⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⢤⣴⣶⣛⣠⡾⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣌⠻⠓⠀⢻⣽⡷⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⡟⠀⢸⣆⠀⣹⣄⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⢼⣿⡳⢽⣿⣸⠏⠳⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡳⠀⠻⠿⣸⣿⣿⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣿⡁⠈⢻⣿⣤⡾⠛⡿⠁⣤⠇⢨⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠘⡟⢦⣤⣀⣿⣯⣇⡀⠀⣠⡯⠞⡟⠁⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⣀⡤⠞⠻⢿⣄⠀⠀⢹⡌⠻⣿⣉⡀⣿⡿⠟⠁⠀⢸⣁⣀⣀⣀⣠⡼⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⡊⠙⣿⣏⠁⠀⠀⠀⠀⢹⡄⢀⡴⢣⠀⣿⠿⠿⣿⠀⠀⠀⠀⠈⠳⣖⡛⢉⣡⡤⠤⠤⠝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⠖⠋⠻⡄⠀⠙⢷⠀⠀⠀⢀⣠⠟⠉⠀⠘⡶⣿⣾⡿⣿⠀⠀⠀⢀⣠⠄⠸⣭⡟⠉⠓⢤⣰⡄⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣢⣖⢻⡄⠀⣼⡇⣰⡾⠋⠀⠀⠀⠀⢰⠇⣿⣿⣷⣿⡀⠤⠖⠛⠀⢠⣶⡛⠓⠒⢲⣄⡈⢷⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠈⠁⠈⠳⣧⣤⡼⠋⠁⠀⠀⠀⠀⠀⠀⢸⠉⢸⡏⠉⣿⠁⠀⠀⠀⠀⢻⡿⠛⠲⢴⣀⠀⠹⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⣇⠀⣿⠀⠀⡀⠀⠀⣞⣖⣄⣠⣎⣈⣹⡼⡿⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⢹⠀⢸⠾⠑⣟⠀⠀⣧⠀⠀⠈⠙⠛⢻⡿⡿⠧⠾⠃⠀⠉⠉⠑⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠐⠺⠶⢼⣧⣼⣿⣀⣤⢽⣄⡤⣤⣤⠾⠋⠀⣽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⣺⠟⡿⢤⣄⣠⡿⠙⢷⣄⣄⡀⠀⢀⣀⣤⣦⠤⡿⠁⠀⠈⠙⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠻⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡋⢁⣠⠞⠁⡼⠁⠀⠀⠀⠀⠀⣼⠋⡟⠙⠛⠉⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⠗⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⡾⠁⢰⠁⠀⠀⠀⠀⣠⣶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡷⣀⠀⣠⠖⠲⣄⣹⡄ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⢀⡞⠀⠀⡟⠀⠀⠀⢤⣾⣿⠇⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⠀⠀⠈⠀⢇ ⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣿⣇⡤⢼⡆⠀⠀⠠⠟⠁⣯⡀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⣠⣸ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠒⠿⠁⣿⣳⡀⣸⢧⣀⠀⣀⣤⠖⢧⣿⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣻⡟ ⠀⠀⠀⠀⠀⠸⣾⡆⠀⠀⡠⠤⠴⠚⡇⠀⠀⠀⠀⠀⢿⠋⠈⡇⠈⠳⠴⠆⠀⠘⣏⠙⠛⠒⠲⠤⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣤⠼⠃⠀⠀⠀⢹⡀⠀⠀⠀⠀⠘⣆⠀⢹⡄⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⡼⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⣿⠀⠈⢷⠀⠀⠀⠀⢸⡄⣇⠀⠀⠀⢸⠁⠀⢸⣿⠉⢢⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢴⡦⠤⢧⠀⠀⠀⠰⠛⣿⠀⠀⠈⡆⠀⠀⠀⢸⡇⢸⠀⠀⠀⡏⠀⠀⢸⠋⡇⠀⠟⠀⠈⠁⠈⢳⣾⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣄⣠⡤⠾⣇⠀⠀⠀⢷⠀⠀⠀⢸⡇⢸⠀⠀⠀⣷⠀⠀⡟⣰⠃⠀⠀⠀⠀⠀⠀⢨⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡿⠋⠀⠀⠀⠀⢿⠀⠀⠀⢸⠀⠀⠀⠠⡇⢸⠀⠀⠀⡇⠀⢰⡟⠃⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠹⣆⣀⡀⠀⠀⣾⡄⠀⠀⠸⣤⣀⣀⡤⠷⣾⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⣛⣽⠿⠿⠿⠛⠛⠛⠋⣿⠃⠀⠀⣠⣯⣏⡼⠀⠀⣇⣀⣀⣴⡇⠀⢸⣀⠀⢀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡞⠁⠀⠈⢳⣤⡶⣋⡤⠚⢻⡇⠀⢸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣤⣀⠀⣧⣤⣤⣤⣾⠟⠋⠁⠀⠀⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢀⣀⣠⠴⠞⠉⠀⠀⠀⢨⠟⣁⡴⠿⠥⣀⡀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣆⢿⠀⠀⠀⠈⠉⠑⠒⠶⠤⢼⡄⠴⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⡄⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠉⠙⠒⠦⢤⣄⡀⠀⠀⠀⠈⣧⢳⠀⣠⡤⠚⠋⠁⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⣄⣀⠀⠉⠙⠓⠒⠀⠈⣮⣏⠹⡄⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⡀⠀⠘⣜⣦⣷⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣯⣕⣲⣿⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀