠀⠀⠀⠠⠴⠊⠀⣀⡤⠞⠁⠀⠒⣩⠃⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠘⢦⣈⠁⠀⠀⠠⠤⠚⠁⢀⣠⠔⠂⠐⣒⡝⠁⠀⠀⠀⠜⠉
⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⠋⠉⠉⠉⠉⠁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠤⠤⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⢀⡏⠉⠑⣲⢲⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠉⠀⡼⠀⠀⢀⠇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠦⠔⠒⠊⣀⠤⠔⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⡠⠤⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢄⣸⢃⡌⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠛⠂⠉⠀⠁⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⠀⠀⡴⠖⠶⢤⡀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠢⢴⣾⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣠⠞⠉⠈⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⡀⠀⠀⠀⢠⡏⠀⠀⣀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣠⣄⣀⣠⠶⠛⠁⠀⠀⠀⠹⡄⠀⠀⢸⡇⠀⣾⣻⣿⣷⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢧⡀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠉⠺⢿⣿⣿⣯⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠙⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠙⢲⣤⣀⣀⠀⢀⣀⡤⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣢⠁⣸⡭⠟⠋⠉⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠘⡙⠚⣉⡠⠴⠚⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⣀⣠⣶⡴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠉⠉⠛⠛⠛⠛⠋⠉⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠽⢦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠄⠀⢦⣀⡠⠖⢋⡡⠚⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠁⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⢀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⡴⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢎⠀⠀⠀⠀⠈⢀⠜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⠚⠁⠀⡜⠀⠀⠀⠀⡰⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠊⠀⢀⠏
⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠄⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⢊⡽⠃⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⡀⠀⠀⢀⣀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠳⢄⣀⡀⠀⠀⠙⠓⠒⠛⠛⠦⣄⣠⡤⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠴⠒⠛⠲⣤⣀⣀⣀⣠⡤⠖⠛⠲⠦⠤⠴⠔⠋⠉⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠊⠓⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠤⠤⢄⣀⠀⠠⠄⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠈⠁⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠐⠦⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣀⣤⠐⠒⠲⠀⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠒⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⠠⠐⠒⠤⠄⠀⠤⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣼⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⢀⡀⠊⣴⣿⣟⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⣿⣿⣿⣵⣆⠀⠀⠀⠀⢠⠎⠉⠀⢰⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣹⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣯⣽⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠁⠛⠿⣍⣿⣿⣿⡶⠁⠀⠀⠀⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⣠⠀⠀⣿⡇⠀⠀⠀⠀⣀⣹⣮⣴⣶⣶⣦⡤⠀⠀⠀⠀⠄⢀⣸⡿⠃⠀⠀⠀⢠⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠉⠀⠀⠉⠉⠉⠙⠻⢡⣿⣷⣤⠀⠈⠉⠉⠀⠀⠀⠀⠀⢟⡛⣿⣿⠝⠀⠀⠀⠀⠀⠀⢰⡄⠀⢿⡇
⠀⠀⠀⣿⡀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⠀⠀⠀⠀⢀⠐⠻⣕⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⢹⡇⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡟⠀⠀⠀⠀⠈⠙⢦⣀⠙⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠁
⠀⠀⠀⠘⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⡀⠀⠀⠀⠀⠀⠙⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠹⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣀⣀⡀⠀⠀⠀⣀⣠⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠗⠀⠀⠈⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⢦⣍⣀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠀⠀⢤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣉⠻⠷⣤⣀⠙⢷⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠍⠛⠳⠾⠿⢦⣄⡹⡄⠀⠀⣠⡶⣾⣛⡛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠒⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠈⠓⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣤⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠬⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢝⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣠⠤⠖⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣀⢲⣤⣭⣲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠡⢄⣀⠀⠀⠀⠀⠀⢀⡤⢊⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣵⣒⠶⢶⣶⣦⣤⣤⣤⣾⣶⡦⠾⠛⠉⠀⠠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⣉⠉⠉⠙⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡀⠀⠀⢀⣀⡠⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⡎⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢶⣦⣶⣶⡖⢠⣶⠀⢰⣶⣶⣆⣶⣤⣶⣶⣶⣶⣶⡶⠶⠖⣒⠒⢶⣶⣶⣶⣶⣶⢶⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⢀⣬⣭⣭⣶⡿⠋⠀⠘⣿⣿⣿⣽⡿⡿⣿⣹⢯⡟⡴⠂⠀⠀⠀⠀⠙⣿⡿⢿⣛⣾⣿⣿⢆⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⣹⣦⣶⣾⣿⠡⠸⢷⡀⣈⢢⡟⠛⠑⡁⢠⠤⠠⠴⠀⠁⠈⢻⣮⣽⢿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⡄⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⣟⣛⣹⣿⣿⣷⣄⠀⡝⠦⣏⡳⠀⢀⠀⠘⠄⠀⡇⠀⠂⠀⠈⣿⣿⢿⣿⣻⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻
⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣽⣿⣿⣯⠽⣿⣿⣷⣦⣀⠞⠉⠉⠓⠦⣣⠋⠀⢠⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠉⠀⠀⠀⠀⠀⠀⠈⣿⣏⣻⣹⣿⣿⣿⠟⣿⣿⠿⣿⣿⣿⣿⣶⣷⣘⠁⡈⠀⠋⠁⠀⠀⡀⢸⣷⣯⣟⣻⣿⣿⣿⣿⣧⡀
⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣍⣿⣿⣿⣿⣿⣛⣞⣻⣿⡟⠿⢿⣿⣿⣿⣶⡄⠰⠈⠁⢀⠀⣿⣿⣿⣽⣿⣿⣿⣏⣿⢻⣷⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣯⣼⣯⣼⡿⠿⠶⢿⣿⣿⣿⣿⣿⠀⠀⡄⠈⣸⣿⡿⡿⢿⣿⣿⣿⣿⡿⢿⣿⣷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣇⣿⢻⣿⣷⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⡅⣰⣿⣿⡿⢳⣾⣿⣿⣿⣿⠟⣿⢿⣿⣷⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢿⣿⢿⣿⣷⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣧⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⡄
⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣾⣿⣿⣿⣿⣿⠏⠀⠾⠏⠀⠀⠀⣀⣠⣴⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⡄
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣿⣿⣿⣿⣿⡟⠦⣄⡀⣀⣠⣴⣾⣿⣿⣧⣿⣿⣼⣿⣟⣹⣿⣦⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⣫⣼⣟⣥⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⣬⣿⣿⣿⣿⡟⣻⣿⣿⣿⡿⠿⠛⠋⠁
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⠿⠟⠋⠉
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿
⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⡀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢣⡀⠈⠁⠀⠀⠀⢹
⠀⠀⠀⢠⢒⣩⣤⠴⠶⠥⣄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⡐⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⠉⢦
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠄⠀⢀⣄⣠⣀⠜⠀⠀⢀⡞⢻
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠞⢳⠂⠀⠀⠈⣠⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠠⢤⣀⠴⠃⠀⠀⠀⠴⡟
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠈⣉⠟⠀⠀⠀⠀⢰⠎
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣇⠘⢄⠀⠀⠀⠀⠐⡊⠀⠤⠔⠊⠀⠀⣩⠟⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⣀⣒⣊⣀⣠⣴⣊⣀⣈⠽⠃⠀⠀⢀⠌⠁
⠀⠀⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⡄⢠⠄⢀⣀⣀⣀⣀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⡎⠀⠀⡸⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣁⣠⠤⠞⠀⣀⠤⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡉⣀⣀⠜

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⢻⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣯⣖⢀⣀⡐⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⠿⣽⣿⢟⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣯⠺⣿⠆⠀⣹⣿⡛⠟⠻⠉⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠚⠉⢥⡀⢰⡶⠦⣴⢾
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠠⠤⠐⠒⠐⠀⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠻⣅⠖⠓⠀⠈⠉⢀⠀⢛⣥⣾
⠐⠁⠠⠤⠤⠤⢤⣤⣀⣀⣄⢀⢀⣀⡀⣀⢀⡀⣀⣀⣀⣀⣀⣀⢀⣵⣦⣐⣀⣀⣄⣤⣤⣬⠽⠿⠿⢟⠻⠿⣞⠿⠉⠈⡉⠉⠀⠀⠀⠀⢰⠁⠚⢹⣿
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠁⠈⠁⠉⠈⠁⠉⠉⢉⣉⣀⣉⣀⡀⠀⠀⠀⠀⠈⠉⠀⡀⠔⠋⠀⠘⠈⠀⠀⠀⠀⢀⠀⠈⠉⡤⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠄⣀⣄⣠⣨⣁⡀⠀⢈⣵
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢳⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠑⠄⡀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡀⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⠓⠤⠤⣤⣤⣀⣤⡤⠄⠄⠒⠛⢒⡸⢇⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠓⠒⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠄⠁⣈⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠠⠃⡼⠁⠀⠊⠈⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡰⣌⠢⠐⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠈⠳⡄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠁⠀⠀⠀⠀⠀⠀⠙⠾⣶⢤⣀⡀⠀⠀⠀⠤⢄⣀⡀⠀⠀⠉⣫⠉⠉⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠓⠒⠒⠒⠒⠒⠲⡖⠚⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠳⡀⠀⠀⠀⠀⢱⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠠⠄⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠴⠓⠢⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⠟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⣀⣀⣠⣤⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠉⠉⠉⠉⠙⠚⠻⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡛⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠑⢶⡶⠶⠶⠤⠤⠤⠴⠶⠒⠚⠉⠁⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷
⠀⠀⠙⢷⣶⣤⣭⣓⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⢨⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⣾⣿⣿⣿⣿⣿⡟
⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡲⢤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠶⠒⠢⠤⠄⡀⠀⣀⣠⣀⡶⠋⢑⡵⣫⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣝⣛⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⠶⠟⠋⠁⠀⠀⠀⢔⡽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠻⣝⡛⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠒⠢⠌⠉⠉⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⢾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⡽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⢠⠞⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡟⠛⣇⠀⠄⠀⢖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⡀⢀⡀⠀⠸⠃⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠀⠤⠤⠤⠤⠄⠀⡀⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢳⡀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠑⠄⡀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡀⠄⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠈⠓⠤⠤⣤⣤⣀⣤⡤⠄⠄⠒⠛⢒⡸⢇⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠓⠒⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⠄⠁⣈⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠠⠃⡼⠁⠀⠊⠈⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡰⣌⠢⠐⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠈⠳⡄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠁⠀⠀⠀⠀⠀⠀⠙⠾⣶⢤⣀⡀⠀⠀⠀⠤⢄⣀⡀⠀⠀⠉⣫⠉⠉⠁⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠓⠒⠒⠒⠒⠒⠲⡖⠚⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠳⡀⠀⠀⠀⠀⢱⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠎⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠠⠄⠀⠀⠀⠀⠀⢀⠤⠚⠉⠁⠀⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠴⠓⠢⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⣉⠙⠋⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠛⠛⠉⠀⠈⠛⠛⠫⠭⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣌⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⣀⠠⠴⠶⠖⠒⠒⠠⠀⠀⠀⠿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠠⠴⠓⠚⣉⣡⣄⡀⣀⡤⣀⣀⣤⣀⣤⢈⣠⣾⣿⣿⠅
⠀⠀⠀⠀⠀⢀⠀⠒⠈⡭⢭⣚⣷⣿⣿⣿⡿⣿⣿⣿⣿⣟⣿⣿⣿⣿⢿⣿⣽⣷⢟⠕
⢀⣤⣤⣶⣿⣿⣿⣷⣦⣭⣵⣿⣻⣿⣿⡿⢿⣦⣝⠻⣿⣿⣿⠿⡿⠟⠋⢀⣚⡍⠉⠈
⠉⠉⠉⣩⡿⣻⣿⣿⣿⣿⣿⣿⣿⣎⡻⣿⣿⣽⠿⢧⢴⣴⢘⠁⠦⢚⡉⠋⠀⠁
⠀⠴⠚⣁⣴⣿⣿⣟⣻⣟⣙⡉⠉⠩⠛⣋⠡⡴⣂⣉⡦⠐⠈
⠀⣰⣾⣿⠿⠻⠍⣉⠛⣀⣷⡄⠀⠈⠗⠂⠉⠽⠏⠙⠂⠁
⠀⠀⠰⠀⠀⠊⠀⠀⠀⠉⠉⠉⠉⠒⠀⠄⠤⢠⣶⣇⣛⣳⣏⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠳⠎⣿⡄⣐⣠⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⠶⠖⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠉⠛⠿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠈⠛⠿⢦⣈⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢳⣤⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⠿⡿⢿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣯⣅⣀⢀⣀⣠⣤⣤⣤⡙⣿⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠾⠿⢻⢏⠉⠁⠉⠘⡁⠉⢹⣷⠞⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣝⠻⢿⣦⡈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣶⣤⣟⣩⣽⠿⠶⢒⣀⣫⣄⣡⣠⡀⠀⠘⠁⠀⠴⠂⢀⠀⠁⠂⠁⠛⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡭⢀⠈⠓⠄
⣀⣀⠀⠀⠀⠀⢀⣈⣙⣧⣟⣃⠠⣾⣷⣾⣿⣛⣛⣛⣉⣩⣤⣭⡽⠛⠉⠁⠈⠀⠀⣀⡴⢊⡁⣠⡄⠀⠀⠀⠀⠈⠁⡻⢛⣧⡼⠏⣿⠛⣿⢿⣿⣿⣷⠀⠙⠒⠒
⠙⢿⣿⣶⣶⠒⠒⠚⠻⣿⣿⣿⣷⡌⠹⣿⣿⣿⣿⣿⣽⣶⣾⣿⣿⣡⣤⣀⡴⠀⣼⣿⠟⠋⠀⠉⢀⣴⠀⠀⠰⠀⠠⣰⣨⡿⠃⠀⠀⢼⠘⢃⣸⡿⣿⣇
⠀⠀⠈⢿⣛⡓⠃⠈⠿⠿⠿⣿⣯⣿⣷⡌⠛⠯⣀⣰⣿⣿⠿⠿⠟⢋⣵⡿⢇⣼⣿⣁⡴⢾⣄⣠⠿⠛⠉⠀⠄⢀⣠⣿⠏⠀⠀⠀⠀⠀⡠⢾⣥⠅⢿⣿
⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣄⣨⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⡿⠿⠶⠿⢥⣤⣬⣚⣛⠉⢠⠿⠛⠐⠀⢠⣾⠁⢾⡿⠛⠋⠀⠀⠀⠀⠄⠀⣡⡾⣿⣳⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⣠⣶⣤⣀⣀⠈⢽⣿⢿⠿⣶⣶⣤⣶⣿⣿⣿⣿⣵⣀⣾⣿⣿⣿⠶⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⢉⣴⣿⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⣬⡙⢻⣿⢟⡃⠟⠈⣙⡉⠣⠝⣻⡿⢿⡿⠋⠉⠉⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣰⣺⣧⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣵⣾⣿⣴⣯⣶⠟⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⡀⠐⠀⡠⠚⣽⣡⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣿⣷⣶⣦⣦⣄⣠⣠⠤⣄⢀⢠⣼⣿⣾⣧⣶⣴⣶⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢻⡟⣿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣎⢧⣄⣤⣤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠐⠿⢿⣶⣿⣻⣻⡟⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠒⠢⠤⠉⢉⣛⣉⠉⠉⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣓⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇⣿⣿⡏⣶⡦⠉⣿⡿⠿⠿⢛⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡶⠤⠖⠩⡅⠠⢷⣬⡽⡅
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⡍⡳⡀⠁⠀⠈⠠⠀⣡⣺⡇
⠀⠀⠀⠀⠈⠙⠉⠛⠀⠔⠒⠒⠒⠒⠆⠂⠲⠔⠲⠖⠶⠶⠽⠒⠒⠒⠒⠚⠛⠉⠭⠉⠉⠱⠁⠄⠀⠀⠀⠀⠀⠈⠅⣠⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠁⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠉⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠸⠂⠀⠀⠺⠃⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⣀⠜⠂⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⣰⢉⣤⣶⠶⠟⠛⠒⠙⠷⡄⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⢦⡜⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣽⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⣀⣠⡤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠉⢉⡴⠦⢶⡧⠔⠁⠀⠀⠀⡰⠋⢰⠃
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡰⠛⠉⡽⠀⠀⠀⠈⢀⣴⠇
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣤⣄⠀⣠⠞⠁⠀⠀⠀⣀⡥⣿
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠤⠔⠛⡏⠁⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠉⠁⢀⡄⠀⠀⣀⡤⡞⠁⠀⠀⠀⠀⢀⡤⠏
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠧⡀⠀⠀⠀⠀⠒⠋⡡⠀⠀⠐⠒⢉⠀⠀⢀⣠⠞⠁⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⣀⠀⠀⠀⠠⠖⠋⠀⠀⣠⠴⠚⠁⠈⣉⡭⠋⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⢒⠆⢩⠖⠢⠤⢤⡤⣤⣤⠤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⣸⠀⠀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⡴⠃⠀⠀⢀⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠚⠉⠉⣠⠤⠖⠋⠁⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⢄⡠⠤⠶⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣦⡄⢀⠀⣀⣀⠀⢀⣿⣿⣿⣿⣿⣿⠇⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡄⠀⣰⣿⣿⣿⣶⡀⠈⠻⠛⠋⠉⠀⠀⠀⠋⠀⣠⣶⣿⣿⣿⡿⡇⢺⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣳⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠻⢟⢀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠈⠉⡇⠀⠐⣦⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢿⣶⣿⣈⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉
⠀⠀⢠⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡾⠋⠁
⠀⠀⠈⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠛⠉
⠀⠀⠂
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠕⡯⢗⣫⠴⣟⣦⡴⢆⣀⣄⡀
⠀⠀⠀⠀⣠⣀⣐⣤⣼⣦⣤⣷⣼⣿⣿⠶⢄⡀⠀⠀⠀⢀⣀⠀⣷⣮⢿⣒⣫⠵⣒⣚⣫⣭⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢷⣯⣾⡟⢻⣿⣿⣿⣾⣿⣿⣷⣕⣊⡛⢭⡵⢶⣿⣿⣿⣟⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣭⡽⠏⠤⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠲⠶⠂⠀⠀⢲⣢⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣙⣛⣚⣉⣓⡛⠻⢿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣟⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣟⢿⣹⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣽⣷⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⡎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠋⠒⠲⠆⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠈⠉⠁⠀⠁⠀⠀⣀⣤⡀⠀⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠓⢀⣀⣀⡀⢀⣤⡤⠤⠌⠁⠀⠰⣶⣤⣤⣤⠀⣠⠌⠁⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⠟⠁⠀⠈⣅⠀⠉⠉⠢⡐⢦⣐⠲⠤⢝⠊⣉⣙⣥⣶⡟⢋⣩⣽⣿⣶⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣾⣧⠂⠀⠀⠦⠠⠶⠆⠂⠀⠐⠛⠂⠉⢀⡁⠈⠁⠉⠀⠉⠹⢿⣻⡵⠞⠛⠉⠉⠉⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⡐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⡓⣀⣤⡀⠀⠀⠀⢀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠛⠀⠐⠲⠟⠓⠒⠲⣶⣴⠶⠂⢒⣓⣒⣒⠒⠓⠒⠛⠛⠛⠿⠋⠭⢿⡝⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠀⠀⠀⠈⠉⠉⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⣖⠀⠘⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⣀⠉⠀⢀⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠒⠂⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠛⠓⠀⠉⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣤⣀
⠀⠀⠀⠀⣀⡴⣿⡿⠿⠿⠛⢿⣿⣆
⠀⠰⠊⠭⠭⠤⣿⣷⣤⣀⣱⡎⣻⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡷⠶⠤⠄⢠⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠉⢋⠋⠄⡀⠉⢠⡍⠽⢖⣒⠲⢯⠬⣽⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠶⢄⡀⠈⠀⠬⣟⠷⠶⢭⣷⢶⣍⣛⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠓⠈⢟⡊⠙⢻⢿⣍⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢙⠢⣄⠑⢤⡙⠦⣓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢱⣟⢻⡑⣀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠟⠛⠒⠢⣿⣷⠮⠛⢷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢏⢁⠚⡷⠐⢖⡞⠠⢀⠆⠀⠀⠈⠁⠀⠀⠀⠀⣈⣿⣅⣀⠀⢀⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠠⠤⢄⣨⣤⡤⡄⢀⠀⣤⠤⠀⠚⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠉⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣴⣿⣆⢤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⠮⣿⣟⠟⠋⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣀⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢰⣇⣀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⣀⣤⠤⠶⠖⠒⢺⣇⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠚⠉⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡄⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠤⣀
⠀⠠⣄⣀⣀⣀⣤⣤⣘⣷⡀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠾⠛⠷⣦⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠙⢢⡀⡀
⠀⠀⠈⠉⠉⠁⠀⠈⣉⡉⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠉⢢⠀⠀⠀⠀⢱⠘
⠀⠀⠐⠲⠶⠶⠞⠋⠉⣉⣉⣙⢷⣄⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⣴⣿⠅⠀⢀⡴⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠛⠿⠟⠛⠉⠙⠳⠶⠶⠶⠖⠋⠛⠶⠶⠶⠶⠶⠛⠉⠉⠉⠉⠉⢀⣠⠔⠋⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠴⠒⠚⠉⠉⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠋⠉⠉⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣠⣤⣠⣤⡶⡾⠿⠿⠿⢿⠿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣶⣀⠀⠀⠀⠀⢀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣆⠀⠈⠀⢸⡏⠀⠀⠀⠄⠀⢀⣠⣤⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⣼⣁⣠⣦⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠠⠀⠀⣠⠠⠡⢦⠶
⠀⠀⠀⣒⣦⠀⠀⠤⡀⢄⣀⣤⣾⠋⠀⠀⠀⠸⣷⡿⠿⠟⠛⠓⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣶⣶⣿⣾⣿⣿⣶⣶
⠀⠀⢸⣿⠻⣳⣈⣫⣿⣿⣷⣿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒
⠀⠀⢀⣷⣿⣿⣿⣿⡿⠝⢸⣿⠀⠀⠀⢀⣶⡎⠲⠒⠶⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠛⠁
⠀⠀⢄⣀⣀⣉⣉⣀⣤⣄⣈⣿⣶⣿⣶⣾⣷⣏⡵⠀⠐⢀⣠⣤⣶⣤⣄⣀⡀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⣿⡿⠷⠁⠁⠉
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢠⡿⠛⠛⠻⢿⣿⣾⣿⣶⣶⣶⣶⣶⣶⡷
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⠀⠀⠈⢿⣿⣿⣿⣍⣉⠉⠉⠉⠁
⠀⠀⠈⠝⣿⣿⣿⣿⠛⠁⠀⠀⠙⠈⠉⣙⣟⣯⣻⠖⠊⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣤⣴⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢀⠀⡤⠄⣐⣤⣎⣤⠎⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⣬⡏⠉⠀⠀⠙⠻⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠰⢖⣿⣿⣭⣾⠿⢹⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⣠⣶⣿⣅⠀⠀⢠⣠⣤⠐⠓⠂
⠀⠀⠀⠀⠀⠻⠛⠛⢛⣁⡤⢷⠛⡿⠻⡛⣝⣉⡿⣍⡐⣄⣟⠭⡭⢯⣿⣿⣿⠿⠇⠀⠀⢀⠍⢦
⠀⠀⠀⠀⠀⠀⠐⠊⠈⢠⡂⡤⠖⠻⠛⠛⠋⠑⠂⠋⠈⠉⠟⢗⠣⣜⣿⣿⣁⠀⠀⠀⠤⠀⡠⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣝⣩⣍⣩⣍⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠁⠎⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢱⢢⡀⠀⠼⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠇⠀⠳⡀⠠⠆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠸⢠⢱⠀⢧⠀⠀⠎⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠃⠈⠀⠙⡜⡇⠀⢀⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡄⠀⣀⣠⣠⣿⣷⠴⠾⡞⣿⣿⡒⠒⠒⠒⠒⠒⠒⠶⠤⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⢻⣟⣋⣩⠭⠥⠶⠶⢹⡄⠑⡄⡇⢿⣿⣄⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠉⡉⠉⠉⠉⠉⠙⣷⣾⠠⠄⠀⠀⠁⣨⠁⠀⢆⣷⣼⣿⣿⣧⠠⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⡀⠀⠀⠀⠹⣆⠠⠀⠀⠀⢌⠏⠀⠀⣼⢿⣿⣿⠋⠤⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠹⣆⠀⢀⣰⠊⠀⠀⣼⠓⠂⠙⠀⠀⣀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠘⣯⠉⠀⠀⠀⣰⢃⠀⠘⠀⠀⣐⡯⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠦⢤⡰⠀⠤⠈⣧⠀⠀⣰⠇⠈⢐⠒⠉⠁⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣹⣾⣿⣿⣿⣄⣠⠞⡀⠀⢀⡧⠀⢠⡟⠀⣀⠃⢀⣴⣲⣲⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠁⠉⠉⠙⠋⠀⠈⣈⣠⡞⠁⢀⡾⠁⠀⠠⣾⣇⠈⣿⠿⣿⣿⣿⣿⣆⡠⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠐⢂⠀⡴⠊⠉⠀⠀⢀⡾⢁⠐⠕⠀⠛⠯⣜⣻⣿⠿⣿⣿⡿⠿⣗⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢸⠁⡦⠀⠀⣰⡞⠁⠈⠀⠂⠀⠀⠀⠉⠋⠙⠋⠉⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣀⡼⠋⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠦⢿⡓⢟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⣜⣷⡂⠀⠀⠀⠈⠢⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠲⠦⠭⠁⠀⠀⠀⠀⠀⠀⠓⠘⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣍⣛⣋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⢻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠜⢠⢀⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠭⠍⢩⡭⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⣠⣤⣛⣿⣿⣿⠿⠿⠓⠀⣀⡀⣀⣀⣀⡀⣀⡴⢃⠀⠀⠀⠀⡀⣀⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡊⠙⠋⢉⣁⣤⠶⠾⠛⠛⡛⣿⣿⣿⣿⣿⣷⣂⣘⣿⣿⣿⠿⠿⠟⠛⠋⠈⠁⠀⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠈⠉⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣙⢋⠁⠈⠀⠀⠀⠐⣈⢋⠉⣀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠰⠿⠟⣻⡏⢩⣿⣧⠀⠀⠁⠀⠹⠀⢰⠀⡸⣎⡻⡿⢿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣋⣤⣶⣾⣿⣿⡗⠠⠤⠤⠀⠀⠺⠦⠘⠿⠳⣼⡣⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠛⣀⣀⣤⠾⠛⠛⠿⣿⣿⣿⣿⣿⡟⠛⣻⣷⣤⠀⠈⠙⠢⠀⣉⠙⢶⣆⣹⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠒⣚⣛⣻⣿⡦⢄⣈⣠⡄⠉⠹⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⣛⣿⣿⡿⣿⣯⡵⣖⠨⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠴⠚⣋⣭⡷⣿⣿⠘⣻⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⣴⢎⡟⣡⡿⣫⣟⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠄⠉⣹⠟⠿⢻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀⢸⡟⢻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡿⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠃⠺⠛⠟⠟⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣠⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡇⠀⠉⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠉⣀⣵⣦⣀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠚⠉⠁⠀⠀⠀⣷⡄⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠛⠲⠦⣄⣠⠃
⠀⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠢⢤⣤
⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⣳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠴⠒⢚⣩⠔⠉⠀⣀⢼⡿⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠔⠛⠂⠒⠒⠊⣡⣎⣩⣷⡧⢏⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⠙⣯⠁⣤⢤⡾⢓⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⣛⣛⣭⠖⠉
⠀⠀⠀⠀⠒⠒⠤⣄⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠀⠀⠈⠉⠒⢲⣤⠤⣤⣀⣀⣀⣀⣀⣀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠂⠀⠀⠴⢶⣔⣒⣊⣸⠖⠒⠐⣲⠞⣼⣀⡠⠤⠒⣀⠀⠤⠤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣈⡁⢀⡐⠀⠀⠀⠉⢲⣯⡭⠴⣞⢡⣤⡀⠉⠡⠄⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢸⣿⣇
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⣻⣿⣿⣿⠃⠀⢸⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠋⠀⠀⢸⣿⡏⠉⠻⣿⣶⣦⣤⣀⣀⣀⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠋⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠈⠿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢴⡀⠘⢻⡿⠿⠛⠉⠁⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⡑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠉⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠹⣯⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣦⣽⣯⡦⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣶⠂⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠶⣄⠈⢇⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠑⠀⠀⣀⣀⠙⠓⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⢀⣀⡼⠿⠿⠟⠃⠸⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⡤⢖⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠋⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣶⣦⢰⣶⣶⣶⡦
⠀⠀⠀⠀⣠⣾⣿⣿⠛⠉⢁⡀⠀⠀⠀⠀⠀⢹⡿⠟⠘⠛⠛⠛⠋
⠀⠀⢠⣾⣿⣿⡿⣧⠴⣿⣍⣳⣄⠈
⠀⠀⠸⠟⠋⠁⠀⠀⠀⠙⣿⣿⣿⣧⠀⠐⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⡀⠀⠁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠀⠀⡀⠀⠉⠲⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢣⡀⠈⠁⠀⠀⠀⢹
⠀⠀⠀⠠⢒⣉⣤⡤⠶⠥⣄⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠈⠋⠁⠀⠀⠀⡰⠈⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢶⠉⢦
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠤⢄⣀⣠⢀⠜⠀⠀⠀⡼⢺
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠉⣠⠞⢓⠀⠀⠀⠈⣠⠃
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠠⢤⣀⡤⠋⠀⠀⠀⠤⡿
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠈⢉⠟⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠰⣄⠀⠀⠀⠀⠔⣊⠀⠤⠤⠊⠀⠐⣊⠝⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣀⣔⡊⠁⣠⣤⣚⣁⣀⡭⠃⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠈⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠤⠤⡄⢠⠄⣀⣀⡀⣀⣀⣀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠁⡞⠀⠀⡸⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣉⣀⣀⠜⠁⣀⡠⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⢁⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢶⡄⠀⠘⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⡰⢘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠠⣄⠁⠉⠙⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣽⣷⠆⢤⣤⣬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⡟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⠒⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠚⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣠⣦⡤⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢿⡆⠐⠉⠁⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⡷⣛⣃⣀⠀⠀⠀⠀⠀⠀⣀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠹⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠟⠛⠛⠛⢿⣷⣄⠈⠀⠀⣉⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠺⠛⠉⠁⠀⠀⠀⠀⠀⢀⡸⠟⠃⠀⠀⠀⠈⡶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡴⠋⠚⠃⢉⣹⠃⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⡀⠀⣤⠶⡿⠛⠉⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠼⠻⣄
⠀⠀⠀⠀⠀⠀⢠⠏⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⡗⠀⠀⠀⣴⢞⣤⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠞⡟⣦
⠀⠀⠀⠀⠀⢀⡎⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀
⠀⠀⢀⣴⣶⣿⠁⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡷⠀⠀⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣥⠺⣽⣦
⠀⠀⠉⠉⠉⡛⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡄
⠀⠀⠀⠀⠐⠃⢀⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢲⡟⠀⠐⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢶⣷⣿⠃
⠀⠀⢀⡖⢪⡅⢜⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣾⡿⠀⠀⡀⠀⢿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡲⢤⣤⣻⡟
⠀⢰⣏⠀⠰⣌⡁⢠⡁⠀⡀⠀⠀⠀⢀⣄⠠⣄⠀⠀⢀⣀⣴⣿⠟⠀⠀⠀⠀⠀⠜⢷⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠘⠄⢁⡀⠾⠋
⠀⠀⠀⠙⠿⢿⣝⣿⣏⡺⠛⣤⠀⣀⠀⠀⢄⢤⣤⣴⣿⣻⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣦⣀⡄⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⣦⣄⣠⢞⡅
⠀⠀⠀⠀⠀⠙⠻⢿⣏⣟⣶⣾⣿⢋⡹⠷⣦⣾⡿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣽⣿⣄⣬⢠⡞⢶⢠⡎⠑⣀⣢⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣟⠛⠛⠛⠋⠁⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣟⡰⠶⠿⠛⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⢹⢿⣿⡿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⢸⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠛⠋⠉⠛⠙⠛⠛⠉⠉⠹⠋⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠼⠟⠿⠿⠛⠛⠛⠛⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣿⣿⣿⠿⡀
⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢿⣄⣊⣀⢀⣄
⠀⠀⠀⣄⠹⣷⣾⣶⡤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣹⣿⣿⣿⣿⡄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⢻⣄⠘⣿⣶⣤⣤⣤⡀⣒⣬⡤⢄⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣭⣭⣵⣶⣦⡀
⠀⠀⠀⠀⠻⣷⣌⢿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣶⣶⣶⣶⣔⣿⣿⣯⠉⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⠿⠙⡿⢿⣿⠿⠿⠿⠿⡿⢿⣿⡿⠿⠿⠿⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠢⢀⠀⠀⠚⠤⢴⣆⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠃⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠘⠛⠠⠴⠖⣶⡂⣀⣀⡀⠀⠀⢽⣿⣿⣷⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠑⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠉⠉⠁⠚⠉⠉⠉⠃⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠀⠀⠐⠀⡠⠀⠠⠀⢀⠀⠂⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⡀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⣄⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⡶⠶⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠞⠉⠀⣀⡀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠏⠀⠀⠈⢿⣿⣷⡀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⣠⣶⣿⠃⠀⠀⠙⣧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣿⠀⢰⣶⣴⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣷⣄⣴⡆⠀⣿⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣆⠀⠻⣿⣿⣿⠟⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢿⣿⣿⣿⣿⠃⠀⣿⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠙⢧⣄⠀⠀⠀⣀⣴⠏⢀⣤⠶⠛⠛⠛⠳⠶⣤⡀⠹⣦⡀⠉⠛⠉⠁⣠⡾⠁⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠉⠙⠛⠋⠉⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠙⠶⠶⠶⠞⠉⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠇⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⢾⡻⢦⣀⣀⠀⠀⠀⠀⣀⣠⠴⢛⡵⠋⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠙⠶⣌⣉⠛⠛⠛⠋⣉⣥⠶⠋⠀⠀⠀⠀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠶⣤⣄⣈⡉⠛⠛⠛⠛⠉⠀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠚⠛⠛⠛⢳⡟⠁⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠙⣷⠶⠒⠲⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠉⠻⢦⣀
⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⣇
⢰⡏⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢹
⣾⠁⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⠀⠀⠈
⣿⡀⠀⣀⣤⡶⠛⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⢦⣄⡀
⠈⠙⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠛⢻⡶⠶⠶⠶⠶⠶⠶⢶⡖⠛⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡾⠁⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢞⣉⡀⣠⣍⡳⣄⠀⠀⠀⠀⠀⠀⣠⣶⣋⣄⢈⣙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣋⣩⡇⢸⠉⢻⣎⣷⠀⠀⠀⠀⣴⣿⡟⠉⣯⢸⣏⣛⣮⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⠤⣄⠀⠈⠙⣷⡀
⠀⠀⠀⠀⣀⣠⡴⠛⠻⣄⣀⡙⠷⠸⠀⠀⠀⠸⣇
⠀⣠⠶⠛⠉⠀⠀⢁⡠⠤⠶⠀⠀⠀⠀⠀⠀⠀⡟
⠸⣧⣤⣤⣤⠴⠾⠛⠋⠻⣍⡉⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⡴⢇⠀⠀⠐⠲⠶⢺⡟
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠁⠐⠶⠶⠚⣿
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠒⠲⠶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠒⠒⠒⠒⠚⢉⡥⢾
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⣴⣄⡀⣠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⢠⠆⣤⠀⠀⠀⠀⠀⠀⠒⢛⣉⡴⣻
⠀⠀⠀⠀⢸⣧⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣉⣠⣀⣀⣠⣤⠴⠟⠉⣀⣤⣾⡁⠀⣀⠤⠞⣡⠄⠀⠀⠀⠀⢀⣙⣫⡥⠖⠋
⠀⠀⠀⠀⠈⢷⣥⣬⠓⡒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠯⣤⣤⣉⣉⣉⣭⡭⠭⠤⠖⠒⠉⠁⠀⠀⢀⣙⠒⠶⠬⠖⣊⠁
⠀⠀⠀⠀⠀⠈⢿⣄⣛⠡⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣭⠭
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠉⢡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣤⣄⡀⠀⠀⠀⠀⠀⢤⣦⣤⣤⣤⣴⣶⠏⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⣤⣤⣄⣀⣀⣀⣠⣿⣄⣀⣤⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣼⡿⠉⠉⢹⣿⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠟⢋⣁⣠⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠈⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠷⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣠⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⣿⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣬⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢿⣤⠶⠾⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⢀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⣠⠖⠋⠉⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⢀⠀⠀⠀⠀⣀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⣾⣆⣀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠒⢤⡀
⠀⠈⠛⠒⠚⠛⠉⠛⠚⢿⣄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠳⡄⠀⠀⠀⠙⡌⢆
⠀⠀⠤⣤⣤⣤⡴⠖⠶⠶⠻⣦⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣴⡋⠀⠀⣸⠀⠀⠀⠀⣱⠈
⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠙⠾⣿⣷⠶⠛⠻⢦⣤⣤⣤⠤⠲⢦⣤⣤⣤⣤⡴⠞⠛⠛⠛⠛⠉⢀⡤⠞⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠚⠉⠀⠀⠀⠀⢀⡰⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠚⠉⠁⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠶⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⣀⣠⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣧⣶⣷⠿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢾⡏⠁⠀⠈⣿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣊⣁⡤⠴⠒⠻⣤⣴⣾⣯⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡸⠋⠉⢹⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⢀⣤⣿⣿⡇⢀⣠⣶⣿⣿⡿⠿⠿⠿⠿⠿⠿⠶⣦⣤⣀⣀⣤⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣁⣭⠔⠻⠿⢿⣿⣷⣿⠟⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡞⠁⠀⠀⠀⠀⢺⣿⣿⢁⡀⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡇⠀⠛⠀⠀⠀⠤⠣⠟⣿⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⣀⣠⣤⠴⢖⡂⠈⠣⣀⡀⡀⠀⠀⠀⠀⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠴⠶⠶⣶⡶⠒⠒
⠀⠀⠀⠀⠀⠈⠳⠬⠓⠲⠦⠤⢬⣝⠻⢷⣴⣦⣀⣴⣵⣺⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⣤⠈⣲⠄⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣍⣀⣀⣈⣉⣙⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠒⠒⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠤⠄⠒⠒⠒⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣀⣠⣶⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠴⠒⠂⡴⠖⣲⢦⣤⣄⣀⠀⠀⠀⠀⠀⢸⣿⡞⣽⣿⡿⠛⠛⠛⠻⠯⢏⠒⢄
⠀⠀⠀⢲⢄⣰⣯⣤⡾⠛⠳⠀⠀⠀⣀⣠⣤⣴⣶⣿⣻⣻⣿⢽⣮⣛⣀⣴⠤⣥⣄⢀⠀⠙⢿⣿⣿⣷⣦⣤⣠⣾⣶⣤⣠⣶⡄⠀⠀⠀⠀⠀⠀⠈⠒⠈
⠀⠀⠀⠀⠰⢝⣿⣻⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣿⣶⣤⣵⣟⡽⠚⣳⢻⣿⣿⡿⣿⣿⣿⣶⣞⣻⣾⡿⠏⠷⢿⣯⡿⡣⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠙⠺⢯⣿⣿⡍⠙⠛⢻⣿⣿⣧⠣⡻⣯⠉⠻⢾⣏⢻⣷⠿⣿⣿⢿⣿⡿⠿⠛⠋⠁⠀⠀⠈⠀⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣇⡀⡀⠀⠈⠉⠀⠀⠀⣹⢧⡀⠈⠻⣆⠀⠕⣶⠙⠃⠀⠀⠀⠀⠀⠀⢀⣠⣶⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠹⠗⠊⠀⠀⠀⠀⠀⠀⠀⢄⣠⣼⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣷⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠿⣦⢀⣀⣠⣤⠦⠺⢿⣿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⣤⠀⠀⠀⠀⠠⢿⣌⡉⣉⣵⣶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⡀⠿⢧⣄⡀⣴⣆⡍⠛⠒⠒⠈⣧⣀⠀⠀⠄⠀⠤⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠉⠈⠁⠀⠀⠀⠀⠄⠁⠙⠛⠠⠽⣤⡗⠀⠀⠀⠡⢆⠀⠀⠀⠀⢀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣶⣦⣀⣀⡀⠀⠀⠀⣀⣄⣀⣀⣠⣄⡀⠀⠀⠀⢒⣴⣍⣑⡶⣴⣶⣧⣌⣶⣶⣶⣾⣶⣾⣷⣮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣿⢿⣿⣏⠀⣈⠛⢺⣛⣾⣿⣿⣿⣿⣷⡂⠀⣤⣤⣿⣯⣤⣿⣿⣻⣦⡬⠿⠟⠹⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠉⠛⠙⠛⠛⠛⠛⠛⠃⠛⠛⠋⠙⠛⠋⠉⠉⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠉⠉
⠀⠀⠀⠰⢶⣶⣶⣶⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⢤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⡄⢀⠤⠀⠀⢀⣒⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠰⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⡿⠃⢀⣼⣿⣿⣿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠰⣶⣿⣿⣿⣿⣿⣷⣾⠛⠿⠿⠿⠿⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠟⠛⠒⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣉⣉⡛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠉⠙⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⢀⣿⣿⣿⡟⢑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡽⢿⣿⡟⠛⠛⠛⠓⠤⢈⣉⣒⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡍⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⣛⣺⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢷⣟⣛⡿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣿⣿⣿⠿⠿⢿⣷⣦⣭⣭⣶⡟⠻⠋⠩⠛⠹⠿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⢯⠍⠉⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣏⣼⡿⢡⢊⣀⡈⠀⢀⠀⠀⣠⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠚⠃⠚⠛⠛⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠭⠭⠭⠭⣭⣽⣉⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡿⠋⢁⣀⣤⣄⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⠁⠀⠀⠀⠙⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠲⡄⠀⠀⠸⣽⠃⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⣏⠙⠓⠚⠛⠋⠀⠀⠾⠃⠀⠀⠀⠉⠉⠙⣲⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡄
⠀⠀⠀⠀⠀⠈⠙⠲⣦⠤⣤⣀⣀⡀⠀⢀⣀⣠⣤⠖⠋⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣠⡭⠽⠿⠿⠛⢉⡇⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣖⣴⢿⣿⠃⢸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢻⣠⡤⠶⠖⠛⠛⠛⠋⠉⠉⠸⠿⠛⣡⢸⠃⠀⠈⡼⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠼⢡⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠲⠶⠦⣤⣀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡣⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⠯⠥⢤⡄⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡆⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠀⢀⠞⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠸⣆⠀⠳⣄⡈⠙⠲⠦⣷⣦⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠷⣦⣄⣙⠛⠶⠦⣤⣀⣉⠛⠓⠶⠶⠶⠶⠶⠾⠛⠉⠁⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⠍⠉⠛⠛⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣲⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⢏⡉⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡴⣾⣿⣭⣤⣤⣤⣶⣤⣤⣶⣷⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⠴⠾⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⡟⣰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⣵⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢁⠴⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⢀⣴⣾⣿⣿⣿⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠾⣿⣿⣿⠿⣿⢿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠊⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠰⠎⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠁⠚⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡄⢀⡞⢀⠀⢠⠏⠀⠀⢀⡆⠀⠀⠀⠀⠀⣀⡻⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠈⣠⠃⠀⠆⢀⠀⠀⢫⡤⠆⣀⠀⠀⠞⢻⣅⣘⢷⠀⠀⠸⠀⡄⠀⢰⢂⠘⠁
⠀⠀⠀⠀⠀⢀⠰⡇⢰⣧⢢⠖⣰⠃⣰⠇⠀⡄⣊⣡⡄⣈⡀⠈⠉⠉⠁⠀⠀⠀⢰⡇⠀⠘⠸⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⣆⠀⠃⣼⢡⠋⣰⢣⢞⣡⣤⡀⡿⠃⣷⣴⣶⣶⡶⡰⠿⣿⡆⠀⡄⢸⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⡄⢸⢃⡇⢰⣏⣴⣿⣿⢟⣷⣶⣶⣾⣿⠿⣵⠗⡃⠀⠛⠃⠀⠇⠀⢠⡇⢸⠀⡄⠁⠀⢰⠃⠀⠀⡀⠈
⠀⠀⠀⠀⠀⣄⡏⠀⣼⢠⣿⣯⠙⠋⣰⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠌⠀⠀⠀⢠⠀⠇⠀⣨⠀⠀⠀⠘⠀⣶⢸⠁
⠀⠀⠀⠀⠀⢌⠁⠀⠉⠔⠁⢀⡀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠂⠀⠸⡇⠀⢠⡧⠀⠀⡀⠂⠀⡏⠘⠀⠆
⠀⠀⠀⠀⢠⡘⣰⣶⣿⡇⠀⣹⣶⣷⠀⣠⣴⣿⣿⣿⣟⡻⣷⣤⣤⣦⣿⣶⣤⣀⣘⡇⠀⢸⡇⠀⠰⡇⠠⠲⠆
⠀⠀⠀⠀⠘⡇⣽⣿⠏⠁⠀⠉⠻⠈⢺⣿⣿⣿⣿⠟⠉⠁⢼⡸⢿⣿⠿⠟⠛⣿⣿⠟⢷⣾⡧⣠⡀⠀⠀⢰⡃
⠀⠀⠀⠀⢠⣿⣏⣡⣴⣴⡶⠂⠀⠀⢸⣼⠯⣻⣿⠄⠈⠀⢈⠀⠀⣁⠴⣷⣼⠿⢻⣿⣿⣏⡄⣴⢬⣄⣰⠋⠀⠀⡆
⠀⠀⠀⠀⢸⣿⠟⣿⢡⣌⠋⠃⠀⠀⠘⣿⣞⣿⣽⢖⡄⣠⣴⣦⢴⢙⡷⢿⣥⣌⣙⠿⠿⠿⢶⣯⣿⣯⡿⢻⣶⣀⣡⣄
⠀⠀⠀⠀⢠⣿⣿⣧⣠⣿⡀⠀⢀⣶⠀⠘⢿⣿⣿⣾⣿⠘⡿⢀⡆⠔⠃⣶⣻⠍⠿⣹⣗⡢⢶⣾⣿⣭⣾⣿⣟⣿⣿⡿⠶⠄
⠀⠀⠀⠀⢸⡏⣿⣿⠿⠛⠉⠀⠹⢿⣿⠛⠒⢹⣿⢿⣿⣿⣿⣿⣿⣿⣾⣮⣏⣑⠀⣽⣿⡴⣿⣥⣿⡝⣽⣿⣿⣿⡿⠶⠂
⠀⠀⠀⠀⠀⠀⠴⠷⢦⠀⠀⠀⢀⡀⠻⠯⠒⠤⠈⠀⠀⠉⠻⠿⢿⣿⢿⣛⣿⢿⣿⣿⣿⠿⠿⣥⣶⠁⠀⠔⡋
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠠⠖⠀⠹⠏⢈⠉⠀⠀⠀⠠⠀⢤⣤⠄⠠⠀⠈⠉⢉⣿⡏⠠⠤⠀⢀⣈⡁⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣲⠄⢀⣀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⢀⡴⠋⢸⠀⢀⣀⠀⠀⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⢡⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡃⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠠⠡⠤⠠⠭⠕⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠴⠶⠼⠓⠒⠀⠀⠀⠀⠉⢙⣦⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⡿⠛⠋⠽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢏⠀⠀⠀⣀⠙⠮⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠀⠀⠈⠀⠀⠉⠐⠂⠦
⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠃⠰⢜⠁⠀⠀⠀⠀⠘⠠⠂⠀⠀⠀⡁⠀⠁⣀⣀⣉⡅⡠⠤⠀⣀⡀⣀⣠⣷⠂⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠈⣁⠃⠀⠀⠀⢌⠁⠀⣀⠐⠀⣀⡴⠾⢋⣉⡉⠀⣀⣀⡀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣿⠆⠀⠀⠠
⠀⠀⠀⠀⠀⠉⠀⢂⠛⠀⠀⠀⠀⠀⠀⡠⢐⣡⠞⠿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⢢⠀⠀⠀⠀⠀⣿⣶⢞⠉⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⣠⢞⣴⡿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⣠⣟⢔⡀⠙⠳⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣵⣿⠏⠀⠀⠀⠀⢀⣀⣴⣿⣦⣀⡀⠀⠀⠀⠀⠀⢈⣼⣿⣦⣤⣴⣾⣿⣻⠿⠅⡠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣏⢘⠀⠀⠀⢠⣿⣷⣭⣹⣿⣿⣿⣿⣷⣦⣴⣶⣿⣿⣿⣿⢟⣿⡿⢿⣿⠿⣷⣿⣦⠁⠠
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⣿⣿⣿⠘⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣛⣧⣿⣿⣏⢛⣿⠟⣫⠻⣻⣅⣰⣇⡈⠀⢾⣿⣢
⠀⠀⠀⠀⠀⠀⠈⣩⣟⣿⣿⣿⣿⣿⣿⣧⣀⡀⢤⣽⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⡿⠛⠓⠛⠛⠛⠻⠏⠁⠟⢻⡻⠍⣋⠉⠉⠁
⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣾⣿⣿⣿⣿⣿⣷⣀⡀⠐⠛⠛⢩⣶⣯⣤⣤⣤⣤⣯⣴⣺⣿⣥⣤⡄⠀⠄
⠀⠀⠀⠾⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⢯⣽⡿⠿⢿⣋⡟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠩⢼⡿⠿⠛⣻⣭⣭⣭⣥⣤⣤⠤
⠀⠀⠀⠀⡀⠀⡀⠀⣀⠴⣶⣾⣬⣤⣤⣤⣤⣀⣿⢠⣤⡤⠟⣆⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠿⡭⠲⠿⠿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠒⠁⠚⠛⠛⠏⠙⠻⠿⠟⠛⠛⠛⠻⠷⢥⣬⣬⠍⢣⡀⢀⣀⣀⠴⢂⣀⣀⠀⠀⠀⠀⡀⢀⠉⢑⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢐⡲⠿⣟⣿⣿⣿⡾⢿⣶⣾⠷⠶⠶⠿⠷⠶⠾⠿⢾⣿⠖⠒⠒⠚⠁⠀⠀⠤⡠⠦⠅⠛⠂
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠹⠛⠻⠿⠿⢽⣶⣒⣲⣒⣒⣂⡀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠓⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠁⠑⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⡿⠛⠉⣡⣨⣿⣿⣿⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠓⠁⠀⠀⢈⣹⣥⡴⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠻⣿⡄⠀⠀⢀⣤⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡈⠿⡤⠀⢲⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢷⠀⠀⢰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡶⠀⡇⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠉⣀⢬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦⣭⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣯⡙⢟⠀⠉⠘⠓⢾⣻⡿⣿⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣡⡄⠠⠀⠈⠀⠈⠉⠃⠺⢠⣿⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡈⠿⠗⠀⠀⠀⠀⠀⠀⠀⠈⠀⣛⠐⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡍⠻⠍⠀⣼⠟⠁⠀⠖⠓⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣶⠀⠠⣠⠀⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣂⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣄⠀⠳⠆⠀⠊⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣧⡄⠈⢠⡤⠰⠚⠂⠀⠀⠀⠀⠀⠀⡄⠀⢀⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣃⢠⡄⠶⠀⡴⠀⠉⠀⠀⢀⠀⢀⡤⢤⣠⣶⣿⣿⠟
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⠀⠹⣶⣴⢆⡠⡀⠈⠀⠀⠔⠊⠀⢉⣤⣾⣿⣿⣿⠃
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⠂⢩⠿⣯⣦⠀⠓⠀⠀⡉⣁⣴⣾⣿⣿⣿⠟⠁
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠙⠻⣿⣶⣾⡿⢟⠩⣍⣶⣻⣽⣿⣿⣿⠟⠁
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠛⠧⢾⡷⣙⣿⣿⣷⣧⣶⣿⣿⣿⣿⣿⡿⠃
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣼⣿⠒⣯⣽⣿⣿⣿⣿⣿⣿⣶⣿⠟⠋
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉
⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⢿⣿⣿⣷⣾⣦⣿⣼⣻⣷⣶⠿⠾⠒⢲⡤
⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠙⠻⢾⣭⣿⣿⣿⣟⣷⣯⢴⣾⣟⣶⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣗⠿⣿⣟⢛⣿⡿⣶⢶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠉⠉⠙⠂⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣿⣭⣿⡿⣷⣶⣭⣌⣋⡛⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣬⣍⠻⣿⠿⠿⣷⣦⣥⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣻⣇⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠿⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⡾⠋⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠈⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣿⠀⠀⣀⣀⣤⣤⡶⠶⠶⠾⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⢻⣿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠻⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⣀⣀⣀⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⡠⠞⠋⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠘⣧⣄⣀⣤⣿⣄⣀⣀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠙⠢⣄
⠀⠀⠛⠶⠶⠶⠛⠛⠶⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⣄⠀⠀⠀⠈⠳⡐⣄
⠀⠀⢀⣀⣀⣀⣀⣤⠶⠦⠼⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⠁⠀⠈⡆⠀⠀⠀⠀⣧⠘
⠀⠀⠀⠉⠉⠉⠩⠤⠤⠴⠒⠶⣭⣿⣦⣤⣴⠿⣦⣀⣀⣀⣀⣀⣤⣀⣀⠀⠀⢀⣀⣤⠶⠿⠶⠾⠿⠟⠃⢀⣠⠞⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⢠⠞⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠒⠒⠉⠉⠁⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⠿⠟⠿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠙⢿⠟⠋⢠⣾⣶⠀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠃⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠤⢶⣾⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣹⠆⠀⠀⠀⢀⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠆

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢊⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠏⠘⠛⠉⢻⣿⣿⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠠⣀⠀⣠⠠⠜⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣤⣤⣶⡶⢶⡴⡲⡲⣦⣤⣄⣀⣀⣀⢀⡄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⡚⠟⠿⣻⣿⠋⠀⠘⠀⠐⠀⠙⠋⠯⠿⠛⢿⣍⡐⠂⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠠⠀⣀⣤⣔⣶⣾⠟⢩⡁⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠃⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢖⠀⠑⢜⡩⢜⡄⠀⠀⡁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢰⠀⠛
⠀⠀⠀⠀⠀⠀⠡⣄⡀⠉⠠⣖⡫⣆⣰⠶⡄⠤⠀⠂⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡃⠀⠀⠀⠀⠀⠀⠀⡴⢇
⠀⠀⠀⠀⠀⠀⠈⠄⢇⠀⠀⠈⠉⠻⠶⣶⣧⣄⡀⢀⠈⢃⣛⡶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠊⠢
⠀⠀⠀⠀⠀⠀⠀⢉⡍⣯⡀⠀⠀⠀⠀⠀⠈⠉⠛⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠄⠁⠉
⠀⠀⠀⠀⠀⠀⠄⢓⡥⢿⠐⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⣤⣾⣖⡶⢦⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠙⢢⡐⣶⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠻⣷⢾⢤⠍
⠀⠀⠀⠀⠀⠠⠄⠀⠀⢉⡖⠎⠹⣿⣶⣆⠀⠀⠀⡀⢦⣤⣤⣶⣤⣀⡀⣀⣀⡐⢀⣴⣿⣿⢟⣿⡗⠞⢱⡙⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⣯⣙⢻⣳⣤⣄⣠⣔⣇⢻⣿⢿⠉⣿⣿⣿⣿⣿⣿⢿⠹⢞⠛⠦⠰⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⢛⡷⣻⠿⡿⣷⣾⢧⣭⣍⣉⣟⣝⣛⠅⠀⠐⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠐⠓⠝⠿⠛⠶⠶⠷⠾⠎⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣤⣴⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣄⣀⣀⣠⣤⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⣋⣤⣾⣿⣿⠿⠿⣿⣿⣿⣷⣮⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣍⣛⣛⣋⣡⣠⣤⣀⡉⠉⣤⣬⣉⣉⣤⣤⠀⠈⠉⢛⣛⡛⠋⠉⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣭⣭⣽⣭⣽⡿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⢀
⠀⠀⠀⢀⡄⠀⠛⠀⠀⠀⠀⠀⢠
⠀⢀⠔⡗⠀⣀⣀⠀⢀⠀⠀⠀⠈⢀
⠄⠤⠔⠂⠉⠀⠈⠉⢳⡄⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠀⠒⠀⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠁⠒⠀⠀⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡔⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠠⣄⠄⢀⠀⠀⢀⠀⠀⠀⠈⠀⠂⠀⠀⠈⠈⠀⠈⠛⠂⠓⠲⠤⢥⡤⠘⠿⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠘⠙⠲⣦⡀⡁⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⠀⢐⣦⠤⣤⣤⡀⢀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠡⠟⠀⡒⠲⣞⢳⣤⣥⣀⣀⡀⠔⠉⠀⠀⠀⠀⢡⢂⠂⡸⣣⣈⡙⠧⠑⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⡀⠀⠘⠄⠀⠑⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⡠⢭⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⡀⠀⠀⠀⢈⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡈⠀⠀⢀⣀⠀⡐⠀⠀⢠⡼⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣠⡖⠒⠒⠶⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠂⠀⠠⡆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠗⡂⠠⠐⢂⣿⣦

⠀⠀⠀⠀⢀⡀⢠⡄⢀⡄⠀⠀⠀⠀⠀⠀⣦⠀⣇⠀⢠⡄
⠀⠀⠀⣄⢸⡇⣾⣧⣸⣇⣾⠀⠀⣷⡀⢀⣿⢸⣿⠀⣿⠁
⠀⠀⡀⢿⣾⣿⣿⣿⣿⣿⣿⣧⡀⢿⣷⣘⣿⣿⣿⣿⣿
⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⡿⢧⠻⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠰⣼⣿⣍⠛⠆⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣩⣿⣟⠓⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠈⢙⣿⡷⠆⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠛⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠛⠦⠤⣀⣀
⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠀⠀⢀⡾⣻⣿⣿⣿⣿⣿⣿⠿⠿⠐⠒⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡀⠀⠀⢠⠞⠑⠻⠿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⠾⠋⢠⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠋
⠀⠀⢀⣾⣿⡷⢠⣄⣀⠀⠀⠀⣀⣠⣤⣶⠶⠟⠛⠉⠁
⠀⣠⡿⠟⠋⣀⣈⣿⠿⠃⡠⠚⠋⠉⠁
⠘⠉⠐⠚⢛⣿⣿⣿⠿⠟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣡⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⢀⠖⠀⠈⣽⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠘⣿⣿⣿⣿⣿⣦⡀⠀⠀⠁⠀⠀⠀⣿⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⠀⠻⣍⣻⣿⣿⣤⠀⠀⠀⠀⣿⣿⣿⣿⠿⠁⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⣤⠀⢸⡇⠀⠀⢀⣀⡠⢷⣶⣶⣶⣶⡤⣀⠀⠀⠠⢀⣸⡿⠃⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢰⣿⣷⣦⣀⡉⠉⠀⠀⠀⠀⣐⢿⣿⣿⡎⠀⠀⠀⠀⠀⠀⢶⡀⢸⣧
⠀⠀⠈⣿⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠀⠀⠠⣉⠛⠿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠿
⠀⠀⠀⢿⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠱⢦⣬⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠸⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣶⣶⣶⡾⣾⣿⣿⣿⡤⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠘⣷⡀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠒⢬⣋⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡀⠐⠠⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣍⣛⠶⣤⣈⡻⢦⡀⠙⢆⠀⠀⠀⠀⠀⣀⣐⣀⣤⠶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠛⠛⠷⢬⣷⣠⣤⣞⣛⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣿⣟⣿⣿⣛⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣻⣿⣛⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣅⣸⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣟⠛⣿⣿⣿⣿⡿⠋⠉⠉⠻⠟⠛⠛⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠘⠛⠛⠀⠀⠈⢿⣿⣿⡷⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣤⣤⡀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣀⣠⠀⠠⠖⠒⠛⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⣤⣭⣍⣙⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠁⠀⠀⠀⠀⠀⠀⣴⣲⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⡿⠿⢿⡿⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⣿⣯⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣭⣿⣿⣗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⠰⡆⢠⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢙⠒⠒⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⣤⣄⡀⠀⠀⡀
⠀⠀⠀⠀⣠⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⢀⣤⣴⡆⠀⣿⢂⣻⡖⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠚⠛⠃⠙⠿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣀⣤⣤⣶⣾⣛⣬⣤⣿⣿⣿⠇⢠⣧⣸⡿⠀⣠⣐⣦⣀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣿⡇⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠏⠀⠀⢛⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⠋⠀⠀⠠⣾⣿⣿⡿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠃⢠⠆⠡⣤⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣧⣀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣇⣾⠋⠁⣼⣿⣾⣿⣿⣿⣟⢛
⠀⠀⠀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢳⡟⢓⠴⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⠿⠫⠀⢸⣹⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⡿⠛⣋⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣤⣠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣿
⠿⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡉
⣯⡛⣿⣛⣛⡿⢛⣻⣿⡿⠒⠭⣤⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⠿
⣯⣽⠿⠿⠿⠿⣽⢿⡿⠿⠿⡷⠖⢃⡠⠀⠀⠉⠛⠻⣿⠟⠿⠟⠻⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡗⠀⠀⠀⠤⢶⣯⡴⠦⠷⠿⣉⣤⢿⡖⠀⠒⠀⠀⠠⣶⣤⠾⠾⠧⠘⠿⠗⠂⠐⠒⠂⠛⠛⠛⢛⠛⣿⣿⣿⣿⣿⣷
⣶⣄⣤⣠⠄⠈⠀⢀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠠⠶⣿⡟⣳⠛⢛⣓⠛⠟⠻⢖⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣥⣬⣅⣄⣠⣿⠊⠀⠀⠀⠀⢀⣠⣼⣿⣿⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠋
⡿⠿⠟⠉⠉⢺⣿⣷⣄⠀⠀⠀⢉⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠋⠉⠁
⣶⣶⣿⡶⡿⢿⣿⣿⣿⠷⣶⣼⡋⠉⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣁
⣟⡋⠀⠁⠉⢻⣿⣿⣿⡄⠈⠻⣿⣿⣶⣶⣤⣤⣄⡀⠀⠈⠀⢀⡀⠀⢀⣀⣤⣽⣀⡀⣥⡀⠀⢴⡤⠠⣄⡀
⢻⣯⣽⠁⢀⣾⣿⣿⣿⣿⣷⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣐⣿⣷⣶⢄⣀⣀⡀
⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣽⣦⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣭⣙⠀⠀⠀⠁⠉⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀
⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣵⣶⣿⣿⣷⡀
⠀⠀⠀⠀⠛⠛⠋⠉⠉⠉⠈⠙⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠁⠀⠀⠀⠀⠀⠈⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⠛⠻⠿⠿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣰⣷⣿⣿⠟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣾⠒⠺⢷⣶⣦⣷⣴⣾⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠟⠉⠀⠁⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣶⣶⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢀⣰⣬⠥⠤⠒⠵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠟⠁⡉⣽⣿⣷⣦⡤⢤⣄⣀⣠⣤⠄⠤⠔⣒⡂⠥⢌⣠⠭⠖⠛⡉⠀⠄⣂⣤⠞⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⡀⡃⠀⠀⢀⣌⣨⣷⣿⣿⣿⣿⣷⣦⣤⠴⠒⠖⠚⣩⣭⠴⢒⢋⡍⢀⣂⣠⠵⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠠⠞⠀⢀⣠⣶⣿⣿⣟⠻⡟⣤⣿⣿⠟⣣⡤⠴⠞⡛⠁⣠⣤⡶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣟⡄⢰⡔⣿⡶⣼⣿⣿⡿⡟⠀⠀⣢⣶⣿⣿⣟⣫⣱⣾⣾⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡻⣹⣞⣾⣿⣿⠏⠉⣨⣵⣄⣠⣤⣿⣿⠟⣻⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣧⣝⡿⣟⣿⠓⠀⠀⡚⣿⣿⡿⠿⠋⢠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⡄⠻⠳⣃⠛⠁⠀⠀⠀⠉⠈⢉⠁⢀⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠸⢲⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘

⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙
⡇⠀⠀⠀⠀⠀⠀⠀⣦⡀
⡇⠀⠀⠀⠀⠀⠀⣄⢹⣿⣦⣀
⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣙⠻⣶⣤⣀⡀
⡇⠀⠀⠀⠀⠀⠐⣦⣻⣆⠙⠛⠶⠄⠉⠛⠻⢷⣶⣤⡀
⡇⠀⠀⠀⠀⠀⠀⡘⢿⡿⢷⣦⡀⠐⠤⣤⣀⡀⠀⠙⣿⡆
⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⡀⠀⠀⠀⠉⢻⡆⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣠⣤⢶⣶⣤⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣍⣉⠁⠀⠀⠀⠈⣷⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⡾⠋⠙⠛⠛⠀⠀⣠⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣭⣉⣀⠀⠀⠀⠹⡄⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠶⠶⠶⠚⠛⠛⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⠿⡋⠀⠀⠀⠀⠀⠈⢻⣧⣄⡀⠠⠤⣴⣶⣄⡉⠻⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣟⡁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣋⣁⣤⣤⣶⣾⣿⡿⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠛⢛⣩⡿⠟⠋⠁⠀⠈⠁⠀⠘⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⢸⣿⣿⠀⣾⣿⣆⣿
⡇⠀⠀⠀⠰⣶⣦⣤⣤⣾⠟⠁⠀⠀⠉⣀⣤⠖⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⣿⣿⡟⠀⣿⣿⢻⣿
⡇⠀⠀⠰⣾⣿⣿⣿⡿⠃⠸⣦⣴⡶⠿⠋⠁⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢀⣿⣿⡇⢸⣿⡿⣿⣿
⡇⠀⠠⣶⣿⡿⠛⢛⡉⠁⣰⡟⠀⠀⠀⠀⠀⠴⠚⣋⣭⣴⣾⣿⣿⣿⣿⣟⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣿⡇⠀⢸⣿⣿⠃⣼⣿⣷⣿⣿
⡇⠀⣴⣾⣿⡟⠛⣉⣤⡾⠛⠀⢀⣀⣀⣤⣴⡶⠟⣋⣽⣿⣿⣿⣿⣿⣿⣿⣷⣍⠻⣿⣿⣷⠀⠀⡄⠀⠀⣾⡇⠀⣿⣿⡇⠀⣿⣿⡿⢠⣿⣿⣼⣿⣿
⡇⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠉⣡⣀⠈⠉⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢘⣿⣿⠀⣾⣿⣶⣼⠇⣷⠀⣿⣿⡇⣧⣝⣻⣧⣜⣿⣿⡏⣿⣿
⡇⠀⠘⠛⢻⣿⣿⣿⣿⣿⠋⣥⡾⣿⠏⣬⣿⢯⡻⣿⣻⣶⡦⡍⢹⣿⣿⣿⣿⣿⣿⢸⣿⣿⢠⣿⣿⣿⣿⠀⣿⢀⣿⣿⣇⣿⣿⣿⣿⡿⣿⡿⠁⣿⣿
⡇⠀⠀⠀⠈⠉⠉⠛⠛⠃⠘⣡⡾⠋⠀⠉⠙⠛⠿⠿⢿⣿⣷⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣇⢻⣿⠀⢸⣌⡻⣿⣿⣿⢹⣿⣿⢱⣿⢡⡄⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⠍⠅⢿⢻⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣧⠹⢸⡞⣿⣿⣿⣿⠇⣿⣿⢇⣿⢡⣿⡇⢻⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢸⡿⢻⣿⣿⣿⣿⠀⣿⢾⡿⣿⡆⢸⣷⣿⡏⣿⡟⣸⣿⠏⣼⣷⣿⣿⣿⣸⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡿⣿⣿⡏⢸⣿⣾⣷⣿⣿⡈⣿⣿⡇⣿⢡⣿⠏⣼⣿⣿⠿⣻⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢹⣿⡇⣿⣿⣿⣿⣿⣯⣧⢻⣿⣰⢃⣿⣿⣾⠿⢋⣥⣾⣿⣿⡿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣡⣴⣆⢻⠀⣿⣽⣿⣽⣿⣿⣿⣾⣿⢣⣾⣟⣫⣵⢾⣿⣿⠟⣿⡿⢱⣿
⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣐⣚⣛⣛⣛⣻⣿⣷⣶⣿⣿⣿⣿⣯⣽⣿⣿⣇⣾⣿⡿⢟⣵⣿⠿⣣⣾⡿⢡⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿
⣿⠿⠿⠿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣛⣿⣿⣟⣿⣟⣿⣻⣿⣿⣿