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