⠋⠁⠉⠉⠈⠀⡾⣽⠛⢻⡽⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠁⠉⠁⣾⡿⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠨⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡲⢦⡙⢮⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢃⡼⢡⣟⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀ ⠀⠀⣠⣴⣶⣤⣤⣈⣙⡦⢻⡌⢯⣃⣤⣌⣥⣴⠒⠲⠶⠶⠤⣤⣀⣀⣀⣬⣭⡟⢰⣟⣀⣀⣈⣭⣭⣭⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⡇⢿⠉⠛⠒⠺⠟⠶⠚⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⣾⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⡈⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡿⠀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠂ ⠀⣠⠞⣿⠁⣀⠀⠐⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠄⠀⠀⣹⣟⠻⣆⠀⠈⠛⣦⠀⠀⠀⠀⠀⠀ ⠴⣫⠞⡥⠋⠽⠂⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠛⠉⠀⠀⠀⠂⠩⠗⠈⠳⣌⢳⡄⠀⠻⢀⡀⠀⠀⠀⠀ ⡞⠁⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⡀⠘⣦⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⢷⣴⠤⣄⣀⡀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⢠⡞⣡⣿⡤⠄⠀⠀⠀⠀⠀⠀ ⢦⡝⢲⣄⣈⣩⠔⡫⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⢤⡀⠀⠀⠘⠢⠤⠄⣱⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⣾⠁⠀⠀⢸⡁⠀⠸⡀⠀⠀⠀⢀⣐⡤⠖⠒⡒⠲⢤⣀⠀⠠⠀⠀⢀⡿⠀⢹⠀⠀⠀⠀⠀⠀⡇⣾⠃⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀ ⠀⡧⣿⠀⠀⠀⠀⠈⠓⢚⡨⠛⠉⠉⠉⠀⠀⠀⢰⠁⠀⠀⠈⠉⠓⠒⠒⣯⡀⡴⠋⠀⠀⢀⣀⣀⣀⡇⣿⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀ ⠀⢣⣹⠦⣤⣀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠒⠀⢳⡀⠀⠀⡀⠀⢀⣠⡽⣻⡿⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⢫⠟⠀⢠⠃⠀⠀⠀⠀⠀⠂⡀⠀⠀⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢳⡀⠀⢹⣋⣭⡶⠛⠉⠀⠀⠙⠙⠿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠐⣯⣿⡄⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠈⡇⠀⣠⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⢹⢸⠃⢸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⢠⣇⡄⢸⢹⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣸⡄⢸⡇⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣼⡼⠀⡜⣿⣇⣤⠾⣋⣭⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡏⣧⠀⣷⡄⡀⠘⢷⣄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡀⠰⠇⢀⡼⡽⠁⢰⣰⣟⣿⠖⠋⢁⡟⢙⣀⣠⠤⠤⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡹⡆⠉⢷⣅⠄⠀⠈⠉⠓⠒⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡴⠟⠈⠀⢀⠏⡽⠋⠀⠀⠀⠸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠈⢷⣹⡄⠀⠙⠳⢤⣀⣀⡀⠀⠀⠀⠀⣁⣀⣀⣤⠶⠟⠉⠀⠀⠀⢀⢞⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⡟⣻⡌⡀⠀⠀⠈⠉⡏⠉⠉⠉⠉⠉⠉⠀⣼⠀⠀⠀⠀⠀⢠⢯⡾⠐⠦⢄⡀⠀⠀⠀⠀⠀⠴⠒⠁⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⢀⡿⣰⠋⠁⠀⠀⠀⠀⠰⠧⠖⠚⠙⠲⠤⢤⣠⠿⠀⠀⠀⠀⠀⢨⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜ ⠀⠀⠀⠀⢸⡇⣇⠀⠀⢀⡴⢙⣗⣲⣶⣶⣤⣤⣤⣤⣴⡶⠶⠶⢦⡀⠀⠀⠘⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀ ⠤⠀⠀⠀⠘⢷⣝⠳⠚⣋⡴⠟⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⣝⣷⣦⡶⢋⣙⠛⠶⣄⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀