Skiers Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢺⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣅⠀⣨⣿⣿⣿⣿⣿
⠀⠀⠉⠉⠒⠲⠤⣴⡶⠾⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣾⣯⣽⣛⠋⣉⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠯⣷⣲⣦⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣒⡪⠭⢛⠋⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠻⠽⣷⣶⣴⡂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣕⣒⠩⠍⡋⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠒⠒⠁
⠀⠀⠀⠀⠀⢀⠂⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠁⠢⢄⠀⢀
⠀⠀⠀⠀⠀⠘⣄⣰⠛⠀⠐⢄⠀⠀⠈⠉⠒⠤⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣔⢖⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣆⢴⠀⠸⡗⠢⢄⣀⠀⠀⠈⢄⠀⠂⡠⠀⠂⠀⠀⠐⠀⠀⠉⠀⠀⠙⢦⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠘⢄⠀⣀⠀⣨⠃⠀⠀⠈⣦⠈⠓⠀⠤⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠉⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢈⠑⠤⡍⣉⣀⣠⠴⠚⠀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠀⠀⠀⡀⠤⠒⠊⠁⠀⠀⢤⡁⠀⢀⠈⠀⠂⠀⠀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠀⠀⠀⠀⠀⢢⡀⠀⠳⣄⠀⢅⠠⡔⠂⠀⠤⠂⡐⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠠⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⣣⣙⣈⣀⣑⠢⠄⠀⠉⠀⠲⠑⠰⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢒⠉⠖⠒⠒⠂⠁⣠⣄⣀⣀⡠⠤⠒⠊⠁⠀⠰⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣐⣲⢏⣀⣀⡠⠔⠄⣀⡠⠤⠤⠄⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⡄⠴⠊⠁⠀⠀⠀⠀⠀⠀⣀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠢⠀⡀⠖⠀⠠⢔⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣀⠀⠂⢀⡀⠠⠔⠓⢄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠒⠠⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠈⠠⠆⠀⠀⠑⡀⠀⠀⠀⢀⣀⡠⠤⠒⠂⠉
⠫⣐⠂⠀⠠⠀⠀⠀⠀⠀⣀⣒⠂⠱⠤⣴⣀⣐⣀⣀⣤⣤⣴⠦⠥⠒⠚⠉⠁
⠐⣎⠍⠉⠉⠉⠩⠭⠭⠉⠀⢂⣈⣠⠤⠤⠒⠒⠊⠉⠉

⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠲⠄
⠀⠀⠀⢀⠴⠀⠩⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠑⠂⡀⣈⢅⠒⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠃⠦⢎⣁⣬⠭⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⢒⣀⠄⠄⣀⡰⢖⠒⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⣀
⠀⠐⠀⣀⣀⡔⠁⠀⡰⠄⠒
⠀⠈⠉⠀⠀⠉⠠⠔




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠦⣴⡞⣳
⠀⠀⢿⠽⠣⢄⣀
⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⢿⡿⠿⠿⢿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣏⣤⣈⠉⠛⠻⢿⣿⣿⣳⢶⣾⣮⣲⣔⡢⣤⡀⠀⠙⢿⡇⣿⣿⡋⠷⢽⣛⣿⡇
⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣾⣅⣄⣀⠀⠛⠿⣯⣕⣚⠿⣿⣿⣿⣿⣿⣷⣦⡿⠷⣿⡋⠀⠀⠈⢛⡿
⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣯⣻⣶⣤⣀⠙⠿⣿⣝⡏⡙⠻⢿⣿⣅⠀⠀⠀⠉⠓⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣷⣝⣷⣦⣌⣻⣿⣿⣷⣤⣉⣙⠻⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣾⡿⠯⠍⢻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣟⣛⣛⣽⣿⠿⠋⠀⠀⠀⠉⠻⢤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⣠⡶⣫⣭⣍⡛⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣾⣿⣾⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠓⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢈⠙⠻⠶⠶⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠳⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣿⣿⡏⠙⠤⠠⠄⠀⣀⣾⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠻⣿⠧⣿⣷⠀⠀⡀⠀⠈⠉⠹⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡉⠃⠀⠐⢿⠄⠏⢻⣿⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣾⣟⠑⠀⠀⠀⠈⠀⠀⠻⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠉⠻⠂⠀⠀⠀⠀⠀⢠⣾⣿⣿⠛⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⢴⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠿⠿⣿⡟⠉⠛⠿⣿⣿⣷⣦⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣇⣀⠀⢻⣷⠀⠀⠀⠀⠀⠈⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⡿⣿⡿⣆⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠛⢿⣿⣿⣮⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠸⣿⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣶⣦⣿⣿⣿⣟⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠯⣿⣿⣿⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⢿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⠻⠿⠷⠂

⠑⠦⣴⡞⣳⠄
⠀⠀⢿⠽⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⢿⣿⣿⣦⣤⣾⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣀⣈⠙⠛⠻⢿⣿⣿⣿⢶⣶⣶⡲⣤⡢⣤⣀⠀⠈⠻⣿⢹⣿⡟⠻⢌⣛⣻⣿
⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣭⣗⣄⡀⠀⠻⠿⣿⣕⡮⠿⣿⣿⣿⣿⣿⣷⣦⣴⠿⣾⡟⠋⠀⠀⠛⣿⡇
⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣳⣦⣤⣀⠙⠿⣷⣗⡻⡛⠻⢿⣿⣏⠁⠀⠈⠉⠓⠦⡴⠞⠉
⠀⠀⠀⠀⠀⠈⠙⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣝⣷⣦⣄⣹⣿⣿⣷⣤⣉⠙⠻⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣾⡿⠿⠭⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⢿⣿⣻⣿⣿⠟⠁⠀⠈⠙⠻⢦⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⡀⠀⠀⠀⢀⣤⢖⣫⣙⠛⢿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣶⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡉⠛⠷⣦⣤⡤⠤⠄
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣾⣵⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡺⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⣿⠑⠰⢭⣽⣷⣴⣶⣤⣤⣄⢀⣀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣮⠳⠀⠚⠋⠉⠉⠉⠉⠉⠁⠀⡿⠿⣿⠂
⠀⠹⠟⠦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⣩⠀⣿⣿⡄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠑⠀⢤⣄⣀⠀⠀⠀⣠⣄⠀⠀⢸⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠿⠂⠀⠈⠑⠯⠄⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⣀⡭⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⣶⣶⡤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣼⣿⡿⣿⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠾⠃⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠤⢖⡂⠠⣿⣯⡿⠐⢯⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣟⡳⣿⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣤⣤⣄⣀⠐⠀⠤⠤⣀⣠⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣤⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠑⠒⠤⢄⣀⠀⠀⠀⠀⡖⠲⣶⡖⠛⠻⡿⠿⠇⠻⣷⠀⠀⠀⠀⢀⢀
⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⣶⡶⣿⣆⡸⢌⠒⢠⣄⠀⡈⠱⠉⠀⡀⠀⡠⢃⢪⢊⠜⠔
⠀⠀⠙⢖⠢⠤⡀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀⢨⡙⠦⠔⡼⠁⠁⠀⠀⢀⡜⡐⡱⡡⡳⡡⢊⠊⡰
⠀⠀⠀⣀⡀⠀⠈⠒⢠⠀⠸⠟⠢⢄⡀⠀⠀⢸⣿⣿⣿⣿⡿⠓⢢⣤⣊⠱⠃⠀⠀⠀⢀⠊⠜⠔⡔⠑⡐⡡⠃⡔⠡
⠀⠀⠐⠀⠉⠂⢄⡀⠆⢕⠀⠀⠀⠀⠈⠑⠲⣾⣿⣿⣿⣿⣷⣤⣿⢦⡋⠀⠀⠀⠀⠀⢃⢈⠌⢎⠎⠔⠐⢁⠌⡰⡱
⠀⠀⠀⠈⠑⠦⣤⡀⠀⠀⣀⠉⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡇⠀⠀⠀⠀⠀⠃⠂⢀⡠⠴⠦⢄⠈⡴⡝⡰
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠢⢈⠀⠰⡄⢦⣶⣿⣿⣿⣿⠃⠈⣹⣿⣿⣿⣿⠀⠤⠤⠖⠒⠒⠚⠉⠀⠀⠀⠀⠉⠒⠲⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠐⠉⠉⠩⠉⡀⣠⣾⣿⣿⠿⠛⢯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⡀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡙⠢⢄⡀⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢍⠓⢦⣬⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠨⡉⠻⠟⢋⡀⠀⠀⠀⠈⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠲⢄⠑⠹⠳⠦⠤⠀⠀⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠈⠓⢄⡀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠉⠲⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠯⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣀⠀⠉⢳⠢⠄⠄⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠋⠙⢷⣌⣀⣀⣀⣤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡒⡪⢊⠍⢠⠋⠀⠀⠈⠛⠲⣒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡖⢳⡀⠘⢄⠀⠀⠀⠀⠀⡀⠑⢍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⢄⡋⠒⠄⣉⠉⠉⠁⠐⠢⡄⠈⠆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⠒⠤⢄⡉⢴⢤⠔⠒⠓⠒⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡄⠀⠀⠘⢣⣼⠞⠴⠐⢺⣝⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠁⣠⠞⠀⠀⡰⠡⠊⡌⠀⠀⡻⡏⠉⢹⡤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⠏⠁⠀⠀⠀⡰⠱⠁⢰⠀⡠⠊⠀⠈⠁⠊⠀⠀⠀⠉⠉⠉⠙⠛⠒⠈⠋⠓⠲⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠰⠁⡇⢀⠆⠀⠣⡀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡇⠀⠐⣎⠀⠀⠀⠈⠂⣄⠤⠊⣁⠔⠊⠀⠀⢀⡠⠔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠃⠀⡘⠀⠑⢢⣤⠔⢉⡠⢓⣍⠀⠀⣀⠴⠊⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⣃⡠⠒⣁⠤⠛⠓⣶⠋⣨⠖⢉⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⢠⢾⣶⠾⣁⠔⠊⠁⠀⢀⡮⢓⣽⠡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢀⡰⠟⡫⠕⠈⠀⠀⠀⡠⠒⣁⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⡡⠔⠉⠀⠀⠀⡠⠒⣩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⣁⠔⠉⠀⠀⢀⡠⠐⡩⠔⠉
⠀⠀⠀⠀⠀⢠⠒⠐⠂⣁⠔⠊⠀⠀⢀⡠⠒⢁⠔⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠨⣁⣈⡡⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠊⠉⣆⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠂
⠀⠀⠀⠀⠀⠂⠀⢰⣀⠸⢧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠘⡆⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠡⢔⡢
⠀⠀⠀⠀⠀⠀⠀⠪⠋⡀⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣬⡵⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠇⣣⡇⠸⡽⡦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡉⡇⢸⡡⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠒⠶⡇⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⡇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠃⠘⢠⡅⠈⡅⠀⠠
⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⠀⢐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡦⡬⢼⡇⠀⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠁⢺⠁⣠⢿⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡈⠀⠀⠁⠉⠛⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠉⡉⠻⣦⡇⠀⠀⢠⡾⠋⡁⡀⠃⠀⠀⠀⠁⠁⠠⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠄⠀⠘⢁⣒⣚⣀⢿⣇⠈⠀⡾⠀⢀⣒⡖⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠾⠋⠭⠛⣿⣿⠀⠀⣯⣴⠋⢙⠫⣦⠃⠀⣀⠀⠀⠀⡇⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⢄⠀⠀⣀⠀⠀⠀⠨⠅⣿⣿⠀⠀⢸⢹⠀⢐⠀⣇⡠⠊⠀⠁⠄⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⡄⠃⠄⠂⠑⠊⠀⠢⡄⠲⡤⣴⠟⢻⠀⢤⣀⡿⡖⢲⠊⠉⠀⠀⠀⠀⠆⣘⠠⡀⠊⠀⡑⠄⢀⠤⣀
⠀⠀⠀⢀⠔⠂⢄⡀⠀⠰⠑⢎⠀⠀⣠⠀⠀⠀⠀⡀⡆⠀⡇⣿⠀⣿⠀⢠⢠⡇⡇⢸⡀⠀⠀⠀⠀⢸⠀⡟⠀⠈⠒⢄⠀⠈⠁⠀⢀⠱⣀⠀⠈⠦⡀
⠀⠀⠐⠁⠀⠠⠀⠀⠀⢠⠀⢀⡡⠚⠰⠀⠀⠀⠀⠀⣇⠔⠒⡛⢦⣽⠀⠀⢹⡷⠓⠒⡓⣄⡂⠀⠀⠈⢰⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠉
⠀⠀⠀⠀⠊⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⣢⠀⠀⠀⣰⡟⠀⢀⡃⣼⣿⠊⠀⣸⣷⠀⠠⠀⠟⣷⠀⠀⠀⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⢄
⠀⠀⠀⢾⣶⣷⣤⣤⣀⣀⠔⠤⡀⣀⣠⢨⣀⡀⣠⣹⡓⠂⠀⠲⣿⣏⢏⠀⣿⣻⠲⠶⠞⠛⣿⣿⢱⠀⣃⠄⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠈⠁⠙⠛⠛⠺⣇⣻⠞⠿⠀⡿⠾⠶⠛⢻⠉⢹⣿⡟⡿⠗⠛⠚⡾⢶⡎⠉⠚⠏⠺⠏⢸⠷⢄⣼⡹⠧⢼⣷⡊⢳⣀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠔⠀⠀⠀⣠⡦⣷⣲⠂⠀⣸⠀⢹⣟⠀⣧⠀⠀⣀⣏⢐⡇⠀⠀⣁⣀⡀⣆⠀⠀⠁⠀⠀⠀⠈⠓⠻⡷⢤⣾⣴⣌⣱⡒⡤
⠀⠀⠀⠐⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠃⠀⠀⠈⠉⠉⠉⠙⠛⠛⠿⠿⠿⠖⣦⠒⠀⠠⣄⠀⢀⡀⠀⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠁⠈⠂⠉⠐⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠈⠈⠂⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⠞⢆⠠⢀⠀⠀⠀⣠⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⡟⣹⣿⡀⠀⠘⠀⠀⠐⠺⠿⡏⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠉⠀⢈⣿⠃⣿⣿⣧⣤⣴⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠈⢻⠃⠉⢈⣿⣯⣽⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠙⢻⣿⡁⠁⠀⠀⠀⠀⠀⠂⠘⣣⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠉⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⣴⢻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡷⣴⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⣿⣿⣿⡿⠛⠿⣷⣿⣿⣿⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠀⠀⠀⣿⣇⡀⠀⠀⠈⠉⠛⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣶⣶⣦⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣵⣿⣿⣯⣿⣯⣷⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠻⢿⣿⣿⣷⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⢹⣿⣯⣿⣾⣽⣇⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢸⣿⣿⣿⡹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣤⣀⣿⣿⣿⣏⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣵⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣶⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠙⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⣾⢟⣻⣻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢠⣿⢻⠏⠉⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⠀⢸⣟⣾⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⠖⠫⢹⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠋⠉⠀⣄⣲⠄⠀⢿⢹⣾⣟⣻⣿⣟⣀⣀⣠⣤⣾⡋⢀⣼⣠⡬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⣄⠀⠀⠛⠛⠳⠷⣞⣀⣙⣿⣿⣏⠉⢻⣿⣿⣿⣹⣳⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⡀⣴⠧⣧⡀⣀⠀⠀⠀⠈⠻⣿⠋⠉⢻⠀⢸⣿⡿⠽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⢤⢰⡆⣷⡿⠛⣾⡇⠙⠳⢀⣀⣈⠉⢀⡀⢀⢀⡆⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣋⡁⢀⣠⡓⠚⣶⣃⣋⠀⠀⢟⢀⣄⠀⠀⠈⠁⠀⠀⠉⢉⠎
⠀⠀⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠙⣭⣿⢾⣩⡇⢘⣿⢫⢟⣙⣓⣈⣙⣈⣀⡀⠂⠠⠠⠤⠄⡏
⠀⠀⢻⣿⣿⣿⣷⣄⣀⣶⡤⣤⣄⣰⣧⣀⠴⣶⣟⣻⣿⡿⢿⣿⣿⣿⣿⡿⠛⠉⠉⠉⡉⢻⣿⣶⡶⠲⣶⡇
⠀⠀⠘⣧⣻⣿⣿⣿⣿⣿⣃⢀⣶⡏⠉⠁⠀⢿⣿⣿⠏⠀⠸⣿⣿⡿⠋⠀⠀⠀⠀⣼⢇⢩⡙⢛⡿⠧⢊⡇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣭⣛⣻⣷⣼⣮⣿⣿⡿⠁⠀⠀⠀⠹⠇⠀⢠⠀⠀⣄⢸⡇⣼⠞⣠⢻⣅⡀⣾⠃
⠀⠀⡀⠀⠀⢈⡛⠿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡋⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⢄⣿⠸⠀⡉⠰⢉⡿⠿⠿⠋
⠀⠀⠈⠑⠦⣀⠈⠐⠄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣷⣽⣹⣧⠀⣠⡉⠀⣠⠐⠎⡆⠀⠞⠽⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠉⠂⢄⠘⠲⠤⣀⠙⠻⣿⣿⣿⣿⣟⣿⣿⣾⣯⣸⣆⣇⣧⠚⠛⠂⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠲⠤⣌⣙⡢⠤⢉⠛⢿⣿⣶⣿⢿⣿⣿⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢓⢦⣌⡂⠌⠻⢿⣿⡽⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⠀⠂⠤⣛⣿⣽⣿⣿⣿⣿⡇⠀⠀⡀⠠⠀⠀⢀⠀⠠⠍⠀⠀⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠻⠿⣿⣿⣟⡥⠤⠔⠂⠀⢀⡀⠀⠤⠤⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠩⠷⠖⠋⠉⣉⠲⠄⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡈⠠⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠁⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠓⠚⠉⠁⠀⠀⠀⡄⠂⣈⠽⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡉⡀⠠⠀⠤⣶⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⣿⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⢠⠉⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣨⢉⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣤⠈⢒
⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⢯⠄⢀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠼⠟⠄⠒⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⠹⠄⠀⠀⠀⢀⣤⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠋⠀⠐⡢
⠙⠙⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠻⠛⠛⠃⠀⠀⠐⠁⠀⠀⠀⠀⠘⠉⠠⡾⠊⠀⢀⣴⠡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⠟⢠⡄⠀⣰⣶⣆⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢀⡀⠀⠀⠀⠀⠀⠴⠃⠈⠉⠀⠈⢁⢩⠛⢟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠁⢩⠿⣿⣿⣿⢿⣷⠀⠈⠝⠲⠆⣠⠀⠣⢄⣥⣤⣾⣴⣿⣟⡷⣮⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠃⠀⠈⢻⣿⡾⣿⣔⣂⠀⠰⠂⣀⣘⣧⣬⣽⣶⣿⣿⣿⣿⣿⣿⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⡀⠀⠀⠀⢀⣹⣷⣽⣿⣿⣷⣿⠿⠟⠛⠛⢻⢿⠋⣿⣿⣻⡿⣿⡛⣷⣿
⠀⠀⠀⠀⠀⢐⣀⠀⠀⠀⠀⠀⠀⢖⡞⣨⣤⣶⠶⠿⣛⣿⣿⢿⡛⠛⠉⠁⠨⢧⠀⠚⠺⠤⣧⠰⣿⣞⣽⣄⣽⣯⣿
⠀⠀⠀⠀⣀⡻⢿⣤⣤⠃⣀⣀⣀⡮⢸⣙⣯⠿⠿⠛⠋⠁⠀⠈⠃⠀⠀⠄⠀⠀⠀⠀⡀⠤⢤⣄⠙⣭⢿⣿⣿⠏⢁
⠀⠀⠀⠀⠉⠁⠂⣀⡠⠔⢛⡠⠁⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠐⠚⠂⠤⣬⡯⠟⣻⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣻⣿⡟⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠿⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠟⠿⠚⠻⠼⠟⣿⣽⣷⣾⢻⣿⣷⣦⣤⣤⣿⣇⣴⣶⠶⣦⡀⠙⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠁⠀⠀⠀⠀⠀⣠⠌⢻⣶⣿⣻⣿⡈⠉⠉⣉⠜⣫⣤⣴⣶⡈⠻⠷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⣀⠀⠀⠀⠀⠀⠨⢾⣟⣿⡟⠛⠿⠟⠿⣋⣡⣤⣤⣈⠻⣷⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣀⠀⠀⢁⡾⢿⣿⡿⠿⣶⡶⡿⢛⣉⣉⣉⡉⠻⣷⣤⣤⣬⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠙⠉⠁⠀⠀⢛⣛⠛⠾⣷⣦⣤⡶⠟⣋⣉⣉⠛⢿⣦⣄⣈⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠻⢷⣦⣈⣡⡖⢋⣉⣉⡙⠻⣦⣍⡛⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⠛⠛⢶⣬⣉⣥⠀⠀⠀⠉⠙⠳⠤⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⠿⣦⣬⣉⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⢀⡀⠠⠤⠄⠂
⠀⠤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣰⢰⢰⡆⣆⣶⢲⡆⣶⠂⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣾⢸⡇⡟⣿⢸⡇⣿⠀⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢈⣁⡁⠉⣈⣁⢙⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠙⠀⠋⠉⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠞⠹⡆⠑⢄⡀⠀⠀⠀⣰⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠈⠀⠀⠀⠲⣌⠀⠂⠹⠾⣀⡚⠇⠈⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⢀⡀⢡⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⢨⡁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⠆⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠠⣀⡄⠳⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡦⠀⠀⢡⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣻⠏⠀⢐⡥⡀⠀⠀⠀⠇⢠⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠓⠲⣖⠆⠨⣧⠀⠀⠀⠸⡞⠀⠀⠀⠀⡿⡥⠀⠀⠀⡷⠇
⠀⠀⠀⠀⠀⠀⠠⣤⠶⣠⠜⠲⢾⣂⠐⢾⡄⠀⠀⠀⣇⠀⠀⠀⠀⢱⠀⠀⠀⢀⣅⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣮⣤⠼⣷⣶⠷⠶⠚⠛⠀⠀⢠⠻⠀⠀⠀⠀⠈⣧⡇⠀⢸⡏⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢯⢠⡄⠀⡇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠤⠤⢼⠤⠧⠐⠧⠧




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣃⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣾⣿⣫⣿⣿⣟⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⠉⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡻⣿⣀
⣿⣷⣶⣦⣤⣀⣀⣉⣀⣀⣀⣈⣙⣷⣶⣦⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⢿⡾⣿
⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⠠⢤⣴⣶⣶⣶⡦⠀⠀⠀⠀⠀⢠
⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣥⣄⣉⠛⠿⣿⡿⠟⠛⢁⣀⣴⡶⢄
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠄⠂⠂⠀⠀⠈⠛⠙⠊⠉⠁⠀⠀⠐⠀⠤⣀⠀⢄
⠀⠀⠀⠀⠀⢀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠑⡄⠁
⠀⠀⠀⠀⢀⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠲⠶⠂⣴⢨⣷
⠀⠀⠀⠀⢸⣿⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⠀⠀⠃⠹⡟⢷⠀⠀⠼⢈⣿
⠀⠀⠀⠀⠀⠛⠀⣧⣤⣄⣀⡀⠀⠀⡠⢂⡴⠛⠳⣄⠑⡄⢠⣤⠷⠂⠀⣀⢶⠘⠋
⠀⠀⠀⠀⠀⠀⠳⢷⣬⣉⣙⣛⠛⣫⠔⠊⠀⠀⠀⠈⠢⡪⣐⠐⣒⣀⣩⣴⠿⠂⣠⡤⠶⠒⠛⠛⠛⣏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⠁⠀⢀⡾⠁⡄⠀⢀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠇⠀⣿⠀⢸⠇⠀⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢼⢥⡆⠠⣯⠁⠠⠀⠀⠐⠀⠀⠀⣸⣀⡇⣷⠀⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣀⣀⠒⠻⢿⣿⣿⠷⠒⠂⢀⣰⣤⡀⠀⠐⣤⠀⣸⣿⣂⣿⣽⡇⢸⣯⠀⠀⠀⠀⠀⠀⢰⡄⣿⡋⠓⠿⠄⣰⡎
⠀⠀⠀⠀⠀⠀⠀⡀⠐⣈⠀⠀⠭⠉⠉⠩⠄⠙⠁⠚⠈⠨⠭⠍⠀⢈⡐⠀⡙⠳⣿⣟⠉⠛⣻⣧⣸⡷⡀⠀⠀⠀⣆⠀⣸⡇⠈⠁⢀⣴⠞⠉
⠀⠀⠀⠀⠀⢀⠀⡰⠋⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠂⠈⠙⠷⢶⣤⣤⠾⠋⠀⠀⠀⠀⠙⠿⣯⣤⡶⠾⠋⠁
⠀⠀⠀⠀⢠⣿⠀⡇⢀⠈⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣦
⠀⠀⠀⠀⢸⣿⠀⠃⠀⠀⠀⠙⠃⠀⠈⢦⡀⠰⠀⠀⠀⠀⠀⣠⡄⠰⠟⠀⠀⢸⣿
⠀⠀⠀⠀⠘⠻⢠⣷⡄⠀⠀⠀⠠⠀⡂⠊⣠⠾⢦⡈⠀⠀⠀⠉⠀⠀⠀⣠⣶⠸⠟
⠀⠀⠀⠀⠀⠈⢶⣧⣍⣛⠂⠠⠶⢚⠕⠞⠁⠀⠀⠙⢆⢤⡠⠤⠴⢒⣊⣡⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⢿⣿⣿⣿⣥⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿⡿⠈⢿⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣿⣿⣿⠀⠀⠀⠈⠉
⠀⠀⠀⠠⠤⣄⣀⣄⣀⡀⢀⣠⣾⡿⢋⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⣀⣀⣠⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠶⠦⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿⣦⣄⠀⠀⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⠿⣿⣷⣄⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣘⣿⣷⣄⡙⢿⣷⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠿⣛⣿⣿⡿⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠿⠿⢷⣦⣀⣀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⣀⣠⣶⣿⠿⠋⢁⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣤⣴⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠲⠶⢶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣉⠙⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⣾⣿⣿⣿⣿⡿⣿⡏⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⡎⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣼⣿⡿⣿⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣿⡿⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⢀⡀⠀⠀⠠⣀⣀⣀⠀⠀⢀⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠠⠤⠤⠤⠿⠿⠿⠿⠷⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠀⠈⠉⠙⠛⠲⠶⠤⣭⣽⣿⣿⣿⣿⠿⠿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⠶⠦⣬⣭⣍⣓⣒⣶⣤⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠿⣷⣦⣄⣀⣴⣾⣿⣷⡄⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠻⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣶⣤⣄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢷⣶⣶⣾⣿⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⢿⣶⣶⣶⡾⠃





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠆⡶⣪⠟⠋⠒⢒⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⣼⠟⢀⡤⠒⠉⠁⠀⠀⠉⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡴⠋⢀⠤⠒⠊⠉⠉⠉⠙⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣀⠔⣁⡠⠤⠤⢄⣀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⢀⢀⢀⡀⠀⠀⠀⠀⣷⣼⠁⡎⠀⠀⠀⠀⡀⠌⠑⠦⡀⠀⠀⢳
⡴⡄⠀⠀⠀⠰⠶⠀⢠⡛⢶⠁⢠⠊⠷⡉⠀⠀⠀⣀⣀⠈⡿⡞⠀⠀⠀⣰⠋⠈⣇⠀⠀⠨⡢⣄⣈⠣⠤⠤⠤
⠲⡩⠀⠀⠀⢠⢀⡀⠀⠀⠀⠑⢄⠀⠀⠑⡄⠀⢮⡐⠶⠼⠟⢀⠀⠀⢠⠇⠀⠀⣿⡤⠒⠒⠓⢦⠉⠉⠉⠉⢲
⢠⠴⡐⠢⣄⢀⣈⣛⡀⠀⢀⡀⠀⠑⡀⠀⠘⢄⠀⠉⠑⣲⡀⢸⠀⠀⠸⡀⠰⣦⠛⠆⠀⠀⢀⠜⠀⠀⠀⠀⠉
⠀⠈⠒⢄⠀⠁⠀⠀⠈⠓⢠⢫⠗⠀⠈⠢⡀⠈⡢⠖⠉⢁⠱⡌⢇⠀⠀⠘⠊⠑⠦⠤⠤⠖⡇
⠀⠀⠀⠀⠉⠓⢆⣠⡤⠠⢤⠉⠒⡄⠀⠀⣞⠈⢳⣄⡴⠁⡔⣹⣦⡳⢄⠀⠀⠀⠀⠀⠀⠒⠉⡲
⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⢄⡨⠒⢁⠀⠀⠸⣍⠛⠋⢠⠊⣌⠎⠀⠙⠢⣍⡒⠀⠄⠄⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠅⡠⢂⡤⠋⠉⣒⣦⡼⢼⠆⠀⠀⠀⠀⠉⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣓⢦⣼⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⣷⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⡙⢦⣼⠑⢆⠀⡤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⢓⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠓⠚⠻⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡺⡟⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠛⣒⡲⢤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢒⡜⠀⠆⠀⠀⢾⢦⡏⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠘⠂⣀⣦⣀⠀⣠⣼⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣧⣉⡉⠁⣈⠥⠚⣽⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠻⣉⡉⣇⣠⠎
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠰⣇⡀⠀⡷⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⢳⣀⣤⣀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠟⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⢐⡷⠯⠞⠁⠀⢀⣠⠴⣊⠥⠒⠉
⠀⠀⠀⠀⠀⠀⣿⣅⣄⡼⡏⢹⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣿⣿⣿⡿⠟⣫⠟⢄⡀⠈⠀⠀⣀⠤⢚⣩⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠙⠾⠷⢖⠙⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠷⠚⠉⢀⡤⢒⡉⠓⢄⣈⠥⠒⠉⠀⠤⠴⡋⠀⡖⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠉⠒⠒⢀⠉⠉⢀⡠⠔⠈⢳⠀⠀⠀⠠⠀⣤⠀⠀⠓⢀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠁⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⢀⡀⢠⠎⡀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⣠⡤⠶⠒⣚⠞⠁⠀⠀⢀⣠⡴⠾⠋⠀⠀⠀⠀⢀⡤⠂⠁⠀⠥⠞⠁⠈⠁⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣴⠋⠉⠀⠀⢀⡞⠁⠀⢀⡤⠚⠋⠁⢀⡠⠔⠂⣙⡶⠊⠀⢀⣀⣀⢠⡀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⠷⠤⠐⠉⣷⠀⠀⠀⠀⣧⣀⣀⠜⣄⢠⠴⠚⢁⡠⠔⠊⠁⣀⠴⠚⢁⡠⠔⣋⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠣⣄⣠⣴⣯⠀⠀⠀⠀⢆⠀⠀⢀⣼⣀⠴⠚⠁⢀⡠⠔⠋⢁⠤⠒⡡⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣎⡝⢢⠀⠀⠘⣿⣿⣿⣆⢀⡠⠔⠈⢹⣿⣿⣿⠀⣀⠤⠚⠉⣀⠔⢊⠡⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡰⠛⣱⠞⠀⠀⠀⣈⡿⠛⠋⢳⡠⠔⠊⠈⣿⣿⢿⠋⢁⡠⠔⡩⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣠⠒⢊⣤⣀⠭⠛⠁⣀⠐⢛⣢⣤⣉⠺⢓⠡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⢉⡩⠛⠉⠀⠀⣠⠴⠋⠉⣉⠝⡋⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⣠⠄⠊⠁⠀⢀⡠⠖⠉⢀⡠⢖⡩⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⣀⡤⠒⠉⠀⠀⣀⠴⠚⠁⣀⠤⠚⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⢁⡠⠔⠊⠁⠀⢀⡠⠔⠋⢁⣠⠔⠋⠁
⠀⠀⣀⣀⣤⠴⠚⠉⣀⠤⠒⠉⠀⠀⣀⡤⠒⠉⢀⡤⠒⠉
⠈⠛⠻⠮⠥⠖⠒⠉⠀⠀⢀⣀⠔⠊⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠭⠥⠄⠒⠉

⠀⠀⠀⠀⣐⡩
⠀⠀⠀⠤⠤⣄⡠⠀⠀⣀⣀
⠀⠀⠀⠒⣊⠔⠲⠂⠠⠾⠴⠂
⠀⠀⢀⣩⠽⣤⢀⠙⠷⣖⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⠤⠚⣹⠒⢴⣿⣤⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠠⠤⠤⣆⠙⠓⢶⠷⣾⡓⢒⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⠀⢠⠟⠁⠀⠀⠀⠐⠆
⠀⠦⣤⠴⠚⢳⡶⣠⣰⠋⠉⠉⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡠⠇⡐⣱⣤⠂⠀⠀⣀
⠀⠈⠿⠶⠟⠿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢘⡄⠙⠁⣄⠀⠜⠋⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⢰⡆⠇⣠⠀⢠⡠⢠⡶⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣰⠃⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣐⠃⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠊⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⣄⣀⠀⣠⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣄⣀⣀⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣦⣄⠈⠉⢹⣿⣿⡦⠭⣤⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡀⠀⢻⣿⣷⣶⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡿⠃⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⣀⠀⠤⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢠⡀⣰⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠲⠶⠦⠭⣭⣭⣿⣒⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣟⣓⣲⡶⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⠶⠶⠮⣭⣭⣝⣒⣒⣒⣀⣤⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣤⣄⡈⠻⣦⣤⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⢿⣦⡀⠉⠉⠓⢎⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⣿⠳⣄⠀⢀⡼⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡴⠏⠀⠉⠛⠋⠁⠀⠈⠳⠶⠖⠋⠉⠙⠳⠦⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠄⡄⠁⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⡴⠶⠦⣤⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⣠⠂⠁⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣀⣀⡀⠀⠀⠈⠉⠙⠛⠶⣌⠻⣦⡀⠀⣠⠇⠀⠀⠀⣠⡾⠃⠀⠀⠁⢣⣾⠁⣰⠓⠦⢀⡀
⠀⠀⠀⠈⠳⣶⣦⣶⠶⠦⢄⡀⠙⠛⠓⠶⢯⣷⣄⠀⠀⠀⠀⠀⢼⣷⡀⠉⠉⠁⠀⠀⠀⣠⢷⠃⠀⠀⠀⠀⠘⢿⣷⠙⢤⣠⣄⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠲⡝⣆⠀⠀⠀⠀⠘⣯⢳⡀⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⣠⠔⠇⣼⢀⠀⠀⠀⠇⠀⠘⣿⣆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢀⡟⠘⢆⠀⠀⠀⢠⠏⠀⠙⢦⣄⣠⣴⠟⠀⠈⠓⢶⣾⣧⣤⣨⡎⡏⠀⠀⣰⠂⠀⢀⣈⣁⣀⠀⢀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⢯⣤⣤⣤⣵⣖⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠋⠒⠒⠒⠛⠋⠉⣼⣿⣯⣩⣶⣿⣍⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢰⡀⠀⠀⠀⠀⠳⠆⠻⣿⡿⠟⢿⣿⣿⡿⠃
⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠈⠙⠒⣲⠃⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠁⡂
⠀⠘⢷⣤⣀⣀⣀⣀⣀⡀⠀⠀⠻⣶⣤⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⣴⠀⠀⠈⢃⢀⡄⠀⠀⠀⢠⡆⠀⠀⠀⢀⢰⠇
⢀⡀⠀⠙⠛⠿⠶⠶⢮⣍⣳⣄⠀⠀⠉⠛⠛⠻⠶⣦⡀⠀⠀⠀⢀⡰⠋⢀⠀⠀⠀⢀⠋⠀⠑⢦⡀⢀⡞⠀⠀⠀⠀⡼⠁⠀⠀⠁⠚⠁
⠀⠈⠛⢦⡀⠀⠀⠀⠀⠈⢻⡿⣧⡀⠀⠀⠀⠀⠀⠀⢻⡦⠔⠊⠁⠀⠀⠀⠃⠀⡠⠁⠀⠀⠀⠀⡹⠋⠀⠀⠀⢀⠎
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⣸⠇⠹⣷⡀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠘⢎⡳⣤⣤⡶⠋⠀⠀⠙⢿⣦⡀⠉⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⣜⠁⠀⠄⠀⢀⠀⠁
⠀⠀⢤⣤⣄⡀⠈⠙⠛⠛⠛⠳⣤⢴⣆⢣⢻⣀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠝⢦⡀⠀⠠⠂
⠰⣤⣀⠀⠙⢿⣦⠀⠀⣀⡤⠀⠉⠭⣷⠀⠁⠙⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠐⣄⡠⠋
⠀⠈⠙⠻⢷⣾⣿⣓⠈⣉⡀⣀⠠⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢿⡷⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⣤⣐⣀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⠀⣤⣤⣬⣀⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣦⣄⣀⣠⣀⠀⠀⠉⠙⠓⠾⢭⣔⣋⠈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢶⣿⣿⣷⡄
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢠⡖⠢⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠈⢳⡍⠛⠦⠀⣀⠤⠴⠀⠀⢀⠠⠊⣁⣼⡆⠀⠆⠱⡀⢻⡀⠙⣢⠴⣒⣄⣀⠂⠤⠊⣁⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⢣⡀⠹⣄⠐⠋⠔⢋⣁⠀⠐⠁⠀⠊⣱⡞⠀⠐⡆⠀⠣⡀⠱⠄⠁⠋⠠⢄⣀⠁⠀⠊⣰⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⠀⠑⠤⠈⠁⠀⠀⠀⠀⠉⠛⠲⠤⣤⠉⠀⢀⣦⠙⢄⡀⠈⠂⠀⠀⠀⠀⡀⠈⠛⠲⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⢧⣙⣒⠠⠤⠀⠀⠀⠀⠀⠈⢆⠀⠀⢠⠂⠀⠀⣼⠈⠑⠒⠤⠥⣅⣀⡀⠀⠀⢹⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠉⠉⠁⠒⠒⠀⠶⠒⠂⠀⢁⠀⠀⡠⢧⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠦⣀⡀⠐⠤⠤⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡂⣈⠑⠲⢬⣁⡒⠒⠤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢄⣰⣤⣈⣉⡒⢖⡀⠀⠀⠈⠙⠋⠛⠒⠒⠂⢀⠑⠉⠈⠑⠲⡿⡩⣤⣭⠉⠀⠁⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠐⠀⠀⠀⠀⠀⠈⡋⢣⠀⠀⠆⠐⠶⠴⠒⢃⠏⠀⠀⠀⠀⠀⠀⠀⠂⠽⣀⣘⡐⠻⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣒⠖⠀⠀⡏⠀⠁⡀⠀⢀⠀⢀⡀⠀⠀⠀⠈⠩⠟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡄⣀⠀⠒⡀⠒⢂⠀⠀⠀⢀⡀⣠⡴⠾⢠⠳⣄⠙⠚⠓⣠⡶⠄⢴⠀⠀⠀⣤⠴⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠁⠀⠈⠬⠉⢉⠘⠀⢀⣀⡨⠤⢀⢾⡃⢈⣤⡀⠀⠀⠀⠀⠀⣀⡄⠀⠐⠒⠒⡠⣾⠅⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠐⡁⡘⢂⡨⠔⠣⣄⡀⠀⡠⠞⠁⠀⠀⠀⠀⠈⢤⠌⡡⠖⠚⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢧⣀⠆⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠠⣛⡉⠉⠀⠀⡀⠀⣠⠄⠐⠀⠈⠀⠀⠀⠠⣛⡉
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠳⠤⠴⠋⠀⠀⠀⠀⡠⢂⣞⠔⠀⠀⠀⠀⠀⢀⠄⡈⢛⠧⠞⢋⣙⠃⣼⡷⢡⠊⢄⠀⠀⢀⠄⠈⡻⠴⠚⣓⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⣌⢅⠔⠀⠀⢀⡔⠀⠯⠊⡔⠁⠀⠀⠀⠀⠀⠀⢱⣆⠀⢀⠔⠁⠟⢃⠖⢀⠤⠤⠉⠁⠈⣢
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠸⣤⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠙⠦⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⢤⡤⡤⠤⢤⠤⠤⡄⠀⠀⠀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣸⠠⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠛⠚⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠉⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠈⠒⠉⠋⠙⠛⠛⠛⠿⠿⠟⠒⠋

⠀⠀⠀⠀⣐⡩⠠
⠀⠀⠀⠠⠴⣄⡠⠀⠀⣀⡄
⠀⠀⠀⡒⣉⠔⠒⠂⠠⠺⠔⠂
⠀⠀⠤⡭⠽⣦⢘⠛⠓⣞⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⠤⠚⣹⠒⢶⣯⢤⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠠⠴⠤⣆⡉⠓⠶⠶⣾⣑⢂⠉⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠐⠇
⠀⠶⣤⠔⠛⣳⠶⣤⡤⠁⠈⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡰⢃⡀⣵⣦⠂⠀⢀⣀
⠀⠈⠿⠖⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⠄⠘⠁⠄⠀⠘⠋⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢰⠆⠃⣴⠂⠐⡔⠰⠶⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⣰⠃⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⡿⠈⠻⣿⣿⣦⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠉⠛⠟⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⣼⣿⣿⡿⣻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⣾⣿⣿⡏⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⣿⣿⣿⡟⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⠛⠛⠛⠛⠃⠠⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠚⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣤⣀⡀⢙⠗⠂⠤⠤⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠉⠈⡟⣧⠤⢤⠤⠶⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢏⡩⣠⠊⠀⠃⠀⠀⠀⠉⠙⠭⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠙⣦⡀⠣⢀⠀⠀⣀⣀⠤⠈⢢⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠑⢼⡈⠐⠢⠄⡀⠀⠈⠑⡄⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢰⠉⠉⠲⡖⢺⣻⠁⢀⣩⣸⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⠎⠀⠀⡔⡱⢺⠉⠉⣥⡼⠷⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣺⠤⠐⠉⠀⠀⡜⡔⠁⠇⠀⡠⠊⠥⢄⡸⠛⠒⠶⠶⠤⠤⢤⣄⡀⢤⣄⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⠀⠀⠀⠀⡜⠘⠀⡘⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡘⠀⠠⡰⠁⠀⠈⠢⣀⠀⢀⡠⠐⣊⠝⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡇⠀⢠⠛⠦⡀⠀⣀⠄⠛⣥⠔⠈⠀⠀⣀⠤⠂⡡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠃⠀⠈⠀⡠⠜⢋⡦⢖⣩⡶⢳⡤⠐⢉⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣠⣤⣤⠗⣉⠤⠊⠁⠀⣰⢭⡲⢋⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⠀⠀⢀⣼⠿⣛⠕⠊⠀⠀⢀⡠⠚⡳⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡩⠔⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣉⠔⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠠⠤⠤⠒⣉⠄⠊⠀⠀⢀⡠⠒⡡⠔⠉
⠀⠀⠀⠀⠀⠈⠐⠂⠉⠀⠀⣒⠒⢊⡡⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠔⢩⡖⠉⠀⠀⠀⠀⢀⠀⡔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⢠⠴⠁⠤⣀⡀
⠀⣠⢀⣠⠀⡀⠀⠀⠀⢀⡤⠏⡀⠀⠀⠘⠁⠀⠀⠀⠀⣀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣇⠀⠀⠀⣿⣅⠤⠾⣿⣆⠈
⣼⣟⡩⠌⡑⣷⠀⠀⢀⡀⠶⠀⠑⠄⠀⠀⠉⡇⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⡄⠀⠀⠸⢫⡄⠀⢾⡿⠻⢶⡔⠉⠙⣯⠛⢥⣿
⣿⣩⢶⠰⣟⢻⣾⣿⣁⠐⠀⠜⠀⠒⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡀⠀⡞⢷⡁⠈⣧⠜⢁⠒⢷⣾⢧⡘⠶⣤⣙⣶
⣿⡄⠚⡞⢧⠸⣿⣟⡡⣆⣀⠶⢤⣄⠘⣀⡀⡀⡀⠀⡀⠀⢀⣷⠀⠀⢀⡀⣀⣀⣴⣀⣠⠟⠟⢱⣦⠾⡆⢘⠆⡠⠴⡏⠳⣜⢻⣄⢑⠀⠈⢿⣿
⢀⡔⠻⡧⣾⠟⢉⣡⡄⠈⣠⣀⢠⡈⢱⣮⣿⣿⣿⣾⣷⣷⠴⣿⢍⣿⣾⣿⡟⢿⣿⣿⣟⣠⠖⠮⣧⠔⠳⡼⠊⠀⢠⡌⢆⠈⣿⣾⠉⠳⣦⣀⣿
⣹⢇⢀⣷⣸⠿⠋⠁⠛⣟⠁⠸⢺⣧⣄⠈⢻⣿⣿⠿⣿⠗⠂⡝⠀⢿⣿⣿⣡⠸⣿⣿⠋⠀⣤⣤⣀⢺⡔⢰⢋⣀⠼⢷⡎⠉⢿⠛⠣⠀⠈⠉⢻
⠀⣴⡟⣿⣥⠖⠘⢁⡟⠉⣠⠰⠁⠁⠈⠳⢮⣿⣾⢶⣿⠪⠊⣃⣸⠞⣿⡫⠃⠐⢻⠷⠂⠀⣠⣄⡈⠻⣿⡏⠀⢀⠀⠀⢟⠒⠢⣧⠀⠈⠦⣀
⣾⣁⣳⣿⡏⠐⠲⡋⠀⣴⠃⢀⠀⠘⢥⠀⠀⢹⢿⣞⠁⠀⠈⢐⠁⠀⢈⡖⠁⢤⠜⠐⣀⣨⠁⣡⣈⠙⢿⣿⠔⠻⡄⠀⢸⠣⣄⠈⢻⡀⡄⠈⢻
⠈⢉⡿⠃⠀⠀⣀⡬⠛⠁⠀⠀⠻⣆⢘⡗⠛⠮⠀⠙⠂⠒⠛⠚⠢⠄⠀⠘⠀⠀⠈⠈⠁⠀⠀⠁⠀⠟⢋⠄⠀⠈⠛⠱⠉⠀⠀⠙⠻⣯⡁⢀⠈
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠲⠀⠀⠀⠙⠻⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⢠⠾⠤⣀⠀⠀⣀⣐⣄⠈⢻⠾⠿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⠉⡑⠲⠜
⠀⠀⠀⠀⡴⡃⠀⠀⠒⠂⡀⠤⢶⠤⠤⠤⠤⣤⠤⠤⠴⠆⣰⠙⠮⠭⠙⠢⠄
⠀⠀⠀⠀⠉⢁⣀⡤⠖⠂⢡⣀⣌⣀⡀⠀⠉⠀⠀⠀⠀⠈⠀⢴⡤⠆⠠⠆⠀⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠶⠤⠀⠀⠀⠀⣼⢀⣀⣀⣀⠀⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⢀⠀⣨⠉⠀⠀⠈⠳⡷⢤⣀⢘⠁⢈⠄⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠘⡈⠀⢃⡇⠀⠀⠀⠀⠹⣦⠀⠈⠓⠊⢀⡠⠽⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⠉⠀⠢⣄⣀⢱⡀⠀⠀⠀⠀⢹⠀⢀⡤⠚⠉⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠀⠀⠢⡂⠀⠀⠀⠹⠀⢳⣀⡤⠤⢤⡼⠚⠁⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠹⣄⣀⠀⠀⠀⠀⢙⡖⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠹⡈⠉⣑⠶⠂⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣃⠀⠀⣀⡤⠗⠋⠀⠀⠀⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⣀⡤⠖⠋⠁⠀⠀⠀⣀⡤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢾⣉⣀⣀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⣱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠡⠤⢌⡉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠯⠧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢣⠃⠈⠀⠸⢾⠀⢀⣀⣠⣤⣤⣤⣤⡀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠐⠳⡂⢼⣿⣿⣿⣿⣿⠿⠿⠿⡿⢻⢀⡴⠁
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣇⠀⠀⠀⢏⡀⡹⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⣱⠖⢢⡤⣤⣶⣾⣿⣿⠿⠟⠋⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠟⠙⠁⡠⢔⡪⠐⠈
⠀⠀⠀⠀⠹⠿⢭⠓⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣙⠝⠒⣁⠌⠒⢄⡐⠅⠊⠁⠠⠂⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠈⠀⠠⠁⠠⠀⠀⡧⠀⠀⠀⠆⠀⠈⡀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⣀⣠⠤⢤⠔⠁⠀⣀⣤⠞⠃⠀⠀⢀⠄⠂⢀⠔⠀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠸⡀⠀⢴⠉⠀⠀⡔⠁⠀⠔⠋⢁⠠⠐⡀⠔⠂⣀⠄⢠⠄⢀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢍⠁⣠⡇⠀⠀⢈⠒⠈⣱⢈⠠⠒⢁⡠⠒⠉⠄⠊⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣆⠒⡄⠀⢻⣿⣷⣀⠄⠊⢻⣿⣿⢀⠄⠊⡁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠥⠚⠀⢀⠄⠉⠥⠜⠂⡠⢘⠛⢿⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠘⠒⠛⠁⢀⠤⠛⡋⠝⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⡁⠔⠊⠀⡠⠔⢊⡠⠐⠉
⠀⠀⠀⠀⠀⢀⠠⠐⢉⠀⠒⠉⢀⠠⠒⢁⠤⠂⠁
⢠⣤⣤⠔⢈⠡⠐⠈⠀⡀⠔⠊⡁⠔⠈
⠀⠈⠉⠉⠀⠤⣤⠒⡉⠤⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄
⠀⠀⠀⠀⠐⠴⠄⠄⠀⠦⠐⠀⠦⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢐⡂⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣤⠄⢀⣤⣡⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠄⠀⠈⠁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⡼⢣⢄⡗⠄⠒⠒⠒⠒⠙⣋⠉⠁⠀⠀⢀⡠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢀⠠⠂⢋⠴⠀⠉⠉⠉⠉⠉⠀⣀⡤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠖⠀⢁⠀⠀⢀⠀⠀⠀⠀⡠⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠃⠀⠀⠈⢢⡘⡌⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠖⠁⢀⣀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠎⠀⠀⣀⠯⢋⣉⠉⠀⠀⠀⠀⠀⡠⠒⠉⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⡠⠊⠁⡞⠁⠀⠑⠄⠀⠀⡠⠊⠀⠀⠀⠂⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠀⠀⠰⠀⠀⢢⠀⠀⠠⡎⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⠀⡆⠀⠀⠀⡜⠤⠀⠀⠀⢀⣸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡗⠒⠒⠒⠒⠉⠈⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⣀⣀⣈⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⠒⣩⠁⢠⡀⠀⠀⠀⠀⠀⢠⠉⠀⡠⠒⠁⢀⣀⡠⠄⠴⢒⡶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠠⠒⠒⠙⣀⣀⡤⠤⠄⠒⠒⠋⠉⠉⠉⡀⣀⣀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣠⣤⣤⡀⠤⠤⠤⠐⠒⠒⠋⠉⠁⠀⣀⣀⣠⠤⠤⠒⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣤⣤⣤⣤⣤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠛⠒⠠⠝⠻⠥⠀⠒⠛⠉⣁
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠂
⠀⠀⠀⠀⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢾⣿⡓⠒⢸⠀⣧
⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⢀⣅⠐⠀⠈⠀⣿⡳⠀⢘⢠⡿
⠀⠀⠀⠀⠀⣼⣟⡛⠶⠶⠦⣢⠔⠁⠀⠑⢄⣇⠛⠍⠀⣐⣴⡄⢀⣀⣤⠤⠴⢶⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠁⡴⠋⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢐⡇⢠⡂⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⣀⣀⠀⠀⡀⠀⠀⠀⠀⢸⣷⢸⣷⡇⣸⠆⠀⠀⠀⠀⢀⠀⣷⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠂⠬⠹⠟⠩⠤⢐⠚⢋⠀⠀⠸⠦⣿⠿⠻⣿⣇⣾⡅⠀⠀⢠⠀⢸⡇⠛⠀⣩⡴⠛
⠀⠀⠀⠀⠀⢀⠔⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠉⠻⠦⣭⣭⠟⠀⠀⠀⠈⠳⣮⣥⠶⠞⠉
⠀⠀⠀⢀⡇⢸⠠⠀⠹⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢘⢰⡇
⠀⠀⠀⠸⡇⢨⡀⠀⠀⠈⠀⠀⠳⢀⣅⠀⠀⠀⠰⠆⠈⠉⢀⢸⡇
⠀⠀⠀⠀⠠⣼⣓⠦⠄⢠⡥⢂⠔⠋⠈⠳⡄⡀⢀⠠⠠⢔⣻⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠞⠁⠀⠀⠀⠀⠀⠘⠶⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠖⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠤⢀⠢⠈⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⡑⣠⣴⣿⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⣿⠏⠁⣠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢡⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢀⣠⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⡿⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠟⠋⣠⣾⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠛⠉⠁⢠⣼⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠛⠁⠀⢀⣤⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠛⠁⠀⢀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⠿⠛⠁⠀⣀⣤⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⢀⣠⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠓⠛⠒⠛⠒⠛⠚⠓⠑⠛⠃⠙⠒⠛⠂⠚⠻⠂

⠀⠀⢰
⡆⢀⣯⠌⠀⢀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠳⣿⠒⠀⢵⡯⡄⠀⡇⠀⠀⢀⡆⠀⠀⠀⣄
⣴⣛⡑⠞⢀⣘⡇⠀⡇⠀⠲⣾⡃⢀⣆⣰⡋⣢⡇⡀⠀⠀⠀⠂⠀⠀⠀⠀⠒
⣿⣾⣉⠄⢉⣁⡀⠀⢀⡛⢂⡟⡁⢻⣿⡿⠧⠈⢿⣇⠀⣘⠃⠀⠐⠂⠀⠀⢠⡀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠀⠀⠀⢀
⣥⡘⠲⡶⢤⡭⢀⢀⡿⡍⠀⣼⢃⣺⣿⡇⠦⠄⠙⣿⣿⣷⠾⣀⣿⣠⡃⢀⣴⢀⣷⣠⣸⡇⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⢠⣷⣴⣜⣢
⠉⠉⠉⠙⠓⠐⠈⠘⠷⣾⡓⠏⠈⡽⣧⠘⢘⣛⠈⢹⣿⣄⡂⣹⣿⣟⠃⣾⠃⠈⣿⣿⣯⠱⣾⣿⣥⣤⣆⠀⠀⢀⠀⣠⣶⣶⣿⣿⣿⣷⣿⣃⣿⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⣾⠿⢄⡀⣉⠀⠀⠲⣿⠍⠀⠠⣽⣆⠡⢽⡧⠀⠼⣿⠧⠈⢻⡯⠠⢿⣷⣿⣴⣾⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢨⣝⣉⢀⣄⣀⣿⣦⠄⢤⢾⣏⠈⠽⣿⣞⡒⣻⡉⠀⠘⣿⡂⠹⣯⣹⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠲⠶⢿⣖⣂⣙⣯⣝⡸⣷⣰⣆⣽⠿⠤⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠒⠀⠀⠀⠀⠀⠂⠀⠀⢀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠑⠦⠤⠊
⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠐⡄⢀⡔⠏⠉⢏⠉⠉⠉⠑⠒⠤⣀⠀⠈⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠤⡤
⠀⠀⠀⠀⠀⠀⠈⠙⣦⢀⡄⠀⣱⡦⣀⠀⠀⠀⠀⠑⡀⠀⠅⠀⡀⠠⠀⠀⠀⠄⠀⠐⠊⠁⠈⢫⣪⣟⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠘⡌⠡⠈⠈⠀⠲⠌⠁⠀⠢⣄⠐⠦⡀⢁⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠲⠽⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡈⠢⣀⠂⠒⠃⠀⠀⣀⡴⠉⢄⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⠀⠀⠀⠀⠄⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢸⠉⠛⠛⠋⠁⢀⣀⠤⠓⠠⠀⠀⠐⠀⠒⠂⠤⢀⡀⠁⠈⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠠⠴⠊⠁⠀⠀⠀⡀⠀⠈⢧⡀⡀⠢⠀⠀⣀⠀⠘⢉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⢦⡘⠆⠩⣐⠀⠈⠉⠤⠁⡈⣄⢈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣔⡁⢄⣀⡔⣁⠀⠄⠁⠀⠀⠀⠀⠀⠀⣀⠼⠒⠲⠒⠒⠂⠈⠀⠀⠐⠀⠁⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠠⠀⣈⠁⠡⠈⠀⢀⠜⠲⠀⠀⠒⠊⠉⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠥⠚⠢⠤⠤⠒⠉⣠⠤⠒⠒⠒⠒⠒⠆⠠⠤⣤⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠵⠀⠚⢀⠀⠀⠀⠀⣀⣀⠠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⡀⠔⠁⠀⠐⠪⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⠀⠀⠠⠀⠐⠂⠉⠢⡀⠀⠀⠀⠀⠐⠈⠀⠄⠐⠂⠁⢂⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⠈⠒⠂⠀⠀⠈⢧⠀⠐⠀⣀⣀⠤⠔⠒⠈⠉
⠱⣅⡐⠒⠀⠀⠀⠀⠀⣒⣒⣀⡀⠬⠷⠶⣎⣀⣀⣀⣠⣤⣴⡶⠮⠕⠒⠋⠉
⠐⢆⠩⠍⠉⠉⠭⠭⠭⠀⠒⢀⣀⣉⠤⠤⠔⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⡓⢾⣄⠀⠉⠙⠷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⣷⣦⣤⡖⠛⠧⢤⡀⠘⣦⠈⢿⣦⣄⠀⠀⠙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⠞⠁⠘⠉⠈⢹⠿⠿⢦⣄⠺⢤⡀⠙⠀⠀⠈⠛⢿⣶⣄⠈⠉⠙⠿⠿⢶⣄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠈⡇⠀⠀⠀⠀⠉⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⠖⢄⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⣀⠀⠀⢀⣴⣧⡄⠁⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠄⠀⠀⣿⣿⣍⠁⠀⠀⡦⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠈⠿⣦⡁⠀⠀⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣤⡶⠁⠀⠔⠀⠀⢸⡇⠀⢸⣶⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠋⠁⠇⠀⣘⠥⠂⠀⣸⠀⠀⠀⣉⠻⢮⣥⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣿⠀⠀⠀⣯⣤⠄⠉⠙⠛⠶⢤⣌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣶⣿⡟⠀⠀⠀⠀⢿⣄⠀⠀⡿⠁⡄⡀⠀⠀⠀⠀⠀⠉⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡼⢿⡦⠀⠸⠾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⢧⠀⠀⣁⡘⢷⠀⠀⠈⢯⡤⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣶⣶⣶⣶⣦⣤⣴⣤⣤⣵⣾⣿⣇⣼⠀⠀⢀⢸⣿⣤⠁⠀⠐⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣷⣶⣿⣿⣧⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉