⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⡏⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠢⠤⣄⡀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⣿⠃⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠱⣶⣤⣴⠋⠀⠀⠀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠈⢹⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣽⢋⡭⠛⠛⠒⠵⠤⣤⡤⠴⠒⠳⢄⡀⠀⡏⠀⠀⡼⢿⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⡞⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢙⡆⡇⠀⢀⠇⠀⠙⢦⡀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠀⠀⣠⣾⢷⣄⡀⠸⣧⡀⠀⡴⠋⠀⣧⠀⢸⠀⠀⠀⠀⠉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣒⠲⠤⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⡇⢠⣷⠶⣤⡀⠁⠀⢷⢶⣶⠋⠀⢸⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠀⠈⠉⠛⠳⣄⡀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⢸⡝⠉⠙⠻⣄⠀⠈⠣⡏⢣⡀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⣤⣶⣦⠀⢀⣀⠀⠀⠀⠉⠲⣼⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢰⢸⠁⠀⠀⠀⠈⢣⡀⠀⠘⢦⡙⢦⠀⠉⠑⠲⠤⣄⡀⠀⠀⠀⠀⠀⡴⠋⡄⢀⣾⣿⣿⡿⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠘⡆⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⠀⠑⣄⠀⠀⠀⢀⡗⠀⠀⠀⠀⠸⡁⣠⠤⣌⡻⠿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠸⡀⢣⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠈⠳⣄⢀⡞⠀⠀⠀⠀⠀⠀⠳⡙⠲⠤⣙⡦⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠈⢺⣦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠒⠪⠭⢖⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣀⢤⡤⠒⠚⠙⢉⡖⠤⣀⠀⠀⠀⠀⠀⠃⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢱⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠙⢯⡒⢤⣄⣀⠀⠀⠀⢀⣠⠬⠽⢗⣂⠀⠀⠀⢸⠆⠀⠀⠉⠒⠤⣄⣀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠚⠀⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠙⢿⣖⣤⣍⣏⣩⡟⠱⣁⠔⠒⠈⠑⢖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢢⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀⠀⠤⠤⠤⢄⣙⣿⣯⡓⠎⢿⣄⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢀⠀⠀⠈⢎⠆⠀⡌⠀⠀⠀⠀⢀⡠⠤⠒⠂⠉⠉⠉⠑⠒⠢⢤⣀⡀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠾⣦⡀⠙⠿⣢⠤⣀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⡱⡀⠀⠀⠀⢠⡇⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠉⠉⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⢀⠎⠇⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣦⡀⠀⠀⢸⡀⠀⠀⡎⡝⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢖⡲⠀⠀⠀⡎⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠈⢪⢻⢦⡀⢸⢧⠀⠀⠉⠀⢀⠴⣲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠱⣳⡹⡄⡿⡀⠀⠀⠐⠕⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢣⢹⢣⠃⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠛⣾⢿⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣈⠆⠀⠀⠀⠀⠀⣏⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢧⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡇⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣸⠀⠀⠀⠀⡎⡆⠀⠈⠓⠦⢄⣀⡀⠀⠀⡰⠁⠈⢣⡀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠁⠀⠀⠀⠑⢄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠱⡖⣦⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢯⠉⠙⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢇⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠒⠒⠤⠤⢄⣀⣀⣀⡠⠤⠔⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⠈⠉⠁⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀