⠀⠀⠀⠀⠀⣴⠉⡙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣚⡯⠴⢬⣱⡀⠀ ⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢹⣿⣿⣄⢻⣿⣷⣝⠷⢤⣤⣤⡶⢋⣴⣑⠟⠿⠿⠿⣿⣿⡀⡇⠀ ⠀⠀⠀⠀⢸⢸⣿⡄⢁⣸⣿⣋⣥⣶⣶⣶⣶⣶⣶⣿⣿⣶⣟⡁⠚⣿⣿⡇⡇⠀ ⢀⣦⠀⠀⠈⢿⣿⣧⠀⠘⣿⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⣿⡆⠀⢻⡆⠀⠀⠀⠀⢻⡄⠀⠀⢀⡟ ⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣏⠀ ⠀⠀⠛⢶⢰⣶⢢⣤⣤⣄⠲⣶⠖⠀⣙⣀⠀⠀⠀⠤⢤⣀⣀⡀⣀⣠⣾⠟⡌⠀ ⠀⠀⠀⠘⢄⠃⣿⣿⣿⣿⠗⠀⠾⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠸⠟⣡⣤⡳⢦ ⠀⠀⠀⠀⠀⢻⡆⣙⡿⢷⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢡⣴⣾⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⡼⢁⡟⣫⣶⣍⡙⠛⠛⠛⠛⠛⣽⡖⣉⣠⣶⣶⣌⠛⢿⣿⣿⣿⣿

⠀⠀⠀⣠⣤⣀⠀⠀⣀⡴⠲⣤⡤⠤⣄⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠈⠉⠉⢸⠃⣾⠟⢲⡤⢾⡄⠀⠀⠀
⠀⠀⢨⠏⠀⠀⠀⠀⠈⠛⠛⠳⢾⣟⣴⡇⠀⠀⠀
⠀⣀⣸⡀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠉⠠⡧⠤⠀⠀
⠀⠉⢼⡤⠀⠛⠀⠀⢤⡄⠀⠘⠃⠀⣰⠗⠂⠀⠀
⠀⠀⢴⡿⠗⠲⣄⣀⣀⣀⣀⣀⡴⠖⠯⡝⠂⠀⠀
⢀⡴⠻⢇⡠⠤⠏⠙⢻⡿⠋⠙⠦⠤⣠⠟⢦⡀⠀
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀
⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠞⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠳⢦⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠤⠒⠂⠉⠉⢡⠋⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⠀
⠀⠀⡎⠀⢠⠤⣄⣠⠒⣎⠀⠀⢀⠜⠀⠀⡆⠀⠀⠀⠀⠀
⠀⠀⠓⠤⠬⡂⢰⠼⣅⡱⠉⠉⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡟⠁⣠⠔⠒⠒⠒⠒⠢⢄⠀⠀⢱⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢣⢸⠱⠟⠀⠠⠄⠀⠒⠂⡣⢀⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢙⣖⡉⠉⠻⠝⠉⠍⣲⡋⠁⠀⠀⠀⠀⠀
⠀⠀⢠⠀⢤⠀⠸⡤⠇⠀⠀⠀⠀⠀⠦⠜⠀⡤⠼⠁⢹⠀
⠐⠒⢸⢦⠼⠀⠀⢑⠋⢹⠀⠀⡎⠈⣞⠱⠀⣣⡤⣻⢻⡀
⠀⠀⠀⠉⠉⠚⠃⠈⠤⠜⠓⠚⠱⠤⠋⠀⠀⠉⠉⠚⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇
⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃
⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱
⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌
⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁
⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆
⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆
⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀
⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜
⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄
⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘
⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊
⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀