⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠈⠀⠀⡃⠀⠀⠐⠀⠀⠀⠀⠀⠀⢄⠃⠀⠀⡀⠀⠀⠆⠀⠀⠀⠌⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡂⢀⠀⠀⢀⣃⣀⡈⡠⠠⠠⠀⠄⠄⠃⠁⡀⠀⡅⠀⠀⠀⡁⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⢀⣪⡦⣣⢿⡟⠛⡟⡳⡗⠞⠛⠿⣯⣃⣄⢀⢀⢀⠂⠁⠀⣠⡔⠀⠀⠀⡁⣠⢴⢪⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠳⡀⠂⡀⣀⣵⢟⡃⠃⠁⠅⠿⠀⠀⠀⠔⠅⢌⠈⠀⣿⠂⡥⡽⠫⢾⠭⡝⡋⠁⣆⡄⡳⣙⡃⠏⠃⠀⠀
⠀⠀⠀⢠⡄⠀⠀⠀⠀⡀⠀⠀⠈⢁⡽⠻⡇⡁⡀⡖⡒⠂⠻⠔⡧⡁⠄⢅⠃⠀⢠⡯⠀⠄⡀⠁⠅⡍⡅⡭⢊⢨⠱⢭⢒⡉⠁⠂⠀⠀
⠀⠀⠀⠀⠉⠳⢄⣀⠀⠀⠠⣠⢢⡇⡁⠀⢻⢆⠀⡇⠄⡀⠀⡀⠂⠄⡀⡀⠀⣀⢯⡒⡄⠃⠀⠀⠀⠀⠀⠁⠂⡒⡒⡣⠁⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⡉⡍⠛⠝⠀⠀⠀⠀⠀⣟⣆⠅⠈⠀⠁⡉⣀⡀⣀⣀⡬⡶⠋⡁⠁⠀⠀⠀⠀⠄⠈⠔⣇⡚⠊⠅⠁⠑⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠤⡊⠂⡁⠁⠁⠀⠀⠀⠀⠀⠘⠭⠯⠿⠯⠯⠴⠦⠎⣧⠫⣰⠃⠁⠀⠀⠀⠀⠀⡢⡀⢇⡏⠉⠉⠈⡑⢄⡀⠀⠀⠀⠀
⠀⢠⡤⢊⣁⠄⠁⠀⡁⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠉⠋⠍⠉⠀⠀⡀⠀⠠⡅⠰⠑⠩⠉⠡⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠉⡍⠉⠋⢕⡵⡴⢰⢄⠀⡂⠀⡀⠄⠀⠀⠀⡀⠀⠀⠀⡀⣀⡀⣐⣀⡂⢈⡄⣃⡧⡃⡃⠈⠀⠀⠈⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠂⠉⠃⠂⢂⠗⠄⠧⣔⣺⡌⠣⡁⠉⡃⠁⣍⡋⠨⡁⡁⢐⠌⡃⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠃⠀⠀⠀⡂⠈⠀⠀⠂⢈⠀⠅⠀⡡⡔⠁⠁⠀⠀⠀⡂⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠨⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁
⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀
⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀