⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠤⣄⣀⠀⠀⠊⠁⣼⡶⠿⣦⠀⠙⠁⢐⢶⢀⣴⠿⠋⠁⠀⢰⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠑⠌⠉⠓⠤⠀⠀⠀⣠⠊⢰⠀⣠⡞⢡⡾⠛⠁⠀⠀⠀⠀⣾⣇⣴⣶⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⡁⢴⠤⣄⡀⠈⠓⠀⢀⡾⠃⠀⢻⠛⠋⠉⠉⠓⠀⠀⠀⠀⠀⢀⡿⠿⠞⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣀⡀⠀⠀⠀⠠⢲⣷⠾⣤⣤⣈⣆⠀⠉⠓⡄⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠉⠛⠒⠦⠴⠧⠬⠦⡀⠀⠋⠈⠀⠀⠀⠈⢺⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣠⠀⠀⠁⠀⠀⢾⣻⠡⢴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⡀⠀⠈⠀⢀⣴⣖⠿⡿⠷⠶⠖⠛⠛⠿⠿⣿⣉⡀⠀⠀⠀⠉⠓⠦⢷⠤⢴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡦⠭⢶⣄⣰⠟⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠥⣀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣮⠗⠤⠀⠀⠀⢀⣽⡿⠖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠤⡠⣇⠀⣰⡞⢟⡉⠹⣍⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠫⣉⠛⠉⠀⠀⠀⠀⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠹⣦⣿⣧⠀⠙⢳⣾⣿⣿⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⢑⣢⣄⣀⠀⢠⣿⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣥⣤⠖⠀⢸⡇⣿⣧⣄⠀⣳⢚⣉⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⣹⠛⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⢾⡟⠁⠀⢀⣼⠃⢻⣷⡘⡏⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠷⠾⠃⠀⢸⡟⠀⠠⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⡿⣿⣿⣿⣿⣿⡛⠛⡿⢉⡿⠀⣾⡟⡇⢹⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⢀⣀⢸⣷⠠⣠⣬⣿⣿⣿⣿⣿⣻⠷⣤⡀⠀⠀⠀⠈⠀⠰⣿⡿⣿⢰⣉⣿⡇⡼⠃⢸⠇⠀⢸⣷⣻⡼⠀⠈⠑⠢⠤⠤⢤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣿⣇⠈⢉⣩⡿⢿⡿⢻⡿⢿⣿⢿⣶⡄⠀⠀⠀⠀⣿⣤⠸⠿⠞⠛⠋⠀⢠⠏⠀⠀⠈⣿⣽⣇⠘⣦⡀⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠼⠉⡽⣿⡏⠙⢿⣤⠀⠳⣜⠷⣷⣏⣻⠿⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⡞⢀⠄⠀⠀⢻⡿⡈⢆⠀⢫⢙⠳⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⠔⡇⢷⠈⣷⡀⠀⠈⠋⠐⠛⠋⠉⠀⠀⠀⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡎⠀⠀⠀⢀⣇⠁⠘⣆⠈⢫⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠂⢃⣾⠧⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢿⡇⠀⠀⠀⢀⡏⣿⢄⢸⡧⡀⢹⣬⣑⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⠀⢀⠎⡟⠀⠀⢠⣈⡳⢄⠀⠀⠀⠀⠀⠈⠙⠿⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⢧⡏⢣⠀⣸⠀⢠⡇⢹⡄⠉⠀⠱⡄⢷⡀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠋⣁⠴⠁⣸⠃⣤⠀⠀⠛⣷⡒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢷⠈⣷⣟⠀⣴⣿⡞⣧⠀⠁⠀⠘⠾⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠥⢠⣴⣿⡫⢺⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠤⠞⠋⣉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⣧⡇⢹⡟⡅⠀⠀⠀⠀⢂⠀⠀⠑⠦⢄⣄⣠⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡏⠀⠈⢷⡀⢀⡀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣿⠋⡙⢯⣚⡷⡤⠀⠀⠀⠀⠀⠹⡦⡤⠤⣤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣿⠁⠀⡀⠀⠳⣘⠤⣿⡏⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⡋⢠⣿⡄⡇⠀⠘⡇⠙⢄⠀⠀⠀⠀⠀⠙⣑⣦⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣿⢔⣰⠁⠀⠀⢸⠇⢸⠁⠀⢹⣿⡟⢷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⢰⠃⠰⣿⣧⡇⠀⠀⣇⡀⠈⢣⠈⠑⢄⡀⢀⣀⣩⣧⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⠿⢺⣣⠀⠀⢠⢻⠀⡟⠀⠀⠈⣿⣏⠀⠈⠛⠿⣶⣤⣤⣤⣶⠟⠋⠀⠀⠀⠞⠀⠀⣧⣿⠙⠀⠀⢼⡇⠀⠀⠱⣄⠀⠈⠻⠿⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡤⠤⠴⠚⠛⠉⠀⠀⡽⠁⠀⢀⡏⡘⢠⡇⠀⠀⢀⣿⡏⡆⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⣻⡏⠀⠀⢰⣾⣇⠀⠀⢠⡈⠲⡄⡀⠀⠀⠀⠀⠀⠀⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣢⡤⠤⢄⡠⠊⠀⠀⢠⣞⣴⠃⣸⠀⠀⠀⠈⣿⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⢠⢿⠃⠀⠀⠀⣿⣹⣆⠀⠀⠱⡄⠵⣌⡑⠲⣤⠤⠤⠤⠤⠤⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠀⠀⠒⠉⠀⠀⢀⣴⠟⠛⠋⠀⣿⠀⢀⡄⣾⡿⣇⠀⢣⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⣿⠏⠀⠀⠀⠀⣿⣮⣿⣦⣄⠀⠙⢶⣄⣹⠦⢬⣷⣦⣀⡀⠀⠀⣈⡤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣠⣤⣤⡴⠶⠀⡠⠀⠄⡞⠘⣰⠀⠀⠈⣿⣶⣷⠾⠋⠘⢿⠀⠈⡆⠀⠀⢱⡀⠀⠀⠀⠀⠀⣞⢀⣴⡿⢃⡴⠀⡀⠀⠐⢿⠈⠛⢿⣿⣿⣶⢶⡛⠛⢶⣖⣀⣀⣉⠙⠉⠉⢁⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠋⠁⠀⡼⠀⣠⡎⢀⠀⠠⡇⢰⡇⠀⠀⠀⠘⢯⡀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⡀⠀⠀⠀⠘⠛⠛⠗⢲⠏⠁⢰⠃⠀⠀⠘⣇⠀⠀⠀⠉⠛⠷⣿⡟⠾⡿⢷⣤⣤⣴⣶⣶⣿⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣿⣴⣿⣀⣎⣠⣴⡇⣾⣷⡀⠀⠀⠀⠢⡳⣄⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡞⠀⠀⢀⡞⠁⠀⠀⠀⠠⠐⠶⡽⣹⣓⡗⠚⠁⠀⠈⠉⠁⠀⠉⠉⠛⠿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠽⠿⠿⡟⢻⠉⠛⠻⠿⢿⡹⣷⣀⠀⠀⠀⢹⣸⠂⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡿⣤⡼⠁⢀⣰⠞⠓⠉⠉⠉⠁⠀⠀⠴⠋⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠱⣜⣆⠀⠀⠀⠀⠀⠈⠙⠳⣄⡀⠨⣿⠉⠛⠓⠲⠶⢤⡀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠁⠀⣴⣿⡥⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⢻⠀⠀⠀⠀⠀⠀⠈⠳⠾⠁⠀⠀⠉⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣿⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠚⠀⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀boobies⠀⠀⠀⠀⠀⠀⠀boobies⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠛⠃⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⢧⣄⠀⠠⠤⠤⠴⠶⣶⡤⠔⠊⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠤⠈⠋⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠋⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡄⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠀⠀⠀⠀⠀⠀⢀⣠⠴⠟⠋⠁⡠⠄⢘⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡤⠊⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⢻⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠁⠀⠀⢀⡄⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠀⠀⠀⢸⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣶⣤⣲⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⢹⡟⠂⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣅⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢸⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑⠄⠂⠀⠀⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⣿⡿⠿⣿⠅⣇⣈⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡟⠀⠸⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠫⣥⡿⠛⠛⠻⡉⡇⠀⡜⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⣟⣯⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⠙⣿⣷⣶⣤⣄⢰⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠀⠀⠹⣷⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⣠⣶⡿⠁⢀⣴⠋⠀⠀⠀⠀⣱⡇⢰⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠜⠁⠀⠀⠀⢽⠋⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣇⡞⢨⣿⣎⡻⢍⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢻⡄⠀⠀⢠⣶⡶⠟⣷⣶⠿⠷⢮⡴⠖⠋⣁⡀⠤⠤⠒⠒⢿⣿⠁⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣾⠀⣾⣟⣰⡿⢁⠝⢭⡒⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣤⣌⣷⠀⢤⡾⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠀⢠⡟⢀⣿⣿⠏⡠⢃⡴⠂⠈⣾⣋⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢀⡞⣉⣯⢻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡇⢸⣿⣏⠜⡡⠊⠀⠀⣼⣿⠿⠁⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠁⢀⣴⣿⢾⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠤⣀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠸⠇⣾⣯⢋⠔⠁⡐⢀⣾⡿⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣎⣴⣿⢿⣿⢾⢋⣿⡿⠁⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠖⠛⠛⢷⣄⠀⠀⠀⠘⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠄⠀⠀⠀⠀⢠⡿⣡⠋⢠⣎⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢋⡝⣡⣾⣿⣣⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠉⠉⠉⠉⠉⠙⣻⣦⡄⠀⠹⣿⢶ ⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⢠⠴⢶⡀⠀⠈⣯⠀⢻⠀⠀⢀⣿⣷⠏⢠⢏⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣠⡿⢻⢟⣏⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣷⣄⠀⢻⣄ ⠀⠀⠀⠀⠀⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⢈⡇⠀⠀⢹⡂⢸⠃⢠⣾⣿⡏⡰⢣⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸⡿⣟⣠⠃⢮⣿⣿⣿⠇⠀⠐⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⣼⣿ ⠀⠀⠀⠀⠀⣰⡽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⠿⠁⠀⠀⢸⡇⠀⢠⣿⢿⣿⠏⢠⣿⣿⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠄⠀⠉⠈⠁⠘⣿⣾⣿⣟⣿⡟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠈⠉⠚⠻⣿⡙⢿ ⠀⠀⠀⠀⢠⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡄⠟⡏⣰⠋⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠸⣿⡟⢹⣿⠁⠀⠀⢠⡞⠣⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠑⠺ ⠀⠀⠀⢠⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⡼⢠⠇⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣷⣿⠇⠀⠀⠀⠈⣇⠂⠱⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠟⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠿⣿⣿⡿⡟⠀⠀⠀⠀⠀⠈⢆⢹⣧⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⢸⢹⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠂⠀⣀⣠⡴⢶⠛⠋⠉⠀⠀⠲⡿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠈⢺⡇⡆⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⠀⡏⢸⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣴⣠⣴⠞⠋⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⢀⠀⢰⠃⡜⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠉⠀⠀⠀⣀⠀⠀⠀⠱⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠁⠀⡜⠀⡇⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣽⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⠋⠁⠀⠀⠀⠀⢀⡌⠁⠀⢆⠀⠀⡇⠀⠀⢠⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠇⠀⠁⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣇⡨⢉⠛⠓⠶⠦⣤⣄⣀⣀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣋⠝⠋⠀⠀⠀⠀⠀⠀⡠⠴⠛⠀⠀⠀⠘⡄⠀⠃⠀⠀⡾⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢠⠊⡰⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠉⠛⣿⣷⣖⠠⣀⣠⠈⠉⠛⠛⠾⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢶⣿⡥⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⡐⠐⠀⢰⡇⠀⠀⠀⠃⠀⠀⠀⠀⣀⣴⣷⢾⠇⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Smegsyyyy ☆🌟✮⋆˙✧₊⁺✩₊˚.⋆☾⋆⁺₊✧ Hope its not to inapropiate ( ∩´͈ ᐜ `͈∩)

^ ^ ^ ^ ^ ^ ﾐ・◦・ ﾐ ꒰˵• ﻌ •˵꒱ ˵・◦・˵ ૮꒰˵・◦・˵꒱ა ૮꒰˵• ﻌ •˵꒱ა ૮꒰ﾐ・◦・ﾐ꒱ა ૮꒰ﾐ• ﻌ •ﾐ꒱ა ♡< ♡< ♡<

𝑵𝒐𝒕 𝒎𝒆 𝒃𝒆𝒊𝒏𝒈 𝒇𝒖𝒍𝒍𝒚 𝒂𝒘𝒂𝒓𝒆 𝒕𝒉𝒂𝒕 𝒔𝒐𝒎𝒆𝒐𝒏𝒆 𝒐𝒏 𝑷𝒐𝒌é𝑭𝒂𝒓𝒎 𝑸 (𝑨 𝒔𝒐𝒓𝒕 𝒐𝒇 𝒗𝒊𝒓𝒕𝒖𝒂𝒍 𝒑𝒆𝒕 𝒘𝒆𝒃𝒔𝒊𝒕𝒆 𝒘𝒊𝒕𝒉 𝑷𝒐𝒌é𝒎𝒐𝒏, 𝒌𝒊𝒏𝒅𝒂 𝒍𝒊𝒌𝒆 𝑪𝒉𝒊𝒄𝒌𝒆𝒏 𝑺𝒎𝒐𝒐𝒕𝒉𝒊𝒆 𝑰 𝒈𝒖𝒆𝒔𝒔?) 𝒊𝒔 𝒂𝒄𝒕𝒖𝒂𝒍𝒍𝒚 𝒇𝒖𝒓𝒓𝒚 𝒑**𝒏 𝒂𝒓𝒕𝒊𝒔𝒕 𝒘𝒊𝒕𝒉 𝒂 𝒗𝒆𝒓𝒚 ~𝒇𝒓𝒆𝒂𝒌𝒚~ 𝒆𝟔𝟐𝟏 𝒂𝒄𝒄𝒐𝒖𝒏𝒕 𝒕𝒐𝒐 𝑻𝒐𝑻 𝑱𝒖𝒔𝒕 𝒃𝒆 𝒄𝒂𝒓𝒆𝒇𝒖𝒍 𝒐𝒇 𝒘𝒉𝒐 𝒚𝒐𝒖 𝒄𝒐𝒎𝒆 𝒂𝒄𝒓𝒐𝒔𝒔 𝒚𝒐𝒖 𝒏𝒆𝒗𝒆𝒓 𝒌𝒏𝒐𝒘 𝒕𝒉𝒂𝒕 𝒕𝒉𝒆𝒚 𝒅𝒓𝒂𝒘 𝒚𝒊𝒇𝒇 :𝟑 𝑱𝒖𝒔𝒕 𝒘𝒂𝒏𝒕𝒆𝒅 𝒕𝒐 𝒗𝒆𝒏𝒕 𝒕𝒉𝒊𝒔 𝒐𝒖𝒕 𝒂𝒔 𝒊𝒇 𝑰 𝒅𝒊𝒅 𝒐𝒏 𝒕𝒉𝒆 𝒐𝒕𝒉𝒆𝒓 𝒘𝒆𝒃𝒔𝒊𝒕𝒆, 𝑰 𝒘𝒐𝒖𝒍𝒅 𝒈𝒆𝒕 𝒃𝒂𝒏𝒏𝒆𝒅 ᐠ( ᐛ )ᐟ

⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣭⣶⣿⣯⣬⣤⣬⣥⣯⣥⣽⣧⣭⣦⣥⣦⣤⣥⣤⣤⣤⣤⣤⣴⣤⣴⣤⣴⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣧⣥⣦⣤⣮⣥⣤⣤⣴⣤⣴⣤⣴⣤⣤⣤⣤⣤⣤⣦⣬⣤⣥⣬⣬⣥⣬⣿⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣤⠈⣿⣿ ⣿⣿⣿⣿⣿⠋⠉⠉⠈⠁⠉⠈⠉⡈⠅⣉⠈⠁⠉⠈⠁⠉⠈⠉⠉⠉⠁⠉⠈⠁⠉⠈⠁⠉⠉⠉⠉⠈⠁⠉⠈⠁⠉⠉⠉⠁⡍⠉⠈⠁⠉⠁⠉⠉⠈⠉⠁⠉⠉⠈⠉⠁⠉⠉⠈⠉⠁⠉⠁⠉⠈⠉⠱⠉⠉⠋⠉⣏⠡⠉⠈⠁⠉⠈⠉⠉⠈⠁⠉⠈⠁⠉⠈⠉⠉⠉⠈⠁⠉⠈⠁⠉⠈⠉⠁⠉⠈⠁⠉⠈⠁⠉⠈⠁⠉⠙⣿⣿⣽⣿ ⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠒⠰⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠐⠀⠂⠡⠁⠀⠀⠀⠄⠀⠀⠂⠀⠂⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⢏⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⡂⠐⠗⡁⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢹⣿ ⣿⣿⣟⣿⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣈⠬⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠁⢁⡜⠛⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠀⠄⢆⠀⣡⠀⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢠⣿ ⣿⣿⣯⣿⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠋⠖⣍⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⡶⡀⠃⠀⠉⠘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢸⣿ ⣿⣿⣏⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⢧⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠄⠁⠁⡠⠐⠁⡀⠀⢈⠦⣤⠠⠄⠙⠀⠀⠀⠀⠀⠉⠈⠒⠓⠾⠳⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠑⡇⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢀⣿ ⣿⣿⣟⣿⡅⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⡆⣤⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠄⠀⠁⠘⡁⠀⡋⢋⢁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡭⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢈⣿ ⣿⣿⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠤⡆⠏⡊⣻⣿⢿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠂⢤⠈⠀⠀⠀⠀⢠⣤⣤⣴⣦⣴⣾⣷⣾⣾⣆⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⡹⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢈⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡦⣎⣾⠇⠑⠊⠁⠀⠀⠉⠁⠭⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⣀⣠⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠠⠃⡌⢃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣿ ⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⡍⠌⠷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣦⡾⠟⠟⠛⠻⠻⣿⣿⣹⢻⣟⡿⣿⣿⣷⣦⣤⡊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢚⣿ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣤⣶⣤⣶⣿⡿⠿⢿⠻⠈⣿⣿⡿⢿⠛⠂⠿⠟⠉⠁⠀⠀⠀⢀⠀⠀⣿⣷⢭⣻⣏⡞⣷⣹⣛⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢺⣿ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⠛⠃⠀⠈⢀⣴⡿⠋⣡⣼⣦⣄⠀⠀⠀⢠⠀⡐⠀⡈⠀⠀⣿⡿⣜⢯⣝⡳⣯⢿⡟⢶⣯⣿⣿⣿⣿⣧⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡟⠁⠀⣇⣀⣄⣤⣤⣀⠀⠀⠀⠀⠀⣴⣵⡇⠠⣿⢸⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⡆⠀⠀⣀⣴⣶⣿⣿⣿⡿⠛⠛⢻⣿⣿⣿⢿⣿⣷⣦⡀⣀⣤⣿⣿⣷⣾⣿⢿⢿⣿⣷⡄⠀⢠⡀⠌⠐⠀⢀⣾⣿⡟⣼⣫⡞⣽⡱⣏⣞⣷⣿⡿⠛⠛⠛⠛⠛⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠅⠀⡀⠀⠈⠉⠀⠀⡀⠾⠁⠀⠀⠀⠀⢠⣏⠋⠀⠀⠀⠐⣿⣸⣿ ⣿⣿⣿⣿⡅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣴⣾⣿⡿⠛⠋⠈⠋⠀⠁⢰⣤⣿⣿⣿⢧⣏⡿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣾⣯⣾⣿⡀⠀⠀⠀⠀⠀⣀⣾⣿⢏⣾⡱⣏⠿⣥⣳⣿⡛⠋⠀⠀⠀⠠⠄⠠⡄⠀⠤⠛⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⢧⡇⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⡗⣆⠀⠀⠀⢈⣿⣰⣿ ⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠙⠁⠀⠄⠃⠠⠁⠀⡁⠀⠀⠛⢿⣿⣿⣵⣻⣿⣿⣿⣟⣯⣽⣿⣿⣿⣿⣿⣿⣿⣦⣀⢀⣴⣿⣿⢻⡝⡾⣜⣳⣭⣿⡾⠟⠛⠛⠛⠛⠀⠈⠀⠉⠐⠀⠀⠀⠘⠦⠀⣼⣿⣿⣷⣄⠀⠀⢀⣄⣤⠷⠏⠁⠀⠀⠀⠀⠁⡣⡆⠀⠀⠀⠀⠀⠀⠨⣃⠀⠀⠠⣿⣰⣿ ⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡟⠫⠔⠃⠈⠀⠀⠁⠀⠈⠀⡁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣬⢳⣝⣳⣽⣾⡿⠋⠁⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⣤⣤⣶⣴⣾⣿⣟⡞⣿⢿⣿⣷⣤⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣇⠀⠀⢰⡆⠄⠁⠒⠀⠀⠐⣿⣰⣿ ⣿⣿⣿⣿⡅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡷⠀⠀⠉⠀⠀⠁⠀⠐⠀⠀⢀⠀⠀⠀⢰⣿⠻⠀⠙⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣷⣭⣷⣿⣿⠿⠋⠁⠀⠀⠑⠀⠐⠀⠁⠀⢀⣴⣿⡿⠿⠻⣩⣿⣿⣿⣿⣞⣭⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣾⡗⠀⠀⠀⠀⠀⠀⢈⣿⢸⣿ ⣿⣿⣿⣿⡆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠉⢀⣴⡆⠀⠀⢀⠂⠀⠄⠀⠁⠀⠂⠀⠀⢰⣿⣦⣮⣤⣿⣿⣭⡁⢐⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⢀⠂⠈⠀⠀⠂⠀⠀⢀⣾⣿⢫⠀⠀⠀⣷⣿⣿⣿⣿⣿⣧⣏⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡿⠿⡦⣀⠀⠀⠀⠀⠀⠠⣿⢸⣿ ⣿⣿⣿⣿⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠀⢀⣾⡟⠁⠀⠂⢈⠐⠈⠂⠀⠀⠀⠀⢀⣴⣿⣿⡿⣯⣉⣛⣹⣿⠿⣿⣇⡀⠸⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢈⠁⢀⠀⠀⠀⠀⠆⠀⠀⢸⣿⠏⠾⣄⡀⠀⣿⣿⣿⣿⡽⣿⣿⣾⣻⣿⣿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡄⠃⠁⠀⠀⠈⠓⢑⡦⣣⠀⠀⠐⣿⢩⣿ ⣿⣿⣿⣿⡇⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢀⣾⡿⠁⠀⠀⠁⠈⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⠉⠈⠉⠉⢴⡀⠙⣿⣷⣆⣘⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠀⠉⠀⠐⠁⠀⡄⠀⠀⢸⣿⣏⠁⠿⣿⣷⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣟⠈⣿⣿⣿⣷⠆⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⡶⠋⠁⠀⠀⠀⢈⣿⢹⣿ ⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡾⣿⣶⣤⣀⣠⣄⣠⣶⣶⣿⣿⠿⡿⣭⣻⣾⣿⣿⣿⣦⣀⣀⡀⣻⣅⣴⣿⣿⣿⣻⢏⡾⣭⣿⣿⣿⣿⣿⣶⣶⣿⣶⣶⣦⣀⣀⡀⠀⢀⡀⠀⠂⠠⠀⠀⠹⢿⣶⣄⢻⠙⠋⣿⣿⣿⣿⣿⣿⣿⡟⣿⣯⡀⠈⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⢸⣿ ⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣷⡽⢮⡽⣻⠿⣿⠿⣿⢏⡷⣭⢿⣵⣿⣿⣿⡿⠛⠉⠛⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠁⠀⠀⠀⠉⠛⠛⢿⣷⣶⣾⣷⣆⠀⠀⠃⠀⠀⠀⠛⢿⣿⣷⣾⣿⣿⣿⣿⣿⡿⣷⡹⢞⣿⣧⠀⣸⣿⣿⣿⣷⡆⠀⠀⢀⠀⢁⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢹⣿ ⣿⣿⣿⣿⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣟⢧⣻⡵⣻⣎⠿⣜⣹⣾⣿⣿⣿⣿⡟⠁⠀⢠⠀⡀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⡟⠋⠐⠀⠀⡀⠒⠄⠰⠀⡀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣤⠀⠈⠁⠀⠀⠀⠀⠈⠛⣿⣿⣿⡿⣏⢷⣣⡝⣏⡞⡿⣴⣛⢿⣿⣿⣿⣧⣤⠰⠋⡤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢚⣿ ⣿⣿⣿⣿⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣏⢾⡱⢯⡵⣾⣿⣿⣿⠿⣿⢿⣿⣿⠀⠀⠀⠂⠁⠈⠄⠡⠄⠀⠀⠀⠛⢿⣿⣿⣿⠋⠀⠐⠂⠄⠡⠀⠀⠀⠀⠄⠀⠄⠡⠀⠀⠀⠀⠈⠻⣿⣿⣿⣤⣤⣀⠀⠈⠁⠀⠀⠀⢀⣿⡷⣹⣚⡷⣹⢮⡳⣝⠶⣹⠞⡿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠨⣿ ⣿⣿⣿⣿⡇⠀⢀⡄⠈⠀⠀⠀⠀⠀⣀⣿⣿⣿⠺⠿⣿⣜⣧⣛⣷⣿⠟⠋⠀⠀⠀⠀⠚⣿⣿⣶⢇⠀⠡⠀⠠⠀⠀⠀⠠⠀⠀⠀⢺⣿⡟⠃⠀⠀⠀⠠⠈⠠⠀⠠⡀⠀⠅⠁⠀⠀⡀⠈⠄⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣯⢳⠧⣝⣞⡹⢧⡻⣽⢿⡧⣟⣵⢣⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠐⣿ ⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⡀⣷⣿⢿⣾⡿⠋⠀⢀⠠⠄⠘⠄⠀⠀⣿⣿⣿⡆⠀⠤⠀⡡⠀⠀⡀⠀⠀⠀⠘⢻⣿⣿⡜⠛⠃⠀⠀⠀⢀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡛⠁⠉⠙⠻⠻⣿⣿⣼⣲⡝⣧⣻⢬⡳⣝⡞⣮⣛⣮⡽⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⡅⠀⠀⠀⠀⢰⣼⣿⣿⠿⣿⣿⡿⣹⣿⠏⠀⠀⠐⠀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣿⡀⠄⠀⠡⠀⠰⠀⠀⠀⠙⠿⢷⣿⣿⣿⡾⠟⠛⠀⠀⠄⠀⢂⠀⠀⡀⢀⣤⣤⣴⣶⣮⣴⣶⢦⡾⠿⣿⣽⣿⣿⣿⠀⠃⠀⠖⡀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣷⣽⣎⡽⢶⡭⣷⣹⢾⣽⣿⣿⣶⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⢈⡁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣏⠷⣿⠏⠀⠀⠀⣠⣄⣠⣴⣿⣿⡿⣿⣹⣿⣿⣿⣷⣮⢀⠃⠲⣧⡀⠀⠀⣠⣤⣾⣿⣿⡇⠀⠀⠀⡀⠀⠂⠀⢀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡻⣟⡳⣞⣿⣿⣿⣿⣿⠀⠀⠀⠣⠀⢀⠀⠐⠀⠀⠈⠙⢿⣾⢻⣿⣿⣼⣣⡝⣧⢏⡿⣜⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠈⡁⠀⡀⠀⣴⣿⣽⣿⡿⣹⣟⡼⢫⣿⠄⠀⣠⣾⣿⣿⣿⣏⠷⣣⢟⡼⣹⢿⣿⠙⢿⣿⣷⣤⣀⣀⣂⣤⣶⣿⣻⢻⢿⣿⣿⣶⣄⠀⠘⠿⠇⠀⠀⣵⣿⣿⣿⣿⣿⡟⣽⡲⢧⣟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡡⠄⠀⠀⠀⡀⠀⢀⡰⠿⣯⡳⡽⣻⣿⣷⡹⣎⢯⣷⡹⢞⣿⣿⣿⣿⡄⠀⠀⠀⠄⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡏⠀⢈⡇⠀⡁⠀⣴⣿⣾⣿⡿⣱⠾⣭⢳⢿⣦⣾⣿⣿⣿⡛⡶⣭⢻⣹⢏⡾⣱⣿⣿⡀⣀⡹⢿⣿⣿⣿⣿⣿⣯⣧⣳⣯⣷⣿⣿⣿⣿⣷⣶⣶⣾⣶⣿⣿⣿⣿⣟⣯⣖⢯⣳⣟⣧⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⡠⠀⠄⠀⠞⠀⠤⠀⠀⢈⡱⠎⣘⣿⢵⣿⣿⣿⡷⡽⣎⣷⣹⣻⣿⣿⣿⣿⡇⠀⠀⠀⡈⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡏⠀⠨⡅⠀⠀⢠⣿⣻⣿⣿⣿⡵⣻⡜⢯⣾⣿⣷⡉⣹⠶⣙⢷⣫⠷⣩⢞⣵⣿⣿⡟⠁⠀⠃⠀⢙⡿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠷⠎⢏⣩⣿⣿⣿⣷⣤⣀⠀⠀⠀⠸⠀⠀⢈⣷⣿⣿⣏⠾⣽⣿⣿⣽⣿⣳⠮⣕⢯⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡏⠀⠘⡅⠀⠀⢸⣿⣿⣿⣿⣿⡗⣧⢻⡽⣿⣿⣲⡝⣣⢟⡹⣎⢷⢫⣗⣫⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⡟⢻⠻⣿⣿⣿⠎⠙⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣯⠷⢧⠟⠁⣀⣠⣾⣿⣿⣿⣿⣿⠛⢿⣧⣄⡀⠀⣠⣴⠟⢫⣼⠳⣏⣿⣿⣿⠿⠋⠙⢿⣿⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠈⡅⠀⠀⢸⣿⣿⡇⠘⣿⣿⣾⣿⣿⣞⣻⣿⣿⣧⣏⡷⣹⢎⡷⣾⣿⡿⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣇⢰⠀⢸⣿⣿⡀⠀⡄⠀⣔⠀⣄⣀⣼⡛⣿⣿⣿⣿⣷⣦⣾⣾⣿⣟⢫⣴⣿⣿⣿⣿⠀⠀⠛⣿⣿⣿⣿⣧⣾⣏⣷⣿⣿⣿⡟⠉⢀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠈⠁⠀⠀⢸⣿⣿⣿⣘⡀⠈⠛⢿⣿⣿⣳⢎⡿⣻⣿⣿⣷⣿⣿⣿⣏⡅⠀⠀⠀⠀⠀⠢⠀⠀⠀⠈⠀⠤⠠⢻⣿⣿⣿⣸⣶⣶⣿⣿⣧⠀⠀⣼⡟⣧⣿⣿⣧⣿⣿⣿⣿⣿⣏⡙⢋⣱⣿⣿⣿⣿⢿⣿⣿⣿⡇⠐⠀⠀⠘⣿⢿⣿⣿⣿⡟⠛⠋⠀⠀⠀⠁⣀⣶⣿⣿⠿⣿⣿⣿⣟⡛⠀⠀⡀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠐⠃⠂⠂⠀⣫⢻⣿⣯⡀⠀⠀⢈⣿⣿⣿⣯⣶⣓⢮⡳⣭⠿⣿⣿⣿⡶⠀⣄⠀⠤⠢⠀⠂⠄⠀⠀⡀⠀⠀⠄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡹⣭⢻⣿⣿⣿⡏⠃⠀⠀⠀⠠⣾⣿⡿⠇⠀⠀⠀⠀⢀⣠⣴⣾⠟⠛⣿⣯⣿⣿⣿⣿⡟⠀⠀⢠⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⠃⠠⣁⠀⠈⢽⢹⣿⣧⠀⠁⠀⣿⣿⡝⣿⢿⣿⣮⣷⡱⢯⣹⣿⣿⡗⠀⠀⠀⠈⠈⠁⠖⠀⠀⠀⠂⠀⠀⠔⠂⢉⣺⣿⡿⣿⣿⣿⣿⣿⣿⠛⠟⡿⠙⠈⠔⠙⣻⣿⣿⣿⣿⣿⢷⣯⣳⡟⣾⣿⣿⣿⡇⠀⠀⢁⣀⡀⣠⣿⣿⠀⠀⠈⠃⣡⣼⣿⠟⠛⠁⠀⣶⣿⣿⣿⣿⣿⡿⠡⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⠂⠀⠐⠀⠀⠀⠀⢻⣿⣧⡀⠀⠈⣿⣟⣭⢳⡝⣿⣿⣿⣧⡯⣝⣿⡧⠐⠀⠀⠀⡀⠒⢘⠀⠀⠀⠀⠒⠀⠀⠀⢸⢿⣿⡇⣽⣯⣿⣿⢿⡄⠠⣴⠄⣶⣦⣴⡟⣫⣿⣿⣿⣿⣎⢿⣛⢶⡹⢾⣿⣿⣉⠇⡀⢀⣾⣿⣿⣿⣿⣏⠀⠀⠀⡿⠟⠉⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠖⣿⣿⡹⣾⢷⣽⡛⢿⣿⣷⣯⣿⣯⠀⠀⠀⠄⠁⠀⠄⡍⠀⠀⠀⠀⠀⠀⢘⣼⣸⣿⣷⢹⣿⣿⣿⣮⣅⣠⣏⣴⣿⣿⣿⣷⣿⣿⣿⡿⢯⡝⡾⡿⣜⡳⢾⣿⣿⣛⢀⣷⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠁⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣷⣶⣷⣀⡄⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣧⣐⠋⣿⡷⣹⢯⣶⣟⡳⢮⡽⣻⣿⣿⣦⡄⠄⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⢯⠷⡿⣼⣙⢧⡻⣟⣿⣿⣿⣿⣿⣿⣿⣿⠛⢁⣀⣀⢐⠃⠀⢀⣰⣾⣿⢯⣳⣯⣿⣿⣿⢻⠭⣟⠿⣿⣿⣤⡄⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣿⣯⢷⡹⣞⣧⣛⣧⣳⣽⣿⣿⣿⣦⡀⢀⠄⠈⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⢸⣷⣻⣿⠋⠀⣤⣂⣶⣤⣿⢿⣿⣿⣿⣷⢮⢽⣮⢻⡵⣣⢟⣎⢷⣽⣿⣿⠛⠛⠛⣿⣿⣦⡀⠉⠀⠁⠀⠀⣠⣾⣿⢏⡷⣫⣾⣿⣿⣿⣿⣧⣟⣼⣻⣾⣿⣿⣷⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⢄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣷⡺⣵⢫⢶⣽⣾⣿⣿⣿⣿⡿⣿⣿⣷⣧⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣽⣿⣦⣿⣟⣿⣿⣿⣿⣿⣿⡹⣎⢷⣮⢳⡳⣝⢮⣿⣿⡿⠁⠁⠈⠀⠀⠉⠛⣿⣿⣯⣤⣤⣼⣾⣿⣿⣻⣾⣿⠿⠃⠀⠟⠻⣿⣿⣿⣷⣿⣿⣿⡿⢷⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡆⠀⠀⣀⠀⠀⠀⠈⠀⠃⠂⠀⠀⠄⣁⠄⠉⡿⣿⣿⣿⣿⣿⣛⠿⠟⠯⠝⢿⣿⣿⣿⣿⣿⣿⣯⣭⠁⠀⠉⠂⠉⠀⠈⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣹⢶⣹⣟⢾⣧⢏⡷⢭⣿⣿⠿⡀⠀⣤⣀⣰⡋⡀⡀⠈⡛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⠻⠋⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣵⢫⢗⣮⢻⠼⣹⣝⣳⣾⣿⣾⢶⣿⣿⣿⣿⠇⠀⠐⠀⠸⢣⣽⣿⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⣿ ⣿⣿⣿⣿⡅⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⠀⣿⣟⠻⠀⠈⠐⢠⡀⠂⢠⡢⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠀⠀⠌⠀⠼⣿⣿⡿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿ ⣿⣿⣿⣿⡃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⠀⠸⢿⣦⠀⢀⣼⣿⣿⣿⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣟⠉⠉⠉⠉⠉⠘⣿⡿⠁⠀⠀⠀⣤⣾⣿⣟⣛⢶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⣿ ⣿⣿⣿⣿⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣖⢻⣧⣠⣼⣿⣷⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣿⣿⣿⣀⣠⣰⣾⡿⢩⣽⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢤⣿ ⣿⣿⣿⣿⡃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⠋⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢸⣿ ⣿⣿⡿⣿⣷⡀⢀⣄⣀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣠⣀⣤⣠⣤⣤⣤⣤⣤⣾⣟⣛⣿⡇⣠⣤⣤⣤⣠⣤⣤⣠⣀⣄⣀⣀⣀⣀⣀⣀⣀⣠⣀⣠⣄⣠⣄⣤⣠⣄⣤⣄⣤⣄⣤⣄⣤⣠⣠⣄⣠⣄⣤⣠⣄⣤⣤⣴⣦⣤⣿⣛⣻⣿⣿⣿⣿⣿⠛⣛⠃⢀⣄⣠⣀⢀⡀⢀⣀⢀⣀⢀⣀⠀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣄⣠⣄⣠⣤⣬⣿⣿⣿ ⣿⣿⣇⠛⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣷⣶⣶⣾⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿ ⢽⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣶⣴⣶⣤⣶⣤⣶⣶⣶⣶⣴⣶⣤⣤⣶⣦⣴⣶⣤⣴⣤⣴⣤⣴⣤⣴⣤⣴⣦⣴⣦⣴⣦⣶⣦⣶⣦⣴⣦⣴⣶⣤⣶⣤⣶⣤⣴⣦⣴⣦⣴⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣴⣦⣤⣦⣤⣴⣤⣶⣤⣶⣤⣶⣤⣴⣤⣴⣤⣴⣦⣴⣧⣤⣦⣤⣤⣤⣴⣿⣿

ᐟ) ᐛ (ᐠ �𝒆𝒏𝒏𝒂𝒃� �𝒆𝒈� �𝒍𝒖𝒐𝒘� �� ,�𝒕𝒊𝒔𝒃𝒆𝒘� �𝒆𝒉𝒕𝒐� �𝒉𝒕� �𝒐� �𝒊𝒅� �� �𝒊� �𝒂� �𝒖𝒐� �𝒊𝒉𝒕� �𝒏𝒆𝒗� �𝒕� �𝒆𝒕𝒏𝒂𝒘� �𝒔𝒖𝑱� ��: �𝒇𝒊𝒚� �𝒂𝒓𝒅� �𝒆𝒉𝒕� �𝒂𝒉𝒕� �𝒐𝒏𝒌� �𝒆𝒗𝒆𝒏� �𝒐𝒚� �𝒔𝒐𝒓𝒄𝒂� �𝒎𝒐𝒄� �𝒐𝒚� �𝒉𝒘� �𝒐� �𝒖𝒇𝒆𝒓𝒂𝒄� �𝒃� �𝒔𝒖𝑱� �𝒐𝑻� �𝒐𝒕� �𝒏𝒖𝒐𝒄𝒄𝒂� �𝟐𝟔𝒆� ~�𝒌𝒂𝒆𝒓𝒇�~ �𝒓𝒆𝒗� �� �𝒕𝒊𝒘� �𝒔𝒊𝒕𝒓𝒂� ��**�� �𝒓𝒓𝒖𝒇� �𝒍𝒍𝒂𝒖𝒕𝒄𝒂� �𝒊� )?�𝒔𝒆𝒖𝒈� �� �𝒊𝒉𝒕𝒐𝒐𝒎𝑺� �𝒆𝒌𝒄𝒊𝒉𝑪� �𝒌𝒊𝒍� �𝒅𝒏𝒊𝒌� ,�𝒐𝒎�é�𝒐𝑷� �𝒕𝒊𝒘� �𝒕𝒊𝒔𝒃𝒆𝒘� �𝒆𝒑� �𝒂𝒖𝒕𝒓𝒊𝒗� �𝒐� �𝒓𝒐𝒔� ��( �� �𝒓𝒂𝑭�é�𝒐𝑷� �𝒐� �𝒏𝒐𝒆𝒎𝒐𝒔� �𝒂𝒉𝒕� �𝒓𝒂𝒘𝒂� �𝒍𝒍𝒖𝒇� �𝒏𝒊𝒆𝒃� �𝒎� �𝒐𝑵�

)∩͈` ᐜ ͈´∩ ( etaiporpani ot ton sti epoH ✧₊⁺⋆☾⋆.˚₊✩⁺₊✧˙⋆✮��☆ yyyysgemS ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠇⢾⣷⣴⣀⠀⠀⠀⠀⠃⠀⠀⠀⡇⢰⠀⠐⡐⠸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⡥⣿⢶⡴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣿⠾⠛⠛⠉⠈⣠⣀⠠⣖⣷⣿⠛⠉⡿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢐⠀⠀⠀⡰⠊⢠⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡾⠀⠀⠃⠀⡄⠘⠀⠀⠀⠛⠴⡠⠀⠀⠀⠀⠀⠀⠋⠝⣋⠚⠶⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⣀⣀⣄⣤⠦⠶⠓⠛⢉⡨⣇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠁⠀⠇⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⢠⠀⠀⡇⠀⠀⢆⠀⠁⡌⢀⠀⠀⠀⠀⠁⠋⠾⣴⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣽⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⡇⠀⡜⠀⠁⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡀⠱⠀⠀⠀⣀⠀⠀⠀⠉⠛⠿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣴⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠀⠀⠀⠀⡜⠃⢰⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠋⡴⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⡏⢀⠀⠀⠀⠀⡀⠱⠀⠀⠀⠋⠞⣴⣠⣴⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣸⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⠀⠀⠀⠀⠀⢸⡏⠀⠀⠃⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⡆⡇⢺⠈⠀⠀⠀⠀⠀⠀⠀⠁⣻⡿⠲⠀⠀⠉⠋⠛⢶⡴⣠⣀⠀⠂⢠⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⠀⠀⠇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠏⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⣤⢀⠀⠀⠀⠀⣧⢹⢆⠈⠀⠀⠀⠀⠀⡟⡿⣿⣿⠿⠶⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠃⣿⣿⣼⠀⠟⣧⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠏⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡴⢀⠀⠀⠀⠀⠀⠀⠀⡇⠱⠂⣇⠈⠀⠀⠀⠇⣿⣷⣿⣀⢀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣾⠀⠇⢠⡼⣇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⠀⠀⠀ ⠺⠑⠉⠀⠀⠀⠀⠀⠀⠁⠚⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠣⡞⢠⠀⠀⠁⣿⢹⡟⣿⠸⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠀⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⢀⠋⣰⡏⠟⡄⣿⠘⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⢠⠀⠀⠀⠀ ⢿⡙⣿⠻⠚⠉⠈⠊⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡟⣿⣟⣿⣾⣿⠘⠁⠈⠉⠀⠄⢀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⣿⣿⢠⠏⣿⢿⣿⢠⠀⡇⢸⠀⠀⠁⠿⣠⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⡽⣰⠀⠀⠀⠀⠀ ⣿⣼⣧⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⢀⠀⠀⠐⠀⠇⣿⣿⣿⢮⠃⣠⣟⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⢣⡰⡏⣿⣾⢠⠃⢸⡂⢹⠀⠀⡇⢈⠀⣏⢠⠀⠀⠀⠀⠀⠀⠀⠇⣁⠀⠀⠀⠀⠀⠀ ⣄⢻⠀⣄⣷⠻⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⡠⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣏⢟⢻⡿⣠⣟⣿⢰⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡿⣾⢏⢠⠏⣷⣿⢀⠀⠀⢻⠀⣯⠈⠀⡀⢶⠴⢠⠀⠀⠀⠀⠀⠀⠀⠁⡸⠀⠀⠀⠀⠀⠀⠀ ⢶⣿⠹⠀⡄⣦⣻⠙⠉⠉⠉⠉⠉⠀⠁⠉⠋⠖⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣣⣿⣾⣡⡝⢋⡟⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠁⠟⣾⣠⣎⢠⠋⣡⡿⢠⠀⠀⠀⠀⠄⣤⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣆⣿⠘⠀⠀⠀⣄⢷⠛⠛⠖⠶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠁⡿⣿⢋⢾⣿⢿⣿⣴⣎⣏⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⡿⣾⢀⡐⠁⠔⢋⣯⣾⠇⠸⠀⠀⠀⠀⠀⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣆⣿⠈⠀⠀⠀⠀⠀⠀⣀⠤⠒⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⢾⣿⣴⢀⠁⢿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠸⠀⠀⠀⠁⠿⣿⣼⠀⠀⠊⡡⠜⣏⣿⢸⡇⢸⠀⠀⠀⠀⠀⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡶⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣷⢻⣯⣉⡞⢀⠀⠀⡏⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⣋⣾⠈⠂⡴⢃⡠⠏⣿⣿⢀⡟⢠⠀⠀⠀⠀⠀⠂⣷⠀⠀⠀⠀⠀⠀⠀⠀⠋⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⣆⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠋⡾⢤⠀⣷⣌⣤⠀⠀⠀⠃⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢾⡒⢭⠝⢁⡿⣰⣟⣾⠀⣾⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠀⠀⠀⠃⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⣿⢿⠒⠒⠤⠤⡀⣁⠋⠖⡴⢮⠷⠿⣶⣷⠟⡶⣶⢠⠀⠀⡄⢻⠀⠀⠀⠀⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢻⢍⡻⣎⣿⢨⡞⣇⢰⠇⢠⠀⠀⠀⠀⠀⠀⠀⠋⢽⠀⠀⠀⠁⠜⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⢰⡇⣱⠀⠀⠀⠀⠋⣴⢀⠁⡿⣶⣠⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⣷⠹⠀⠀⠏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣷⢰⣄⣤⣶⣷⣿⠙⣼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣯⣟⠀⠀⠀⡀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⡜⠀⡇⡉⠻⠛⠛⡿⣥⠫⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠈⠏⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠸⠀⡟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⣈⣇⠅⣿⠿⡿⣿⣿⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣿⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⠀⠀⠀⠂⠀⠀⠂⠄⠑⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡟⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠛⢸⠏⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣅⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠀⠀⠀⠂⡟⢹⠀⠀⠀⠗⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣄⣲⣤⣶⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣿⢸⠀⠀⠀⠋⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠘⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢸⠀⠋⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣹⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⡄⢀⠀⠀⠁⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡦⢻⣧⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠁⠊⡤⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣼⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⢘⠄⡠⠁⠋⠟⠴⣠⢀⠀⠀⠀⠀⠀⠀⠤⠤⠦⠲⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⠁⠞⡠⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠈⡄⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢷⣦⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠋⠟⣿⣶⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⠀⠀⠋⠈⠤⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠊⠔⡤⣶⠶⠴⠤⠤⠠⠀⣄⢧⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡆⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣾⣠⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢦⠳⠀⠃⠛⠀⠁⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢸⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀seiboob⠀⠀⠀⠀⠀⠀⠀seiboob⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣷⠀⠚⠈⠀⠀⠀⠀⠀⠀⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⣿⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠀⠀⣦⠙⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡴⣮⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⡴⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣸⠀⠀⠀⠀⠉⠀⠀⠁⠾⠳⠈⠀⠀⠀⠀⠀⠀⢻⣌⣷⠘⠀⠀⠀⠀⠀⠀⠀⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠞⡥⣿⣴⠀⠁⠉⠟⡾⣠⠀⠀⠀⠀⠀⡀⢤⠶⠲⠓⠛⠉⣿⠨⡀⣄⠳⠙⠈⠀⠀⠀⠀⠀⣆⣜⠱⠀⠀⠀⠀⠀⠁⠚⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠴⠀⠀⠁⠉⠉⠉⠓⠞⣰⢀⠁⡼⣤⡿⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠂⣸⢹⠀⠀⠀⣀⣷⡹⢿⠿⠻⠛⠉⢻⡟⠿⠿⠽⠾⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⣷⠿⠛⠉⠉⠀⠁⠉⠈⠀⠁⠚⡗⣓⣹⡽⠶⠐⠠⠀⠀⠀⠁⡞⢀⠀⠀⡞⢀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠱⠀⠀⠀⠀⠀⠀⣄⡳⠢⠀⠀⠀⡀⣷⣾⡇⣴⣠⣎⣀⣿⣴⣿⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣿⣶⣶⣴⣤⣤⢷⡿⠾⡟⣿⠷⠛⠉⠀⠀⠀⣇⠘⠀⠀⠃⢰⠁⠏⢲⠗⠛⠛⠘⠀⠀⠀⡀⢻⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⡀⢯⠘⠀⠀⠀⡇⢰⡇⠠⠀⢀⡎⣠⠀⡼⠀⠁⠋⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢁⠉⠉⠙⣉⣀⣀⣖⢶⠛⡛⢶⣶⣿⣿⢿⠛⠈⢿⠐⠀⡀⠀⡴⢃⡿⣴⢀⣞⠀⠀⠀⠀⠀⡀⢱⠀⠀⡆⠈⠀⢿⠘⠋⠾⣷⣶⣿⠈⠀⠀⣰⠘⡞⠄⠀⡠⠀⠶⡴⣤⣤⣠⠋⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⣈⠀⠀⡀⣀⣦⣷⢬⠦⣹⣄⢶⠙⠀⣄⣦⣿⣮⣿⠀⠀⠀⠀⠏⣿⢠⠀⠇⢀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢣⠀⣇⡿⣾⡄⢀⠀⣿⠀⠋⠛⠟⣴⢀⠀⠀⠉⠒⠀⠀⠉⠖⡴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠽⠤⠤⠤⠤⠤⣤⠲⡑⣌⠵⡄⠱⠀⠀⣆⣹⣿⠀⠀⠀⠃⢿⢠⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡇⣿⠈⠀⠀⠀⣸⠃⣴⣞⢠⠀⠀⠊⡠⢄⠤⡤⣢⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠉⠀⠀⠀⠀⠀⠀⡀⡄⠲⡈⢠⠀⠀⣇⣾⢰⠀⠀⡏⣻⠀⠀⡆⠀⠀⠀⠀⠀⠀⠃⠚⠙⠀⠀⠀⠀⡆⡏⣿⢀⠀⠀⡇⢠⡘⡏⢀⠀⠁⡽⠀⠀⠉⠛⠚⠴⠤⡤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢦⠿⠻⠈⠀⣄⠱⠀⠀⡇⢼⠀⠀⠙⣿⣧⠀⠀⠞⠀⠀⠀⠋⠟⣶⣤⣤⣤⣶⠿⠛⠈⠀⣏⣿⠈⠀⠀⡟⠀⢻⢠⠀⠀⣣⢺⠿⣪⠴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠔⣧⣩⣀⢀⡀⢄⠑⠈⢣⠈⡀⣇⠀⠀⡇⣧⣿⠰⠃⢰⠉⠟⣾⣴⢀⠀⠀⠀⠀⠀⠀⣄⣦⢷⡟⣿⢹⠀⠁⢸⠇⢸⠀⠀⠁⣰⢔⣿⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠄⣦⣑⠙⠀⠀⠀⠀⠀⢄⠙⡇⠘⠀⡇⡄⣿⢠⡋⡿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣷⠻⡏⣿⠤⣘⠳⠀⡀⠀⠁⣿⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠞⠤⣤⠤⡤⡦⠹⠀⠀⠀⠀⠀⡤⡷⣚⢯⡙⠋⣿⢻⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⡀⢀⡀⢷⠈⠀⡏⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡶⣤⣠⣄⢄⠦⠑⠀⠀⢂⠀⠀⠀⠀⡅⡟⢹⡇⣧⣿⣿⣷⠘⠀⠀⠀⠀⠀⠀⠁⠉⠈⣉⠋⠞⠤⠀⠀⠀⠀⠀⠀⡀⣿⢻⠀⠀⠀⢺⡫⣿⣴⢠⠥⠻⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠯⠾⠘⠀⠁⠀⣧⡞⣿⣴⠀⣟⣷⠈⢷⠈⠀⠀⠀⠀⠀⡀⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡒⣷⠛⠀⠀⣤⠃⣸⠁⠴⣁⠋⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡀⢷⡄⠱⠀⠉⡄⢹⡇⢠⠀⣸⠀⢣⡏⢧⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠿⠙⠈⠀⠀⠀⠀⠀⢄⡳⣈⢠⠀⠀⡟⠎⢀⠀⢉⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠾⣑⣬⢹⡀⡧⢸⢄⣿⡏⢀⠀⠀⠀⡇⢿⣡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⣾⢠⠀⠀⠀⠀⠀⠀⠀⡄⢷⠘⠧⣾⢃⠂⡵⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠻⠈⡀⢫⠈⣆⠘⠁⣇⢀⠀⠀⠀⡎⢀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣅⠀⠀⠀⠉⠋⠛⠐⠋⠈⠀⡀⣷⠈⢷⡇⠔⣧⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠳⢙⢫⠀⢆⡈⡿⢻⠀⠀⠄⢀⡞⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠿⣻⣏⣷⠷⣜⠳⠀⣤⢿⠙⡏⣿⡽⠉⠼⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠴⣀⣀⡀⣦⠘⣇⣽⣿⠈⠀⠀⠏⢠⠀⠋⠛⠞⠿⠸⣤⣿⠀⠀⠀⠀⡄⣶⢿⣿⢿⡿⢻⡿⢿⡿⣩⢉⠈⣇⣿⠙⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠤⠤⠢⠑⠈⠀⡼⣻⣷⢸⠀⠇⢸⠃⡼⡇⣿⣉⢰⣿⡿⣿⠰⠀⠈⠀⠀⠀⡀⣤⠷⣻⣿⣿⣿⣿⣿⣬⣠⠠⣷⢸⣀⢀⠤⠢⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣽⠀⢹⡇⡟⣾⠀⡿⢉⡿⠛⡛⣿⣿⣿⣿⣿⡿⠿⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⠠⠀⡟⢸⠀⠃⠾⠷⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠙⡏⡘⣷⢻⠃⣼⢀⠀⠁⡟⢾⣿⣿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠛⣹⠏⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣉⢚⣳⠀⣄⣧⣿⡇⢸⠀⠖⣤⣥⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⣿⢠⠀⣀⣄⣢⢑⠬⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢃⠉⣿⣿⣾⢳⠙⠀⣧⣿⣦⠹⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣶⣴⠀⠀⠀⠀⠉⠛⣉⠫⡟⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠢⡑⣍⠹⡉⢟⡞⣰⠀⣇⡠⠤⠀⠀⠀⠇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠖⡿⣽⢀⠀⠀⠀⠤⠗⣮⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡴⣀⠀⠀⠀⠀⠀⣀⠥⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⡿⠟⣰⣄⢶⠭⡦⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡶⢴⠤⢷⠦⠓⠉⠀⠀⠀⡀⣉⣿⠿⠿⠛⠛⠖⠶⠷⡿⠿⣖⣴⢀⠀⠈⠀⡀⠀⠀⠀⠀⠃⠟⠀⠀⠀⠀⠀⠀⠀⣄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢴⠡⣻⢾⠀⠀⠁⠀⠀⣠⣀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢺⠈⠀⠀⠀⠈⠋⠀⡀⠦⠬⠧⠴⠦⠒⠛⠉⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣿⣴⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠀⡄⠓⠉⠀⣆⣈⣤⣤⠾⣷⢲⠠⠀⠀⠀⡀⣀⣄⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⠉⠞⠿⡿⢀⠀⠀⠀⠀⠀⠓⠉⠉⠋⠛⢻⠀⠃⡾⢀⠀⠓⠈⡀⣄⠤⢴⡁⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣶⣴⣇⣾⠀⠀⠀⠀⠁⠛⡾⢡⡞⣠⠀⢰⠊⣠⠀⠀⠀⠤⠓⠉⠌⠑⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⢰⠀⠁⠋⠿⣴⢀⢶⢐⠁⠙⠀⣦⠿⡶⣼⠁⠊⠀⠀⣀⣄⠤⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣴⣤⣤⣤⣦⣤⣧⣴⣦⣴⣤⣴⣤⣴⣤⣶⣤⣶⣤⣶⣤⣴⣤⣦⣤⣦⣴⣴⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣦⣴⣦⣴⣦⣴⣤⣶⣤⣶⣤⣶⣴⣦⣴⣦⣶⣦⣶⣦⣴⣦⣴⣦⣴⣤⣴⣤⣴⣤⣴⣤⣴⣤⣶⣴⣦⣶⣤⣤⣶⣴⣶⣶⣶⣶⣤⣶⣤⣶⣴⣶⣴⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⢽ ⣿⢻⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣾⣶⣶⣷⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⣿⠛⣇⣿⣿ ⣿⣿⣿⣬⣤⣠⣄⣠⣄⣀⣄⣀⣀⣠⣀⣀⣀⣀⠀⣀⢀⣀⢀⣀⢀⡀⢀⣀⣠⣄⢀⠃⣛⠛⣿⣿⣿⣿⣿⣻⣛⣿⣤⣦⣴⣤⣤⣄⣠⣤⣄⣠⣄⣠⣠⣤⣄⣤⣄⣤⣄⣤⣄⣠⣤⣄⣠⣄⣠⣀⣠⣀⣀⣀⣀⣀⣀⣀⣄⣀⣠⣤⣤⣠⣤⣤⣤⣠⡇⣿⣛⣟⣾⣤⣤⣤⣤⣤⣠⣤⣀⣠⣀⣀⣀⠀⡀⣀⣀⠀⠀⣀⣄⢀⡀⣷⣿⡿⣿⣿ ⣿⢸⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⣶⣧⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢹⠋⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃⣿⣿⣿⣿ ⣿⢤⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣿⣿⣶⣽⢩⡿⣾⣰⣠⣀⣿⣿⣿⣴⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⣿⣿⣿⣿⣿⣷⣿⣼⣠⣧⢻⣖⣿⠿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣿⢶⣛⣟⣿⣾⣤⠀⠀⠀⠁⡿⣿⠘⠉⠉⠉⠉⠉⣟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠩⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡍⣭⣿⣿⣿⣼⢀⠀⣦⢿⠸⠀⠀⠀⣷⣿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡃⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣿⣿⣿⣿⡿⣿⣿⠼⠀⠌⠀⠀⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⠿⠹⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⢻⡢⢠⠂⡀⢠⠐⠈⠀⠻⣟⣿⠀⠐⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡅⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣯⣿⣿⣿⣿⣽⢣⠸⠀⠐⠀⠇⣿⣿⣿⣿⢶⣾⣿⣾⣳⣝⣹⠼⢻⣮⢗⢫⣵⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⠹⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⢿⢘⠀⠀⠀⠀⠀⠇⣿⣿⣿⠿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⠋⠻⠿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⢿⡛⠈⡀⡀⡋⣰⣀⣤⠀⡀⠿⣿⣿⢭⡷⢏⣧⢾⣟⣹⢶⣹⡿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢻⠀⠀⠈⠀⠉⠂⠉⠀⠁⣭⣯⣿⣿⣿⣿⣿⣿⢿⠝⠯⠟⠿⣛⣿⣿⣿⣿⣿⡿⠉⠄⣁⠄⠀⠀⠂⠃⠀⠈⠀⠀⠀⣀⠀⠀⡆⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⢷⡿⣿⣿⣿⣷⣿⣿⣿⠻⠟⠀⠃⠿⣿⣾⣻⣿⣿⣾⣼⣤⣤⣯⣿⣿⠛⠉⠀⠀⠈⠁⠁⡿⣿⣿⢮⣝⡳⢳⣮⢷⣎⡹⣿⣿⣿⣿⣿⣿⣟⣿⣦⣿⣽⣿⣿⣿⣿⣿⣿⣻⠙⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀⣧⣷⣿⣿⡿⣿⣿⣿⣿⣾⣽⢶⢫⣵⡺⣷⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⢄⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⠀⠀⣷⣿⣿⣾⣻⣼⣟⣧⣿⣿⣿⣿⣾⣫⡷⢏⣿⣾⣠⠀⠀⠁⠀⠉⡀⣦⣿⣿⠛⠛⠛⣿⣿⣽⢷⣎⢟⣣⡵⢻⣮⢽⢮⣷⣿⣿⣿⢿⣿⣤⣶⣂⣤⠀⠋⣿⣻⣷⢸⡆⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⢀⠈⠄⢀⡀⣦⣿⣿⣿⣽⣳⣧⣛⣧⣞⡹⢷⣯⣿⣴⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⡄⣤⣿⣿⠿⣟⠭⢻⣿⣿⣿⣯⣳⢯⣿⣾⣰⢀⠀⠃⢐⣀⣀⢁⠛⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⢧⣙⣼⡿⠷⢯⣳⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠀⠄⡄⣦⣿⣿⣻⡽⢮⡳⣟⣶⢯⣹⡷⣿⠋⣐⣧⣿⢹⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⡄⣀⣷⣶⣷⣿⣿⣿⣿⣿⣿⣾⣰⢀⠀⠀⠀⠁⠀⠀⠄⣿⣿⣿⣿⣿⣿⣾⣷⢀⣛⣿⣿⢾⡳⣜⡿⡾⡝⢯⡿⣿⣿⣿⣷⣿⣿⣿⣴⣏⣠⣅⣮⣿⣿⣿⢹⣷⣿⣸⣼⢘⠀⠀⠀⠀⠀⠀⡍⠄⠀⠁⠄⠀⠀⠀⣯⣿⣯⣷⣿⢿⡛⣽⢷⣾⡹⣿⣿⠖⠀⣷⣿⣿⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡏⣿⣿⣿⣿⣿⣼⢀⠀⠀⠀⠉⠟⡿⠀⠀⠀⣏⣿⣿⣿⣿⣾⢀⡀⠇⣉⣿⣿⢾⡹⢶⣛⢿⣎⣿⣿⣿⣿⣫⡟⣴⣦⣶⠄⣴⠠⡄⢿⣿⣿⣯⣽⡇⣿⢿⢸⠀⠀⠀⠒⠀⠀⠀⠀⢘⠒⡀⠀⠀⠀⠐⡧⣿⣝⡯⣧⣿⣿⣿⡝⢳⣭⣟⣿⠈⠀⡀⣧⣿⢻⠀⠀⠀⠀⠐⠀⠂⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⡿⣿⣿⣿⣿⣿⣶⠀⠁⠛⠟⣿⣼⣡⠃⠈⠀⠀⣿⣿⣠⡀⣀⢁⠀⠀⡇⣿⣿⣿⣾⡟⣳⣯⢷⣿⣿⣿⣿⣿⣻⠙⠔⠈⠙⡿⠟⠛⣿⣿⣿⣿⣿⣿⡿⣿⣺⢉⠂⠔⠀⠀⠂⠀⠀⠀⠖⠁⠈⠈⠀⠀⠀⡗⣿⣿⣹⢯⡱⣷⣮⣿⢿⣿⡝⣿⣿⠀⠁⠀⣧⣿⢹⢽⠈⠀⣁⠠⠃⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⠀⢠⠀⠀⡟⣿⣿⣿⣿⣯⣿⠛⠟⣾⣴⣠⢀⠀⠀⠀⠀⠇⡿⣿⣾⠠⠀⠀⠀⠃⡏⣿⣿⣿⢻⣭⡹⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠄⠀⠀⡀⠀⠀⠄⠂⠀⠢⠤⠀⣄⠀⡶⣿⣿⣿⠿⣭⡳⢮⣓⣶⣯⣿⣿⣿⢈⠀⠀⡀⣯⣿⢻⣫⠀⠂⠂⠃⠐⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⡀⠀⠀⡛⣟⣿⣿⣿⠿⣿⣿⣶⣀⠁⠀⠀⠀⠋⠛⡟⣿⣿⣿⢿⣿⠘⠀⠀⠐⡇⣿⣿⣿⢿⣿⣿⣿⣿⣱⢋⡙⣏⣿⣿⣿⣿⣿⣧⣿⣿⣧⡟⣼⠀⠀⣧⣿⣿⣶⣶⣸⣿⣿⣿⢻⠠⠤⠀⠈⠀⠀⠀⠢⠀⠀⠀⠀⠀⡅⣏⣿⣿⣿⣷⣿⣿⣻⡿⢎⣳⣿⣿⢿⠛⠈⡀⣘⣿⣿⣿⢸⠀⠀⠁⠈⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣠⠀⡀⢀⠉⡟⣿⣿⣿⣷⣏⣾⣧⣿⣿⣿⣿⠛⠀⠀⣿⣿⣿⣿⣴⢫⣟⣿⣾⣾⣦⣷⣿⣿⣿⣿⡛⣼⣀⣄⠀⣔⠀⡄⠀⡀⣿⣿⢸⠀⢰⣇⣿⣿⣿⠁⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⡿⣿⣾⡷⢎⣹⡷⣏⣧⣿⣿⣻⣞⣿⣿⣾⣿⣿⠘⡇⣿⣿⢸⠀⠀⡅⠈⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⢿⠙⠋⠿⣿⣿⣿⣏⠳⣼⢫⠟⣴⣠⠀⡀⣄⣧⢿⠛⣿⣿⣿⣿⣿⣾⣠⣀⠁⠟⢧⠷⣯⣿⣿⣿⣿⣿⢿⠛⠛⠛⠛⠛⠙⠎⣿⣿⣿⠻⢻⡟⣿⣿⣿⣿⢛⠛⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⣿⣫⣗⢫⢷⣎⡹⢟⣣⡝⣲⣿⣿⡽⢻⣧⡗⣿⣿⣿⣿⣿⢸⠀⠀⡅⠘⠀⡏⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⢯⣕⠮⣳⣿⣽⣿⣿⣽⠾⣏⣿⣿⣷⢈⠀⠀⠸⠀⠀⠀⣀⣤⣷⣿⣿⣿⣩⢏⠎⠷⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⡿⢙⠀⠃⠀⠁⡟⣿⣿⣵⢞⣩⠷⣫⢷⣙⠶⣹⡉⣷⣿⣾⢯⡜⣻⡵⣿⣿⣿⣻⣿⢠⠀⠀⡅⠨⠀⡏⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⡈⠀⠀⠀⡇⣿⣿⣿⣿⣻⣹⣷⣎⡽⡷⣿⣿⣿⢵⣿⣘⠎⡱⢈⠀⠀⠤⠀⠞⠀⠄⠀⡠⣷⣿⣿⣿⢻⣿⣿⣿⣿⣿⣧⣟⣳⢯⣖⣯⣟⣿⣿⣿⣿⣶⣾⣶⣶⣷⣿⣿⣿⣿⣷⣯⣳⣧⣯⣿⣿⣿⣿⣿⢿⡹⣀⡀⣿⣿⣱⡾⢏⣹⢻⣭⡶⡛⣿⣿⣿⣾⣦⢿⢳⣭⠾⣱⡿⣿⣾⣿⣴⠀⡁⠀⡇⢈⠀⡏⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠄⠀⠀⠀⡄⣿⣿⣿⣿⢞⡹⣷⢯⣎⡹⣷⣿⣻⡽⡳⣯⠿⡰⢀⠀⡀⠀⠀⠀⠄⡡⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⡲⣽⡟⣿⣿⣿⣿⣿⣵⠀⠀⠇⠿⠘⠀⣄⣶⣿⣿⢿⢻⣻⣿⣶⣤⣂⣀⣀⣤⣷⣿⢿⠙⣿⢿⣹⡼⢟⣣⠷⣏⣿⣿⣿⣾⣠⠀⠄⣿⢫⡼⣟⣹⡿⣿⣽⣿⣴⠀⡀⠀⡁⠈⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣿⣿⣜⡿⢏⣧⡝⣣⣼⣿⣿⢻⣾⢿⠙⠈⠀⠀⠐⠀⢀⠀⠣⠀⠀⠀⣿⣿⣿⣿⣿⣞⡳⣟⡻⣿⣿⣿⣿⣿⣿⣿⣴⢀⠀⢀⠀⠂⠀⡀⠀⠀⠀⡇⣿⣿⣾⣤⣠⠀⠀⡀⣧⠲⠃⢀⣮⣷⣿⣿⣿⣹⣿⡿⣿⣿⣴⣠⣄⣠⠀⠀⠀⠏⣿⠷⣏⣿⣿⣿⣿⣿⣽⠀⠀⠀⠀⡁⢈⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⣶⣿⣿⣽⢾⣹⣷⡭⢶⡽⣎⣽⣷⣿⣿⣿⢿⠛⠉⠀⠀⠀⡀⠖⠀⠃⠀⣿⣿⣿⣽⣿⠿⡾⢦⣶⣴⣮⣶⣴⣤⣤⢀⡀⠀⠀⢂⠀⠄⠀⠀⠛⠟⡾⣿⣿⣿⢷⠿⠙⠀⠀⠀⠰⠀⠡⠀⠄⡀⣿⣿⣿⣴⣠⣀⣀⠀⠀⠀⠀⠐⠀⠀⠏⣿⣹⡿⣿⣿⠿⣿⣿⣼⢰⠀⠀⠀⠀⡅⠀⠀⡇⣿⣿⣿⣿ ⣿⠀⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⣿⣿⡽⣮⣛⣮⡞⣝⡳⢬⣻⣧⡝⣲⣼⣿⣿⠻⠻⠙⠉⠁⡛⣿⣿⣿⣿⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⢀⠀⠀⠀⠃⠛⡜⣿⣿⢻⠘⠀⠀⠀⡀⠀⠀⡡⠀⠤⠀⡆⣿⣿⣿⠀⠀⠄⠘⠄⠠⢀⠀⠋⡿⣾⢿⣿⣷⡀⣇⣿⣿⣿⢠⠀⠀⠀⠀⠀⡄⠀⠀⡇⣿⣿⣿⣿ ⣿⠐⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⢿⢣⣵⣟⡧⢿⣽⡻⢧⡹⣞⣝⠧⢳⣯⣿⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⠻⠐⠀⠀⠀⠄⠈⡀⠀⠀⠁⠅⠀⡀⠠⠀⠠⠈⠠⠀⠀⠀⠃⡟⣿⢺⠀⠀⠀⠠⠀⠀⠀⠠⠀⠡⠀⢇⣶⣿⣿⠚⠀⠀⠀⠀⠋⠟⣿⣷⣛⣧⣜⣿⠿⠺⣿⣿⣿⣀⠀⠀⠀⠀⠀⠈⡄⢀⠀⡇⣿⣿⣿⣿ ⣿⠨⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⣿⣿⡿⠞⣹⠶⣝⡳⢮⣹⡷⣚⣹⡷⣿⢀⠀⠀⠀⠁⠈⠀⣀⣤⣤⣿⣿⣿⠻⠈⠀⠀⠀⠀⠡⠄⠀⠄⠀⠀⠀⠀⠡⠄⠂⠐⠀⠋⣿⣿⣿⢿⠛⠀⠀⠀⠄⠡⠄⠈⠁⠂⠀⠀⠀⣿⣿⢿⣿⠿⣿⣿⣿⣾⡵⢯⡱⢾⣏⣿⣿⣿⣿⣾⣼⢠⠀⠀⠀⠀⠀⠀⡄⢀⠀⡇⣿⣿⣿⣿ ⣿⢚⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋⠰⣤⣧⣿⣿⣿⢿⣛⣴⡿⡞⣏⡝⣣⢷⣏⡿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠁⠈⠀⣤⣿⣿⣿⢻⠙⠀⠀⠀⠀⡀⠀⠰⠄⠒⡀⠀⠀⠐⠋⡟⣿⣿⣿⣿⣿⣿⢻⠛⠘⠀⠀⠀⡀⠀⢠⠀⠁⡟⣿⣿⣿⣿⣾⣹⣜⠿⣎⣻⡵⣻⢧⣟⣿⣿⣿⣿⢸⢀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⡇⣿⣿⣿⣿ ⣿⢹⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⢁⠀⢀⠀⠀⡆⣷⣿⣿⣿⣸⠀⣧⣿⢞⡹⣷⡿⣿⣿⣿⣿⣿⣾⣷⣿⢿⠛⠀⠀⠀⠃⠀⠀⣆⣷⣾⣶⣷⢿⠛⠛⠉⠀⠀⠀⠁⠉⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠛⠉⠛⡿⣿⣿⣿⣵⢿⣭⡷⢏⣿⠿⣿⠿⣻⡽⢮⡽⣷⣿⣿⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⣿⣿⣿⣿ ⣿⢸⣿⠠⠀⠀⠀⠀⠀⠀⠀⠁⠛⠼⢀⠀⠀⠀⠀⠀⡄⣷⣿⣿⢻⠈⡀⣯⣿⡟⣿⣿⣿⣿⣿⣿⣿⠋⠙⢻⣄⣶⢿⠹⠀⠀⠠⠂⠀⡀⢀⠀⡀⣀⣀⣦⣶⣶⣿⣶⣶⣿⣿⣿⣿⣿⣭⡾⢏⣻⣿⣿⣿⣴⣅⣻⡀⣀⣀⣦⣿⣿⣿⣾⣻⣭⡿⠿⣿⣿⣶⣶⣠⣄⣠⣀⣤⣶⣿⡾⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⣿⣿⣿⣿ ⣿⢹⣿⢈⠀⠀⠀⠁⠋⡶⠀⠀⠀⠀⠀⠀⠃⡼⢀⠀⠀⠆⣷⣿⣿⣿⠈⣟⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣷⣿⠿⠁⣏⣿⢸⠀⠀⡄⠀⠁⠐⠀⠉⠀⠈⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⣿⣿⣘⣆⣷⣿⠙⡀⢴⠉⠉⠈⠉⣶⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠈⠁⠀⠀⠁⡿⣾⢀⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡇⣿⣿⣿⣿ ⣿⢩⣿⠐⠀⠀⣣⡦⢑⠓⠈⠀⠀⠁⠃⡄⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⠿⣿⣿⣻⣾⣿⣿⡽⣿⣿⣿⣿⠀⡀⣄⠾⠏⣿⢸⠀⠀⠆⠀⠀⠀⠀⢀⠁⢈⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠸⡀⣇⣿⠿⣿⣹⣛⣉⣯⡿⣿⣿⣴⢀⠀⠀⠀⠀⠂⠈⠐⢈⠂⠀⠁⡟⣾⢀⠀⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⣿⣿⣿⣿ ⣿⢸⣿⠠⠀⠀⠀⠀⠀⣀⡦⠿⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⣿⣿⣿⢿⣏⣧⣿⣿⣿⣿⣿⣷⠀⠀⠀⢫⣿⣾⢀⠀⠀⠂⠀⠀⠈⠂⢀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠘⡀⢐⡁⣭⣿⣿⣤⣮⣦⣿⢰⠀⠀⠂⠀⠁⠀⠄⠀⠂⢀⠀⠀⡆⣴⢀⠉⡿⣿⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆⣿⣿⣿⣿ ⣿⢸⣿⢈⠀⠀⠀⠀⠀⠀⡗⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⢻⣭⣞⣿⣿⣿⣿⣩⠻⠿⡿⣿⣴⢀⠀⠁⠀⠐⠀⠑⠀⠀⠁⠋⠿⣿⣿⣷⣭⣷⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⠿⡿⣿⣿⣿⣿⠙⠀⠻⣿⢰⠀⠀⠀⢀⠀⠀⠐⠀⠁⠀⠀⠉⠀⠀⡷⣿⣿⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡅⣿⣿⣿⣿ ⣿⣰⣿⠐⠀⠀⠒⠁⠄⡆⢰⠀⠀⣇⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⣤⣷⣿⢿⣿⡞⣟⣿⣾⣴⣶⣤⣤⠀⠀⠀⠐⠀⠀⠀⡀⢀⠀⠁⠋⡿⣾⣽⣳⣝⢳⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠀⠀⠀⡁⠀⠈⠀⠁⠀⠀⠈⠃⠔⠫⡟⣿⣿⣴⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿ ⣿⣰⣿⠠⠀⠀⣃⠨⠀⠀⠀⠀⠀⠀⡆⡣⠁⠀⠀⠀⠀⠁⠏⠷⣤⣄⢀⠀⠀⣄⣷⣿⣿⣼⠀⠦⠘⠀⠀⠀⠐⠉⠀⠈⠀⠛⠛⠛⠛⠟⡾⣿⣭⣳⣜⡾⡝⢻⣿⣿⣴⢀⣀⣦⣿⣿⣿⣿⣿⣿⣿⣽⣯⣟⣿⣿⣿⣻⣵⣿⣿⢿⠛⠀⠀⡁⠀⠁⠠⠃⠄⠀⠁⠙⠏⣿⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿ ⣿⣰⣿⢈⠀⠀⠀⣆⡗⠀⠀⠀⠀⠀⠀⡀⣧⠸⠀⠀⡇⢧⠨⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣿⣿⠻⠛⠤⠀⡄⠠⠄⠠⠀⠀⠀⠋⡛⣿⣳⣥⠿⣏⡱⣾⢏⣿⣾⣀⠀⠀⠀⠀⠀⡀⣿⣾⣯⣾⣽⢯⡿⣿⣿⣿⣿⣿⣿⡿⣏⢧⣿⣿⣿⣤⢰⠁⠀⠋⠈⠋⠛⡿⣿⣾⣴⣁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡅⣿⣿⣿⣿ ⣿⣸⣿⠐⠀⠀⠀⠋⣏⢠⠀⠀⠀⠀⠁⠾⡀⠀⠀⠉⠈⠀⡀⠀⠅⠋⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⣿⣿⣿⠛⠛⠛⠛⠛⡿⣿⣷⣞⣏⡱⣽⡞⣫⣼⡟⣿⣾⢀⠀⠐⠌⡀⢠⠀⡄⣷⣿⢿⢿⣿⣾⣷⣿⣿⣤⣀⡀⣦⣷⣿⢿⣿⣿⣿⢻⠛⠛⡿⣿⣿⣿⣶⣴⣀⠀⠀⡆⣿⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿ ⣿⢸⣿⠠⡇⣵⣴⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⣇⠀⠁⡟⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣧⣿⣿⣿⣿⣯⢶⡟⢿⣯⡳⣝⢯⣜⡿⣿⠀⠀⡈⠀⡐⠀⢠⠀⠀⠀⣄⣦⣼⣡⠋⡿⣴⢀⠈⠀⠃⠛⣿⣿⣿⣿⣿⣿⣿⣾⣶⣦⣤⣠⠀⠀⠀⠀⠀⠀⠀⡀⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿ ⣿⢺⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⠿⣛⣹⣷⡞⣏⣻⢭⣷⣿⠀⠀⢀⠀⠀⠀⠁⠉⠟⠿⠂⠛⢿⡿⣿⣿⠈⠻⢿⠿⡿⣿⣶⣤⣶⣤⣴⣠⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⣿⣿⣿ ⣿⢚⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⡊⣤⣦⣷⣿⣿⡿⣟⢻⣹⣿⣿⠻⠻⠛⠟⠟⡾⣦⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠷⠌⡍⠉⠚⠤⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⣿⣿⣿ ⣿⢸⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢃⡌⠃⠠⠀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣾⣶⣠⣀⢁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠭⠁⠉⠀⠀⠁⠊⠑⠇⣾⣎⡦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣿⣿⣿ ⣿⢈⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠟⡹⡕⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣆⣾⣾⣷⣾⣴⣦⣴⣤⣤⢠⠀⠀⠀⠀⠈⢤⠂⠂⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⢿⣿⣻⡊⠏⡆⠤⡄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⡿⣿⣿ ⣿⢈⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⣶⡭⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢋⡋⠀⡁⠘⠁⠀⠄⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣖⣤⡆⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡅⣿⣟⣿⣿ ⣿⢀⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⡇⠑⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠳⠾⠓⠒⠈⠉⠀⠀⠀⠀⠀⠙⠄⠠⣤⠦⢈⠀⡀⠁⠐⡠⠁⠁⠄⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡥⢧⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⣏⣿⣿ ⣿⢸⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣅⠘⠉⠀⠃⡀⡶⣒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣍⠖⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⣿⣯⣿⣿ ⣿⢠⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠋⠀⣡⠀⢆⠄⠀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠋⠛⡜⢁⠁⠉⠉⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠬⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡅⣿⣟⣿⣿ ⣿⢹⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⡁⠗⠐⡂⣴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢏⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡇⣿⣿⣿⣿ ⣿⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠂⠀⠂⠀⠀⠄⠀⠀⠀⠁⠡⠂⠀⠐⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠰⠒⢩⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿ ⣿⣽⣿⣿⠙⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠁⠉⠈⠉⠁⠈⠉⠁⠈⠉⠉⠉⠈⠉⠁⠈⠉⠁⠈⠉⠉⠈⠉⠁⠈⠉⠡⣏⠉⠋⠉⠉⠱⠉⠈⠉⠁⠉⠁⠉⠈⠉⠉⠁⠉⠈⠉⠉⠁⠉⠈⠉⠉⠁⠉⠁⠈⠉⡍⠁⠉⠉⠉⠁⠈⠉⠁⠈⠉⠉⠉⠉⠁⠈⠉⠁⠈⠉⠁⠉⠉⠉⠈⠉⠁⠈⠉⠁⠈⣉⠅⡈⠉⠈⠉⠁⠈⠉⠉⠋⣿⣿⣿⣿⣿ ⣿⣿⠈⣤⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣿⣬⣥⣬⣬⣥⣤⣬⣦⣤⣤⣤⣤⣤⣤⣴⣤⣴⣤⣴⣤⣤⣥⣮⣤⣦⣥⣧⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣴⣤⣴⣤⣴⣤⣤⣤⣤⣤⣥⣤⣦⣥⣦⣭⣧⣽⣥⣯⣥⣬⣤⣬⣯⣿⣶⣭⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠒⠑⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠒⠒⠶⠶⠤⠤⠧⣰⠀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠋⠛⠛⠒⠒⠒⠒⠒⠖⠤⠤⡤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢦⠑⠀⠀⠀ ⠀⠞⠤⠤⠲⠛⠖⠤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢦⠘⠀ ⠀⢘⠀ ⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈ ⠀⣞⠒⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠴⡤⣀⣀⣀⣀⣀⣀⠤⠀⠈⠀⠀⠀⠁⢹ ⡇⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠤⣀⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇ ⣸ ⠛⠴⣠⣀⣀⣀⣀⣀⣀⢤⠤⠤⠒⠒⠒⠒⠒⠒⠤⠠⣀⢀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠀⠁⠋⠿⣾⠀⠀⠀⠀⡎ ⢸⠀⠀⡁⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⡄⢄⣀⠀⠀⠀⠀⠀⢸ ⢇⠤⢀⠀⠁⠛⠛⠈⡀⡀⢀⠤⠤⠀⠒⠀⠈⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀ ⡀⢱⠀⠀⡀⣀⡤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀ ⠀⡀⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⠀⠀ ⠀⠀⠀⢄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡠⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠔⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠒⠄⡡⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠤⠂⠒⠓⠉⠉⠉⠉⠋⠒⠒⠆⠬⠹⣀⠀⠀⠀⠋⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠒⠉⠀⠀⠀⠀⢂⡈⠱⠊⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀