⠀⠀⠀⢠⠋⢆⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠈⢣⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠘⡄⢀⠔⠁⢣⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⡫⣹⠀⠀ ⠀⠀⠀⢱⡎⠀⠀⠀⠳⡀⣀⣀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⣓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⣸⠅⣿⠀⠀⠀ ⠀⠀⠀⠀⢧⠀⠀⢀⡴⠻⡄⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠳⣌⡑⢬⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡞⠁⠀⢠⠇⠀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⡄⡰⠃⠀⠀⠘⡄⠀⠀⠀⡈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢰⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡇⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠑⢆⡼⠋⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠈⢆⡒⠉⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡀⢇⠀⠀⠹⣄⠀⠀⠀⠀⠀⡇⠱⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠧⢄⣀⠀⠀⡠⠛⠲⢤⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡰⠁⠈⠑⠢⣀⠀⠀⠀⠀⠉⠲⡀⠀⠀⠀⠀⠀⡇⠘⣄⣀⢀⡘⣆⠀⠀⠀⠀⡇⠀⢳⢱⠀⠀⠀⠀⠀⢀⣤⠒⠊⠁⠀⠀⠀⠀⠀⢀⡥⡜⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠙⣲⡤⠒⠊⠀⠱⡀⡀⣀⠀⠀⠇⠀⡇⠀⠀⠀⠘⢦⠀⠀⠀⡇⠀⠀⢣⢧⠀⠀⠀⢠⠎⠈⠙⠓⠲⠤⣀⣠⠶⠃⠀⠀⠳⡀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⠀⢰⠃⠀⠀⠀⠀⠀⢀⠜⠁⠱⡄⠀⠀⠀⠱⣄⠹⣍⠲⡆⠀⢸⠀⠀⢀⡔⢢⡑⢤⠜⡗⠀⠀⠈⡎⡆⠀⢠⠏⠀⠀⠀⠀⠀⡰⠂⠱⡀⠀⠀⠀⠀⠱⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⡄⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⢆⠀⠀⡀⠻⣄⡘⡷⠆⠀⣘⡄⢠⠊⠀⠈⠩⡓⡸⠀⠀⠀⠀⠁⡇⢠⠏⠒⠤⣀⡀⠀⡜⠀⠀⠀⠱⡀⠀⢀⢄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣱⡀⠀⠀⠙⢞⠉⠁⠀⠀⠀⢙⣷⠤⣤⠜⡵⠁⠀⠀⠀⠀⡆⢧⣋⣈⠉⠈⠀⢉⠗⠄⠀⠀⠀⠀⢣⣠⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡞⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠑⡄⠀⠀⠈⡷⠀⠀⠀⠻⣅⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡆⣸⠁⠈⠠⡀⠁⠀⠀⠡⡀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠈⢦⣀⣼⢷⡶⠀⠀⠀⠈⠑⠦⣀⠈⢧⡀⠀⠀⠀⢠⠃⡟⠀⠀⠀⠀⠘⢄⡀⠀⠀⠘⢄⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠴⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢿⣿⣾⣀⠀⠀⠀⠀⠈⠑⠦⣝⣶⣄⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡼⣻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣰⠁⠀⠀⠀⠀⠀⢀⣠⡤⡑⠠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⢋⡴⠛⠻⣿⣿⣿⣿⣿⣯⣒⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⠋⡡⠞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣠⠞⠁⠀⠀⣼⡟⠁⠀⠀⠀⢀⠙⠻⣾⣿⣿⣿⣿⣶⣴⣦⡄⣀⠀⠀⠀⢰⣞⣡⠔⢊⣠⣦⠤⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠼⢶⠞⠁⠀⠀⣠⠂⠀⠉⠲⣄⠀⣤⣤⠶⠤⠤⢤⣀⡙⠛⢿⣿⣿⣿⣿⣤⣤⣴⡾⠿⠿⠿⠷⠂⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡒⠤⣀⣳⡀⠀⠀⠁⠀⠀⠀⠀⠈⠻⢸⡏⠀⠀⠀⢰⣿⠋⣿⣦⠘⣿⣿⣿⡀⠀⠉⣡⣾⣏⣱⣶⢲⡆⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⢪⠸⣿⣿⣿⣿⠀⠉⣿⠇⠀⠀⠀⠙⠿⣿⣿⡿⢁⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠾⣿⣦⢄⡀⠀⠙⠒⣚⣹⣿⠀⠽⠻⡀⢤⣤⣤⣤⣤⡤⢶⠛⣫⠇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⡀⣿⠴⠦⣄⠀⠀⠀⠀⠀⠀⢙⠦⣀⠀⠉⠛⠚⠿⠿⠿⠟⠛⠃⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠫⠭⠬⣄⣹⡄⠀⠻⡇⠀⠀⠀⠀⠀⣿⣄⠀⠑⠦⣄⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣵⡦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡇⠀⠙⡇⠀⠀⠀⠀⠀⠸⢿⣥⣀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣌⠆⡀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣿⠢⡀⠉⠢⣄⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⠞⢻⠀⠈⠓⠀⠀⠙⠳⣤⡤⢤⣀⡀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠀⠀⠀⠀⠀⠂⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠒⠒⠚⡇⠀⠀⠀⠀⠀⢸⠳⣄⣀⡀⠀⠉⠓⠢⢤⡀⠈⠙⠢⢄⣀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢄⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠒⢤⣀⠀⠀⠈⠑⠢⢄⡀⠀⠉⠉⠛⣒⠒⠒⠛⠒⠛⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣸⣄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⡆⠀⠉⢢⠤⢄⣀⣟⣀⠤⠤⠤⠤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠎⠘⣇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢼⣀⡠⠒⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠐⢦⡀⠀⠱⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⣾⣥⠶⢿⡇⠀⠀⠀⠀⠈⣿⠙⠓⠒⠤⢄⡀⠀⠀⠀⠀⣰⡿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⠀⠻⣦⡀⠀⠱⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⠑⠢⢄⡼⠋⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠈⢧⠀⠙⢟⢦⠀⠈⠳⣄⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠚⣧⠀⠀⠀⠀⠀⠀⢀⡼⠉⠑⠢⢄⣠⣤⠤⠼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⣄⢣⠘⣆⠀⠈⠳⡱⢄⠀⠈⠓⠢⠌⠙⠦⣀⠀⢀⢴⣿⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡌⢇⠹⡄⠀⠀⠙⢦⠓⠀⠀⠀⠀⠀⠀⠈⠙⣣⢞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣙⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠘⡄⢹⡀⠀⠀⠈⠳⠀⠁⠠⠀⠀⠀⠀⣴⣥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣉⠫⢒⡢⢄⣀⡀⠀⠜⠀⠀⠹⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀