⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⠉⠉⠛⠻⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⢀⣤⠆⠀⠀⠀⠀⠀⠙⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢹⣟⣚⠓⢸⡏⠀⣶⢦⡀⠀⣠⣄⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠉⢳⡀⠀⠀⠀⠀⠀⢠⣿⣿⣟⢻⡾⣿⣟⠿⠿⣿⡿⠿⣿⠿⣿⣿⣿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣶⠾⠛⠋⢉⣀⣤⠴⠚⠋⠹⡄⠀⠀⠀⠀⣿⣿⣿⣿⠘⡿⢿⢿⠀⣼⣿⡇⠀⢈⣧⡱⠸⣏⢀⢹⡈⢿⡇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⠛⠋⢁⣀⣤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠙⣆⠀⣿⣿⣿⣿⣿⣿⠀⠿⣿⣾⠀⣿⡿⡷⢆⡼⠈⠙⠂⠁⠈⣧⣳⢸⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⠙⢿⣿⣿⣿⠀⢠⣿⠟⠀⢻⡇⢀⠏⠀⠀⠀⠀⣀⠀⢹⡈⠿⡟⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣴⣾⣿⣿⣙⣲⣿⣏⣀⡀⠘⢧⡞⠀⠀⠀⣀⣤⠞⠀⢸⠸⣄⠁⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣷⡄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣹⣿⣿⣿⣿⣈⣿⠏⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⣌⡛⠻⣖⣃⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣦⠀⠳⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⠛⣿⠲⣶⠒⢯⡉⠙⠛⠛⠛⠛⠉⣹⣿⡇⠀⢹⠛⢻⣿⡿⠿⠿⠿⠿⠿⠿⣷⣲⠀ ⠀⠀⠀⠀⠻⣧⠀⠹⣄⠀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠛⠉⠀⠹⣿⣿⡇⠀⠀⣿⠸⠈⢹⢦⡙⢦⡀⠀⠀⠀⡾⣷⣻⡇⠀⢸⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠆ ⠀⠀⠀⠀⠀⠹⣷⣠⣾⣯⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⣿⠀⠀⢸⠀⠙⣷⣈⠲⣄⣸⠇⣿⢹⣇⠀⠈⡇⠀⣿⠇⠀⢀⣀⣤⢠⣤⣤⣿⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠠⣿⠀⠀⣾⢠⠀⠈⢿⣷⣄⠙⢦⡙⢼⣿⠀⡇⢧⠀⣿⢸⢩⣭⡄⢸⡞⠛⠛⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⡇⠀⠀⣿⡼⠀⠀⠀⣿⣿⠳⣄⠙⠾⣿⣇⠸⠸⣶⣿⣸⢸⡯⣥⢼⢷⣿⠇⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠀⠀⣸⠿⠃⠀⠀⠀⣿⣿⠀⠈⢻⣶⡛⣻⣆⠀⠈⠻⣿⣾⣷⣿⣿⣿⣷⣾⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡇⠀⢎⡴⠃⠀⠀⠀⠀⠀⣸⣿⣃⣀⣀⠙⠻⣧⡈⠳⣬⣀⡿⠟⠛⠛⠛⠛⠛⠛⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣧⠖⠋⠀⠀⠀⢠⣾⣿⠛⢹⣿⠉⠉⢿⣆⠀⠈⠻⣦⡈⠻⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢷⣴⡿⠟⠋⣿⣿⣿⣿⣿⣇⡆⠀⠀⠀⢀⣾⣿⠏⠀⢸⣿⠀⠀⠘⢿⣷⡄⠀⠈⢻⣦⡈⢢⡀⠀⠀⠀⠀⢰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠇⠀⠀⢰⣿⣿⠆⠀⠀⢸⣿⠀⠀⠀⠀⠙⡇⡀⣀⣸⣿⣷⣀⠙⠢⣄⢀⣀⣸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣀⣸⣇⣁⣤⣤⣤⣼⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠘⢯⣡⡽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⢀⣄⡸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠿⢿⣿⣛⣻⡿⠿⠭⣽⣿⣿⣛⢉⣉⣬⠭⠭⣽⡗⢶⣿⣿⣿⡞⠛⠉⠁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⢠⣿⠃⠀⠀⠐⠿⡟⣿⣿⠁⠀⠛⠀⠀⠀⢿⡷⣽⣿⣿⣿⡇⠀⣦⡄⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣴⡿⣫⠄⠀⠀⠠⠙⢻⣿⣿⠀⢀⣰⡧⠀⣤⣴⣿⣿⣿⣿⣿⣷⣴⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⡋⠀⠗⠁⠀⠀⠀⠈⠀⠈⣹⠀⠐⣋⣏⢌⣸⣿⣿⣿⡏⠻⣿⣿⣯⡿⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢻⠈⠈⠉⠀⣠⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢨⠀⠁⠀⠠⣼⣿⣿⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⣿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⡇⣂⣼⣿⣿⣏⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠹⡇⠉⣀⣽⠭⠥⠴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠁⢀⣀⣠⡤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⣀⡤⠤⠤⠴⠶⣿⣷⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣶⠾⠋⠁⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⣀⣠⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀