⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⡜⠁⠀⠀⠀⣀⡈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠉⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⡉⠓⠦⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠂⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣖⠂⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⡴⠋⠉⠛⣦⡀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⢤⣙⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣤⡜⠉⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠈⣦⣼⣿⣿⠓⢀⡀⣰⠗⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡧⡀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⣸⣿⡟⠾⠛⠁⠯⠼⠥⢤⠤⠄⠒⠀⠀⠀⠀⠀⢠⠞⠁⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⡀⠀⡴⢻⢫⣽⣿⣇⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠋⠉⠀⠒⡥⠒⠈⣸⣿⣿⣧⣾⣤⡙⠢⡄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⡹⣧⠀⠤⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⢀⣤⡞⠁⢀⣾⣿⣿⠿⠟⢿⣿⣿⣦⣄⣀⣀⣀⣴⡞⠛⠉⠁⠀⠈⢷⡈⢷⠀⠀⠀⠀⠀⢀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⣠⠞⠋⠀⣠⣿⡿⠋⠀⠠⣴⣀⣬⡙⠎⠉⡏⠌⣵⡈⠹⠀⠀⠀⡆⠀⢸⣧⠈⣇⠀⠀⠀⠹⣄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⡾⠁⠀⠀⣠⢿⠏⠀⠀⠀⢀⣧⡙⢿⣴⣢⢇⣿⡆⣿⠙⣄⠀⣠⣇⣅⠀⠸⣿⣆⢨⢧⠀⢣⠀⠻⣄⣴⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠈⠑⠒⠒⠋⢁⣾⠀⠀⠀⡀⠠⣿⠛⢂⠙⠻⣼⢿⣄⢷⣆⣽⢠⣸⠸⣟⡛⡓⠻⢿⡎⢿⣷⠀⠒⠀⢹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⣦⠄⠀⠀⠀⠈⠀⣙⠷⣲⡟⡛⠻⠾⣿⣧⠾⠏⢠⠼⢛⠰⡄⢿⣿⣌⢿⡖⠀⠀⣼⣿⣍⠻⢿⣿⣿⣿⣿⣶⡄⠀ ⠀⠀⠀⣼⠋⠀⣀⡈⢷⣶⠀⠀⢀⠤⠀⣴⣻⢫⢇⣀⡴⠋⠀⣀⣠⣴⣞⣰⠋⠀⠀⠛⢿⣄⠻⣵⣄⣿⣿⡟⢀⣦⣿⣿⣿⣧⣿⣿⡄ ⠀⠀⢸⠃⠀⠀⠀⠀⡈⠉⢷⡀⢀⠔⠸⢿⢇⡾⠞⣩⡴⠶⢾⣟⣯⣴⣻⠇⠀⣤⠀⠀⠐⢛⣿⣿⣿⣿⣿⡅⠺⢻⡏⢹⣿⣿⢿⣾⡇ ⠀⠀⣼⣣⡀⢀⠀⡀⠉⠳⣼⠻⣄⠀⢼⠀⡜⠁⣺⢫⡞⡔⠁⡸⠏⣧⠃⢀⠂⠀⠸⠴⡒⢏⠉⣿⣿⠿⢿⣿⣶⣾⣧⡈⠁⣸⣿⡿⠁ ⠀⠀⢻⠉⣍⠿⣶⣦⣾⡠⠈⠙⣿⣧⡘⢧⠇⠹⠵⡟⡠⠀⡸⣧⢿⠃⠀⢾⡆⢰⡟⠀⡃⣄⠀⣽⡟⣷⣌⢻⣿⣀⣀⣠⣴⡿⢻⠁⠀ ⠀⠀⠈⣧⡤⠤⠾⢽⣿⣛⠿⣿⡬⢤⣹⣮⣷⡀⢰⣿⡠⠀⣾⠇⠀⡼⠀⣩⠇⠊⣠⣤⣷⡏⢸⡿⢀⡏⠙⢦⣽⢟⣋⠉⠁⠀⢨⠇⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠉⣙⡞⠉⠀⠀⠀⠀⠈⠉⠛⠿⣅⡞⢁⣴⣤⠥⠾⠛⠟⠆⠈⠛⠉⠁⠸⡇⢰⠇⠀⠀⠉⠲⢿⣖⣀⡤⠞⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣤⣠⣶⣎⣰⣾⣦⣬⣶⣦⢀⣤⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢇⣀⠂⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠟⠋⠉⠉⠙⠛⢷⣼⠏⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⣿⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡄⢀⢴⣦⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀