⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⡀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠙⠦⣄⣀⡴⠋⠁⠀⠀⢀⣀⣠⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⡀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⡾⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⡇⠀⠀⠀⠀⢀⣾⣧⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣧⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡤⠤⠶⣤⠈⢧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸ ⠀⢸⠀⠀⠀⠀⠀⣼⠁⠈⢻⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠁⠁⠀⢠⣶⣿⠉⠙⡳⣤⠶⠋⠁⠀⠀⢸⣾⠇⠘⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢸ ⠀⢸⠀⠀⠀⠀⢀⡇⠀⠀⠸⣿⣿⣿⣿⣿⡶⡴⠶⠖⠶⠶⢶⣾⣿⣿⣿⣿⡇⢀⣀⣠⣿⡿⣧⠀⠀⠀⢹⡆⠀⠀⠀⢀⡾⠋⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸ ⠀⠘⠀⠀⠀⠀⢸⡇⠀⠀⠘⣿⣿⣿⡿⢋⢠⣀⣴⣤⣶⣄⡀⠈⢻⣿⣿⣿⠀⢸⠀⣿⠆⣷⡜⢷⣝⣓⣼⠃⢀⣠⠴⠋⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸ ⠀⠀⡆⠀⠀⠀⢸⡇⠀⠀⠀⠻⣿⣿⣧⣼⣿⣿⣯⡀⣨⣿⣿⣷⣤⣿⣿⠛⣠⡟⠓⠛⣻⣿⣆⣀⡀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢸ ⠀⠀⢧⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⣿⣿⣿⠟⠻⢿⣷⣽⠿⠻⣿⣿⣿⣿⢀⡟⢠⣶⣿⡭⠿⠿⠯⣽⣗⣦⣄⠀⠘⣧⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠸⣇⠀⠀⠀⢻⠀⠀⠀⠘⢿⣿⡟⢸⣷⡄⠀⠀⠀⠀⣴⡟⢻⣿⣿⠻⣷⣿⠋⣾⡗⠀⠀⠀⠀⠈⣿⣾⣷⣄⣸⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠹⡄⠀⠀⠈⣇⠀⠀⠀⠈⠿⣧⡈⠉⠀⣀⣒⡀⠀⠙⣁⣼⡿⠃⠀⠘⣿⣆⠉⠀⠀⢀⡓⠀⠀⠿⠗⢹⣻⡟⠀⠀⠀⠀⡼⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢳⡄⠀⠀⠹⡆⠀⠀⠀⢠⣶⢽⣿⠾⢁⣹⣷⣶⣿⣿⣿⡦⠀⠀⣀⣤⣿⣿⡛⡶⠦⡤⢤⡤⢤⣴⠿⠋⠀⠀⠀⠀⣰⠃⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠈⢳⡀⠀⠀⠹⣄⠀⠀⠀⢀⣼⣿⠶⠿⠿⠿⠿⣽⣿⣛⢲⠀⠻⢿⣋⣈⠿⢯⢿⣸⣟⣿⣷⣾⠟⢻⣶⠀⠀⠀⣰⠋⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠹⣆⠀⣴⣿⣿⣿⡀⠀⠀⠀⠀⣹⣿⣿⣿⡀⠀⣠⠿⣧⣀⠀⠀⠀⠈⠈⠈⠉⢳⡖⠛⠀⠀⣰⠋⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠘⢧⠿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⠿⣧⠀⠙⣧⣌⠘⠛⠷⠶⠶⠾⠿⠞⠛⣹⡆⢀⡼⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠳⡄⣨⡏⠙⣻⣿⣧⡟⠻⢻⡄⠀⠈⠙⠚⠁⠉⣿⠿⠶⣶⠶⠶⣶⠶⠛⠉⣠⠞⠁⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⣟⡿⠿⠟⠁⠙⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠋⠀⢀⡼⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠈⢧⡀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠙⣆⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⣄⡀⢀⣠⠞⠁⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠲⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠉⠉⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠙⠷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸