⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⣀⠀⢀⣠⢄⠀⢀⡠⢤⠄⠀⠀⠀⠀⠀⠀⠀⡖⠒⠦⣤⠎⠀⠱⠊⢉⣇⣀⣀⣀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠈⢠⣠⡍⢳⠋⠀⠸⠋⠁⠠⠾⢲⡶⠦⣆⡀⠀⢰⡒⠷⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠼⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠛⢓⡤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⣓⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢧⣄⠀⠀⠀⠀⠀⣠⢲⣍⠉⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⡤⠤⢴⠏⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣘⣏⣄⣤⣤⣤⣴⡇⠠⠸⠤⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡽⣛⠧⠤⠄⠀⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⡉⠛⠄⣁⠰⠀⠀⢠⢤⠔⡀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠴⠚⠉⠠⢤⠤⡄⠀⠀⣤⠀⠀⠘⢦⠀⠀⠀⠀⢀⣼⡃⣙⠖⠂⠀⡄⠿⣗⠀⠠⠬⠲⠰⠐⡈⢟⢢⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⢸⠀⣟⣛⡶⣿⠀⠀⠀⠈⡇⣼⣿⣿⡇⠠⡀⠀⠀⠁⠀⠶⣩⠑⢉⠤⡄⠮⣽⠃⠹⢀⠓⠁⡝⢦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠫⠋⠀⠀⡅⠀⠑⠶⡀⡦⡉⠀⠘⠀⣀⡀⢘⣀⡀⢠⣈⠀⠁⠈⢷⣄⡀⠀⠀
⠀⠀⣀⠀⠀⢸⠉⡇⢸⣰⣷⢸⠉⡇⣾⠉⢳⢸⣋⣿⠘⣴⡶⢂⡲⡢⢅⡶⠀⡄⣨⣯⣐⣦⣁⡽⡧⣌⢢⠁⠂⠍⡆⠐⣴⣇⣀⣀⠀⠀
⠀⠀⠹⡄⠀⠘⠀⠃⠸⠁⠛⡿⠶⢷⠛⠲⠋⠸⠀⠘⢄⠈⣷⣼⠷⡽⣧⡫⡿⣭⣳⣰⢢⣷⣬⣀⡻⣳⡱⢶⣀⢱⠄⠰⠂⡁⣰⠏⠀⠀
⠀⠀⠀⠈⠳⢦⣤⠀⣀⣀⣀⡀⣤⣤⠄⠶⠆⠐⠚⠛⠛⠛⠑⠛⣧⡛⣹⣦⠁⣏⡿⠋⣸⡿⢴⠭⢿⢁⠁⢘⠙⣆⡀⠀⠄⠃⢹⠤⠐⠀
⠀⠀⠀⠀⡰⠊⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡷⡧⣸⣯⢷⢩⣄⣰⠂⠐⠀⠑⢸⠹⢤⠘⣆⠼⣆⠒⢠⠰⡃⠀⠀⠀
⠀⠀⠀⠀⠋⢩⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣬⠿⣗⣗⠍⠂⡁⠰⠛⠒⡒⡋⠲⢈⣸⡏⠹⣩⠐⣀⡟⠄⡀⡠⠞⠓⠃⠀
⠀⠀⠀⢰⡒⠋⠉⠙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠉⢋⠛⢿⣳⢯⡆⣗⠛⠁⢀⠸⠴⣳⠒⣳⠐⠋⢳⠊⠀⣨⣟⣒⠀⠀
⠀⠀⢠⣔⠓⠀⠀⠀⣄⣤⢄⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠈⢻⢡⠠⣿⡀⣥⠄⠀⢀⢹⡶⠋⠀⠁⣍⠐⢰⡗⠋⣡⡆⠀
⠀⢀⡴⠋⠉⠀⠀⠀⠀⠚⣻⡼⠙⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⣺⠈⢓⣤⡋⠧⣤⡓⡀⢯⣻⢠⢩⣂⣩⠶⠾⢍⣩⣿⡆⠀
⠀⠻⣤⠖⠀⠀⠀⠀⠀⠀⢩⠃⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠆⡺⠀⠘⡶⠥⡨⢤⡄⡉⠠⡍⢧⡼⠮⠽⠆⠀⠀⠙⠈⠁⠀
⠀⠸⠁⣀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡄⠀⠀⠄⣤⡠⢌⠠⡄⢀⣠⣹⠷⠿⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠙⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣧⢶⢆⠐⠋⣟⣠⠁⠀⠰⠺⢇⣀⣠⡴⠂⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡤⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠹⡗⠑⠠⡤⠄⣛⣵⣬⠱⣸⠄⠐⠧⣟⣀⡤⠀⠀⠀⠀⠀⠀
⠀⠀⢨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⣸⠦⠏⠉⠀⠀⠀⠀⠀⠀⠀⡗⠚⡆⠀⡦⡥⡤⣤⢤⢏⠈⠤⠖⠀⠘⠀⠀⡀⠀⠀⠀⠀
⠀⠀⠿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣖⣅⣀⣀⣄⣀⣀⣠⣠⣀⣀⡐⠮⡽⠴⠞⠓⠲⠄⠀⠀