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⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣈⠙⠓⣲⣶⣴⠞⣡⠾⣿⣿⠓⢺⠀⠀⢀⡯⠊⠀⠀⢤⣾⠀⠀⢸⠀⠘⡇⢀⡴⠁⠀⠀⠀⠈⣠⡾⠃⡰⠁⠘⡄⠀⠁⠉⠝⠋⠟⠉⠋⠁⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠔⢡⢊⠜⠀⠀⠀⠈⡄⠑⡀⠀⠀⠀⠀⠀⢀⡼⢻⠄⢸⢠⠃⠀⠈⠒⠠⢸⡟⡸⢢⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠚⠋⠁⢠⢊⡞⡵⣻⣿⠃⠀⡟⢀⡠⠊⠀⠀⣰⣱⠃⡇⠀⠀⠈⣇⠀⡹⠋⠀⠀⢀⠔⣡⡾⠋⢱⡀⡅⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡠⠒⢁⣴⠕⠁⠀⠀⠀⠀⠀⠈⢆⠈⢄⠀⠀⠀⠀⠀⠀⣸⠀⡿⠃⠀⠀⠀⠀⣠⡿⣸⡵⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠗⠒⣢⣄⣠⠤⢶⠚⠉⠁⠀⠀⠀⠀⠀⣰⡟⢃⡞⣵⣿⡏⢐⡿⠁⠀⠀⠀⢀⣴⣽⡇⠀⡇⠀⠀⣴⣉⠟⠀⠀⡠⠊⣠⠞⠫⠀⠀⠀⠑⣜⡄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡁⠄⠂⠁⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠎⠀⠀⠀⠀⠀⢀⣟⡜⠁⠀⠀⠤⠤⠞⠛⠋⠁⠀⠀⠀⠑⠨⢂⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠉⠁⠀⠀⠀⠀⠈⠑⠠⣀⠀⢀⣀⣼⢋⡜⣿⣩⣿⡟⣠⠞⠀⠀⣀⣠⡾⠟⠁⢸⡁⠀⡇⠀⣰⢣⠋⠀⢀⢊⣴⣾⡇⠀⢸⠀⠀⠀⠀⣿⠻⢦⡀⠀⠙⢆⠀⠀⠀⠠⠔⠚⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋⠉⢁⡾⢥⡓⣼⣿⣾⢿⣛⣶⠶⠶⡟⠋⠉⠀⠀⠀⢸⡅⠀⢻⢀⣿⠃⠀⢠⣾⢻⣱⢚⡇⠀⢸⠀⠀⠀⠀⢿⠀⠀⠙⠢⢄⣀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠈⠉⠀⢀⣡⣥⣴⣾⡟⢦⡹⢼⣿⡽⣿⢁⡏⠀⣸⠃⠀⠀⠀⠀⠀⠈⡇⢀⠘⣾⠃⢀⣴⢿⡏⢶⠏⣏⣿⠀⢸⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠈⠉⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⣶⣿⡿⠿⠛⠉⢹⣞⣧⣝⢮⣿⣽⣿⡼⠁⢰⡟⠀⠀⠀⠀⠀⠀⠀⢹⡸⠀⡞⣠⢋⠎⣼⢫⢏⢸⣧⣿⡆⢸⠀⠀⠀⠀⢾⣻⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠒⠁⠀⠀⢀⣾⢡⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣾⡿⠽⠞⠋⠉⠀⠀⠀⢀⠴⠉⢿⣽⢿⡾⣼⣻⣿⣧⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣷⠃⣾⠀⣿⠋⠆⣿⣹⠕⣳⢸⡄⠀⠀⠀⢻⣿⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠠⣿⠋⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣄⠀⡴⠚⠳⣄⠀⢀⡴⠉⠀⣴⠋⣙⣿⣽⣳⣟⡾⣿⣿⣤⣀⡀⠀⢀⡀⠀⠀⠀⡞⠀⡴⢻⡄⢻⣸⠁⢎⣼⡿⣿⡾⠋⠙⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢻⣷⣽⣆⣀⠈⠓⢄⡀⣀⣀⣠⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣧⠙⠞⠋⠁⣰⠋⡀⠀⠾⠛⠉⠁⠄⣈⡽⡟⢻⣷⠿⠿⠟⠛⠋⠉⠀⠀⢀⣜⡡⠎⠀⠀⢳⣌⢳⣬⣾⢋⣀⣿⣿⡀⠀⣿⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠑⢄⠑⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⣀⣻⣹⣿⡿⣮⣅⠐⢯⣜⠐⠂⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠏⢀⣀⡤⠞⡷⠀⠄⡁⢂⣠⣴⣶⡿⠋⣸⠁⣟⡟⠀⠀⠀⠰⣤⣀⣀⡐⠋⣁⣸⡚⠛⠛⠛⣟⡿⠋⣩⣿⣯⢹⣿⡇⠀⣟⣇⠀⠀⠈⣧⢬⡙⠲⢄⡀⠀⠀⠀⠉⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠐⢭⣅⠈⠒⣏⣿⣿⣷⣿⣿⢦⠈⠳⢤⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⠓⠋⠁⠄⣰⢫⣁⣴⣶⠾⠛⣭⡞⠋⠀⢀⡇⣼⣿⠃⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣻⣿⣔⢀⣴⠋⣠⡚⣿⣿⣿⡷⢿⡇⠀⢩⠸⡄⠀⠀⢻⡋⠁⠀⠠⠈⠲⢄⠀⠀⠀⠀⠳⣢⣀⠀⠀⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⠒⣿⠸⣿⣶⣿⢋⡺⢷⣀⣠⢞⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣐⣠⣥⠶⠛⠋⣩⠞⢁⣶⢿⠏⠀⠀⠀⣼⠇⠙⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣻⢻⡿⣷⡆⣴⡟⣿⠬⡟⣵⡞⣿⠤⣄⣀⣳⣷⡀⠀⠈⣇⠀⠀⠀⠈⠐⠄⠑⢦⡀⠀⠀⠈⠘⠕⡦⣀⠀⠀⠀⠀⠉⠙⢻⣶⠶⣶⣶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣿⣭⣘⠿⣷⠋⣷⣎⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⠁⠀⢀⡴⠚⢡⣴⠿⣋⡾⠀⠀⠀⠚⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣏⡷⣯⡇⣿⢰⡉⠫⣴⠿⣷⠌⢋⡏⡘⣴⢞⡵⣿⣷⡄⠀⢹⠄⠀⠀⠀⠀⠀⠑⠄⠙⣆⠀⠀⠀⠀⠈⠘⠕⣢⢄⡀⠀⠀⢻⡌⠣⣹⡾⣷⣤⣤⣤⣶⡞⠀⠀⠀⠀⠀⠀⠈⠙⠿⣏⠲⠴⠟⠈⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⢋⢜⣼⠟⣥⢛⣴⠇⠀⡀⠀⢰⡄⢀⡟⠀⠀⠀⠀⠀⠤⢴⣾⣿⣯⠿⠿⠟⠓⢣⡟⣾⠛⣄⠙⢋⣠⣶⣿⣠⢟⣵⢫⣽⠏⠪⡻⣄⠀⢳⡀⠀⠀⠀⠀⠀⠈⠠⠈⢣⡄⠀⠀⠀⠀⠀⠀⠁⠋⠁⠀⢺⠘⣆⠹⣷⡳⣎⡷⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠴⠋⣀⣽⡏⢧⡛⣤⢋⡼⣠⣤⣄⣀⣞⡀⣼⠃⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⣡⣴⣿⣶⣾⢟⣹⣏⡴⢻⡜⣧⣿⢧⣀⠙⠮⡳⣄⠳⡄⠀⠀⠀⠀⠀⠀⠑⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠰⣈⢆⢹⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣲⡶⢏⣧⣾⣶⣵⣶⣭⣾⣿⣿⣿⣿⣿⣿⣿⣽⣟⣛⣏⣩⣙⣛⣿⣶⣶⣶⣶⣦⣤⣤⣶⣿⣯⢷⣻⠾⡱⢎⡞⡭⢞⣣⣿⠟⠁⢸⣿⣶⡠⠁⠈⠳⣌⢲⡤⢄⣀⠀⠀⠀⢰⡀⠹⡆⠀⠀⠀⠀⠀⠀⢀⡴⢛⡷⣆⡚⣶⠫⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⢋⠵⣹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣂⣍⣩⣙⣛⣿⣿⣿⣿⣿⣟⣯⢿⣻⣿⣿⣾⣿⣿⣿⣾⣿⣿⣯⣷⣙⣮⣼⣷⠿⠿⠥⢤⡀⠀⠿⣿⣿⣮⣄⠀⠀⠉⠚⠦⣄⠉⠉⠉⠡⣙⠮⣿⡄⠀⠀⠀⠀⢀⡎⢠⣺⢛⣌⢻⡿⡀⠁⢻⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⡜⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⡿⣿⣿⣿⣾⣟⡿⣿⣍⠉⠉⢛⠛⢿⣿⣿⣿⣿⣾⣿⣷⣦⣤⣀⡠⠄⠈⠀⠀⠘⢿⡝⠿⣷⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠑⢌⠻⣄⠈⢻⣍⢚⠀⢦⣉⣛⣉⣼⠣⣹⡄⠀⡟⣶⣹⣛⣟⡷⠞⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠌⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢯⡿⣽⣻⢿⣿⣿⣿⣿⣿⣦⡀⠸⣿⣷⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠻⣖⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠑⠌⠳⣤⣿⢀⣇⠘⡏⠙⠛⠁⡇⣯⠳⣄⡇⣻⣍⡉⢁⣰⣾⣿⣿⣿⣶⣦⣴⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⢻⣿⣿⡿⣟⣷⣿⣿⣿⣿⣿⢇⣻⣿⣿⣿⣿⣿⣿⣿⣳⢯⡿⣽⣻⣿⣿⣿⣿⣿⣦⣌⣉⣉⣉⣉⣀⣉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉⠳⣄⠀⠀⠙⡻⣷⣦⣄⡀⠀⠀⠀⠀⢠⡟⢁⠆⢸⢻⣄⠹⣄⠀⠀⣷⢸⢳⠘⣇⠃⣯⠉⠉⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣖⣒⡦⢤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡤⢸⡿⢋⣾⣟⣷⣻⣞⣷⢯⠏⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⠿⠶⢽⣿⣟⡻⢿⣿⣿⣿⣿⣿⣿⣶⣬⣳⣄⠀⠀⠊⠻⣿⣿⣶⣄⡀⢀⡟⢠⠃⢠⠸⡀⠙⣦⡘⢧⡟⣇⣸⠼⠀⢘⣦⢸⡀⢀⣴⣾⣿⡿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡟⠿⣿⠆⠙⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣦⠀ ⣹⡧⠏⣰⣿⣟⣾⣳⣟⣾⢯⠏⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡷⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠐⠶⣯⣿⣷⣮⣙⡻⢿⣿⣯⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠛⠿⣟⣾⠁⡇⠀⠀⠀⠉⣓⣚⣯⡵⢛⣏⠛⢶⣤⣿⠟⢼⣷⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣾⡿⠿⠿⣿⣯⣿⣿⣿⣿⣟⣿⣻⣞⣿⣿⣷ ⠟⠀⣼⣿⣳⣟⣾⣳⢯⣟⡏⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⡷⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⡉⠛⠛⠿⠿⠷⠶⠤⠭⠭⢟⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣀⣥⣶⣤⣤⣤⣔⠘⠿⢁⣿⡻⣟⣮⠘⡇⠀⠀⣻⣿⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣓⣛⣈⣿⣷⣶⡄⢻⣿⣾⣿⣿⣿⣾⢷⣯⣟⣾⣽⣿ ⠀⣾⣟⣷⣻⣞⡷⣯⢿⣻⡀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣦⣴⣤⣤⣌⣙⠻⢿⣷⣄⣀⣀⣘⣁⡁⠀⠀⠙⠻⣿⣄⠈⠛⠷⣿⠼⠟⣰⣿⡙⠿⢭⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣉⢀⣀⣤⣄⣉⠉⠁⢀⣿⣿⣿⣿⣿⣿⣿⡾⣽⣻⣾⣿ ⣼⣟⣾⣳⣟⡾⣽⢯⣟⣯⢷⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡙⠛⠿⢿⣍⠙⠳⣞⠛⠛⠛⠿⢿⣿⣿⣿⣷⣶⡾⢿⡿⣷⣶⣶⣦⣾⣿⣷⡙⢷⣤⡈⠻⢿⣟⠉⠀⠀⠀⠀⠀⣀⣀⣈⣩⠏⢀⡾⠟⠋⣻⣿⣿⣿⣿⣧⡻⣿⣿⣿⣟⣷⣯⣿ ⡿⠾⠓⢿⡾⣽⢯⣟⣾⣻⣏⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣦⡈⠙⢷⣶⣦⣄⡀⠈⠙⠻⢿⣿⡾⠑⠁⠀⡏⢧⠈⣿⣿⣟⢦⡙⢿⣦⡀⠉⠻⣿⣿⣿⣷⣦⣝⠿⠟⠋⣀⣼⣷⣾⣿⣿⣿⣿⣿⠻⣿⣷⡘⢿⣿⣿⣟⣾⣿ ⣤⣴⣶⣾⢿⡽⣯⢿⡞⣿⡿⣼⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⣛⡛⠡⢀⣩⣥⣀⡼⠁⠀⠀⠀⣷⠈⣧⠘⣿⣿⣦⠳⣄⠙⣷⣆⣀⠸⣿⣿⣽⡿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢿⣿⣎⢻⣿⣿⣿⣿