⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢰⡖⠀⠀⠀⠀⠀⠲⢶⡀⠀⠀⠀⢠⡆⠀⠀⠓⠲⠶⠶⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠀⠀⠀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⢏⣴⠾⠋⢉⣋⠛⢻⡶⠷⠛⢶⡀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠤⣿⠀⢿⣀⣀⣀⣀⠀⠀⠀⢀⣠⠾⠟⠽⠿⢷⣛⣉⣉⣭⣙⣿⣿⣇⣴⢾⣻⡦⢠⢾⣅⡀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⣿⣧⠘⢷⡈⠉⢉⣙⣻⣾⠿⢿⣿⣄⢀⣴⣟⠉⢩⡁⠀⢹⡾⠿⣿⠟⠉⠉⠙⠲⠶⣌⣻⣤⡴⠶⠦⣤⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⣸⣿⣿⣷⡀⠻⢦⡋⠉⠉⢁⡉⠉⢹⡟⢹⣿⠸⣆⣿⡇⢠⡟⠀⣸⡿⠀⠀⠀⠀⠀⠀⣼⠳⡶⠾⠛⠲⣦⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠸⢿⣿⣼⣿⣟⠷⣤⣙⡷⢶⣿⣠⣴⣾⣷⣞⣛⣚⣋⣛⣳⣿⠷⠶⢿⣧⣀⣀⠀⠀⠀⢸⡏⣼⠳⠀⠀⠀⢸⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⡇⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠒⠲⣶⡙⣿⣶⡿⠿⠟⠒⠚⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠶⠮⣭⣍⡛⠶⣾⣿⡃⠀⠀⠀⢠⡟⠈⠳⣦⡈⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠞⠉⠳⠾⣣⡿⠙⠶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡇⣿⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣌⡉⠠⣤⣀⡿⠀⠀⠀⠀⠙⠳⠦⣤⣤⣍⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠠⣤⠖⠛⢷⠸⣯⠤⠄⣀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣭⡵⠿⣱⣿⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣦⡙⠳⢦⣀⠀⠀⠀⢀⡴⠀⣠⣿⡀⠻⣿⣆⠀⠀⠠⠶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⣶⢿⣄⣠⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠳⣮⣿⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠙⠷⣤⡴⠋⢀⣴⠋⠈⠻⣦⡈⠿⣴⠛⠁⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⣼⣧⠤⣟⠀⠉⠁⠀⠈⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⢀⣴⠶⢀⣾⠛⣹⣷⠶⠶⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣄⢀⣀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠳⣴⡿⠁⠀⠀⡀⠈⠻⣆⠹⣆⠀⠀⠀⠀⠀⠸⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⢻⣆⣴⠀⠀⠀⠻⣦⠀⣿⠀⢀⣴⠗⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⣇⠀⠀⠀⠀⣸⣿⣿⠟⠁⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠁⠸⣏⠈⠀⣽⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠈⠳⣦⣴⡶⠁⠀⠀⡘⣧⣙⣛⣶⡀⠀⠀⢸⡇⠀⠀⠉⠃⠘⠷⣦⡀⠀ ⠀⠀⠀⠀⣀⠹⣧⡀⠹⠙⢷⣠⢤⣤⡿⣀⣌⣛⣋⣥⣶⢶⡶⠶⠞⢷⣄⣀⣀⣀⡀⠀⠘⠓⠶⠶⢶⣶⢟⢙⣷⣽⣧⣀⣀⣼⡿⠋⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⠶⣚⣿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠷⠞⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⢈⣷⣄⠘⣯⠀⢀⣀⣨⡵⠾⠛⣧⠈⣷⣠⠶⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠏⠳⣮⣵⡂⠙⠋⢹⣶⠶⢶⣿⠿⣍⠉⠁⠙⡿⢿⣦⣄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢠⡾⢁⣸⣿⠟⠀⣠⣿⡿⠋⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣀⣠⡶⠃⠀⢀⣶⣴⣞⠋⢁⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⠚⠈⣿⣆⠈⢻⣏⣭⠗⠀⣠⣴⡾⣿⣿⠁⠀⠀⢹⣧⠀⡄⠀⠀⠀⣀⠀⠀ ⠀⠉⠉⠁⠀⣴⠏⠈⠳⣄⣴⣿⢷⡀⠀⠀⢀⣿⠀⠀⣼⠃⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣠⣾⣿⠃⣠⣾⣿⠟⠁⠀⠀⢀⣴⡾⠋⠀⠀⠰⣶⣿⢿⣥⣀⣤⠶⢿⠿⠛⣩⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⢿⣄⡴⠛⠉⠸⣇⠹⣦⡤⠶⠚⠋⠻⢷⡶⠶⠤⣴⣿⡂⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠰⠿⣿⠃⡎⠻⣦⣴⡿⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣰⠟⣿⠃⣼⣿⣿⠋⠀⠀⢀⡴⣿⠟⠁⢀⣴⣾⣿⠟⢁⣤⡾⠟⠻⣶⣄⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠹⣧⠈⢿⡄⠀⠀⠀⠹⣦⡙⢷⡄⠀⠀⣠⡬⣻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠷⢤⣤⡀⠀⢀⣼⠀⣇⠀⠈⣿⡇⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣰⠏⢰⡏⣺⣿⡟⠁⠀⢀⣴⠏⣰⠏⢀⣴⡿⣿⡿⣁⡴⠟⠁⠀⠀⠀⢈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣦⠀⣷⢀⣀⠀⠀⠈⢷⠀⢻⡀⡤⠤⣶⡿⠒⠶⠶⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⢷⠀⣧⠀⠀⠀⣴⣿⠇⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡏⣀⣿⣼⢯⡟⠀⠀⣰⠟⢡⣾⡟⣠⡿⠋⣰⣯⡶⠋⠀⠀⠀⠀⠀⣠⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⠶⢿⡄⢻⣄⣉⣉⣤⠤⠾⣿⠛⢷⠚⠃⣹⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠹⡀⠀⣾⣿⡟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⢻⣿⠁⣿⣿⢏⡟⠀⢀⡾⢃⣴⣏⣸⣿⣏⣠⣠⣿⠻⠶⣤⣀⠀⠀⠀⣴⠏⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⣦⠾⣇⠸⣯⡿⠀⠀⠀⠀⢻⣀⢸⠛⠉⠿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣼⣿⡟⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡄⢠⡟⠁⢰⣿⣿⣠⣿⠏⠾⠁⣠⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⢷⣄⣰⢋⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⡁⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⣿⢓⣶⣶⠶⣶⠛⣿⣿⣄⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⣹⣶⡟⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⡾⠁⡾⠁⢀⡟⠀⣿⣿⡏⢀⠀⣰⠏⣰⠟⣿⢿⣿⠋⠙⣿⣿⣿⣿⣿⣿⣿⣦⠀⢻⡏⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⢀⣴⡿⠋⣽⢃⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⣠⡟⠛⠋⢱⡆⡏⢸⣇⣤⣽⣷⣾⣉⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢩⡟⠠⣶⣤⡀⢀⣾⡟⠀⠀⠀⣼⠃⢸⠇⠀⣾⢁⣼⢃⡟⢠⡏⣰⠇⣼⢣⣾⠇⢸⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣳⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⢀⣴⡿⠋⠀⣸⢇⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⢻⣄⣠⣾⢁⣇⣸⣟⠉⠉⠉⠹⠛⠛⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡿⠀⠀⠈⠛⣿⣿⣯⣀⠀⠀⣸⢧⣆⣸⣶⢰⡇⣼⠃⣸⠃⡼⢁⣤⣿⡇⣾⠏⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⡟⣿⠀⣠⠄⠀⠀⠀⠀⣴⣿⣿⠃⣠⡾⠻⣷⣶⣤⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡇⢸⠛⠉⠉⠉⢙⣿⢉⡷⠀⠀⠈⠃⠘⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠟⠀⣶⠀⠀⣴⣿⠋⠙⠿⣷⣰⠏⣸⠁⢸⡿⠘⢱⣏⢀⡏⠀⢡⣾⣽⢿⣶⠏⠀⠀⠀⠀⢠⣿⣮⣿⣿⣿⣿⣿⣿⠏⠀⠹⠁⣿⣰⡏⠀⠀⠀⢠⣾⣿⣿⠁⣰⠏⠀⠀⠈⠙⣿⣿⣷⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣸⠀⢸⣤⢤⣤⣤⡟⢁⣾⣁⣀⣀⠤⠀⡆⠀⠀⠀⠀⠀ ⠀⢸⡆⠀⠀⠸⡆⠀⢀⣴⢏⡿⣦⣴⠟⠀⠘⠛⠁⠀⠀⠀⢰⡟⠀⣿⠀⢸⣇⠀⣾⠉⢸⠃⠀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢻⣿⡇⠀⠀⢠⣿⡿⢱⡇⣼⠏⠀⠀⠀⠀⢰⣿⡏⠙⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠘⢷⠎⢻⣭⣉⣉⣸⣧⡇⠀⠀⠀⠀⠀ ⠀⠀⣧⠀⠀⠀⢻⣤⣼⢏⡾⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢹⡀⠘⣿⡆⣿⠀⣿⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⢿⣄⠀⣿⡟⠁⣿⣰⠏⠀⠀⠀⠀⠀⣾⡟⠀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⢰⡟⢠⡏⠀⠀⠀⠀⡾⠀⣼⠀⠈⣹⡿⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠈⣿⠋⣼⠁⣸⠃⢀⣀⣤⠶⠶⠶⠖⠛⠋⠉⠙⠓⠾⣧⣄⣻⡁⣿⠀⡿⢀⣿⡿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡟⠀⠀⣿⡟⠿⣶⣄⠀⠀⢰⣿⠁⣴⣿⣿⠹⣇⠀⠀⠀⣠⡶⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠰⢦⡄⠀⣼⠃⣰⣯⣈⣫⣿⡇⣾⠀⠀⠀⣤⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⣼⠃⣰⣏⡴⠛⠉⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣀⣈⣉⣉⣛⣻⣷⡟⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣦⣀⠈⠙⢷⡀⢸⡇⣸⣿⣿⡇⠀⢿⠀⠀⣰⣿⠃⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⢸⡟⣰⠿⢷⣶⣤⡾⢃⣴⠏⠀⠹⢻⡎⣱⠇⠀⣴⠟⠈⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⣼⠃⣠⣿⡟⠀⣤⡀⠀⢠⡶⠛⢶⠟⠻⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⢻⣶⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣷⣄⠈⢷⣼⢡⡿⣿⡿⠀⠀⠘⢀⣼⣿⠏⠀⢀⣾⣿⠃⠀⠀⠀⠀⡀⠀⠀⡾⠀⣉⣀⡀⢰⡏⢰⢏⣀⠀⡬⠛⣸⢧⣿⣶⡞⠁⢀⡀⠀⠀ ⠀⠀⠀⠀⣰⡟⣸⢇⣾⣿⡟⠀⠀⠹⣷⡀⠈⢷⡀⠀⠀⣠⣿⣿⣿⣯⣿⣽⣿⣟⣿⣦⢹⣿⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡄⣿⡞⣽⣿⠃⠀⠀⢠⣾⣿⠏⠀⣠⣿⡿⠁⠀⠀⠀⠀⣼⠃⠀⣼⠃⠀⠉⣉⡿⢟⣡⡿⣀⠙⣷⣴⣿⢁⣾⢉⣿⡃⠘⠋⠀⠀⠀ ⠀⠀⠀⠀⠉⣰⠏⣸⣿⣿⠸⣧⠀⠀⠻⣧⠀⠀⠛⠿⣾⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣅⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⣘⠷⠀⠈⢷⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣿⠁⣿⡟⠀⠀⣴⣿⡿⠃⠀⣴⣯⡟⠁⠀⠀⠀⢀⣾⡏⢀⣼⢃⢲⣄⣴⠿⠶⣛⡿⢛⡿⢾⣟⣼⢃⡾⣿⣿⢹⣿⠃⠀⣶⢶⠀ ⠀⠀⠀⠀⠀⠉⢸⣿⣿⡏⠀⢿⣧⡀⠀⠹⣦⣄⣀⠀⠈⠙⢿⣽⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⣞⣛⡳⣦⡀⠈⠛⢶⣀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⠇⣠⣾⣿⡟⠁⢠⡾⣳⠏⠀⠀⠀⠀⢠⣾⣿⢁⣿⠿⣟⣫⣭⣶⣾⣿⣿⣷⣌⣛⣶⡌⣷⡞⠁⠈⡿⣸⣿⣷⣾⡇⣿⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⣟⣧⠀⠀⢻⣿⠆⠀⠈⠻⣿⣻⢶⣄⡀⠹⣧⣿⣿⣿⣿⣿⣿⢻⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⡟⠉⠉⠉⠙⠻⣦⠀⠀⠙⣦⡀⠀⠀⠀⠀⣿⠀⠀⢿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣴⣯⣾⠏⠀⣴⢏⡾⠃⠀⠀⠀⠀⣰⣿⣟⣵⡿⣷⣤⣛⠿⣭⣴⠿⠋⣹⡿⠛⣯⡱⣾⠟⠀⣶⣼⢇⡿⣿⣮⣹⢧⡏⠀ ⠀⠀⠀⠀⠀⢿⣿⣥⡿⡟⢻⡄⠀⢹⣷⣄⠀⠀⠀⠉⠳⢮⣝⣀⣸⣿⣿⠿⠏⠀⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠻⣄⡀⢀⡴⠋⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡟⠁⣠⠾⣱⠟⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⣫⣾⢟⣿⣦⣝⠷⡾⢫⡔⢛⣾⣷⢹⡄⠀⠘⣿⡛⠁⠈⠹⣿⣼⠃⠀ ⠀⠀⠀⠀⠀⠈⢸⣿⣿⡇⠀⣿⣄⠀⠀⠉⠛⠶⠶⠶⠶⢶⣿⣿⣿⣿⣏⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠸⣆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⠻⣿⣿⢿⣾⢋⣤⠞⢁⡾⠋⠀⠀⠀⠀⣰⠟⠙⣿⣿⠟⣡⡾⠛⢿⡿⠟⢿⣿⠻⠃⠀⣿⣏⣉⣭⠾⠁⠀⠀⠘⢷⡀⢀⠀⠈⠙⠷⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣹⠇⠀⢿⢿⣷⣄⡀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣴⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣄⣠⣼⣿⣿⡿⣿⡿⢋⣴⠟⠀⠀⠀⠀⣠⡾⢃⣴⣾⡿⢃⣼⡿⣧⠀⠀⠀⠀⣠⡟⠀⠀⣸⠇⣿⠁⠀⠀⠀⢠⣶⣶⠀⣱⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠉⠙⠿⣿⣿⣾⣿⣿⣿⠃⢹⣿⡷⠒⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠙⢧⡀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣡⡾⢋⣴⠟⠁⠀⠀⠀⣠⡾⣫⡴⣿⣵⠟⣰⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⠀⢠⡟⢠⡇⠀⠀⠀⠀⠘⢛⡉⠸⠋⠁⠀⠞⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣌⠛⠶⠦⠤⠤⠶⣶⣿⡿⠋⣩⠿⠁⠀⠘⣿⣷⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠓⠒⠛⢁⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣴⠟⠁⠀⠀⠀⣠⣾⡿⢿⣿⢀⣾⣷⣾⣿⣿⣿⣿⢻⣿⣿⡟⢱⣧⡟⠀⣿⠀⣸⠁⠀⠀⠀⠀⠀⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣄⢀⡝⡳⠦⣤⣀⣀⣀⠀⠀⠀⠚⠋⠀⠀⠀⢸⣿⣏⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣶⣤⣄⣀⢰⣾⠿⢿⡏⣀⣀⡀⠀⠈⢹⠆⠀⠀⠀⠀⠀⣀⣠⣶⠾⣋⡴⢿⠅⠀⠀⣀⣠⠾⣻⣿⠃⣸⡿⢿⣿⡟⠁⠉⠉⢩⡿⣿⣿⡏⣠⣾⣿⠇⣾⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠠⣝⣿⣝⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣿⠀⢠⡟⠉⠉⠉⠉⠙⠛⠛⠓⠒⠒⠚⢿⣿⣦⠴⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⢿⣿⣍⣛⢾⣿⢿⣤⣍⣉⣉⣹⣇⣾⣤⣤⣴⣶⣖⣛⣽⢟⣥⠞⠋⠀⢀⣤⠶⣛⣩⡵⠞⢋⣩⡴⠋⣻⣶⣍⢻⣦⡀⢀⣾⢰⣿⣿⣻⡿⣿⠋⡾⠃⣀⣸⠃⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣤⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣄⣠⣾⡷⢦⣼⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣆⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡟⠛⠿⣿⣿⡿⢿⣄⣠⣿⣿⣿⣿⠟⠋⠉⠉⢉⣭⣿⣿⠿⠋⠁⠀⠀⣠⣿⣁⠻⣿⣛⡒⠚⠋⢉⣠⣾⣿⡉⢭⣾⣿⠟⣿⣃⣾⣿⡿⣿⢰⠏⠈⢠⡟⠉⠻⠟⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⡛⠂ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⣿⣾⣿⣿⣿⣧⣴⣿⣿⣟⣽⠟⠁⠀⣀⣴⣾⠿⠟⠉⠀⠀⣀⣤⢶⣟⣉⣭⡿⠿⠶⣭⣙⢶⣟⠋⣡⣾⣯⣿⡌⡏⢁⣤⣾⢫⡿⠋⢰⡇⡿⠀⠀⠈⢷⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠙⠦⠤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡤⠞⠉⠛⢿⣿⡏⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⠶⠿⠟⠉⢁⣀⣠⡴⠶⠛⠉⠉⠙⠛⠛⠷⠶⠶⣿⣿⣿⣿⣿⣿⣫⣿⣭⣭⣾⣿⣿⣿⣧⡟⠀⠀⠘⠻⠃⠀⠀⢀⣼⠿⣦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⣼⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣶⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠐⠚⠛⠉⠙⠻⠾⠃⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠆⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣹⡶⠞⢱⡟⡿⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣡⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢺⡇⠻⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢠⡟⢿⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣠⣿⡿⠟⣀⣀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣸⠛⢦⣈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣤⡀⠀⢷⡙⢷⡟⠀⣸⠃⢸⡿⣿⣿⣿⣿⣯⣿⡿⢻⣿⠀⣰⣿⡿⠟⠛⠋⠉⠉⠉⠉⠉⠛⠻⠿⣿⣛⣶⡶⣶⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠄⠀⠀⠀⢠⡟⠀⠀⠙⠳⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣽⣿⣦⣤⣶⣦⡀⠀⠀⠀⠀⠀⢀⣀⡐⣯⡀⠁⢨⡇⠀⠈⠳⣼⣇⣰⡏⠀⠀⠀⣿⣿⣯⣾⣿⡿⠀⣾⣩⣾⡿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢷⣶⣦⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠲⣛⣭⣶⣿⣿⠋⡀⢤⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⣶⣦⣄⡈⠳⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡻⠟⢋⣵⠞⠉⠙⠛⢲⣶⠞⠋⢻⣯⣽⣿⣿⣷⣶⣿⣤⣶⣶⣶⣿⣿⣿⣷⣤⣀⠀⢻⣏⣾⣿⡟⠁⢸⣿⠋⢉⣠⡶⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⣦⣴⣿⠟⠱⠾⣯⡙⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣶⣿⣿⣿⣿⣷⣿⣧⣿⣆⣙⣻⣦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠸⠿⢦⠄⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⣿⠟⠁⣠⠟⠁⠀⠀⣴⠟⠉⠁⣤⣶⣿⣿⣿⣿⡿⢿⣿⣿⣿⡱⠿⢟⣿⣿⣿⣷⣿⣽⣷⣿⣿⣿⣿⠁⢀⣾⢃⣀⣿⣥⣤⣤⣄⠀⣀⣤⣴⣶⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠙⠀⠀⣠⣭⣿⣿⣿⣿⣷⡖⠖⠒⠒⠒⠚⠋⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣈⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣟⣿⠃⠀⣀⡿⠀⠀⠀⢸⠁⠀⢀⣾⣿⣿⣿⣿⣿⣟⢽⡎⠛⢉⣨⡿⠞⠋⡉⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⠀⣼⣿⣫⡿⠃⠀⠉⠉⠉⢉⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠉⠛⠲⠶⠦⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣾⡇⠀⠀⢿⣿⣿⡿⠿⠿⣿⠿⢿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠀⠀⣠⡟⢀⣰⣿⣿⣿⣿⣿⣿⢿⠿⢦⣤⣰⡟⠁⢀⣴⠞⠃⢸⣿⣿⣿⠏⣿⣿⣿⡿⣏⣾⣿⡿⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀⠀⠀⠀⣀⠀⠀⠀⠀⢸⣷⣿⠻⣿⡿⠬⣿⡿⢿⣿⠏⠀⠀⠀⠈⢿⣿⣤⣶⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢷⡄⠀⠀⠀⠀⠀⠀⣾⠋⠙⢶⡿⣿⣿⣿⡿⠿⠏⠀⠀⢹⡿⠋⠀⣴⠟⠁⢀⣠⣾⣿⣿⠃⣼⡏⣿⣿⠁⣿⡿⣏⠀⠀⢀⣠⡶⢶⣾⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⡀⠀⠙⢦⡀⠀⠀⠀⢹⣷⣦⣀⣀⡀⣀⣴⠟⠁⠀⠀⠈⠛⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣸⡷⣿⣿⣿⢦⣄⣤⡀⢘⡿⠃⢀⣾⠃⠀⣴⣿⢏⣾⡟⠁⢰⣿⠇⢻⡇⢠⡟⠸⠋⠀⣘⣫⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠈⠳⣄⠀⠀⠀⠉⠛⣻⣯⣍⡉⠁⠀⢠⣤⠤⢶⣶⡀⠀⠀⠉⠉⠛⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡄⠸⢾⣄⠀⠀⠀⠀⠀⣀⣹⣆⣰⡏⣼⣿⣿⣿⣣⡝⠻⢿⡿⠁⠀⠘⣧⣤⣤⣽⣿⣿⣿⡇⠀⠟⢸⠀⢸⡇⢸⢃⣠⠶⠛⠉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⠽⢟⣳⠀⠀⢀⣛⠶⢮⡻⣦⠀⠀⠀⢀⡟⣸⠃⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⣼⣇⠀⣀⡙⠑⠂⠀⠀⢸⠋⠀⣸⡟⣱⣿⣿⣿⣋⣹⠓⠶⣾⠁⠀⠀⠀⠀⠀⣸⠟⢷⣿⠟⠁⠀⠀⢸⠀⣼⡇⣼⠟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⣛⣭⠶⠞⠋⠁⢠⣶⣿⡿⣶⡾⢇⣼⠀⠲⣆⣼⢡⡏⠀⠀⠀⣸⢃⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀ ⠀⠀⠈⢻⡀⢿⣿⡄⠀⠀⣠⡾⣠⠾⣿⢀⣿⠟⣿⠋⣭⡉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡏⠀⣾⠁⠀⠀⠀⠀⢸⣴⡟⠻⠃⣴⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢻⣧⣙⠳⢦⣀⡀⠀⣿⣿⣿⣿⣏⠳⣌⢷⣾⡛⠿⣿⡞⠁⠀⠀⣠⣟⣼⠁⠀⠀⠀⠀⠀⣠⠿⢷⡄⠀ ⢀⡀⠀⠈⠉⠀⠉⠳⣤⣾⡏⠘⠋⠀⠇⢸⣿⠀⢻⣿⣄⣀⣙⣳⣿⠀⠀⠀⠀⠀⢸⠁⣸⠇⠀⠀⠀⠀⠀⢸⡿⢻⣦⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣶⣯⣝⠶⣿⣏⣿⣿⣿⠿⣽⡆⣿⣿⣶⣾⢿⡄⠀⢠⡟⠉⠁⠀⣧⠲⠀⢀⣼⠋⣠⣿⡇⠀ ⠈⠻⣦⠀⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠈⢹⠀⠈⣿⣿⣿⡏⠉⢿⠀⠀⠀⠀⠀⠈⠀⠏⠀⠀⠀⠀⠀⡆⢸⡇⢸⣿⠟⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⣾⣿⡏⣷⢹⡇⠈⠻⣾⡿⢇⣻⣿⣷⡶⢾⣯⣿⣾⣿⣿⠁⠀⣾⣿⡷⠀⠀⣗⣀⣠⡾⢁⣴⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣿⡟⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⣧⣾⢃⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠛⣯⠙⣿⣦⠀⠀⣄⢻⣬⣉⠻⠾⠋⠾⠿⠟⣿⠟⠁⠀⢠⣿⠀⠀⠀⣧⣿⣿⣿⣷⣾⣿⣯⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠼⣿⣴⣆⣀⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⡇⣩⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢿⣄⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⡏⣠⣄⣼⡀⡾⣼⠀⠀⠀⠈⠨⠿⠦⣤⣤⣤⠴⠟⠁⠀⠀⠀⠀⢹⡇⠀⠀⠈⠉⢻⣽⣿⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠈⠉⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣿⠆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠷⢶⣶⣆⣤⡀⠀⠀⢾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠟⣿⡁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠻⣾⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡟⠀⣼⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠶⢦⣼⣿⣿⠛⠉⢀⣴⣿⣟⣿⡙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣄⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⠷⣄⡀⠈⠀⠙⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⣰⢷⡄⠀⢦⡘⣿⡁⣸⣣⢹⡎⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣀⠀⠀⠀⠀⠈⠻⣿⢧⣤⣠⣟⡀⠙⢷⣄⣨⡿⢻⣿⡀⠀⠀⣹⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢻⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⣿⣧⡾⠁⢠⡆⢀⣀⢀⣀⣀⠀⠀⢀⡾⣿⣿⣿⣿⣿⣶⣿⣿⡍⠈⠉⢀⡟⠀⠀⠀⣼⠇⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢶⣶⡤⠴⢞⣴⢿⣿⠃⢠⡟⠀⣿⡀⠈⠀⣹⢀⣴⠟⠀⠻⣿⣿⣿⣿⣿⣿⠌⠻⣦⣰⠿⠁⠀⠀⣼⠏⠀⠀⠀⢠⡏⠀⢸⡏⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠉⠙⠛⠉⠁⠀⣿⣦⡟⠀⢠⣾⣷⢠⡾⣿⣿⠁⢰⡄⢲⡻⣿⣿⣿⣎⣿⠀⠀⢨⣿⡷⠀⠀⣼⠇⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠀⢀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣴⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⣿⡏⠀⣼⣿⣿⠀⠀⡇⠈⠃⣿⣿⣿⣿⣿⠂⠘⣾⣽⡇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠁⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠈⠀⠀⠈⣻⣶⣤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠋⢹⡇⢰⡏⣾⠀⢠⣏⣿⡟⠀⣴⠃⠀⢀⣿⣿⣿⣿⠟⠀⠈⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢿⡇⠀⠀⠀⠈⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣧⣿⣴⡇⢀⡿⣿⠟⠁⠸⠃⢀⣠⣾⠿⣿⡟⠁⠀⠈⠁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣲⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣿⣟⣡⣤⣴⣶⣿⣿⡿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⣀⣀⡈⣉⣙⠟⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⣹⠀⠀⡀⣿⢻⡿⣨⣄⢷⠙⡀⣟⣠⣤⢧⣿⠻⠈⠀⠀⠀⠀⣀⣀⠀⠁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡎⢹⣣⣸⡁⣿⡘⢦⠀⡄⢷⣰⠀⡀⣦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠆⠙⠀⠈⡀⣄⠷⠘⡀⣷⠘⠀⠀⠀⠀⠀⠀⣄⢦⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⡙⣿⣟⣿⣴⢀⠉⠛⣿⣿⣼⢦⠶⡿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⣼⠀⡟⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⣆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⢷⣾⠻⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡁⣿⠟⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⢾⠀⠀⡀⣤⣆⣶⢶⠷⠙⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠆⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠿⠛⠉⠈⠀⠀⡄⢷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠟⣿⣽⢻⠉⠈⠀⠀⡇⢹⠀⠀⠀⠀⠁⠟⠴⣤⣤⣤⠦⠿⠨⠈⠀⠀⠀⣼⡾⡀⣼⣄⣠⡏⣿⣿⣿⣿⣿⣿⣰⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣄⢿⠈⠀⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡴⣩⡇⣿⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣈⣀⣆⣴⣿⠼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣤⣯⣿⣾⣷⣿⣿⣿⣧⠀⠀⠀⣿⢠⠀⠁⠟⣿⠟⠿⠾⠋⠾⠻⣉⣬⢻⣄⠀⠀⣦⣿⠙⣯⠛⡿⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⢃⣾⣧⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠃⡟⣿⢿⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠏⣿⣴⢁⡾⣠⣀⣗⠀⠀⡷⣿⣾⠀⠁⣿⣿⣾⣿⣯⢾⡶⣷⣿⣻⢇⡿⣾⠻⠈⡇⢹⣷⡏⣿⣾⣇⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠀⠀⠟⣿⢸⡇⢸⡆⠀⠀⠀⠀⠀⠏⠀⠈⠀⠀⠀⠀⠀⢿⠉⡏⣿⣿⣿⠈⠀⢹⠈⠀⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⣦⠻⠈ ⠀⡇⣿⣠⠋⣼⢀⠀⠲⣧⠀⠁⠉⡟⢠⠀⡄⢿⣾⣶⣿⣿⡆⣽⠿⣿⣿⣿⣏⣿⠶⣝⣯⣶⣿⣿⣿⢸⡇⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣾⣦⢻⡿⢸⠀⠀⠀⠀⠀⠇⣸⠁⢸⠀⠀⠀⠀⠀⣿⣳⣙⣀⣄⣿⢻⠀⣿⢸⠇⠀⠋⠘⡏⣾⣤⠳⠉⠀⠉⠈⠀⡀⢀ ⠀⡄⢷⠿⣠⠀⠀⠀⠀⠀⠁⣼⣟⣠⠀⠀⠁⡞⣿⠿⡛⣾⢷⣌⠳⣏⣿⣿⣿⣿⠀⡀⣀⢦⠳⣙⣧⢻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣠⠀⣴⠃⠻⡟⣴⢸⠀⠀⠀⠀⠁⣾⠀⡏⢸⠀⠀⠀⠀⠀⣿⠀⠀⡉⣭⠋⣿⠟⣿⢀⣿⠾⣠⡾⣠⠀⠀⡄⣿⢿⡀⢻⠈⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡟⢃⣸⠀⠀⠀⡏⢡⣼⣆⠲⠀⣼⢇⡾⣶⡿⣿⣶⢠⠁⠋⠞⠶⣭⣛⠟⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⢀⠀⠀⠁⠟⣼⡇⣼⠀⢸⠀⠀⠁⠟⣿⢷⠟⣸⠀⠀⠀⠀⠀⠁⣾⠶⠓⣹⣋⣿⣿⣿⣱⡟⣸⠀⠋⢸⠀⠀⠂⠑⡙⣀⠀⣇⣼⢤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠃⣸⡟⢀⠀⠀⠀⣦⡻⢮⠶⣛⢀⠀⠀⣳⢟⠽⣠⣀⣇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⠛⠶⣠⢃⢸⡇⢸⠀⢸⠟⠀⡇⣿⣿⣿⣽⣤⣤⣧⠘⠀⠁⡿⢿⠻⡝⣣⣿⣿⣿⣼⡏⣰⣆⣹⣀⠀⠀⠀⠀⠀⣄⢾⠸⡄⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣤⠦⠶⠛⠉⠉⠀⠀⡀⣶⢶⠤⣤⢠⠀⠁⡉⣍⣯⣻⠛⠉⠀⠀⠀⣄⠳⠈⠀⣆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣵⣫⣘⠀⠋⠸⡟⢠⡇⢻⠇⣿⢰⠁⡟⣾⢏⣿⣴⠀⠃⣾⢀⠃⡿⢘⡀⣤⣄⢦⣿⣿⣿⡷⣸⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⠦⠲⠛⠈⠀⠀⠁⠟⣴⣀⡀⣀⣀⣦⣷⢹⠀⠀⠀⡀⢦⠙⠀⡀⣦⣿⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣿⣿⣿⣿⣾⢶⡶⣠⢀⠀⠀⣏⡿⣿⠁⣿⣿⡏⣼⠃⣿⣿⣾⣠⢀⠁⠟⣴⠀⠋⡿⢹⠀⠀⠏⠿⡿⣿⣿⣿⡿⢶⠙⠋⣾⠀⠀⠀⠀⠀⠀⡄⢷⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠋⡶⣠⣀⣶⣤⣿⢿⠈⠀⠀⠀⠏⣿⢿⡿⣿⠬⡿⣿⠻⣿⣷⢸⠀⠀⠀⠀⣀⠀⠀⠀⡀⣿⣿⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣾⣠⠀⠀⠀⠀⠀⠋⡿⣿⣾⣏⡿⣿⣿⣿⠏⣿⣿⣿⢸⠃⠞⣴⢀⠁⡟⣰⣤⢦⠿⢿⣿⣿⣿⣿⣿⣿⣰⢀⡟⣠⠀⠀⠀⠋⡴⢀⠁⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⡿⢿⠿⣿⠿⠿⡿⣿⣿⢿⠀⠀⡇⣾⣿⣀⣿⣿⣿⣿⣿⣿⣿⡿⢻⠀⠀⠀⠀⠦⠶⠲⠛⠉⣿⣿⣿⣿⣿⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⣿⣿⣿⢉⠉⠉⠉⠀⠃⡿⣫⣿⣼⠀⣿⣿⣿⣿⣿⣿⣾⣤⣀⠁⡉⠋⠞⡿⣨⢉⠛⡎⢽⣟⣿⣿⣿⣿⣿⣾⢀⠀⠁⢸⠀⠀⠀⡿⣀⠀⠃⣿⣟⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡀⣿⣈⢄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠋⠚⠒⠒⠒⠖⡖⣷⣿⣿⣿⣿⣭⣠⠀⠀⠙⠈⠀⠀⠀⠁⠛⡿⣿⣿⣿⣶⣴⣤⣀⠀⣄⣤⣤⣥⣿⣀⢃⣾⢀⠁⣿⣿⣿⣿⣷⣽⣿⣷⣿⣿⣿⢟⠿⡱⣿⣿⣿⢿⡿⣿⣿⣿⣿⣶⣤⠁⠉⠟⣴⠀⠀⠁⠟⣠⠁⠟⣿⡾⢀⠀⠀⠀⠀⠀⠀ ⠀⠄⢦⠿⠸⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⡀⣦⣻⣙⣆⣿⣧⣿⣷⣿⣿⣿⣿⣶⢴⣤⣀⢀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣦⠶⠻⡙⣯⠾⠱⠟⣿⣴⣦⣤⣀⢀⠀⠀⠀⠀⠀⠁⠛⡶⣠⢉⠋⣿⢸⠁⡟⣿⣾⣏⢻⠀⣀⣤⣷⣿⣿⣿⣶⣶⣶⣤⣿⣶⣷⣿⣿⣽⣯⢻⠋⠞⣶⢲⠛⠙⠉⠞⣵⢋⠟⡻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣦⠳⡈⣄⣦⣶⣶⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠀⣀⢤⡀⠋⣿⣿⣶⣭⣛⠲⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈⠁⠉⠉⠉⠀⠀⣦⣶⢷⡿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠋⡿⣾⣩⣾⠀⡿⣿⣾⣯⣿⣿⠀⠀⠀⡏⣰⣇⣼⠳⠈⠀⡇⢨⠁⡀⣯⡐⣀⢀⠀⠀⠀⠀⠀⡀⣦⣶⣤⣦⣿⣽⢿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠳⠙⠀⠀⡟⢠⠀⠀⠀⠄⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣻⠶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⣦⣶⡶⣶⣛⣿⠿⠻⠛⠉⠉⠉⠉⠉⠋⠛⠟⡿⣿⣰⠀⣿⢻⡿⣿⣯⣿⣿⣿⣿⡿⢸⠃⣸⠀⡟⢷⡙⢷⠀⡀⣤⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⣈⢦⠛⣸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⣫⣸⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠟⡿⣿⣠⣠⠀⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢠⡀⢿⡟⢠⡇⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⣯⠻⡇⢺⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡾⣡⣿⠀⠀⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⡿⡟⢱⠞⡶⣹⣿⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠆⡴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠻⠀⠀⠀⠏⣿⣠⠀⠀⠀⠀⠀⠀⠃⠾⠻⠙⠉⠛⠚⠐⠉⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⣶⣥⣭⣯⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⣇⣿⣼⠀⠀⡄⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣤⣦⠿⣼⢀⠀⠀⠃⠻⠘⠀⠀⡟⣧⣿⣿⣿⣾⣭⣭⣿⣫⣿⣿⣿⣿⣿⣿⠶⠶⠷⠛⠛⠙⠉⠉⠛⠶⡴⣠⣀⢁⠉⠟⠿⠶⣤⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠉⡏⣿⢿⠛⠉⠞⡤⣿⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠤⠦⠙⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⡀⢷⠈⠀⠀⡿⡇⢰⠋⡿⢫⣾⣤⢁⡏⡌⣿⣯⣾⣡⠋⣟⢶⣙⣭⠶⠿⡿⣭⣉⣟⢶⣤⣀⠀⠀⠉⠟⠿⣾⣴⣀⠀⠁⠟⣽⣟⣿⣿⣴⣧⣿⣿⣿⣾⣿⠉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⢿⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠀⠀⣄⣿⣿⠸⠀⠀⠀⠀⠀⠀⠀ ⠂⡛⣯⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⠉⠟⠻⠉⡟⢠⠈⠏⢰⣿⡿⣿⣾⣃⣿⠟⣿⣾⢭⡉⣿⣾⣠⢉⠋⠚⡒⣛⣿⠻⣁⣿⣠⠀⠀⠁⠋⠿⣿⣿⣭⢉⠉⠉⠋⠟⣿⣿⣿⣿⣠⣄⢿⡿⣿⣿⠿⠛⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣀⣆⣹⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⣼⢦⡷⣾⣠⣄⠻⠈⠀⠀⠀⠀⠀ ⠀⠀⣄⣶⣤⢿⠙⠈⠀⠀⠀⠀⠀⠀⡀⣀⠃⣸⣀⠃⡾⠋⣿⡿⣻⣿⣿⢰⣾⢀⡀⣦⢻⣍⣶⣻⠋⡴⣩⢋⠞⡵⣩⣛⠶⣤⢀⠀⠋⠞⣥⢟⣽⣛⣖⣶⣴⣤⣤⣾⣇⣹⣉⣉⣍⣤⢿⣿⢾⣛⣍⣿⢿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠶⠴⣦⣿⢿⠚⠒⠒⠓⠛⠛⠙⠉⠉⠉⠉⡟⢠⠀⣿⠀⠀⠀⡁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⢷⣝⣿⣝⠠⠀⠀⠀⠀⠀⠀⠀⡿⠀⠃⣾⠇⣿⣾⣠⡏⣿⣿⡿⢩⠉⠉⠁⡟⣿⢿⡿⣸⠃⣿⣻⠾⣠⣀⠀⠀⠅⢿⡴⣋⠾⣶⣠⣀⠀⠀⠀⠀⠀⠆⢹⠈⠀⡀⣀⣀⡏⢿⠿⣾⢰⣀⣄⣤⣶⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠈⠀⠀⣏⣿⢸⠀⠀⠀⠋⠚⠀⠀⠀⣀⣀⣀⣤⠦⡳⡝⢀⣄⣠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣤⣶⢿⠻⠀⠀⠀⠀⠀⠁⣸⠀⣿⠀⡟⣧⢱⡟⣿⣿⢻⣿⣿⣿⣿⣾⣷⣾⢀⣿⢿⡿⣾⣠⠀⠀⠀⠁⠟⣴⢋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣄⣤⢁⠛⠒⠓⠙⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠶⣷⣿⠘⠀⠁⠿⣩⠋⡿⣿⣶⠶⠤⠤⠦⠶⠛⣌⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠞⠀⠁⠋⠸⡉⢛⠘⠀⠀⠀⠀⡇⢠⡟⢠⠀⣿⣿⣴⣀⣄⣷⣿⣿⣿⣿⣰⠟⣵⣿⡴⣫⡾⣠⠀⠀⠀⠁⠟⣴⢋⡾⣡⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢀⠀⠀⡀⢧⠙⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠺⠒⡷⣿⢹⠃⣿⣿⣿⣾⣿⣿⠿⠙⠉⠀⠀⠀⡀⣦⣿⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣱⠀⣶⣶⢠⠀⠀⠀⠁⣿⠇⣸⠀⠀⡟⣠⠀⠀⠀⠀⣧⡿⣼⢃⡿⣾⣴⢃⡾⣠⠀⠀⠀⠀⠟⣴⢋⡿⣿⡿⣿⣿⣼⣠⣄⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⣆⠹⠀⡀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⣴⣿⣿⣿⣿⣶⣤⣀⣀⠀⡀⣄⣷⢿⢿⠀⠇⣹⣿⠈⠀⠀⠀⠀⠀⠀ ⠀⠷⠙⠈⠀⢀⡀⢷⠘⠀⠀⠁⠾⣭⣉⣏⣿⠀⠃⠻⣿⢿⠟⡿⢿⠛⡾⣡⠟⣿⣿⠙⠟⣰⠀⠀⠀⠀⠋⡾⢁⠞⣤⢋⣾⢿⣿⣿⠻⠿⣿⣿⣿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⣆⠸⠀⡀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣠⣀⣀⣏⣿⣿⣿⣿⢶⠶⠶⠶⠶⠛⠉⠀⠀⣄⣿⠀⡇⣿⣿⢸⠈⠀⠀⠀⠀⠀ ⠀⠃⣼⣿⠹⠈⠁⡛⣿⠘⠀⡄⢹⣷⣾⢛⡔⢫⡾⠷⣝⣦⣿⢟⣾⣫⠟⣿⣿⣿⣿⣼⢀⠀⠀⠀⠁⠟⣱⠾⣠⠁⡟⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠋⡴⢀⡀⣄⠻⠈⠀⠀⣧⠘⠀⠀⠀⠀⠀⠃⢸⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣾⠳⠀⠏⠿⣿⣿⣸⣀⣝⢮⠳⠉⠀⠀⠀⣄⣷⢹⠀⡄⢻⡟⡿⣥⣿⢿⠀⠀⠀⠀⠀ ⠀⡏⢧⣹⣮⣿⡿⢇⣼⣶⠀⠟⣾⡱⣯⠛⡿⣹⠋⠿⣴⣭⠿⣛⣤⣷⡿⣵⣟⣿⣰⠀⠀⠀⠀⠃⡾⢏⣴⠀⠏⣾⣯⣴⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣬⣷⢿⠀⠀⣿⠀⠀⠀⠀⡀⣦⠙⠀⠀⣦⠻⠙⠉⠉⠉⡟⢰⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣶⢻⣿⣿⣿⣿⣿⣿⣧⠹⡀⣄⢶⣻⣿⠻⠈⠀⠆⣿⢻⠀⠀⣧⣟⡟⣼⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⣾⣷⣿⣸⡿⠈⠁⡞⣷⡌⣶⣛⣌⣷⣿⣿⣾⣶⣭⣫⣟⠿⣿⢁⣿⣾⢠⠀⠀⠀⠀⠏⣳⡾⢠⠁⡟⣿⣾⣠⠇⣿⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⠀⣆⠻⠀⠀⠀⠀⠀⣀⢶⠛⠈⡀⣦⡳⣛⣞⣰⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⢻⣏⣿⣿⣿⣿⣿⣿⣿⣽⢿⠙⠈⠀⣀⣄⣦⠹⠀⡀⣧⢿⠀⡏⣿⣿⢸⠉⠀⠀⠀⠀⠀ ⠀⢶⣶⠀⠃⣿⢹⣿⣿⡾⢃⣼⣟⢾⡿⢛⡿⣛⠶⠿⣴⣄⢲⢃⣼⢀⡏⣾⢀⠀⠀⠀⠁⡟⣯⣴⠀⠃⡿⣿⣴⠀⠀⡟⣿⠁⣿⣷⣿⣿⣿⣿⣿⣿⣾⢠⠀⠀⠀⠀⣄⢷⠈⠀⠷⣘⠀⠀⡀⣄⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣅⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣽⣧⣾⠿⠛⠀⠀⣧⠻⠀⠀⣧⠸⣿⣿⣸⠏⣰⠉⠀⠀⠀⠀ ⠀⠀⠀⠋⠘⡃⣿⢉⣾⢁⣿⣴⣷⠙⣀⡿⣡⢟⡿⣉⠉⠀⠃⣼⠀⠃⣼⠀⠀⠀⠀⠁⡿⣿⣠⠀⠏⣿⣾⢠⠀⠀⠃⣿⣽⡞⣿⡄⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣄⠷⠙⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⣿⣿⣿⢹⣦⣿⣟⣿⣽⣿⣯⣿⣿⣿⣠⠀⠀⡀⢷⠈⡀⣷⠹⠀⠀⡟⣿⣾⢇⣸⡟⣰⠀⠀⠀⠀ ⠀⠀⡀⢀⠁⡞⣶⣿⢧⣸⠛⡬⠀⣀⢏⢰⡏⢰⡀⣀⣉⠀⡾⠀⠀⡀⠀⠀⠀⠀⠃⣿⣾⢀⠀⠏⣿⣼⢀⠘⠀⠀⡿⣿⡿⢡⣼⢷⠈⣄⣷⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⢦⠳⠉⠀⠀⠁⡟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⣶⢻⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⠻⠟⢶⠛⡶⢠⠀⡀⣤⠀⡟⣿⣠⠃⣼⠏⢰⠀⠀⠀⠀⠀ ⠀⠀⠈⠟⣴⠀⠇⣱⡎⢻⠹⠀⠏⣴⢃⡾⣤⣶⢷⠿⣰⡟⢸⠀⠀⠀⠀⠀⠀⠀⡃⣼⠀⠀⠃⣿⣰⠀⠀⢿⠀⡇⣿⣿⣸⡇⢸⡀⢷⠙⠈⣀⣦⣿⣼⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣹⡟⣷⣻⣛⣉⣉⣈⣀⣀⣄⣤⣤⣠⠀⠀⠀⠀⠀⠀⠉⠛⡴⣏⣰⠃⣼⠏⣰⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⠀⠀⠀⣾⡇⣿⣫⣈⣯⣰⠃⣼⠀⡄⢦⠰⣾⠃⣸⠀⠀⠀⠀⠀⠀⠀⠁⣴⠀⠀⠀⡶⣠⠀⠀⠀⣇⠹⣿⣿⣴⠁⣿⢰⠀⠀⣄⣶⠿⡟⣿⠀⠀⡟⢶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⡿⣿⢀⡿⠀⣿⡁⣻⣄⣧⠾⠓⠙⠉⠋⠛⠖⠶⠶⠶⣤⣀⢀⠃⣸⠁⣼⠋⣿⠈⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠃⢸⡿⣹⠈⠀⣼⠀⡾⠀⠀⠀⠀⡏⢠⡟⢰⠀⠀⠀⠀⠀⠀⠏⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣠⠀⡟⣾⠀⠀⠀⠀⠀⠏⣰⣿⠁⡟⣿⠀⣄⢿⠉⠀⠀⠀⠀⠀⠀⠀⠋⠿⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⢸⠀⣿⠀⣿⡆⣿⠘⡀⢹⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠁⡾⢏⣼⣤⢻⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⡇⣧⣸⣉⣉⣭⢻⠎⢷⠘⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣶⣿⠙⡏⣿⢰⠀⠀⠀⠀⠏⣼⡇⢱⡿⣿⢠⠀⠀⡇⣿⢻⠀⠀⠀⠀⠁⡿⣿⣿⣿⣿⠿⠙⠀⠀⠀⠀⠀⠀⠃⡿⣿⣿⣼⠀⠃⢸⠉⣾⠀⣇⢸⠀⣿⠀⡟⢰⠀⠀⠀⠁⠛⠘⠀⠟⣴⣦⡿⢏⣴⢀⠀⡆⠸⠀⠀⡆⢸⠀ ⠀⠀⠀⠀⠀⡆⠀⠤⣀⣀⣁⣾⢁⡟⣤⣤⢤⣤⢸⠀⣸⠀⠀⠀⠀⠀⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⣷⣿⣿⠙⠈⠀⠀⠏⣰⠁⣿⣿⣾⢠⠀⠀⠀⡏⣰⣿⠁⠹⠀⠏⣿⣿⣿⣿⣿⣿⣮⣿⢠⠀⠀⠀⠀⠏⣶⢿⣽⣾⢡⠀⡏⢀⣏⢱⠘⡿⢸⠁⣸⠏⣰⣷⠿⠙⠋⣿⣴⠀⠀⣶⠀⠟⡷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠘⠃⠈⠀⠀⡷⢉⣿⢙⠉⠉⠉⠛⢸⡇⢸⠀⠀⠀⠀⠀⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣤⣶⣷⠻⡾⣠⠃⣿⣿⣴⠀⠀⠀⠀⠄⣠⠀⣿⡟⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠀⠀⠏⣾⡇⣿⣤⢁⡼⠃⣸⠃⣼⡇⢰⣶⣸⣆⢧⣸⠀⠀⣀⣯⣿⣿⠛⠈⠀⠀⡿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠛⠛⠹⠉⠉⠉⣟⣸⣇⢁⣾⣠⣄⢻⡇⢸⠀⠀⠀⠀⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⢇⣸⠀⠋⡿⣴⢀⠏⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠇⣿⣳⣼⡇⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⡇⢸⠇⣾⢣⣼⠇⣰⡏⢠⡟⢃⣼⢁⣾⠀⠇⢸⠃⣼⠀⠀⠀⡟⣾⢀⡀⣤⣶⠠⡟⢩⡟⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣉⣾⣷⣽⣤⣇⢸⡏⡆⢱⠋⠛⡟⣠⢹⠀⠀⠀⠀⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⢃⣽⠋⡿⣴⢀⠃⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⡏⢻⠀⣦⣿⣿⣿⣿⣿⣿⣿⠙⠋⣿⢿⣿⠟⣰⠏⣰⠀⢀⡏⣿⣿⠀⡟⢀⠁⡾⠁⡾⢀⠀⠀⡀⣤⢀⠀⠀⠀⠀⡟⣶⣹⠉⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣸⠀⠀⣄⣿⣿⠛⣶⠶⣶⣶⢓⣿⠀⣿⠀⠀⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⢀⡁⣟⣾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣼⢋⣰⣄⢷⠙⡈⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⢡⡟⣠⠁⠾⠏⣿⣠⣿⣿⢰⠁⡟⢠⡄⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡟⣿⣼⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠿⠉⠛⢸⣀⢻⠀⠀⠀⠀⡿⣯⠸⣇⠾⣦⠻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣼⢁⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣶⣠⠏⣴⠀⠀⠀⣀⣤⠶⠻⣿⣠⣠⣏⣿⣸⣏⣴⢃⡾⢀⠀⡟⢏⣿⣿⠁⣿⢻⣿⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⡟⣿⣾⠀⡀⠹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣹⠃⠚⢷⠛⣿⠾⠤⣤⣉⣉⣄⢻⡄⢿⠶⡶⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣿⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠟⣠⠀⠀⠀⠀⠀⠋⡶⣯⣰⠋⡿⣠⡟⣾⢡⠟⣰⠀⠀⡟⢯⣼⣿⣀⡏⣷⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣰⠇⣿⣴⠀⠀⠀⣧⠀⢷⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠶⠶⠒⡿⣶⠤⡤⡀⢻⠀⢷⠈⠀⠀⣀⢀⣷⠀⣦⢹⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣾⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⢈⠀⠀⠀⠁⠟⡴⣁⡿⣿⡿⣴⢀⠏⣰⠏⣴⢀⠀⠁⡟⣿⣺⡏⢰⠏⣰⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⠀⡇⣿⠈⠀⣇⠀⣼⢀⠀⡀⣤⢤⠷⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⡬⣠⠀⠀⡄⢷⡙⣦⠹⠀⠀⠀⡄⢿⠈⣧⠹⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡾⣠⣄⣶⠻⠟⡾⣤⢁⠟⣿⣾⣴⢀⠁⠟⣿⡴⢀⠀⠀⠋⣿⣿⣼⠃⣿⠟⣰⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠃⡿⣴⣦⠻⡎⠃⣿⠿⠰⠀⠀⠃⣼⠀⠀⠀⠀ ⠀⡂⣿⣴⠤⠶⡶⢷⠻⠋⠚⠶⡤⣦⠹⣇⠸⠉⠛⡴⣄⢿⠀⣧⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⣩⠛⠿⢿⠶⣤⣀⣥⢿⣿⣶⠰⠀⠀⠋⡾⣴⢀⠀⠀⠁⠟⣿⣾⣠⠃⣿⣾⣠⡟⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠀⠃⣼⠀⠀⣿⢀⠀⠀⡀⢷⣿⣴⣄⠳⠈⠏⣴⠀⠁⠉⠉⠀ ⠀⠀⣀⠀⠀⠀⡄⠀⣧⢹⠀⠀⠁⣿⣿⡾⣴⣠⠀⠗⣭⣏⢻⠈⣆⣿⠈⠚⡤⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⣴⢁⠋⣞⣴⣶⢀⠀⠃⡶⣠⣀⠀⠀⠀⠋⡾⣠⠀⠀⠀⠀⠋⡿⣿⣠⠀⠟⣿⣸⢁⡾⢠⠀⠀⠀⠀⠁⠉⠉⠉⠉⠀⣄⣦⢿⡿⠙⠁⠉⣍⠿⣿⢶⠶⣶⢹⠋⠙⡂⣵⣮⠳⠏⣴⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠛⠶⣠⣷⠈⣧⠛⠾⡵⣨⣀⢀⠀⣯⠘⣄⣷⢈⠀⡀⢀⠀⠀⠀⠀⠀⠀⠃⠞⠷⠙⠀⠀⠀⠀⠀⠁⠋⠟⣿⣚⠶⣬⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡶⣠⠀⠀⠀⠀⠋⡿⣼⣀⣀⣧⣽⣷⢙⢟⣶⢶⠶⠶⠓⠘⠀⡀⣀⣀⣀⣄⢷⠞⠶⡶⢶⣶⣥⣋⣛⣌⣀⡿⣤⢤⣠⢷⠙⠹⡀⣧⠹⣀⠀⠀⠀⠀ ⠀⡀⣦⠷⠘⠃⠉⠀⠀⡇⢸⠀⠀⡀⣶⣛⣙⣧⡘⠀⠀⠁⡶⣴⣦⠳⠈⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⣽⠀⠈⣏⠸⠁⠉⠛⠶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠶⣠⢀⠀⠀⠀⠁⠟⣿⣿⣸⠀⠀⠀⠀⣇⠻⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠗⣴⢀⠀⣿⠀⣦⠻⠀⠀⠀⣴⣆⢻⠀⣧⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⡆⠸⠀⠀⠀⠀⠀⣆⠹⣆⠻⠈⡀⠀⠀⠁⡿⣴⠳⡈⣦⠻⠈⠀⠀⠀⠀⠀⣀⢀⣄⣶⣴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠟⠶⠶⣷⣹⠛⣾⢀⠶⣴⢀⠄⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠓⠈⠀⠁⠉⠀⣟⠤⣧⣼⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠳⠈⠀⠀⠁⠛⣴⠿⡈⣦⠻⠈⠋⣴⢀⠋⡴⣤⠷⠙⣄⠷⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⢸⣿⣮⠳⠈⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠿⣠⣄⢿⣶⠈⠀⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠶⠠⠀⠀⣆⣿⠻⡀⣿⣠⠀⡴⢀⠀⠀⠀⣀⢦⠳⡙⣦⠶⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣿⣱⠿⡵⣭⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠾⣠⣀⠄⠤⣯⠸⢷⠛⠖⣤⠠⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠳⣍⣤⣤⠦⠳⠙⠀⠀⠀⠀⡿⣀⣤⠠⡉⣌⢦⠳⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠁⣿⡇⢸⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⠶⠙⡿⣣⠾⠳⠉⠞⠴⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢦⠳⡈⣦⠳⠈⡟⢠⠀⠀⠀⡃⣿⣾⠶⡛⣍⣭⠮⠶⠒⠛⠙⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠚⠒⠟⠿⡿⣶⣿⡙⣶⠲⠒⠶⠳⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣾⡇⠹⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⠈⣧⢸⠀⠀⠀⠳⣼⡏⢸⠀⠀⠀⣀⣀⣧⢿⠶⠷⣿⣳⣛⣋⣚⣛⣞⣷⣾⣴⣠⣿⢶⡷⣙⣤⠷⣟⣿⣼⣿⢿⠸⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⡙⣦⠲⠛⠾⡶⠳⣼⠀⠀⠀⠀⠀⠀⡿⣸⠀⡟⢠⡇⣿⣆⠸⣿⢹⡟⢹⠉⡉⢁⠉⠉⡋⢦⠻⡀⣷⣿⣿⣸⠁⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣤⠦⠶⡴⣤⣻⣌⠶⠲⠙⠉⠉⠟⣿⠿⡾⢹⠀⡁⢩⠉⣟⣴⢀⣄⣿⢿⠿⣾⣻⣙⢉⠉⡈⢷⠘⣧⣿⣄⣶⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠀⠀⠀⠀⠀⠀⡀⣅⢾⢠⡦⣻⢾⣴⣇⣿⣿⣙⣭⣉⣉⣛⢷⠿⠽⠟⠾⣠⢀⠀⠀⠀⣀⣀⣀⣀⢿⠀⣿⠤⠶⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡤⣤⢀⠀⠀⠀⡀⠀⠀⠀⡀⢶⠛⠷⡶⢻⠛⣋⢉⠋⠾⣴⢏⣴⣀⣦⠻⠈⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⠀⠀⠀⣤⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⢤⠶⠶⠲⠓⠀⠀⡆⢠⠀⠀⠀⡀⢶⠲⠀⠀⠀⠀⠀⡖⢰⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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