⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠁⢸⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡄⢸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢿⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠉⠉⢡⣼⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣾⠲⣄⠈⠻⣦⣀⡶⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢸⡀⠈⠀⠀⠈⠻⡇⠀⠈⡇⠀⠀⢶⣤⡀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢸⠱⢤⠀⠀⠀⠀⠻⡀⠀⢿⡄⠀⢸⠀⢹⡆⠀⠀⣀⠀⠀⠀⢭⡙⠦⣾⠋⠉⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⠘⠻⣄⣺⠀⢸⡇⠀⢸⠈⢻⡀⠀⢘⡙⣷⡅⠀⠀⠀⠢⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠜⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠛⠻⣿⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢳⡀⠀⠀⠙⢿⠀⢸⣧⠀⢸⠀⢸⡇⢸⡏⢹⡟⡇⠀⠀⠀⠀⠘⢂⠙⢦⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃ ⢳⣤⣀⣀⠀⠠⠄⠸⡆⠀⠀⠀⠀⠀⢱⡀⠀⠀⠈⣧⠀⠻⣇⢸⠀⢸⡆⠈⡇⢸⣯⡁⠀⠀⠀⠀⠀⠀⠑⡀⠳⣄⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢦⡄⢸⠀⠀⠀ ⢸⢼⣿⣟⣛⡻⢷⣶⣶⣤⣀⣀⠀⠐⠚⠇⠀⠀⠀⠘⡀⠀⠘⢻⡆⠀⣇⠀⡇⠘⣿⣿⠀⠀⠀⠀⠀⠀⠠⡀⣦⣸⣟⣷⡤⣤⣤⣤⣤⣤⠶⢶⡶⠶⣤⣀⣠⡶⣤⣶⣾⣁⢤⡉⠀⠀⠀⠰⠖⠒⠀⠂⠦⠤⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢠⣤⣤⡄⢰⡟⣿⠸⡇⢸⠀⠀⠀ ⡜⠐⠀⠈⠿⢿⣷⣘⡿⠿⠭⣽⣿⣷⣶⣶⣤⣄⣀⡈⠉⠀⠀⠀⠳⠀⢿⡄⡇⠀⣧⣾⠆⠀⠀⠠⡀⠀⠀⠉⣦⠠⠴⠚⢓⠲⠶⠾⣅⠉⢣⡈⠓⢲⠚⠁⣙⠶⠿⢶⠶⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⠀⣴⠲⣶⢠⡞⠙⡆⠀⡟⠉⣻⠃⢸⠀⢀⣿⠸⡇⢸⡇⡇⢸⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⢹⣯⡳⠀⠀⠀⠉⠹⣮⡉⠻⠷⢿⣿⣟⠐⠲⣦⣄⣀⣀⠙⢧⡀⢈⣽⣷⠀⠀⠀⢈⣦⡖⠉⠁⠀⢴⣾⡋⠀⠀⠀⣽⠷⠞⠳⣤⠚⣳⡾⠁⠀⠀⠈⢳⣦⠀⠉⠙⠦⣄⡀⠀⠀⠀⠀⢀⣼⠃⣿⠀⡇⠀⣿⢘⡇⠀⡇⠀⡇⠀⡇⠀⢸⠀⢸⡟⠀⡇⢸⡇⣧⢸⡆⣶⣤ ⢹⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢳⡀⣹⣆⠀⠀⠈⢻⡖⠋⠙⠻⣿⠻⢿⣷⣿⣶⣿⡟⢀⠔⠛⢃⣀⣀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠠⠈⠈⠃⠀⡀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠈⠉⠳⢄⡀⠐⠋⡇⠀⣿⠀⠁⢠⡿⠈⠇⢀⡧⠀⡇⢀⡇⠀⣸⠀⣸⡇⠀⢹⢸⡇⣿⣼⣿⣿⣿ ⢸⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⢸⠛⢦⣹⠀⠀⠀⢠⠱⡄⠀⠀⡿⡀⠀⠀⠛⢧⣿⠏⠁⠠⢴⣿⢿⣿⣿⡿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣷⣦⡀⠙⢢⣤⣷⡀⠋⠀⠀⠘⠃⠀⡀⡀⠀⢀⡄⢸⣇⣠⣿⣀⣿⣤⣴⣿⣿⣿⣿⣿⢿⣿⣯ ⢸⡄⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠸⡇⠀⢹⠀⠀⠀⢸⡀⡇⠀⠀⣷⠻⡄⠀⠀⣸⠗⠚⠋⠉⣿⠁⢿⣾⣤⣷⣤⣼⡟⣧⠀⠀⠠⠄⠉⠧⣴⣆⢠⠀⠀⡌⠀⢀⡤⠟⣿⣩⣧⣼⣿⣳⠛⣿⠒⠒⠤⢽⣿⣷⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠿⣿⡿⣿⢻⢁⣿⣿⠃⡿ ⢸⡇⠀⠀⠀⠀⠀⠸⡟⢿⡀⠀⠀⠀⡇⠀⠈⡆⠀⠀⡎⠃⢸⠀⠀⢸⠀⣇⣠⢦⠧⠑⠦⣀⡀⠈⠳⠬⢛⠿⠿⠟⣁⣴⣿⡆⡀⠀⠀⠀⠀⠀⠙⠀⢆⡀⠱⡄⢠⣷⣄⠙⠻⢿⣽⣿⣟⣀⠟⠀⠀⠀⠠⣾⣿⣿⣴⡟⢡⡄⢸⡇⢹⡇⢹⠁⢸⡇⢸⠃⠀⡏⢀⣿⢧⡇⡼⣼⢹⡟⢸⣧ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⠀⠀⣇⠀⠀⡇⠀⢸⡇⠀⢸⡀⣿⡇⡸⠰⢏⠢⠀⠈⢅⠲⣦⡀⠀⠀⠀⢀⣠⡿⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⡜⡾⡏⣌⠀⠈⠁⠈⠉⠉⠀⠀⠀⠀⡠⠞⢁⣀⣿⠿⡇⢸⠁⢻⠀⢸⡇⢸⠀⢸⡇⢸⠀⠀⡗⢠⡟⢸⢱⡇⡟⣼⠃⣸⡗ ⠘⠋⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠘⢇⣀⣸⠀⠀⠸⣄⡈⠃⠀⠀⠹⣽⡗⠁⢀⣈⠑⢦⣦⡀⠉⠻⠝⣆⢦⣠⠿⠏⢠⠎⠳⠀⣀⣀⣀⣀⣀⣀⣀⣀⡑⡟⠇⠈⠮⣅⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣁⣍⠀⠁⡀⠀⣹⠀⢸⡇⢸⠀⢸⣧⣸⠀⠀⡇⢸⢁⡏⡜⣸⠁⣿⣠⣿⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠉⠀⠀⠒⠒⠚⠒⠒⠒⠒⣴⠏⠤⠤⣀⣺⠷⠶⢾⡟⠀⠀⠀⣘⠉⠀⠀⠀⠈⠲⣶⣟⣉⠉⠉⠉⠉⠉⠉⣛⣛⣷⡄⠀⠀⠀⠙⠦⠀⠀⠐⢀⣄⣉⣁⣄⡀⠀⠀⠉⣷⣷⠷⢶⣾⣷⣿⣷⣾⡖⠛⠿⢿⠑⣶⣧⣼⣾⣿⣿⣿⣿⣿⣿⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠐⠂⣀⣤⠾⠕⠒⠐⠀⠀⠀⠀⠈⠙⠻⣿⠀⢀⡀⢴⣿⠟⠋⠉⠀⠀⠀⢤⠤⣶⣼⣁⠀⠠⠿⠉⠉⠉⠙⠒⣶⣿⣿⠉⠙⠲⠶⢯⣿⠀⢠⠃⠀⣦⣿⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡼⠿⠳⠀⠀⠙⠓⣲⡒⠒⠛⠃⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣽⠟⠁⠀⠀⠀⠀⠀⠀⠖⠠⠤⠤⢄⡉⠠⠤⠤⢤⣤⡖⠋⠀⣼⡟⠀⠀⢰⡄⢠⣿⢀⣿⣶⣿⡏⠁⠀⣸⣿⡿⠿⠟⠛⠛⣻⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣻⣭⠵⠶⠿⠚⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠻⠃⠀⠀⠀⠀⠀⠀⠀⠤⠂⠒⠒⠐⠂⠈⠛⠻⠘⠋⠀⠀⢀⣜⣛⠳⠤⣤⣸⡇⠸⢟⡿⠛⠉⠉⣩⣤⠾⠛⢽⠁⠀⠀⠀⠀⠀⢈⣿⣿⡗ ⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⣥⣤⣤⢶⡒⠛⢉⡠⣴⣺⠿⠒⠓⢂⡠⣄⣀⡀⠀⠚⠩⠐⠳⠒⠒⠭⠥⢤⡤⠴⠖⠚⠛⠛⠛⠒⠒⠤⢤⣀⠠⣗⢶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣄⠉⠉⠛⠓⠚⠛⠛⠛⠛⠛⠉⠛⠻⠀⠀⠀⡜⢀⣠⣤⠶⠂⢀⣾⣿⣿⡇ ⠀⠀⠀⠴⡆⡄⠀⠀⠀⠀⠀⠀⠤⠤⠶⠶⡿⠿⣋⠽⠚⢉⡰⠚⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⣄⣀⡀⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⠈⠻⠶⢦⣄⣤⣅⡠⢀⣀⣀⣀⣀⣀⡠⠤⠶⠖⠛⠉⠉⠀⠀⠀⠼⢿⣿⣿⡇ ⠀⢤⣰⠆⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡠⠒⣉⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠉⠛⠉⠐⠆⢱⡄⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡙⠲⢄⡲⢄⡉⠙⢯⣉⣉⠉⠛⠉⠁⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧ ⠀⢘⣿⡹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⡡⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⡸⠏⠀⠀⠀⣩⣦⡉⠒⠀⠙⢯⣳⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣨⣯⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠠⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣷⠀⠀⠀⠀⠈⠢⣄⠀⠀⠈⠓⠤⣀⠀⠠⣒⢒⠈⠉⠀⠀⠀⣿⡁⠀⠙⠓⠒⠠⣌⣳⣄⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⢸⣿⣳⢐⢛⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⢀⣀⣤⠤⠚⠁⠀⠀⠀⠀⢠⣂⣠⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⣀⠀⠀⠀⠐⣠⡾⡇⢀⠀⠀⠀⣿⡌⠄⣄⠀⢢⡀⠀⠙⣄⢄⢠⠔⠤⠭⣻⠔⠃⠀⠀⠈⠒⢤⣽⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠐⠂⠘⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⣏⡑⠀⢊⡇⠀⣋⠅⠋⠀⠀⢀⣠⠤⠖⠚⠉⠀⢀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠖⠪⢦⢤⣀⠀⠀⠀⠀⠈⢁⠤⠋⠤⡰⠋⡴⠁⠀⡌⠀⠘⢸⢹⠘⡄⣜⣦⣄⣣⣰⡘⣾⣿⣯⢍⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⣠⣴⠶⠒⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠ ⠇⠟⡇⡄⡣⢀⣣⠦⠷⠖⠒⠒⠚⠁⠀⠀⠀⠀⠲⣽⠂⠀⠀⢒⣀⠬⠟⠦⡀⠀⠀⠀⠻⣿⠿⠗⢤⡔⣀⡦⠀⠀⣀⣀⡠⠎⢠⠀⠀⣀⣰⠃⠈⡆⣧⠙⣌⢛⢇⠑⡁⢹⡄⢣⡈⠁⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠙⣇⠀⠀⠀⢀⡤⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢮⠞⣧⣶⣾⣥⡁⠒⢀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠀⠀⣴⠿⠚⠎⠳⢄⣀⠀⠀⠁⠸⠶⠿⣯⣄⢴⣪⢗⣫⡴⠶⠃⣀⠖⢹⠏⡀⢸⢧⠘⣦⡘⠒⢆⠑⣄⠈⢾⡀⠑⢆⠲⣄⠀⠙⠦⠈⠉⠁⠀⠀⣰⣾⠟⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣁⣲⠿⡫⢅⣶⠷⣬⣀⡀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡠⢎⣡⠶⠈⠑⠀⠀⠀⠀⠈⠉⠁⠞⠉⠉⠁⣴⡷⠟⢡⢄⠎⢀⡇⢸⠈⠳⡹⣿⣖⣮⣳⣌⣦⣰⡝⠶⢌⣑⢮⠳⠾⠀⠁⠀⠀⠀⣬⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⣿⡀⡐⠈⠉⠙⠳⠞⠻⠂⠉⠉⠉⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠻⡴⠚⣁⡤⠖⠛⠀⠀⠤⠊⠁⠀⢀⠄⢀⡴⠋⠉⠀⣠⠃⡞⠀⠘⠀⢸⠀⡄⠹⡙⠞⢯⠃⠙⢿⡍⢧⠈⠀⠁⠀⠀⠀⠀⢀⣀⡐⠶⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣽⡾⡟⣷⠈⡈⠀⡀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠁⠈⢁⣤⡴⠒⣀⡴⠊⡡⢪⠖⠁⠰⠁⠀⠀⢀⡜⠁⠘⠀⠀⠀⢰⠈⠀⠉⣆⠹⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣄⠉⠻⣦⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡜⠾⠻⠙⠿⢿⢻⣟⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⣁⢔⣿⠿⢥⣿⣿⠿⣦⠾⣤⣄⢀⡠⠋⠀⠀⠀⠀⠀⠀⠃⢤⠀⡄⠘⡄⠁⠈⠑⠀⠀⠀⠀⠀⠀⠀⠠⡤⠔⠁⠈⣧⡀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡑⠁⠀⠜⠐⠀⠜⠻⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢟⣥⢋⣠⡤⠄⠀⣀⠀⠀⢀⣤⠿⢛⠃⠀⠀⠀⠀⠀⠀⠀⢠⠾⠸⠳⠀⠃⠀⠀⠀⣄⣠⣤⣴⡶⠚⠛⠛⠛⠳⣤⣜⠛⢿⣧⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢏⠊⠒⠁⠉⠈⡵⠁⠁⠀⠉⠙⠻⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢚⣿⡿⢋⣠⡴⠟⠉⠉⠀⣤⡾⠋⠙⡿⠀⠀⠀⠀⠀⠀⢠⣶⡿⠞⠉⠙⠲⣄⡈⠁⠉⠻⢿⣿⠇⠀⠀⠀⠀⠒⠶⢤⣈⣙⠳⠶⣍⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⣀⠀⠀⠀⢀⢀⣿⣿⣿⣿⣶⡿⠋⠀⠀⣴⠶⢺⣟⠃⠀⠀⠃⠀⠀⠀⠀⠀⠰⣊⡋⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⣈⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⣤⣁⣀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀