Little finger Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠲⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⠉⠉⠙⢶⣾⡯⠁⠈⠓⢦⣀⡴⠒⠶⢦⡀⢠⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢿⡦⠀⠀⠈⢿⣷⠄⠀⠀⠈⣿⣧⠀⠀⠈⣧⣿⣿⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣜⣿⣇⡀⠀⠈⢿⣷⡀⠀⠀⢿⣿⠖⠒⣦⢹⣶⡙⠒⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⣿⣿⣿⣿⣄⡀⠘⣿⣷⡦⠔⡏⠤⢖⡺⢟⢸⣿⡃⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡈⢻⣿⣮⣿⣿⡿⠋⠥⢄⠀⠀⠉⠉⠁⣠⠊⢸⣿⡇⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣴⣾⡏⠀⣼⣿⠧⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢨⣿⣿⣿⠟⠀⠀⠀⠀⠠⠒⣿⣏⣿⢟⣤⡀⣿⠟⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⡗⢸⣧⣻⠋⣹⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠻⠟⢋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣸⣿⡈⢀⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⡜⠉⢿⣿⣿⣿⣿⣿⣇⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠹⣿⣿⣿⣿⡿⡁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣻⣿⣿⣿⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢿⣿⠡⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⡏⠆⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢼⣶⣦⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣿⣿⣿⣿⣿⣦⣄⣤⣀⣀⢠⠄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢹⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⡱⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⣿⣿⣿⡦⠄⠀⠀⠀⠀⠀⠜⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠭⣭⣭⣭⣭⡭⠥⠴⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠶⣄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡀⢀⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢸⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⣷⡏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⣧⡴⠞⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣀⣀⡀⠀⣰⠏⠀⠀⠀⠀⠀⠈⣷
⠀⣠⣤⠴⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢙⡿⠀⠀⠀⠀⠀⠀⠀⣼⠟⠋⠉⠙⠳⣦
⣾⠁⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈
⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠘⣧⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠘⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠶⢦⣄⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠘⣦⡀⠀⠀⠀⣀⡼⠻⣄⠀⠀⠀⠀⢀⣼⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠙⠛⠛⠛⠉⠀⠀⠈⠓⠶⠶⠖⠛⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢦⣤⣤⣤⣤⣤⡶⠖⠛⠉
⣿⣿⡿⠛⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢀⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠿⢛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠰⣍⣛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠈⡈⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠇⠀⠀⣀⠊⠓⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠈⠴⢦⢀⠀⣿⣯⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⡔⠃⠀⠀⠀⠐⠡⠻⠷⠬⠷⣤⠤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠃⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢰⣎⣿⣿⠗⢶⣆⣺⡼⣾⣼⣼⣾⣾⣶⣂⣇⣔⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⢀⣴⠚⠃⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠀⠀⣠⠰⠚⠁⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⣠⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⢏⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⣿⣿⣿⣄⣞⣜⣜⡽⣤⠴⠴⠼⠿⠿⠾⠛⠻⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠋⠁⢀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠴⠂⠋⠉⠉⠉⠁⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⢀⠀⡀⣠⣶⣾⣿⣶⡤⣦⣲⠢⢰⣰⣀⣇⣴⣤⣤⣴⠧⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠃⠎⠙⡛⠉⠋⠉⢻⠻⠛⢛⠛⠵⠜⠛⠋⠫⣉⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⢀⣤⣶⣶⣼⣼⣌⣼⣴⣴⢤⣀⣦⣄⣆⣅⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⣠⠀⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⣀⣴⣾⣿⣿⡷⣙⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣷⣇⣦⣽⣿⣼⣦⣸⣽⣰⣃⠀⠀⠀⠉⠰⢦⣄
⠀⠀⠀⠀⠀⠀⠄⠠⣠⢨⣾⣿⣿⢿⣓⣿⠿⠋⠁⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋⠉⠛⠛⠋⠉⠉⠀⠀⠉⠙⠛⠛⠛⠛⠲⠿⠦⠤⣤⠾⠇
⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⡻⣿⣽⠿⠋
⠀⠀⠀⠀⠀⠈⢿⣿⠿⢫⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠘⠋

⣶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠲⢦⡠⠴⠶⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⣤⣄⠀⠀⠱⠀⠀⠀⠀⢳⠊⠉⠑⠢⡄⠀⠀⡟⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⠁⠀⠀⡸⡇⠀⠀⢣⠀⠀⠀⠈⣇⠀⠀⠀⠸⡄⢠⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠁⠢⠞⢠⠇⠀⠀⠈⡇⠀⠀⠀⢸⡀⠀⠀⠀⡇⠸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⡏⡰⠚⠐⢢⡄⠀⠀⠀⠀⡇⠀⠀⠀⢱⠇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣰⠋⢷⡇⠀⠀⢘⡇⠀⡀⠀⢀⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⡇⠀⠈⠷⣄⣠⠞⣷⠀⠁⠀⠈⡇⠊⠉⠂⣸⠀⠀⠀⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⢇⠀⠀⠐⢤⡀⠀⠘⢦⣆⣀⡴⣧⡀⠀⣠⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢀⠑⠒⠶⠶⠆⠀⠀⠀⠀⠠⠀⡀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠉⠁⠒⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡛⣙⣟⣉⡛⣻⡛⣻⠟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⠉⢳⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⠀⣿
⢀⡀⠀⢠⠤⣴⠒⡦⠦⣤⢤⠀⠀⢀⡀⠀⡇⠀⡗⠲⡤⢤⡤⣄⠀⠀⢀⠀⠀⡇⠸⡇⢸⠦⢤⡤⡄⠀⠀⣀⠀⢸⠀⢸⠀⢸⠀⣿⢤
⣏⠉⠳⣼⣀⣿⢀⣇⢀⣇⣠⡇⠰⡏⠙⠢⣇⠀⣇⢀⣇⣸⣅⣸⠀⢸⡉⠙⢦⣇⠀⠀⢸⡀⣸⡀⣿⠀⢾⠉⠑⢼⡀⠀⠀⠀⠀⢿⣀
⠈⠳⣄⠀⠉⠙⢯⠀⠉⠈⠉⡇⠀⠈⠢⡀⠈⠉⠛⡅⠈⠁⠈⢹⠀⠀⠙⢦⡀⠈⠉⠳⡄⠉⠁⠉⢽⠀⠀⠑⢄⠀⠉⠉⢢⡀⠀⠀⠉
⠀⠀⠈⢳⠀⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⡆⠀⠀⠁⠀⠀⠀⣿⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⡞⠀⠀⠀⠀⠀⠘⣆⣀⣀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣰⠃⠀⠀⠀⠀⠀⢳⣀⣀⣀⣀⣀⡼


⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢰⠛⣿⠀⡟⠓⣦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⡞⢳⡄⠀⠀⢀⡤⡄⠀⠀⠀⠀⢠⠚⢲⠀⢰⠛⣦⢤
⠀⠀⠀⢸⠀⣿⠀⡇⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠁⢸⠀⠀⠀⠀⠀⡇⢸⣇⡀⠀⢸⠀⢹⠀⠀⠀⠀⢸⠀⢸⣀⣸⠀⣿
⣠⢤⡀⢸⠀⠛⠀⠇⠀⠇⠀⡇⠀⡠⢄⠀⡔⠙⡏⠈⡟⢻⠀⢸⠀⢀⡤⣄⠀⡇⢸⡏⢹⠋⢻⠀⣼⠀⢀⠤⡀⢸⠀⢸⠁⢹⠀⠛
⠣⡀⠙⠾⢤⣀⠀⠀⠀⠀⠀⡇⠘⢧⡀⠑⠷⢤⣧⡴⠧⡼⠀⢸⠀⠘⢄⠈⠳⠧⣌⣧⠼⢤⠜⠀⣸⠀⠻⣄⠈⠺⢤⣸⣤⠞
⠀⠈⠢⡀⠀⠈⠳⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀⠀⠈⠧⠀⠀⠀⢸⠀⠀⠀⠑⢄⠀⠀⠙⠆⠀⠀⠀⣿⠀⠀⠈⠳⣄⠀⠀⠹⠄
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠠⠠⠖⠀⠁⠀⡒⠿⠛⣓⡶⠀⠀⠀⡅⢀⣀⠀⠉⠉⠀⣤⡤⢴⡶⠶⠶⠒⠛⣛⠛
⠀⠉⠐⠫⡡⠐⠐⣀⠤⠄⠉⡠⠔⠊⠁⠀⠀⠀⠀⠜⠉⠉⠀⢀
⠀⠀⠀⠀⠐⠾⣗⢀⠠⠒⠁⠀⠀⠀⠊⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⢀⠀⠐⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠀⠀⠠⠀⠀⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒
⠀⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⢠⢾⡝⠋⡅⣿⠀⣀⠀⠀⠀⠀⠀⠢
⠀⠚⠀⠀⠀⠐⡀⢀⠀⠈⡀⠀⠀⠀⡙⢯⠉⠉⢿⠀⢻⣤⣾⣿⡄⢐⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣆⣀⡷
⠀⠀⠀⠀⠀⠀⠸⣍⠀⠠⠞⠀⠀⠸⡈⠄⣣⠀⠈⣧⠀⢿⣿⣿⡇⠈⠀⠀⠴⠀⠀⠀⠀⢄
⠀⠀⠀⠆⠀⠀⠀⢻⣤⠀⢀⠀⠀⠀⠱⡌⢘⢧⠀⠘⣧⠘⣿⠟⠋⠀⡠⠀⠀⠀⠀⠀⠰⡾
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠊⠀⠈⠀⠀⠘⡄⢩⠗⠀⠹⠖⠁⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⣇⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢀⠁⠀⠀⢸⣇⠀⠀⠁
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣯⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠐⠀⠘⠁⠹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠈⣧
⠀⠐⡄⠀⠀⣤⣀⢀⡀⢀⠀⠀⢁⠀⠀⢐⣗⣁⠤⠔⠂⣁⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⠒⠤⠀⢸⡇
⠀⠀⡄⠀⠀⣸⣿⡌⠀⢨⡀⠀⠈⠀⠀⠀⣽⠻⠿⠿⠟⠚⡅⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠓⠀⠀⠐⠚⠀⠀⠀⠆⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠚⠁⠀⠀⠀⠂⠀⠀⠀⠀⠤⢤⣤⡤⠶⠛

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

⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⡀⠀⠀⠀⠄⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⡀⠤⣤⣄
⠀⠀⠀⣀⣴⡇⠀⠀⠀⣦⠉⠙⣿⣿⣿⡶⣶⣀⣀⠀⠠⢀⡿⠇⠀⢀⠀⣀⣉⣉⠉⠉⠉⠉⠉⠉⣉⣀⣀⣈⣱⠀⠀⠀⢰⣿⣿⡆
⠀⠀⢀⣿⣿⡏⠀⠀⢐⣿⡂⠀⢝⣿⣿⣻⣷⢯⠉⠙⠿⢿⠃⣾⣾⣿⠀⠉⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⣛⠉⠋⢻⣿⡿⠇
⠀⠀⠸⣿⣿⣗⠀⠀⠐⣿⠇⠀⠀⠙⠛⠚⠿⠔⠀⠀⠀⠈⠋⠉⣻⠃⠀⣿⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠶⠚⠛⠉⠛⠻⠿⠋
⠀⢀⣀⣿⣿⣗⠁⠀⠨⣿⣅⡀⠠⠄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠁⠀⠀⠘⣇⠀⠈⠉⠉⠛⢷⠄⠀⢠⠴⠒⠲⣶⠒⠒⠤⡀
⠀⠸⣿⣿⣿⣇⣀⣁⣨⣿⣿⠇⢠⠖⠒⢲⢒⢀⣆⣰⣾⣶⣶⡉⠁⠘⠙⠀⢿⠀⠀⠀⠀⠀⣼⡀⠀⣂⠀⣀⡂⠀⣀⡂⠀⡀
⠀⠀⢻⢸⣿⣿⣿⣿⣿⡏⢿⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠿⠉⠉⠉⠁⠀⠀⢼⡇⠀⠀⠀⠀⣿⣅⡀⢿⣿⣿⣶⣶⣶⣿⣿⠇
⠀⠀⢠⡀⠻⠿⣿⠿⠟⢀⠄⠠⣴⣶⣶⣶⣿⣷⠀⠀⠀⠀⠀⢠⡄⢀⡴⠀⢸⣿⠀⠀⠀⠀⣿⢧⡁⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠙⠲⢦⡥⡴⠖⠋⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠇⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠭⣇⣄⠀⠀⠀⣠⡶⠗⠲⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣀⠐⠀⠈⢹⡆⠆⣿⣷⠀⠀⢰⢻⢥⡏⣾⢿⠃⣸⡟⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⢀⣀⡇⡄⠀⠀⠀⠀⠀⣟⠀⠀⣿⠉⠉⢻⣟⠁⡟⠀⠀⣤⠟⢁⠇⢻⡿⠔⠂⠘⣿⣺⢱⣿⡀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠉⠙⠻⠗⡆⠀⠀⠀⠀⠀⠃⠀⢠⣿⣀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠠⠀⣺⢩⣰⣿⡇⠀⢱⣶⣦⣤⣀⣼⣿⡀
⠀⠘⠶⣦⣤⣤⣤⣿⣿⣶⠾⠃⠀⠀⠀⠀⠈⠁⠀⠸⡇⠀⠀⠀⠀⠘⠆⠀⠀⢻⠀⠀⠁⠈⠹⢠⣽⡿⠁⠀⠸⣿⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠉⠉⠑⡴⠁⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠁⠀⠈⠒⠉⠈⠐⠒⠤⡀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠀⠈⡐⣠⠄
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⣿⠄⢰
⠀⠀⠀⣀⠤⠤⢰⡀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢣⠘⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠿⠟⠀⠈⢢
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡤⠃⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡠⠖⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⡆⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⢀⠁
⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡠⠘⠀⠀⠔⠓⠒⠒⠒⠶⠀⠀⢹
⠀⠀⠀⠈⢢⡄⠀⠀⠀⠀⠀⣀⠔⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠦⣆⡀⠀⢠⠒⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠈⠢⠤⠤⠔⠀⠀⠀⠀⠆⠀⠀⢈⠓⠄⣀⠄⡜⠀⠀⠀⢰⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢈⠀⠀⠀⠀⡁⠀⠀⠀⢘⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣀⣀⡀⠇⠀⠀⠀⠉⠒⠒⠒⠊⠣⠤⠄⠠⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠂⠀⠉⠉⠉⠉⠉⠁⠀⠐⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣶⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣴⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢠⠒⠒⢄⠸⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠇⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠸⢀⠔⠒⢢
⠀⠀⠀⠈⠢⣀⠀⠈⠣⣀⠘⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠃⠀⠀⠀⢀⠔⠀⠀⡜⢀⡠⠋⠀⠀⡠⠊
⡈⠁⠉⠒⠤⢀⠑⠤⡀⠀⠑⠌⡒⢄⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⠆⠀⠀⡠⠔⠁⢀⠔⡈⠔⠁⠀⡠⠔⢁⠠⠐⠊⠁⠉
⠈⠀⠀⠀⡀⠀⠈⠁⠚⠶⠀⠀⠈⠉⠀⠀⠀⠈⢢⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡠⠔⠁⢀⠔⠁⠀⢠⠊⠀⠀⠀⠈⠉⠀⠀⠰⠞⠂⠉⠀⠀⡀⠄⠐⠊
⡎⠀⠀⠀⠐⠋⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠙⠭⠀⣀⣁⣈⡁⠠⠄⠊⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠎⠓⠀⠈⠉⠈
⠈⠁⠀⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠒⠂⠀⠉
⠀⠀⠀⢌⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⢉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠒⠠⢄⡀⠀⠀⠀⠀⢀⡠⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠣⣀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣴⣶⣤⣤⣤⣤⣤⣴⣦⣬⣥⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠉⠁⠉⠑⢤⡀
⠀⠀⠀⠀⠀⢀⡠⠔⠒⠲⡇⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡴⢦⡀⠀⠀⠑⡄
⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⢠⠋⠀⠀⢳⠀⠀⠀⠹⡀
⠀⠀⠀⠸⠀⠀⠀⠀⢀⡠⠔⠒⡶⠤⡀⡠⠊⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⢰⠀⠀⠀⣰⠃⠀⣀⢎⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠁
⠀⠀⠀⠀⢣⠀⠀⠄⠀⠀⣾⢶⡆⠀⠀⠀⡠⠖⠂⠐⠲⡤⠂⠀⠀⡠⠼⠀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⢠⠐⠷⠀⠀⠀⠀⣿⣄⡇⠀⠀⣼⡷⠀⠀⠀⠀⢘⡩⠠⠋⠀⠀⠀⠀⠁⠈⠑⢆⠀⠀⠀⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠉⠑⢤
⠀⠀⠀⠈⠢⠤⠴⠃⠀⠀⣿⣽⠇⠀⠀⣿⡿⣄⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⢻⣷⡿⠀⠠⠚⠁⡠⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡘⠀⢀⡠⠖⢊⡽⠃⠀⠀⠀⠀⠀⠀⠀⡼⠤⠒⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠒⠀⠀⠀⠐⡆⠀⢃⠀⠀⠀⠀⠀⠀⠠⡄⠒⠛⠒⠲⣇⡴⠋⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠸⡄⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠑⠤⢈⡙⠭⠅⠀⠀⠀⠀⠀⠀⠈⢀⠇⠀⠀⠙⢦⣀⡠⠐⠀⠁⠀⠱⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⢀⠀⠀⠀⢀⣀⡠⢞⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡅⠀⠀⠨⠉⡄⠈⢇⠀⠀⠈⢳⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⡇⢘⠀⠘⡄⠀⠀⠀⣧⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠁⠀⡄⠀⡇⠀⠀⠀⠸⡄⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⠀⢸⢨⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠓⠒⡶⠂⠀⠀⡠⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡘⠀⠀⠀⠀⢸⡞⠀⢀⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠛⠒⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢠⠃⠀⠀⠀⠀⢸⠁⠀⡸⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⢲⠃⠀⠀⠀⠀⠀⡜⠉⠹⢇⣀⣀⣀⣀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠊

⣌⠙⡾⣿⣿⣿⣦⠀⠀⠈⠓⠲⠄⢡⣶⣟⠇⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡷⠃⠀⠀⠀⣴⡿⣛⢻⣿⣮⣿⡿⠀⠀⠘⢆⡴⢟⡐
⠼⣧⢷⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠈⠳⣄⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢘⣿⣿⣯⣾⠿⠛⠋⠁⠀⠀⠀⠈⣧⣾⣿
⣚⣭⡿⠟⠁⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠖⠋⠈⠉⠉⠀⠀⢠⣀⠀⠀⣠⠀⠀⠘⢯⣌
⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⡜⠁⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⣯⠀⠀⠀⠀⠈
⠀⢀⣀⣤⣴⣶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣤⠖⠀⠀⢼⣿⠅⠀⠀⠀⠀⠀⣠⣴⣶⣶⡄⠀⠀⠀⣼⡇⠀⠀⢹⣧
⣾⣿⣟⣛⣩⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠰⡟⠓⠊⠉⣇⠀⠀⢸⣿⣧⣿⣿⣼⣿⡆
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣴⣦⣾⡁⠀⠀⠀⠀⣰⣷⡟⠉⠀⠀⠀⠀⠈⠳⠀⢀⣘⣦⠀⠈⠻⢿⣿⣿⠿⠟
⠉⠉⠉⠉⠀⠀⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠉⠀⠀⣀⡀⠀⠀⠀⠀⠒⠟⢿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣶⣤⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣠⡾⢛⡯⣉⣻⣦⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⠤⢶⣶⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣼⣿⢳⣯⡐⢫⣿⣟⢻⢄⡀⠀⠀⠈⢷⠀⠀⠀⠸⡄⠈⢻⣿⣿⣿⣿
⣿⣿⠟⠀⠀⠀⠀⢿⣿⡟⠻⣿⣿⣿⣿⠃⠀⠀⣴⣷⣿⣿⣿⣻⡈⠲⣤⡍⢥⡿⠀⠙⠀⠀⠀⠈⣷⠀⠀⠀⠱⡀⠘⢿⣿⣿⣿
⣿⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⠝⠾⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣼⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠶⣿⡦
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⢀⣴⣾⣿⡆⠀⠀⠀⣰⣦⠶⠋⠁⠀⢠⠞⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⣿⣶⣄⣴⣾⣿⣿⢟⣁⣄⡀⠀⠀⠀⣾⣿⣿⣿⣧⡀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠙⠿⢷
⡿⣟⣽⣝⣿⣿⣯⣄⡅⠉⠀⠀⠀⠈⠻⣿⣯⣽⣻⢿⣦⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣦⡿⢿⣿⡷⡀⠀⠀⠀⠀⢀⣠⣬
⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⠀⠀⠀⡞⢡⡴⠛⣋⢣⢹⡇⠀⢼⣟⣿⣿⣿⣷⠄⠀⠀⠀⠀⠻⣿⣌⢻⣿⣷⡀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⣿⣿⠇⠀⡀⡄⠀⠀⠀⠀⣇⡜⢨⣶⣿⡋⣼⠃⠀⠈⠛⠛⠛⠛⠁⠀⠀⢀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⡀⢿⠿
⠿⣿⣿⣿⡿⢏⠀⠈⠉⡗⡄⠀⠀⠀⠈⠻⢮⣭⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠘⠷⢄⡀⠀⠀⠈⠙⠉⠀⠀⠀⠈⠁⠐
⠀⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡀⠘⢻⡅⠀⠀⠀⠙⠲⣄⡀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢻⡗⠒⢲⣟⠀⠀⠀⣧⠀⠀⠀⣀⠀⢠⣽⠿⠃⠈⠒⠲⣤
⣿⣿⣿⣿⡆⠀⠀⠚⠿⠋⠀⠀⠀⠀⠈⢳⣦⣄⠀⠀⠀⢠⣿⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠉⠓⢦⣀⣴⣸⡿⠀⠀⢠
⠛⠿⠛⠛⠀⠀⠀⠀⠀⢠⣾⢿⡿⣆⠀⠀⠛⠓⠀⠀⢠⣿⡇⣀⣀⣀⢸⣿⡄⠀⠀⠰⣿⡯⢀⣤⣶⣦⡀⠀⠛⠿⠛⠁
⣢⣄⣠⣤⣤⣀⣀⣀⣀⣿⣃⣉⣠⣈⣲⣄⣀⣀⣀⣀⣸⣿⣷⣿⣿⣿⣼⣿⣇⣀⣀⣀⣁⣠⣿⣿⣟⣿⣿⣆⣀⣀⣀⣀⣀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠠⣠⡆⠀⠀⢢⠒⢲⣾⣷⣤⣄⣀⠀⠀⢰⣿⠁⢀⠀⣘⣀⠀⠀⠚⠛⠛⠛⠀⠀⢁⠀⠀⠀⣾⣿⡄
⠀⠀⣸⣿⡇⠀⠀⣻⡂⠐⢿⣿⣿⣾⠍⠙⠻⣿⢲⣶⣿⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣟⣛⣘⠙⣿⡿⠃
⠀⠀⢻⣿⡇⠀⠀⣿⠇⠀⠀⠉⠉⠛⠁⠀⠀⠈⢁⠹⠃⠀⣧⠀⠤⠤⣠⣀⠀⠀⠈⠋⣉⣉⣉⠛⠋
⠀⣴⣾⣿⡇⠀⠀⣽⣷⡄⣈⡀⢠⠤⠄⢠⣴⣶⡀⠀⠠⠤⠘⡆⠀⠀⠀⢸⡇⠀⠊⠁⠀⠛⠀⠉⠁
⠀⠈⡿⣿⣿⣿⣿⣿⠟⠀⠁⠀⠈⠀⠛⠛⠻⠿⠛⠒⠂⠀⠀⣧⠀⠀⠀⢸⡆⠀⣷⣾⣶⣤⣶⣷⡾
⠀⠀⢄⠙⠿⠿⠿⢁⠄⢠⣶⣶⣶⣶⣆⠀⢀⣀⠀⣤⢀⡤⠀⣿⠀⠀⠀⢸⣷⡁⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠙⢲⡴⠚⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠛⠸⣇⠀⢿⡇⠀⠀⢸⡗⣷⣆⣀⠀⣴⠟⠉⠢⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠉⠛⣿⠿⢿⡿⠛⡆⠀⢀⣼⠀⢸⣿⠀⠀⢹⣯⢣⣿⠃⢸⡏⠀⠀⠀⣿⡆
⠀⠀⠐⠒⢾⠯⠀⠀⠀⠀⠘⠀⢀⣿⠀⠸⡏⠀⠁⠀⢸⠀⠀⢰⡿⠀⠀⢸⣛⣹⣧⠀⢸⣥⣄⣀⣠⣿⠁
⠀⠳⠦⣤⣤⣼⣿⡶⠾⠃⠀⠀⠀⠉⠁⠀⡇⠀⠀⠀⠘⠆⠀⠸⠇⠀⠀⠘⠣⣿⠟⠀⠰⢿⣿⢿⣿⡿⠁


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

⠈⣀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠄⠀⢀⣤⢀⠉⠀⠀⠀⠀⠀⠀⠀⠸⣧⣥⣀⣤⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠉⠉⠁
⠷⣾⢠⠆⣠⡶⠶⠶⣤⠀⠀⠂⡤⠀⠀⠀⠀⠀⠀⣢⣤⠀⢀⡀⡠⠄⢀⠉⠈⠉⠛⣮⣤⠀⠀⠀⠀⠀⢀⣠⢾⠷⣾⡰⠆⣠⡶⠶⠶⣤⠠
⠋⠈⠉⢰⢿⠀⢀⠀⠘⡇⢀⣤⣧⠀⠀⠀⠉⠄⢠⠏⠙⠀⢩⡀⠀⠀⢸⣆⠀⠀⠀⠀⢀⣠⠤⠶⠿⠞⠒⠂⠞⠉⠈⠉⢈⣟⠀⢀⠀⠘⡇
⠀⠀⠀⠀⠻⣦⣤⣤⡾⠃⠐⠎⠀⡑⠦⠤⢤⠖⢟⣲⣶⠀⠈⢧⡀⠀⠈⠹⣧⠀⠀⢣⠀⠀⠀⠐⠢⣄⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⡾⠃
⡶⠶⠤⢦⠀⠀⡀⠀⠀⠂⢄⣀⡀⠀⡈⠁⠂⠅⠀⣙⡏⠀⠀⠘⣿⡄⠀⠀⠘⣧⡀⠀⡆⠀⠀⢤⡴⠦⠿⠶⢶⡶⠦⡤⢦⠀⠀⡀⠀⠀⠒
⠛⠲⢦⡀⠀⡴⠃⠀⠀⠀⠫⣄⣈⡻⠻⢄⡀⠀⠀⠈⠀⠀⠄⠀⢸⡽⣆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⡀⠀⠼⠁
⠀⠀⠀⠉⠠⢤⠀⠀⢲⡀⠀⠀⠹⡗⠆⢢⣎⣹⠔⠠⠀⠀⠀⠀⠘⢻⡿⣦⠀⠀⠈⢿⣄⠀⠀⠀⠀⠂⠀⠛⡄⠀⠀⠀⠉⠠⢤⠀⠀⠦
⠀⢠⣤⢤⣠⣠⣤⡀⠀⠑⠀⡀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠉⠑⠃⠀⠘⠃⠈⣿⡗⠀⠀⠀⠀⠀⠀⡇⠀⢠⡤⣤⣤⣠⣤⡀⠀⠃
⠂⢢⠠⢸⡿⠥⠤⢥⠤⣾⡍⠏⠉⠀⠀⠀⠠⡄⠀⠄⠀⢀⡠⠔⠒⠆⠤⠀⢰⡀⠀⢀⠀⣿⣿⣀⠀⡀⠀⢠⡷⠂⢢⠠⢸⡿⠥⢄⢧⠤⣾
⠦⣤⠒⠀⠓⠖⠨⠛⡓⢿⠁⡃⠀⠀⠀⢿⠀⠀⠀⠀⠀⢠⡄⠐⠆⠃⠘⠂⠀⠁⠀⠸⠀⠐⠋⠁⠠⠁⠀⠘⡷⠦⣤⠒⠐⠓⠖⠨⠚⡓⠿
⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀⣀⣿⡀⠀⡀⢸⡄⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡧⢀⠃⠀⠀⠀⠈⡁⠇⠄⣀
⠈⠣⡀⠀⣀⡴⡟⠱⠖⠯⠐⠢⣱⠀⠀⠈⡇⠀⠠⣿⠀⠀⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⡈⠁⠘⠣⡀⠀⣀⡔⡟⠱⠒⠯
⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠤⠀⠀⠀⡀⠀⢻⠀⠀⢹⠄⠀⠀⠀⠰⠶⠇⢹⣷⡚⠁⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⡠
⠈⠳⣄⠀⠀⠂⠀⠒⠈⠀⠀⢶⠀⠀⠀⠀⢸⣄⠀⢸⡇⠀⣾⡦⠀⠈⠀⠈⠈⠂⠀⡠⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠂⠀⠒⠈
⠚⠓⠺⠶⣦⣤⣄⣀⡀⠀⠀⠰⣧⡀⠀⠀⠘⠇⠀⢸⣷⠀⠈⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⡀⠀⠀⠀⠙⠛⠓⠺⠶⣦⣤⣄⣀⡀
⢀⠀⠀⠀⠈⠦⣄⡉⠓⠀⢠⠀⢻⠅⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠢⠤⡈⡀⠀⠀⠀⠒⠒⠂⢁⣀⠀⠀⠀⠰⠀⠀⠀⠈⠦⣄⠉⠓
⠐⠆⣀⡀⢀⠠⠈⠳⡀⠰⠋⠀⠈⣨⢧⡄⠀⠐⠋⠐⣿⣄⠀⠁⢠⢶⣦⣤⣄⡈⠁⠐⠂⢌⠀⠉⠁⠀⠀⠀⠀⠐⢆⣀⡀⠀⠠⠈⠳⠀⠰
⠀⡸⠻⠏⠍⠩⣹⠃⠈⠳⠀⠀⠀⠹⣼⣟⣠⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠏⠍⠉⣹⠃⠈⠣
⠀⣿⣿⣶⣷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠏⠤⠀⠀⠄⠀⢾⣽⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠂⠀⠀⠐⠀⠀⠀⢀⠀⡿⣿⣾⣷⣶⡶
⢰⡿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠚⠁⠃⣠⠂⠀⢀⠃⠀⢠⡀⡃⠀⠀⠀⠀⠔⠀⠀⠀⢼⢰⡿⡿⣿⣿⣿⡇
⠺⠛⠛⠻⠛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠈⠀⢰⡶⠞⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠛⠛⠻⠛⢛⠅
⣀⣢⠀⡀⠀⣀⣀⣀⠀⠀⠋⡀⢀⠐⠋⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠛⠛⠶⠻⠶⣦⣠⠀⠀⠃⠀⠀⠀⠀⢀⣀⣀⣢⢀⡀⠀⣀⣀⣀
⡭⠿⠾⢁⣾⠋⠉⠉⠻⡄⠀⠀⡏⠈⠀⠀⠤⠀⠀⡾⠿⠀⡔⠒⠈⠁⢰⡀⠀⠀⠀⠙⠛⠀⠀⣀⣤⣠⢰⡚⣽⠭⠻⠮⠡⡾⠋⠉⠉⢻⡌
⠀⠀⠀⠈⣽⡀⠰⠀⣠⡇⢐⡿⠋⢦⡀⠀⠀⣉⣼⢁⣀⠀⠸⡆⠀⠀⠘⢿⡄⠀⠀⡔⠐⠚⠉⢩⡉⠉⠀⠀⠀⠀⠀⠀⠰⣷⡀⠰⠀⣠⠇
⣀⣀⠀⡀⠈⠛⠛⠛⠋⣀⠀⠀⠀⠀⠩⠉⣙⠁⠘⢺⡿⠀⠀⢸⣦⠀⠀⠀⢻⣄⠀⠘⡄⠀⠀⠀⣈⣓⣤⣀⣀⣀⣀⢀⡀⠈⠛⠛⠛⠉⣀
⢯⣉⡉⠙⠀⢠⠆⠀⠀⠀⡴⠒⠢⣄⣦⠀⠀⠀⠐⠲⠂⠀⠀⠀⢻⢧⡀⠀⠀⢻⣆⠀⠃⠀⠀⠙⠋⠉⠉⠉⠙⢯⣉⡉⠙⠀⢠⠆

⠀⠀⢀⠤⠐⠒⠒⠠⢀⠀⠀⠀⠀⠔⠊⠉⠉⠑⠢⡀
⠀⠰⠁⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⠀⠀⠀⠀⠀⠀⢱⠀⢀⣀⡀
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠊⠁⠀⠈⠳⡄
⠀⠘⡄⠀⢠⠖⠉⠉⠉⠉⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⢄⣈⠄⢊⠀⠀⢀⢶⣿⠀⠑⠐⠂⠀⠁⠐⠢⢄⡠⠊⠁⢡⠀⠀⢀⡇
⠘⠤⡀⠀⢈⠆⠀⣰⣏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸
⠀⠀⠀⠀⢀⣀⡘⠿⠁⠀⠀⠀⠐⠐⠲⣄⠀⠀⠀⠀⠀⡰⠁⠀⡠⠃
⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⠀⢀⣴⣾⠀⠈⣇⢀⠠⠐⠮⠀⠀⠈⠑⢢
⠀⠀⠀⠀⠐⠄⠰⠂⠀⠀⠀⣾⣷⡿⠆⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⠖⠚⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠈⠉⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡠⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢠⠄⠀⠀⠁⠙⢌⠐⡀⠀⠰⡖⠊⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠤⠲⢤⡀⠀⠈⠀⠀⠀⡸⠠⣀⠀⠀⢀⡠⢲⠋⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢠⡁⠀⣀⣀⡠⠖⠁⠀⠀⢣⡀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠢⣀⡀⠑⣂⠤⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠊⠉⠉⡂⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢄⠀⠀⠀⠀⢹⠓⠤⠤⠤⠒⠁⠀⠀⠀⢤⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢸⠉⠋⠉⠉⠑⢌⠢⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡟⡀⠀⠀⠀⠀⠀⠑⡘⣄⠀⠀⠀⢱⠀⠀⠰⡀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡸⠀⢡⠀⠀⠀⠀⠀⠀⢡⠘⡄⠀⠀⠀⢃⠀⠀⠙⠦⣀⠀⠀⠀⢇⣀⢀⣑⡤⠊
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⣰⠁⠀⠈⡆⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠈⡄⠀⠀⠀⠈⠉⠓⡲⠂⠀⠠⠊⠀⣠
⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⣠⣃⣀⠠⠤⠃⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠉⠉⡰
⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢇⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠚⠁

⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣠⠐⠉⠀⠀⠀⠀⠈⣳
⠀⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠻⢶⠶⠖⣐⠶⠁⠉⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠘⠷⠒⠖⠲⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⢀⠀⠀⢀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠰⠶⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⠀⠈⠓⢤⠀⠀⠀⠀⠉⠁
⠰⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⠀⠀⠀⠀⠈⠳⡄
⠀⡇⠴⠀⠀⠀⠀⠐⠒⠦⡀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉
⠀⠐⠐⡂⠀⠀⠀⠀⠀⠑⢼⡆⠀⠀⠀⡈⠁⠂⢷⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠘⡈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦
⠀⠀⡄⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠙⠛⡇
⠀⠀⠇⠤⠒⠀⠘⠈⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠽⣆
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠊⠁⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⣆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠈⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡀⢀⠠⢀⣴⠆⠀⠀⠀⠀⠯⠸
⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⣤⠴⠶⠋⠁⣀⣦⠀⠀⠂⠀⠡
⠓⢲⠀⠸⢇⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠉⣀⣀⣠⠤⠒⢋⡠
⠒⠋⠀⠀⠀⠁⠀⠀⠀⠠⠆⠃⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠣⠅⠤⠔⠂⠉
⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠌⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠀⠂

⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢆⣀⣀
⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠂
⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡄⠘⠁
⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠃⠘⠢⡁⢸⠀⠀⡇⠀⢣⢰⠀⠀⠂⣿⠀⢸⢰⡀⠀⠁⠀⠀⠀⠀⠀⢀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⠀⠈⠀⠁⠈⠁⠀⠉⠀⠁⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⢀⡀⠀⡀⠀⠀⠀⡀⢉⠀⡁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣨⠀⢈⡆⠀⣧⠸⡀⠀⠇⢸⠀⡇⢈⠑⡄⠀⠀⢀⣠⡀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⢿⣿
⠀⠀⠀⠀⢰⣬⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢸⣿
⠀⢠⡀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿

⢀⠢⠁⠀⡀
⠌⡁⣇⢀⠄⠴⣧⢆⠄
⠠⠀⡍⡄⡠⣾⣿⣷⣄⡀
⠐⢌⠁⡆⠁⠈⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡻⣿⣿⣿⣷⣄⣀⠤⠤⠐⠒⠲⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢞⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠙⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⢳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠑⠄⠀⠀⣀⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠠⣘⣷⠬⡟⣆⠙⠲⢤⣤⡤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠉⠳⣄⣀⣀⠀⠀⠀⠀⢀⣀⠀⢠⠞⢁⣢⡠⠇⠘⢷⡀⠠⢶⡄⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡟⠁⠈⠙⢦⡀⠀⢫⠈⠁⢈⡠⠊⠁⠀⠠⡀⠀⠉⠓⠋⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⠉⠒⢦⡙⣄⠀⠳⣄⠀⠁⠀⠀⠀⡀⢄⡪⠗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡆⠀⠹⡆⠀⠀⠀⠀⢞⠉⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠃⠸⠧⠏⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠹⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡘⢆⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣇⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⠲⣄⠘⡌⠳⣄⣀⠴⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⢦⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⣧⣹⡖⠛⡇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠳⢦⣀⣇⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⢳⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠛⠛⠓⠚⠛⠋⠉⠀⣀⡴⠚⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣤⣤⣤⣤⣤⣖⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣘⡃⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⠁⣠⠶⠚⠛⠓⠦⡄⠀⢸⠋⠀⠀⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠙⠓⢤⡀⡼⠁⠀⠀⠀⠀⠀⠸⡆⢸⠀⣴⠛⢲⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣷⡈⢰⡇⠀⠀⢻⡀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⣀⠀⠀⠀⠀⠀⢰⠏⠙⠾⠀⠀⠘⠀⣧⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢦⠀⢀⡰⠋⠀⠀⠀⠀⠀⠸⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣼⠁⠀⢠⡠⠤⠤⡀⠀⠀⠀⠑⠋⠀⠀⢀⡠⠤⣄⡠⢀⢀⡏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡏⢣⣈⡺⢁⠔⠐⠾⣆⠀⠀⠀⠀⠀⢠⡧⠆⠲⡌⠳⣊⠜⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢰⠀⣿⠀⢃⣴⠀⠀⠹⠀⠀⠀⠀⠀⡟⣤⠀⠀⠘⡌⡯⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣈⢀⠀⣇⢿⡀⣸⣿⢣⣀⣠⡇⠀⠀⠀⠀⣿⣟⢣⣀⣀⣿⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⣀⡟⠸⣷⣿⣿⣿⣿⣿⠃⠀⠤⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⣿⡿⠋⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⠏⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠷⣄⡀⠀⠰⣀⣀⡠⠀⠀⢀⣠⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣠⡾⢻⠛⠲⠶⠶⠶⠖⢚⡿⠈⠁⠀⠀⣤⣖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢠⡟⣰⣿⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⣀⡀⠀⠀⣾⣼⠁⠃⠀⠀⠀⠀⠀⠸⣄⡀⢀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢩⠏⢀⣴⠯⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⣤⠀⠀⠀⠀⠀⠀⠀⣤⢠⡟⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡠⠀⠘⣏⢳⡇⠀⠀⠀⣤⠀⠀⠀⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠣⣰⠏⠉⢸⠃⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⣀⢀⣠⡇⠀⠀⢸⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠁⠀⣀⢾⠃⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠁⠀⣸⠀⠀⢀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠤⣙⢢⠄⠀⢹⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣠⣾⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠶⠒⠚⠉⠉⠒⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢸⡁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣀⡻⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣣⠼⠋
⠀⠀⠀⠀⠀⢣⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⡞⣩⢤⠨⢵⡽⣷⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣴⣶⡤⢣⡟⠀⠀⠀⠀⢸⣿⡿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠖⠛⠁⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠘⠳⠿⠷⠶⠋⠀⠀⠀⠀⠀⠀⠙⢿⣾⡿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠐⣦⣤⣤⣴⡆
⠀⠀⠀⠀⠀⢺⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢹⡄
⠀⠀⠀⠀⣤⡟⠙⠙⠋⠉⠙⠛⠛⠙⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠉⠛⡟⠛⣿⠛⠛⠛⠛⠛⠛⢿⠟⠋⠀⠀⠀⠀⠀⠀⣼⣿⣯⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣿⣿⣧⣿⣟
⠀⠀⠀⠀⠀⠀⡇⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡯⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠁
⠀⠀⠀⠀⠈⠻⢷⣶⣶⣶⣄⣠⣶⣶⣾⢿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠞⠉
⠀⠀⠀⠀⠀⣀⣀⣹⡿⢿⣩⣍⣿⣿⣏⣀⠉⠉⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⣿⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⠺⣻⣿⠇
⠀⠀⠀⠀⢀⠈⠿⠿⣿⣿⣿⣿⣿⣿⠇⠀⣀⡀⠀⠀⠀⠀⢿⣯⣹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⡻⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⡙⠿⣿⣿⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠊⣳⣀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠒⠒⠄⠀⠊⠀⠀⠀⢀⣠⠼⠓⠉⠀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢿⡀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠊
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⢨⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⢁⡴⠋⠀⠀⣂⠈⠓⠂
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡄⠀⠀⠙⠹⠿⠟⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⠀⠏⠀⠀⠀⠀⠈⠙⠓⠺⢤⡤⠴⠄
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⠦⠀⠀⠀⠀⠀⢀⠔⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⣡⣀⣓⠒⢢⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢀⣴⠿⣿⡿⢟⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⢀⠀⢀⣠⣾⣿⣿⢖⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⢔⣸⣿⠟⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠄⠊⠀⢟⣫⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠠⠀⠀⣠⠈⠉⠓⠲⠤⣀⡀⠀⠀⠈⣆⠀⠁⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⣼⢧⣀⣀⣀⣀⣀⣀⣉⠆⠀⠀⠘⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⠟⠉⠉⠙⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⣀⢸⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⠀⠀⠀⠀⢸⠁⠀⠀⣀⠀⠀⠀⠀⠉⢠⠀⣼⠉⢡⠀⠀⣠⣤⣶⠶⢶⠀⣼⡤⠤⢀⣀⣀⠀⠀⠀⠀⢠⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠃⢨⢀⣴⡶⠶⠿⠦⢄⡀⠀⠙⠲⣄⠀⠀⢘⡁⠉⠀⠘⢶⠋⢁⡀⠿⠀⠀⠀⣭⠂⠚⠛⠛⠋⠀⠀⠀⠀⢸⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠈⠁⠒⠒⠒⠚⠛⢲⠚⣩⠔⠊⠉⠁⠉⠉⠒⠤⣴⠶⠶⠶⠶⠶⢦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⡠⠤⠆⠀⠀⠀⠄⡀⠈⢆⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⣏⢹⡏⠋⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⡗⠶⠶⣤⣤⡤⢤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡎⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢢⡁⠀⠀⡁⢸⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠰⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠢⢲⠃⡄⠀⠃⢨⠀⣸⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢹⣀⠜⢠⣾⡜⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⢠⠃⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⡜⢿⠓⢸⡔⠇⠀⠑⡀⠀⠀⠀⢰⠂⠀⠀⡋⠉⣳⣦
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠉⠓⠶⠤⠤⠤⠶⠞⠛⠁⠀⠚⠀⠈⠃⠚⠛⠃⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋

⠀⣠⠔⠚⠉⠉⠉⠒⢄⠀⠀⠀⢀⡠⠐⠂⠀⠐⠒⠤⡀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠦⡀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠓⠦⡀
⡐⠁⠀⠀⠀⠀⢀⡀⠀⢣⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠞⠁⠀⠀⠀⠀⣀⠈⢦⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⢦
⡇⠀⠙⠀⠀⠀⠈⢁⠀⢸⠀⡇⠀⠀⠀⠆⠐⠇⠀⣠⠀⢰⠀⠸⠀⠘⠃⠀⠀⠈⠉⠀⠈⡇⠀⡇⠠⡄⢀⡀⢠⡄⢹⠀⢸
⢣⠈⠢⣀⠀⠀⣀⠞⠀⡜⠀⢣⠐⢇⠠⣀⣄⣠⠤⠜⠀⡄⠀⢸⡀⢲⣖⣖⣺⣹⣭⡟⢀⡇⠀⢣⠀⠳⣈⠁⠀⣠⠞⠀⡸
⠀⠳⢄⡀⠉⠉⢀⡠⠞⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠑⢄⡉⠛⠚⠒⢁⣠⠎⠀⠀⠀⠳⢄⣈⠉⢉⣁⡠⠞⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢀⡤⠒⠒⠛⠒⠢⣄⠀⠀⠀⠀⢀⡤⠖⠒⠒⠶⢄⡀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠦⣀⠀⠀⠀⠀⢀⡠⠖⠒⠚⠒⢦⡀
⢠⠋⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⠞⠁⠀⠀⢀⠀⠀⠈⢣⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⣆
⡇⡀⠀⠈⠁⠈⠁⠀⠠⠈⡆⢸⠁⠀⠶⠀⠀⠘⠓⠀⠀⣷⠀⡘⠀⠀⠀⠁⠀⠀⡤⡀⠀⡇⠀⡇⠀⣠⡀⠀⠀⢀⣀⠀⢸
⢇⢣⠀⠀⠀⠀⠀⠀⣰⢡⠁⢸⡀⢤⣔⣒⣒⣒⢦⠟⢀⡏⠀⢱⠀⢀⢔⣚⠉⠉⠉⠂⠀⡇⠀⢇⠀⠈⢡⠔⢤⠈⠁⠀⡜
⠈⠢⣙⠢⠤⠤⠤⣚⠵⠃⠀⠀⠳⣄⠙⠢⠤⠒⠁⣠⠞⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⠢⣀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⢀⡤⠒⠚⠓⠒⠦⣄⠀⠀⠀⠀⢀⡠⠖⠚⠛⠒⢤⡀⠀⠀⠀⢀⡤⠒⠚⠛⠒⠦⡀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠒⠦⣄
⢠⠋⠀⠀⠀⠀⢀⠀⠈⢳⡀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠙⡄⠀⢠⠋⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠱
⡇⠀⠨⠛⠀⠐⠻⠀⠀⠀⡇⠀⡇⠀⡤⠢⠈⠀⠔⠄⠀⣷⠀⣾⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠐⠀⢀⣀
⢧⠀⠐⠒⠒⠒⢶⡲⠂⢀⠇⠀⣇⠀⠀⠀⢰⡦⠀⠀⢀⡏⠀⠸⡀⠀⠀⠀⣀⡀⠀⠀⡸⠀⠀⢇⠀⠒⡖⢾⠉⠉⠉
⠈⠳⢄⡀⠀⠀⠀⣀⡴⠋⠀⠀⠈⢦⡀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠑⢄⡀⠋⠀⠈⣠⠔⠁⠀⠀⠈⠳⣄⡙⠋⠀⠀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⣤⢄⠀⣀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⣀
⠀⠀⠀⠀⠀⠀⣼⠃⠤⠂⣀⣽⣿⠓⢦⢄⠀⠌⡷⠢⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⣤⢤⡔⠻⣿⡷⣀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⢹⣲⠀⠀⠀⢩⡏⠙⠑⢂⠂⠀⠀⠈⠁⠟⠢⠀⠀⠀⠋⠛⢸⣧⢨⣖⠛⠃⢹⡁
⠀⠀⠀⠀⠀⠀⣼⡇⠀⣀⡤⠋⠀⠀⠀⢦⣶⣀⡄⠀⢀⠔⣀⣤⣠⣄⡐⢄⠨⢿⣘⣿⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⢀⣯⡃⠸⡿⠀⠀⠀⠀⠀⠀⠀⠉⠷⣯⡜⠈⠈⡟⠙⠋⠈⢋⡷⡼⣿⡏⠛⠁⠀⠀⠈⣿⢰⣷⣀
⠀⠀⠀⠀⠀⢸⣿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣼⣧⣄⡀⠀⠀⣿⡇⠀⠀⠀⠸⢿⣿⠾⢿⣶⠶⡿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⡇⠰⠒⣶⠒⣶⠒⢲⠖⢦⣴⠞⠉⠁⠀⠀⠀⠉⠛⢶⣄⢹⣷⠀⠀⠀⠀⠀⣯⠈⡏
⠀⠀⠀⠀⢠⣿⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡶⢲⡖⢶⠖⣿⢠⢷⡄
⠀⢀⠤⣰⣺⣻⡧⠔⡹⡇⠀⠀⣀⠀⣀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢿⣿⡇⠠⡀⢀⠀⣀⠀⡟
⠀⢠⠐⠘⠣⠭⠇⢰⠀⡇⠐⠶⠿⠖⢿⠶⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⢧⡀⡟⠛⠑⣟⠀⡇
⠀⠂⠀⢠⠄⣀⣸⠘⡀⡇⠀⠀⠀⠀⢸⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠇⠀⠀⠇⠠⠀⠀⣿⠀⡇
⡄⠀⠀⠘⠒⣾⢃⢤⢵⢷⡀⠀⠀⢀⣿⡄⠀⣠⠋⠙⠷⣤⣀⡀⢀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠰⢠⣿⣤⠷⡀
⠣⡀⠀⠙⠛⠋⢭⢒⠎⠀⢳⡀⢀⡎⠉⠹⡴⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢀⠀⠉⠈⠉⠀⠁⢠⠏⣠⢻⡄⢱⡀
⣀⣈⣐⣲⣄⣐⣀⣉⣀⣀⣀⣁⣈⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣤⣤⣤⣤⣀⣉⣀⣈⣀⣁⣀⣁⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣼⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡀
⠀⠀⠀⠀⠀⠀⡴⢿⢹⣯⡄⠀⢶⡶⠀⠀⠀⠀⠀⠈⠉⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⢠⠲⣜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⢺⡇⠀⠀⠀⠀⠀⣠⣤⠀⣠⣤⠀⣤⢠⡄⣠⠀⣄⢠⣤⠀⣤⣄⢠⡄⣤⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠙⠿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡏⠘⠂⡧⢸⡇⣿⢸⡇⣿⣇⣿⠀⣷⠸⣇⣼⠀⣷⡏⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇⣰⠀⣇⢸⠇⣿⢸⡇⣿⠸⣿⠀⣟⢸⡇⢹⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠈⠉⠁⠉⠀⠉⠀⠁⠈⠁⠈⠀⠈⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡮⣵⣦⣄⠀⠀⠀⠀⠤⣤⠄⡤⡤⢀⡠⠄⢰⢦⡤⢤⢰⠆⡄⡄⢠⡄⠀⠀⠀⠀⣠⣬⣉⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠂⠞⠊⠸⠆⠘⠈⠇⠸⠚⠆⠃⠇⠸⠁⠀⠀⠀⢺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠻⢿⣿⠀⠀⣀⡀⣠⣤⣤⣤⣶⣦⣶⣦⣤⣤⣤⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡽⠿⣯⣼⡃
⠀⠀⠀⠀⠀⣴⡄⠀⠀⣾⣋⠀⠁⠈⠀⡙⣷⠀⣿⣷⢺⣛⡟⣖⣲⢲⣒⣖⣖⣲⣻⣛⣾⡿⠠⡄⠀⠀⠀⠀⢠⣟⡁⠈⠀⠁⢈⣳⡄⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⡸⠀⠀⠀⠀⠃⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣷⡆⠀⠀⠀⢻⡧⠇⠛⠚⠓⠸⣸⡇⠀⠀⠠⡇
⠀⠀⠀⠀⠀⢭⠀⠀⠀⠙⠷⣤⡆⢰⣤⡾⠏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⢦⣴⣷⣦⡴⠟⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⡞⣽⣿⣿⣿⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣤⣀
⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢫⣧⡄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡏⠀⢹⣿⠁
⠀⠀⣾⣿⣯⣀⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⠙⠁⠀⠀⠀⠀⠀⠀⣠⡞⢹⡛⣛⣿⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣿⣿⣷⡀
⠀⢸⣿⣿⡿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⢻⣿⡇
⠀⠀⠿⣿⣿⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡋⠙⣶⣶⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⡏⠈⣉⢹⡇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣼⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠊⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠀⠀⠀⠀⠀⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢹⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⣦⡀⠀⠀⢀⣼⠋⠀⠀⠀⢀⡾⠃⠀⠀⣠⡴⠟⠋⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠈⣷⠀⣠⡞⠁⠀⠀⠀⢠⡾⠁⢀⣤⠞⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣴⠏⠀⠀⠀⠀⣰⠟⢀⡴⠛⠁⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡿⠃⠀⠀⠀⢀⣼⣫⡾⠋⠀⠀⠀⠀⢀⣤⠞⠋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠟⠁⠀⠀⠀⣠⣿⠟⠉⠀⠀⠀⠀⣠⡴⣋⣥⠶⠛⠉⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠁⠀⠀⠀⢀⣤⣾⡿⠞⠋⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣭⡴⠶⠶⠶⣄⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠁⠀⠀⠀⠀⣀⡼⠂⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⢞⣛⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣭⡥⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣀⣤⠶⠟⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⠁⠀⠀⠱⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠉⠑⠒⠀⠀⠀⠈⠛⠀⠀⠀⢠⠁⠀⠀⠀⠼⡆
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈
⠀⠀⢀⡎⠀⠀⠀⠀⠀⣀⡤⠤⠶⠤⣄⠀⠀⠀⠀⠀⠐⠀⠀⠛⡄⠀⢀⠀⠰⠀⠒⠲⢦⣀
⠀⠀⢸⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⣀⣤⢷⣀⣠⠴⠶⠶⠠⣤⠊⠀⠀⣠⠖⠋⢳⠀⠀⠀⠙⢧⡀
⠀⢀⠸⠀⠀⠀⡘⠀⠀⠀⠀⡤⠚⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢀⠊⠑⠧⠀⣠⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⣿
⠈⠦⢤⠤⠜⠁⠀⠀⢀⡾⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠙⣧⠀⠀⠀⠀⠠⠊⠀⠸⠀⠀⡆⠐⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠃⠒⠊⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡼⠃⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠠⣴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡨⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢦⡀⣀⣀⠀⠀⠀⠀⠀⠀⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣢⠀⠀⠀⠀⡴⠋⠁⠀⠀⠁⠠⠼⠃⠀⠒⠂⠀⠐⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡞⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢠⠀⠀⢠⣤⣤⡤⠶⠛⠁
⠀⠀⠀⠀⠀⣠⠶⠐⠦⢄⡀⡠⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⡰⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢁⡴⠋⠉⠛⢳⠎⠀⠉⠉⠀⠀⠀⠀⢀⣠⡋⠀⠀⠀⠀⣀⣤⠴⠚⠛⠉⠉⠉⠉⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢼⠃⠀⠀⠀⠹⣦⣀⠀⠻⠦⣐⠐⠋⠉⠀⠉⠲⣤⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣷⢻⠀⠀⠀⠀⠀⠈⢿⡉⠉⢻⠉⠀⠀⠀⠀⠀⠀⠘⢧⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠁⠀⠀⠀⠀⠀⠀⢷⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡴⠐⣆⠀⠀⠀⠀⠀⢠⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠘⣆⠀⢀⣠⠞⠁⠀⠙⣦⡀⠀⠀⣀⡼⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠙⠒⠛⠙⢧⠀⠀⠀⠹⡄⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠂⠀⠀⢹⡶⠀⠀⠀⠈⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⠏⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣼⠁⠀⣠⠃⠀⢀⠄⠠⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡿⢄⡈⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢻⠃⠀⠀⠀⠀⠀⠀⡇⠀⢉⡷⠆⠀⠀⠈⠈⠁⣲⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠒⠛⠁⠀⢿⠀⠀⠀⠠⣤⠄⠒⣁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⣀⣀⣀⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⢰⣾⡿⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⢨⡌⣤⣤⠀⢠⡄⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠋⠀⠉⠀⠀⠀⠀⢱⡄⠀⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠟⠟⠀⠸⠇⠿⠹⠀⠸⠇⡿⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣀⣀⣀⢀⣀⣀⣀⣀⡀⡀⣀⡼
⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⡘⠀⢰⡆⠀⠀⠙⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⢠⣤⠀⢠⡀
⠀⠀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠐⣴⠃⢀⠃⠀⢸⡇⠀⠀⠀⠀⠂⠃⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⠉⠁⠈⠁⠈
⠀⠀⢤⡀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⢘⡃⠀⠀⠀⠀⢀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢀
⠀⠶⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⠁⠀⠀⠀⠀⠘⠘⣄⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠰⠀⠀⠀⠰⠆⠀⠀⠀⢀⡀⠀⠌⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠸⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠐⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠀⠀⠀⠀⢸
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣬⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⣀⡀⠀⢀⠀⠛⠀⠙⠀⠀⠀⠀⠿
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠨⠀⠀⢉⡙⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠒⠂⠁⠀⠁⠈⠁⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⡈⢻⡟⠻⠿⢿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣤⠀⠀⢠⣤⣴⡆⠀⣿⣿⡆⢴⣶⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣶⣶⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡤⢼⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣎⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⠀⠀⠀⠽⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⡀⠀⠀⢰⣆⠀⠢⡄⠀⠀⠀⠀⣉⣠⠀⠀⠏⠉⠻⠇⠀⠀⠀⠲⣏⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⠀⢰⠀⠀⠀⠀⠀⡀⢨⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⡟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⣄⠀⠀⠀⠀⣳⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡄⠀⠀⢀⣽⠻⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⡇⠀⠀⢸⣿⡏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢾⣿⡆⣀⡼⢠⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡄⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡇⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣷⠈⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠂⠉⠁⠀⠀⠀⠀⠀⠉⣬⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠃⠀⠀⡰⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠶⢻⣋⡛⠀⠀⠀⠀⠀⠀⡀⣠⠖⢚⡷⣄⠈⣿⣷⣦⡀
⠀⠀⠀⢠⠀⣄⣴⣁⠎⡰⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠾⢋⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢹⡗⣾⣿⡶⢺⣶⡿⠛⠉⠉
⠀⠀⠀⣾⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣥⣤⡿⠟
⡀⠀⠀⠙⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄⣀⣄⠀⠀⠀⠀⣀⡀
⠁⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⣧⣵⢊⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣿⣿⣾⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠿⠿⠟⠻⠿⠃
⠃

⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⣀⠴⠛⠋⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣄⠀⢶
⠀⣀⣤⠔⠋⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⡴⠄⠀⠀⠀⠀⠀⢰⣿⡿⢛⡙⢻⣿⣇⠈⠆
⠀⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣘⣋⣼⣿⡟⠀⠘
⠄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁
⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋