⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡾⠋⠈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡞⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡰⠋⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⡰⠃⠀⠀⠀⠀⠀⣠⣶⠯⠝⠛⠛⠲⣄⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢏⡼⠁⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⢠⢏⠞⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠀ ⠀⠀⠀⣞⡎⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀ ⠀⠀⢸⡽⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⡟⡇⠀⠀⠀⠀⠀⢀⣇⠀⣿⣄⠀⠀⠀⣶⡀⢸⡟⢦⡀⢸⣷⣄⢿⣇⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸⣻⢦⡿⡿⢷⡀⢠⡷⠻⣮⣷⠀⠙⢾⣿⠟⠿⣿⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⢻⡄⠀⠀⠀⠀⠀⢸⡟⡆⠙⠃⠀⠙⠛⠃⠀⠈⠛⠁⠀⣰⠃⣀⣴⣿⠆⠀⠀⣠⡟⠀⠀⠀ ⠀⠀⠈⣧⡀⠀⠀⠀⠲⣾⣇⠹⢦⡀⠀⠀⠠⢒⣒⣒⣠⠤⣞⡻⠽⠚⠉⠼⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣦⡀⠀⠀⠈⠙⠙⠛⠛⠛⣛⠛⠓⠒⠚⠉⣉⡤⢀⣀⣀⣤⡴⠾⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣽⡿⡤⢠⡲⠶⠶⠶⠽⣿⣶⣤⣴⡾⠋⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠀⠀⠀⠀⠀⠀⠉⢙⡞⠁⠀⠀⠀⠐⠯⠤⣤⠤⠽⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡸⡆⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣤⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⣿⠔⡶⠤⣤⣞⡁⠀⢀⡴⡏⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣹⡆⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣻⣷⡻⡄⠀⠀⠙⣲⠟⢡⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⡿⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⠖⠲⣿⣇⠀⢠⡾⠋⠀⢸⡇⠀⠀⠀⠀⢲⡶⠿⢤⠀⠀⡏⣿⣣⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⢸⣸⡯⠭⢇⣇⣴⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⢺⠶⣶⢺⡀⠀⢁⡇⣏⣇⠀⠸⣵⡀⠀⠀⠀⠀⠀ ⠈⢿⣟⣠⢾⡞⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⡸⡄⠀⢱⣳⠀⠀⠀⠀⠀ ⠀⠀⠙⠶⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⢿⠀⣇⢳⠀⠀⢳⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⡏⠛⣿⠉⠀⢸⣼⡀⠸⡜⡆⠀⠀⢫⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠟⣿⠹⠀⠀⠀⡟⡇⠀⢱⣧⠀⠀⠈⢿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢣⢻⠀⠀⢿⠀⠀⠀⠈⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡌⣇⠀⠸⡇⠀⠀⠀⠸⣷⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⢙⠍⣿⠀⠀⠀⢳⠹⡄⠐⠧⠤⡤⠤⠞⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠙⠉⡏⠉⠀⠀⠀⠈⢧⢳⡀⠀⢰⠋⡄⣠⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢆⢣⠀⠘⢞⣗⣻⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠫⢧⣰⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣴⡿⠧⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⡒⢶⠤⣄⣀⣀⣀⣀⣸⣇⣠⠴⠚⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃⠀⢠⠓⠶⠾⠿⠛⠚⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡼⠂⠀⠀⠀⠀⠀⢹⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⡇⠀⠀⠀⠀⠀⠀⠈⢇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢈⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠸⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⡀⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⡷⡆⣖⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠿⠿⢷⡬⠗⠀⠀⠀⠀⠀⠀⠀⠓⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀