⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⢛⣭⣭⣭⣙⣻⣶⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⢶⣤⡶⠟⣋⣩⣉⡛⠷⣦⠀⠀⠀ ⠀⠀⢠⣿⢡⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢡⣾⣿⣿⣿⣿⣦⠙⣧⠀⠀ ⠀⠀⠸⣟⠸⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⢀⣿⠀⠀ ⠀⠀⠀⠹⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠻⣿⡿⢃⣼⠇⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠸⠻⣧⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⣧⠀⠀ ⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢿⡄⠀ ⠀⣸⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⣷⠀ ⠀⣿⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⡄ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇ ⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣇ ⠀⣿⠀⠀⠀⠀⠂⢀⣠⣤⣄⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⡇ ⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣠⡄⣠⠀⣤⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⣸⡇ ⠀⣿⠀⠀⠘⠐⠄⠘⠻⠿⠟⠁⠀⠀⠀⠛⢻⡟⣻⣿⡄⢠⡀⠀⠙⠿⠟⠛⠁⡠⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠄⠀⠀⢀⣿⠁ ⠀⣿⡀⠀⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠵⠇⠀⠻⠏⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣾⠃⠀ ⠀⠸⣧⡀⠀⠀⠀⣵⡟⡛⣷⣶⣦⣄⣶⢳⡞⣦⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢀⣤⡿⠃⠀⠀ ⠀⠀⠈⠻⢦⣄⣰⣿⠟⠛⠛⢳⣮⡹⣦⠳⣜⡲⣭⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢄⠀⠀⠀⠀⠀⢀⡔⣀⣤⡶⠟⠋⠀⠀⣠⡆ ⠀⠀⣀⠀⠀⢸⡟⠁⠀⠀⠀⠀⢽⣧⣉⠛⣚⣿⠗⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠈⠐⠂⠀⠰⠿⠛⢿⡍⠀⠀⠀⠀⠸⠋⠀ ⢠⣄⢻⡄⠀⢿⡇⠀⠀⠀⠀⢠⣿⠋⠙⠛⠋⠉⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⠙⠁⠀⠀⠈⠻⣶⣤⣤⣶⣿⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠀⠀⡀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣶⠛⠛⢩⣭⣭⢩⡔⢲⣶⣶⢲⡖⣶⣬⡍⣭⣭⡝⠛⢻⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀ ⠀⣴⠞⢩⠥⣶⡮⣍⠳⣎⠶⣩⢞⡱⢺⣯⣞⣶⣳⢮⣷⣳⡎⡵⢫⣕⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⣿⣦⡘⠧⢭⡳⣌⠷⣌⡳⡱⢮⡱⣋⠷⣙⠞⣭⢳⡓⢯⡱⣿⣍⢻⡜⢿⣦⡀⠀⢀⣀⣀⠀⠀⠈⠀⠀⠀⢸⣷⠀⠀⠀⠀ ⠀⣿⠈⢹⠿⠶⣦⣭⣭⣀⣛⣛⣒⣁⣉⣈⣁⢋⣐⣃⣛⣓⣡⣭⣭⠶⡶⠟⣛⢛⣿⡛⠛⠉⠀⢀⠀⠁⠀⠀⢸⡿⠀⠀⠀⠀ ⠀⢻⡆⠀⠳⡐⠲⣄⠀⠉⠙⡍⡙⢫⠉⠉⠉⠉⠉⡩⢍⡉⠁⠀⠀⢀⡗⢌⣾⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠈⢿⡄⠀⠈⢣⠌⢲⠀⠀⠘⡌⠡⠇⠀⠀⠄⠀⠖⡠⡚⠀⠀⣠⠞⣠⡛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣀⠈⢎⠌⣆⠀⠀⡍⢆⠃⠀⠠⠀⢰⠃⡜⠁⠀⡴⢃⠜⣲⡼⢿⣆⡀⠀⢀⣀⣀⣠⣴⡾⠟⠁⠀⠀⠇⠀⠀⠀ ⠀⠀⠠⠀⠈⠙⠻⠶⣮⣬⣦⣀⣱⣌⣱⢀⣀⣀⣢⣹⣀⣤⣾⡶⠾⠛⠉⠀⠀⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀