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