⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢈⠉⠐⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠐⠄⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢠⠄⠐⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠈⢧⠀⠀⠠⡈⠑⢄⢄⠁⠀⢁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠓⡄⠀⠀⠀⠱⡄⠀⠀⠬⠀⠣⡁⠀⠘⢆⠀⠄⠱⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⢀⠀⡀⢦⡀⠁⠘⡄⠀⠀⠀⠑⡄⠀⠀⠀⠀⠘⢆⠀⠈⢗⢄⠠⠈⠃⢄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠈⠀⠀⠀⠀⠀⠀⣋⠀⠀⢀⠀⠀⡇⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠉⠙⣏⠒⠂⠀⠘⡄⠀⠀⠀⠀⠈⢦⠀⠈⡆⠢⡁⠐⡄⠁⠤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠬⡀⠀⠀⠀⠀⠀⠀⢆⠀⠐⠀⠂⠀⢱⠀⢀⡤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⢸⡳⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⢧⠀⢱⠀⠘⡄⠰⡀⠀⠀
⠀⠀⠀⠀⢀⠔⡡⠒⡠⢄⠐⢄⠀⠀⠀⠈⠀⢠⠀⠀⢂⠀⢀⣼⡞⠁⠀⠀⢿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣇⠘⢦⠀⠀⢹⢢⡀⠀⠀⠀⠈⣇⠀⡄⠀⠈⡄⠁⠀⠀
⠀⠀⠀⠔⡡⠘⡄⢃⠔⢂⠆⠈⡆⠀⠀⠀⠀⠘⡄⠀⠀⠰⠋⠀⡷⡀⠀⠀⢸⣱⡀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⡟⡄⢸⣀⠀⠱⡄⠀⢧⠘⢦⠀⠀⠀⠈⡆⡇⠀⠀⠘⡄⠀
⠀⠀⠈⡰⢁⠒⡈⢄⠊⡔⡸⢰⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠙⡄⠀⠀⣇⠹⡄⠈⣦⠀⠀⠀⠀⠀⠀⠀⠸⣽⣭⣧⣤⣦⣽⣶⣾⡀⠂⠳⡄⠀⠀⠘⡇⠀⠀⠀⠃⠀
⠀⠀⡀⠡⢌⠂⠡⢂⠡⡰⠃⢸⠀⢣⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡀⣙⣤⢒⣹⣴⡝⢆⠘⡦⡀⠀⠠⠀⢀⠀⠀⡇⢣⣧⣶⣶⣤⠈⢆⡆⠀⡇⠈⢦⠀⠘⠇⠀⠀⠀⠀⠀
⠀⣀⢨⠴⠒⣀⠀⢋⠀⣈⠁⢃⠀⠘⡀⠀⠀⠀⠀⠈⠣⡀⠀⢀⣠⣷⡿⢿⠻⡉⢣⡀⠀⠱⢜⢟⢤⡀⠅⠈⠆⡀⢸⣼⣿⣿⣿⣿⣧⠈⠇⠀⢰⠀⠀⠳⡀⣧⠀⠀⠀⠀
⡭⠂⠁⠀⢸⠀⠠⡀⠐⡀⠡⠈⡄⠀⢣⠀⠀⠀⠀⠀⠀⢹⣾⠛⠋⢩⣾⣿⣿⣿⣦⣧⠘⡀⢀⠛⢦⡙⠺⣀⢐⠰⣸⢸⣿⣿⣿⣿⣿⡆⠀⠀⠸⡀⠀⠀⠱⡇⠱⠀⠀⠀
⠀⠀⡇⠀⠀⠀⠀⠈⡀⢡⠀⡇⢁⠀⠘⡄⠀⠀⠀⠀⠀⠀⢣⠙⠢⣾⣿⣿⣿⣿⣿⡌⠳⠄⠈⡄⠐⡀⡀⠠⠙⠦⡙⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⢣⠀⠀⠀⠉⠀⠱⡀⠀⠀
⠀⠀⠰⠀⠐⡄⠀⠀⠰⢀⡠⢁⠔⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⢇⠀⠸⣿⣿⣿⣿⣿⡗⠀⠘⡀⠐⠂⠡⠀⠀⠀⠐⠀⠀⠀⠙⠛⠛⠁⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠈⢔⠠⠀
⠀⠀⠀⠂⠀⠈⢁⠀⠈⣁⠠⠁⠀⣀⡀⣈⣆⠀⠀⠀⠀⠀⠀⠈⢇⠀⠙⢿⣿⣿⠟⠁⠀⠀⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢱⠀⠀⠐⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⡄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢣⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠐⢆⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡈⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠑⢄⡀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡉⢄⡙⠦⡀⠀⠀⠀⠀⠈⠐⢤⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⠂⠠⢰⠏⡱⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢚⣡⠦⠗⠚⠲⢴⡂⠍⠦⡀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡄⠀⠀⠀⠀⠀⡞⠰⠨⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠒⠒⠒⢠⡉⠁⠀⠷⡚⠋⠁⠀⠀⠀⠀⡆⠙⣆⠒⡨⠳⢄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢇⠀⠀⠀⠀⠀⡏⡡⢃⢆⢭⣦⡀⠀⠀⠀⠀⠀⠠⣀⠈⠓⢄⠀⠀⠀⡆⠔⠋⠀⠀⠀⠀⡌⠉⠁⠐⢣⣀⠘⢦⡑⠰⡈⡙⠦⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡧⢑⠞⡰⠉⠀⠈⠓⢄⠀⠀⠀⠀⠈⠑⢤⡀⠙⠢⡀⠸⡀⠀⠀⠀⠀⠀⠇⠣⡀⠀⠀⢀⠑⢌⢣⡁⢆⠡⢒⡈⠍⡒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⣇⢛⠀⠃⠀⠀⠀⠀⠀⠈⠒⢄⢀⠎⠢⢄⠈⠛⢔⠨⠕⣹⣄⠀⠀⠀⠀⣘⣄⠐⠀⠀⠀⠀⠈⢆⢹⡄⠃⢆⡘⠰⡈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡄⠀⠀⠀⠀⣇⢪⢸⠀⠀⠀⢄⠀⠀⠀⠀⠀⡇⠀⠈⠆⠱⡀⡀⡁⠐⢂⡼⠁⠀⠀⠀⠡⡀⠐⠤⠀⠀⠀⠀⠸⣀⢱⡈⠆⢨⠡⡘⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠅⠀⠀⠀⠀⡇⢾⠀⡄⠀⠀⠀⠉⠢⣄⠀⢰⠁⠀⠀⠘⠀⢣⡁⢸⠁⠀⠀⢣⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⢸⠈⢢⠳⣌⠢⢁⠆⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠧⠌⡆⢇⠀⠀⠀⠀⠀⠀⠑⢌⡆⠘⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢩⠂⠀⠐⠁⠀⢨⠄⠈⠳⡌⠰⢀