⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢶⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣏⢀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣴⣾⣿⣿⣷⠀⠙⠟⠛⠿⠻⠷⠶⠶⣶⣶⠶⠶⠴⢾⣡⣠⣾⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠙⠋⠘⠿⠭⠖⠒⢦⣄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠘⠛⠿⠿⠛⢥⣀⣀⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⠑⠢⣄⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⠶⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢳⣠⣶⣾⣿⣿⣷⣦⣍⠁⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⢿⠀⠀⠀⣰⣿⡿⢋⣡⣾⣿⣿⣿⣿⣷⡀⣰⣿⠟⣡⣴⣾⣿⣿⣿⣿⡄⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⣸⠋⠉⠲⣤⡶⠚⠛⠳⢦⣄⠀⠈⠳⣄⠀⠀⢸⡄⠀⣰⣿⡟⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣟⣴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⣼⠋⠀⠀⠀⠀⠀⠙⢷⣄⠀⠘⢷⣄⢸⡟⠋⢹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡿⠀⠀⠀⠀⠀⠀ ⣿⣠⣤⣠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠹⣦⣷⡀⠐⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⡹⣿⣿⣿⣿⣿⣿⠃⠀⢸⠃⠀⠀⠀⠀⠀⠀ ⡇⢱⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⢻⣷⡀⠈⠻⣿⣷⣬⣩⣿⣿⣿⣿⠏⠀⠀⡙⣻⣿⣶⣿⣿⣿⠟⠁⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⣿⢸⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠘⢷⣄⠀⠀⠉⠙⠛⠛⠛⠉⣠⠖⠦⠞⠁⠘⣆⠀⠉⠀⠀⠀⠀⣠⡿⢁⣀⣀⣤⣤⣀⠀⠀ ⢸⡆⢳⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⠶⠛⠳⣦⣄⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢼⢇⣀⣀⣤⣶⣿⠿⢛⡽⠋⠀⢀⣀⣹⢷⡄ ⠀⢻⡼⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⠗⠒⠢⡀⠀⣮⣝⠛⢶⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⢛⣿⠁⢰⣋⡴⢊⣉⠙⢿⣯⢸⡇ ⠀⠈⢻⣆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⣿⣿⣿⣿⠆⢸⡿⣤⣄⣀⣀⣀⣀⣀⣠⣤⠴⠞⠋⢽⠀⠀⠉⣠⣿⢹⣰⣿⠿⣼⠃ ⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⠑⠒⠋⣦⢸⡇⠀⠀⠉⠉⠹⡏⠁⠀⠀⠀⠀⠀⣼⠀⠀⠈⠷⠖⣆⣨⡏⣰⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢀⠏⢸⣇⡞⠙⡆⠀⠀⡇⠀⠀⢀⠔⠋⠁⣿⠀⠀⠀⠀⠀⠈⢉⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆⡀⠀⣀⣤⣋⠀⢸⣿⠶⢠⡇⠀⠀⣿⠀⠀⡏⠀⠀⠀⣿⠀⢀⣤⠶⣞⠳⠿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠋⠉⣹⠿⠎⣿⠀⠘⡇⠀⣠⣿⠀⠀⢣⡀⠀⠀⣿⠀⠈⠀⢀⡼⠂⠀⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⠀⠀⠙⠒⣦⣿⡇⠈⢧⢀⡿⣿⠀⠀⠀⠱⡀⠀⣿⠀⠀⠀⣏⠀⢀⣰⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣠⣾⣽⡧⡀⠈⠋⢀⣿⠀⠀⠀⢠⠇⠀⣿⠓⠶⠶⠼⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠘⣟⢹⡄⠀⢠⣿⠀⠀⠀⡏⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡻⢔⣿⠋⢷⣄⠀⠙⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀