⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⠿⣿⣿⣿ ⣿⣿⢋⠄⠀⠘⠝⠿⢻⠿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠏⢻⣯⣭⡉⠛⠛⠋⠁⠉⠉⠉⠛⠛⠻⠿⠿⢿⡿⠿⠿⠿⠟⠛⠛⠿⠋⠉⠉⠙⠋⠀⠈⠀⢀⣤⡍⠉⠛⢻⡿⠛⠻⢿⠿⠛⠫⠀⠈⠉⠠⠅⠀⠄⠀⢿⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠒⠚⠚⠁⠉⠉⠉⠀⠀⠀⠀⠀⣤⡾⢯⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢸⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢙ ⣿⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣾⡟⠀⢸⢰⠂⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⡆⡎⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⣿⣱⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢸⣾⡄⠙⢦⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠊⢰⡇⡇⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹ ⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⢸⡏⡇⠀⠀⠱⡌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡴⠁⠀⢸⠁⡇⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠘⡇⡇⠀⠀⢀⣨⠇⢙⣦⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⣠⠚⢠⣋⠀⠀⠀⠸⢸⡇⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⡠⢆⡇⠸⢖⣊⠭⢶⣶⣯⠿⠶⠒⠒⠒⠋⠉⠋⠗⠙⠉⠑⠒⠶⠾⠭⣑⣲⠬⣍⣲⠤⠇⢸⡇⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⡸⠁⠈⠷⠚⠉⢀⠔⡫⠋⠀⠀⠀⠀⠀⠀⠀⠤⢀⠐⠄⠀⠀⠲⠄⠀⠀⠀⠉⣙⢶⡉⠑⠲⣾⠳⣄⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⣿⡗⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⠙⠒⠂⠀⠀⡴⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣦⠙⢦⡀⠀⠠⠼⠆⠀⠀⠀⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⢟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢸⢻⠈⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡼⠃⠀⠀⠀⠀⠀⠀⢠⡟⢳⡄⠀⣟⡆⢀⡧⣵⣼⠶⠶⠶⠶⠶⠿⠶⢦⣤⣤⣬⣧⣬⣤⣤⣄⣀⣀⡐⠦⢶⣏⡇⡼⢳⡀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⢳⡄⢻⣳⣸⣦⣤⣽⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣱⣖⣠⡀⠘⠀⠁⠉⠛⠀⠘⢾⠁⠈⢳⡄⠀⠀⠀⠀⠀⠀⠘⢷⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⣶⣿⣀⣀⣀⣀⣽⡜⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⢻⣶⠚⢃⡀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⡞⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠀⢠⡇⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⢄⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢷⣶⢿⡿⠛⠋⠙⠁⠀⠀⠀⢿⠿⠷⣶⣶⣤⣄⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶ ⢟⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙ ⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠲⠖⠊⠉⠉⠉⠉⠉⠉⠀⠐⣿⢿⡀⠈⠁⠁⠉⠉⠉⠉⠉⠉⢉⠉⠑⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⠽⠒⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⠀⠀⠀⠀⠈⠉⠉⠙⠉⠐⠀⠀⣠⠏⠀⠀⠀⠀⠘⢆⠀⠐⠋⠉⠉⠉⠉⢈⡉⣹⣀⣴⣾⣶⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⣿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠶⠶⠛⠛⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⡄⠀⠀⠈⠣⡀⠀⠀⠀⢀⣴⡿⠛⢻⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⣦⠀⠀⠀ ⣧⠀⠀⠀⠀⢀⣀⣤⡤⠤⠖⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣤⣤⣀⣀⣀⣠⠞⠀⠀⠀⣠⠋⠘⢦⠀⠀⠀⠱⣄⢀⡠⠊⠀⠀⢠⢸⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀ ⣽⡴⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠛⠓⣄⡼⠁⠀⠀⢀⡔⠁⠀⠀⠀⠳⡀⠀⠀⠘⢢⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⢰⠟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠳⣀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠋⠀⠀⢀⠞⠁⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⠙⢦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⠞ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⣾⣥⠀⠒⠒⠒⠒⠒⢂⡤⠐⠒⠒⠒⠒⠒⢒⣶⠐⠂⠒⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣡⢃⣼ ⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢦⡀⠀⠀⡖⠋⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢻⠃⣸⠁ ⡙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠉⠲⣼⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡡⠀⡴⠛⣸ ⡟⠘⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣱⠃⠄⠀⠘⣾ ⣆⠘⣬⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣯⣀⣀⣀⣘⠷⣄⡀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣺⠁⣠⠀⢀⠀⣽ ⠹⣆⠈⢿⣮⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⢋⡾⠀⢸⡏⠀⠙⡇⠈⠙⠷⢦⣄⡀⠀⠀⢸⣿⢷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⡴⠁⠚⠁⠀⠀⣴⠿ ⡇⠸⣆⠈⢿⣶⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠚⣋⣉⣥⠶⢚⣿⠇⠀⠘⢳⡆⠠⠿⣄⡀⠀⠀⠈⠉⢳⣶⣜⢻⡄⣌⣉⣉⣙⡛⠓⠶⠶⠦⢤⣤⣤⣀⣀⣀⣀⣠⣾⢿⣽⠀⠀⡆⠀⠀⠀⠰⠋⢳ ⡗⠀⠸⣦⠀⠙⡆⠻⡀⠀⠀⠀⢀⣠⣤⣴⠶⠛⠛⣉⣥⡤⠲⠛⠋⢉⣠⣤⢾⣿⠀⠀⠀⠘⡇⠀⠀⠀⡏⠙⠒⡄⠀⡜⠀⢹⣿⠃⠀⠹⣀⠉⠉⠛⠓⠂⠤⠤⣤⣌⣉⡉⠉⠉⣩⣥⣿⡗⠀⠀⠀⢠⠀⠀⠀⠀⣼ ⣏⠀⠀⠘⣆⠀⠩⣄⠘⠿⡿⠛⠋⢉⣤⠤⠖⠚⠉⠀⢀⣤⣴⣶⡿⠛⠋⠀⠈⣾⠀⠀⠀⢸⡇⠀⠀⠸⢤⣄⣠⡟⢦⡣⢤⣼⡏⠀⠀⠀⠈⠓⢶⣤⣤⣤⣄⣀⠀⠀⠒⠩⠝⠛⠛⣿⣯⣿⣧⡐⣠⠟⠀⠀⠀⠀⣙ ⣷⣀⠀⣐⣸⣆⡀⠉⢀⣀⣶⡶⣟⢋⣀⣠⣤⣶⣾⣿⣿⣿⣋⣁⡀⠀⠀⠀⠠⣸⠀⠀⠀⢸⡇⠀⠰⠀⠀⠀⠀⡇⠀⠙⠶⣽⡃⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣄⣽⣿⣿⣿⣿⣤⣀⣀⣀⡀⠬