⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣽⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠓⠿⠿⠽⠿⠿⠻⠛⠉⠈⠀⠀⠀⠀⠉⠟⠿⡻⢻⠿⠿⠛⠀⠀⠀⠀⠀⠉⠃⠛⠿⠿⠿⠿⠷⠿⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⣿⣯⣿⣿⣷⣻⣿⣾⢿⣿⣯⣿⣟⠿⠟⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠞⣿⣻⣿⣿⣯⡿⣿⣷⣿⣷⣽⣿⣿⢯⠻⠈⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠋⠓⣿⣷⣯⡿⣽⢿⣷⣯⢾⣿⣟⣯⢷⣿⢯⣿⡷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣽⢾⣿⡽⣾⣟⡽⣾⣻⣿⣳⣿⡷⣽⣾⣿⢿⠙⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠟⡿⣷⣽⣾⣻⢷⣻⣽⣻⣷⣟⢯⣳⣽⣾⡽⢾⣻⣾⣟⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣳⣾⣟⣯⢷⣻⣽⢾⣻⣷⣟⡷⣯⣞⣻⣽⣿⣳⣿⣯⢿⠘⠀⠀⠀⡇ ⠀⠀⠀⡿⣟⡾⣽⣻⣷⣟⣯⡷⣏⡼⣻⢧⣳⣮⡟⣧⣞⣏⢷⣯⣟⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣯⣗⢯⣳⣼⠿⣧⣜⣻⣧⡽⣫⢷⣭⢿⣯⡷⣯⣟⣯⣳⣿⠘⠀⠀⡇ ⠀⠀⡟⢷⣻⣷⣞⡽⣻⢶⣤⣠⣀⣀⣀⣀⣀⣀⣀⢤⣦⣖⡽⠶⣹⢷⣯⡷⣿⣿⣿⣿⣿⣿⣻⣽⢾⣹⣾⡝⢺⣴⡤⣀⣀⣀⣀⡀⣀⣀⣀⢤⣦⡷⣛⢶⣻⣾⣟⣿⠈⠀⡇ ⠀⠃⣽⣾⡽⣻⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡗⢮⣛⣯⣿⣿⣿⣿⣿⣿⣻⣽⢟⣯⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⣯⢷⣯⢿⠀⡇ ⠀⡇⣟⢯⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠿⣯⣿⣿⣿⣿⣿⣿⢿⣯⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣱⢿⣯⠘⡇ ⠀⡇⣟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣱⣿⢘⡇ ⠀⡃⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡿⠰⡇ ⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣛⢧⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡳⢧⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡝⢧⡌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣦⡙⣲⡜⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⠳⣍⠳⢬⣛⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣣⡜⢫⡳⢮⣝⠳⣍⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢭⡭⢎⡹⢴⣠⢄⣤⡴⡛⢧⣍⠭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣡⣌⣉⣡⣌⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣌⣉⣡⣌⣉⣡⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⣁⣈⣉⢉⡟