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