⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⢛⣩⠭⠍⠛⠛⠛⠛⠛⠻⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⡛⠁⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣴⣶⣿⣿⡟⢋⣠⠞⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠻⠛⢿⣿⣿⠟⠉⢙⣯⣻⢵⣈⣠⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠁⠀⢠⣾⠇⠈⠉⠚⠻⠶⢶⣤⣄⣀⡀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⣠⠎⢀⣼⢃⣤⡴⠿⠤⠤⠄⠀⠀⣠⢜⠁⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠉⠛⠋⠁⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⢿⣿⢣⣾⠯⢀⣼⠇⢀⡞⢁⡴⠃⠀⣀⣤⣾⠕⠁⠀⢉⣽⣿⢧⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠋⣾⣿⣿⠏⢀⣼⠏⢠⠏⣰⣫⣴⣶⡾⣿⣟⣁⣀⣤⡾⣟⣽⡷⠛⠈⢳⠦⣠⠀⠀⠀⢰⡆⠀⠀⢸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⣨⡧⠀⣎⣿⣿⠿⠿⣾⣿⡿⠗⠶⠽⠷⠚⣋⣁⣀⠀⠀⠸⡄⡞⠀⠀⡄⡞⣇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⠉⢰⢻⡏⢠⣿⣿⠁⠀⠀⣾⠉⠉⠂⠀⠀⠀⠐⠾⠿⠿⣿⣦⣄⣻⠁⠀⢰⣧⡷⡼⠀⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡇⢀⠏⠀⢇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡟⠁⢀⣼⣾⡇⠘⣄⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣵⡇⣼⠀⠀⢸⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢀⣴⡿⠋⢰⣇⣼⡿⠿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀ ⣀⣀⣠⣾⠿⢿⡿⣇⡟⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⢆⠐⠒⠒⠤⠤⣀⠠⠴⢞⡿⣋⣴⣿⠿⣄⣴⣿⣿⣿⠁⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀ ⠙⠉⠉⠀⠀⢸⣷⢸⣇⠀⢰⣿⣿⣿⣿⣿⣷⡀⠀⠀⠑⠢⠤⠤⠚⠁⠴⠒⠛⡿⣫⣿⣿⢿⣽⣿⣿⠿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⣾⡉⠀⣾⣿⣿⣿⠿⣿⡇⢽⣦⡀⠀⠀⠀⠀⠀⠀⣀⡤⢼⡞⠁⢸⣧⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣿⠇⢻⣿⡄⠸⣿⣼⣾⣿⢷⠒⠒⢻⣿⠭⠒⠊⢹⠄⠊⢹⣿⣿⡏⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣯⣿⣧⣿⠀⠈⢿⣧⠀⢻⣿⣿⣿⣿⣷⣀⡼⠧⠶⠖⢒⣲⠖⠒⠚⠉⠉⠉⠛⠛⠓⠶⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠘⢿⣿⡆⠀⠀⠉⠀⣸⣿⡟⣠⠟⠉⠀⢀⣠⣴⡪⣭⣶⣶⣶⣶⣶⣶⣶⠶⢤⣤⣤⣄⣀⡈⠻⢝⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠿⣯⣯⡷⠖⠊⠹⢛⣭⣴⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣦⣌⢻⣿⣿⣿⣶⣤⡙⠛⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢿⢮⣤⣶⣾⣿⠿⡟⠙⣠⠀⡴⠀⢀⠎⢝⡛⢿⣿⣿⣿⣷⣜⢻⣿⣿⣿⣿⣶⣄⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⣆⣼⣿⡇⣠⢹⠋⠀⠀⡜⠀⠀⠉⢂⠈⢻⢿⣿⣿⣷⡹⣿⣿⣿⣿⣎⠈⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣯⣀⠀⠀⠈⣿⣿⡟⠁⣞⠀⠀⢰⠁⠀⠀⠀⠘⡆⢸⡀⠹⣿⣿⣿⣞⣿⣿⣿⣿⣾⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣿⣿⡻⠳⡄⠀⢸⣁⣿⣇⠧⠀⢀⠃⠀⠀⠀⠀⢀⢰⡿⠀⠀⠹⣿⣿⣿⣜⣿⣿⣿⡿⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⣿⠇⠈⠙⢳⣾⡿⠓⣾⣿⣸⢻⣦⣄⡎⠀⠀⠀⠀⠀⠘⢠⣷⣄⠀⠀⢸⣿⠙⣿⣿⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠙⢲⣼⡽⠚⣿⣿⣿⣻⣶⢤⣴⣒⡚⠉⠁⣀⣼⠀⠀⢸⢱⣗⢘⣽⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣿⠬⠛⢿⢷⣄⣀⣇⡏⠛⣻⠶⣻⠀⠀⢈⣾⡟⡆⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⡟⠉⣑⡦⠒⠉⠀⢉⠚⠓⠶⠧⡾⠃⠀⠀⣼⣿⡇⢹⡀⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠋⡄⠤⠚⠁⠀⠑⢄⠀⠀⡇⠀⠀⢰⣿⣿⣿⠀⢷⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢀⠀⠀⠀⠀⠀⢣⠀⣇⠀⢀⣾⣿⣿⣿⠃⢘⣧⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢻⡿⠿⠿⠿⠿⠿⠛⢿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠘⣴⣿⣾⣿⣿⣿⣿⣿⠀⠘⣿⣷⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣹⡅⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣤⡀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠷⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠷⣦⣄⣀⣠⣴⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⣹⣿⣿⣿⣿⣿⢃⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⠸⡶⢆⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣷⡺⢷⣆⣽⡄⢻⢷⣤⣄⡀⠱⣼⣛⣤⠵⢽⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣏⢙⣓⣙⡉⢹⡾⡏⣌⣿⣄⣆⠈⠉⠁⠀⠉⣁⣠⠴⠮⠿⢿⣿⡦⣄⠀⠀⠀⠀⠀⠀ ⢀⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠀⠀⠛⡄⣿⠿⠛⢎⣿⠻⡂⣬⣍⣉⣠⣤⢺⠶⢖⡶⣿⣿⣪⡳⡀⠀⠀⠀⠀ ⢸⣿⣷⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠙⢦⣖⣄⣼⢽⡶⣽⣿⡿⠿⡛⢻⠯⢦⠀⢣⡀⢫⡻⣿⣷⠀⠀⠀⠀ ⢸⠙⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⡒⠺⣿⣿⣿⣟⣓⡽⢚⣭⣁⣀⣤⡽⣢⢣⠀⢡⣸⡏⠒⠝⣿⣻⠀⠀⠀⠀ ⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⠿⣿⣿⣿⠋⢹⣏⣴⣿⣿⣿⣿⣿⣿⣿⡯⡇⠀⢻⠠⠴⣾⠛⣷⠳⡀⠀⠀ ⠀⡇⠠⣿⣿⣽⣷⠉⠛⢿⣿⣿⡀⢸⣿⠀⠈⣿⣾⣮⣼⡗⣩⢽⡟⣿⣿⣿⣿⣿⣿⡌⠀⠀⠸⡄⠘⣆⣽⣞⢿⠀⠀ ⠀⡇⠀⠈⢻⣿⣿⣇⣤⣾⣿⢡⡇⢸⣿⠀⠀⡇⣻⣿⠁⠐⢡⣿⡇⣿⣿⣿⣿⣿⣿⡟⡆⠘⡆⢹⡀⢿⣿⢸⣾⠟⠁ ⠀⡇⠀⠀⠀⢻⣿⣿⠋⣿⣿⣸⣰⠸⣿⠀⠀⣿⣿⡏⠀⢀⣾⣿⢧⣿⣿⣿⣿⣿⣿⣿⠀⠀⣹⢻⢧⡿⣿⣼⠃⠀⠀ ⠀⡇⠀⠀⠀⠀⢻⣿⣀⣿⣿⣿⣿⡀⣿⠀⠀⢻⣿⣷⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⡼⣷⡇⣾⠟⠀⠀⠀ ⡰⡇⠇⠀⡀⠀⠀⠻⣿⣿⣿⣿⡟⡇⣿⡄⠀⢘⣿⠿⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠋⣷⣽⣿⢿⡀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢃⢹⡇⠀⣿⡟⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡞⢠⡏⣹⣤⡻⡏⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡛⣻⣾⣿⣸⡇⣼⡿⠀⠀⢰⢿⣿⢱⣿⠁⠀⣽⡟⢠⣴⣿⡟⢠⡶⡇⣿⣾⡼⣾⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⡴⠃⠀⢿⣿⣧⡝⠀⠀⢀⠟⠛⣿⣸⣿⣀⣀⣀⣴⣿⣿⠟⠙⡜⡆⡟⢿⠋⠛⣿⡄⠀⠀

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