⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠦⠢⠐⠲⠤⠤⢠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠀⠀⠀⠀⠀⠔⠈⠉⠐⢄⠀⠐⢁⠲⢫⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⠀⠀⠀⠀⢸⠀⣠⣾⣷⣾⠀⠀⠃⡀⠃⢿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⣿⠀⠀⠀⠀⠀⡆⣿⣿⣿⡟⠀⠀⠘⠀⢰⢺⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢿⠏⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⡠⠄⠀⠀⢈⡼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⢤⣤⣦⣼⡆⠀⠀⠀⠀⠀⠀⠂⣩⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⢂⠜⠡⠀⠌⡿⡏⠳⣖⣠⠒⠒⣭⢟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡈⠐⡈⢼⡊⠄⡁⢂⢱⣻⠀⠌⡆⢂⠈⢊⡔⢩⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡌⠠⢁⠐⡈⡖⠠⠐⠂⠄⢧⠷⠀⢬⠀⣄⠀⢲⢡⢣⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣼⡧⠧⠴⠤⠧⣦⠵⠬⠐⢸⣹⡀⠂⡅⠐⠡⡠⠏⣌⠶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡉⢠⡰⢀⠌⡐⢠⡀⠌⡉⢌⡼⣹⢧⡐⠈⡦⢃⠈⢞⡨⢗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⡉⢱⡼⠁⠄⣥⢷⢠⠃⡘⣷⢶⣋⠶⣹⠫⢷⣆⠠⠑⢹⢮⡛⡾⠀⣄⡀⢀⠤⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡼⢁⢢⣴⣿⡇⠌⢰⣛⡾⠒⡅⠄⢻⢾⣠⠵⠋⢈⠳⣎⢟⣻⢿⢺⣻⠥⠤⠛⢉⠁⢢⢹⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡇⢈⡺⣽⠛⢧⡐⢨⣟⠇⠠⢱⡐⢸⢾⡉⠒⠢⣌⡠⢙⣞⣯⠾⠚⠉⡀⠠⠀⠌⠢⠊⡜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣹⡀⢿⢁⠐⡈⢳⡀⡏⠠⢡⠢⠽⣸⡏⢁⠂⠡⢀⠉⢦⡙⢂⠐⡈⠐⠠⡁⠬⠊⠀⣠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡜⠁⠳⣿⠀⢂⠐⠠⢉⠣⢁⠂⠆⠀⠉⠀⠈⠁⠒⠤⢁⠌⢞⣦⡔⣠⣁⡃⠅⡂⠔⡼⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⠁⠌⡐⠠⠈⠄⡈⠐⡀⠂⠤⢈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣶⡤⣴⠤⢧⠾⣛⢭⠳⣤⡀⠀⠀⠀⠀
⠀⠀⠀⣴⠻⠍⡐⠠⢀⠡⢈⠐⠠⠁⠄⣁⠂⢄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡅⠂⠪⠌⢑⡊⠮⡱⢆⡛⢦⡀⠀⠀
⠀⢀⡞⠁⡁⠂⠄⡁⢂⠐⠠⠈⠄⠡⠈⠄⠌⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠉⢚⡭⢎⡵⡀⠀
⠀⡾⠀⠂⠄⡁⢂⠐⠠⠈⠄⠡⠈⠄⠃⠌⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠽⣎⠶⡹⡄
⢸⠀⠌⡐⠠⠐⠠⠈⠄⠡⠈⠄⠡⢈⠐⡈⠄⡁⢂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⢣⢏⡵⣹
⡏⠐⠠⢀⠡⠈⠄⠡⠈⠄⠡⢈⠐⡀⢂⠐⠠⡐⠠⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡞⡥
⡇⠘⠠⠀⠄⢃⠘⡀⢃⠘⠠⠀⠄⠠⢀⠘⠠⢀⠃⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⢸⢣⣛
⢧⠈⠄⠡⠈⠄⢂⠐⠄⡈⠄⠡⢈⠐⠠⢈⠐⠠⢈⢸⡀⠀⠈⠀⠁⠂⠀⠤⡤⡄⠮⢄⡄⠀⡀⠀⠀⠀⠀⠀⡴⢣⢏⠶⣩
⠸⡄⠈⠄⠡⠈⠄⠨⠐⡈⢞⢤⣂⢌⡰⢠⢌⣂⡐⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢠⠁⠐⠀⠁⠀⢖⢨⡵⣋⢎⡳⡑
⠀⢳⡁⠌⠠⠁⠌⠠⢁⠐⡀⠊⠌⠓⠓⠭⢲⢦⠗⣌⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡐⣳⠭⣮⠟⠁
⠀⠀⢳⡌⠠⠁⠌⡐⢀⠂⠄⠡⠈⠄⡁⠂⠄⡉⠚⣬⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⡏⠀⠀⠀