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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⠢⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣠⡶⢠⣀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠆⠶⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠦⡀⢀⠀⠀⣿⣼⣦⣷⣿⢠⠀⠀⠀⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣷⢿⠿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠋⠛⠾⠶⠶⠤⠤⠤⠥⠤⠶⠶⠶⠷⠿⠛⠛⠛⠛⡟⢻⠉⠉⠛⠛⠛⠛⠿⠿⠿⡿⣽⣬⣲⣀⣀⣀⣀⣀⣉⣛⣭⢶⠻⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⡿⣶⣒⠑⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⠦⠻⡛⣝⠪⠀⠔⣿⣠⣀⣤⣤⣤⣫⣟⣷⣯⣒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣦⠶⣽⢷⠙⠀⠀⠀ ⠀⠀⠁⡿⣳⠿⠳⠞⠶⣦⣘⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣉⣯⣉⣿⣬⣤⢤⠤⡥⢴⠤⠤⠤⠤⠴⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠶⠛⡙⣦⣿⠹⠀⠀ ⡀⣷⣿⢻⡟⣿⢾⢶⠶⠓⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣿⣀⣀⣒⣞⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⣁⠛⣋⢋⣟⣿⠘⠀ ⠀⡿⣿⣷⣽⡆⠰⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢤⠤⠤⠦⠶⠒⠒⠒⠒⣿⠒⠒⠒⠒⠒⠒⠐⠤⠤⣀⢀⠀⠀⠀⠀⠀⣀⢀⠀⣜⣟⢶⡦⣿⣧⣿⣿⣿⢸⠉ ⠀⡄⣿⣬⢛⠉⡤⣤⢴⠦⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⢹⠛⣟⣾⣷⣯⣷⣿⡴⢀ ⠀⡇⣾⢿⣉⣦⢿⠻⡉⢤⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⣷⣉⢋⠞⣠⣏⣿⢰⠀⠀ ⠀⡄⢿⣆⣿⠻⡈⢦⣓⣮⠳⠙⣈⣄⠦⠒⠙⠉⠀⠀⠳⠒⠖⠷⠷⠤⢼⠤⠤⠤⠤⠤⠤⠤⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠯⠶⣤⣀⢁⡟⣼⢠⠀⠀⠀ ⠀⠀⣆⢻⡀⣦⡿⠻⠉⢀⠠⡒⣉⠤⠒⠛⠀⠀⣀⢄⡇⠀⠞⢶⣠⠀⢸⠀⠀⠀⠂⠙⠀⠀⣄⠲⠉⠘⠀⠀⠀⠀⠀⠋⠴⣠⠀⠁⠋⠾⣴⣇⢸⠀⠀⠀⠀ ⠀⠀⠀⣇⢸⠀⣿⣤⣷⢿⠻⠙⠀⠁⠀⠀⢦⠙⠀⠉⡜⣤⢥⠭⠤⡧⢴⠤⠠⠀⠀⡀⠀⠀⠋⡴⢁⠀⠀⠀⠁⠋⡴⢃⠁⠋⠾⣴⣀⠀⠁⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⡿⢫⠝⡿⡾⣹⣿⣦⣴⢣⠀⠀⠀⣁⡜⢛⠴⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⡀⣀⢄⠤⣀⠀⠏⣾⣷⣿⠻⠙⠀⠀⡟⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣏⣼⣟⣾⣱⡼⣟⣠⠀⠀⡀⠀⠀⠋⣾⡞⢀⠀⠁⠟⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⢧⣾⠀⣆⣿⣽⢷⠗⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⣿⣿⣠⠀⣠⠏⢠⠀⠀⠀⠀⠋⡿⢺⡠⠀⠁⠟⣴⢀⡋⣟⣷⢿⠛⠙⠀⠀⠀⠀⠀⠀⠁⠟⣶⢭⠸⠀⡀⢸⠙⠀⡀⣧⡽⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣧⢸⠀⠏⢠⠀⠀⠀⠀⠀⡟⣟⣦⢀⠋⠿⣿⣴⣀⠚⠓⣿⠒⡙⣦⡻⢮⠙⠂⠀⠀⠁⡾⢋⡠⢀⠀⠀⠀⢠⡄⠘⠀⠀⣿⡟⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⡞⢿⠈⢣⠀⠀⠀⠀⠀⡟⢿⣼⠇⡟⣿⡴⢀⠉⠟⢡⡉⣿⠛⠐⠀⡀⣷⡻⢮⢮⠈⡏⢿⢠⠀⠀⠀⠀⠀⠀⠀⢆⠀⠁⡟⣰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⣯⢷⠛⠉⠀⠀⠆⢻⣧⣸⡿⣼⣀⣀⠀⠁⣿⣿⣿⣿⣿⢿⠀⠀⠀⣦⢿⣜⢙⢱⢿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⠀⣼⠸⡀⣿⣤⢦⢶⢷⡿⣿⣿⠉⠛⠟⠿⡶⣤⣧⣿⣿⣤⣧⢿⠿⠙⠈⣆⣿⡝⡾⣿⡏⠀⠉⠋⠛⠚⠶⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠚⢻⢰⡿⣇⠘⠀⠁⡿⣷⣿⣿⣻⣴⢀⠀⠀⠀⠀⣀⣉⠈⠉⣉⢭⣻⣧⠹⣯⣿⢿⣿⣼⣡⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣷⢸⣟⣾⢧⠋⡾⢃⣿⣻⣿⢸⠉⠏⡿⣶⣴⣥⣛⣶⣤⣡⣋⣛⣛⣯⣿⣿⣿⢀⣿⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⣿⠀⣿⢿⢡⡟⣴⠃⣿⣿⣾⣿⣿⣼⣠⠀⠋⠾⣴⢋⠿⡐⢀⠀⠀⡀⣿⣿⣿⣿⡇⣽⣟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡟⢇⣷⠏⣿⣹⡾⢡⠟⣿⣽⡿⢧⣽⣿⠋⠟⣴⣠⠀⠀⠀⢀⠀⠀⠋⠃⡿⣿⣿⣾⣿⣿⣾⡏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣿⣾⡏⣿⣸⣿⣿⣵⣿⣿⣿⢿⣿⡿⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡦⣷⣻⣟⣯⣿⡇⢹⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⣿⣿⣷⣿⢋⣿⣹⡿⣿⣞⣼⣼⡼⢀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⡀⣏⣿⢸⡇⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⣟⣺⣾⣀⡾⡇⣾⣯⣷⢀⣿⢃⢹⠘⠋⡾⣠⣇⣵⢾⠿⡼⢀⠀⠀⠀⠀⠁⡿⣿⠘⢻⡄⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⣾⣧⡇⢠⡟⢟⣿⢿⣿⣇⠘⣿⡇⣻⡿⣿⠶⠲⠛⢛⡍⣹⢹⠀⠀⠀⠀⠟⣷⣙⣯⢿⣏⠘⣿⡼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⢫⣳⣿⡿⣶⢟⡴⣼⣿⡇⢿⡏⠟⣷⣿⣾⣭⣺⣶⠠⣀⣸⣄⣤⠶⠶⡿⣻⡙⣀⣿⣿⣿⢻⣿⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⣿⢿⣾⣠⠁⠏⣸⠀⣼⡾⣿⡞⢿⣿⡿⣿⣻⣙⠉⠋⠛⠛⢠⠀⠀⠀⠀⡏⣿⣟⣾⣿⣿⣿⣯⣧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⣿⣠⠁⠟⣷⣿⢹⠀⢸⢡⣷⢿⡌⣷⣻⣮⣙⣌⣶⣿⣿⢛⠙⠈⠀⠀⠀⣇⣹⣍⣿⣿⣿⣿⣻⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⣿⠀⡟⢠⠁⣄⣿⡏⢼⡄⡟⢿⣎⡙⣦⣜⠷⣙⣄⣤⣲⣽⣾⣿⢿⠙⠀⠀⣿⣾⣷⣯⣿⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣾⠸⣿⠀⡄⠁⣿⢉⠈⠀⣻⣿⢿⡘⠢⣟⠹⡀⣤⠶⠛⠈⣄⡷⣿⣷⠘⠟⣴⠁⣿⣿⣽⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⢠⣧⠀⠃⣤⣿⣶⢿⠀⢏⣾⡻⣯⢿⡺⣟⣼⣦⣻⣙⣄⢷⠘⣧⣿⣾⣿⠟⣿⣾⣥⣿⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⣿⠸⡇⠀⠀⡏⣿⢿⠉⠟⣾⢀⡀⣤⣟⣮⠻⣙⢭⠻⣙⣮⠻⣿⡟⣿⢿⣷⣿⣿⣽⣱⠸⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⢿⡇⠀⠆⣾⠲⠃⡿⣳⠙⠀⠀⢳⡀⣢⢿⣓⣭⣦⠶⣶⣶⣾⣿⣽⢞⣴⢀⣿⣿⣶⢱⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⣿⡼⠰⡏⢀⠏⣼⢘⡀⣤⠲⠙⡀⣦⠿⡒⢿⡙⣉⢭⠯⠟⣎⣷⣿⢸⠀⡄⣷⣧⢨⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⢹⠀⠀⡟⣷⠙⣄⠳⠈⠀⠀⣄⠦⡓⣄⠭⡻⣛⣛⢶⣷⠏⣏⡿⢻⠀⠀⡟⣷⣦⡾⠀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⣷⠁⡟⣰⠀⣀⣶⠾⣳⢿⠻⠉⠉⡉⣉⣉⣉⠛⠛⡶⣽⣍⠫⣿⣿⠸⠃⡾⣶⢷⢘⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡆⣶⣠⠀⠀⠀⠀⠀⠀⡀⢀⡀⣄⣤⣤⣠⣄⣤⣤⣤⣤⣔⣠⠀⣆⣷⠙⠀⠶⣿⢻⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠹⠀⣶⣀⠃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠸⠀⠁⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⠏⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀