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⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡞⠀⠀⢀⣠⠞⢁⠀⠃⠀⣠⣿⣋⠶⣉⠶⣩⠖⣹⢊⣿⢣⢇⡫⢖⡩⢖⡹⡜⠼⡱⡍⢶⣩⣿⠃⠀⠸⣿⡜⣥⢚⡴⢣⣍⠳⣍⡾⢧⣻⢧⡟⣿⣷⢏⡷⣽⣺⢭⡟⡾⣽⣿⣶⣶⣤⣤⣤⣴⣾⣿⣿⡿⠟⠛⠋⠛⡂⠀⣀⡸⢿⣿⣷⠀⣾⣿⡿⠛⠉⠉⠛⠻⣿⣿⣿⣿⣿⣾⣽⢦⡛⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⠀⠌⢠⡀⠃⠋⡀⠄⠈⠂⢈⣴⣿⣟⣧⣝⠬⣓⠦⡛⡴⢻⣏⠞⣬⠱⣎⡱⣋⠴⣩⠳⣱⡙⢦⣿⠇⠀⠀⠈⣿⡗⡸⡜⣢⠳⣌⣳⠾⡽⣏⡷⣛⡾⣽⣿⣯⢽⡶⣫⣟⢾⣝⣧⡻⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⣠⠛⠀⠀⣿⣿⣷⡾⠉⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡛⠻⣿⣷⡘⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡐⠀⠰⠀⠀⠀⠉⠀⠀⠀⠀⢠⣾⣿⣛⣮⢯⣟⣷⢯⣖⣙⠖⣿⢥⡛⣤⢛⡤⣓⡍⣞⣡⣷⣡⠞⣹⡟⠀⠀⡀⠀⣿⣯⠱⣎⣵⣳⢯⣽⡻⣽⣹⣽⣫⡽⣞⣿⣯⢾⡽⣳⢯⣛⣮⢷⣻⢟⡾⣽⣻⢷⣿⡟⠀⠀⢠⡤⢚⠇⠀⠀⣰⡿⠋⠁⠀⠀⢻⡀⢷⣄⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⡄⠈⠻⣷⣜⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣳⣟⣾⣛⡾⣭⢿⣽⣻⢿⣿⢦⣳⡜⣦⢳⡜⡲⡜⣼⡟⢿⣞⣿⠇⠀⢀⠀⠀⣿⣿⣻⡽⣞⣭⣟⣶⣻⣳⢯⡶⣯⡽⢯⣿⣿⣳⣻⡽⣏⡿⣞⣯⢷⣯⢟⣳⢯⣿⣿⠃⢀⠔⠊⠀⡜⠀⢀⣰⣿⠁⠀⠀⠀⠀⠀⣷⠀⠙⢿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡀⠀⠈⠻⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⡆⠐⡀⠀⠀⠀⣼⣿⣟⣾⣳⢿⡼⣯⢿⣽⣻⣞⣭⣿⣯⣟⣷⣻⡽⣯⢿⣽⣻⢿⡇⠈⣿⣿⣠⣾⣿⣀⣤⣽⣿⣳⠿⣽⢾⡽⣞⡷⢯⣻⢷⢯⣟⣯⢿⣿⣳⢯⡽⣯⢿⡽⣞⡿⣞⣯⣟⡿⣾⣯⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠹⣿⣯⢿⡽⣞⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣼⣿⣟⣾⣳⢯⡿⣽⢯⣟⣾⣳⣟⣾⣿⣷⣻⣞⣷⣻⡽⣯⢶⣯⣿⠷⠶⣽⡿⢋⡿⠟⠋⠉⢹⣿⣽⣻⡽⣯⢿⣽⣻⢯⣟⣯⣟⡾⣽⣻⣿⡽⣯⢿⡽⣯⢿⣽⣻⡽⣾⣽⣻⡽⣟⣿⣻⣟⡿⣿⣿⡿⣿⢿⣿⣇⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⢹⣿⣯⢿⣽⣞⡿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣾⣳⢯⡿⣽⢯⣟⣾⣳⣟⡾⣽⣿⣞⣷⣻⣞⣷⣻⣽⣻⢾⣿⠀⡀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣳⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⣟⡷⣿⣿⢿⡽⣯⢿⣽⣻⣾⣷⣻⢷⣯⡷⣿⢯⣷⢿⡾⣟⡿⣿⣿⣯⣿⣻⣿⣆⠀⠀⣼⣿⣿⣧⣄⠀⠀⠈⣿⣿⣻⢾⣽⣻⣽⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣾⣳⢯⡿⣽⢯⣟⣾⣳⣟⡾⣽⣻⣿⣞⣷⣻⣞⣷⣻⢾⣽⣻⡇⢀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⢾⣻⣾⣽⣟⡾⣷⢯⡿⣷⣻⣽⣿⣿⣿⣻⣽⣯⣷⣟⣿⣷⣿⣻⡾⣿⣽⣟⣯⣿⣻⢿⣽⣟⣿⣿⡷⣿⣽⣿⣷⣾⣿⡿⣽⡿⣿⣷⣤⣠⣿⣿⢯⣿⢾⣽⣞⣷⣻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⣟⣾⣽⣿⡽⣯⢿⣞⣷⣻⢾⡽⣷⣻⣿⣟⣾⣳⣟⡾⣽⣻⣞⣿⠃⠨⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⣟⣿⣿⣳⣿⣻⣽⣟⡿⣷⣟⣷⣿⠿⣿⣿⣳⡿⣞⣯⣿⣿⣷⣿⣻⣽⣾⣿⣽⣾⣿⣻⡿⣾⢿⣿⣿⣟⣾⣟⣿⣟⣯⣿⢿⣽⡿⣽⡿⣿⣿⣿⣯⣟⡿⣾⣽⣾⣻⣞⡿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣽⡾⣽⣿⣯⢿⣽⣻⢾⣳⣟⣯⢿⣳⣿⣿⣿⣞⣷⣯⢿⣽⣳⣿⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⢿⣽⣿⣟⣾⣟⣷⣿⣻⣽⡾⣟⣿⡃⠹⣿⣿⣽⡿⣯⣷⣿⣿⣿⡿⣟⣯⣿⢯⣷⣿⣻⣽⡿⣿⣿⣿⣯⣿⣾⣟⣾⡿⣽⣿⣳⣿⢿⣽⣟⡿⣿⣿⣿⣽⣟⣾⢷⣯⢿⣽⢯⣟⣿⣿⣿⣶⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠧⣿⡿⣽⣿⣿⣻⢾⣽⣻⣽⢾⣯⣟⡿⣾⣿⣿⣾⣻⣿⣯⡷⣟⣿⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣯⣿⣿⣿⣽⣾⣟⣾⡿⣽⣿⣻⣿⡅⢀⣹⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿⣽⣿⣟⣾⡿⣯⣿⣿⣽⣿⣿⣳⣿⣯⣿⣟⣿⡷⣿⣯⣿⣟⣾⡿⣷⣟⣿⣿⣿⣿⣿⣾⣿⣽⣟⣿⣾⣷⣿⠿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⢻⣟⣿⣿⣷⣻⣟⣾⣽⢾⣟⣾⣽⣻⢷⣿⣿⣿⣿⣿⣳⡿⣿⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⢯⣷⣿⣿⣷⣟⣯⣿⣟⣿⡷⣿⣿⣿⡿⠟⠋⠻⣿⣷⣿⢯⣿⡿⣿⣿⣿⣿⣿⣾⡿⣿⣟⣿⣾⣿⣿⣿⡿⣷⣿⣷⡿⣯⣿⣟⣷⣿⡾⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢌⡻⣿⣿⣿⣿⣳⣯⣷⣻⣟⣾⣟⣾⢯⣿⣻⣿⣿⣿⣿⢿⣿⣿⡷⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣯⣿⣿⣿⣾⢿⣳⣿⣯⣿⣿⣿⣧⠀⠀⠀⠀⠘⢿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣷⣿⣿⣟⣯⣿⢿⣾⣿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⢬⡱⣿⡿⣿⣿⣷⣻⣾⣽⡾⣷⣯⢿⣻⡷⣿⣿⣿⣿⣯⣿⣾⡿⢠⠀⠀⠈⠉⠛⠻⠿⣶⣦⣄⠀⠈⣿⣟⣿⣷⣿⣿⣿⣿⡿⣟⣯⣿⡿⣟⣿⣿⡄⠀⠇⢀⣀⠀⠉⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣥⣶⣬⡙⢿⣿⡿⣿⣿⣿⣻⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⡓⣿⡇⢿⣿⣾⣟⣾⢷⣿⣻⣾⣟⣯⣿⢷⣿⣿⣿⣷⢿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣽⣿⣜⣻⣿⣿⣿⣿⣿⡿⣿⣷⣿⢿⡿⣿⣿⡄⠊⠁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⠏⣾⠟⠁⠀⠈⢻⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡧⣍⣿⡇⢸⣿⣿⣿⣯⣿⢾⣯⣷⢿⣻⣾⣟⣯⣿⣿⣿⣿⣿⣿⣽⣶⣤⣀⣀⠀⠀⠀⠤⢀⠀⠀⠀⠀⢻⣿⡲⣝⢿⣿⡝⣿⣿⣿⣷⡿⣿⣿⢿⣿⣿⣶⣿⣿⣿⣿⣿⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡾⢸⡿⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⣿⡿⣝⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢦⣹⣇⠀⣿⣿⣿⣿⣿⣻⣽⣾⡿⣟⣷⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠐⠀⠀⠀⠻⣿⣮⣳⢻⣿⣎⠻⣿⣷⣿⣿⣻⣿⣿⣿⣯⢹⣿⣿⢿⣿⡀⠀⠀⣿⡏⣽⡏⠙⢻⣿⣿⣿⣿⡇⣼⡇⠀⠀⠀⠀⠀⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿⣻⢼⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡜⣿⡀⠘⣿⣿⣿⣿⣿⣽⣷⣿⢿⣻⣾⣟⣿⣿⣿⣞⣿⣿⡏⠉⠉⠉⣿⣿⣿⣿⣿⠛⠿⣦⡀⠀⠀⠈⠪⠻⣿⣷⣎⡿⣷⣌⡛⢿⣿⣿⣿⣟⣿⣿⣻⣏⡞⣄⠻⣷⣤⣴⡿⣸⢹⡇⠀⢸⣿⢿⢻⡟⠁⣿⠁⠀⠀⠀⠀⠀⣽⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⢧⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⡄⠹⣿⣿⣿⣿⣿⣾⣟⣿⣿⣽⣿⣻⣾⣿⣿⣿⣿⣧⠀⠀⠀⢹⣿⢛⡍⢻⣆⠀⠈⣿⣆⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⡇⢿⣜⣎⡷⠬⠭⠩⠞⠖⣿⠃⠀⡾⢏⡾⠝⢀⣸⡏⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣯⣿⣿⣿⣿⣿⣆⠀⠀⠈⢿⣮⠹⣌⠻⣦⣠⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⢿⣿⣿⣿⠃⠈⢿⣎⠀⠀⠀⠀⣀⡴⠏⣀⣴⠯⠛⠉⣠⢇⣿⣿⣦⣄⣀⡀⢀⣸⡟⣘⠻⠿⣿⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⠀⠸⢻⠏⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⢦⡀⠀⠈⠻⣷⣩⠓⠈⠉⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠏⠀⠀⠀⠉⠙⠓⠛⠛⠉⠉⠉⠁⠀⣀⣤⣾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠳⢦⣍⠻⢿⣿⠧⠃⠀⠀⠀⠀⠀⠀⡘⠀⠰⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣏⠳⠦⠤⣈⠛⠶⠤⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣋⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠷⢶⣤⣤⣿⣿⣶⣍⡐⠄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠑⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣴⣾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠛⠻⠿⣿⣿⣿⣦⠑⡀⠀⡋⠀⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢠⠎⠀⠀⠠⡄⢐⡄⠈⢿⣿⣿⣿⣿⣿⣿⡾⣽⣻⣿⡛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⢹⣧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡇⢰⠀⠀⠀⢢⠀⠀⠀⢠⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠟⠳⠃⠠⡤⠀⡾⠒⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣿⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⠀⢠⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⡘⠀⠀⠀⠀⢃⠀⢀⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠀⡁⠘⡄⠀⢀⣀⣀⠠⠔⠊⡇⠀⢴⠂⢀⠐⠁⡠⠠⠔⠃⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣮⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣦⣤⣤⣀⡀⣼⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣰⡟⠠⠁⠀⠀⠀⠀⠈⢄⡈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠃⠐⢠⠇⡀⠘⡖⠁⠀⢦⡠⠐⠈⡰⠄⠈⢠⠎⠉⠈⠄⠐⠂⢲⢠⣿⣟⢷⣻⣿⣿⣿⣿⣶⣿⣿⣳⣟⡿⣷⣦⣄⣀⠀⠀⠀⢀⣠⣤⠶⠟⠋⠁⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠞⠈⠹⣿⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⡾⠋⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠈⠃⢸⡄⠀⠀⠀⢀⠶⠀⠁⠀⡀⠘⠃⠀⢀⠠⠀⠀⠀⢹⣿⣿⣾⣿⠿⠋⠁⠀⠉⠀⢸⣿⡷⣾⣹⣿⡯⠛⢛⣩⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠹⣷⠀⣀⣀⣀⣤⣤⣤⣴⣶⢶⡾⠛⠋⠉⠀⣼⠃⠀⠀⠀⠹⣯⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⢶⡁⠈⡓⠠⠚⠉⠂⠒⢂⡀⠤⠐⠂⠁⣀⠤⠐⠊⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠀⣀⠀⠀⠀⠸⣿⣿⠶⣛⣭⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠹⣿⣿⣿⣿⣿⣿⠁⡎⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⡙⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣈⠁⠐⠂⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠘⡷⣀⠁⠀⡀⠤⠒⠈⠁⡀⠠⠺⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⡠⢊⣫⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡙⣿⣿⡿⣿⣟⠘⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠐⠌⠻⣶⣌⡉⠛⠛⠛⢛⣻⡿⠟⠿⠿⠿⠿⠋⡡⠂⠀⠀⠈⠉⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠇⠀⠑⠒⠂⠁⠀⡠⠄⠰⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢘⣶⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡙⣾⣿⣿⣏⣀⣀⣤⣀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⣛⠿⠶⠿⠟⠉⠠⢮⠋⠙⠳⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣀⠀⠀⡠⠄⠀⠀⠄⠀⠀⠀⠠⠀⠠⠠⠠⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣢⠄⠈⡍⢱⠀⢯⢰⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡸⣿⣿⡟⣋⣭⣍⠙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠓⠀⡈⢐⠖⠉⠀⢀⠤⣀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠸⣴⡀⠵⠀⣄⠈⡘⣿⣼⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠹⣟⢸⡱⣖⣺⡇⣼⣿⣿⣿⣧⡀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠈⡍⠀⠎⢀⣼⠏⢁⡠⢎⡉⠁⠒⠠⠄⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠀⠙⠏⡀⠚⡉⡝⢠⡾⠋⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡹⣄⣙⢓⣋⣴⣿⣿⣿⣿⣿⣿⣶⣶⣤⣌⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠐⠀⡍⠀⡊⠀⢀⠈⢀⠗⣢⢤⠧⡀⠀⠀⠀⠀⠛⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⢣⡀⠂⡸⠃⠐⠃⡀⠙⢠⣿⡁⠀⠰⠃⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡙⣿⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⠃⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠑⢠⠂⠠⠀⠀⣥⠈⢀⡡⢠⠌⢀⠀⠶⠙⢣⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡔⣛⢧⡠⠂⠀⠜⠉⠀⠀⠀⠀⠐⠂⢸⣿⣿⣆⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠘⡏⣧⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠢⢀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⠚⠋⠷⠀⠀⡉⠑⠂⠠⣠⡀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠊⢀⡠⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢿⣿⣿⡄⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡇⢸⠻⢿⣿⣿⣿⡿⠟⠉⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡶⠤⠝⠓⣶⠤⠤⢈⠉⠒⢂⡈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢿⣿⣿⣦⣀⣀⣼⣷⡄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣻⣭⣿⡇⠘⠀⠀⢻⣿⠋⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠑⠀⢈⠗⠒⠀⠘⠺⠁⢁⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣸⢷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⢛⣭⣶⣿⣷⠾⠛⠁⠀⠀⠀⠈⣷⣤⣤⣤⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢂⠹⣯⡟⣷⡀⠀⠀⠀⠀⠀⣀⣤⡶⢟⣫⢵⣺⣽⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⡹⣷⡀⢁⣤⡶⢟⣫⡵⣞⣽⡾⠟⢫⣥⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢻⣷⡹⣿⣫⡽⣞⣯⡷⠟⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢻⣷⣿⡷⠟⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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