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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⠂⠀⠀⠀⠀⠀⠀⠀⢍⠁⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⣤⡤⢤⣤⣤⠄⣀⠀⠀⠀⠱⣄⡀⠀⢀⢠⣤⣇⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣯⠯⡋⣽⣿⣂⡤⢕⡫⣿⣴⣦⡀⣈⠾⠤⢊⡿⣿⣯⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡼⠿⠭⢵⣭⣚⣿⠟⣩⣰⣟⢞⣽⣷⡟⢀⣜⢆⠀⠀⢱⢏⠉⢸⢸⠀⠀⠀⠀ ⠀⣀⣀⡀⢤⣴⠶⡶⠶⡶⢾⠿⣻⠟⡿⢻⠭⡉⠍⣀⠁⠀⠀⠈⠉⠉⠙⠚⠛⠭⠾⡯⣿⣽⠫⡇⠈⢻⠛⠀⠰⣧⣌⡆⠘⠘⠀⠀⠀⠀ ⣟⢟⠵⡫⢛⠱⣊⠔⡡⢒⢡⠎⠡⡪⢚⠕⡫⣻⠎⠕⠳⠦⠖⠠⠄⡀⠀⠀⠀⠀⠀⠀⠉⠛⡭⣇⠙⢂⠧⢲⢠⡉⠁⡇⠀⠀⠀⠀⠀⠀ ⢕⡥⡪⠐⡡⢊⠕⠉⢐⠑⠅⡐⡩⠐⢕⠅⣺⠛⡆⡩⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠱⠈⠓⢮⡤⡀⠁⡟⢶⠃⠀⠀⠀⠀⠀⠀ ⢿⣊⠔⡡⢚⠁⡊⢂⠔⡡⢊⡐⢃⠐⡰⣴⠃⡸⠁⣀⣀⡀⠀⠀⠀⠠⢀⣀⡀⠘⣦⢀⣄⡀⠀⢇⠀⠀⠘⢍⠛⣟⠁⠀⠀⠀⠀⠀⠀⠀ ⠙⠷⢮⡂⠕⡠⠎⡡⢊⠔⠈⠔⠡⡊⢠⠏⢠⠃⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣿⠀⠀⠑⣦⣸⠀⠀⠀⠀⠑⡌⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⢭⡀⠡⣊⢕⠁⡊⡨⡾⠀⣾⡶⠟⢛⣷⡄⠀⠀⠀⠀⣰⣷⣿⡛⢻⡇⠀⠀⡇⠈⠓⢤⠀⠀⠀⠈⢦⠘⢧⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢕⣠⣢⣪⠇⢸⡟⠀⠀⣿⣯⣿⠀⠀⠀⠀⢻⢯⣟⠇⠈⡇⠀⠀⣧⠀⠀⢣⠙⡦⣄⡀⠀⠙⠢⡀⠉⠓⠶⢄ ⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢹⠀⣾⡇⠀⠀⠙⠟⠋⠀⠀⠀⠀⠈⠓⠋⠀⠀⣽⠀⠀⢻⡆⠀⢰⠄⠀⠃⢹⣷⡶⢴⢪⣲⣄⠀⠀ ⠀⠀⠀⢠⣪⠖⠙⠢⡀⠀⠀⠀⠀⣿⠀⢹⠑⠀⠠⠀⠈⣀⣀⡀⠀⠀⠀⠒⠀⠀⠐⣾⠀⠀⠀⡇⠀⢸⠆⠐⡘⠈⡏⠮⡳⢟⢮⡻⢛⠶ ⠀⠀⠀⠀⠙⠢⡀⠀⠈⠢⡀⠀⠀⡿⠀⢹⣖⠉⠀⠀⢺⣶⣶⣶⣷⡄⠀⠀⠀⠄⠂⣿⠀⠀⢨⡧⠀⢸⡆⠀⡇⡄⣿⠼⠮⠥⠟⠺⠦⠛ ⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⡈⠒⢤⡇⠀⠀⠙⢤⡀⠀⠈⠻⢿⣿⠻⠃⠀⠀⠀⠀⠀⣻⠀⠀⢸⡜⠀⢨⡇⠀⢃⣇⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⣂⠀⣸⡇⢸⠀⠀⠀⢸⢳⡤⢤⣀⣀⣀⣀⣄⠄⠀⢒⡯⢿⡀⠀⠘⣿⠀⠀⣇⠀⠘⢹⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⠀⠘⠀⠀⢘⣘⣼⡣⣦⣿⡾⡟⠉⣀⠠⠖⡉⠜⢒⡣⢀⠀⢻⣆⠀⣿⠀⠀⣿⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠼⢟⠀⠀⠒⠉⢅⣾⢋⢰⣽⢏⢀⡤⡏⠀⣴⣪⡴⣬⣥⠤⠀⠁⢦⢿⡀⣿⠀⠈⡼⠀⣿⡄⠀⠀⠀⠀⠀ ⡀⠤⠄⠀⠒⠙⠺⣙⣤⡀⠀⠀⠐⡈⠂⠄⠀⠀⢭⠛⣦⠃⠀⢿⡄⠹⡮⣥⡦⠀⠀⠀⠀⠀⠀⠈⡌⠇⡿⢰⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⠀⠀⠉⣏⣋⢆⠀⠀⠱⠀⠄⠀⠀⢱⣠⡿⠄⢀⡜⠋⠛⢹⣿⣷⠆⠀⠀⠀⠀⠀⠀⡇⢰⣧⠘⡀⣿⠀⢸⡇⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⢹⣹⠈⠃⡀⠀⡟⢀⡀⠀⠈⡄⡜⢉⡥⠵⠐⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⠀⢷⣿⠀⠈⢿⡀⠀⠀⠀⠀ ⠏⡷⠀⠀⠀⠀⠀⠀⠘⣬⡇⠀⠈⢲⠁⠘⠥⣄⡈⢡⠔⠺⢕⣿⠶⣞⢿⣟⠿⠀⠀⠀⠀⠀⠀⢀⠃⢠⣿⡀⠈⣿⡄⠀⠘⣷⡀⠀⠀⠀ ⢛⢾⠂⠀⠀⠀⠀⠀⠀⡗⡇⠀⢀⠏⠀⠰⣎⣥⡤⠿⡞⢉⣿⡟⡆⡎⢞⡯⣟⠀⠀⠀⠀⡰⠃⠈⡆⢸⣼⢡⠀⠸⣿⡀⠀⠘⣷⠀⠀⠀ ⡡⡑⢶⠄⠀⠀⠀⠀⠀⡧⣦⠔⡏⠀⠀⠀⠀⡐⠀⠀⢿⠛⠉⣧⢘⣜⡪⢱⠏⠁⠀⠀⡰⢡⠎⠀⡇⠈⣿⣜⢇⠀⣿⡜⡄⠀⣿⠀⠀⠀ ⢖⠤⣥⠀⠀⠀⠀⢀⠠⠷⡷⡺⠁⠀⠀⠀⠰⠁⠀⠀⠘⣶⢞⢻⡿⣒⠙⢺⠋⠀⠀⡼⠃⠁⠀⢀⠇⠀⠏⣟⡿⠀⡇⢻⠱⢠⠇⠀⠀⠀

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⣿⢿⡹⠸⣿⡇⣟⡻⡝⢯⡛⡽⢭⢳⡙⢶⡩⠳⠹⠌⢣⠙⠌⣁⠊⠔⡁⢂⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⣿⣿⡄⢻⣿⣿⣿⣷⣀⠁⣹⣿⣷⣶⣭⣻⢷⣦⣀⠀⢷⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠐⠉⠎⠱⣋⢞⡹⢎⠯⡽⢭⡻⣝⣻⢞⣻⣽⣛⣿⡟⣸⣿⣿⣿⣿⣿⣿ ⠓⡎⠱⠀⣿⣧⠈⠳⠙⡨⠑⡉⠂⡅⢈⠄⡐⢁⠂⠌⠠⢈⠐⠠⢈⠐⡀⠂⠈⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡜⠻⡇⠀⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣷⣌⣧⣳⡀⢸⣿⡄⠀⠀⠀⠀⠀⢀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠱⢣⠳⣍⠮⡝⡶⣙⢮⣳⠃⣟⢿⡻⣟⣿⣿⣿ ⠀⠀⠄⠀⢸⣿⠀⠡⢁⠐⠡⠐⠁⠐⠀⠂⠀⠀⠈⣀⣁⠀⣠⣥⣤⠀⠠⠁⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⣶⣤⣤⣄⣀⢹⣿⣿⣿⣿⣌⠦⣗⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣷⡀⠀⠀⣀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠞⠱⣎⠵⢐⠯⡞⣵⣛⢮⢷⡻ ⠀⠀⠀⠀⠈⡷⡃⠀⠂⠌⡀⣤⣬⣴⡆⢸⣿⠍⠀⢩⣿⠀⢿⣟⡿⠀⠀⠂⠀⢉⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢈⠝⠻⢿⣿⣿⡆⢿⣿⣿⣿⣭⣀⠛⠡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣨⣾⣿⣿⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠎⠝⢦⡝⣎⢧⣛ ⠀⠀⠀⠀⠀⢳⠵⠀⢁⠂⠄⢸⣿⡽⣦⠀⣿⠤⠦⠞⠛⠃⠘⠋⠉⠁⠀⠀⠀⠈⠄⠀⠀⠀⢀⣀⣀⣄⣀⡈⠻⠿⠿⢿⣿⣿⣿⣿⣮⣿⣿⣿⣷⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠒⠡ ⠀⠀⠀⠀⠀⠨⣋⡄⠀⠠⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⠻⠿⢿⣿⣿⣦⠹⡝⣖⢶⣲⣖⣂⣉⣉⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠥⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⣍⢛⠿⣷⣄⡈⠑⠦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡉⡻⢿⣿⣿⣿⣿⣿⣿⠇⢃⣀⣤⣤⣤⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠨⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠳⣷⣬⣝⣿⡦⠐⢀⣁⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⣮⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⠟⢋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣵⣿⣦⣬⣝⡛⠿⢿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣮⡻⣿⣿⣿⡻⢟⣛⣿⣿⡷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⢋⣠⣾⡟⣿⡿⡃⣰⣿⣿⣿⣿⣿⡿⢋⣾⡿⢋⣽⢻⣿⣿⣿⣿⣿⣿⣿⣧⢹⡟⣿⣿⣿⣿⣜⢿⣿⣿⣮⣛⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠂⠀⠰⠈⠀⠀⠄⠀⠀⠀⠀⠀⠂⠭⢙⡻⠿⣿⣿⣿⡛⠉⣁⣺⣿⣿⢋⡾⣿⠎⣼⢫⣿⠿⠛⣡⠏⣴⡿⠋⢡⣿⣿⠁⢿⣿⣿⣿⣿⣿⣿⣿⡇⢿⠈⡝⢿⣿⣿⣷⣭⡻⣿⣿⣷⣝⡻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠈⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⡂⠐⠠⣥⣿⣿⡿⢁⣭⣾⢋⡞⢃⠉⢡⠇⢑⠁⠊⣩⠒⣰⣿⡿⡿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡜⡜⣦⣕⡙⢿⣬⣑⠶⣶⠿⢿⣿⣿⣷⣄⠂⠋⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣁⣼⣿⣿⡿⣂⣴⣶⣿⡿⠟⢁⡥⠶⠃⡸⢋⡴⠃⢄⡞⢉⣼⣿⡟⣴⠣⢱⡀⠘⠿⣿⣿⢿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⣝⠛⠂⠍⠐⣒⢿⠿⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠟⠛⢡⣤⠞⠋⣁⡀⠠⠔⣩⠶⠁⢠⠶⡭⠋⢀⠎⣠⢞⣿⢏⣴⠇⡒⣸⣿⡄⠀⡜⣿⣇⢿⣿⣇⠻⣷⣿⣿⣿⠻⣯⠉⢁⣀⠰⣆⠶⣬⣉⣛⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡴⢭⣛⠶⣋⢥⢌⡀⣐⠀⢹⡼⠁⣠⢞⡽⢀⠴⣏⠟⡁⣜⢋⡼⢣⡾⢃⣾⠃⠌⣰⠿⠋⢁⣆⠀⠌⢿⡈⢿⣿⡄⠘⢿⣿⣿⡁⠈⠡⠙⡼⠻⠜⠻⡖⡽⢎⣉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠋⠹⠭⠞⠣⠛⠡⠔⢫⢀⢶⡹⢮⣕⢮⠻⠁⡊⠰⢂⡺⢡⠟⣰⢏⠆⠸⠁⡁⢂⣴⡿⠿⠇⠀⠈⢣⠈⢿⣧⠀⢀⠻⣿⣧⢂⠐⣀⠈⠱⢲⠲⡔⢲⡝⢮⠱⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⠶⠯⢙⣑⣨⡤⡔⡰⠀⠉⢠⣄⢀⠃⠀⠀⠀⠈⠳⠝⣦⠲⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢌⠳⡐⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣍⢻⡄⠋⠖⠁⡠⠡⠀⠏⣉⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⠒⣭⠰⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠒⡘⡌⠆⠁⢠⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢆⠳⡔⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⢿⠿⠿⠟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠓⣬⢱⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢦⡑⢄⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⡠⢇⡚⢤⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⢮⠽⣜⡲⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢥⠓⣌⠣⣎⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠤⡙⠮⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠠⡐⠌⠄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢌⠳⡌⢎⠵⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡕ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡠⠌⢂⠡⡐⠌⡰⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠱⡸⣌⠚⡥⢒⠌⠻⣿⣿⣿⣿⣿⣿⣿⡟⢦⣙ 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