Stick figures Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄
⠀⠀⠀⠀⠀⠔⠈⠀⠈⠈⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠲⡠⠀⠒⠀⠗⠜⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠒⠄⠀⠀⠀⠀⠀⠀⢤⠞⠀⠈⠐⠠⢄
⠀⠀⠀⠀⠺⡀⠀⠀⠠⠀⢠⢁⠞⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠂⢥⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠈⠆⣄⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠐⢆⡈⠂⢠⠀⢖⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⣀⡜⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠠⢤⠪⠊⠀⠀⠀⠀⠀⠀⠀⠹⠀⠰⠁
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠛⠏⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣀⣐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠠⠆⠀⠀⠀⠀⠀⠀⠞⠁⠀⡀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⡀⢀⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢤⠄⡅⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢂⡠⠁⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣊⠕⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠁⠀⣐⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⢀⢀⠀⠠⢄
⠀⠀⠀⠀⡁⢴⠃⠈⠀⠁⠉⢆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠁⠐⢌⡕⠤⡀⠀⠀⠀⠀⣘⡇⠄⠂⠉⠀⠈⣗⠀⠁
⠀⠀⠀⠀⠈⠈⢀⠀⠀⠀⣀⠚⠜⠀⠀⠀⠀⠀⠀⠀⡈⠀⣁⢢⠄⠶⢲⡄⢀⠄⠀⠀⠀⠀⣀⠜⠀⠐⠀⢀⠠⠛⠀⠀⢀⡀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠀⢀⡀⠄⠛⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠍⠙⠆⠀⠀⠺⠉⠀⠀⢀⡀⠀⠀⠡⠘⠀⢠⠌⠘⡤⠀⠔⠀⠁⠀⠀⠀⠀⠀⠁⡠⠀⠤⠊
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠒⠈⠀⠀⠈⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠠⠔⠈⠁⠀⠈⡀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣈⣄⠀⠀⠀⠀⠀⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠋⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠠⠤⠇
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠘⠒⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⣨⡇⠀⠀⠘⣾⡀⠀⠀⠀⢻⣷⣄⠀⠈⣾⡆⠀⠀⠀⠀⣸⡇⠀⠀⢠⣿⣦⠀⠀⢀⣼⣧⠀⠀⠀⣾⡷⡄⠀⠀⣠⣷⠇⠀⠀⢠⣽⢤
⠀⠀⠀⣼⠃⠀⠀⠸⣧⠄⠀⠀⠞⣹⠃⠈⠀⠀⢹⡇⠀⠀⠀⢠⠞⠃⠀⠀⠈⣿⡏⠀⠀⠀⢹⡏⠀⠀⠀⡽⡇⠀⠀⠀⠛⣿⠀⠀⠀⠈⡟⡆
⠀⠀⠀⠈⠀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁
⠀⠀⠀⢤⡀⠀⠐⢄⣶⡠⠄⠀⣀⣀⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⢰⠀⠀⠀⠀⣦⣴⠀⠀⠠⣀⣆⡠⠀⠀⣴⠤⣢⠀⠀⠰⣠⣄
⠀⣀⡴⡾⢷⡃⠀⢀⣿⡁⠀⠀⢰⢿⡙⠒⠀⠀⣷⣒⠀⠀⠀⣼⡛⠁⠀⠀⠀⣽⡇⠁⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠈⣿⡇⠀⠀⠺⣿⣎
⠀⠀⠐⠁⠀⠉⠠⠊⠀⠉⠂⠀⠚⠀⠃⠀⠀⠀⠉⠀⠁⠀⠀⠐⠃⠀⠀⠀⠀⠇⠳⠀⠀⠀⠿⢿⠀⠀⠀⠜⠈⠇⠀⠀⠀⠄⠇⠀⠀⠰⠃⠸⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀
⠀⠀⠹⣬⣄⠀⠀⠰⣻⣮⠀⠀⠢⠼⣶⠢⠀⠀⣶⡷⡄⠀⠀⠳⣿⠄⠀⠀⠠⣿⡞⠀⠀⢀⣼⣷⡄⠀⠤⢲⡿⠴⠂⠀⢠⣿⡄⠀⠀⠘⣾⡄
⠀⠀⠀⣿⠛⠀⠀⢰⠋⣏⠀⠀⠀⢸⣿⠀⠀⠀⢹⢹⠀⠀⠀⠀⣿⡀⠀⠀⠀⣿⡄⠀⠀⠀⣝⢻⠁⠀⠀⢸⣧⠀⠀⠀⠀⣿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⣶⣀⠄⠀⠀⢀⣲⡤⠀⠀⠀⣤⠀⠀⠀⠀⢴⣦⠀⠀⠀⠰⣆⣀⠀⠠⢄⣰⣀⠆⠀⠀⣶⠀⠀⠀⠀⢀⣰⡆⠀⢀⣀⣶⣀⡀⠀⠠⣀⣴
⠀⠀⢹⡗⢦⠀⠀⠜⢿⢄⠀⠀⢳⣿⣔⡒⠀⠀⡠⡟⠁⠀⠈⢩⣿⡀⠀⠀⠀⣹⣇⠀⠀⢸⣿⠉⠀⠀⠀⠁⣿⠏⠀⠀⠀⣿⠀⠀⠀⢰⠶⡟
⠀⠀⠼⠀⠀⠀⠀⠀⠼⠈⠃⠀⠘⠀⠁⠉⠀⠐⠁⠃⠀⠀⠀⠀⠀⠳⠄⠐⠚⠁⠈⠧⠀⠀⠿⠀⠀⠀⠀⠉⠟⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⢀⠀⠀⢀⡀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⡀⡀
⠀⢀⣐⣢⡇⠀⠀⢀⢿⡍⠀⠀⢀⣼⣧⡀⠀⠠⠤⣧⠤⠀⠈⠲⣥⠤⠄⠀⢈⣶⣃⡀⠀⠀⣩⢯⠀⠀⠀⢚⡿⠴⠀⢀⣶⣾⠁⠀⠀⠒⢲⣷⠃
⠀⠀⠀⡼⢻⠀⠀⠀⡴⡇⠀⠀⠀⡞⢳⠀⠀⠀⡴⠛⡄⠀⠀⣴⠛⣄⠀⠀⣿⢫⠀⠀⠀⠀⡿⡆⠀⠀⠀⡼⠛⡇⠀⠈⠀⡏⢳⡀⠀⠀⠀⣿
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛
⣿⣿⡷⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡈⢳⣚⠇⠀⡀
⠀⠀⡀⠀⠀⡀⠖⠀⠀⠀⠖⠰⠀⠀⠀⠀⠀⠐⠆⠀⠀⠠⠀⠁⠀⠀⠠⠜⡒⠒⠀⠀⠀⠀⠀⠀⠀⡀⠦⡀⢀⠃
⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠂⠀⠀⠀⠀⠀⠈⣤⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠛⠀⠂⠀⠀⠀⠀⠈⠀⠉⠀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠉⠈⠀⠀⠀⠁⠉⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢀⠠⠀⠠⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠁⠈⠁⠈⠃⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠈⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⡀⠀⠀⠄⠀⠀⠊
⠀⠀⠄⠜⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠱⠰⠀⠀⠁⠊⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⢠
⠀⢀⠐⠂⠀⠀⠐⠁⠀⠀⠒⠈⠀⠀⠀⡀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠄⠀⠀⠀⠖⠐⠀⠀⠂⠲⠀⠀⠀⠀⠀⠀⠰⠓⠶⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠐⠈⠁⠀⣶
⠀⠀⠂⢠⡄⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠠⠄⠐⠀⢀⠀⠈⠀⢚⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠢⠀⣈⠁⠈⠁
⠀⠀⠀⠀⠉⠂⠠⠐⠤⠀⠀⠁⠀⠀⠀⠀⠂⠀⠂⠨⠜⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⢂⠀⡁⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡄⢀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠒⠁⠐⠅⠀⠀⠀⠀⠐⠀⠀⠍
⠀⠀⠀⣠⠤⣄⡀⠀⠀⣀⡤⢤⡀⠀⠀⠀⢀⠀⣀⠀⠀⡀⢀⠀⠀⠀⠀⢠⡀⡀⣀⠀⠀⠀⠀⠀⠀⣠⠠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠛⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⢩⢋⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢰⠃⠀⠀⠀⢀⣀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡁⠐⣿⣷⠀⠘⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠁⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⢉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠉⠛⠿⢭⣍⣉⣁⣀⣀⡤⠴⠚⠁⢀⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢻⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢧⠈⢳⡀
⠀⠀⠀⠈⠙⠓⠒⠒⠒⠶⠤⡴⠋⠙⠶⡦⢤⣄⣀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢧⣀⣀⡠⠃⠒⠚⠛⠓⠾⠿⠿⠶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣛⠀⠀⣈⠇
⠀⠀⢀⡠⠤⠐⠒⡈⠉⠀⠠⠤⢈⡋⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⡀⡠⠜⠋⠀⢀⣀⡬⠽⠚⠉⠐⠒⠒⠒⠶⠤⠤⠤⢤⣄⣀⣀⣀
⠀⠀⠀⠈⠙⠒⠤⢌⣁⡀⠂⠀⠀⢀⡁⠐⠂⠠⠉⠁⠐⠂⣮⣉⣁⣉⣩⠷⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠲⠤⢤⣈⡑⠂⢀⡠⠔⠊⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠄⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡠⠄⠢⡄⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠠⢀⠀⠀⢠⣰⠄⠠⠤⣄⠀⠀⠈⠀⠀⢴⡄⣤⠀⣀⠀⠀⠀⠐⠂⠚⠀⠀⢙⣄⡆⣀⠀⠀⠃⡰⢊⠍⠓⠛⠳⣼⣄⠈⢷
⠀⠀⡀⠀⠀⠄⢀⠀⠈⢳⠇⠀⠀⠀⠘⡆⠀⠀⠀⢢⡜⠉⠈⠙⢿⡄⠀⠀⠈⠐⠀⣠⠊⠀⠈⠹⡇⠀⡞⠉⡼⡏⠐⠀⠀⠀⢸⡿⣀⣸⠄⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠈⠀⠀⠸⣆⠀⠀⠀⢠⡇⠀⠀⠀⢸⡀⠁⠀⠁⢸⠃⠀⠈⠀⠀⠀⢿⠀⠀⡅⢀⡇⠀⠓⡇⠀⡹⢤⡀⠀⢀⡜⠀⠀⢧⡀⠀⠀⠉⠀⢀
⠀⠀⠀⡴⠊⣒⢦⣀⣀⣠⠏⠓⠀⢐⡉⠳⡄⠀⠀⡴⠓⠦⠀⠔⢻⠀⢀⣀⣀⣀⣊⡉⠙⠂⠐⠻⡄⠀⠈⢁⡞⠀⠀⠈⠀⠀⢻⢀⡤⠀⠀⣀⡀⠀⠀⠉
⠀⣤⣰⠇⣸⢈⡟⣹⣩⠏⠳⡄⠈⠉⣀⣦⣵⣾⣿⣲⣄⠀⠀⢀⠔⡵⠫⠏⠟⠙⣿⣌⢦⡀⡐⣦⠞⠉⠉⠳⣤⠄⣠⠀⡀⠀⡅⠻⣄⣤⠀⠳⣿⡀
⠀⠙⠦⠠⠏⢸⠉⠀⢀⡀⠀⡿⠀⠄⢰⣿⠇⠉⠁⠠⠘⡇⠀⠾⠸⡇⠀⠀⠀⠀⣽⢸⠈⠇⢈⡇⠀⠀⠠⠄⢹⠁⠻⠼⠿⢸⠀⠀⠀⠈⠙⣾⠁⠙⢦
⠀⠀⠀⠀⠀⠈⠳⣄⡁⢠⣼⡁⠀⠀⠘⣟⠀⠀⠀⠄⢀⡇⠀⠆⠀⠙⣢⠭⠤⢶⡁⠈⠀⠀⠀⢳⡀⠈⠂⢀⡞⠀⠀⣧⠀⠈⣳⣄⣠⣃⢰⡃⣤⠀⣸
⠀⠀⠀⠀⠀⢀⠔⡿⠀⠀⣧⠹⣄⠀⠀⠈⢳⣦⠤⣔⢻⣄⠀⠀⠀⡼⣽⠀⠀⢸⠻⡄⠀⠂⡴⡿⠩⡍⢪⠙⣯⠳⡀⢿⡠⠞⡟⠀⠀⣿⢧⡙⠉⠉⠁
⠀⠀⠀⠀⢠⠋⢠⡇⡀⠀⢹⡄⠸⡆⠀⢠⠎⢹⠈⠉⠘⡏⢧⠀⢰⢃⡇⠀⠀⢸⡇⢻⡀⢸⢡⡇⠀⠙⠊⠀⠸⡆⢙⡆⠀⣸⠁⠀⠀⢹⠀⠹⣄
⠀⠀⠀⠀⠘⠦⣼⠀⠉⠉⠒⣧⠐⠃⠀⡏⠀⢸⠀⠀⠀⢿⢸⡇⡟⢸⠁⠀⠀⠀⡇⠈⣇⠘⢾⣄⣠⣤⣀⠤⣀⡷⠊⠀⢠⠇⠀⠀⠀⠸⡏⠓⠘⠂
⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣼⣦⣤⣤⣿⣤⣼⣦⣤⣤⣾⣾⣴⣧⣿⣤⣤⣤⣤⣿⣤⣿⣤⣾⣤⣬⣤⣤⣤⣤⣿⣤⣤⣾⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣶⣾⣿⣾⣷⣿⣾⣿⣷⣿

⠀⠀⠀⣀⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢖⠀⠂⣠⠀⠀⢀⣀⠀⠀⣀
⠀⠀⠠⠋⡄⠆⠈⠀⠀⠀⢁⠄⠒⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡔⠡⠀⡑⡤⠃⠀⠘⠁⠐⠂⠘⠃
⠀⠀⠠⠐⠄⠀⠁⠄⠀⠀⠄⠀⠁⠁⠀⡀⠀⠀⡀⠊⠉⠀⠀⠀⠀⡀⠔⠂⢔⠂⠀⠈⢄⠂⠀⡡⠀⠀⠀⠀⠃⢀⣘⠄
⠀⠀⠀⢈⠀⡀⠀⠀⠀⠁⠀⠂⢤⠔⠡⠈⠀⠀⡀⠀⠠⡀⠀⠀⠉⡁⠉⠁⠀⠀⠀⠀⠀⠨⠧⡀⠀⠀⠀⠀⠀⡸⢄
⠀⠀⠀⠀⠀⡇⠈⠄⠀⠀⠀⠠⠁⠐⣄⠀⠀⠀⠈⢰⡄⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠠⠁⠀⠈⢠⡀⠀⠀⡐⠀⠀⠁⡀
⢠⡎⠀⠀⠀⡇⠀⠠⠆⠀⠲⡤⠈⠢⠉⠀⠀⠀⡀⠉⠈⠀⠀⠀⠆⠀⡠⠀⠛⠀⠀⠰⠆⠀⠄⠀⠈⠁⠀⠛⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠠⠐⠂⠁⠀⠀⠘⠁⠢⠀⠛⠀⠀⢀⠈⢀⠑⠀⠀⠀⠀⠀⡎⣀⡁⠄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣈⢸⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⠀⠀⠰⠰
⠀⠀⠐⠖⠂⣀⠰⠖⠀⠀⠐⠂⠀⠂⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠉⠀⡀⠀⠀⠈⠁⠀⠉
⠀⠀⠀⠠⠂⣉⠓⠄⠀⢀⡶⠓⠒⢦⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⢠⢀⡆⣜⠬⠆⠀⢀
⠀⠀⠀⠠⠐⠄⠊⠀⠀⠘⡓⠁⣠⠄⠀⠀⠈⠠⠀⢑⠀⠀⠀⠀⢠⡉⡄⠈⡄⠀⠀⠀⠀⠀⡇⢨⠠⣂⣀⢀⡰
⠀⠀⠀⢀⡄⠈⠐⠄⠀⠀⡈⢹⠂⠆⠀⠀⠀⣠⢬⣎⠀⢄⠀⠀⠉⠓⠉⠓⠐⠐⠂⠁⠀⠀⠑⠍⠁
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠁⠘⠢⡀⠀⠀⠀⢀⡀⡌⢺⣊⡠⠄⠀⠀⠀⡀⠀⡆⡄⠀⠀⠀⠀⠀⢠⠅⡀⠤⢀⡄

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⣿⡄⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⢠⣾⠃
⠀⠀⠀⠀⠀⠈⢿⣎⣛⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣭⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣥⡀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣋⣠⡿⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣴⢿⣿⣿⣿⡿⣦⡀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠃⠀⠀⢰⡿⢃⣿⣿⣿⣿⡎⠻⡦⠀⠀⠈⠻⣾⣿⣿⣿⣷⠟⠁⠀⠀⢠⡾⠋⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⡿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠇⠘⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⣴⣶⡆⢀⣼⠟
⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠸⣷⡀⢠⣶⣶⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠻⣧⣈⣛⣁⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⣙⣋⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣦⣤⣤⣤⡄⠀⠀⠀⠀⢀⣾⠏⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠢⠄⠁⠀⠀⠀⠀⠀⢁⠖⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠨⠁⠀⢀⣄⠁⠀⠀⠀⠀⢀⡤
⠀⠀⠂⠀⠀⠂⠐⠂⠀⢠⠄⠀⠀⠀⠓⠒⠂⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⠁⠀⠀⠀⠒⠐⠀⠂⠀⠀⠀⠀⢀⠁⢀⠒⠀⠀⠄⠀⠈⠀⠩⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡄⢄

⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠂⠤⢀⠀⠀⣤⠈⠂⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⠔⠒⠲⢄
⠀⠀⠀⠀⠀⠨⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡤⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠆⠀⠠⠄⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠙⠀⠴⠀⠀⠶⠀⠛⠀⠀⡀⠐⠀⠊⠁⠀⠀⠀⠀⢀⡂⠀⠐⡀⠀⠀⢀⡀⠄⠒⠂⢂⠄⢀⡀⢀⡀⣨⠀⠀⠀⡠⡀⣀⠀⠀⠉⠢⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠀⡀⠀⠐⠆⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⡂⠀⠰
⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀
⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⢈⡁⠄⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠐⠲⠠⠂⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⣀⠈⠀⠀⠀⠆⢀⠀⠀⠀⠀⡃⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⢤⠀⠀⠀⠀⠀⠀⠑⠂⠐⠉⠀⠀⠀⠀⠀⢈⡁⠀⣉⠀⠀⠀⠀⠀⠅⠀⢂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡝⠀⠀⠀⢀⣤⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣿⡿⠿⢻⠿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠠⠄⠀⠁⠀⠠⠀⠀⣾⣿⡿⠿⠿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠙⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⢠⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠰⠃⠀⠀⠀⢀⠄⠀⠀⠀⠜
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢾⣿⡆⢠⠄⠀⠀⠀⠀⢾⣿⡆⠀⠀⠀⠀⠀⠀⢾⣿⠆⢀⡀⠀⠠⣄⠀⢰⣿⡆⢀⡤⠀⠀⠀⠀⢀⣴⣄⢀⡄⠀⠀⢠⡀⣾⣷⢀⡤⠞
⠀⠀⣠⠴⡿⠶⠏⠀⠀⠀⠀⣠⠼⣯⡀⠀⠀⠀⠀⢠⠶⠺⡷⠦⠞⠁⠀⠀⠙⠶⠶⣿⠶⠞⠁⠀⠀⠀⠀⢈⣿⣯⠞⠀⠀⠀⢸⣧⠼⢿⠉
⠀⠀⠏⠀⣇⡀⠀⠀⠀⠀⠀⠏⢀⣏⠉⠛⠂⠀⠀⣘⠀⢀⣇⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣼⣙⣦⠤⠆⠀⠀⠀⠀⠀⢘⣆⡀
⠀⠀⢀⣰⠋⠙⢦⠀⠀⠀⠀⣠⠞⠉⠳⣄⠀⠀⠀⠉⠳⠞⠀⠉⠹⣄⠀⠀⠀⢰⡟⠁⠉⠓⣆⠀⠀⠀⠀⣿⠉⠹⡆⠀⠀⠀⠀⠀⣠⠏⠈⠹⡆
⠀⠐⠋⠀⠀⠀⠈⠃⠀⠀⠘⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠀⠀⠀⠈⠁⠀⠒⠒⠛⠀⠀⠛⠀⠀⠀⠀⠘⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⢀
⠻⣄⠀⣾⣿⠀⠀⠀⠀⠈⠳⣄⣾⣿⣆⣴⠟⠀⠀⠀⠀⢾⣿⠆⣴⠀⠀⠠⣄⠀⠰⣿⣿⠀⠀⠀⢠⣄⣀⠰⣿⣷⢀⣀⣠⠙⠲⣤⣿⣿⣣⠖⠋
⠀⠈⠙⣿⠷⠶⠚⠋⠁⠀⠀⠈⠙⡟⠉⠀⠀⠀⠀⠰⡖⠺⡟⠛⠃⠀⠀⠀⠈⠓⢲⡟⠦⠤⠖⠋⠀⠀⠉⠙⢻⠛⠉⠁⠀⠀⠀⠀⠈⢻⡁
⠀⠀⢰⣇⣀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⣀⠀⠀⠀⣀⠉⢈⣧⣀⠀⠀⠀⢠⡤⠤⢾⡀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⣀⠀⠀⠀⠀⠀⣠⡬⣧
⠀⢀⣀⡿⢸⡇⠀⠀⠀⠀⠀⠀⣾⠁⠀⠈⠙⠒⠀⠈⠳⠏⠚⠋⠁⠀⠀⠀⠷⢀⣠⠿⠂⠀⠀⠀⠚⠋⠉⠉⠁⠉⠉⠉⠙⠛⠀⢰⡇⠀⠻⣄⡀
⠈⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⢀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰⡄
⠀⠘⣧⣿⣿⡞⠁⠀⠀⠀⠀⠀⣾⣿⠆⣀⡄⠀⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠰⣿⣿⢀⡆⠀⠀⠀⠀⣾⣿⣿⣿⠄
⠀⠀⠈⢹⡏⠀⢠⡇⠐⠛⠉⡿⠋⠛⠚⠉⠀⠀⠤⠖⢚⣿⡇⠀⠀⠀⠀⢀⡞⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠉⠀⣀⡴⠀⠀⠀⠉⢿⠁
⠀⠀⣠⠼⠓⠛⠋⠀⠀⠀⡾⠳⠶⡄⠀⠀⠀⠀⠀⠀⠞⢀⡇⠀⠀⠀⠀⠀⢀⣾⡀⠉⠉⠉⠀⠀⠀⠀⠖⠋⣨⠷⠛⠁⠀⠀⠀⠀⠀⠘⣇⣴⡤
⢀⡼⠁⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠛⠀⠀⠀⠀⠀⢠⡴⠯⠷⠀⠀⠀⠶⠲⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠰⣆⠀⠀⠀⢀⡴⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠷⣤⡴⠋⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢿⣿⠇⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢿⠷⠀⠀⠀⠀⠀⠀⠈⠛⠛⡟⠛⣦⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⠀⠀⠀⠀⠀⠀⢀⣼⠛⠋⠀⠀⠀⢀⣼⡟⠲⠏
⠀⠀⣠⣾⣦⣄⠀⠀⠀⠀⢀⡾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀⠉⠀⠀⠀⠀⢀⣴⣋⣇⣀⠀⠀⠀⠀⠀⢀⣴⣻⡏⢧⡀⠀⠀⠀⠈⢙⣟⡀
⠀⣼⠁⠛⠋⠸⡆⠀⠀⢀⡏⠀⠈⣧⠀⠀⠀⠀⢀⡴⠞⠉⠀⠈⣧⠀⠀⣠⠶⠋⠀⠉⢻⡀⠀⠀⠀⢀⡴⠋⠀⠹⡇⠀⠃⠀⠀⢀⣠⠞⠁⠉⣷
⠀⠁⠀⠀⠀⠀⠙⠀⠀⠘⠁⠀⠀⠘⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠛
⠀⠀⣀⢀⣤⣀⡀⠀⠀⠀⠀⠀⣠⣤⡀⡀⠀⠀⠀⠀⢀⣄⣤⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⣇⣹⣿⣃⡇⠀⠀⣀⣀⣀⣻⣿⣃⡇⠀⠀⠀⢀⣞⣻⣿⠁⠀⠀⠀⠀⠀⠀⢻⣟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⡴⠋⠀⠀⠀⠀⠀⣹⣿⣁
⠀⠀⠉⠉⡏⠉⠁⠀⠀⠀⠀⠀⠈⡏⠈⠀⠀⠀⠀⠀⠉⠉⣏⡽⠂⠀⠀⠀⠀⠸⣯⣏⡗⠀⠀⠀⠀⠀⠀⢿⣹⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠋
⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⣠⠷⣄⠀⠀⠀⠀⠀⠀⣰⢿⣅⠀⠀⠀⠀⠀⠀⣸⢯⡀⠀⠀⠀⠀⠀⠀⠀⡽⢦⡀⠀⠀⠀⠀⠀⠀⢠⢷
⠀⢠⠞⠁⠀⠈⢳⡄⠀⠀⢀⡴⠃⠀⠈⢳⡀⠀⠀⠀⢰⠃⠀⠘⣆⠀⠀⠀⠀⣸⠃⠀⢹⡄⠀⠀⠀⠀⠀⡼⠃⠀⢷⠀⠀⠀⠀⠀⠀⡞⠈⣧

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢴⡄⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠘⣧⡀⢾⣿⡇⠀⠀⠀⠸⣧⡀⠀⢿⣿⠆⠀⣰⡟⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⢰⣾⣾⣷⣷⣦⠀⠀⠀⠈⠻⣷⣿⣶⣦⡀⠀⠀⠈⠛⢻⣿⣿⡿⠛⠋⠀⠀⠀⣠⣶⣾⣿⣶⣄⠀⠀⠀⠀⠀⢠⣶⣿⣷⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠈⢿⡄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣴⠏⢸⣿⣿⡇⠙⣷⡀⠀⠀⢰⡟⣿⣿⣿⠻⣧
⠀⠀⠀⠘⢻⣿⣿⡟⠟⠀⠀⠀⠀⢀⣿⢿⣿⠀⠘⠃⠀⠀⠀⢸⣿⢿⡇⠀⠀⠀⠈⠋⠀⢸⣿⣿⡇⠀⠘⠃⠀⠀⠿⠁⣿⡿⣿⠀⠻⠆
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⡄
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠘⣿⠀⠀⠀⠀⠀⠀⢸⣿⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⡇
⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⢀⡤⠀⠀⢠⡄
⠀⠀⠀⢸⡇⣴⣶⣘⡷⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠹⣦⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⣠⣼⣿⣥⣀⠀⠀⠀⠀⠙⣷⣿⡿⠃⠀⠀⣤⣄⣀⣀⣠⣽⣿⣤⣀⣀⣀⣤⠀⠀⢀⣬⣿⣯⣀
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣠⡾⠋⣿⣿⣿⠙⢷⡄⠀⠀⠀⢸⣿⣿⡿⣦⡀⠀⠉⠉⠉⢹⣿⣿⡏⠉⠉⠉⠁⠀⣰⡟⣿⣿⣿⠻⣧
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠰⠟⠀⠀⣿⣿⣿⠀⠈⠿⠀⠀⠀⢸⣿⣿⡇⠘⣧⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠀⢻⡇
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⡟⠹⣿⡀⠉⠀⠀⠀⠀⢸⡟⢸⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣴⡿⠁⠀⠹⣷⡀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠾⠿⠀⠀⠀⠀⠀⠀⠀⠿⠻⠿⠀⠀⠀⠀⠾⠟⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠸⠗⠸⠟⠀⠀⠀⠀⠀⠀⠀⠻⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⣰⡟⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⣿⡀⢠⣶⣦⠀⣿⠂
⠀⠀⠀⠀⣠⣽⣯⣄⠀⠀⠀⠀⠀⠀⣠⣽⣯⡾⠋⠀⠀⠀⢀⣤⣽⣯⣤⣀⠀⠀⠀⠀⠀⣠⣽⣯⣤⠀⠀⠀⠀⠀⠈⠿⣮⣿⣥⡾⠋
⠀⠀⠀⣰⣿⣿⣿⡿⣧⠀⢀⣤⣤⠾⢻⣿⣿⡇⠀⠀⠀⢰⡟⢹⣿⣿⡏⠹⣧⠀⠀⢀⣼⢻⣿⣿⡟⢷⡀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠠⡟⢸⣿⣿⡇⠹⡆⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠿⠀⢸⣿⣿⡇⠀⠻⠇⠀⠾⠃⢸⣿⣿⡇⠈⠷⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⠇⣿⡇⠀⠀⠀⠀⠀⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠸⣿⡀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠘⠟⠻⠇⠀⠀⠀⠀⠀⠀⠿⠂⠀⠙⠿⠀⠀⠀⠀⠘⠿⠸⠇⠀⠀⠀⠀⠀⠀⠘⠟⠻⠇⠀⠀⠀⠀⠀⠀⠀⠻⠟⠿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⠀⡀
⠀⠀⠀⠀⠀⠀⣰⢋⣽⡿⡇⢀⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⠤⣴⠤⠄⠀⣀⢄
⠀⠀⠀⠀⠀⠀⢹⣏⣈⣰⠇⠈⢉⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⡟⢀⣤⠞⣀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠿⠬⠽⢷⣦⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠖⣻⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠛⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⣿⠦⢴⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⡿⢿⡛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣀⣸⣷⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⡛⠻⡟⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡏⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣎⣷⡠⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⢳⠀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠹⢦⣤⡴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣤⠞⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⣤⣠⡼⢿
⠀⠀⠀⠀⠀⠀⠀⣸⣇⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⢾⣧⣤⣬⡇
⠀⠀⠀⠀⠀⠀⢠⠟⡏⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠻⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸
⠀⠀⠀⠀⠀⠀⢤⣞⡁⢈⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠀⢸⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠞⠛⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢤⡀
⠀⠀⠀⠀⢀⣠⢻⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⠀⠀⠀⠀⢠⠞⠉⠙⢷⠀⠀⠀⠀⠀⠀⠀⢰⡷⢸⡁⠀⠀⣷⠰⡷
⠀⠀⠀⠀⠘⠛⡆⢉⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠀⠀⠘⢦⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢓⣶⡞⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠙⠋⣿⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⠓⠚⢉⣀⡀⠀⠀⠀⠀⠀⠉⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣿⡉⠓⣚⠉⠉⠁⠀⠀⠀⠀⢀⡼⢻⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⣬⣭⠙⠛⢁⣦⣀⣰⣴⡀⣠⣞⣥⣿⣀⡀⠹⠃⠀⠀⠀⠀⠀⢴⣾⣛⡉⣉⣙⡶
⠀⠀⠀⠀⠀⠀⠀⢠⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⡽⢹⡄⢀⢸⡏⠉⠉⣿⡏⠙⣧⢻⣟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿
⠀⠀⠀⠀⠀⠀⢀⡼⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢴⣿⣇⠘⠛⠋⢸⡇⠀⠀⣿⡇⠀⣈⣿⡿⣿⡿⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠙⠙⠃⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⢄⣸⣇⡤⠀⠀⢀⣿⣀⠀⠀⠺⣿⡿⠀⠀⢳⣶⡀⠀⠀⢳⣶⡏⠀⠀⢀⣸⣇⠀⠀⠀⢳⣀⡼⠁⠀⠀⣸⡾⠁
⠀⠀⠀⠀⣿⣯⠀⠀⠀⠛⣿⡟⠁⠀⠀⣿⡇⠀⠀⢸⣿⠿⠀⠀⢸⣿⡇⠀⠀⠋⣿⡏⠑⠀⠀⠰⣿⡇⠀⠀⠺⣿⡇
⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠿⠇⠀⠀⠀⡇⡇⠀⠀⢸⣿⠇⠀⠀⢸⢿⠇⠀⠀⠀⠇⠇⠀⠀⠀⠼⠛⢣⠀⠀⠀⡿⡇


⠀⠀⠀⠐⣤⣤⠂⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⣀⣠⣆⣀⡀⠀⠀⣀⣀⣶⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⣰⣿⣿⣷⡀⠀⠀⠀⠉⢹⣿⠁⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠾⣿⡿⠆
⠀⠀⠀⣠⠏⠱⡄⠀⠀⣾⠏⠉⠉⠉⢿⡆⠀⠀⢠⠏⠙⢦⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠐⠚⠛⠛⠓⠂⠀⠀⡴⠋⠱⡄


⠀⠀⠀⢲⣠⡄⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡤⣠⠆⠀⢤⢠⡄⠀⠀⢠⣤⣤⠄⠀⠀⣤⣠⠀⠀⠀⡄⡄
⠀⠀⠀⠀⣿⣷⡆⠀⢀⢾⣿⡷⡄⠀⢰⣿⣿⡆⠀⢀⣴⣿⡇⠀⠀⠀⣿⣷⣄⠀⠀⣿⣏⠀⠀⣴⣿⡇⠀⠀⠠⣷⡧
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⡟⠀⠀⠀⣿⡟⠀⠀⠸⣿⡇⠀⠀⢀⣿⢇
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠙⠛⠀⠀⠀⠘⠛⠃⠀⠀⠀⠛⠃⠀⠀⠀⠋⠃⠀⠀⠀⠛⠃⠀⠀⠋⠘⠈⠃

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠠⠤⣬⣥⠤⠄⠀⠀⠀⢆⢠⣄⡄⠀⠀⠀⠘⢦⣛⡞⠀⠀⠀⢄⣨⣧⣠⠄⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠱⣼⡴⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⣿⣏⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⢴⣿⣷⠄⠀⠀⠀⠠⣿⣧
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠒⠒⠛⠛⠒⠂⠀⠀⡰⠋⠈⠳⡄⠀⠀⠀⠸⠼⠀⠀⠀⠀⠒⠚⠛⠛⠚⠂⠀⠀⠀⡇⡇


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣒⣀⡢⢀⠀⠀⠀⠀⢘⡟⠀⠀⠀⢀⣤⣤⡭⣛⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠗⣐⣻⠿⣗⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⢿⠷⠶⠶⢿⣿⣿⣿⠇⠀⠀⠀⣠⣤⣄⣸⡆
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡀⠀⠈⢿⣿⠟⠉⠉⠈⠙⢃⡄⠀⠐⣾⠁⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠈⣛⡟⠀⠀⣰⣿⣿⣟⣋⣿⠁
⠀⠀⠀⠠⡀⣾⡿⢛⣻⣿⣿⡀⠀⠀⢱⣀⠀⠀⠀⠀⠀⢻⡆⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠃⠀⢠⣇⢀⡀⢹⡟⠁
⠀⠀⠀⠀⠙⢿⣷⠋⠀⠐⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⢸⠉⠑⠒⠊⣳
⠀⠀⠀⠀⠀⠸⠛⠆⠀⠀⣸⠀⠀⠀⠲⠶⣤⣄⡀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⣠⡤⠤⠶⢾⡟⢁⣀⡀⠀⠸⡀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢉⣤⣤⣤⠟⠈⠙⢦⡀⠀⠀⠀⢻⣿⡀⠀⠀⠀⡏⢰⠠⡀⠀⠙⠛⠙⠿⠴⠶⠝⡗⢠⡞⠁
⠀⠀⠀⠀⠀⠀⢷⡀⠀⠐⣿⣶⠿⠟⣋⣤⠶⠶⠤⣄⡙⢀⠀⠀⢹⣹⣧⠀⠀⠀⠀⠸⡄⠀⠈⠀⠀⠀⠀⠀⢠⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⣿⠁⢠⠞⠉⠀⠀⣀⣀⡀⠈⠿⣆⠀⢀⡿⠈⢧⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡀⠀⠀⢀⡴⠚⣉⣠⢤⠠⡲⠁⢀⣼⠃⠀⠈⢷⡀⠀⠀⠀⠀⣉⡛⠛⣛⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⡋⣰⠟⠋⠉⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠉⠉⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⡀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣤⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠈⠉⠙⠛⠛⠿⢷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⢦⣤⣄⣀⣿⣦⣀⣀⣀⣀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⢿⡟⠛⠿⡻⡙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠑⠱⠀⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⣦⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠄⠄⣸⣯⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⠙⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠟⠻⣿⣿⣿⣶⣶⣾⡇⡀⡀⠀⣸⣿⣼⣤⣿⣷⣴⣜⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢴⡿⠛⠁⣀⣤⠼⠶⠴⠷⢭⡻⣿⣿⣷⡈⡦⢸⣿⣿⣽⡿⠉⡻⢈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠐⠶⠝⠐⣋⣡⣤⣶⣾⣿⣿⣶⣽⣿⣯⡉⠛⠄⢽⣿⣿⣵⣶⣶⣶⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠛⡟⠁⣿⣿⣿⣿⣿⣿⠟⢩⠉⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢀⣤⣾⣯⡉⠳⡄⠀⠀⢣⠀⠀⠀⠀⢀⠤⠊⠀⡴⠋⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣤⣴⣾⡆
⠀⠀⠀⠀⠀⣾⣧⠈⠀⠈⠀⢰⠀⠀⢸⠀⠀⠀⠂⠁⢀⡠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡈⠙⣿⣷
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⡇⠀⠀⡠⠜⠁⢀⡀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡛⣵⣼⣿
⠀⠀⠀⠀⢀⣤⣿⣇⠀⠀⣇⣴⠋⣀⠴⡎⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣄⣠⣴⣶⣤⣀⠀⣾⣷⣽⣿⣿
⠀⠀⠀⢀⣾⣦⣄⠉⢢⡀⣿⠁⡜⠁⢸⠷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠉⠛⠋⠙⢻⣿⣿⣿⣿⣿⣷⣽⡟
⠀⠀⠀⢸⡟⣼⠀⠁⢀⡑⢼⣸⣧⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢈⣿⠏⢻⣿⡙⣿⡿⠁
⠀⠀⠀⢸⣷⢿⠀⠀⠀⠉⢻⠡⣽⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⣠⣤⣞⣧⣶⣌⡻⣩⣿⣧⣶⣘⣿⠟⠁
⠀⠀⠀⠀⢿⣾⡀⠀⠀⠀⡏⠻⣿⣷⣦⠈⢆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠛⠉⠉⠀⠈⠙⣿⡏⠙⣻⡿⣹⠏
⠀⠀⠀⠀⠸⣭⣿⡄⠀⠀⡇⢀⢻⢻⣯⡧⠈⢦⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⣦⣤⣤⣤⣽⣷⣾⣿⣳⠏
⠀⠀⠀⠀⠀⣿⡦⢣⡀⣀⡀⠀⣼⠘⣿⡇⢠⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⢿⢻⣿⡟⠋
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣿⡥⠞⠁⠀⢻⡟⢦⣕⣦⡀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣯⠉⠁⠀⠀⠈⠙⠻⣶⣦⣤⣀⡀⠀⠀⡀⣀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠻⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⣧⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠙⢷⣶⠖⠃
⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⣿⠟⠿⣦⣤⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⣴⠋
⠀⠀⠀⢠⣿⠙⢿⣤⡀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⣿⡆
⠀⠙⠛⠛⠁⠀⣠⣾⣿⠉⠉⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣿⠁⠀⢠⣿
⠀⠀⠀⠀⢀⡼⠋⣾⠇⠀⠀⠘⣿⡌⠻⣦⡀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⢀⣤⠾⠋⠀⢸⡿⠀⣠⡿⠁⣾⡄
⠀⠀⠀⢠⡿⠁⢸⡿⢀⣴⠆⠀⠻⣧⠀⠈⢿⣦⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⢃⣀⡤⠞⠋⠁⠀⠀⠀⢉⣤⠾⠋⠀⠀⢿⣇
⠀⠀⢠⣿⠁⠀⣩⡴⠛⠁⠀⠚⢶⣬⣀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠙⢿⠟⠛⠉⠁⠀⠀⢀⣀⣤⠴⠞⣫⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠘⠿⠖⠚⣉⠀⠀⠀⠀⠀⠀⢨⣍⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀⢤⠤⠶⠶⠶⠚⠛⠉⠁⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⣀⣸⡿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠛⠛⠛⢻⡟⠉
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠘⠛⠛⠛⠛⣿⡟⠓⠛⠛⠛⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠀⠀⠀⠙⠛⠛⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠒⠛⠋⠀⢀⣀⡤⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣶⣾⣶⣬⣻⣿⣿⡆⠀⠀⠀⠙⢷⣄⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠆
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠂⠀⠹⣿⣿⣿⣿⣿⠛⠉⠉⠙⢿⣿⣿⣿⠀⠀⣀⣀⣀⡈⠛⠀⣼⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⡿⠁⠀⣀⣀⠀⠉⢻⣿⣿⣷⣤⣴⣾⣿⣿⣿⣿⣿⡇⠾⠿⠿⢿⣿⠆⠀⠸⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠁⣰⣿⡿⠿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⣀⠀⠉⢻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠿⣿⣷⣝⣿⣿⠀⠀⠀⠀⠈⠙⢻⣿⣿⣷⡶⢾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣷⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦
⠀⠰⠿⠶⠊⠉⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⠀⠀⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⣴⡀⠀⢀⣠⣴⣤⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢳⣦
⠀⠀⠀⠀⠀⠙⠿⠛⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣿⣿⣷⠀⠀⠀⣀⣤⣶⣾⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⡿⠿⣿⣿⣧⡠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣥⡶⣾⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣷⣝⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣋⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨⢽⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⠀⠀⠀⠲⣄⣀⣠⣤⣾⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣦⣿⣿⣿⣿⣿⣷⣝⣻⣿⣿⡏⠀⠀⠀⠀⠈⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣾⠟⠁⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡉⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣏⡉⠉⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣶⣦⣄⡈⢿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿⠛⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⣶⣶⣶⣶⣶⣶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀⢿⣿⡷
⠀⠀⠀⠀⠀⠀⣰⣾⣷⡄⠀⠀⢀⣀⣤⡴⢒⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⠉⠉⣽⣿⣿⣦⣉
⠀⠀⠀⠀⠀⠀⠈⠛⢛⣡⣴⣾⡿⠟⠉⢀⣾⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠛⢛⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⡆⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣄⡹⠿⠇
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⣿⡌⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠂
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄⣀⣠⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠈⣿⣿⣿⣿⣟⠁
⠀⠀⠀⣰⡿⠋⢉⣿⠿⢿⣿⠛⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⡿⠁⠀⢸⠏⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠛⠋⠉⠻⠏⠉⠉⠉⠉⠙⠛⠒
⠀⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠻⡄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠘⠿⠇⠀⣠⡴⠂
⠀⠀⠀⠸⣿⡿⢃⣀⣀⣀⣠⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣥⣶⣶⣶⣶⠟⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⣠⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠘⠉⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢸⣿⢻⡿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⢸⡇⢸⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣶⣦
⠀⠀⠀⠀⠠⡀⠀⠀⢾⣿⡷⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠙⠿⣛⣀
⠀⠀⠀⢰⡇⢹⣄⣀⣠⣥⣤⡀⠀⣠⡇⣼⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣶⣤⣤⠦
⠀⠀⠀⣾⡷⢿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣌⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠹⣿⣿⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⠏⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡏⠹⣿⡇
⠀⠀⠀⠀⠀⣾⠋⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠿⠀⠀⢹⣷⡀
⠀⠀⠀⠀⡸⠁⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠈

⣿⣶⣶⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠈⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⠂⢰⣶⡄⠰⡄⠀⠀⠀⠀⣾⣿⠆
⢀⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⣻⣏⠀⠀⠀⠀⣀⣜⠛⠃⠀⠀⠀⣀⣼⣿⣧⡀⠀⠀⠛⠦⣬⣿⡤⠶⠃⠀⠀⠀⣶⡦⠁
⡾⣿⣿⡟⣇⠀⢀⡀⠀⠀⡞⣿⣿⢳⠀⠐⢿⣿⣿⠀⠀⠀⠀⢰⠇⣿⣿⡇⢹⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠰⣿⡇
⡇⣿⣿⡇⣿⠀⣸⣇⠀⢸⢀⣿⣿⠸⡇⠀⠈⢿⣿⣳⠆⠀⠀⠸⣦⣿⣿⣧⣼⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⠆
⠀⣿⣿⡇⠀⢸⣿⣯⠇⠀⣼⣿⣿⣧⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⣿⢸⣷⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⢀⣿
⠀⠿⠻⠇⠀⠀⠿⠿⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠿⠻⠇⠀⠀⠀⠀⠸⠇⠀⠿⠀⠀⠀⠀⠤⠬⠥⠤⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⡀⢀⣸⠛⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢸⡿⠿⠿⣶⣶⣴⣿⣿⣿⣤⡀
⠀⠀⣧⢸⣿⠳⠶⢶⣤⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠙⣷⡀⢸⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣿⢸⣿⣤⣭⣍⠉⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣾⣝⠿⠃⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⠒⠛⡏⣽⡏⠀⡇⠀⠀⠀⠀⠀⠀⣰⡿⣶⣤⣶⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠸⡿
⠀⠀⠋⠉⠉⠓⠛⠀⠀⠃⠀⠀⠀⠐⠿⠿⠿⠿⠿⠟⠛⠿⠶⠟⠀⠀⠀⠀⠀⣠⠖⢚⣻⠻⢦⡀⠀⠀⠀⣾⣿⡟⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠺⡿⠀⠀⡧⠀⠀⢰⣿⣿⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠸⣿⠗
⠀⠀⣴⣶⣤⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⣠⣽⣯⡴⣿⣿⣥⠞⠃⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣬⣛⠃⠀⠀⠀⠀⠰⣿⣷
⢠⡿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⢦⡀⢠⡴⣶⣿⡀⣀⡄⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⢠⡄
⢸⡇⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠙⠏⢀⣿⡏⠉⠉⠀⠀⠀⠀⢸⠏⠉⠉⢿⣽⣿⣿⣯⡿⠉⠉⢹⡇
⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣼⡏⠀⠀⠀⠀⠀⢾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⣀
⠀⠐⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢰⡟⠀⠀⠀⠀⠀⢀⣼⠟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠛⢻⡟
⣀⣈⣿⣿⣃⣚⣛⣛⣂⣀⣂⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣛⣋⣀⣀⣻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣀⣀⣿⣁⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠈⠀⠁⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⣐⢦⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠺⠗⠀⠘⠛⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠑⠒⠐⠐⠂⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⢀⡠⠐⠁
⡄⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣍
⠑⠄⠘⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠰⣿⣿⡶⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉
⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⣀⠤⠔⠊⠁⠀⠀⠀⠙⣿⠁⠀⠀⠈⠙⠲⠦⣄⣀⣀⡀⠠⠤⠴⠐⠂⠹⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠆⠀⠀⠀⠀⠀⠮⠭⠽⠂
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋⠉⠉⠉⠉⠻⢶⣄⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠉⠁⠀⠀⣠⡶⠶⢦⡀⠀⠀⠻⣦⠀⠀⢀⠏⠠⠀⠉⠓⠶⠤⣀⣠⠞⣉⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⠀⢸⡇⠘⣆⠀⠙⣆⠀⠀⠹⣇⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⡁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⢠⡶⠾⢶⣄⠀⠀⠀⠈⢧⠀⠘⣧⣤⠼⠄⠀⠀⢹⣾⠁⠛⠀⠀⠀⢀⡴⠋⠈⠃⠀⠀⠀⠀⠀⣀⣹⠶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⣿⠀⢀⡟⠀⡆⠀⢻⡄⠀⠀⠀⠈⠳⠟⠋⣀⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣀⡤⠴⠚⠋⣥⠀⠀⠁⠀⢣
⠀⠀⠀⠀⠀⠀⣇⠀⠈⡇⠀⣿⣀⣬⡅⠀⠀⠀⠀⠀⠠⢋⣤⣶⡦⠀⠀⠀⠈⠻⣄⣠⠎⢀⣀⡤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠡⠞⠋⢉⣁⣀⣀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣳
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢋⣵⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⡌⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⡜⢀⣿⡏⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠀⠀⠂⣠⠏⠀⣸⣿⠃⠀⠀⠀⠀⠠⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣀⡀⠀⠀⠀⠒⠲⠤⠃⠀⣀⣾⡿⠁⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡆⠀⢰⠋⣀⣀⣀⣉⣀⣀⣀⣤⣴⣾⣿⡿⠁⠀⣴⡟⡸⠀⠀⢀⣤⡴⠶⠟⠻⠷⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠙⢦⡘⢦⣄⡉⠉⠉⠛⠿⠿⠿⠿⠛⠋⣀⣴⡿⠋⢠⠃⢀⡼⠋⠁⠀⠀⠀⣠⠄⠀⠀⠉⠛⠷⣶⣤⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠓⠪⢝⡛⠶⠶⣦⣤⣴⡶⠶⠟⠋⠁⠀⠀⡞⢠⡟⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⡰⢳⡾⠁⠀⠀⢤⣄⣛⣁⣤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣮⡑⠢⢄⣀⣀⡤⠚⠁⣼⠁⠀⠀⢀⣀⣈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣬⡳⠀⠀⠀⠀⠀⠀⢺⣆⠸⠏⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⢀⡤⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⠀⠀⠀⠀⣼⠃
⠀⠀⠀⡞⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣠⣶⠏⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣍⠢⡀⠀⠀⠀⣼⠏
⠀⠀⠀⠹⣄⠀⠀⡇⢀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⢿⡇⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⢆⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠼⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢿⠀⣠⠚⠉⠉⠓⠒⠦⣵⣒⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠈⡆⢇⠀⠾⠿⢿⣿⣿⣶⣌⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⢀⡼⠈⠑⠲⠦⣤⣀⠉⠛⢿⣷⡄⠈⢷⡄⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡀⠀⣉⣵⠚⠁⠀⠀⠀⠀⢤⡄⣠⠋⠀⣇⠀⠀⠀⠀⠉⠛⠶⣄⡈⠃⢀⣼⠇⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠚⠁⠈⠳⢄⡀⠀⠀⠀⢀⡼⠁⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠉⣛⡿⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⡤⠋⠀⠀⠀⠀⠀⠙⢦⣀⡀⣀⣠⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡷⠀⣀⣀⠀⠛⡤⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣩⣿⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣒⣊⡡⠞⠋⢩⣰⠞⠁⣠⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡦⠀⠀⠐⣤⡷⠀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢧⣀⣀⣀⣀⡀⠀⢠⠀⢸⡕
⠀⠀⠀⠀⠀⠐⠺⢄⡗⠀⠀⠀⠐⢿⣤⣠⢤⡔⠋⢩⣭⡿⣄⡐⡀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣀⡀⠙⣻⠃⠀⡜⡇⠀⢹⡄
⠀⠀⠀⠀⠀⡇⠠⡞⠷⢶⡀⡆⢱⣤⠼⠟⣼⣁⠀⠉⢁⠥⣍⠀⢰⠀⠀⠀⠀⠀⠀⢠⡟⠉⢰⠃⠀⡞⡀⢠⡁⢁⡀⠘⣣
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣯⡀⠀⠈⠉⠉⣀⣀⣼⠖⠟⠀⠈⡆⠀⠀⠀⠀⢀⡼⠀⢀⣟⠓⢒⣆⡄⠘⢺⠘⢂⣄⣇⠄
⠀⠀⠀⠀⠀⠥⠤⠤⠤⠤⠜⠉⠋⠉⠀⠀⠚⠋⢿⠁⠀⠀⠀⠤⠤⠄⠀⠀⠀⢶⣯⡀⠀⠐⣗⠐⠐⣗⡇⠂⢢⠐⠀⣼⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢄
⠀⠀⠀⠀⠀⠀⡴⠊⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⢯⡀⠀⣸⠃⣀⣤⠤⠄⠀⠀⠀⠠⠚⠹⡀⠀⠀⢠⠖⠲⣄
⠀⠀⠠⠤⡄⠀⠻⣄⣠⠜⢁⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠲⠭⠿⠓⠉⡁⠀⠀⠀⠀⠀⠀⠀⢤⣀⠱⠀⠀⣾⠁⢀⡼
⠀⠀⠀⠀⠿⠳⣄⣼⠷⣴⡅⠀⡙⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠈⠉⠙⠒⢲⠿⡍⠉
⠀⠀⠀⠀⠀⠀⠛⠹⣇⣤⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢡
⠀⠀⠀⠀⠀⠀⢠⡀⢭⣯⡽⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠂⢤⣀⣤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠸⡇⠘⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⣹⡄
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⣆⠀⠈⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣧⣀⡤⠏⠀⢦⠀⠀⠀⠀⠀⠀⢀⡀⢻⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣙⣤⡴⠃⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⢂⣤⢀⣬⠀⠀⠀⠀⠀⢀⡒⠭⣀⡿⠋⠁⠀⠀⠀⠀⣴⣾⣯⣉⡏⠑⢄⣠⣠⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣼⠈⠷⠋⠁⠈⠁⠀⠀⠀⠀⠀⣘⡦⢅⣾⠇⠀⠀⠀⠀⠀⠀⣹⡃⠈⢙⣳⡶⠌⠁⠀⠓⠦⣶⣧⡀
⠀⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣤⣼⢻⡀⠀⠀⠀⠀⠀⠛⠋⠁⠸⣿⠁⠀⠀⣀⣠⠔⢫⣽⣏⣛⣶⣄
⠀⠀⠀⠀⠀⡼⠁⠉⠓⠦⣤⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠘⠛⠁⠀⢠⡽⠻⣭⣿⣟⣁
⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠐⠠⠐⠛⠟⠚⠛⠉⠩⠿⠃
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠟⠛⠿⠿⣦⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠉⠛⠛⠛⠛⠛⠉⣡⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⣀⣻⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣟⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣿⡏⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⢻⣿⢻⣿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⣿⣿⡇⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢸⡟⣿⡟⠟
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⡿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⣿⣿⡇⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠿⢸⣿⢻⣿⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⡿⢿⡇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⡟⣿⡇⠿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠙⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⡿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠸⢿⣿⢻⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻⡟⢻⡟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿⡟⣿⡇⠿
⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠶⠖⠛⠉⠉⠉⠙⡆
⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠋⠀⠀⠀⠀⠀⣤⣶⣶⣅
⠀⣠⣴⠿⠛⠋⠉⠙⢿⣿⢟⣛⣵⣿⣿⣿⠟⠛⢿⣿⠀⠀⢀⣀⡤⠼⣿⣿⣿⣿⣷⣄
⢰⡿⠁⠀⠀⠀⠀⠀⠘⣿⠏⢁⣈⣿⣿⣿⣤⣶⣤⣽⣧⢰⡏⠁⠀⢠⣾⣿⡿⣿⣿⣿⣷⣦⣤⣄⡀
⠈⠿⣦⣤⣤⣤⣤⣤⣄⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠦⢤⣿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣠⣾⣿⣿⣷⣄⢹⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠉⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠿⣿⣿⡟⠋⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢿⣿⡿⠋⠉⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⢋⣤⣴⣶⡶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⣀⡹⣷⣠⣾⣟⣿⣿⣿⡿⣿⡏⠘⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⢷⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠾⠛⠉⠙⣿⢿⣿⣿⣿⣿⣿⠇⣿⣇⠀⠈⠻⠿⣿⡿⠿⢿⣿⣿⠏⠘⣧⣀⠀⣀⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠙⠛⠛⠛⠁⢠⣿⣿⡀⠀⠀⠀⣀⣤⣾⠟⠋⠀⠀⠀⠈⠉⠉⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⣉⣉⣢⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠢⡄⠀⠀⡇⢰⠉⠀⢠⠃⡴⡵⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠘⡄⠀⠇⠈⠀⠀⢣⣸⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠉⠀⠀⣀⣤⠤⠤⠀⠱⣀⠆⢀⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢄⡀⠀⠀⣀⠔⠈⠁⠀⠀⣀⣀⡀⠰⠃⠀⢀⣀⣀⠀⢇⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠲⢅⡸⡄⠀⠀⢠⠞⠉⠀⠀⠀⠀⢰⠋⠉⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⣠⠶⠂⠀⠀⠑⢌⢢⠀⠉⠀⣠⡶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡜⠀⠀⢸⡇⠀⢠⡶⠋⠀⠀⠑⢵⢄⠀⠋⠀⠀⠀⠀⢒⣡⠶⣚⠳⠆⠰
⠀⠀⠀⢠⠊⠀⠀⣀⡈⠁⠀⠸⠁⠀⠀⡞⢄⠈⢻⠳⣄⠀⠀⢠⢞⠭⠒⠉⠀⠀⠀⡇⠀⠀⠀⠀⢀⠔⢖⠀⠀⠐⠢⣄
⠀⢀⠔⠁⠀⢀⡞⠁⠀⣀⡄⠀⠀⢰⣰⠃⠈⢇⠀⢃⠈⠓⢄⠘⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡰⠁⢣⠈⢆⠀⠀⠀⠈⠆
⠀⢈⠀⠀⠀⠸⡇⠀⣸⠋⠀⠀⠐⣵⠋⠀⠀⡘⠀⠘⡀⠀⠀⠉⠐⠂⠤⠤⠤⠚⠁⠀⠀⢀⡴⢣⠀⠀⠡⡈⢣⠀⠀⠀⡙
⠀⠀⠉⠒⠤⣀⡀⠀⠙⠀⠀⢤⡚⠁⠀⣀⠔⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠐⡄⢣⡀⠀⠑⡄⠱⣄⡰⠁
⠀⠀⠀⠀⠀⠀⡇⢙⠒⠢⠤⠄⣀⣉⣁⣀⠠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠘⣦⡱⠤⠤⠬⠶⠊
⠀⠀⠀⠀⠀⠀⠡⡘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢁⠠⢤⡀⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠿⣔⠒⠒⠒⠂⠐⠢⡀⠀⠀⠀⠀⠀⣠⠒⢁⡠⣒⣵⢞⡳⣊⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠥⡻⠃⠀⠀⣀⠔⠊⠉⢆⢷⠹⠯⡢⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⣁⠔⠊⠀⢀⡤⡊⠀⠀⠀⡠⠔⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⢀⠠⠒⠁⠳⣘⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡠⠔⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⣀
⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⣠⡶⠇⣀⣀⠀⠀⠀⠀⢠⣶⣶⠀⠀⢸⣇⠀⠀⢀⣤⣤⡀⠀⠀⠀⢠⣾⣷⢈⣿⠆⢠⡾⠁⢀⣤⣄
⠀⠀⠰⣏⢻⣟⣀⡀⠀⣴⠌⠿⣦⣀⢿⡿⠃⠀⠀⠀⣠⣽⣯⣴⠶⠾⠛⠀⢠⣌⣿⣋⣽⠀⠀⢀⣤⣽⣵⡟⠁⠀⠀⠙⢷⣬⣿⣻⡄⠀⣠⠄
⠀⠀⠐⠛⢿⣿⣿⠛⢶⠏⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠹⣿⣿⣿⠃⣠⣤⠶⠋⣿⣿⡟⠙⠂⣴⡟⢹⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣟⠳⢦⡟
⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⣾⣿⣿⡇⠉⠻⢶⠄⣿⣿⣿⠀⠀⠀⠀⣰⣿⣿⣇⠀⠀⠈⠻⣾⣿⣿⣧⣀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⣰⡿⠛⣿⡄⠀⠀⠀⠀⣿⡇⢻⣧⠀⠀⠠⣿⣿⣿⣿⢆⣴⡶⠀⣿⡇⠀⠉⣻⣿⠀⢸⣿⣿⣿⡧
⠀⠀⢀⣿⠋⠉⠉⣿⠀⠀⠀⠘⣿⡁⠀⠘⣿⣄⠀⠀⠀⣿⡇⢠⣿⠃⠀⠀⣿⡄⠀⠻⠟⠋⠀⠀⣿⡇⠀⢰⣿⠃⠀⢸⡇⠰⣿⡀
⠀⠀⠸⠏⠀⠀⠸⠿⠀⠀⠀⠀⠻⠇⠀⠀⠈⠻⠷⠀⠀⠿⠇⠺⠏⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠸⠇⠀⠘⠿⠄




⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣻⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠲⣤⡀⠀⢰⣿⣿⣄⠀⢀⣴⠗⠀⠹⣧⡀⠠⣿⣿⣦⡀⠀⠘⣷⡀⠀⠀⣿⣿⣆⠀⠀⣼⠇⠀⠻⣦⡀⣾⣿⡦⣤⡾⠁⠀⠀⠀⢸⣿⣷⡀
⠀⠀⠀⠀⠈⠛⠷⣶⣭⣥⣾⡿⠋⠁⠀⠀⠀⠈⠛⢦⣬⣭⣼⠇⠀⠀⠈⠻⠶⣶⣬⣭⣼⠷⠞⠋⠀⠀⠀⠈⠻⣬⣭⣾⣏⠀⢠⣄⠀⣠⣦⣭⣵⣿⡀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢻⡏⠀⠀⠀⠀⠀⠘⣿⣿⡟⠓⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠉⠀⠀⠙⠿⠋⢹⣿⣿⠍⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣿⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡉⠀⠀⠀⠀⠀⢠⣿⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⣸⡟⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⣄⢴⣿⣷⠀⠀⣀⡀⠀⠀⠻⣦⡀⢰⣿⣷⣄⣠⡟⠁⠀⠀⠀⣠⣾⣿⡆⠀⣼⠃⠀⠀⢷⣄⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⣤⡀⠀⣾⣿⡶⣆
⠀⠀⠀⠀⢻⣶⣍⣥⡶⠟⠋⠀⠀⠀⠀⠈⠻⢦⣭⣵⣾⠋⠀⠀⠀⠀⠸⣧⣭⣭⣴⠞⠋⠀⠀⠀⠀⠙⠻⢶⣮⣭⣥⣿⠀⠀⠀⠀⠀⠈⠛⢶⣌⣋⠸⣯
⠀⠀⠀⠈⠋⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠈⠁⠀⠀⠀⠀⢩⡿⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠝⠳⠶⡦⠀⠀⠀⢀⣼⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠘⣷⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠋⢡⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⢙⣿⣟⠁⠀⠀⠀⠀⢀⣾⠟⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠋
⠀⠀⠀⠀⢀⣾⢿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿
⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⣤⠀⠀⠀⠀⠀⣰⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢹⣆⢠⣶⣦⣠⡿⠀⠀⠀⠘⣷⡀⣰⣶⣦⢰⡏⠀⠀⠀⣤⡀⠀⠀⢠⣶⣄⠀⠀⣰⠏⠀⠀⠀⠀⢿⡄⢠⣶⣶⣀⠀⠀⠀⠘⣷⡀⠀⣴⣶⡄
⠀⠀⠀⠀⠻⣟⣫⣻⣿⡇⠀⠀⠀⠀⠈⢻⣾⣛⣣⡟⠀⠀⠀⠀⠈⠻⣦⣴⣟⠿⢋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠻⣆⣛⣋⣸⠇⠀⠀⠀⠈⠻⣦⣙⣛⣹⡧
⠀⠀⠀⠀⠀⢿⣿⣿⠉⠓⠀⠀⠀⠀⠀⢨⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⡓⠀⠀⠀⠀⠀⠸⣿⣿⡿⣿⠂
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠛⠁⠀⠀⠀⠀⠀⢠⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠈⠁
⠀⠀⠀⠀⠀⣿⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣻⡟⢻⣿
⠀⠀⠀⠀⣰⡿⠁⢻⣧⡀⠀⠀⠀⠀⠀⠀⢰⣿⢡⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡆
⠀⠀⠀⠀⠛⠁⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠘⠋⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠙⠃

⣶⣶⣶⣶⣶⡾⣶⣾⣿⡿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⢷⡾⠷⠶⠶⣶⣶⡷⠶⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⣤⣤⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣻⣟⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⣿⣿⣿⡟⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣿⣿⣿⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠸⣿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣟⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣟⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢸⣿⣿⡇⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⣿⣿⡇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠋⢿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢰⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⢀⣤⣄⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣘⣿⣟⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣭⣄⣘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣿⣿⣿⣏⣩⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⣿⡿⠟⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠸⠿


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⡶⠶⢶⣶⡶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠂⠐⢢⠀⠀⠀⢀⡠⠤⠖⠢⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠘⢦⠀⠢⡖⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⠏⢀⡴⠒⠒⠦⣤⣘⡄
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⢀⣤⠶⠒⠒⠀⠈⢶⠚⡇⠀⠀⠀⠀⣀⣤⣀⠀⠀⢀⣤⠶⠶⢤⣀⠀⠀⡇⠀⢸⠀⡸⠀⠀⢠⠔⢁⡠⢟⡠⠤⡀
⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⡟⠁⠀⢀⣀⣤⡄⠈⢆⢣⠀⠀⡴⠛⠉⠉⠉⠑⠀⠈⠀⠀⠀⠀⠈⠁⢠⣃⡤⠃⢠⠇⠀⠀⣇⣰⡯⠚⣁⠤⠒⠋
⠀⢀⠞⠉⠀⠀⠀⣠⡶⠖⠒⠀⠀⠀⢰⡟⠉⠀⠀⠀⠘⣎⡆⠀⠀⢀⣠⣤⣤⡀⠀⠀⢠⠶⠿⠷⠦⠀⢸⣁⣀⡤⠋⠀⠀⠀⠈⠑⠒⠉
⠀⠘⣄⠀⠀⠀⢰⠏⠀⠀⢀⣀⡀⠀⠈⠀⠀⠀⣠⢦⠀⠸⣹⡀⠀⠛⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠣⡀⠀⠈⠀⠀⣼⠟⠉⠁⠀⠀⣠⢃⡴⠃⠘⡆⠀⡏⢳⠀⠀⠀⠀⠀⠐⠤⠤⠂⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⡳⢄⡀⠘⠃⠀⠀⠀⢀⣩⡶⠋⠀⠀⢀⠇⠀⡇⠀⢣⠀⠀⣠⠴⢖⣻⣛⣛⣛⣛⣳⡀⢠⠃
⠀⠀⠀⠀⢀⠃⢠⠟⢦⡀⠀⠰⢟⡉⠁⠀⠀⠀⣠⠎⠀⠀⡇⠀⠀⢣⡀⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⢸⡀⡎⠀⠀⠈⠓⢄⡀⠉⠑⠒⠒⠋⠁⠀⠀⡰⠃⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⢣⡧⣀⡀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠙⢤⣉⠓⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠘⡆
⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⣒⡪⠝⠁
⠀⠀⠀⠀⠀⠀⠷⠒⠒⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢸⣿⡷⣦⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⣾⣿⡦⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⣴⣾⣷⣇⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⡆⠀⠀⠀⢠⣾⣶⣿⠄⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣿⡦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣫⣿⣿⣿⠄⠀⠀⠀⠀⢀⣾⢻⣿⣿⣿⣆⢀⣼⢟⣿⣿⠹⣦⡀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⢹⣿⣿⣷⡀⠀⠀⠀⠐⠛⠁⢸⣿⣿⠃⠙⠛⠁⣸⣿⣿⡆⠈⠛⠀⠀⠀⠀⠙⣿⣿⣿⠋⣿⣿⣿⡛
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⢾⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠐⢿⣿⠿⠃
⠀⠀⠀⠀⢠⣾⠿⢻⣿⠀⠀⣿⠘⣿⡀⠀⠀⠀⠀⠀⢠⣿⢻⣿⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣦⣄
⠀⠀⠀⠀⠀⠁⠀⠸⠟⠀⠀⠿⠀⠹⠷⠀⠀⠀⠀⠀⠺⠏⠘⠿⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⠀⠸⠇⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡧⣿⣿⠶⡄⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣷⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⣷⢼⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣾⡏⠀⢨⣵⡼⣇⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣧⠀⠀⢀⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⣸⢧⣾⣅⠀⢹⣷⣦
⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⣿⣿⣦⣀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣸⣿⣯⢀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡃⠈⠿⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠛⣼⣿⣿⡌⠛⠁⣿⣿⡟⢹⠇⠀⠀⠀⠀⠀⣸⣿⣿⡟⠿⠃⠘⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠼⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⠷⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠷⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠛⠻⠿⢻⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠻⠟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠿⠇

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣽⣯⣬⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠇⠀⠀⠀⠰⢷⣄⠀⠀⠰⣿⣿⠇⠀⠀⠀⠀⠘⣷⣀⠀⠸⣿⣿⠀⢀⣰⡿⠁⠀⠀⠀⠀⠸⣿⣿⠂
⠀⠀⠀⠀⣠⣶⣾⣷⣦⡀⠀⠀⠀⠀⠀⢀⣶⣾⣷⣶⣄⠀⠀⠀⠀⠙⠛⠿⢷⣾⣷⣶⣄⠀⠀⠀⠀⠈⠙⠻⣷⣾⣷⡾⠛⠉⠀⠀⠀⠀⠀⣠⣶⣾⣷⣦⡀
⠀⠀⠀⢰⡟⣿⣿⣿⡟⣿⡀⠀⠀⠀⢠⡿⢻⣿⣿⣿⠻⣶⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⢻⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣤⣶⠶⠟⣿⣿⣿⡟⣿⡄
⠀⠀⠀⢾⡇⣿⣿⣿⡇⢻⡇⠀⠀⠀⢸⡇⢸⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣿⣿⠘⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢹⡇
⠀⠀⠀⠀⠀⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣷
⠀⠀⠀⠀⠀⣿⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣼⡿
⠀⠀⠀⠀⠀⢿⡇⢿⠇⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠇⢻⡟⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⡿⠁


⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢀⣠⡾⠃⣠⣄⠘⢷⣄⠀⠀⢰⣦⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠘⢿⣦⡘⢿⡿⣃⣴⠿⠃⠀⠀⢻⣦⣄⡀⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟
⠀⠀⢀⣠⡾⣿⣿⣿⡿⣦⣄⠀⠀⠀⠀⠈⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⢷⣄⡀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠹⢿⣄⣿⣿⣿⣇⣼⠿⠃⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣠⡿⠃⠀⠀⠀⢾⣿⣿⣿⣿⣿⠇⠀⠀⢀⣤⣴⠿⣿⣿⣿⡿⢷⣤⡀
⠀⠀⠀⠀⠙⣿⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⢨⣿⢻⣿⠁⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⠇⠀⠈⠁
⠀⠀⠀⠀⢠⣿⠇⢻⣧⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⢸⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡿⢸⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠻⠏⠀⠀⠿⠃⠀⠀⠀⠀⠀⠘⠿⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠇


⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⣘⣻⣟⡀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣋⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣆⠀⣤⣤⣤⣴⠟⣿⣿⣿⡟⢷⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣦
⠀⠀⠀⠘⠿⣿⣿⣿⡿⠿⠀⠀⠀⠉⠀⠀⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⢠⣶⠾⠛⣿⣿⣿⡅⠀⠀⠀⢀⣼⠟⠁⣿⣿⣿⡇⠙⢷⡄
⠀⠀⠀⠀⠀⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⡇
⠀⠀⠀⠀⠀⣿⡇⢹⣷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡇
⠀⠀⠀⠀⠀⣿⡇⢸⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢿⣇
⠀⠀⠀⠀⠀⠙⠃⠀⠛⠃⠀⠀⠀⠀⠀⠀⠙⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣀⠀⢠⡆
⠀⠀⠀⢿⣟⡀⠀⣠⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠲⢦⣀⡀⣿⡗⠀⠀⠀⠀⠀⠀⠀⢘⣿⡁⠀⠀⠀⠀⠀⠈⠳⣜⣿⣣⠾⠃
⠀⠀⠀⢿⣿⣟⠶⠇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⢹⣿⡿⢶⣄⡀⠀⠀⠀⣾⠋⣿⣿⠦⠶⠆⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⣸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠈⠉⠀⠀⠀⠙⠀⢿⣿⣄⠀⠀⠀⠀⠀⢀⣿⣿⡇
⠀⠀⣰⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠿⠂⠀⠀⠀⠀⢸⡇⢹⡇
⠀⠀⠿⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠀⠺⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠈⠻⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢶⡀⢀⣤⡄⠀⠀⠀⠀⠀⢀⡴⢀⣀⠀⠀⠀⠀⠀⠀⣸⠃⢠⣶⡄⢰⡆⠀⠀⠀⠀⢴⡏⣴⣦⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠈⠙⢶⣿⣅⠀⠀⠀⠀⠀⠛⢦⣼⣟⡀⠀⠀⠀⠀⠀⠈⠛⣶⣿⠶⠚⠃⠀⠀⠀⠀⠀⢹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⣥
⠀⠀⠀⠀⢸⣿⡿⠗⠀⠀⠀⠀⠀⢀⣿⣿⠛⢦⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡼⠃⠀⠀⠀⢀⣠⡾⢿⣿⡀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣼⠟⢿⡀⠀⠈⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠰⣿⠋⠉⣿⡀⠀⠀⠀⠀⠈⠁⢀⣼⣿⠃
⠀⠀⠀⠰⠶⣿⠃⠀⠀⠀⠀⠀⠈⣿⠀⠈⢷⣄⠀⠀⠀⠀⠀⠸⣿⠿⠛⠀⠀⠀⠀⠀⠀⠙⠇⢀⣾⠃⠀⠀⠀⠀⠀⠀⣼⠟⣷⡀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⣿⣂⣠⡿⠀⠀⠀⠀⡄⠀⠸⣿⣂⡼⠇⠀⠀⠀⠀⠀⢀⣸⣿⠂⠀⠀⠀⠀⠀⠺⢧⣘⣿⣃⣼⠇⠀⠀⠀⠀⠀⡀⢘⣿⡃
⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠿⠶⢻⣿⣿⠀⠀⠀⠀⠀⣠⣤⢾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⢀⣤⠿⣿⣿⠇
⠀⠀⢸⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⡀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠀⣀⡄⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿
⠀⠀⢸⡇⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣷⠀⠀⠀⠀⠀⠀⣿⡁⠹⠿⠋⠁⠀⠀⠀⠀⢼⣇⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⠁⣿
⠀⠀⠸⠇⠺⠃⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠙⠁⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠤⠒⠒⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⡠⢲⣀⢮⠙⠓⢶⣄⢇⠰⠁⠈⠑⠢⠤⠄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠞⠁⠐⢺⠀⠀⠉⠉⠀⠀⠙⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣀⣀⡠⠤⠤⠄⠤⠤⠤⣀⡘⢄⠀⠀⠀⣘⣀⣀⣀⡀⠀⠀⢠⠃⠴⠭⢄⣱⠀⢀⣔⣂⣄⠀⢰⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠂⢴⠁⠀⠀⠀⠈⡆⢠⠃⠀⠀⠀⠀⢸⠉⠉⠉⠉⠛⠓⢺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡸⠔⠊⠉⠉⠉⢁⠇⡏⠉⢲⢶⡊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⠒⠤⣀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⡠⠊⠀⠈⢆⠘⡄⠈⠑⠒⠒⢊⠇⠀⣠⠎⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⡄⠙⠤⣀⣀⠴⠃⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣌⠛⠛⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠻⣦⣤⡶⠛⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⠋⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⠻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣰⣦⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠰⡆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣾⣾⠆⠀⢰⣷⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⡄⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⣿⣿⢿⣿⣿⣿⡿⣿⢿⣿⡿⣿⣿⣿⢿⢿⡿⣿⣿⡿⣿⢿⡿⢿⡿⣿⡿⣿⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⢛⣿⣿⣿⣿⣿⣿⣛⠛⠛⠯⠭⠭⠿⢟⣛⣻⣿⣿⣿⣿⣿⠿⠭⠽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⡿⡿⣿
⣿⣷⡇⣿⢧⡏⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⡘⣇⣿⡇⣧⣿
⣿⣿⢻⣽⡼⣸⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⡇⡇⠈⡇⠃⠿⠃⢹⠹⢹⢿⣿⣿⣿⣿⣿⣿⣿⣎⢧⢻⢸⣧⣿⣿
⣿⣿⣿⣿⢳⣿⣽⣿⣿⣿⣿⣿⣿⠟⡇⠏⢸⠀⠃⠁⠀⠁⠀⠀⠀⢸⠀⠸⠀⡇⡿⣿⣿⣿⣿⣿⣿⣞⣾⣾⣺⢸⣿
⣿⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠾⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⡀⡀⣠⢀⣀⡄⡀⡀⣀⣀⢀⣀⢀⢀⣀⡀⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿
⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢊⠢⠀⠄⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠁⠀⠀⠀⠀⠀⠔⢕⠴⡖⠉⡄
⠀⠀⠀⠀⠀⠂⠁⡄⠊⠀⠀⠠⠄⡀⠀⠀⠑⠠⠈⠢⣤⡀⠠⠂⠠⠄⠂⠀⠀⠀⢘⠸⢤⡤⠐⠁⠀⠀⠀⠀⠀⠑⠈⣭⠠⠀⠸⠂
⠀⠄⠒⡄⠠⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠈⠁⠀⠀⠀⠀⠆⠔⠀⡄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⣠⣁⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⠀⠐⣀⠀⡀⠀⠀⠀⡀⣀⠌⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠁⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠠⡀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⣈⠀⠀⠀⠀⠀⢀⠂⠉⣁⡀⠠⠀⠀⠀⠀⠀⠓⠘⠀⠚⠁⠀⠃⠸⠀⠀⠀⠀⠠⠂⣅⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠀⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤
⠀⠀⠀⠀⠀⠂⡠⠤⡆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡀⣀⠲⠠
⠀⠀⠀⢀⡀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡀⠈⠒⠐⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠆⠡⠂⠈⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠈⢘⠀⠀⠀⠀⠼⠂⠐⢄⠀⡠⠀⠀⠀⠀⠤⠁⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠎⠊⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠛⠻⠆⠀⠀⠀⠟⠛⠟⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠛⠛⠻⠓
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠉⠀⡐⠀⠀⠀⠐⠀⠁⠀⠑⡀⠀⠀⠀⢀⠔⠀⣉⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⠀⡲⣄⠀⠀⢀⡴⠚⠋⠙⢳⣶⣤⣂
⠀⠀⠠⠀⣈⠉⠀⠀⠀⠈⠄⠀⢀⣀⠐⠁⠀⠀⡀⠘⠄⠂⠐⠀⠘⢀⠰⠀⠀⠀⠀⠀⠈⢃⡈⠙⠂⠸⠀⠀⠘⢀⠀⠘⠚⠙⠛⠉⠓
⠀⠀⠀⠔⠹⠂⡀⠀⠀⠀⠀⡀⠘⠁⠂⠀⠀⠀⡍⠀⠤⢀⣓⠠⠂⠀⢠⠃⠀⠀⠀⠀⠐⠋⠩⠀⠂⠁⠀⠀⠀⠀⠀⠹⠑⠂⠈
⠀⠀⢐⠀⠸⠀⠀⠈⠀⠈⠀⠀⠀⢀⠸⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢆⠃⢰⠀⠀⠀⠀⠀⠀⠀⢠⠆⠦⠁⠀⠀⠀⠀⠤⣀⠀⡀⡀⠄⠀⠀⠀⠀⠀⢚⠔⢇⡐⠀⠀⠀⠀⠀⢐⢐⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠀⠀⠀⠀⠀⠀⠀⠉⡈⠀⠖⠂⠀⠀⠀⠀⠈
⠀⠀⠀⢠⡔⣰⣦⠀⠀⠀⠠⢴⠐⢰⠀⠀⠀⠀⠀⡄⢀⡄⠀⢸⡄⢠⠀⠀⠀⠀⠀⡴⠀⡀⢤⠀⢀⠀⠀⠀⠀⠀⠰⠔⠦⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⣉⡉⠩⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠉⠉⠉⠒⢦⡤⠤⠤⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢁⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⡠⢆⠀⠀⣀⠀⢰⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠳⠊⠀⢸⣡⠂⠸⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠙⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠈⠉⠚⠒⢲⡞⠛⠉
⠀⠀⠀⠀⠀⠀⢀⡀⣇⡑⣠⠇⢰⠃⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠈⢓⡤⠚⠉⠑⠻⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⣇⠘⣄⠰⡄⠀⠀⠀⠀⠀⠀⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠳⠼⢻⠁⠁⠀⠀⠒⠒⠒⢳⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⢀⣀⣤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠉⠉⠁⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢀⣠⠄⠘⢄⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠂⠉⠁⠀⠀⠀⠈⠢⡀⠀⠙
⡠⠤⢄⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦
⢣⡀⠀⠈⠑⠦⡀⣠⠊
⠀⠙⠢⣄⠀⠀⠈⠧
⠀⠀⠀⠀⠉⠒⠒⠒


⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠕⠚⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⡀⣈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡀⣀
⠀⠀⠀⠀⠀⠀⢞⠀⢀⠂⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠤⠔⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⣰⠛⠁⡀⢈⢳⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠢⠄⣈⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢲⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢳⡀⠀⠥⠴⡸⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡔⠀⠀⡏⠲⠤⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢍⡒⣶⢈⠴⠋
⠀⠀⠀⠀⠀⠀⢀⡴⠃⡇⠈⠢⡤⠞⠁⠀⠀⠀⠀⠀⠸⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢸⢧⠀⠀⠀⠀⠀⠀⠀⠰⠦⣀⠀⠀⠀⠀⠀⣸⠗⠒⠋⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠎⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠤⠤⠤⠤⣴⣶⣶⡶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣧⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⡶⢶⡄⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣾⠀⠙⠇⠀⣧⡴⣳⠄⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣤⣤⣤⣤⣿⠟⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠛⣉⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇⣠⠀⠀⠀⠀⠀⢰⡞⠋⠉⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣿⣟⣴⡞⠃⢀⡀⠸⣿⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣰⢟⣿⣿⣷⣞⢻⡿⣼⡟⣇⠀⠀⠀⠀⢹⡄⠀⠀⣀⣤⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠶⣤⡾⠛⠋⠉⢻⣿⣿⡟⠁⠈⠁⣿⠀⠀⠀⢀⣀⣷⠶⠛⠉⠙⣏⠻⢿⣿⣿⣶⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⡴⠿⠤⠤⠤⠶⢶⡟⠛⠛⠶⡶⣶⠿⠶⢶⡿⢻⡏⣿⠀⠀⠀⠀⢹⡆⠀⠁⠘⠏⢻⡿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢧⡻⣄⣠⠞⣁⡞⢡⡟⠀⠀⠀⣴⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠈⠳⢼⣟⣛⣩⡴⠋⠀⠀⠀⣰⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢧⡀⠀⠀⠀⠀⠀⠀⠙⢯⣿⠀⠀⠀⣀⣰⡷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡟⠲⠶⠶⠦⠴⠶⢶⣿⡷⠛⣿⠉⢹⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠘⢦⣄⣙⠛⠛⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡇⠀⠀⠀⣻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠲⢦⣴⡶⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⡀⣀⡀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣰⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣆⠀⠂⣠⠀⠀⠀⣀⢀⣀⣀
⠀⠀⠀⠞⢁⢠⢀⠡⠀⠀⢀⠊⡨⠂⠠⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠔⠉⠀⠑⣄⠄⠀⠀⠋⠀⠆⠀⠹⠃
⠀⠀⠀⠀⢌⠀⠐⢀⠄⠀⢀⡈⢀⠘⠚⠈⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣠⠤⣀⠤⠀⠈⠚⡐⠀⠀⢃⠏⠀⠀⠐⠸⠀⢀⠜⠘
⠀⠀⠀⠑⠂⠀⠐⠈⠀⠐⠎⠐⠄⠀⡊⢌⡀⠆⠀⠐⠀⠀⢀⠈⠀⠀⠖⠋⠐⠃⠈⠁⠀⠀⠀⠈⢐⡆⠁⠀⠀⠀⠀⠀⠀⣋⠁
⠀⠀⠀⠀⠁⢸⠈⢂⠀⠀⠀⠀⢀⠜⠡⡀⠀⠀⠀⠈⠂⢨⠐⠁⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⢀⠂⠂⠑⠀⠀⠀⠀⠀⡐⠡⠑⠄
⠀⡠⠊⠀⠀⢸⠀⠀⢂⡀⠀⣀⠈⡠⠀⠸⠆⠀⠀⠀⠠⠋⢂⠀⠀⠀⣀⠄⠀⠑⢠⡄⠀⠀⢀⡂⠀⠀⠀⠘⠇⠀⢠⡔⠀⠀⠀⠈⣢
⠘⠇⠀⠀⠀⢸⠀⠀⠈⠁⠀⢈⠊⠀⡈⡢⠀⠀⠀⣤⠀⡄⠈⣤⠀⠀⠉⢀⠌⠠⠀⠀⠀⠀⠉⠁⡠⠃⢄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠉⢈⠁⠁⠀⠀⠀⠀⠀⡀⠁⠀⠁⠀⠀⠀⠆⡤⠄⠒⠀⠀⠀⠀⠐⠃⠖⡖⠁⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⡆⡀⠀⠀⢀⢀⠀⠈⣀⠀⠀⠀⠀⠤⠀⣇⠀⠀⠀⠀⠀⠀⣀⡄⣇⠀⠀⠀⠀⠀⣀⠆⢐⣀
⠀⠀⠀⠛⠋⢀⣄⠑⠋⠀⠀⠉⠁⠀⢉⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠊⠠⠉⠑⠀⠀⣰⡷⠋⠙⠲⠆⠀⠀⣴⣄⡀⠀⠀⠀⠀⠀⠀⢠⡀⣠⠀⠀⠀⠀⠀⠀⢀⢀⠇⠈⠣⠅
⠀⠀⠀⠀⠌⠢⠐⡡⠀⠀⠊⡣⠀⣠⠄⠀⠀⡐⠁⠔⢀⠁⠀⠀⠀⠀⢠⡎⢠⠀⣡⠀⠀⠠⡀⠀⠀⠇⢨⠀⢁⣀⡀⡠⡌
⠀⠀⠀⠀⣠⠂⠁⢢⠄⠀⠀⠈⢹⠆⡴⠀⠀⠂⢢⣤⣪⣂⠀⠄⠀⠀⠉⠙⠊⠑⠂⠂⠒⠊⠀⠀⠀⠑⠬⠍⠠⢀⠀⠁⠃
⠀⠀⠀⠀⠁⢠⡄⠀⠀⠀⠀⠁⠜⠢⡀⠀⠀⠀⠀⢀⢀⠑⡴⠌⢠⡄⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡄⢐
⠀⠀⠀⠀⠠⠂⠡⠀⠀⠀⠀⠀⡒⢠⠁⠀⠀⠀⠀⠋⠘⠃⠉⠋⠁⠀⠀⠀⠀⠉⠒⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⢋⠉⡑⢦⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢀⡤⠤⢤⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠐⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⣀⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠤⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠈⠓⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⢀⠛⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠁⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⢀⠀⠂⠀⡠⠄
⠀⠀⠀⠀⡄⠀⢰⠋⠈⠳⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠈
⠀⠀⠀⠀⠀⠀⡘⠀⣐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠨⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠄⠀⠀⢀⠔⠒⢤⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠹⡀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠇⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢉⣀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡤⠄⢤⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡜⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢠⣄⡀⢀⡇⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣈⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠔⠈⡇⠀⠈⢠⠀⠀⠀⠀⠠⠆⠀⠀⠡⠤⠀⠀⠀⠀⠠⠌⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠐⠀⡧⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠈⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣶⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⣿⣿⣧⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠈⠙⢿⣆⠀⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣄⣀⡀
⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⣴⣦⡄⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣾⠟⠛⢳⡄⠀⠀⠀⠶⠆⠀⣴⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣦⣄⠀⠈⠻⠿⠃⣿⣿⡏⠀⠤⠀⠐⢄⣀⣠⠾⠁⠀⣿⣧⠀⠀⠜⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠰⠀⠈⢻⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣷⣤⣄⣀⠀⠀⣤⣦⠀⠀⠀⠹⣿⣷⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠛⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣤⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠉⠁⢸⣿⣿⣿⣿⣿⣛⡛⢿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡟⣩⣿⣿⣿⣿⣿⣦⣭⣿⣿⣿⣿⣿⠀⣀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡏⠀⢿⣿⣿⣿⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⠟⠛⠉⠉⠙⠻⣷⣄
⠀⠀⢀⣀⣀⠀⢀⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⣥⣌⣙⣿⣿⠀⢀⠸⣿⣿⡿⢋⣩⣭⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⣿
⠀⣰⡟⠉⠈⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⠀⠀⠀⢠⡿
⠀⢹⣷⣄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣛⡻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣛⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠑⠲⠚⠋
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⡾⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠉⠛⠛⠿⠿⠿⠛⠛⢻⣿⣿⣿⣿⣿⣷⣶⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣏⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣀⠀⠀⠀⠀⣠⣿⣿⡿⠿⣿⣷⣦⡀⠲⠆⠈⠙⣿⣿⣿⡿⠀⣀⣤⣴⣶⣶⣶⣶⣤⣼⠇⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⢿⣷⡀⢀⣾⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡀⠀⠀⠀⠈⣿⡇⢸⣿⡄⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠻⠿⣿⣿⣿⠟⠋⠀⢸⡀⠀⠀⠀⢠⣿⠃⠀⠙⢿⣿⣿⣿⣿⣿⠟⠿⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠦⢤⠶⠟⠁⠀⠀⠀⠀⢸⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⢻⣆⠀⠀⠀⠀⣿⠀⠀⢀⣀⠀⠀⣰⠆
⠀⠀⠀⠀⢾⣿⡷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠹⣧⡸⣿⡿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢿⣿⡗⢀⣴⡿⠃⠀⠀⠀⠻⣦⡰⣿⣿⢳⣦⡿
⠀⠀⠀⢀⣴⣿⣶⣶⣄⣠⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣠⣴⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠿⣯
⠀⠀⠀⠀⠙⣿⣿⣿⡙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⣿⡿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄
⠀⠀⠀⢠⣾⠟⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠸⣿⡙⠻⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢻⣷⡀⠀⠀⠀⠀⠐⣿⡿⢿⣿⠇
⠀⠀⠀⣿⡏⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⢻⣇⠀⢿⡆
⠀⠀⠸⠿⠁⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠐⠿⠃⠀⠀⠀⠀⠀⠀⠿⠇⠘⠿





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡄⠀⢀⣀⡀⠀⠀⣷⠀⠀⠀⠀⠀⣿⡅⠀⣠⣤⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠈⢻⣦
⠀⠀⢸⣇⣰⡻⣿⡿⢀⣠⡿⠂⠀⠀⠀⠀⠙⢷⣄⢿⡿⢃⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠸⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⢃⣴⠿⠃
⠀⠀⠀⠉⢙⡿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⣿⣶⠿⣤⣤⣤⠦⢶⣶⣴⡶⠶⢾⣿⣿⡁
⠀⠀⠀⠀⠀⠀⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀
⠀⠀⠀⠀⢀⡀⠻⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⣼⡿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢻⣿⡄
⠀⠀⠀⠀⠘⠛⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠰⣀⠀⠀⠀⢙⣿⣟⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠘⠿⡿⠃
⠀⠀⠀⠀⠻⣷⣤⣶⣿⠟⣿⣷⣦⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣠⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠋⢹⣧⣀⣶⣏⠉⠋⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⣶⣖⠀⠀⠀⠀⠛⠛⣿⣿⣿⣧⡆
⠀⠀⠀⠀⠀⠉⢉⣽⣿⣿⣿⣯⡍⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⣻⠉⠉⠉⠉⢱⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⡇⡸⠛⠛⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⢀⣛⣟⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡃
⠀⠀⠀⠀⠀⣿⣿⣿⣦⣶⡿⠋⢉⢄⣴⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣿⣿⣆⡀
⠀⠀⠀⠀⣷⣿⣿⣿⡿⠿⠿⠛⣀⣨⣿⣯⣀⣀⣼⣀⣀⠀⠀⠀⠀⠀⣀⣈⣻⣿⣿⣯⣿⣛⣁⡀
⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠈⠙⠋⠛⠛⠄⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢀⣤⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⡟⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⣠⣠⣤⠀⣄⡄⣤⣤⠀⠀⠀⠀⠀⢘⣖⣖⣒⣲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠫⠭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡀⣀⠛⡂
⢦⣀⡌⠀⠀⠑⣏⣹⠀⠀⠀⠀⠀⢠⣽⠾⠿⢮⣤⠀⠀⠀⠀⠀⠀⠀⡿⢠⣤⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⡁⠀⡀⣈⡁
⢀⣀⠰⣿⢿⠗⣀⡀⠀⠀⠀⠀⠀⣰⣿⣤⣤⣾⣵⠀⠀⠀⠀⠀⠀⠀⠤⠏⠩⠥⠄⠀⠀⠀⠀⠀⠀⠀⢀⠛⣃⣃⡙⠃
⠘⠛⠃⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠛⠉⠉⠙⠃
⠀⠀⢀⣠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⣠⠄⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⢸⠛⡛⡟⡟⠺⠀⠀⠀⠀⠀⠀⢸⡟⠿⡿⠿⣿⠀⠀⠀⠀⠀⢀⠌⠀⢳⣄⣦⠈⣆⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⢧
⠀⢸⣠⣇⣇⣧⣴⠀⠀⠀⠀⠀⠀⢸⡀⢤⡷⠀⣽⠀⠀⠀⠀⠀⠀⠀⢐⠢⠸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘
⠀⠀⠀⠆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠤⠄⠀⠀⠀⠀⠀⢤⠶⠶⠶⠶⠴⠴⢦
⠀⡀⣀⡀⢀⣀⡀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠿⣭⡽⢿⣭⠿⠃⠀⠀⠀⢠⠒⣩⣦⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠐⠒⠠⣄⠀⠀⠀⠀⢀⠀⣖⡀⠀⣴⢤⡀
⠀⠀⢠⡄⣄⢤⣤⠀⠀⠀⠀⠈⢦⡀⠈⣓⠟⠋⡀⠀⠀⠀⠀⠀⠰⠁⠮⣿⣣⣷⡷⠈⢳⠀⠀⠀⠩⠍⠀⠀⠈⠈⠛⠻⣽
⠀⢠⣤⡤⡄⣤⢨⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠤⠈⠛⠁⠀⠄⠄⠀⠀⠀⠀⠀⠐⠛⠘⠛⠓

⢀⣀⣴⣮⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠚⢅⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣁⣀⣥
⠀⣧⣽⠘⣡⣣⡝⠀⠀⠀⠀⠀⠀⠴⡧⢤⣤⠜⣠⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠰⠀⢠⣄⠀⠆
⠠⣦⣶⣴⣤⣦⣴⠀⠀⠀⠀⠀⢀⣀⣀⠈⡉⡀⣁⡀⠀⠀⠀⠀⠀⣵⡄⠛⠚⠀⠚⠘⠓⠀⠀⠀⠀⠀⠠⠤⠍⠬⠬⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣀⣉⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣁⣀⣁⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿