Bfdia ASCII Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠉⠀⠀⠀⠈⠉⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⣿⡇⠀⠀⠀⠀⠀ ⢀⣾⠟⠁⠀⠀⢀⣴⠟⠋⠉⠙⠿⣦⡀⠀⢀⣴⠟⠉⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀ ⠸⣿⡀⠀⠀⠀⣿⠏⠀⠀⢀⣤⡄⠈⣷⠀⣾⡇⢠⣤⡄⠀⠀⠘⣷⠀⠀⠀⠀⠀ ⠀⠙⣷⡄⠀⠀⢻⣆⠀⠀⠈⠛⠃⣠⡿⠀⠻⣷⡘⠻⠋⠀⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣦⡀⣀⣽⡿⠶⣶⣶⠿⠋⠀⠀⠀⠙⠻⢷⣶⣶⣾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⣴⡇⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⠈⢻⣦⡀⠀⢀⣾⠟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡶⠟⠛⠛⠛⠋⠉⠉⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⣶⡄ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁ ⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀ ⠀⠀⠙⠷⣤⣤⣤⣤⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⡾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣄⣀⣀⣀⡀⠀⠀ ⠀⠀⠀⢀⣤⣤⣤⣼⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⠛⠛⠛⣿⡄⠀ ⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢸⣧⣄⣀⣀⣀⣤⣴⡾⠟⠀⠀ ⠀⠀⠀⠀⠉⠛⠿⠿⠷⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⢰⣄⢦⡀⢦⣶⢠⣄⠠⣤⢠⠤⣤⣤⢤⢀⣤⢤⡠⡤⠀⢤⣠⡀⠀⢠⠤⣤⣤⢤⠀⣤⠀⠀⠀⣠⡤⠄⢀⣠⡤⣄⡀⠀⠀⡤⣤⣤⢤⡄⢠⡀⠀⠐⣤⡢⣄⢠⣤⠄⠀⠠⣤⡴⢤ ⠘⢻⣬⠃⣼⣉⣸⡽⢠⢯⠀⠀⠹⡃⠀⠻⡻⢪⠀⣇⣀⡸⢻⠀⠀⠀⢈⠸⠃⠀⡰⢿⢆⠀⢘⣿⠀⠘⡚⡗⠀⠘⡃⠀⠀⠀⡯⢹⠀⢀⠿⡷⠀⠀⠻⢧⡝⢸⢻⠀⠀⠀⡏⣇⠖ ⢈⣹⣬⠃⣎⣝⢋⠀⠸⢼⠀⢠⡁⣇⠀⢶⢄⠧⢣⣧⠀⣎⣘⡀⠀⠀⢠⢀⡇⠴⠅⠸⠏⣤⠘⠧⣀⠴⠐⠼⠤⠞⠀⠀⠀⠀⡇⣘⠤⠧⠐⠯⢣⡠⣉⡧⡝⢼⠽⠤⡴⠢⢧⣦⣴ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣶⣖⣒⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⢜⡸⠿⠀⠀⠀⠀⠀⠘⠣⣀⣀⣤⣤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠢⣾⢣⠃⠀⡀⢄⡀⢠⣔⢄⡺⡭⠞⠉⠉⠉⠉⠙⠙⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢎⢿⠁⠀⠀⠑⢌⠀⢠⣫⣫⠎⠀⠀⠀⠀⠀⣀⡤⠀⠀⠈⢦⠀⢒⣥⣶⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⢸⠈⡞⠀⠀⠀⠀⠀⢈⢳⣿⠃⠀⠀⠰⡀⠋⠀⠈⠋⢁⡠⢲⢋⣹⠟⠋⠓⠒⠒⠚⠲⢶⣬⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠓⢤⣀⠀⠈⠑⠒⣖⣶⣾⡿⡞⢸⡏⠀⠀⠀⠀⠈⠒⠤⠤⡤⢫⠔⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⢻⡟⣲⣤⡠⠽⠄⠀⠛⠥⣈⡀⠀⡀⠀⠀⣤⣀⠀⣰⣵⣧⠟⠀⠀⢀⠀⢤⡤⠀⠠⣖⣉⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⢿⡍⠛⡧⣉⠑⠢⣄⡀⠀⠀⠉⢉⡟⣉⠽⠟⠃⢹⢻⣷⡏⠀⠀⠀⠘⢆⠀⠁⠀⠀⠛⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠈⠁⠀⣇⠀⠑⠢⢄⡉⠳⣦⣉⠵⠾⠆⠀⠀⠄⡆⢸⡼⠀⠀⠀⠀⠀⠀⠑⠢⠤⠀⠀⠠⠄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣹⣿⠶⣄⡀⠀⢸⡁⢘⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠉⠁⠠⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡦⣌⣏⠷⠦⣌⠙⠒⠒⢺⡦⠤⢴⣾⣿⡖⣶⣶⣆⡀⠀⠀⡀⠀⢸⠀⠀⠀⣿⠉⠉⢓⣶⣤⣶⡎⠉⠉⠛⠿⢷⣶⣤⣀⡄⢀⡨⠴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡼⠿⠲⢏⡉⠛⠶⣄⡀⣗⠒⠚⠉⠉⠈⠉⠙⣿⣏⢉⡩⠋⠁⠈⠀⠀⠀⣿⠶⠚⠋⠁⠀⢸⡏⠒⠦⢄⣀⢸⣿⠉⠁⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠉⠳⢤⡘⠛⠻⣦⣄⠀⠀⠀⠀⠀⢹⣠⣍⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⢼⡇⠀⠀⢀⣨⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠉⠛⠶⣤⣀⠀⠈⠉⠉⠁⠐⠀⠀⠀⠀⠀⣿⣄⠀⠀⢀⠎⣸⣤⠴⠛⠉⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠈⣟⠻⢦⣄⡀⠀⠀⠀⠀⠀⠁⢀⣿⠈⣳⡤⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠙⢻⣷⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡀⠉⢻⣷⡤⣀⡤⣔⣮⡽⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠳⣿⣿⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣷⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣶⣷⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠟⠁⠈⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⡿⢿⡿⢿⢿⣷⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⣟⣻⡙⡞⢦⡛⡵⢎⠯⡞⡴⢣⡽⣩⠟⡿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠂⠀⠂⠀⢀⣠⣾⡿⢻⡍⡞⡴⢣⡝⣜⢣⡝⠼⣩⢞⡱⣍⠳⡜⣥⢻⡱⢎⡼⣛⢿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⢣⡝⣣⢚⡱⣩⠓⡜⣌⣣⣼⣧⣳⡬⡑⢎⡳⣙⢦⢣⡝⢮⡱⣍⡞⡼⣻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⢏⡜⣣⢎⡥⢣⠓⣴⣹⣾⡿⢟⢫⡙⣛⠻⣿⣶⣧⡑⢎⢦⡙⢦⠳⡜⡼⣱⢣⡛⣿⣧⡀⠀⠀ ⠀⠀⢠⣿⡟⣭⢚⡜⡥⢎⡲⢡⣿⣿⣟⢫⡘⡌⠦⡑⣌⠳⣈⠞⣿⠿⣊⠖⡙⢎⡣⢝⠲⢥⣣⣽⣒⢿⣷⡀⠀ ⠀⢀⣿⡟⡜⡆⣏⠲⣍⢲⢡⢋⠟⣙⠂⡖⠰⡘⢢⡑⢢⠱⢌⡚⢤⣻⣷⣾⣿⣶⠿⡿⡿⢿⠿⡿⡟⣬⢻⣷⡀ ⠀⣼⣿⢸⣑⠺⡔⡫⡔⢣⠎⣜⠸⡄⢋⡔⠣⣕⠢⣉⠆⣍⠢⢍⠆⡱⢛⢆⡲⢌⡣⢵⣉⢎⡳⣱⡙⢦⣋⣿⣇ ⢀⣿⢇⠧⢎⡣⢭⡱⢜⡡⢞⡰⢃⣜⠡⡌⣻⣿⣷⢀⠏⡤⢋⠦⡙⣴⣿⡠⢓⡎⡜⢦⡩⢎⡕⣣⢝⡣⢞⡼⣿ ⢸⣿⡈⢿⣀⠹⣆⢱⠎⣰⠇⡶⢁⣿⡇⠶⣈⣿⣿⣇⠎⣰⠉⡶⢱⣸⣿⣷⢇⡸⡸⢆⠷⡉⣶⢱⡎⣱⢏⡸⣿ ⣸⣧⡙⢦⢣⡙⣆⢣⠞⣡⠚⡴⣉⢿⣿⡆⡱⢿⣿⣿⠘⡤⢓⠬⡑⢬⣿⣿⢢⠱⢥⢋⡖⣍⢆⠧⣚⠥⢮⡱⣿ ⢾⡇⢞⡱⢦⡙⣆⠣⢞⡡⣋⠴⡌⢺⣿⣷⣕⡨⢍⡄⢫⠔⣩⠒⡍⢦⡙⠿⣡⢋⣶⣉⠖⡥⢎⡳⣩⠞⣥⢳⣿ ⣻⡏⣖⡙⢦⡹⢔⡋⣆⠳⣌⠲⣉⠖⣿⣿⣿⣷⣆⠜⡡⢍⠦⡹⡘⢆⡙⣆⣵⣾⣿⠟⣍⠎⡧⡱⢣⠞⡴⢫⣿ ⣽⡗⣢⠝⣦⢓⡣⢜⢢⠳⣌⠳⣌⠲⡡⣿⣷⡉⠻⢿⣷⣬⣶⣥⣽⣶⣿⣿⡿⢏⢲⡙⣆⠻⡔⣭⢣⡛⣜⣿⠇ ⢼⣗⣡⢛⡴⢃⡓⣎⡱⣃⠮⡱⣌⠣⡕⡹⣿⣿⢶⣶⣾⣿⣯⣿⣭⣭⣾⢟⡩⢎⠇⡞⣌⠧⡹⢤⢣⠝⣼⡟⠀ ⢸⡷⣌⠳⣜⢣⡝⢤⢓⡌⣇⠳⣌⠳⢬⡑⢻⣿⣆⠉⠛⠋⠉⢁⣼⡿⡍⢦⠓⡭⣚⡱⢎⡱⡹⢌⡳⣾⡿⠁⠀ ⢸⣿⠰⣫⠜⣦⡙⢮⡸⢔⣊⠗⣌⠳⡌⡵⢣⡙⣿⣷⣦⣤⣾⠿⣏⡱⢎⢣⠛⡴⢣⡱⢍⠶⣩⢮⣿⠟⠁⠀⠀ ⠘⣿⡡⢇⡛⣤⠛⣦⢱⢣⢚⡜⣌⠧⣹⢰⠣⡕⢎⡜⠭⣍⠣⡝⡤⢓⡎⢇⡛⣬⠣⡝⣘⣮⣶⡿⠋⠀⠀⠀⠀ ⠀⣿⡇⢯⡜⢦⡛⡴⢃⣎⢳⡘⢦⢛⡤⢣⡛⠼⡬⢜⡣⡜⢣⠧⡍⢧⢚⡥⠹⣤⢓⣽⣾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⢿⣏⠶⣙⠦⡝⣜⢣⡜⢦⡙⢎⡖⣩⢇⡭⢳⢱⢣⡱⣍⢣⠧⡹⣌⠳⣘⣳⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡸⢥⡛⡼⣌⢳⡘⢦⡙⣎⠶⣑⢎⠶⣩⠖⡣⢖⡬⡓⣎⡕⢎⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣧⢛⡼⡱⢎⢧⡙⢶⡙⢦⡛⣜⢪⠞⣡⠞⣱⢋⡴⡹⢴⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⡜⢶⡙⣎⠶⣙⢦⡹⢦⡹⣌⢧⡛⡴⣋⠶⣩⢖⣹⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣟⡲⡝⣬⠳⣍⠶⣙⢦⠳⡜⢦⡙⢶⡩⢞⡡⣾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⢝⡲⡝⡼⡸⢿⣿⣧⡙⢦⣽⣶⣙⢮⣽⣿⣩⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣮⢱⡙⢶⡙⢮⡙⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⠿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣧⡙⣧⡙⣶⣿⣿⣿⣯⡻⣍⢿⣿⠛⢿⣾⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣜⢦⡝⣿⣿⣿⣿⣿⡷⣩⣿⡏⠀⠀⠈⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡸⢶⢏⡿⣿⠹⣇⢹⣿⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣯⣾⣒⢧⢻⣼⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡜⢮⡹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣏⡝⣻⣿⣔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠙⢿⣾⣽⣿⡿⣿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠉⠻⢿⣧⠈⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠂⠀⠀⠀⠙⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⣀⡀⠀⠀⠀⣰⣿⠃⣀⣀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠄⠀⠄⠀⠀⣴⣿⣿⣷⣶⣾⣿⣿⣿⣿⡟⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠴⠶⢶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡶⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣄⠀⠀ ⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⣿⣿⡅⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆ ⠀⠀⠀⢸⡟⠷⠦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢿⡇ ⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠋⠉⠁⠀⣾⡇ ⢀⣴⣷⣿⡿⠶⣤⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡄⣀⡀⢀⡀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡿⠃ ⢸⡟⠀⠈⣿⡀⠀⠀⢹⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿⣯⣿⡷⣰⡿⠤⠤⣤⣤⣤⣤⣤⣤⠴⢶⢾⡿⢿⣏⠁⠀⠀ ⢸⣇⠀⠀⠿⠷⠶⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠋⣿⠃⣿⡇⠀⠀⣶⣷⡄⠀⠈⣿⠀⢠⣾⡇⠈⣿⡄⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⠀⢿⡇⠀⠀⠘⠉⠀⠀⢠⣿⠀⠈⠉⠀⠀⢸⣷⠀⠀ ⠀⠻⠿⠿⠶⠶⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢐⢸⡏⠀⠈⢿⣦⣀⣀⣀⣠⣷⡿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠈⠙⣛⣛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢸⡇⠀⠀⣤⣶⠟⠛⠛⠻⢷⣦⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⣾⠿⠛⠛⠛⠿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⣿⡄⢸⡇⠀⣼⡟⠁⠀⠀⠀⠀⠀⢿⣧⠀⠀⢀⠀⠀⣸⡟⠀⠀ ⢸⣿⠀⠀⠀⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠈⢿⣾⣿⠀⣿⡇⠀⠠⣾⣷⡄⠀⠀⣿⠀⠀⢻⡇⢠⣿⡇⠀⠀ ⢸⣿⠀⠀⣿⡟⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠻⣷⣤⡀⠙⠛⠂⢿⣇⠀⠀⠙⠉⠀⠀⢰⣿⠀⢀⣼⣿⣿⣫⣿⠀⠀ ⠸⣿⣄⣠⣿⠁⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠈⠻⣿⣦⣄⡀⠈⠻⣷⣤⣄⣤⣴⣾⢟⣡⣴⣿⣿⠟⠿⣿⣿⠀⠀ ⠀⠙⠛⢻⡁⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢿⣆⠀⠀⠘⣿⣛⣿⣷⣦⣤⣍⣉⣉⣁⣠⣼⣿⡿⠛⠁⠀⠀⠀⠙⣷⠀ ⠀⠀⠀⣿⠛⠶⠦⠤⣤⣬⣟⠿⠷⠶⠶⢶⣶⠶⢿⣥⣤⣬⣿⡆⠀⠀⠈⢛⣭⣿⣿⠍⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣤⠾⢿⠀ ⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣿⡄⠀⣤⡈⠻⣿⡞⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⣰⣾⠀ ⠀⠀⠀⠘⠻⠧⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣾⣿⣾⡿⣷⡀⣿⣿⣶⡿⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣤⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠙⠛⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠋⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠉⠉⠀⠀⢠⠇⠀⠀⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠻⠷⣗⣢⢦⣄⡀⠀⠀⠀⠀⠠⣾⠋⠀⠀⠀⠀⢀⡄⠀⠀⢰⠁⠀⠀⠀⠀⠀⢠⡖⠀⠀⠈⣷⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⣷⣦⠀⠀⢠⣿⠁⠀⠀⠀⠀⢠⣿⠃⠀⠀⡎⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢸⡆⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠀⣴⠃⠀⠀⠀⠀⢠⣿⠟⠀⠀⢰⠁⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠈⡇⠛⠛⠙⠻⢶⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢀⡗⠒⠒⠒⠒⢶⡿⠯⠤⠄⠤⠦⠠⠀⠤⠤⣴⠿⠤⢤⢤⣀⣀⣀⣠⢇⠀⠀⠀⠀⣠⡽⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⣱⠃⠀⠀⠀⢸⡔⠀⠀⣀⣄⣀⣀⣀⣀⣨⣁⣀⣀⣀⣀⣀⣀⣀⣠⣀⡀⠀⠀⣰⠃⢠⡼⠋⢀⣀⣤⣤⣶⣶⣶⡆ ⠀⠀⠀⠀⠀⠀⣟⡼⠁⠀⠀⠀⠀⠀⢯⣅⠀⢹⠉⠉⠁⠉⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢦⣼⣁⠠⠿⠛⠛⠉⠉⠁⠀⠀⠀⣽⡟ ⠀⠀⠀⠀⠀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣰⡿⢦⣘⣇⠀⠀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⢀⣵⣳⣶⠋⠀⠉⠙⠻⣶⡄⠀⠀⠀⠀⢠⣾⡟⠀ ⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠈⠉⠻⣶⣶⠷⠴⣶⠶⠶⣶⣿⣾⣿⣿⣭⠀⠈⢳⣆⠀⠀⠀⠀⠉⣷⡀⢀⣴⡿⠏⠀⠀ ⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠛⠛⢋⣩⠵⠚⠉⢁⣿⠀⠀⠀⢹⣇⠀⠀⠀⠀⣿⣷⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠓⠶⠶⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣤⠖⠋⠁⠀⠀⢠⣾⠁⠀⠀⠀⠀⣿⡁⠀⠀⢰⡿⠀⠈⠙⠛⠳⢶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⡴⠛⠁⠀⠀⠀⠀⣠⠿⠃⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠃⠀⠀⠀⢀⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⣴⡫⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⠇⠀⣀⡤⠖⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⡑⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣰⠏⠀⠘⠻⢿⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠀⠀⠀⠀⠀⠀⠀⢠⣱⡏⢠⡏⠀⠀⠀⠀⣀⠼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⢇⡿⠀⣼⠃⢀⣠⣼⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢀⢂⡾⠁⠘⠿⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡀⠀⠀⠀⠀⠀⠀⠆⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢉⣁⣀⣀⡀⠘⠉⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⣤⣶⣛⠉⠉⠉⠉⠉⠙⠓⠦⣄⠀⠸⡆⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣻⠛⠉⠉⠳⡄⠀⠀⣰⠞⠛⠳⣎⠻⣦⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣇⠀⠀⢠⣿⡟⠀⢰⡇⠀⠀⢰⣾⡇⠈⢧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠙⢦⣄⣤⠟⠁⠀⠈⢧⣀⠀⣸⡿⠁⠀⢸⡆⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣈⣩⡥⣶⠆⠀⣼⠀⢀⣠⣤⠴⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣄⣀⣀⣛⣿⣭⣉⡉⠉⣁⣀⡤⠞⠁⠀⣰⣧⣼⣿⡇⠀⠀⢸⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⠀⠈⠉⠉⠉⠁⠀⠀⢀⣴⠋⠀⠈⠛⣧⠀⠀⢸⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⢒⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣸⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⢶⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⢷⣶⡦⣤⣴⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣷⣄⡞⠙⠓⡶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⡀⠉⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⡿⣷⣤⠞⣧⡀⢀⣼⣇⠀⠀⣸⣇⠀⠈⣹⡍⠀⠀⣤⠈⣿⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⢾⣏⡽⢧⣌⣛⣽⣅⣹⣷⣞⣁⢈⣓⣾⣉⠙⠲⠞⣻⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⣧⠈⣯⠉⠉⠉⢹⡍⢹⡏⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠻⠀⢸⡀⠀⠀⠀⣇⠀⠷⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣠⡤⠼⠇⠀⠀⠀⠸⢦⣄⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣉⣉⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣀⣈⣉⣹ ⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠁⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿ ⣿⠃⣰⣿⣷⣦⣄⣉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⢉⣁⡄⠘⣿ ⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠀⣿ ⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿ ⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡁⢠⣿ ⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣾⣿ ⣷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣾⣿⣿ ⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣴⣿⣿⣿⣿ ⣿⣿⣿⣷⣤⣀⡉⠙⠛⠛⠛⠛⠛⠉⣉⣠⣴⣾⣿⣿⣿⣿⣿⣿

⢠⣀⣀⣀⣀⡀⠀⢤⣀⣠⣄⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀ ⠀⣿⣿⣧⠹⣿⣦⠈⢻⢿⣿⡇⢸⣿⣿⣄⠈⣻⣿⣿⠶⠿⠛⢻⣿⣿⣿⠛⠿⡇⣴⣿⣿⡿⢛⣷⠈⢻⡿⠇⠀⠈⣷⣶⣶⡳⠀⠀⠀⠀⠸⡟⢻⣿⣿⣿⡝⠿⠿⠀⠀⣼⣷⡀⠀⠀⠀⠀⢀⣴⣿⡿⠋⢳⣤⠄⣰⣾⣿⡏⠻⣿⣦⣠⠀⠀⠀⠀⠸⠿⠛⣿⣿⣿⡟⠻⢿⠀⠀⣼⣿⡀⠀⠀⠀⠀⢸⣿⣷⡌⣿⣷⡄⢹⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣿⠉⠫⣿ ⠀⣿⣿⡟⢠⢟⡿⠀⢸⢸⢻⠁⢠⡿⢟⡿⠀⡏⡟⣿⠀⠀⠀⢸⢸⡇⣿⠀⠀⠀⣿⣿⣿⢄⡙⠃⠀⢸⡇⠀⠀⠀⡏⡟⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⡿⣸⡇⠀⠀⠀⣼⢿⣿⣇⠀⠀⠀⢀⣿⢿⡷⠁⠀⢠⡧⣼⢿⣿⠏⠀⠀⢹⡿⡟⡄⠀⠀⠀⠀⠀⠀⡇⢿⢹⡇⠀⠀⠀⣸⣻⣿⣧⠀⠀⠀⠀⣼⣿⡟⢃⡜⣻⠃⢸⢻⢻⡇⠀⠀⠀⠀⠀⣟⡏⣟⣀⣴⢦ ⠀⡏⢹⡏⢻⣿⣄⠀⢸⣘⢸⣡⣞⣿⡾⠃⠀⣇⡁⣿⠀⠀⠀⢸⣘⢸⡟⠀⠀⠀⠈⠳⢭⡲⠹⣆⠀⣸⣤⣤⣤⣴⣇⡁⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇⡁⣿⠄⠀⠀⣸⡏⠻⡿⠟⣆⠀⠀⢸⡷⢸⡇⠀⠀⠀⠀⢧⠨⣿⠀⠀⠀⢸⢳⣿⠁⠀⠀⠀⠀⠀⠀⡇⡁⣜⡇⠀⠀⣰⡟⠙⣿⠟⣧⠀⠀⠀⣼⠁⣏⠻⣿⣥⠀⢸⠘⢸⡇⠀⠀⠀⠀⠀⣿⠃⣯⢰⠏⠀ ⢰⡏⢹⡇⢨⢏⡿⡄⢸⠈⢹⠹⣏⠉⠀⠀⢀⡇⢁⡿⠀⠀⠀⣾⠈⢸⡇⠀⠀⢀⣶⡀⢀⡹⢂⣿⠀⣺⢇⠀⠀⢸⡏⠁⣿⠃⠀⠀⠀⠀⠀⠀⢸⠇⠁⣿⠀⠀⣰⡟⠒⠒⢻⡞⠹⣆⠀⠈⢧⣸⡴⠀⠀⣀⡦⠘⣆⣹⡣⠀⣠⣯⣮⠃⠀⠀⠀⠀⠀⠀⢰⡇⠁⡿⡇⠀⢰⣗⠒⠒⠺⡞⠛⣆⠀⠀⡞⠁⣿⢀⡟⣹⡇⢸⠈⢸⠇⠀⢀⣴⡇⠀⣯⢹⡇⠈⣀⣤ ⠘⠳⠾⠷⠿⠟⠊⠰⠿⠶⠾⠆⠘⢦⣀⡀⠸⠿⠾⠷⠆⠀⠠⣧⡤⢼⢷⠀⠀⠘⠛⠽⠿⠶⠟⠁⠘⠿⣛⠆⠀⠚⢷⣲⣛⡖⠀⠀⠀⠀⠀⠀⢼⣤⠤⠿⡌⠉⠫⠿⠇⠀⠘⠻⠶⠿⠷⠆⠀⠉⠛⠖⠾⠟⠁⠀⠀⠉⠟⣛⡩⠝⠁⠀⠀⠀⠀⠀⠀⠀⢼⣧⠤⢿⡆⠉⠫⠿⠗⠀⠘⠻⠶⠿⠷⠖⠳⠶⠷⠿⠿⠓⠁⠻⠭⠿⠧⠟⠿⠟⠁⠺⠿⠾⠷⠾⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⡶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⢟⢫⣭⡽⠿⠛⠶⠶⠶⠦⠿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⣉⡴⣧⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣆⡀⢀⣀⣠⣶⣾⣿⡿⠶⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠶⢦⣍⣉⠉⡴⢣⡾⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡴⣾⠟⣫⣭⣽⠿⠿⠷⠶⠶⠶⠾⠬⣷⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠸⡟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⣮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣤⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣼⡟⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⠿⠟⠛⠋⢉⣉⣉⡁⣿⣿⣿⡿⢈⣉⣉⣉⠙⠛⠛⠿⠿⣿⣿ ⣿⡟⠠⢴⣶⣿⣿⣿⣿⣿⣿⣿⣚⣿⣿⣷⢜⣿⣿⣿⣿⣿⣿⣷⣦⠀⢹ ⣿⣿⣦⡀⠈⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⣛⣋⣉⡥⠀⣴⣿ ⣿⣿⣿⣷⣄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⠟⢠⣾⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡟⠈⣿⣿⣿⣿⣿⠁⢱⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣧⣠⣿⣿⣿⣿⣿⣄⡜⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣷⣤⡆⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⢿⡿⠟⡁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⡄⠈⢻⣿⣿ ⠁⠀⢰⠏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⡄⠀⠀⠈ ⣿⣶⠏⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣆⠠⣴ ⣿⣇⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⠿⠟⠛⢀⣽ ⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⠀⣤⣤⣤⣤⣤⡄⣤⣤⣤⣦⣶⣶⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠀⠀⠈⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠛⠉⠁⠀⠉⠙⠻⣿⣦⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⢀⣼⠟⠉⠁⢈⣿⣦⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⢠⣾⠟⠁⢉⣿⣷⠀⠀⢸⡏⠀⠀⠀⠸⣿⣿⠄⣠⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⣿⡁⠀⠀⠸⣿⣿⠇⠀⠸⣷⣄⣀⣀⣠⣾⠏⠀⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⠀⠹⣧⣄⣀⣠⣾⠏⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⠀⣠⣄⣤⣴⡿⠋⠉⢿⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠉⠙⠛⠉⠁⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⣿⠛⠛⣿⡄⠀⢴⣿⠃ ⠀⠀⠀⠀⠀⠀⠈⠛⣾⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⣿⡄⠶⠟⠁⠀⠈⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣿⡇⠀⢶⣦⣤⣼⡿⠀ ⠀⠀⠀⢀⣀⣀⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣀⣴⣿⠁⠀⠀⣽⡟⠉⠀⠀ ⠀⢀⣠⣿⡟⠻⣿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⡿⠛⠉⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠙⠛⠛⠁⠀⠀⣼⡿⠁⠀⠀⠀ ⢸⣟⣛⠛⠁⠀⠀⠀⢙⣿⣦⣤⣄⣀⣀⣤⣤⣴⣿⠟⠉⠀⠀⢀⡀⣸⣿⠛⠷⣦⣤⣤⣤⣴⡾⠟⣿⣦⡀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀ ⠈⣻⡿⠃⢀⡀⠀⢴⣿⠋⠈⢙⣿⣿⣿⠉⠁⠈⢿⣧⠀⠀⣾⣿⠛⠛⠿⠆⠀⠀⣿⣟⠉⠀⠀⠀⠈⠛⠻⠷⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⢿⣷⣾⢿⣷⣤⣼⣿⠀⠀⣿⡏⠉⠁⠀⠀⠀⢀⣿⠇⠀⠘⠻⢿⣶⣶⣤⣴⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠙⠿⠿⠿⠷⣶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀꒒ ০ ⌵ ୧ ♡꒒ ০ ⌵ ୧ ♡꒒ ০ ⌵ ୧ ♡🅰☪︎ ִ ࣪𖤐 𐦍 ☾𖤓bfdi beef?bfdi beef?🥄

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⠀⠀⠀⠀⢀⣀⣤⠾⠷⣦⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣄⣀⣠⡤⠦⡤⢤⣤⣤⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⡤⠤⢤⠤⡤⢤⠤⣤⠤⣤⣤⣤⣤⣄⡀⠀⠀ ⠀⢠⣞⠻⣯⣥⣦⣼⡴⢬⠭⡭⠿⠿⠷⣬⣴⣁⣆⣥⠾⠿⠿⠿⠿⢛⠛⡛⢚⠳⠾⢦⣥⣆⣰⣠⣆⣩⣽⣭⣯⠿⠿⢛⢛⡛⢛⠓⡛⢛⠚⠖⡛⢖⠻⠶⢷⡔⢢⠒⡤⢻⡏⠀⠀ ⠀⠘⢿⡖⠠⢆⠰⣀⠲⣈⠒⡄⢃⠲⠰⡀⠦⣈⡱⢌⡚⠴⣁⠞⢠⠃⡜⢠⠃⡜⡐⢢⠰⢠⢁⠆⡔⠢⠄⡤⠐⡌⢢⢉⠢⢌⠡⢎⠰⡁⢎⠱⣈⢣⡙⠦⣹⢋⠬⡓⠬⣽⠃⠀⠀ ⠀⠀⣸⠇⡍⢢⠑⣃⠳⡌⠥⡘⠢⢅⠓⡌⠒⡤⢓⡜⣌⠳⢌⠢⣁⠚⡄⢣⠘⠤⡑⢢⠑⢢⢁⠎⡰⢁⠇⡔⢩⠐⡡⢊⠔⡊⡔⢊⠔⠱⣈⠒⣄⡚⢬⡑⣯⢉⠖⡩⢎⣿⠀⠀⠀ ⠀⠀⣿⠰⡘⢄⠣⡑⢣⠘⠤⡑⡑⡊⡔⢌⡱⢈⠇⡲⢌⠳⡌⢃⡄⢣⠘⠤⡉⢆⡑⡊⠜⠢⢌⠒⡡⢎⠰⡘⢄⠣⡑⢌⠢⣑⢰⡉⣎⠱⡄⢣⠰⣉⠖⡘⣧⠍⣎⠱⣂⠾⡇⠀⠀ ⠀⠀⡏⡔⢡⠊⡔⢡⠂⡍⢢⠑⡄⢣⠘⡄⠆⣅⢊⠔⣉⠒⡡⠒⡌⢢⢉⠆⡑⢢⡘⢰⣉⠓⡎⡰⢁⠦⡙⣔⢪⢐⠡⡊⢔⠂⠎⡴⢨⠓⣈⠆⡱⢈⢎⡱⢺⡏⡔⢣⠜⡌⣿⠀⠀ ⠀⠀⡗⣈⠆⡱⢌⠲⣉⠦⣁⠚⢌⠢⡑⢌⠒⣄⠊⡜⢠⠃⡅⢣⠘⡄⡊⠜⡈⠆⡜⢠⢊⠱⡐⢡⠚⡴⣉⢆⠳⣈⠒⡡⢊⠜⡨⢐⠡⢊⠔⡨⠔⡩⢆⡱⢒⣯⡘⢥⠚⡜⣿⠀⠀ ⠀⠀⣗⠰⠨⢔⡩⢚⠤⢣⡑⠎⡄⢣⠘⢢⢉⢄⠣⡘⢄⠊⡔⠡⢊⠔⡡⠎⡘⠌⡔⠣⢌⢢⠉⢆⠡⢂⡑⢊⠡⢂⠱⢄⠣⡘⢄⠣⠡⢍⢢⠱⡈⡕⢪⡔⢣⣻⠜⣌⠣⡝⣾⠁⠀ ⠀⢠⡇⠥⢃⡜⠰⢋⠼⢡⠊⡔⢡⢊⠱⡈⠆⡌⢢⢱⣾⣿⡄⢣⠉⢆⠱⡈⠜⡰⢈⡕⣈⠆⡩⠄⣳⣿⣶⡁⠎⡌⠒⡌⢢⠱⡈⢆⣉⠒⢢⡑⢄⡫⠱⣌⠣⣾⠱⣌⢣⢛⡿⠀⠀ ⠀⣸⠡⢎⢡⠢⣉⠆⡘⡄⢣⠘⢢⠡⢆⡑⢊⠴⢁⠚⡽⢻⠃⢆⡉⠆⡱⢈⠱⢄⠣⡜⢤⠋⡔⢡⠹⠿⢛⠡⢊⠔⡩⢐⠡⢢⠑⣂⠆⠍⢆⡘⠤⣃⠳⡌⢳⣇⠳⡌⢦⢉⣷⡀⠠ ⠀⣿⠐⣃⠢⡑⠤⢊⠔⡨⢂⡍⢢⢑⠢⡘⢰⡈⢆⠓⣠⢃⡜⠠⠜⡠⠑⡌⠒⡌⡱⠜⢢⠑⡌⢢⠑⡌⠢⢅⠃⢎⡰⢉⠢⡑⢊⠔⣪⢙⢢⠱⣂⢇⠳⣌⠣⢿⢢⡙⢤⠣⡜⡇⠀ ⠀⢹⡘⢄⠣⡘⡰⢉⠢⡑⢌⠒⢥⢊⡕⡪⠔⡈⢆⢃⢣⠒⣌⠣⠸⣦⣕⡬⡑⠤⡑⢌⢡⡊⠰⡁⢎⡐⢃⠎⡜⢤⢂⡱⢂⡑⢣⠸⣄⢫⢌⠳⢌⢪⡑⢦⡙⢼⡧⣘⠣⡓⢼⡏⠠ ⠀⢸⡐⢊⡔⢡⠒⡡⢂⡕⡈⢎⠄⠣⢌⡑⢌⠒⡌⢌⢢⠩⢄⠣⡑⠌⢋⣷⡕⢢⣸⣾⠿⢓⠡⡘⢄⠊⢆⡚⢜⢢⢃⡖⢡⠘⡄⠓⣌⠲⡌⠣⢌⠦⡙⢦⠙⣼⠗⣌⢣⡙⣾⠁⢀ ⠀⢸⡐⠣⢌⠢⠥⡑⢢⠐⡡⠎⡌⡑⢢⠘⠤⡉⡔⢊⢄⠣⢌⠒⡌⡘⠄⣿⣿⠷⢿⢢⠘⡄⢣⠘⠤⡉⢆⡹⢌⠣⢎⠰⡁⢎⠰⡉⢄⠣⢌⠱⣈⠖⡩⢆⡙⣾⠱⢌⠦⡱⣿⠀⠀ ⠀⣸⢐⠣⢌⠢⢱⠨⡅⢎⡁⢎⠰⢡⠢⡉⢆⡱⠨⢌⠢⡑⢌⠒⢤⣷⠾⡋⢆⡘⢘⢻⣵⠎⡰⢈⠆⡱⢂⠤⡉⠱⡈⢆⡉⢆⠱⡈⢆⠱⡈⠖⡨⢎⡱⢊⡱⡧⡙⢬⢒⡱⡿⠀⠀ ⠀⣿⢈⠖⡨⠱⣈⠳⡘⢦⡙⣌⠆⡡⢆⡉⢆⠰⡉⢆⠱⢌⠢⡉⡆⣌⠱⢈⠆⡘⠤⢂⠌⡑⢄⠣⡘⢄⠃⢆⠩⡑⠌⢆⠱⡈⢆⠱⣈⠱⡌⡜⡱⢊⡜⡱⣘⡧⡙⢆⠣⡜⡗⠀⠀ ⠀⢹⡌⠆⡅⠣⢌⢣⡙⢦⠱⡌⢆⠱⢠⠘⡄⢣⠘⡄⢣⠌⣢⠵⡘⡤⢓⡌⢢⠉⢆⡉⢆⠱⡈⢆⠱⡈⠎⡌⠱⡌⡜⡈⢆⠱⡈⠖⣠⠓⡜⡰⢍⠣⡜⡑⢆⡷⣉⢎⡱⡘⢿⡀⠀ ⠈⠨⣿⠘⡄⢓⡈⠆⡉⢆⠓⡈⠦⠑⢢⠡⠘⡄⢣⠘⠤⡘⡐⠲⢍⠲⡉⢄⠣⢘⠢⡘⢄⠣⡐⢌⠢⣑⡘⡘⠱⡘⠤⡑⢌⠢⠑⣌⢡⡙⠴⡑⢎⡱⢬⡑⢎⢷⡌⢦⠱⣉⠞⣇⠀ ⠀⣻⠇⡡⠚⡰⢘⠰⠑⣈⠒⡡⢊⢅⣶⣧⡉⠔⡡⢊⠔⡡⢑⠩⠄⠓⡈⠆⠓⡌⢒⢡⠊⡔⣡⢊⡔⢤⠒⠥⢣⢌⡱⡘⣎⢍⡓⢌⣲⣯⣒⣍⣦⣵⣆⣍⡎⣼⣏⣦⠷⠼⠛⠁⠸ ⠀⠈⠻⠷⠳⠖⠓⠳⠛⠶⠷⠶⠥⢾⣿⣿⡧⢾⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠒⠛⠒⠳⠾⠴⠾⠟⠛⠛⠛⠙⠻⠿⢯⣿⡚⣿⣿⡟⠉⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢿⣿⣿⣟⣫⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣉⣙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡔⠁⠀⠀⡄⠀⠀⠀⡀⠀⠅⢀⠖⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⡄⠀⠀⠩⠋⠁⠉⠁⠔⠀⡬⠃⠀⣇⢀⠄⣏⡀⡰⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⡦⡄⠀⠰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⢫⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠠⠔⠥⠌⠀⠘⠠⠤⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡄⡦⠖⡗⠀⠀⠀⠀⠀⠘⡏⠃⠓⠦⡤⣀⡀⠓⠥⠜⠃⠸⠀⠀⠀⠷⠂⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋⠉⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⠈⢹⡀⠀⠀⠀⡀⡀⡀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠉⠶⠤⠄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⢼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡖⡜⠀⠀⠀⢠⠤⠤⠄⠔⠀⠀⠀⠀⠀⠀⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠂⠀⠀⠀⠀⠚⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠬⣒⣤⣀⣀⣀⣀⣀⣀⣀⢄⡲⠟⠏⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠉⠉⠁⢠⠀⠀⠀⣤⡧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡄⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠈⡀⣬⣶⣿⣷⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠟⠉⠹⣿⣦⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⢸⣿⠋⠁⠀⠈⢻⣷⡄⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠢⢤⣀⣀⣴⣿⠛⠁⠀⠀⠀⠸⣿⡇⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⢀⣾⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⡿⠀⠀⠀⠀⠀⢻⣿⡄⠀⢉⠑⡉⠉⠙⠒⠢⣀⠀⠀⠀⠀⠀⠀ ⠀⠄⡐⢈⠐⡈⠄⢂⣰⣦⣴⣤⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡄⠀⠀⠀⠀⠘⣿⣧⣼⣴⣶⣶⣷⣦⣦⣁⠈⢣⡀⠀⠀⠀⠀ ⠐⠠⠐⢀⠂⣐⣼⣾⠿⠛⠉⠛⠻⢿⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⣿⡄⠀⠀⠀⠀⣿⠿⠋⠁⠁⠀⠀⠈⠛⢿⣿⣦⣧⠀⠀⠀⠀ ⠈⠄⡁⢂⠐⣾⡟⠉⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⣰⣿⠟⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀ ⢁⠂⡐⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣄⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠶⢶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠒⠒⠒ ⡀⠂⠄⠁⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⠋⠀⠀⠀⠈⠛⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠂⠄ ⠠⠁⠌⡀⠙⠻⠿⣷⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣴⣶⡿⠿⠃⠠⢁⠂ ⠠⢁⠂⠐⡀⢂⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⢐⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣯⣤⣤⣥⣔⣨⣄⣂⣀ ⠀⢂⢈⣐⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢉⠰⢉⠒⡙⠼⠩ ⠛⠍⡚⠰⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢈⠔⡈⠰⢀⠆⠡ ⢈⠆⢡⠘⢠⣿⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⠀⢸⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣀⠀⠀⢸⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠇⠀⠀⠀⠀⣴⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⢿⣿⡅⠀⠀⢸⣷⡀⠀⠀⠀⣿⡗⠠⢂⠡⣁⠢⠈⠆ ⡊⢄⠃⡌⠄⣻⣷⣴⣾⠿⠛⣻⣿⡀⠀⠀⠀⣾⡇⡉⢛⢿⣶⣤⣀⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠈⠛⢿⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠻⢿⣿⣷⣤⡀⠀⣀⣠⣶⣾⠿⠛⡉⢄⠒⡈⣿⡇⠀⠀⠘⣿⣷⣄⢀⣠⣿⡧⠑⢂⠡⡀⠆⣉⠐ ⡱⢈⠂⡔⡈⠄⠌⣁⠢⠌⡐⡈⢿⣷⣦⣤⣼⡟⠡⠐⠂⢐⠈⠛⠻⣿⣷⣄⣠⣶⣿⣿⣿⠿⠿⠇⠀⠀⠀⠹⣿⣿⣿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠛⠛⠛⠋⢉⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⡿⢛⠋⡐⠌⢂⠅⢂⠒⠠⢿⣷⣀⣠⣴⣿⠹⠻⠻⢛⠩⣀⠱⢈⡐⠰⠐⡠⠌ ⡅⢢⠑⡠⠐⡉⠰⢀⠂⠆⢡⠐⠂⡌⢉⡉⠅⡠⠑⡈⠀⠀⠀⠨⢁⢄⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠐⠡⡘⢀⠎⢠⠉⠔⡎⠉⡍⠩⠉⡅⢊⡐⠡⢂⠡⠄⠒⡠⠄⠃⡌⠐⡄ ⠜⡠⢃⠔⠡⡈⠔⢂⠡⡘⠠⠌⢡⠈⢤⠐⡈⢄⠡⠌⡐⠡⢊⠡⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠁⡔⠡⡈⢄⢪⡝⠆⡑⡀⢃⠡⠐⠂⠤⠑⡠⠒⡈⢡⠐⠌⡰⢀⢃⠐ ⢎⠰⣈⠂⡅⠰⢈⠂⡔⢁⠒⠌⡐⣬⢚⠠⡁⠂⠆⢂⠡⠘⡠⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠰⢁⡐⠂⠤⠐⡌⢐⠠⢡⠈⡌⢁⠆⠡⠄⡑⢠⠡⢈⠒⡀⠆⡨⠐ ⠆⡱⠠⠡⠄⢃⠂⠥⠐⡨⠐⢌⡀⢃⠋⡐⠤⢉⠂⠥⢈⠡⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡷⢁⠂⡌⠌⡐⠡⡐⠨⠐⢂⠡⡐⡈⢄⠃⡌⢐⡁⠢⢁⠢⢁⠆⠡⠌ ⢣⠐⡡⠃⠌⡄⢃⠢⠑⡠⠑⠂⢌⠠⡑⠠⠒⣀⠃⠒⡈⢄⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣤⣀⣀⣀⣀⣠⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠠⢡⠐⠌⡠⠑⡠⠡⢉⡐⢂⠡⠐⡂⢌⠐⢂⠄⢃⠄⠃⡄⠊⠔⡈ ⡡⢊⠔⡉⡐⠐⡂⢡⠘⠠⢡⠉⢄⠒⢠⠁⡃⢄⠊⠡⠌⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⢈⠄⢊⠔⠠⡑⠠⠑⢂⠰⠈⡄⠃⡔⠈⡄⠃⠌⡂⠌⡡⠐⡉⠰⢀ ⡑⠌⠤⡑⢀⠣⠐⡡⠈⢅⠂⠌⡂⠌⢂⠔⡁⠢⠌⡁⢆⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠰⢈⠂⠌⠒⣀⠃⡉⢄⠊⠡⠄⢃⠄⢃⠤⢉⠰⠠⠑⡠⠑⣈⠡⢂ ⡱⢈⠆⡡⠂⢌⠡⡐⠉⡄⢊⠄⡑⡈⠆⠰⠈⠔⢂⠡⠂⢌⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠈⠔⠡⠘⡈⠔⢠⠘⡀⠆⡉⠔⣈⠂⢌⠂⡔⠈⡄⢃⡘⠠⠡⠄⢒⠠ ⡔⢡⠘⡄⠡⠂⠆⡰⠁⡔⢈⠰⢀⠅⡘⢠⢉⠰⢈⡐⠉⡄⠚⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⢿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠏⢠⠉⢌⠂⡑⠠⡉⢄⢂⠡⠒⡈⠔⢠⠘⠠⢌⢀⠣⠐⢂⠄⢃⠡⡘⢀⠆ ⢌⠢⡁⠆⡡⠑⢂⡁⠒⡠⢊⠐⠌⡐⠌⢠⠂⢒⠠⠌⠒⢠⠑⡘⠻⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⢋⠰⢀⠚⠻⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟⠡⢘⠠⠘⠠⠌⡐⠡⡐⠂⡌⢠⠃⠌⡄⠃⠌⣁⢂⠂⡌⢁⢊⠰⢈⠰⢀⠃⡐ ⢊⠔⢡⠊⠄⡑⠂⡄⠃⡔⠠⢉⠰⠀⡍⢠⠘⡀⠆⠌⡁⠆⠌⠤⠑⡠⠙⠻⢿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⡿⠟⠡⡐⠄⣊⠐⡌⠒⢠⠙⠿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⠿⠉⠤⠑⢂⡁⢊⢁⠒⣈⠡⠐⡡⠐⢂⠌⡰⠀⡍⠰⢀⢂⠡⡐⢁⢂⠢⢁⠢⠁⡜⢀ ⢣⠘⣄⠣⠌⡐⠡⢄⠃⠤⡑⡈⢄⢃⡐⢂⠡⠌⡄⢃⠰⢈⠂⡜⠠⡁⢌⡁⢂⠩⢙⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⡉⡐⣈⠡⠐⠌⡀⢆⠠⡉⠤⡈⠔⡈⣉⣛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⡉⢌⠀⢆⠉⡄⠣⢀⠂⡅⢂⠢⡐⠄⡃⠤⢉⠄⡒⢠⢁⠢⣁⠊⢄⠒⡈⢄⢂⠢⢁⠢⢡⠐⢂

⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣛⣉⠛⠛⣳⣬⠟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠦⠤⣤⠀⠀⠁⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠋⣴⣣⠖⣫⡿⢋⣴⠧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢰⣏⣧⠾⢋⡴⣋⣥⡄⠈⢷⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡁⢀⣠⣷⢾⣫⡵⠞⣹⣟⡵⠒⠒⠲⢄⣇⣹⣆⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⠶⢻⣿⣿⣟⠓⠛⠉⠉⠙⠲⠶⢤⣌⣉⣉⣉⣉⣉⣠⠾⠓⠦⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠓⠀⠸⣿⣿⣿⣄⣀⣀⣳⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠒⣇⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀ ⠀⠸⢦⣀⠀⠈⠉⠉⠻⣷⣄⠀⠀⠀⠀⣀⣴⣿⣶⣦⣤⣤⣤⣤⣤⣄⣧⣀⣈⣻⣦⣀⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠛⠓⠒⠚⠛⢷⣤⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠲⣄⡉⢉⣉⣙⣻⡟⠛⠛⠻⠿⠿⠿⠷⠾⠿⣶⣶⣶⣤⣤⣤⣤⣤⣾⣇⠀⠀⠀⠀⠀⢀⣼⡿⠟⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡏⠀⠀⠀⠀⠀⣀⣰⣶⡀⠚⣩⠟⢫⣉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣭⣍⡛⢷⣄⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⠁⠀⢀⣠⡴⠞⢫⡟⠹⡇⣰⠋⠀⠀⠙⢷⡀⠀⠀⠀⢠⣿⣷⡀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠚⠉⠁⠀⠀⢸⠁⠀⡇⠁⠀⠀⠀⠀⠀⠹⣦⠀⠀⣼⠏⢹⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣿⣤⣼⣧⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢷⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠛⢆⣹⣿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀ ⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡇⠙⢿⣿⣿⣷⡀⠹⣿⣿⣿⣿⠀⠀⠀⠉⢉⣉⣁⣀⣀⣀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡀⠂⠀⠀⠀⣀⣤⡾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⣿⣿⣷⡀⠙⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⡿⠟⠁⠀⢀⡄⣀⣴⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣷⣄⠈⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⣠⣾⡾⢻⡍⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⢻⣿⣿⣿⣿⣯⣀⣀⣤⣶⣿⣿⠟⠋⠀⠀⢀⣤⡾⠟⠁⣰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡻⣿⣿⣏⣟⣿⣏⣁⣾⠟⠁⠀⢀⣠⣶⠟⠋⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⣿⣿⡿⢿⣮⣿⠃⠀⣠⣴⠿⠛⠛⠛⠻⠿⠷⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣗⣢⡿⣃⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⠿⠿⠿⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠛⠉⠈⠁⠙⠃⠦⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠼⠋⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢐⡮⠁⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡻⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠼⠅⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢈⡟⠀⠀⠀⠀⠀⠀⢀⣤⡌⣿⣶⣿⠟⠁⢀⣀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀ ⣸⠁⠀⠀⠀⠀⠀⠀⣾⣿⡗⠈⠛⠁⠀⠀⣿⣿⠀⠀⠀⠀⣰⣿⣿⣽⣿⣻⣿⢿⣿⣿⡄ ⡟⠀⠀⠀⠀⠀⠀⠀⠿⡿⠁⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⢯⣿⣿⣟⣾⣿⣻⣿⣯⣿⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠛⠁⠀⠀⠀⠰⢾⣿⣿⣿⣻⣽⣿⣷⣿⣻⣿ ⡇⠀⠀⠀⠀⠀⢀⣴⣿⠿⡛⡉⢉⢉⣙⡻⣿⣄⡀⠀⠀⢰⣿⣿⣿⣿⣟⣿⣷⣿⣿⣿⣿ ⣷⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⢸⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡸⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀ ⠐⣳⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠀ ⠀⠘⣖⡀⠀⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢲⣄⠈⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⢠⣴⠋⠘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⣠⣀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⢀⣨⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠒⠒⠚⠉⠈⣠⣶⣾⣿⣿⣿⢿⣻⣿⢿⣿⣿⣿⣿⣦⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣻⣽⣿⡿⣿⣻⣿⢿⣾⣟⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣟⣷⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠁⠀⠈⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣾⡿⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡮⣝⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡜⣱⢏⡞⣻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⡣⢞⡼⣡⢏⡽⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡧⡝⣎⠶⣱⢚⡜⣣⠟⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⡹⣌⠳⣥⢫⡜⣥⢛⡴⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⡳⣌⠷⣌⠳⡜⢦⢫⡜⣣⠞⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡜⣣⠜⢧⡘⢧⠻⣜⢣⡜⣣⢜⡛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⠞⡴⢋⠶⣙⢎⡳⡌⢧⢚⠥⣎⠵⣩⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠮⣹⡘⡭⢚⡥⣚⠴⣙⠎⣭⢚⡴⢋⠶⣙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣌⢳⠢⡵⣉⠧⣒⢍⡚⣬⠹⢤⠳⣌⠯⡜⣱⢚⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⡞⣘⠦⡛⠴⣡⠓⡍⣎⠼⣐⢫⣌⠳⣌⠶⡙⡴⢋⣽⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢥⣋⠴⣉⠶⣉⡓⢆⡛⡜⢤⡓⣍⠲⣌⠳⡌⡖⣹⠰⣋⠴⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢫⢜⠲⣌⢣⠣⢎⡱⢌⠳⣘⠜⣢⠱⣌⠳⣌⠳⣘⠜⡴⡙⣌⠧⣛⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⡚⡥⢎⠳⡌⢖⡩⢖⡱⢊⡕⢪⠜⡰⢣⢌⠳⡌⠳⣌⠚⡴⣉⠦⣃⠧⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡱⣍⠲⡍⢮⣷⣼⠡⠞⡤⢃⠧⡘⢥⠚⡥⢃⠎⡵⣈⠳⣌⠳⣐⢣⠓⡬⢣⠽⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⣜⠱⣌⠳⣼⣿⣿⣿⡹⡘⠴⣉⠖⡩⢆⡹⢰⢩⣾⣿⣮⡑⢆⠳⣌⠲⣉⠶⣉⠖⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡱⣊⠵⣊⢵⣿⣿⣿⣟⡡⡙⢦⡑⢎⡑⠎⡔⢣⣿⣿⣿⣟⠱⣊⠵⣈⠳⣌⠲⣉⠞⣼⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⡱⢥⢫⠔⣿⣿⣿⣿⢃⠖⣩⠒⡌⢦⢉⠞⡨⣿⣿⣿⣿⡋⢖⡡⢚⠤⡓⣌⠳⣌⠳⡜⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⡱⢎⡚⡜⢻⢿⡛⢇⠎⡜⢤⠋⡜⠤⢃⢎⡱⣿⣿⣿⠳⣉⠒⣌⠣⢎⡱⢌⡓⣌⠳⣘⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⡜⣱⢣⡙⡬⢃⡞⡸⢌⡚⢜⠢⡙⢤⠋⡌⢆⢒⡩⢛⠥⠓⡌⡱⢂⡍⠦⡑⢎⡔⢪⣑⢣⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⠱⢦⡹⢔⠫⡔⢣⠎⡜⣌⠣⢍⠢⢍⡔⢪⠐⡔⠣⢌⠓⡌⡔⠣⣌⢣⡙⢦⡘⣣⢌⣻⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡹⢆⡳⣊⠧⣹⣾⣷⡸⢄⠫⣌⠣⢒⢌⣦⣧⡌⡱⢈⠦⡑⣌⠣⢆⠣⡜⢢⠕⡦⢋⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢩⡖⣥⢳⢩⣿⣿⣷⣭⣶⣤⣯⣾⣿⣿⡟⣥⠑⡌⢢⢱⡄⢫⡌⢳⡌⠓⣮⢱⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣷⢎⡵⣊⠶⣘⠟⡿⢿⣿⣿⡿⢿⡛⢇⠲⣁⠖⡩⠜⣢⢉⠦⡙⢦⡙⣲⢩⣶⡿⠁⠀⠀⠀ ⠀⣀⣤⣤⣄⡄⢀⣴⣿⣿⠛⢻⣿⡰⣍⢞⣡⢛⡬⣓⠬⢎⡜⣡⠞⣌⠳⡌⢎⡱⣉⠦⣍⡚⣥⠳⡜⣥⣿⠟⠀⠀⠀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⠀⠘⠻⣾⣜⢦⣋⠶⣡⢛⡬⣚⢤⢫⣔⣷⣾⣥⢓⡭⢲⢥⡙⢦⣻⣼⣿⣷⡄⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠀⠀⠈⣻⣷⣯⣞⣥⣋⠶⣩⢎⢧⢺⣿⣿⣿⡞⣜⣣⣮⣽⠿⠋⠁⠈⢿⣿⣶⣶⣶⣤⠀ ⠀⠙⠿⢿⡿⠟⠀⠀⢹⣿⣿⣷⣠⣴⣾⣿⠟⠉⠉⠛⠻⠿⢶⣿⣮⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (the person who ows the cooln3ss thing ALSO made this!! soo search cooln3ss 4 more!!)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢐⡪⠭⠁⠒⠚⠒⠂⠉⠉⠭⠴⣂⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠥⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠭⢖⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢟⡢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⣣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠑⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢿⣿⣷⡀⠀⠀⠉⠉⠉⠉⢿⣿⣦⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⡞⠀⠀⢀⠖⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⣱⠁⠀⡰⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢀⡀⠀⠀⠱⣷⡀⠀⠀⠀⠀ ⠀⠀⢀⢳⠃⠀⡰⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠙⢆⠀⠘⡝⡄⠀⠀⠀ ⠀⠀⡜⡏⠀⢰⠁⠀⠀⠎⠀⠀⠀⢀⠔⠁⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢣⠀⠘⡝⡀⠀⠀ ⠀⣰⢱⠀⠀⠇⠀⠂⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠆⠀⠘⡱⡀⠀ ⠀⡇⡎⠀⠀⡀⣀⠊⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠸⠀⠀⢣⢡⠀ ⠀⢰⠁⢠⡄⠈⠁⠀⠱⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠉⠉⠛⠻⢿⣶⣦⡀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢸⠀⠀⠈⡇⡀ ⣸⡎⠀⠆⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⠀⠀⠀⠀⠑⢄⣀⣠⠎⠀⠀⠀⢸⢃ ⡇⠇⠀⢰⠀⠀⠀⠀⠀⠈⢆⠀⢣⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼ ⠇⠀⢸⠸⠀⠀⠀⠀⠀⠀⠈⡄⠀⠢⢄⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀ ⢣⠀⢸⠇⠀⡐⠊⠉⠒⢄⠀⠈⢂⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⡆ ⣸⠀⠘⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⡇⠀⡇⠀⠃ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⢢⠀⠀⠀⡄⡠⠃⠀⣠ ⣧⡇⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂⡐⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡇⢀⠄⠳⠐⠀⢠⢸ ⠉⡸⡄⠀⠀⠀⠱⣄⠀⠀⢀⠇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⡆ ⠀⠱⣽⡀⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢰⢣⠀ ⠀⠀⠘⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠔⠉⠀⠀⡠⡴⠀⢠⣣⠃⠀ ⠀⠀⠀⠈⠫⡳⣄⠀⠀⢖⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡩⠊⢀⣴⡳⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠪⡓⢄⡀⠈⠒⠤⣀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠴⠛⠁⣀⢔⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⣐⠤⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⠬⢀⣀⣀⡀⠠⠤⠤⠐⠚⠁⠀⠀⠀⢀⣠⠤⣲⠯⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠫⠥⣒⡂⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠔⣒⣒⠤⠍⠓⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢈⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠄⡈⠐⠠⠈⠐⠠⠐⠠⣔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠠⢀⠁⢂⠁⠌⠐⠠⠁⠠⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠌⠂⠠⠁⠂⠄⡈⢄⠂⡈⠄⠁⠌⠠⢁⠈⠄⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠡⠈⠄⡁⠌⠀⣤⣾⠇⠠⢈⠐⠈⣤⡈⠄⡈⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠈⠄⠡⢰⣤⣶⠿⠛⠁⡀⠡⠀⠌⠠⠙⠛⠿⢶⣶⠅⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠈⡀⠂⠄⠠⠀⠄⣂⡐⡀⠁⠌⠐⡀⢡⣌⡸⠀⠠⠐⠒⠀⠀⠀⠀ ⠀⠀⠀⡓⠈⡐⠀⠡⠈⠄⢁⠂⣿⣿⠀⠌⠐⠠⠐⢸⣿⡇⠠⠁⠂⢌⠄⠀⠀⠀ ⠀⠀⠀⡁⠐⡀⢁⠂⢁⠈⠄⠠⠻⠟⠀⢂⠁⠂⡁⠘⠛⠃⠄⠡⠈⡈⠄⠀⠀⠀ ⠀⠀⠀⣢⠁⢀⠂⢈⠀⠂⠌⠐⠠⢈⠐⡀⠌⠐⡀⠡⢈⠰⠈⠄⢁⢰⡂⠀⠀⠀ ⠀⠀⠀⠠⠔⠀⡈⠄⢈⠐⢈⠠⠁⡀⠂⠠⢀⠡⠀⠂⣄⣼⠗⢈⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⡠⠐⠈⡀⠌⢀⠐⢠⣄⣁⣂⣄⣢⣥⡾⢟⠁⡐⠠⠨⠑⠀⠀⠀⠀ ⠀⢀⣀⠀⠐⠤⡀⠡⢀⠂⠄⡈⠄⢉⠉⠍⡉⢉⠁⠠⡀⠐⠠⢀⠃⠀⠀⢀⣀⠀ ⢾⡿⢿⡄⠀⢸⣔⡀⠂⠄⠂⠄⡈⢀⠂⡐⠀⢂⠈⡐⠀⡁⢂⡡⠀⠀⣰⣿⣿⣇ ⠀⠀⠘⣧⠀⣾⠀⠒⢁⠐⡈⠠⠐⡀⠄⠠⠁⠂⡐⠀⡁⢔⢸⡇⢀⣰⠏⠀⠙⠛ ⠀⠀⠀⠙⣿⡏⠀⠀⠈⠡⡐⠀⡁⠄⠠⠁⠂⡁⠄⡡⠂⠀⠈⠷⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐⠈⠠⢈⠐⢠⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠢⢅⠰⠌⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⠾⠃⠀⠀⠀⠀⠀⠘⠿⢿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠅⢘⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⢀⢄⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢷⠍⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠢⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠠⡇⡔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⡀⠈⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⡇⠀⢰⢣⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⠄⠀⠄⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⣷⠀⠁⠂⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠈⢜⡄⠀⠀⠀⠀⠀⠀⡄ ⠀⠀⢰⠂⡿⢁⠁⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡚⡀⠀⠀⠀⠀⠀⠆ ⠀⠀⢸⡇⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠀⠀⠀⠀⠠⣓ ⠀⠀⡜⣳⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠰⣡ ⠀⠀⡟⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠆⠃⠀⠀⠀⡶⣡ ⠀⢀⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠄⠀⡶⠀⠀⠀⠀⠀⣤⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣡ ⠀⢸⡚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠳⠚⠁⠀⠀⠀⠀⠀⠻⣤⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⠀⠀⢀⡇⢧ ⠀⠰⣍⢧⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⢰⠀⠀⢸⡏⡖ ⠀⡔⢎⡺⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣄⡀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡄⢸⡀⠀⢸⡘⡵ ⠀⢌⠣⠜⣃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠈⠙⠛⠶⠦⠤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⢏⡇⠀⡟⣘⠲ ⠀⠀⠁⠂⠈⣧⣦⣴⡶⠾⠿⠷⠶⣶⣤⣀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⢢⢿⠰⠈⠁⠀⠃⠄⠃ ⠀⠀⠀⣰⣾⠟⠉⠀⠀⠀⠀⡠⣄⣄⡌⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠢⣫⠃⠈⠘⠀⠀⠈⠀⠀⠀ ⠀⢀⣾⣟⣡⣤⡤⠔⠒⣶⡞⢿⡍⢻⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢖⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡏⢾⣿⣿⡇⠀⠀⠀⠀⠈⢀⠀⡇⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠣⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠈⠙⠛⠥⠤⡀⠰⢒⠞⣁⣴⡁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡄⠀⠀⠀⠀⣮⠈⠉⠁⠉⠉⢐⡈⢆⠀⠀⠀⣿⡇⡀⢀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠤⠒⠁⠀⠀⠀⡀⠀⡀⢀⠀⢀⠀⢀⠀⠀⡀⠀ ⠀⢻⣧⠀⠀⠀⠀⠐⡗⠖⢶⡶⠒⠣⢤⠃⠀⠀⣨⣿⠀⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠂⠌⢀⠡⠀⡁⠄⠂⢈⠀⡐⠠⠈⡀⠐⡀ ⢈⠌⢻⣧⡄⠀⠀⠀⢰⣐⣈⣆⡤⠀⢸⡀⠀⣰⡿⠁⠀⠘⡅⠀⠀⠀⠀⠀⠀⢰⢠⠁⠐⢀⠐⠀⢂⠠⠐⠀⡐⠈⡀⠄⠠⠐⠀⠄⢁⠀ ⠂⡌⠄⡙⢿⣶⣄⡠⠂⠒⣖⡶⠲⢶⣾⣴⣿⣿⣤⣤⣤⣤⣀⣤⣀⣀⣹⣀⠀⢘⡸⠀⢈⠀⠄⠡⠀⠄⠂⢁⠀⢂⠠⢀⠁⢢⠁⡈⠄⠂ ⠡⡐⠈⠔⠠⢈⠙⠻⠿⠿⢷⢿⣻⣾⣛⡭⡀⠀⠄⠠⢈⠉⡉⠩⢍⡉⠩⠛⠛⠛⣿⣆⠠⠈⠄⢂⠡⢈⢂⠡⠌⠄⣂⠁⠎⡀⢂⠐⡈⡀ ⠡⡐⠉⠄⠃⢌⠠⢃⠐⡌⣀⢺⣿⠬⣍⡏⠙⠓⢊⠐⡀⠂⠄⡉⠐⠘⠋⠛⠳⢶⣿⡁⠠⠁⡈⠄⠒⡈⢄⠒⠨⡐⠤⠘⢠⢁⠢⠡⢐⠁ ⠡⢄⠉⠤⠉⠄⢂⠂⡡⠐⡘⣾⣏⢖⡒⡎⢐⣸⣖⠠⢀⠑⠠⡄⠀⠀⠀⠌⡐⠂⣿⣧⢀⠡⠐⢈⠐⡀⢂⠈⡐⠒⢂⠓⠤⠲⠧⠳⠠⠎ ⡁⠎⡈⠄⠃⡌⠐⢂⠡⠘⣀⢻⡿⣮⣒⣇⠂⢻⡆⡐⠠⢈⠐⠣⢀⣠⡔⠠⠐⣱⡿⣿⡄⣂⠡⢂⠰⠐⣀⠢⠄⣁⠂⡩⠀⠅⢂⠡⠁⠌ ⠄⠃⢌⡐⠡⠠⠉⠄⠢⠑⡠⢿⣧⣷⣬⣍⣉⣙⣿⣦⣥⣂⣘⣀⣁⣠⣭⣽⣿⣿⣷⣿⣿⣿⣴⠂⠄⠃⠄⢂⠔⡀⢂⠡⠘⡈⢄⢂⠩⠐ ⢌⠡⢂⠔⡡⢃⠡⢊⡡⠑⡤⢉⢉⢉⣉⣿⣽⢛⣛⠛⠛⠻⠛⢿⣿⣿⡿⢿⡿⣿⢻⣿⣿⣿⣿⡌⠐⡉⠰⢈⠐⠨⠄⡡⢁⠒⠠⠌⣀⠃

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⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢿⣿⣿⡛⠛⠋⠀⠄⡐⢀⠂⡐⢀⠂⡁⢂⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠼⣿⣟⣿⡆⢀⠁⢂⠐⡀⢂⠐⡀⢂⠐⠀⡀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⣤⢦⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠂⢿⣿⣯⠉⠠⠀⠌⡀⢂⠐⡀⠂⠔⠠⢈⠐⠠⠁⠀⣀⡼⠃⠀⠀⠀⠀⠀⠐⣧⢸⣷⠞⣿⠉⡷⠀⠀⢀⣤⣶⢶⢶⣤⡀⠀⠀⣠⡶⢿⡛⡟⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠌⠉⠁⠌⢀⠁⠢⠐⡀⠂⠄⠡⠈⠐⠠⢈⠐⡈⢤⠟⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⣋⣽⢿⣾⠃⠀⣴⣟⠳⡌⢎⡲⢩⣿⢀⡾⣏⡙⢦⠱⡚⡔⣻⡇⠀⠀⠀⠀⠀⠀⠀⢀⠂⠄ ⠀⠀⠀⠀⠘⠀⠘⠀⠃⠠⠘⠠⢀⣃⣜⣠⠀⠠⠀⠻⡄⠀⢀⣀⣼⠿⠿⢤⣜⢿⣧⠛⠀⣠⠟⠀⣸⣟⣃⠧⣸⣇⡸⢃⣿⣿⢧⡘⣣⠜⣣⢣⡜⢻⡇⠀⠀⠀⠀⠀⠀⡘⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢉⡽⠿⣿⠷⠂⠈⣻⡿⠋⠙⠳⣄⠀⠈⢧⠸⡇⠀⣧⠀⢠⡿⣒⠬⢣⢍⠿⣾⣥⣾⡗⣪⠕⡥⣚⣵⠿⡫⢽⡇⠀⡂⠁⠄⡈⠐⡀⢁⠂⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠀⠀⠈⢿⣤⡾⠋⠀⠀⠀⠀⠉⠀⠀⢸⣾⠃⠀⡟⠀⣼⢗⡡⢏⢎⣼⣼⡼⢿⣿⡕⣆⣿⠾⠿⠿⣶⡱⣿⣃⣀⡠⢁⠂⠄⠡⠐⠠⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠀⠀⠀⠀⢀⣀⣀⡀⠉⠀⣠⡴⠶⢶⣄⠀⠀⢠⣿⠋⢀⣾⠁⣠⡿⣘⡜⢬⣶⣿⡄⠀⠀⢹⣏⢾⣧⡄⠀⠀⢸⣏⡝⡭⢛⡻⢷⣦⡈⢀⠂⠄⠁⠂ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣴⠏⠁⣨⣽⡆⣰⣧⡄⠀⠀⣹⠀⢠⠟⠁⣠⠞⠁⠀⢹⡷⣡⠚⣆⠾⣿⣇⣀⣠⡾⢋⡼⣿⣇⣠⡴⣞⢣⠜⡲⣉⠶⡡⢾⣿⠀⠐⠈⠄⠁ ⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⣻⣄⠀⣙⡵⠃⠸⢏⣀⣀⡴⢋⣴⠋⣠⠞⠁⠀⠀⠈⠁⢿⣦⡙⢆⡳⡔⣩⢍⢣⣕⣫⣴⣕⣪⣑⠳⣘⢆⢫⡱⢜⠲⣡⣿⡿⠀⢀⠀⢀⠀ ⣧⢳⣘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⠉⠻⣿⠷⠤⢤⣤⣤⣬⣥⣴⠚⢷⡞⠁⠀⠀⠀⠀⠀⠀⠘⠿⣾⣬⣲⣥⣣⣾⣿⡿⠶⢦⣤⣭⣿⠗⡬⣾⣧⣾⡾⠷⠛⠋⠀⠀⠀⠀⠀⠀ ⣿⣇⠞⡄⡀⠀⠀⠀⠀⢤⣴⠏⠀⠀⠀⠀⠈⠳⣄⣀⣀⣠⠴⠚⠉⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⡍⢉⣽⠟⣿⣇⢛⢦⡒⣱⢊⠵⣊⣿⠹⣦⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣮⣵⣉⣿⡗⢮⣴⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣬⡁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠐⠀⠂⠀⠑⠀⣺⣯⣿⠿⣥⡾⢿⣎⠺⣄⠳⣡⢋⡖⣱⡿⣧⠙⣷⣿⣿⣀⠀⠀⠀⠀⠀⠀ ⠈⠉⠉⠉⢹⣟⡳⠈⢁⡾⣇⠀⠀⠀⠀⠀⠀⣠⡞⢹⡿⣆⡀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣿⣯⣵⣶⡟⢷⡈⢿⡵⢌⡣⢇⡚⣴⡿⠀⢸⣧⣠⣿⣿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠋⣴⡟⣦⢻⣦⠀⠀⢠⣴⣾⡏⠀⠀⡇⠈⢻⣦⣤⢠⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣾⣿⣾⠛⣷⣷⣮⣷⣿⡇⠀⣿⣶⡟⣾⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠋⠉⠓⠿⠀⠉⠛⠛⡿⠁⢸⠃⠀⠀⡇⠀⠸⣮⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⢉⣿⠀⢼⡏⠙⣧⠀⣷⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣛⣛⠃⢀⡿⠀⠀⠀⣿⣀⠀⠉⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⢌⣸⡇⠀⢿⡀⢻⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠁⠀⠘⠿⣤⣤⣭⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠠⠠⠠⠒⠒⠦⢄⡀⠀⠀⠀⡀⡠⠆⠊⠁⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠄⠄⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠖⠉⠁⠀⠀⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢪⡗⠂⠋⠁⠉⠁⠁⠁⠉⠉⠉⠉⠉⠉⢣⠀⠀⠀⠀⣀⠤⠂⠒⠒⡆⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠁⠀⠀⠀⠀⠀⡇⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡿⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡇⠂⠀⠀⠀⠀⠀⡀⡄⠃⠁⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⢲⡄⠀⠀⣇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⡅⠑⠀⠀⠀⠀⡞⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡟⠀⠀⢸⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⠁⡁⠀⠀⠀⠀⠉⡄⣱⣭⣿⡂⠀⠀⠀⠀⣰⣿⣗⢶⠀⠀⠀⠁⠀⠈⡆⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣬⠏⡁⠐⠀⠀⠀⠀⠀⣅⣫⡦⣭⡇⠀⠀⠀⠀⢏⡿⡎⡸⠀⠀⠀⠀⠀⠀⢳⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⡈⠀⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠫⠔⠁⠀⠀⠀⠀⠀⠀⡎⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠩⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⡀⡀⡀⠀⠀⠀⠀⠠⠂⡆⠀⠀⠸⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⣏⠭⠂⠀⠀⠀⠀⡀⢔⡡⠓⠁⠁⠉⠉⠑⠮⡁⢂⠀⠀⢏⣻⡇⠀⠀⠀⡇⠀⢥⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣟⢗⢵⠂⠀⠀⣀⣤⡂⣁⡀⣀⣀⠀⢀⠀⡀⡀⡈⠑⢁⣆⠀⠫⡁⠀⠀⠀⡇⠀⢉⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣳⡦⢽⠀⠀⠀⠇⠄⠠⠀⠠⠀⠄⠡⠁⠅⠴⠄⡎⡃⠀⠈⠀⠀⠀⠡⢀⣠⠇⣀⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣪⣆⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠁⣄⣇⠇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡇⣈⣓⣜⣷⡛⡒⢒⠤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣠⢇⡶⠂⠡⠁⠂⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠹⠷⠲⠊⠏⠣⠍⠭⠽⡏⡁⠉⠙⠫⡈⡁⡩⠉⢉⡀⢔⠁⠅⢀⢒⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⢌⠂⡅⠀⠀⠀⠀⠈⣃⡚⠓⠃⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠊⡇⠀⠀⠀⠀⢔⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣯⣢⡄⠀⠀⠀⡟⡄⠀⠀⠀⢠⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠀⣀⡀⡽⣆⠀⠀⠀⢌⡧⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠰⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠘⣷⣶⣭⣝⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠘⡏⢿⣦⣍⡓⠦⣝⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⡈⣿⣿⣿⣷⣬⣙⠦⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢻⣿⣿⣿⣿⣿⣷⣌⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⢸⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢳⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢨⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣇⠸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⡞⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣆⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠏⣠⠎⣼⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡄⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⡴⢁⣾⣿⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⢻⣿⣿⣿⣿⣆⢳⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⣡⠎⣰⣿⣿⣿⣿⡿⠟⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⣿⡘⣆⠸⣿⣿⣿ ⣿⣿⣿⠏⡴⢡⣾⣿⣿⡋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠙⠿⣿⣿⣿⣧⢹⠀⢿⣿⣿ ⣿⣿⠏⡼⢡⣿⣿⣿⣿⣷⣦⣤⣶⠈⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠛⠉⠻⣷⣄⠀⠀⠀⢹⣿⣿⡄⣇⠸⣿⣿ ⣿⡏⢰⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣶⣶⣾⣿⣿⣧⢹⠀⣿⣿ ⣿⠀⡌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡆⣹⣿ ⣿⠄⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇⢹⣿ ⣿⠆⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠙⣿⣿⣿⣿⠃⡇⢼⣿ ⣿⠀⢳⢸⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⣤⣿⣿⣿⣿⢠⠃⣼⣿ ⣿⣇⠰⡄⢿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡖⠀⠀⠀⠉⢻⣿⡏⠈⠀⢿⣿ ⣿⡿⠁⠰⡜⣿⣿⡿⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢀⣸⡟⣰⠀⠀⠀⢿ ⡿⠀⠀⠀⠒⠊⠁⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠛⠃⠁⠜⠀⠀⣸ ⣧⡀⠀⠀⠀⠀⢠⠴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢀⠀⠀⠀⠀⢀⣠⣿ ⣿⣿⣿⣿⣿⣷⣆⡑⢌⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡔⢉⣴⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠢⣌⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠞⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡓⠒⠦⢭⣽⣿⣿⣿⣿⣿⠿⠿⠟⠋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣶⣶⣦⣥⡀⠀⠰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠋⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠂⢢⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⢁⠎⠀⠈⡀⣙⠠⠐⠄⠆⠡⢅⠅⠅⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⡖⠋⠉⠁⠁⡏⠈⠀⠁⠀⠀⠆⡀⠀⠀⠴⡏⡈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⢦⡀⠀⠀⣀⡎⠀⠈⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠈⠹⣦⡔⠁⠀⡄⠈⡂⢆⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⢁⠀⠀⠈⡇⠀⠀⠀⠁⠀⠀⡇⠀⡢⠀⠀⠀⠀⠀⠀⠀⣤⣅⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢡⠁⠀⠀⠀⠀⠂⠀⢅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⡉⡋⠉⠈⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⠉⠀⠁⠁⠁⠉⠁⠉⡟⠂⠂⠀⠀⠀⣀⣀⡀⠀⠀⠀⣂⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡀⠀⠀⢀⡞⠁⠉⢟⡇⠀⠀⠱⣇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠍⠁⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⡈⠃⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠆⠀⠀⠀⠀⢀⣀⣴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣡⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠦⢝⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠙⢛⡗⠷⠞⠮⢒⡒⡒⣗⠦⠥⠭⠻⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⡅⡉⠖⠒⠐⠒⢒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⡀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠘⠋⠉⡆⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠋⣀⠅⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢣⠙⠷⣤⡀⠀⠀⢹⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣷⣈⠻⣦⡀⣼⠀⠘⢦⡀⠀⠀⠀⠀⣀⡴⠋⠀⢳⡀⠀⠀⠀⠀⠀⣠ ⠀⢠⠾⠁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⢿⣿⣷⡌⢿⡏⠀⠀⠀⠈⠑⠒⠒⠋⠁⠀⠀⠀⠀⠙⠦⣀⣠⠴⠚⠁ ⢀⣿⠀⢠⠁⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⢠⢸⣿⣿⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣯⠀⣆⣀⣤⡏⢉⣐⣀⠉⠓⠀⠀⠀⠀⡇⠀⣠⠟⢁⣲⣄⠀⢺⣿⢃⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠛⣋⠯⠤⣺⣿⣿⠆⠀⠹⣦⠀⠀⡇⠀⠏⠀⢸⣿⣿⣂⡸⢩⡼⠁⢼⣿⣿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣄⠘⠒⠢⠤⠓⠉⠉⠉⣉⣀⡿⠀⠀⡇⠀⠄⠀⠀⡈⠉⢩⣋⡀⡟⠀⠘⠿⠟⠁⣔⣋⡈⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣢⠀⠀⠠⢬⣽⠟⠉⣉⣠⣦⣤⣤⣥⣤⣤⣤⣄⠘⣦⣴⡇⢸⠃⠀⡀⠀⠀⠀⠀⠁⠈⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣷⣦⠐⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣟⣿⠃⢺⡄⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠿⠿⠿⠿⢶⡶⠿⠶⠶⠶⠿⠟⠛⠛⠛⠛⠛⡛⠛⠛⣛⡿⠟⠻⣟⠓⠻⠿⠿⠿⠿⠿⠯⠴⠖⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢄⣀⠀⠀⠀⢀⢠⠰⡤⢚⣠⣶⠟⠉⠀⠀⠀⠈⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢻⡶⣀⣀⣠⡼⢾⣏⠁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⡤⠤⣄⣤⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣆⠤⠀⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠺⠒⠁⠀⡠⣉⠣⡀⠀⠀⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⠃⠉⠉⠊⠀⠈⠀⢱⠀⠀⢠⠀⠀⠀ ⠀⢀⡴⠛⠐⡀⠉⠐⢄⠘⠄⠀⠈⡄⠘⠀⠀⢇⣀⡀⢸⢄⠀⠁⠀⠀⠀ ⠀⠆⠫⢽⠁⠉⣭⠀⠈⡆⠀⢉⠝⠱⢄⠀⠰⠯⠒⡡⠃⠀⣅⠀⠀⠀⠀ ⠐⠀⠀⢀⣀⣀⠥⡄⠀⡇⠀⢨⠀⠀⠀⠈⢰⢻⣳⣤⡀⠀⡈⠀⠀⠀⠀ ⠀⠇⠀⠉⠒⠐⠚⠀⣰⠁⠀⠀⠑⠄⡀⣀⣿⡋⠙⠹⠕⠊⠀⠀⠀⠀⠀ ⠀⠀⠐⠂⠤⡤⠴⣶⣷⣄⣀⣀⣀⣀⣀⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⡸⡇⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠶⠾⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⠎⣺⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠐⠁⠁⠀⠀⠀⠀⠁⠑⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠅⡎⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣓⠂⡅⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⠅⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⢳⠂⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡖⡉⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⡘⢶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⣿⠏⠈⡅⢙⣧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀ ⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠐⡈⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡔⢊⠃⠀⠀⡂⠪⠈⠇⠀⠀⠀⠀⠠⠐⡀⠔⠉⠉⠀ ⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠋⠟⣄⡀⠀⠀⠀⠀⠀⠠⠀⢀⠷⠵⡏⠀⠀⠀⠡⠸⡄⢁⠀⠀⠀⢄⠑⠁⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠄⠁⠀⠀⠀⠀⠀⠘⠀⠀⠁⠂⡉⡳⣶⠀⠀⠀⠀⠀⢰⠋⢀⠂⠀⠀⠀⠘⣬⠇⡃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⠄⠀⠀⠀⠀⡁⠀⠀⠀⢈⢘⣓⠵⠅⠀⠀⠈⡆⠀⠈⠀⠀⠀⠀⠀⠀⢆⡇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠑⠤⠄⡅⠀⠀⠀⡊⠵⢝⠁⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠌⠀⠀⢀⠀⡧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡥⠄⡓⠡⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠁⠁⢀⠖⢩⠃⠀⡎⠄⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⡁⢁⠔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠁⠀⠇⠀⠀⠁⠀⠢⠀⠘⡀⢀⠀⠀ ⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⡀⡧⠐⡃⢴⠀⢧⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⠁⢀⠄⠁⠀⡀⠈⠄⣁⠨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠥⢕⠃⡕⠢⠏⡂⢃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢸⠀⡈⠀⠀⠀⢡⠀⢀⡀⢓⠦⠤ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⡴⠁⠀⢰⢡⣮⡕⠌⡀⠑⠀⠕⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠊⠀⠀⠀⠀⠀⠂⠃⢇⠨⠀⠀ ⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⢹⠞⠁⠀⠀⠀⡎⢸⠫⠁⠀⠐⡈⢀⠀⠐⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⣟⡂⠀⠀⠀⠀⠀⠀⠐⠀⠈⠎⢁⠀ ⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⢎⠎⠀⠀⠀⠀⠐⡀⠐⡀⠈⣋⠳⡀⠀⠀⢀⣀⠐⠡⣱⣃⠑⠄⡀⠀⠀⠀⠀⡠⠂⠐⠂⢏ ⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡏⠀⠀⠀⠀⠀⠀⠀⠁⠂⠕⢗⡵⠜⢛⡠⠐⢃⡮⡊⠤⠫⠳⢄⢈⠀⠐⠈⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⡠⣒⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠯⠂⠀⠀⠡⠈⠙⠦⠀⠀⠀⠀⠀⣇⠖⠉ ⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⢄⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣂⣀⠠⠄⠤⠤⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣰⠟⠉⠀⠀⠙⢷⡀⠀⠀⠀⣠⡶⠞⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⠀⠀⠀⠀⠀⠈⢷⠀⢠⡾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⣇⣀⡀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣠⡞⠛⠛⢷⡀⠀⢠⡾⠛⡙⠻⣆⠀⠀⠀⠉⠙⠳⣤⠀⠀ ⣸⠀⠀⠀⠀⠀⣿⡀⠸⠇⣸⠇⠀⢸⣇⠀⠛⢀⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⣿⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠙⠳⡛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠀⢶⣄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏⠀ ⠀⠙⠶⣤⣀⡀⠀⠀⠀⠀⠙⢛⠶⠚⠋⠀⠀⠀⠀⢀⣤⣴⣶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⠉⠙⠛⠓⠒⢺⡿⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡈⢳⣤⠞⣻⠀ ⠀⠀⠀⠀⠀⠀⣾⠛⢦⡿⢠⡿⣇⠀⠀⠀⠀⠀⠀⣸⠇⢈⡿⠀⢀⠿⠷⣄ ⠀⠀⠀⠀⠀⠀⣽⠟⣧⢀⠿⣤⡙⣧⣀⠀⠀⢀⣴⠏⠀⠻⡶⣿⢸⡟⠶⠛ ⠀⠀⠀⠀⠀⠀⠷⠾⣯⣸⠛⠾⠃⡏⠹⡟⠻⡟⢹⡇⠀⠀⠀⠘⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣰⡇⠀⡇⠀⡇⠈⣧⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣟⠉⠉⠉⠀⣰⡇⠠⣇⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠊⠙⠛⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠷⠶⣦⣤⣤⣴⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠟⠀⢀⣀⠀⠀⠀⠀⣼⣿⠟⠉⢻⣿⡆⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠋⠀⠀⢻⣿⡆⠀⠀⠀⣿⠇⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⣠⡿⠁⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠰⢀⣾⣿⠁⠀⠀⠀⢿⣄⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀ ⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦ ⢼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽ ⠀⠉⠛⠻⠶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠶⠟⠛⠉⠀ ⠀⠀⠀⣶⣶⡀⠈⠉⠛⠻⠶⢶⣦⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣤⣶⣶⠶⠟⠛⠉⠉⠀⠀⢰⣿⣷⠀⠀ ⠀⠀⠀⢿⣿⣷⣀⣀⣤⣴⣾⣿⠿⠟⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠈⠉⠛⠿⢿⣿⣶⣦⣤⣀⣀⣸⣿⣿⠀⠀ ⠀⠀⠀⠘⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠇⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⣾⣿⣿⣿⣿⣷⣄⣿⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣛⣿⣄⣿⣿⣿⣠⣿⣽⣿⣿⣿⣿⣿ ⠻⢿⣿⣿⣿⣿⣿⠟⣿⠉⠁⢸⣿⣿⣿⣷⣙⠿⢿⣿⠿⢟⣻⣿⣿⣿⣿⣿⣿ ⠀⠈⠛⠛⠛⠋⠁⠀⣿⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠻⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡠⢤⣤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡉⠋⠉⠉⠉⠉⠉⠁⣉⣭⡍⠁⠀⠀⠨⡆⠀⣠⠋⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡎⠀⠀⠀⠀⠀⡠⠞⡥⠊⠈⡤⠀⠀⠀⠀⢰⠇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠓⠒⡢⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡅⠀⠀⠀⠞⢁⠤⠋⠀⠀⠀⠘⠧⢤⡰⠝⠉⠀⠀⠀⠙⡧⠀⠀⠀⠀⠀⠀⠀⣀⢠⠞⠁⠀⠀⢠⠏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⡀⠨⡁⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡤⣄⡀⠀⠀⠀⠀⠘⡇⢀⢜⠻⠋⡵⠇⠀⠀⠀⠀⡌⠁⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢨⠏⠄⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⡏⠀⠀⢱⠀⠀⠀⠀⡀⢿⢫⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢱⡄⢀⠀⢁⡂⠀⠀⠙⠒⠁⣶⠆⠙⠒⠚⠁⠀⠀⠀⠀⡤⢻⡇⢈⠤⠖⠶⡀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠏⠀⠈⣽⠦⠤⢄⣀⠀⠀⢠⣀⣸⣀⣠⠀⠀⠀⠀⣤⡶⠾⢿⠟⠋⠉⠉⠉⠉⠑⠵⠀⡢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⡧⠀⠘⡇⠀⠀⠀⠀⠉⠉⠁⢲⠲⢆⠲⡴⠙⢿⠉⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠠⠃⡨⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸⠫⢅⠉⠉⠁⢳⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠣⡀⠀⠀⠀⢀⡀⠜⣦⣘⢦⠤⠤⢼⡜⠀⠀⠀⠀⠀⣇⠠⠀⣁⡠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣤⠀⠀⡴⠛⠛⠛⠋⠑⠖⠀⠀⠀⠈⠉⠉⠉⠈⠉⠒⠦⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⡟⡇⠀⠀⠀⡄⠊⢁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⡀⠀⠀⢹⠍⠉⠉⠉⠉⠑⠒⠒⠔⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢙⣢⣤⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣑⡄⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠉⠉⠉⠓⠒⠲⠦⠤⡤⡤⣤⣤⠶⠛⠋⠉⠉⠉⠉⠉⠁⠁⠁⠉⠒⡶⠃⠀⠉⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡅⠉⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡁⠀⠀⠀⠀⠁⠁⠁⠒⠒⠒⠂⠒⠀⠄⠠⡠⠠⠤⠤⠠⠄⠤⠤⠠⠤⠤⠖⠒⠒⠶⣳⡊⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⣀⣀⣀⢀⣀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠎⢩⣍⢇⠀⠀⠀⠀⠀⠉⠉⠁⠀⡆⢰⠍⠆⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣣⠆⡆⡜⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠐⠈⡆⡇⠠⠠⠤⠠⠤⠔⠒⠋⡆⠀⡭⣷⡀⡀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⣷⠟⠋⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠤⠀⠐⠈⡅⡏⠀⢥⡇⠀⠀⠀⣀⣀⡤⠤⠆⢹⠀⠧⢫⠀⠀⠤⠈⠉⠂⠒⠤⠤⢈⢈⠁⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠉⠉⠁⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣉⡤⠭⠭⠉⠙⠓⠋⠉⠉⡻⠀⢩⠏⠉⠉⡏⠁ ⠀⠀⠀⠀⠁⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⣀⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡜⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠤⠤⠤⣀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠉⠀⢀⣀⠀⠈⢧⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⡴⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠉⠀⠜⠋⠃⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⣇⡤⣄⡀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠁⢀⢠⡆⠀⠠⠴⠋⠀⠀⠀⢀⡞⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⣀⣀⣀⣀⣀⣠⠾⠋⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠈⠁⠀⠀⠀⠀⠙⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠒⠈⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣿⣿⡿⠋⡉⢉⡉⠉⢻⡿⣿⣿⡿⠿⣿⡿⣿⡿⣟⠻⢛⣻⠿⣿⣿⣿⣿⡳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⠁⢸⠀⠀⠘⡆⠀⣷⠓⠒⠚⠛⠻⠽⣷⡉⠀⠀⠠⡀⠙⡽⣹⣻⣿⣿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣞⣿⡿⣿⢝⣆⠘⡄⠀⣀⠼⠀⠛⢠⣴⣦⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⢸⣿⠙⡯⣿⣿⡼⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣽⠃⢸⣿⡶⣶⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣄⡀⠈⢧⠀⢀⣮⣿⡄⠈⠿⣿⣿⣞⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣟⡎⠁⠀⣎⣿⠀⠙⠻⣿⠛⠛⠛⣻⣷⡶⣄⠀⣨⣿⣿⢶⣶⣤⣷⣿⠃⠂⡸⠀⠀⠹⣿⣿⣎⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⢏⡞⠀⠀⢰⢻⡏⠀⠀⢠⡇⠀⠀⣴⡟⠀⢡⣻⢀⢧⠊⠻⣧⠀⠀⠀⣿⣿⢪⠀⠀⠀⠀⠹⣿⣿⣮⢆⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⢯⠏⠀⠀⠀⣼⣿⣧⠀⠀⠀⢇⠀⠀⣿⣧⣀⡜⣿⢸⣸⠀⢀⣿⠀⠀⠀⣿⣿⣯⣻⣄⠀⠀⠀⠘⣽⣿⣯⢣⠀⠀⠀ ⠀⠀⣴⣿⣿⢯⠃⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠈⠢⣀⣈⣻⣟⡡⣃⠈⢿⣶⣿⠇⠀⢀⡴⣿⢿⣿⣷⡹⣀⠀⠀⠀⠘⣿⣿⣷⣣⠀⠀ ⢠⡼⣿⣿⣻⠃⠀⠀⠀⣴⣻⢟⣿⣷⢧⠀⠀⠀⠀⠀⠀⢁⠀⠈⠻⡟⠁⠉⠑⠒⠉⠁⠀⢳⣿⢻⣿⣿⡵⡄⠀⠀⠀⠈⢿⣿⣷⣱⡀ ⣽⣿⣿⣽⠇⠀⠀⠀⡴⣽⢯⣿⣷⢟⣻⠷⣄⠀⠀⠀⠀⢸⣑⢲⠼⣅⣀⡀⠀⠀⠀⠀⢀⣮⠿⠷⢿⣿⢿⡕⡄⠀⠀⠀⠈⢿⣿⣷⣵ ⣿⣿⣧⢿⠀⠀⠀⠐⣟⣿⣿⣛⠵⠋⠁⠀⢀⣉⣒⣦⣤⣀⡻⣍⣙⣒⠽⠃⠀⢀⣀⣴⠞⠛⡩⠔⣠⠬⣿⣟⠞⠀⠀⠀⢠⣿⣼⣿⢿ ⠈⢿⣿⣯⡳⠀⠀⠀⣈⣿⡿⠁⠀⠀⠀⠔⠉⣀⠤⠤⣈⠙⢷⣄⠀⠉⠉⠉⠉⢉⡾⠋⣰⠋⠐⠁⠀⠀⢣⠿⡣⡀⠀⠀⣼⣿⣿⢧⠃ ⠀⠘⣻⣿⣷⣽⢠⣾⣯⠏⠀⠀⠀⠀⡄⠀⣔⠁⣉⠑⠀⢹⡄⢙⣷⣀⣀⣀⣠⣿⣵⠶⠛⠒⠒⠂⠐⠊⠁⠀⠱⣷⣠⣿⣿⣿⡳⠁⠀ ⠀⠀⠈⢻⣿⣷⣽⣱⠇⠀⠀⠀⠀⡜⠀⠀⠙⠠⠤⠤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢽⣿⣿⡳⠁⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⡝⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣦⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⡝⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠵⠤⣄⠀⠀⠀⠀⠀⠀⢀⡠⠖⣿⣿⣟⡝⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⣼⣿⣏⡝⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⡏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⡄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⢿⣷⡀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠋⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠛⠋⠀⠀⠀⠠⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠘⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⡿⠿⠿⠛⠛⣿⡟⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠈⠛⠿⣿⣿⣿⣾⣶⣿⣾⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠘⣿⣷⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⡿⠋⠉⠛⢿⣿⡆⠀⠀⠀⠐⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⡀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣷⣦⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡿⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣇⠀⠀⢀⣀⣀⣀⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣾⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⢀⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⠿⢿⣿⣷⡀⠙⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣿⣇⣼⣷⠀⠀⠀⣸⣿⡄⠀⠀⢠⣶⡄⠀⢠⣿⡿⠋⠁⠀⠀⠀⢸⣿⡇⠀⠀⠈⠙⠻⢿⣿⣷⣶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⡏⢿⣿⣄⡆⣰⣿⣿⣷⣄⠀⣾⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⠈⠿⣿⣿⣿⠏⠀⠻⣿⣿⡿⠋⠙⢻⣿⣀⣀⣀⣤⣤⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣽⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣳⣿⣿⣧⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣦⣀⣘⣻⣗⣀⣀⡀⠈⠉⠀⠀⠀⢸⣿⡿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⣿⠟⠛⠛⠛⠛⠻⠿⠿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣠⣾⣿⣿⣤⣤⣤⣤⣤⣤⣦⠀⠀⠀⠉⠉⠛⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠈⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⣶⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠿⠿⠿⠟⠛⠛⠋⣽⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⣀⠀⠀⠀⠀⢀⣀⣠⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣥⡄⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⣧⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣹⣿⣏⠁⠀⠀⠀⠀⣿⣿⡄⠀⠀⠘⣿⣿⣦⣄⡀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄⠀⠀⠀⢠⢻⣿⣷⡀⠀⠀⠘⣿⣿⢿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⣸⣿⣿⣿⣦⡀⠀⣸⣿⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⣿⣯⠙⠻⣿⣿⣿⡿⠋⠈⠛⢿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⢹⣿⣀⣠⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⢹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣶⣿⡿⠋⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢰⠁⠈⠈⢻⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢀⣀⣤⣴⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⢿⣄⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠉⠁⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣯⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⣶⣶⣶⣾⣿⣿⡟⠛⢻⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠋⠙⠻⠿⣿⣿⣶⣶⣤⣤⣴⣤⣴⣦⣶⣾⣿⣿⠿⠟⠋⠉⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⠟⠛⢻⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣡⣤⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡴⠶⠞⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⢀⣀⣤⣾⣿⣧⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠀⢸⣿⣿⣛⠋⠙⢿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡈⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣤⣾⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠋⠻⠿⠿⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣆⣀⣠⣴⣾⣿⠿⠿⠿⠿⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣦⣄⣀⣐⡀⣀⡀⣀⣀⣀⣀⣤⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣦⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⣀⣀⣀⣀⣀⡀⡀⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣀⣄⣀⣄⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⠂⢀⠠⠀⡀⠠⠀⠄⠠⠀⠄⡀⠆⢠⠐⠠⡐⠄⠂⡔⢠⠂⢆⠒⡐⢂⠲⣀⠣⢆⠱⡌⠦⡑⢎⠲⡑⣎⡱⢣⡝⣬⠳⣙⣎⡳⢭⡳⣝ ⠀⡈⠀⠠⠀⠄⡀⠁⡈⠄⢁⠂⡐⠈⠄⠨⠐⠠⠌⠡⠐⢂⠡⠊⠔⡡⢊⠔⡨⠑⡌⠱⣈⠖⡩⢌⢣⠓⡴⢱⢃⡞⡔⣫⠕⣎⢳⡭⢳⣎ ⠀⠄⠁⠐⡀⠂⡀⠂⠠⠐⢀⠂⠄⠡⢈⠂⡁⠢⢁⠡⠉⢄⠢⢉⢂⠱⢈⠆⡡⢃⠜⡡⢒⡘⠴⡉⢦⡙⠴⣉⢎⠼⣘⢥⡛⣬⢓⡞⡳⣎ ⠀⡈⠀⠐⡀⠄⠐⠀⡁⠐⢀⠐⠈⡐⠠⠐⠠⢁⠂⢂⠉⠄⠢⠌⠄⡊⠔⡨⢐⠡⡊⠔⣡⠘⠴⡑⢢⠜⡱⢌⢎⠲⣩⠲⣍⠶⣩⢞⡱⣭ ⠀⠐⠀⠠⠀⠀⠌⠀⠄⠐⠠⠀⠂⠄⠡⢈⠐⠠⡁⢂⠉⠤⢁⠌⡠⢁⠆⡡⠌⢢⠑⡌⠤⡉⠦⡉⢦⢉⠖⡩⢌⢧⢡⡓⡼⣸⡑⢮⡕⢧ ⠀⢁⠀⠀⠄⠂⠈⠀⡈⠀⠄⡁⠄⠈⠄⠂⡈⠄⡐⠠⢁⠂⠤⠈⠄⢃⠰⢀⢃⠢⢡⠘⠤⡑⢢⠑⣂⢃⠎⡱⢊⢆⡣⢜⠲⣡⢞⡱⢎⡳ ⠀⠂⠀⠈⠀⠀⠂⠁⠀⠁⢀⠠⠀⡁⢀⠂⠠⠐⠠⣔⠤⣈⠄⣅⠊⠧⠰⠈⢤⢜⡀⠎⡰⢁⠣⡘⢤⠩⡬⢡⠃⣎⠴⣉⠮⣑⢮⡱⢫⠵ ⠀⠄⠀⠀⠂⠀⠁⠀⠈⠀⠂⠀⠄⠐⠀⡀⢁⣰⣽⣿⣿⣾⣿⡏⠐⢎⢷⣛⢮⣿⣆⠆⡑⠌⢢⢑⠂⢠⣿⣳⢿⣿⢃⢇⡚⢥⠲⡍⢧⡛ ⠀⡀⠀⠁⠀⠈⠄⠈⢀⠈⠀⠌⠀⠂⠀⠄⢜⣾⣿⡿⣟⣿⣿⡇⠌⡈⢎⢟⡾⣜⣿⣖⠈⢆⢡⠆⢠⣿⣳⢯⡟⢦⡉⢦⡙⡌⢧⡙⢦⡹ ⠀⠀⠀⠐⠀⠀⠂⠀⠀⡀⠐⠀⠀⠂⢁⣪⣿⣿⡿⣿⣿⣿⣿⡇⠐⠠⠘⢌⢷⡝⡾⣽⣎⢄⡞⢠⣿⣳⢿⣿⠜⢤⠓⣢⢑⡚⢴⡙⢦⡓ ⠀⠁⠀⠄⠀⠠⠀⠠⠁⠀⠀⠀⠐⠠⣳⣿⣿⣻⣿⣿⣿⣾⣿⡇⠁⠆⡁⢊⢌⢿⣱⢻⣽⣼⢣⣿⣳⢯⣟⠢⣉⠦⡑⢆⠣⡜⡢⢝⡢⢝ ⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡐⣽⣿⡿⣽⣿⡟⣿⣿⣽⣿⡇⠈⠄⡐⠠⠈⢎⢯⡗⡾⣯⡟⣧⢿⡟⢠⠃⡔⢢⡑⡊⡕⢬⡑⢎⡜⣡ ⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠐⢔⣾⣿⢿⣽⣿⠟⢸⣿⣿⡿⣿⡇⠈⠐⢀⠡⠈⠌⠎⢯⣳⢧⢿⣹⡟⠋⡄⠣⢌⡡⢂⡕⠌⣆⢩⠒⡜⠴ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢬⣿⡿⣽⣻⣿⠏⠀⢸⣿⣿⢿⣿⡇⠀⠌⠀⡐⠀⠂⡼⢈⣷⢫⣟⣾⡄⡃⠌⢡⠂⡔⢡⠘⣌⠰⢊⡱⡘⢥ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⢯⣿⣽⣿⠃⠀⠀⢸⣿⣿⡿⣿⡇⠀⠀⠁⠀⠁⡼⢁⣾⡱⣏⢾⡹⣿⡄⡘⢠⠘⢄⠃⡜⢠⠉⡆⢱⡘⢆ ⠀⠀⠀⠀⠀⠀⠀⠠⣽⢿⣽⣻⣾⣿⣷⣶⣶⣶⡞⣿⣷⣿⣿⣷⣶⠈⠀⠈⣰⢁⡾⢥⡻⣼⢧⡻⡽⣿⣄⠢⠘⢠⠊⢄⠣⡘⡘⠤⡘⢆ ⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⣞⡷⣞⡷⣾⣳⢿⣞⣷⣿⣻⣾⢿⣿⣿⠀⠀⣬⢃⢮⡝⢮⣳⠛⡞⣽⢳⡽⣿⡄⡁⠆⡘⢄⠣⠰⡑⡌⡱⢊ ⠀⠀⠀⠀⠀⠀⠀⠸⠿⠼⠽⠾⠽⠿⠷⠯⠿⠽⢷⣿⣽⣯⣿⡿⠿⠀⣰⣏⢮⡓⣞⣹⠃⠠⠘⡜⣿⢼⣹⢿⡔⢨⡐⢌⢒⡡⢜⡰⢡⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢿⣿⡇⢀⢸⣟⢎⢧⡹⣼⠋⢄⢂⠡⡙⡜⡷⣭⣻⢿⡤⡑⢎⢦⡱⢎⡴⣋⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢦⡐⢦⡱⠎⣿⣿⣿⣿⣷⣿⡟⢮⡞⣦⣽⣷⣿⣾⣾⣷⣿⣾⡹⣶⢯⡿⣿⣿⣿⣾⣽⣿⣾⣽⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠠⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⢉⠉⠉⠌⠡⢉⠩⠉⢍⠩⡙⠍⢏⡹⠎⡵⢊⡗ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⠀⢀⠀⠄⠐⠀⠀⠂⢈⠠⠐⠀⡈⠀⠄⠂⠠⢁⠈⡐⢀⠂⡉⠄⠃⡌⠸⡀⠦⡑⡌⢣⠜ ⠀⡁⠀⠄⠐⠀⠐⠀⠐⠀⠂⠀⠄⠀⡐⠠⠀⠂⠄⠠⠐⢀⠂⠡⠐⢀⠂⠄⠡⢀⡁⢂⠁⡂⠤⢈⠔⢂⠡⢒⠨⠡⢌⠱⡈⢆⠱⣈⠇⢎ ⠐⠠⠀⠂⠄⡈⠠⠈⠄⡐⠠⠁⠄⠂⠄⠠⢁⠂⠔⠠⢁⠂⠌⡐⠈⢄⠂⢌⠰⢠⠐⠤⡈⠔⡨⠐⣌⢢⣑⣌⣒⣡⢎⣢⣑⣎⣱⣌⣚⡌ ⢂⣁⠂⡁⠂⠄⡡⠌⡐⢀⠂⠡⢈⡐⢈⢁⠂⠌⠄⢃⠰⢈⠰⡀⢃⠢⢌⠂⡄⢃⠌⡂⢅⢢⢁⢣⢘⡓⡛⣒⠛⡚⢛⡛⡹⢛⡛⣚⢻⡘

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

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⠀⠀⠀⠀⢀⣀⡤⠤⠒⠒⠒⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⣉⣉⣉⣉⣉⠉⠓⢤⡀⠀⠀⠀⠀ ⠀⢀⠔⢊⡭⠥⢖⣚⡭⠭⠉⠉⠉⠻⡝⣆⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⣠⣾⡿⠛⠛⠛⠛⠛⠛⠻⢿⣶⣉⠢⡀⠀⠀ ⠀⡏⢰⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠘⡆⠀ ⠀⡇⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⢳⠀ ⠀⡇⢸⢸⣀⣀⣤⠤⠴⣖⣒⡶⠿⠭⠭⠭⢭⢳⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⠀ ⠀⢱⣾⠯⠼⠚⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⡜⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⢸⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠁⡞⠀ ⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢀⡎⠉⠁⠒⠤⢀⠀⠀⠀⠀⠀⠈⠇⠘⣿⣷⣤⣄⣤⣤⣴⣾⣿⣿⣿⣿⣿⡏⣰⠃⠀ ⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠤⣴⣎⣵⠂⡇⠀⠀⡞⠀⠀⠀⠀⢀⡠⠛⠀⠀⠀⠀⠀⢸⠀⡟⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⡠⠃⠀⠀ ⠀⠀⢺⡹⠤⣄⡤⡴⣲⡮⠽⠫⠖⠚⠉⠁⢸⡙⡆⢁⠀⡸⠀⢀⡀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⠀⠀ ⠐⢲⠀⠉⣻⣏⠉⠉⢁⠀⠀⠀⠀⠀⣤⣤⣤⣭⡗⢸⠀⠑⡞⠛⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠃⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⡄⠀⠀⠀⠀ ⠀⠀⢧⠀⢸⣸⠀⠀⢀⠀⠀⠀⠀⣾⣿⠟⠀⢻⢿⠘⡆⠀⠉⠲⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢠⠁⠀⠀⠀⠀ ⠀⠀⠘⡀⠸⣾⠁⠀⠀⠄⠀⠀⠸⠿⢇⣀⣀⢸⣸⠀⠇⠀⠀⠀⠀⠑⢄⡼⠀⠀⠀⠀⠀⠀⠀⡇⢠⣼⣠⣀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠠⢟⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡎⣏⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠛⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢼⢽⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢸⡏⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠐⣿⣿⡶⠄⠀⠀⠀⠀⡼⡰⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠈⣿⠀⠀⠈⠀⣠⣄⠀⠀⠙⠉⠀⢰⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⣀⣀⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢇⠀⢻⡇⠀⠀⠰⣿⣿⣷⣤⣐⠄⡀⢸⡼⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣷⡀⠀⢀⣸⣿⡟⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢼⢳⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⠘⠒⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⢰⠃⣿⡻⣿⣦⣾⣿⠛⠀⠀⠀⣷⠃⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⢸⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⡇⣇⣰⣿⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⠨⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠘⣾⠁⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⢹⢧⢹⣿⣿⣿⣟⡺⡄⠀⠀⠀⠀⠀⠀⢸⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠀⠏⡆⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⢺⣀⠁⢀⣘⣿⡇⡇⠀⠀⣀⠤⠤⠤⣸⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣰⣷⣀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⡿⠿⠿⠿⠛⣡⠃⠀⢰⢁⣾⣶⣶⣶⣾⢇⠇⠀⠀⠀⠀⠀⠀⢰⣶⣯⡀⢇⣀⣀⣀⠀⠀ ⠀⠴⢒⣒⣒⠊⣀⣾⣿⠿⠋⠘⡄⠀⠀⠀⠀⠄⠀⠀⢹⢧⠀⡖⠐⠚⠁⠀⠀⢸⠠⣿⣿⣿⣿⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⢉⢿⣿⣧⣶⣶⣌⠉⡆ ⠀⠀⣿⣿⣿⣿⣿⠏⣿⡀⠀⠀⠁⠀⠀⠀⢀⡤⠦⢤⢸⢸⠀⡇⠀⠀⠀⠀⠀⠘⠢⠤⠭⠭⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠨⣿⣿⣿⣿⠁⡇ ⢀⡨⢿⣿⣿⡿⠀⠀⢳⣇⠀⣰⣚⡳⣄⠀⡞⡴⠉⠦⡙⠻⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠹⠿⠿⠟⡡⠃ ⠀⠑⠤⠭⠭⠥⠜⣆⢻⡾⠞⣱⠃⠙⢺⡑⡷⠀⠀⠀⣸⣀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⡉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡄⠱⣌⠢⡀⠀⠀⠘⡇⠀⢀⡴⣱⢃⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⡄⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠳⣝⣶⣆⣤⣥⣤⣾⣰⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⢧⣀⣀⠀⠀⠀⠀⠀⣀⣿⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⢰⣿⢿⣿⣿⣿⢿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⠉⠓⣾⠉⠉⠉⢉⣭⡁⠚⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⣿⠀⠹⠟⠁⢸⣿⣄⣉⣙⡒⢲⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠬⠃⠀⣿⠀⠀⠀⠀⣿⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣻⡏⠁⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⣿⡿⣠⣶⣶⣶⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⠐⠒⠒⠒⠒⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠣⠬⠭⠭⠭⡀⠿⠿⠿⡿⢋⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠭⠭⠭⠭⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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