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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠈⢑⣢⣤⣉⡳⢦⠀⠉⠑⠂⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠐⢒⠶⠃⠀⠀⣼⡃⣼⣿⡧⢿⣇⠀⠀⠀⢀⣿⣹⡧ ⠀⠀⠀⢀⣀⣀⣠⣀⣀⣠⡟⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠒⠒⠠⣀⣀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠈⣹⢿⡸⣱⡏⡐⣈⠀⢂⠀⡐⢀⠠⠀⡀⢀⠀⡐⢒⠂⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⡤⡤⠄⢴⡶⠒⠛⠫⣭⣀⡀⠀⠂⠚⠁⠀⠀⠀⣰⢿⡁⣿⡟⠻⣮⣝⢷⣄⣤⠾⣋⣼⠟ ⠀⢀⣴⠛⢉⠋⠁⠀⠉⠙⠁⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢂⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠤⣄⡩⢟⡵⢫⠋⣏⢹⡍⢫⢝⣿⣏⢻⣹⣿⠿⡿⠛⢻⢶⡶⣶⡞⣞⣻⡿⣉⢇⠒⡬⢊⣴⠝⠋⠀⠀⠀⢨⠳⡀⠉⠉⠓⠤⡀⠀⠀⣠⣟⣻⡅⢻⣧⠀⠈⠙⠛⠟⠛⠛⠋⠁⠀ ⢀⣼⡇⠀⢄⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡁⢆⠀⡇⢸⠀⢀⢤⠀⠈⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠐⠠⢀⠙⠩⣰⠃⠀⢿⠀⡏⡒⣾⣿⣿⣿⣷⢋⡾⠁⠀⢸⢎⣵⣴⣿⣿⣿⡑⠦⡬⠋⣠⠟⠁⠀⠀⠀⠀⠀⢸⡁⢣⠀⠀⠀⠀⠈⠀⣰⡿⣭⣟⣿⡌⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⢣⢤⡈⢠⠒⡄⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠚⠀⠑⠊⠀⣇⠘⠀⠀⠇⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⠾⠿⠿⣿⠀⠀⢻⡄⢇⣹⣿⣿⣿⠟⡴⡻⠁⠀⠀⢘⡞⡴⣻⣿⣿⡧⣘⠝⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⡈⢇⠀⠀⠀⢀⣼⢿⡽⣷⣯⢿⣷⣦⡙⢧⣦⢴⣜⡝⠀⠀⠀⠀ ⠈⣗⡸⣮⡺⠄⠣⠞⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⡠⠂⠐⡄⠀⠀⠀⠀⠸⠀⢸⡆⠀⠀⠀⠀⠀⠄⠈⠢⠈⣷⠀⠀⠀⣿⠀⠀⠘⣧⠸⣿⣿⠟⣇⢻⣴⣷⡀⠀⣠⣾⡷⢲⡥⣿⣿⣡⠏⣰⠟⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠠⣾⢯⡿⣽⣿⣿⣯⣿⡝⠛⠷⠚⠛⠁⠀⠀⠀⠀⠀ ⠀⠈⠳⣌⠀⡔⠠⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠤⠀⠐⠈⠀⠠⠄⠀⢩⠀⠀⢰⠀⠀⠀⠘⡀⠀⠀⠀⡇⠀⣸⣿⡄⠀⠀⠀⠀⠈⠆⠀⡀⣾⠇⠀⠈⣾⠀⠠⠀⢻⡄⢿⣿⠀⠗⢉⣾⣿⣷⣼⣿⣿⡗⠳⠼⠁⡷⠁⡼⠃⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⣿⣷⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢇⡐⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⡒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠇⢀⢿⠋⠙⢆⣀⠀⠀⣰⣀⣴⠟⠁⠀⠀⠀⢹⡇⠀⢇⠈⣇⣾⡧⢖⣪⣿⣿⣿⣿⣿⣿⣿⣿⡗⡤⣼⢁⡞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣻⣿⣿⠛⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠫⣆⠁⢄⠐⡄⠀⠀⠀⠀⠀⡅⠀⠀⣀⣭⠟⠛⠛⠒⠲⣤⣨⠀⠀⠀⠣⡀⠀⡐⠀⠀⠀⠸⣠⡞⠁⠀⠀⠀⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢿⡀⠘⡀⠘⣾⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠞⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠀⣔⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠉⠁⠀⠀⠀⠀⢠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢣⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠈⢿⣿⡵⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠢⢤⣤⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⠉⠉⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⣄⢸⣿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣠⢴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡮⡶⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠑⠠⣉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡏⠀⠀⣸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢃⠀⠀⠀⠀⢩⠒⠠⢕⣲⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡅⠀⢠⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢰⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠸⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⢘⡄⠀⠀⢀⣠⣾⣿⣿⣿⣯⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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