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⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⠟⠃⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠘⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣦⡀⠀⠘⣷⣄⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⢰⡿⠃⣄⠘⢿⣿⣿⣿⣿⣿⠃⢠⡀⠈⢿⣿⡄⠀⠘⣿⡀⠀⠀ ⠀⠀⢸⣿⡤⢶⣿⠃⣼⣿⣷⣄⠙⣿⣿⣿⠃⢠⣿⣿⣦⡀⠹⣷⠶⠶⣿⣧⡀⠀ ⠀⣴⡟⠁⠀⣸⠃⣸⣿⣿⣿⣿⣧⣄⣀⣀⣀⣾⣿⣿⣿⣿⡆⢻⡄⠀⠀⠙⣿⡄ ⢰⣿⠃⠀⢀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣧⠀⠀⠀⢹⡇ ⢸⣿⠀⠀⢨⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡀⠀⠀⠈⡿ ⢸⣿⡀⠀⠸⡇⢸⣿⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠹⣿⠇⢸⡇⠀⢀⣼⡏ ⠀⠻⣷⣤⣀⣷⠀⢿⣄⣀⣴⣿⡟⢻⡿⢿⡟⢻⣿⣤⣤⣼⠟⢀⣿⣧⣴⠿⠋⠀ ⠀⠀⠀⠙⠛⢻⣷⠀⠙⢻⣿⣿⣿⣬⣴⣶⣤⣾⣿⣿⡟⠁⢠⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣄⣉⣉⠋⠙⠋⠙⠋⣉⣁⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢤⢤⣠⢤⣤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⡿⣿⣟⣿⣻⣯⣟⣿⣞⣿⣾⣽⣾⣽⣯⣟⣿⣻⡿⣿⣷⣶⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣪⣴⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣤⣑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣮⣿⣿⡿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣟⣿⣿⣷⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⢁⣾⣿⣿⣿⣹⢷⣿⣿⣿⡿⣿⢹⠉⣇⠹⠰⢆⠱⠈⠆⠱⠀⠇⠰⠁⠎⠰⢀⠇⢉⡸⢉⠹⢏⡿⢿⣿⣿⣿⣿⣷⣏⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠄⣰⣿⡿⣯⢿⣿⡿⢛⠏⠓⠌⠒⠄⠃⠉⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠘⠠⠉⡙⠛⠿⣿⣿⣿⣿⣻⣽⡿⣿⣦⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢂⣼⣿⢿⡽⣽⡿⢓⡘⠄⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⡹⢿⣿⣷⣯⣟⣿⣿⣿⣄⠠⠀⠀⠀⠀ ⠀⠀⠀⢀⢇⣾⣿⢯⣿⡽⢏⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡝⢿⣿⣿⣞⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⡎⣾⣿⡽⣾⢟⡱⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⡹⢿⣿⣾⣻⣿⣿⡆⢠⠀⠀ ⠀⠀⠸⢸⣩⡻⣽⠟⣌⢦⣿⠒⡱⣢⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⢠⣾⡿⣏⣱⣻⣯⠻⣷⠻⡷⣿⠀⠀⠀ ⠀⣀⣷⣾⣤⣭⣿⡸⣼⣿⣤⢼⠧⣱⣿⣦⠀⠙⠠⣀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⢨⣿⡿⣭⠄⣩⣿⡧⢘⡿⠟⣿⣿⠑⠀ ⣰⣿⣿⣿⠿⣽⣯⢷⣿⡿⠖⡿⣘⠶⡟⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠅⠡⠀⢕⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢘⣿⣻⢷⣎⡳⢿⣿⢏⣷⡀⠰⣭⢃⠧ ⣾⣿⣿⣏⡿⣿⣾⢼⣿⡿⡥⢳⠥⣾⣅⣤⡔⠂⠈⠐⠁⠀⠀⠀⢀⢀⢀⠀⠠⠐⢆⡀⢠⠈⠠⡀⠀⠀⢄⠈⠀⠀⠀⠁⠈⠢⠈⠀⢨⡄⢉⣿⣯⢿⡬⣙⣿⣿⢮⣾⣿⣟⢂⢮⣱ ⣿⣯⣿⣧⢿⣿⣿⢾⣿⣿⡳⣭⢲⣹⣿⠋⢀⠀⠀⠔⠀⠀⠄⠀⠀⠀⠈⠐⠊⠅⡀⢄⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣶⣺⣿⣯⣟⡞⢷⣾⣿⣎⣿⡟⡆⣞⡲⡍ ⢿⣿⣞⣿⣿⣿⣾⣻⣿⣟⡷⣩⢖⣻⣷⠤⠃⡀⠀⣰⠄⠐⠄⡁⠀⠌⠂⠈⡠⠄⡑⢢⠀⠂⠀⠠⠄⠒⢄⣢⠀⠈⡀⠐⢄⠀⠀⠀⠀⢺⣿⣿⢷⣯⢟⡺⣼⣿⣞⡿⢉⠴⣣⠿⣵ ⠸⣿⣾⣹⡾⣿⣿⣹⣿⣿⢷⡹⣎⣹⣿⡆⠁⠆⠎⠁⠆⡀⠰⡈⠱⠸⠆⢆⠀⢈⠁⠀⠁⣆⠹⡁⠀⠆⡆⠀⠁⡰⠆⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⡏⣷⢿⣿⡾⣿⣀⡇⢷⢹⣹ ⠀⣿⣿⣷⣻⢿⣿⣿⣿⣿⢯⣳⡝⣾⡿⣑⡈⢉⣥⣷⣿⣆⣷⠹⡄⡀⢎⡜⣄⠢⡌⡞⢸⠐⢧⢈⢀⡬⠢⡈⠄⡀⠀⣶⣦⣤⠀⠀⠀⢀⣿⣿⣷⢯⣿⣼⣻⣿⣽⣿⣿⠶⠋⢼⣹ ⠀⣹⣿⣷⣻⣦⣿⣿⣿⣿⣯⢷⣹⢾⣿⡤⠘⢹⣿⣿⣿⣿⡌⢧⠑⠱⠘⡳⣍⢣⣄⣧⣷⣴⢌⠂⢄⠰⣂⢐⠀⠁⢸⣿⣿⣿⡆⠀⠧⣺⣿⣿⣿⣻⣎⢿⣿⣟⡾⣿⣿⣿⣧⠰⠌ ⠀⢼⣯⢟⡿⣿⣿⣿⣿⣿⣯⣟⡧⣿⣿⡕⢋⡙⠻⡿⠿⠋⢸⣲⢈⢇⣆⠽⣙⢹⡞⠻⠟⠋⢁⡈⠌⠈⡀⢃⠁⠈⠂⠘⡛⠛⠁⢀⠀⠘⣿⣿⣯⢷⣫⢿⣿⣯⢿⣿⣿⣿⡟⠃⡇ ⠀⢸⣿⢮⣝⣿⣿⣿⣾⣿⣿⡾⣽⣻⣿⣆⠛⢩⡀⠼⠀⢖⡺⢉⠚⡄⡾⠐⣨⠎⡆⡌⠀⢂⠱⡈⠊⢂⠓⠌⢖⠌⠀⢠⠀⠀⠀⢑⢂⠸⣿⣿⣟⣯⣽⣿⣿⢾⣼⣿⢯⣿⠇⢀⠁ ⠀⠌⣿⣻⣿⣿⣿⣯⣿⣿⣿⣽⣳⢿⣏⣿⠲⣃⣁⢦⡎⠐⠬⠛⠐⠀⠐⢀⢯⠃⢀⠱⡀⠨⠀⢁⠀⢆⠈⠑⠈⠀⠁⠀⠁⠀⠀⠀⠈⢹⣿⣿⣻⢮⣽⣿⣟⣦⣿⣿⣷⡿⠀⡈⠀ ⠀⠂⠼⣟⣿⣿⣿⣿⣿⣻⣿⣿⣽⣻⣿⡟⢴⠂⣼⠀⢂⢌⠀⢀⠀⠀⢀⠈⣃⠈⡅⡆⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢯⣟⣻⣿⠾⣼⣿⣷⣾⠇⠠⠁⠀ ⠀⠀⢀⢹⣞⡿⣿⡿⣽⣿⣿⣿⡷⣿⣿⡾⣸⣋⡥⠐⡉⠀⠈⠀⠀⠀⡀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⢾⣿⣯⡟⣾⣳⣿⣞⢣⠂⠀⠀ ⠀⠀⢀⢊⢻⣾⣱⣻⣼⣻⣿⣿⣿⣿⣿⡷⠅⣹⠀⡀⠁⠀⠐⡀⠀⠐⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷⣏⣿⣿⠻⠼⣗⢻⢟⣣⠃⠀⠀⠀ ⠀⠀⠀⠂⢆⠹⢷⣿⣾⣽⣿⣿⣿⣿⣿⣟⡱⢩⡄⠰⠀⢮⠐⢄⡂⡄⢂⣶⣌⣧⡐⣨⡤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣽⣿⠧⠿⠙⢾⠓⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠡⢈⢂⠣⡜⡽⣫⢿⡿⣿⣿⣿⣿⣳⣲⣅⣳⣯⣬⣓⣶⣽⣾⠟⣏⠾⠌⠝⠙⠑⠋⠉⠉⠉⠁⠈⠐⠀⢀⣤⣤⣤⣄⣄⡄⣀⣾⣿⠿⡉⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠀⠎⡰⢱⠸⣁⢿⡸⣏⣿⣹⣿⣿⡿⢿⠉⡉⣿⣿⣿⠿⢀⡸⢀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣿⣿⠉⠇⠏⠉⠉⢿⣏⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢁⠘⠄⢣⠑⡍⠶⣙⠞⣶⠻⢎⡑⡈⠆⡁⠒⣤⣏⡅⠲⠈⠥⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠻⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⡈⠌⢢⠑⡌⢣⠝⡪⠔⣉⠠⠔⣁⠂⡐⢣⡽⠌⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠠⠑⠢⡑⢌⡱⠎⢋⠺⡣⠂⡐⠄⢣⣱⠓⠈⣁⡀⡴⢨⠂⠐⣄⠰⢀⡀⠀⠄⠀⠀⠄⠀⠈⠦⠄⠀⠀⠀⢳⣀⠀⠄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⡁⢊⠅⠸⠄⠁⠀⡄⠛⠁⡜⠡⣈⠳⠥⠂⠀⠈⠁⡠⠄⢠⠈⣀⠀⢆⠘⡄⠀⡀⠀⠒⠢⠀⠀⠂⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠐⠄⠊⠁⠀⠀⢉⠀⢂⠭⢰⣱⠋⠀⠀⡘⠀⠀⠀⠤⢀⢨⢣⠞⢣⠸⢎⠢⡐⡱⠌⡤⡠⠠⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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