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⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣯⢿⣽⣻⢷⣻⣞⡿⣞⡿⣾⡽⣯⣿⣿⡿⣯⢿⣻⣟⡷⣯⢿⣳⡿⣾⣽⣻⢾⣽⢾⣳⢯⡿⣿⣿⣯⣟⡾⣽⣻⢾⣽⣻⢾⡽⣯⣟⣾⣻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠆⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢠⣾⠟⠛⢿⣷⣀⣤⣤⣀⠈⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣯⢿⣽⣻⢾⡽⣯⢷⣯⢿⣽⣻⣷⣿⣿⣟⣯⢿⣻⢯⣷⢯⡿⣽⣯⢿⣽⣳⢯⣟⡿⣞⡿⣽⡿⣽⣳⢿⡿⣿⣿⣳⣯⣟⡾⣽⢯⣟⣷⣻⢾⡽⣯⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⢿⠋⠁⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⢠⣿⠋⠀⠀⢠⣿⠟⠉⠛⢿⣿⣿⠃⠀⠀⠀⢀⣼⣿⣿⡿⣯⢿⣽⣻⢾⡽⣯⢿⣽⣻⣞⣿⣾⣿⡿⣟⣷⢯⣟⣯⣿⣻⢾⣯⣟⡷⣯⣟⣾⣽⣻⢾⡽⣯⣟⣷⣻⣽⢯⡿⣽⣻⣟⣿⣷⣯⣿⣽⣻⣞⡷⣯⢿⣽⣳⣟⣾⣻⣿⣿⣷⡀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠛⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⣿⣿⣄⣀⣠⣾⠋⠀⠀⠀⣸⡟⠀⠀⠀⡀⢠⣾⣿⣿⢿⡽⣯⣟⡾⣽⢯⡿⣽⣻⣞⣷⣿⣿⣟⣯⣿⣻⢾⣯⣟⣾⣳⢯⣿⢾⣽⣻⢷⣻⣞⡷⣯⢿⣽⣳⣟⡾⣽⣞⡿⣽⢷⣻⡾⣽⣻⢿⣿⣷⣿⣾⡽⣯⣟⣾⣳⣟⣾⣳⢯⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠈⠉⠛⠿⣦⠀⠀⠀⢿⣿⡀⠀⠀ ⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣤⣀⠀⣰⡿⠁⠀⠀⠀⣱⣿⣿⣿⢯⡿⣽⣳⢯⡿⣽⣯⣿⣷⣿⣿⢿⣯⢷⣻⣽⣳⣯⣟⡾⣽⢾⣽⣻⣞⡿⣾⡽⣯⢷⣯⢿⣽⣻⢾⡽⣞⣿⣳⣯⢿⡽⣯⡷⣟⡿⣽⣻⢾⡽⣿⢿⣿⣷⣿⣞⣷⣻⢾⣽⣻⢾⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀ ⠀⠀⢠⣿⡿⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠈⠙⠻⢿⡿⠁⠀⠀⠀⣰⣿⣿⣿⡽⣯⣟⣷⣻⣯⣿⣿⣿⣿⣿⣽⣾⣟⣾⢯⣟⣾⣳⣟⣾⣽⣯⣟⣾⣳⣯⣟⣷⣻⣽⣻⣞⡿⣾⣽⢯⣿⣽⣞⣷⣯⣿⣽⣳⣿⣽⣻⣷⣿⣯⣿⣽⣯⣟⣿⣻⣿⣿⣿⣿⣾⣽⣻⣾⣽⣿⣿⣦⠀⠀⠀⠀⠠⣿⠏⠀⠀⠀⢀⣀⣀⣤⣴⣷⠀⠀⠀⢹⣿⡆⠀ ⠀⠀⣾⣿⠃⠀⠀⢀⣿⠟⠉⠙⢿⣶⣶⣶⣶⣶⣾⠃⠀⠀⠀⢰⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡆⠀⠀⠀⠀⢿⣆⣠⣴⣾⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⣿⣿⡀ ⠀⢰⣿⡟⠀⠀⠀⣼⡏⠀⠀⠀⣾⡿⠁⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⣾⣿⠇⠀⠀⢠⣿⣇⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣷⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿ ⢀⣿⣿⠀⠀⠀⢸⡟⠻⠿⢶⣾⣷⣤⣄⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣻⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠄⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣻⣿⣿⡆⠀⠀⠀⠈⢿⣷⣤⣤⣤⣴⣶⠾⠟⠛⠃⠀⠀⠀⢸⣿ ⢸⣿⡇⠀⠀⠀⣼⠀⠀⠀⢀⠀⠈⠉⠙⢻⣿⠀⠀⠀⠀⣸⣿⣿⢷⣯⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⡐⢠⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢷⣻⢾⣿⣷⠀⠀⠀⠀⠀⠹⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⣼⣿⠇⠀⠀⠀⣿⠀⠀⠀⣼⡇⠀⠀⠀⣿⡟⠀⠀⠀⠀⣿⣿⣿⣻⣞⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢂⣴⠏⢀⠡⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣯⣟⡿⣿⣿⡄⠀⠀⠀⠰⣶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠂⠀⠀⠀⣿ ⣿⣿⠀⠀⠀⢸⣟⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣷⣻⣞⣷⣻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠐⡀⢻⢀⠂⡐⢨⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⡷⣯⣟⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⢀⣿⡇⠀⠀⠀⢐⣿⣿⣷⣻⣞⡷⣯⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⡐⠠⢸⡆⠐⠠⠉⣿⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣾⣽⣳⢯⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⠀⠀⠀⢸⣿⣶⣶⣴⣿⣶⣦⣶⣾⣿⡃⠀⠀⠀⢘⣿⣿⣷⣻⢾⣽⣳⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠠⢀⠡⠈⡇⡈⠄⠡⢸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⢷⣯⣟⣯⣿⣿⡇⠀⠀⠀⠀⢻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⣿⡆⠀⠀⠀⣿⣿⡷⣯⣟⡾⣽⢯⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⢢⣁⣷⡤⠈⠄⣿⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣟⡿⣾⡽⣞⣿⣿⡇⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⣿ ⣿⣿⡆⠀⠀⠀⣠⣤⣤⣤⣶⣶⣾⣿⣿⣿⡟⠁⠀⠀⠀⣿⣿⣿⣳⢯⡿⣽⣻⣞⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡁⠄⠠⠙⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠐⠠⢈⢻⠀⠌⣼⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠟⠡⢀⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⡿⣾⣽⣻⢷⣻⣽⣿⣿⡇⠀⠀⠀⢰⣿⠏⠁⠀⠀⠉⠉⠉⠉⠙⠁⠀⠀⠀⣿ ⢸⣿⡇⠀⠀⠀⠛⠋⠉⠉⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢻⣿⣿⡽⣯⣟⣷⣻⢾⡽⣿⣿⣟⡿⣿⣿⣿⣟⣿⣻⢿⣿⣦⠁⢂⠘⠻⢿⣿⣟⣿⣻⣟⡿⣿⣿⠃⠠⢁⢂⡿⠀⠌⣿⣿⣟⣿⣻⣟⣿⣻⣿⡿⠟⠛⡉⠄⠡⣼⣿⣿⣻⣟⣿⣻⣟⣿⣻⣿⡿⣽⣳⢯⣟⣯⢷⣻⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣿ ⠸⣿⣷⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣷⣻⢾⡽⣯⢿⡽⣿⣿⣽⣳⣯⣷⢯⡿⣽⢯⣿⣧⡐⠠⢈⠐⠠⠙⣿⣷⣟⡾⣽⣻⣿⣧⠐⠠⠈⠄⡈⠐⣼⣿⣟⡾⣯⣟⡾⣷⡿⠁⡐⠠⠐⡈⣰⣿⣿⢯⣷⣻⡷⣟⣾⣳⣿⣿⡽⣷⣻⣟⡾⣽⢯⣿⣿⡏⠀⠀⠀⠀⠘⢿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠰⠆⢰⣿ ⠀⣿⣿⡄⠀⠀⠀⣠⣾⡟⠋⣀⣀⣠⣤⣤⣶⣆⠀⠀⠀⠀⢿⣿⣿⢾⡽⣯⢿⡽⣯⢿⡽⣿⣿⣳⣟⣾⣿⠿⣯⣿⣞⣿⣿⣶⣦⣬⣤⣅⣠⠙⠿⣿⣯⣷⣻⢿⣷⡠⢁⠂⠄⣱⣿⡿⣾⣽⣳⣿⡿⠟⢁⣐⣠⣥⣶⣾⣿⡿⣽⢯⣟⣷⣻⣟⣾⣿⣿⣳⣟⣷⣻⢾⡽⣯⢿⣿⣿⠁⠀⠀⠀⠀⣀⠀⠈⠉⠛⠛⠛⠿⠿⠷⠆⠀⠀⠀⣸⣿ ⠀⢹⣿⡇⠀⠀⢰⣿⡿⠿⠿⠛⠛⠋⠉⠉⢹⣷⠀⠀⠀⠀⠸⣿⣿⣯⢿⡽⣯⢿⡽⣯⢿⣽⣿⣿⣞⡷⣿⡀⢀⠛⢿⣾⣽⣿⣟⣿⣻⢿⣿⣿⣷⣮⡙⢿⣯⣿⣻⣿⡄⡈⣼⣿⢿⣽⣷⡿⢟⣭⣾⣿⣿⡿⣿⣟⡿⣯⣷⣻⣽⠿⠛⣿⣳⣯⣿⣿⣳⣟⣾⣳⢯⡿⣽⢯⣿⣿⠏⠀⠀⠀⠀⣸⡿⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣿⡿ ⠀⠈⣿⣿⡀⠀⠀⠉⣷⠀⠀⠀⣤⡀⠀⠀⠈⢿⣧⠀⠀⠀⠀⢻⣿⣿⣯⢿⡽⣯⢿⣽⣻⢾⡽⣿⣿⣽⣻⣷⠀⠂⠄⡀⠠⢀⠉⢿⣿⣻⣞⣷⣻⢿⣿⣷⣌⡻⢯⣿⡷⠰⣿⣯⡿⢛⣭⣾⣿⡿⣿⡽⣾⣽⣳⠿⠋⢉⠉⡉⠁⠄⣼⣿⣷⣿⣿⣳⣟⣾⣳⢯⡿⣽⢯⣿⣿⡟⠀⠀⠀⠀⢰⣿⠃⠀⠀⠉⣿⠿⠿⣿⣶⣦⠀⠀⠀⣸⣿⠃ ⠀⠀⢹⣿⣇⠀⠀⠀⣿⡄⠀⠀⠹⣿⡀⠀⠀⠘⣿⣆⠀⠀⠀⠀⢿⣿⣿⣯⢿⣽⣻⢾⡽⣯⢿⡽⣿⣿⣳⡿⠀⡁⢂⠰⣧⡀⠌⢈⠛⠛⠻⣿⣯⣟⡾⣽⢿⣿⣦⡏⢁⠐⡈⣠⣴⣿⡿⣿⣽⣻⣷⡿⠿⠛⠁⠄⡈⢄⡂⠄⠡⢸⣿⣷⣿⣟⣷⣻⣞⡷⣯⢿⡽⣯⣿⣿⡿⠁⠀⠀⠀⠀⣾⡏⠀⠀⠀⣸⡟⠀⠀⠀⣿⡇⠀⠀⢠⣿⡟⠀ ⠀⠀⠈⣿⣿⡀⠀⠀⠸⣷⡀⠀⠀⢻⣷⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⢻⣿⣿⣟⡾⣽⢯⡿⣽⢯⡿⣽⣿⣿⣷⣀⡐⢀⠂⡈⠛⢦⣄⡂⠌⡀⠌⢿⣿⣿⣽⣻⣞⡿⣿⣆⠂⣼⣿⣿⣻⣽⣳⣯⣷⠏⠀⠄⢂⢁⣢⠼⠋⠠⢈⠐⣸⣿⣿⣟⣾⣳⣟⡾⣽⢯⡿⣽⣷⣿⡿⠁⠀⠀⠀⠀⠀⠹⣷⣤⣄⣴⣿⡇⠀⠀⣸⡟⠀⠀⠀⣾⣿⠃⠀ ⠀⠀⠀⠘⣿⣧⠀⠀⠀⢻⣷⡀⠀⢀⣿⣧⣶⡾⠿⠛⠁⠀⠀⠀⠀⠀⢻⣿⣿⡿⣽⢯⡿⣽⢯⣟⡷⣯⢿⣿⣿⣿⣷⣄⡐⢀⠂⡈⠙⠳⣤⡂⠄⠉⠻⣿⣷⢯⡿⣽⣿⢨⣿⣟⣷⣻⣾⠿⠛⢁⠠⣡⠾⠚⠋⢁⠐⣈⣴⣶⣾⣿⣿⣟⣾⣳⣟⡾⣽⢯⡿⣽⣿⣿⡿⠁⠀⠀⠀⠀⢀⣀⣀⠈⠉⠋⠉⠈⠻⢿⠿⠟⠀⠀⠀⣸⣿⠏⠀⠀ ⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⢿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢯⡿⣽⣻⢾⡽⣯⣟⡿⣿⣷⣯⢿⡇⢀⠂⠄⡁⠂⠄⠙⠦⠁⢂⠹⣿⣿⡽⣯⣿⠐⣿⣽⣞⣿⠋⠠⠐⣠⠟⢁⠐⠠⢁⠂⠄⣻⣿⣽⣿⣿⣻⣞⣷⣻⢾⡽⣯⢿⣽⣿⣿⠟⠁⠀⠀⠀⢀⣾⡿⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠈⢹⣄⠀⠀⠀⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⡷⣯⢿⣽⣳⢯⡿⣽⣿⣿⣿⣧⣀⠌⠐⠠⠁⠌⡐⠠⢁⠂⠄⡘⢿⣿⣳⣯⠘⣿⣳⣿⠏⢀⠁⠂⠄⠂⠄⡈⠐⠠⢈⣤⣿⣿⣿⣟⣾⣳⣟⡾⣽⢯⡿⣽⣿⣿⡿⠋⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠈⠙⠿⣷⣦⣀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⢿⣧⡀⠀⠀⢻⣷⡄⠀⢀⣴⣾⡷⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣟⡾⣽⢯⣟⡷⣯⢿⣿⣟⡿⣿⣿⣷⣮⡀⠄⡁⠂⢌⣐⣤⣤⣿⡟⠇⡈⠻⣋⣥⣤⣦⣌⣐⡈⠐⢠⣴⣿⣿⣿⣻⣿⣿⣻⣞⣷⣻⢾⡽⣯⢿⣽⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⢻⣷⡀⠀⠀⢹⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣽⣯⣟⣾⡽⣯⢿⡽⣿⣿⣷⣻⢾⡽⣿⣷⣾⢿⣿⣻⣟⣿⣻⣿⣄⢄⣽⣿⣿⣻⣟⡿⣟⣿⣷⣾⢿⣻⣞⣷⣿⣟⣷⣻⣞⡷⣯⢿⣽⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⣿⡦⢀⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠹⣿⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣳⡿⣽⢯⣟⣷⣻⣿⣿⣯⣟⣷⣻⣽⣻⣞⣷⣻⣞⣷⣻⣿⠩⣿⣟⣾⣽⣾⣻⣽⡾⣷⢯⣟⣷⣿⣿⣻⣞⣷⣻⢾⣽⣯⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⠀⣿⣾⣧⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣯⣟⣾⣳⣟⣾⣻⣿⣿⣾⣽⣻⢷⣻⢾⣽⢾⣳⣟⣿⢘⣿⡽⣞⡷⣯⣷⢯⡿⣽⣿⣿⣿⣻⣞⣷⣻⢾⣽⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠉⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢿⣿⣿⣷⣿⣞⡷⣯⢿⣿⣷⣯⣟⣯⢿⣾⣻⣽⢾⣿⢈⣿⢿⣽⣻⢷⣯⢿⣽⣿⣿⣻⣞⣷⣻⣾⣿⣿⡿⠟⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣾⣿⣿⣿⣽⣻⡾⣽⢯⣟⣿⠨⣿⣻⢾⣽⣻⣾⣿⣿⣿⣾⣷⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⣠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡟⠀⠀⠀⢀⣴⣶⠶⣶⣄⠀⠀⠀⢀⣤⣶⣶⣤⣀⠀⠾⠿⠟⠋⠁⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⣾⡏⠀⠀⠈⢿⣇⠀⠀⣾⡟⠁⠀⠙⣿⡄⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⣿⣆⠀⠀⢀⣿⡿⠀⢸⣿⡅⠀⠀⠀⢹⣷⠀⠀⠀⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⢀⣈⡿⠿⠞⢻⣿⠇⠀⠘⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⡛⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⣿⣄⣀⣠⣾⡏⠀⠀⠀⢿⣷⡀⠀⢀⣾⡏⠀⠀⠀⠀⠸⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠌⣽⠛⠿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⡿⠟⠛⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡆⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⢟⡟⢉⣍⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀