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⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿
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⣻⡿⢏⢥⡻⢬⡍⢳⡘⢦⢣⢝⡢⡓⡜⠰⢂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀ ⡿⢏⡜⣲⡙⢦⡙⢧⡙⣎⠞⢦⠡⢁⠈⠀⠀⠄⠀⢈⠀⠈⢀⠈⠀⠈⠐⠈⠀⠁⡀⠁⠈⠀⠄⠁⠀⢁⠂⠄⠀⢀⠀⠀⠉⠲⣄⡀⠹⣧ ⡱⣩⢚⡥⣙⢦⡙⣦⡙⢦⡛⣬⢓⡆⣴⣤⣦⣴⣬⣦⣴⣤⣆⣤⣈⡀⠐⢀⣈⣴⣴⣶⣶⣶⣦⣤⣌⡀⠀⠠⠀⠠⠀⠈⠀⠄⡈⠧⣀⠈ ⣱⢣⢏⡖⣭⢒⡝⢦⣝⢣⠞⣴⣿⠿⣛⣿⣿⣿⣦⡄⠉⠉⠙⢻⣿⣿⣿⣿⠟⠋⠉⣨⣿⣿⣿⣏⠛⠿⣿⣶⣄⠀⠠⠁⠀⠄⡀⠀⠹⡄ ⢎⡳⢎⡜⢦⢫⢜⡣⢎⢧⣛⣿⠋⡀⢾⣿⣿⣿⣿⣿⣶⠀⠀⢀⣼⡿⢿⣾⠗⠀⣾⣿⣿⣿⣿⣿⣧⡀⠈⠛⣿⡧⠀⠀⠁⠐⡀⢁⠂⢜ ⡹⣜⢣⢞⡱⢎⢮⡱⣋⢦⡹⣿⣷⣈⠻⣿⣿⣿⣿⣿⠟⠀⢠⣿⣿⠀⡍⢿⣿⡄⠹⣿⣿⣿⣿⣿⡟⠋⠀⣰⣿⠗⠀⢈⠀⡐⠠⠀⠌⠰ ⠳⣌⢳⢪⡕⣎⠶⡱⣍⠶⡱⢻⣿⣧⣳⡰⠩⠿⠟⡁⢀⣠⣾⡿⡁⢆⠈⢆⡹⣿⣄⣩⠍⡛⠟⠉⠀⣀⣴⣿⠋⠀⡐⠀⠂⠀⠄⠡⠘⡠ ⡹⡌⢧⠳⡜⡜⢮⡱⢎⡳⣍⢣⠞⡽⢻⣿⣷⣷⢶⣶⣾⣿⡿⣵⢏⡶⣍⠶⣰⢹⣿⡙⢻⢷⣶⣶⡿⢿⠛⠁⢀⠠⢀⠠⠁⡈⠄⡁⠂⠁ ⡱⢎⢇⡻⣌⢳⢃⡞⡥⢳⢜⡣⡝⡼⣡⠂⣽⣿⣿⣿⣿⣿⣿⣽⣞⣳⣭⢳⣣⢿⣿⣿⣶⡆⠀⠀⠀⣀⠠⢀⠂⠀⠂⠀⠀⡐⠀⠄⠠⠁ ⡱⢎⢮⡱⢎⡣⢏⡲⣙⢬⡚⡴⣹⢒⠡⣼⣿⣿⣿⣿⣿⣿⣿⣿⡽⣟⣿⣿⣿⣿⣮⣟⣽⣿⣶⣀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠄⡁⢈⠀⠄ ⡱⣋⠶⣱⢋⠶⣩⠖⣭⢢⢓⡱⢎⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢮⣿⣽⣾⣷⣿⣿⣿⡆⠀⠀⠀⠈⠀⠀⠀⠀⠒⣀⠂⡀⢀ ⡱⢣⡝⢦⣋⠞⣥⠺⣔⢣⡙⢦⢃⡱⢛⢿⡟⣿⡿⣿⠿⣿⣿⣿⣿⣾⣿⣿⡿⣿⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢀⠠⠁⠄⢂⠐⠠ ⡱⢣⢎⡳⣌⢏⠶⣩⠖⣣⡙⢆⡇⢆⡉⢂⠉⠐⠡⠉⠊⡙⠿⣿⣿⡟⡿⠏⠓⠉⠋⠉⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠂⠄⣈⠐ ⡱⣃⢮⠱⣎⠺⡜⣥⢛⡤⣙⠶⣘⢢⡑⢢⠈⠄⠐⡀⠄⠀⠁⠐⠀⢈⠀⡁⢀⠠⠄⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠂⡈⠐⠠⢈ ⡱⡜⣢⢛⡴⢫⡜⢦⡍⢶⣉⠶⡑⢦⡉⠆⡌⡐⠀⡐⠈⡐⠈⠄⡈⠄⡀⠐⡀⢀⠀⠁⠀⢀⠀⠁⠀⠀⡀⠀⠀⠁⠀⢀⠀⠄⠠⢁⠂⠄ ⡱⢥⢣⡍⣖⢣⠞⡱⢎⠧⡜⢎⡙⢦⡉⠖⡰⢀⠁⠠⠀⠄⡐⢀⠠⠀⡀⠁⡀⠄⠈⠐⡀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠈⠄⠠⢀⠱⠀⡌⠐ ⢧⢋⠖⣱⢪⠱⣎⠵⣫⠜⣜⢣⡝⣢⠙⣆⠱⠀⠌⡀⠂⠄⡀⠄⠀⠂⢀⠁⠀⡐⠈⠀⠄⠐⠈⠀⠀⠈⠀⠀⠀⠄⠡⠈⠄⢂⠄⡃⠤⢁ ⢧⣋⠞⡥⢎⠳⣌⠳⢬⡙⣤⠳⡸⢄⠫⣄⠣⢉⡐⠠⠁⠠⢀⠂⠁⢂⠀⠌⠀⠄⠠⢁⠠⠈⠀⠄⡐⠀⠈⠀⠄⠈⠄⠡⣈⠢⡘⢠⠒⠠ ⣧⢻⡜⣱⢋⠶⣌⡹⣂⠗⡢⢝⡰⢋⡱⢄⠃⢆⠰⠁⠠⠁⢂⠐⠨⡀⢂⠄⠡⠈⡀⢂⠠⢈⠐⠀⠀⢁⠊⡐⡈⠌⡐⠡⣀⠑⡌⢂⠡⢃ ⣭⢳⣭⢣⢏⡞⡴⢣⡕⣫⢱⣊⡔⢣⢰⡈⣔⣨⡐⣌⢠⠐⡀⠌⡀⠡⠀⠂⠄⠁⠀⢀⠠⠀⠀⠁⠈⠀⠀⠁⠌⠢⢅⠣⢄⠣⡘⡌⡑⢢ ⣯⣗⣮⣛⣮⣽⡹⣧⢻⣜⣧⡟⡾⣏⢷⡻⡜⢧⡛⠾⡹⢏⠿⣳⠯⣷⢳⣳⢎⣶⢣⣖⡦⣖⢦⡌⡔⣈⡐⢀⠀⡐⠈⢘⢢⢣⠱⣌⠱⣂ ⣟⣮⢷⣻⣞⣷⣻⣽⣻⣞⣶⣝⢦⣉⢦⡑⣌⢂⠌⡐⠡⢈⠂⡅⡘⢀⠃⠌⠊⠔⡉⠌⠃⠍⠂⡙⠘⠠⢉⠃⠎⡐⢈⡤⣓⢎⡳⣌⠳⣌ ⣿⡽⣯⣷⢿⣞⣯⣷⡿⣯⣿⡾⣿⣽⡾⣽⢾⡽⣮⣵⢻⣬⢳⡜⣜⣣⠻⣜⡛⢶⡱⢎⡖⣦⡱⣤⢲⡰⣆⣜⣲⣜⡳⣞⡭⡞⡵⣎⡟⡼ ⣿⣿⢯⣿⣻⣯⣿⢷⣿⣟⣷⡿⣟⣾⣟⣿⢯⣿⣳⣯⣟⡾⣧⣟⡾⣖⣟⣶⣹⢧⣛⣮⡽⡶⣝⣮⠷⣝⣮⡽⢶⡭⣷⡹⣞⡽⣳⡝⣾⡹ ⣿⣻⡿⣯⣿⣻⣽⣿⣳⡿⣯⣿⣟⣿⢾⣻⡿⣽⣯⣷⣿⣻⣽⣯⣿⣽⣾⣳⣯⣿⣽⣾⣽⣻⣽⣞⡿⣽⡾⣽⢯⣟⣶⣻⡵⣏⡷⣹⠶⣽
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⡄⠈⡓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠂⢹ ⠈⡷⡄⠈⠲⢤⣈⠻⠉⠛⠉⠉⠁⠒⠖⠉⠉⠉⠒⠶⢦⣤⠴⠒⢉⣡⠴⠀⢀⠏ ⠀⢸⡿⡂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡞⠉⠀⢀⣠⡞⠀ ⠀⠀⢙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡼⡟⠀⠀ ⠀⠀⡼⠋⠀⣤⣀⠀⠀⠀⠀⠀⠈⠐⣂⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡟⠁⠀⠀ ⠀⢠⡇⠀⠀⠘⠛⠃⠀⠀⠀⠀⠾⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀ ⠀⢸⡇⢺⡀⠀⢠⡒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠸⡇⠀⠀⠀ ⠀⢸⡇⣘⠑⡀⠀⠙⢏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣔⣇⠀⠀⠀ ⠀⢸⡇⡁⠀⢳⣶⣾⣷⣦⣄⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠸⡇⠁⠀⠀⢏⠉⠀⠀⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠀⠀⠀ ⠀⠀⠯⣀⣈⣀⣈⣐⣲⣄⣄⣤⣴⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⡧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⢿⣿⣶⣶⣦⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠋⢀⣤⣶⡿⠟⢋⣉⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣿⣿⣿⣿⡦⠀⠀ ⠀⠀⣴⡟⢁⣴⣾⡿⠟⢁⣴⡾⠛⠛⠛⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠁⠀⢀⣾⣿⣿⣷⡀⠀⠀ ⠀⣸⡟⠀⠛⠋⠉⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⠛⠛⠀⣿⡇⠀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⣼⡇⠀⣴⣶⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠺⢿⣷⡀⠿⠿⠛⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠘⠿⣶⣦⣤⣤⣶⣶⣾⣿⣭⣿⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣤⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠟⠉⢀⣀⣀⠉⠛⢿⣇⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣤⡤⠴⠶⣿⣿⠋⢠⣾⡟⠉⠛⢿⣆⠀⢻⣧ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢠⣿⢿⡿⢿⣶⣾⣿⡆⢸⣿ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢸⡷⠾⠷⠾⠷⠿⢿⡇⢸⡿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⣿⡇⠀⠀⠀⠀⠀⣸⡇⣸⡇ ⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⡇⠀⠀⠀⠀⢠⣿⢁⣿⠀ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠃⠀⠀⠀⠀⣾⡇⢸⣿⠀ ⠀⢻⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⠸⣿⠀ ⠀⠈⣿⡄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⠀⠀⣸⡏⢰⣿⣤⣀⣀⠀⠀⢿⡇⠀⣿⠀ ⠀⠀⠘⣿⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣸⡏⠀⠈⠙⠳⣄⢸⣿⠀⣿⠀ ⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⣤⣀⠀⠀⠀⢸⡏⠀⣿⣤⣤⣤⣤⣤⣼⣿⣿⠀⣿⠀ ⠀⠀⠀⠀⠙⣷⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⣼⡇⠀⢿⣇⣽⣯⣿⣹⣇⣼⠇⠀⣿⠀ ⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠘⣿⣍⠉⠉⢻⣿⠟⠀⣰⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠦⣄⣀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠙⠛⠛⠛⠉⢀⣴⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠈⠻⢷⣦⣤⣤⣤⣤⣴⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⡿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⣤⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⢠⡶⠀⡠⣖⣲⣲⠖⢲⣶⡀⠀⠀⠑⢼⣔⣲⢂⣰⠒⠂⠀⡟⠛⢶⣒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣀⣀⣠⠴⠛⠒⠤⠴⠚⠉⠀⠉⠉⠀⠀⠈⠛⠲⢄⠀⠀⠀⠀⠀ ⠀⢀⡤⣖⠒⠚⠋⠉⠉⠛⠛⠁⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⣀⠀⣈⣓⣦⠀⠀⠀ ⠀⢸⠀⠈⠛⠉⠉⠑⠦⠤⠤⢤⣀⣀⠀⢀⣀⣀⡠⠴⠚⠢⠤⠤⠖⠋⠀⠉⠓⠚⠁⠀⠈⠉⠁⠀⣨⠇⠀⠀ ⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣾⠀⠀⡞⠁⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⠀⠀⣠⣾⣿⠀⢨⠇⠈⢣⡀⢀⣳⣄⣀⣞⠀⠀⢀⣸⣄⣰⡀⢀⠀⠈⠁⠀⢰⠃⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠸⠿⠟⠁⢰⡋⠀⠀⢀⠟⠉⠀⠀⣀⣈⠓⣾⠋⠀⠀⠀⠉⢻⡀⠀⣠⠖⠁⠀⠀⠀⠀⠀ ⢀⡜⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⡏⠀⠀⢠⣿⣿⣿⣇⠈⡇⢠⣾⣿⣷⡀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢸⡁⠀⠾⠃⠀⠀⠀⠀⠀⠀⡴⠻⡷⠸⡇⠀⠀⢸⡘⡿⢯⡟⠀⡞⢸⣿⣿⣿⠃⡏⢀⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⠀⠹⣄⠀⠀⠙⠛⠉⢀⡼⢧⣄⣙⣫⡥⠚⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⢀⣤⠀⢀⡼⠀⡄⠀⠀⠈⠛⠒⠤⠴⠚⠋⢦⡓⠦⣤⣤⣤⣤⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⡀⠀⠀⠀⢀⣼⣿⡿⠀⣞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⡇⠀⠀⠀⠸⠿⠋⠀⠀⢘⡆⠀⠀⠠⠖⠚⠉⡽⠉⠛⠒⡖⡖⠒⠚⣿⠉⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡀⠀⠀⠀⠸⠓⠒⠒⢴⡇⠛⠒⠒⣻⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡆⢀⣤⠀⠀⠀⠀⠀⠘⣆⠀⠉⠁⠀⠀⠀⠈⠒⠒⠒⠋⠁⠀⠈⠉⢽⡆⠸⡧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠃⠉⠁⢀⣤⠤⢤⣀⡀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠛⠓⣾⣧⡆⢙⡇⠀⠀⠀⠀⠀⠀⠀ ⠻⢤⣀⠀⢺⠀⠀⠀⠈⠙⠓⢦⣀⣠⢤⡄⠤⣤⣤⣴⣿⠋⢣⡞⢁⣀⣠⣤⡿⢿⡝⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣏⡑⠺⣆⠀⠀⠀⢠⡶⠷⠿⠤⢤⣽⣎⣠⣿⣯⣽⣷⣾⣿⣿⣿⣿⣿⡟⠉⠙⣮⠷⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⣟⠹⣟⣺⣦⣀⠀⡟⢛⣷⣲⣶⡶⢥⣴⣤⣤⣤⣤⣈⣉⣩⣿⣿⠛⠛⠓⠤⠴⠃⠀⣜⠻⣟⣻⣲⡄⠀ ⠀⠀⢿⣧⣿⡿⠿⣿⢿⣷⣿⠿⠿⠿⢧⣀⣙⣉⣭⣿⣿⡿⠟⣛⣿⠏⠛⠛⠓⠲⢶⡀⢠⣌⠳⣌⠻⢿⡁⠀ ⠀⠀⠀⠀⠉⠛⠿⣦⣸⣇⣀⣠⣴⢾⡟⠛⠉⠁⠀⠙⢻⠛⡟⠛⠁⠀⠀⠀⠀⠀⠀⠙⢦⣙⠳⣌⠳⢦⣹⡆ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣾⠃⠀⠀⠀⠀⠀⠸⡧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⠟⠿⠿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⡇⠀⠀⠀⠀⠀⠀⣴⣿⣤⣷⣄⣠⣴⣾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠃⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣍⣽⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣦⣀⣴⣾⣿⣷⣄⠙⠛⠿⠽⠻⠿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠯⠛⠻⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣧⣿⣴⣷⣟⠱⠟⡒⠿⠿⠦⢤⣤⡬⠍⠁⠠⠟⣿⣧⣤⣀⣸⣇⡀⠀⢠⣀⠟⠉⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿ ⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⢿⣧⣴⡆⣠⠀⠈⠙⣦⡴⠖⠋⠉⠁⠀⠀⠀⠈⠉⠳⢦⣄⠈⠀⠀⠀⠀⠀⣸⠴⠾⠛⠿⣿⣿⣿⣿ ⡣⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢠⣅⣰⣶⠿⣿⣶⡄⢁⣈⢻⣿⣿⣿ ⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢫⡍⠙⣿⣷⣾⣿⣾⣿⣦⣽⣿⣿ ⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⢹⠀⠘⣿⣿⣿⣿⣙⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠿⣿⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⣬⣛⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣞⡁⠀⠀⠀⠀⣠⣴⠾⠿⣿⣶⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⢀⣴⡟⠉⠉⠁⣸⣿⠋⠉⠛⠿⠏⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢆⠀⠀⢀⡟⠁⠀⠀⠀⠉⠉⠳⠤⠀⠀⠈⣿⡆⠀⠀⠸⠉⠃⠀⠀⠀⣤⠀⠀⠀⢀⣀⡀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⡀⠀⠈⣧⠀⠀⣇⠀⢤⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⢡⣾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡤⢬⣧⠀⠻⢄⣼⣶⡖⠒⣲⣶⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣿⣿⣿ ⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣀⣦⡿⠀⠀⠀⠙⠿⠥⠴⢛⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿ ⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡄⠀⠀⠀⢀⣴⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣷⣸⢿⣄⠀⠙⠧⣬⣿⠿⠟⠁⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⡇⣸⣿⣎⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣏⣿⡹⣿⢸⣿⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣻⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⠻⠿⣿⣿⡆⠑⠂⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣽⣿⢻ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡃⠐⣿⣟⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⣴⣾⣿⣻⣿ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⢿⣿⡧⢰⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⢣⣾⣿⣿⣿⡟⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢹⡟⢶⣿⠿⣿⣿⣿⣾⣿⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠃⠀⠀⢀⣴⡾⠯⢞⣵⣿⣿⣿⣿⣿⠠⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢷⣴⣿⣿⣿⣿⡿⣷⡟⢷⡀⠑⢶⣤⣤⣤⣤⣴⣾⣿⡀⣀⣀⣴⣶⡿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⣿⣦⡙⢦⡀⠀⠳⠬⠽⢯⣝⣿⣫⣹⠯⠄⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠛⠛⠋⠹⢿⣿⡿⢿⣿⣇⠀⠀⢸⣿⣿⣿⣟⣿⣟⣿⣿⣏⣿⣾⣟⢦⣀⠀⠀⠀⠈⠁⠈⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⣀⣠⣤⣭⣽⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣤⣴⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠉⠉⠉⠒⠲⢤⣀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⣀⣀⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣹⣀⣀⡤⠤⠤⠤⠤⠤⠤⢄⣀⣈⣇⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⣊⡭⠥⠔⠒⠲⠦⠤⢭⣉⣳⣄⣤⣴⣒⣊⡭⠭⠭⠭⠭⠭⣿⣶⣻⣦⣀⠀ ⠀⠀⠀⢀⡴⠚⢹⠃⠀⠀⠀⠀⠀⠀⢀⡤⠖⢚⣡⠖⠋⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣙⣿⡛⠉⠁⠀⢀⣀⣀⣠⣤⣤⣤⠤⣭⣝⣿⣄ ⠀⠀⢠⡞⠁⠀⣾⠀⠀⠀⠀⠀⠀⣾⣛⣛⠋⠉⢀⣀⣀⡠⠤⢶⣶⢿⣿⣿⣤⡀⠀⠀⠈⡷⠒⠚⠉⠉⢠⣿⡿⢿⣿⣿⣦⡀⠀⠉⢻ ⠀⢀⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠯⣉⠀⠀⠀⢠⣿⣿⣶⣿⠛⢻⣿⡆⠀⣰⠁⠀⠀⠀⠀⣿⣿⠿⣿⣏⣹⣿⣧⢀⣠⡞ ⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢬⣙⠒⠤⢼⠿⢿⡿⠿⠿⠿⠛⠛⢉⡼⠛⠓⠒⠒⠶⠟⠛⠛⠛⠛⠛⠋⢩⡿⠛⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠒⠒⣲⡾⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠋⠁⠀⠀⠀⠀⠈⠛⠢⢤⣤⠤⠤⠴⠒⢿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⡀⠀⣀⡀⠀⠉⠉⠙⠓⠒⠲⠦⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠚⠉⢉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠉⠉⠉⠉⠉⠓⠒⠶⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠁⣀⣀⣀⣀⣠⣴⠟⠁⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⠒⠒⠒⠒⠒⠲⠦⠤⠤⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣿⠀⠀⠀⠀ ⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠶⠶⠶⠶⢶⡦⠶⠒⠋⠁⠀⠀⠀⠀ ⠟⠿⢿⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠦⣭⣉⠓⠒⠶⠦⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⢤⣤⣤⣀⣀⣀⣉⣉⣉⣉⣉⡉⢉⣉⣉⣉⣉⣩⣭⠟⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡟⣡⡟⣱⣿⡿⠡⢛⣋⣥⣴⣌⢿⣿⣿⣿⣿⣷⣌⠻⢿⣿⣿⣿⣿⣿⣿ ⠏⢼⡿⣰⡿⠿⠡⠿⠿⢯⣉⠿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣦⣍⠻⢿⣿⣿⣿ ⣼⣷⢠⠀⠀⢠⣴⡖⠀⠀⠈⠻⣿⡿⣿⣿⣿⣿⣿⣛⣯⣝⣻⣿⣶⣿⣿⣿ ⣿⡇⣿⡷⠂⠈⡉⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣍⡤⣤⣤⣤⡀⠀⠉⠛⠿ ⣿⢸⣿⡅⣠⣬⣥⣤⣴⣴⣿⣿⢿⣿⣿⣿⣿⣿⣟⡭⡄⣀⣉⡀⠀⠀⠀⠀ ⡟⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣈⠀⠀⠀⢀⣶ ⡧⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿ ⡇⣿⠃⣿⣿⣿⣿⣿⠛⠛⢫⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⡇⣿⠘⡇⢻⣿⣿⣿⡆⠀⠀⠀⠀⠈⠉⠙⠻⠏⠛⠻⣿⣿⣿⣿⣿⣭⡾⢁ ⡇⣿⠀⠘⢿⣿⣿⣿⣧⢠⣤⠀⡤⢀⣠⣀⣀⠀⠀⣼⣿⣿⣿⣿⣿⠟⣁⠉ ⣧⢻⠀⡄⠀⠹⣿⣿⣿⡸⣿⣾⡆⣿⣿⣿⠿⣡⣾⣿⣿⣿⣿⡿⠋⠐⢡⣶ ⣿⡘⠈⣷⠀⠀⠈⠻⣿⣷⣎⠐⠿⢟⣋⣤⣾⣿⣿⣿⡿⠟⣩⠖⢠⡬⠈⠀ ⣿⣧⠁⢻⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⠈⢀⡴⠈⠁⠀⠀ ⠻⣿⣆⠘⣿⠀⠀⣀⡁⠀⠈⠙⠛⠋⠉⠀⠀⠀⠀⡀⠤⠚⠁⠄⣠
⣿⠟⣽⣿⣿⣿⣿⣿⢣⠟⠋⡜⠄⢸⣿⣿⡟⣬⢁⠠⠁⣤⠄⢰⠄⠇⢻⢸ ⢏⣾⣿⣿⣿⠿⣟⢁⡴⡀⡜⣠⣶⢸⣿⣿⢃⡇⠂⢁⣶⣦⣅⠈⠇⠄⢸⢸ ⣹⣿⣿⣿⡗⣾⡟⡜⣵⠃⣴⣿⣿⢸⣿⣿⢸⠘⢰⣿⣿⣿⣿⡀⢱⠄⠨⢸ ⣿⣿⣿⣿⡇⣿⢁⣾⣿⣾⣿⣿⣿⣿⣸⣿⡎⠐⠒⠚⠛⠛⠿⢧⠄⠄⢠⣼ ⣿⣿⣿⣿⠃⠿⢸⡿⠭⠭⢽⣿⣿⣿⢂⣿⠃⣤⠄⠄⠄⠄⠄⠄⠄⠄⣿⡾ ⣼⠏⣿⡏⠄⠄⢠⣤⣶⣶⣾⣿⣿⣟⣾⣾⣼⣿⠒⠄⠄⠄⡠⣴⡄⢠⣿⣵ ⣳⠄⣿⠄⠄⢣⠸⣹⣿⡟⣻⣿⣿⣿⣿⣿⣿⡿⡻⡖⠦⢤⣔⣯⡅⣼⡿⣹ ⡿⣼⢸⠄⠄⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⡜⡌⡝⡸⠙⣼⠟⢱⠏ ⡇⣿⣧⡰⡄⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣋⣪⣥⢠⠏⠄ ⣧⢻⣿⣷⣧⢻⣿⣿⣿⡇⠄⢀⣀⣀⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠂⠄⠄ ⢹⣼⣿⣿⣿⣧⡻⣿⣿⣇⣴⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣰⠄⠄⠄ ⣼⡟⡟⣿⢸⣿⣿⣝⢿⣿⣾⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠄⡀⡀ ⣿⢰⣿⢹⢸⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠄⠄⣸⢰⡇ ⣿⣾⣹⣏⢸⣿⣿⣿⣿⣿⣷⣍⡻⣛⣛⣛⡉⠁⠄⠄⠄⠄⠄⠄⢀⢇⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣙⠣⠄⠀⠀⠀⠉⠉⠉⠛⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣡⡴⠾⣿⡉⠛⢿⣦⠀⢀⣰⠶⠛⠛⠻⢶⣄⡙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣶⣤⣀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⢃⢴⣿⣿⣿⣶⡀⠹⣶⠟⣡⣾⣿⣿⣶⡄⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢁⡴⢧⡀⢉⣛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠈⣿⣿⣿⣿⣿⣷⠀⠟⠀⣿⣿⣿⣿⣿⣿⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⣰⡿⠁⠀⣹⠟⢋⣡⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣷⡀⠸⣿⣿⣿⡿⠃⠀⣦⠀⠛⣿⣿⣿⣿⡏⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡾⠛⠉⡿⠸⡏⠀⢀⡾⠉⢉⣾⠯⣥⡈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠸⣬⣿⡆⠀⠀⠁⠀⢀⣀⠘⢷⣤⡈⠉⠙⠃⣨⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡏⠉⢇⡞⠶⢷⡀⠹⣄⠘⠀⣰⡟⠀⢀⡞⠉⠁⠺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣤⣴⣶⠞⠁⠀⠀⠙⠿⢾⣷⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠠⠀⠈⠓⠀⠠⢷⣄⠘⢷⣀⠹⡄⢠⡼⠀⠀⠀⢀⣿⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠻⣆⡑⠏⠀⠀⠀⠀⣼⣿⡍⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⢻⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠻⣦⣤⣤⣴⣿⣋⣹⣷⠀⢠⡈⢻⣿⣷⣦⣄⣤⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠘⢿⣆⡈⢷⣄⠀⠀⠀⠙⡄⠀⠛⠂⣀⠘⠠⠟⣿⣿⠁⣿⣀⣼⠟⠉⣀⠀⠸⣿⡟⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠻⠧⣄⣿⣷⡀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠈⠙⣿⣿⣿⣿⡿⠷⠂⠹⢧⠀⣾⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀ ⢸⠀⠀⠀⠀⠀⠀⠹⠿⣿⣻⣦⡀⠀⠀⠀⠀⠀⢀⡀⠀⠑⠾⣿⣿⡿⠸⠆⠠⠆⠀⠀⢸⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡾⠃⠀ ⡞⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⢙⣿⣦⡀⠀⠀⣴⠟⡁⠀⠀⣰⣿⡟⠓⢰⣆⡼⠦⢄⠀⠬⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢞⡵⠛⠀⠀⠀ ⠇⠀⠘⠻⣦⣄⠄⠀⢠⡀⠀⠀⠛⠛⣷⣄⡀⠉⠀⠽⢀⣾⣿⠟⢀⣴⢾⡟⢧⡀⡀⠙⣆⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⢃⡴⠋⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠉⠛⢷⣄⠀⠙⣄⠀⠀⠀⠙⣏⡛⢷⣄⣘⢻⣿⡏⠀⢾⠁⠸⣷⣈⣿⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣵⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠸⣦⡄⠀⠀⠀⠀⡙⢷⣄⠈⠀⠀⠀⣀⡞⠁⡇⠈⣹⡿⠋⢷⠀⢸⡆⢠⣾⡿⠋⠙⠷⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣠⣿⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠈⠀⠇⣃⡼⠟⠁⠀⠀⠳⢤⣷⡿⠟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⣠⠙⠓⢶⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⣘⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡀⠀⠀ ⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⣼⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧ ⠀⢰⠃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⡇⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⣷⠀⠀⢺⣿⣿⠂⠀⢠⡄⠀⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⢠⠏⠀⠀⠀⠉⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣰⠃⠀ ⢿⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢀⠀⠀⠀⡼⠁⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠀⠀⣼⠁⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠁⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡵⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⡇⠀⠰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⢀⣤⠞⠁⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠻⡄⠀⠀⠀⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⠤⠤⠴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⣤⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠚⠋⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉⠙⠀
⠀ ⠀ (\__/) (•ㅅ•) Don’t talk to _ノヽ ノ\_ me or my son `/ `/ ⌒Y⌒ Y ヽ ever again. (  (三ヽ人  /  | | ノ⌒\  ̄ ̄ヽ ノ ヽ___>、__/ |( 王 ノ〈 (\__/) /ミ`ー―彡\ (•ㅅ•) / ╰ ╯ \ / \>
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠄⠤⠐⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⠤⣀⠀⠀⠀ ⠀⠀⠀⠀⢀⠤⣖⣶⣭⣷⣼⣄⠁⠀⠀⠀⠀⠀⠀⢐⣫⣭⣴⣶⣦⢄⠀⠀⠀⠀ ⠀⠀⠀⣪⣿⣿⣿⠿⢿⣿⣿⠻⣄⠀⠀⠀⠀⠀⢀⣼⠿⠿⢿⣿⣿⣿⣧⡀⠀⠀ ⠀⠀⣩⣿⣿⡟⣿⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣤⣼⣿⣿⠻⣿⣿⠀⠀ ⠀⢀⣿⣿⡟⠀⠹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⢹⣿⡄⠀ ⠀⠈⢿⣿⡃⠀⠀⠀⠉⢁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠀⠀⠀⢰⠟⡇⠀ ⠀⠀⠀⠉⠗⠖⠀⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠙⠛⠒⠀⠐⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⣢⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⠿⣿⣿⣿⣿⣿⠿⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣈⡭⠭⣭⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀
▕╮╭┻┻╮╭┻┻╮╭▕╮╲ ▕╯┃╭╮┃┃╭╮┃╰▕╯╭▏ ▕╭┻┻┻┛┗┻┻┛ ╰▏ ▕╰━━━┓┈┈┈╭╮▕╭╮▏ ▕╭╮╰┳┳┳┳╯╰╯▕╰╯▏ ▕╰╯┈┗┛┗┛┈╭╮▕╮┈▏
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠚⢉⣩⣭⡭⠛⠓⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠃⢀⡴⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⣠⠋⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⣸⠁⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⡇⠀⡾⡀⠀⠀⠀⠀⣀⣹⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⢸⠃⢀⣇⡈⠀⠀⠀⠀⠀⠀⢀⡑⢄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⠀⢻⡟⡻⢶⡆⠀⠀⠀⠀⡼⠟⡳⢿⣦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⣸⠀⢸⠃⡇⢀⠇⠀⠀⠀⠀⠀⡼⠀⠀⠈⣿⡗⠂⠀⠀⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⡏⠀⣼⠀⢳⠊⠀⠀⠀⠀⠀⠀⠱⣀⣀⠔⣸⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀ ⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢸⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⣸⠀⠀⠹⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⡏⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡇⠀⠀⢰⡀⠀⠀⠀⠀⠀⡇⠀⠀ ⢰⠇⡄⠀⠀⠀⡿⢣⣀⣀⣀⡤⠴⡞⠉⠀⢸⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀ ⣸⠀⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⠀⠀⢸⠀⠀⢀⣿⠇⠀⠀⠀⠁⠀⢸⠀⠀ ⣿⠀⡇⠀⠀⠀⠀⠀⢀⡤⠤⠶⠶⠾⠤⠄⢸⠀⡀⠸⣿⣀⠀⠀⠀⠀⠀⠈⣇⠀ ⡇⠀⡇⠀⠀⡀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠸⡌⣵⡀⢳⡇⠀⠀⠀⠀⠀⠀⢹⡀ ⡇⠀⠇⠀⠀⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⢧⣀⣻⢂⠀⠀⠀⠀⠀⠀⢧ ⣇⠀⢠⠀⠀⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣆⠀⠀⠀⠀⠀⠘ ⢻⠀⠈⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⢮⣧⡀⠀⠀⠀⠀ ⠸⡆⠀⠀⠇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⢢⡀
.....⠀  。゚゚・。・゚゚。     ゚。  。゚      ゚・。・゚    ︵    ︵   (  ╲  /  /    ╲   ╲/  /     ╲   ╲ /     ╭ ͡ ╲   ╲    ╭ ͡ ╲  ╲  ノ  ╭ ͡ ╲
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⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢣⠀⠀⠙⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⡁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⡀⠀⠸⠀⠀⠀⢀⠏⣳⠴⣶⠶⠞⠛⠉⠉⠉⠓⠛⠒⠢⢄⡈⢏⠢⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡀⠉⠑⠒⢒⡶⠚⢀⠵⠊⠀⠀⠀⠀⣀⡴⠦⠄⠀⠀⠀⠀⠀⠙⠢⡘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠳⡀⠀⣠⡔⠁⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⡼⣲⠿⣾⡅⢸⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠱⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠇⡗⢲⣴⣟⣻⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⡀⠀⢱⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⡼⠁⠣⡀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣧⡈⠢⡀⠣⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠀⠐⢣⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⢡⠀⢃⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠘⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡾⠀⠀⠀⠀⠀⠀⡎⠀⢣⠀⢇⡁⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣸⠃⠀⢀⠀⠀⠀⢠⠁⠁⠂⢃⢈⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠈⡗⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⡇⠀⢠⡞⠀⢀⢜⠇⠀⣠⠃⠀⠀⢀⠎⠀⠀⠀⢠⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⢰⠀⢣⠀⠀⢸⠇⠀⠀⠀⠀⠀⢣⠰⠟⢀⠰⠫⣃⡠⢊⠇⠀⠀⡠⢋⠀⠀⠀⠀⠸⠀⢠⡏⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠇⠀⠸⠀⠀⣧⡀⢀⣾⡀⠀⠀⢧⠀⠸⣀⡭⢥⣒⣒⣦⡄⠇⠤⠔⠊⠀⣴⣒⣒⡢⢤⠃⡠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⠀⡏⠻⣮⠈⢇⠀⠀⠈⢷⠄⣹⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠧⡞⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠏⠀⠀⠀⡇⠀⢠⠇⠀⠈⠣⣌⣦⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠏⠀⠀⠀⠀⢡⠀⡾⠀⠀⠀⠀⠀⠉⠷⣄⠀⠘⢶⠤⣄⣀⠀⢀⠔⡖⠉⠉⠉⠉⠓⣄⡤⠒⣪⠟⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠘⣶⠁⠀⠀⠀⠀⡟⡉⠉⠉⠑⢢⣤⡻⠉⠛⣽⢟⠘⠀⠀⠀⠀⠀⠀⢸⡥⣚⣁⡀⠈⢦⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⢹⣷⡀⠀⠀⠀⣄⠸⡄⠀⠀⠀⠀⣷⢃⢸⠉⢿⣿⣈⣙⢢⣴⡗⠊⣉⡷⣄⠀⢒⠴⣊⡉⣭⡏⠁⠐⠒⠂⡤⠤⠤⠤⠭⠭⠁⠀⠀ ⠀⠀⠀⠙⢿⣦⢄⠀⠘⣦⠘⣆⠀⠀⠀⢸⣸⡀⡗⣍⣍⢙⣿⣿⡏⢧⣠⣶⡇⠀⠉⠒⠉⠀⣿⣏⡇⠂⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⢮⡀⠉⠆⠸⣆⠺⠍⣉⠉⠉⠀⠉⠑⠒⠯⠁⢰⣀⣭⡻⢴⣀⣀⣀⣠⣾⠥⢴⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⢸⣄⠀⠀⠈⢲⠀⠤⠀⠀⠒⠒⠒⢹⣓⠉⠉⠉⠉⠉⠉⠛⠍⣑⠂⠄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⡤⠔⠃⠀⢠⠀⣸⠛⠵⣦⢄⠈⠆⠀⠀⠀⠀⠀⠀⢧⠈⠢⢀⠀⠀⠀⣀⡀⠀⠀⠉⠐⠀⠇⠂⠰⣶⣰⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⣄⣀⣀⣤⠯⠜⠁⢷⠠⣄⣑⣛⠖⠶⠶⠒⠂⠉⠉⠁⠀⠀⠀⠉⠉⠒⠒⠒⠒⠂⠉⠉⠉⠉⠉⣀⣀⣀⢀⣀⠀⠀⠀
⠄⠄⠄⣰⣿⠄⠄⠄⠄⠄⢠⠄⠄⢀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⢰⣿⠿⠄⡀⠄⠄⠄⠘⣷⡀⠄⠢⣄⠄⠄⠄⠄⠄⠄⠄⣠⠖⠁⠄⠄⠄⠄ ⠄⣤⢸⣿⣿⣆⠣⠄⠄⠄⠄⠸⣿⣦⡀⠙⢶⣦⣄⡀⠄⡠⠞⠁⢀⡴⠄⠄⠄⠄ ⢰⣿⣎⣿⣿⣿⣦⣀⠄⠄⠄⠄⠹⣿⣿⣦⢄⡙⠻⠿⠷⠶⠤⢐⣋⣀⠄⠄⠄⠄ ⢸⣿⠛⠛⠻⠿⢿⣿⣧⢤⣤⣄⣠⡘⣿⣿⣿⡟⠿⠛⠂⠈⠉⠛⢿⣿⠄⠄⠄⠄ ⠄⡇⢰⣿⣇⡀⠄⠄⣝⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡄⠄⠈⠄⣷⢠⡆⠄⠄⠄⠄ ⢹⣿⣼⣿⣯⢁⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⠶⣲⣵⠟⠄⠄⠄⠄⠸ ⠄⢿⣿⣿⣿⣷⣮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣟⣡⡴⠄⠄⠄⠄⠁ ⠄⠰⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀⠄⠄⠄⠄ ⠄⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⡞⠄⠄⠄⠄⠄ ⠄⠄⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠈⠻⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣾⣿⣿⣿⣿⣿⡿⠋⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣿⣯⣟⣿⣿⣿⡿⣟⣯⣷⣿⣿⡏⣤⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣞⢸⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣇⣿⡆⠄⠄⠄⠄⠄⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠒⢂⣠⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢄⠈⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠈⠦⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡴⡿⡇⠁⡔⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⣄⠀⠀⠈⠓⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠖⠋⡏⢀⠀⢉⢴⡗⠚⢁⣴⡾⢛⣛⣦⣴⣶⣶⣶⣶⣓⣒⠲⠤⢄⡀⠀⠀⡏⣷⢤⣀⠀⠘⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠫⠬⠏⠀⠀⢹⣩⠴⠛⣒⣹⣾⠿⠚⣫⢟⡡⠊⠁⠀⣠⡼⠉⠙⠻⣽⣦⣀⠀⠀⢀⡇⢬⠇⣿⣍⠓⢦⡙⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡯⠀⠀⠀⠀⠀⣠⣷⠖⠋⣩⠟⠁⣠⠎⢠⠏⠀⠀⠀⡴⠃⠀⠀⠀⡄⢻⡇⢹⣷⣤⡞⠱⣼⠿⢿⣿⡷⠄⠀⢽⠀⠀⠀ ⠀⣠⠔⠚⠉⢉⡭⠛⠉⣉⠲⣾⣟⣉⣀⡞⠁⠀⡰⠁⣰⠃⠀⠀⠊⢸⠃⠀⠀⠀⠀⡇⢘⣷⠀⢣⠙⢶⠴⠁⠠⢼⣧⢤⣤⣀⠻⣄⠀⠀ ⡾⠁⠀⢀⣴⠁⠐⣪⠝⣫⣿⢿⠀⢠⠎⡄⠀⡸⠁⢀⡏⠀⠀⠀⠰⠃⠀⠀⠀⠀⢠⠃⠈⡟⠀⠀⣇⠈⣧⣀⠀⠼⢄⠀⡾⠈⠉⠻⡄⠀ ⠃⠀⣰⠟⢁⡤⢪⠆⡴⣳⢿⠂⣧⠏⡔⠀⢀⣓⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⡇⠂⠀⢸⡀⠘⢷⣟⣟⢛⡿⣅⠀⠀⠀⡟⠀ ⠀⠀⠃⡰⠋⢀⡏⣸⢱⡟⠈⣧⡞⣸⠁⠀⢸⠀⠀⡏⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⡇⢀⡏⡇⠀⠀⠀⡇⠀⠘⡏⠻⠏⠀⠙⢷⢆⠈⠀⠀ ⠀⠀⡞⠀⠀⡼⢰⢣⡿⠀⠀⣿⢠⠇⠀⢀⡟⠀⠀⡇⠀⠀⠀⣸⢳⡇⠀⠀⠀⢰⠁⣼⠀⢷⠀⠀⠀⢧⠀⠀⡇⠀⠀⠈⢦⠈⣿⢷⠀⠀ ⠀⠀⠀⠀⣼⠃⣿⣿⠃⠀⢸⡿⣸⠀⠀⣿⡟⠛⠲⢿⣗⣄⡀⢅⠈⠀⠀⠀⠀⢸⢀⠇⠀⢸⣀⠀⠀⡼⠀⠀⢱⠀⢧⠀⠈⣆⢸⣧⢣⠀ ⠀⠀⠀⠀⢩⢰⠏⡟⠀⠀⠸⣇⣿⠀⠀⠐⢿⡄⠀⠀⡀⢜⠛⣿⠷⣦⣤⣀⣀⠺⠞⠀⠀⠀⠻⡍⢑⡇⠀⠀⢸⠀⡈⢂⠀⠘⣄⠯⣯⣇ ⠀⠀⡀⢀⣿⣸⢸⠃⠀⠀⢰⣿⣿⡂⠀⢠⠈⢿⣄⣀⣵⣞⣯⣽⣶⡿⠈⢩⡯⠙⠓⠲⠤⣄⣀⣹⢼⠀⠀⠀⢸⠀⢣⠘⡄⠀⠘⣧⠘⡎ ⠀⠀⣰⠏⣿⣿⣾⠀⠀⠀⠘⢸⣝⣇⡆⠀⢳⠠⡀⠈⠉⠛⠿⠉⠁⠀⠀⠙⣷⡀⠀⠀⢀⠠⣝⢻⡿⢶⣦⣤⣼⠀⠈⡆⠘⡄⠀⠘⡆⠑ ⢠⠜⠁⠀⣿⣿⡇⠀⠀⠀⠀⣸⠘⡿⣾⡄⠈⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠤⣼⣬⣷⣛⣥⣶⢾⠟⡏⣿⡆⠀⢣⠀⠸⡀⠀⠧⠀ ⠋⠀⠀⠀⢸⣹⠇⠀⠀⠀⠀⡜⢸⠛⠮⡻⡦⢬⡦⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢟⡿⢋⡖⣼⠃⡇⢳⡀⠈⢧⠀⠙⡀⠀⠀ ⠀⠀⠀⠀⠀⣹⠀⡠⠀⡐⢠⠇⠸⠀⢀⡟⢻⡷⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠗⢋⡠⣾⠊⣿⡀⣧⣈⣷⡀⠀⢣⠀⠘⢆⠀ ⠀⠀⠀⠀⢀⡇⢀⡇⢠⠇⣾⠀⡇⠀⡎⡇⢸⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣶⠯⠚⠁⠀⢿⢇⡇⠀⣨⡿⠢⣄⠑⣄⠈⠃ ⠀⠀⠀⠀⢹⠀⢸⠀⡎⢸⠃⢸⠀⠀⢡⣧⡟⣇⠀⠀⠈⠲⣄⣀⣀⣳⠞⢯⡉⣏⣹⣏⣁⣿⠶⠚⠋⠉⠛⠻⣷⠀⠰⣅⠒⢌⣷⡞⢷⡄ ⠀⠀⠀⠀⡟⠀⡜⡜⢠⠏⢀⡏⠀⠀⢸⣿⠙⣎⢳⡀⠀⢠⣀⡭⠴⡋⠓⢄⡙⠼⡿⠉⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⣆⡀⠘⣧⢸⡟ ⠀⠀⠀⢸⠃⢰⠋⢠⡏⠀⡞⢀⣀⣠⠾⣌⣽⢟⢿⢳⣄⣼⣷⣶⢶⡀⠑⠄⠉⢨⠇⢺⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸⡏⠒⠤⠀⢀⣿⣸⠁ ⠀⠀⠀⡏⠀⠇⣠⠾⠋⠉⠉⠉⠉⠀⠀⠈⣮⣯⣽⠀⣯⣿⣿⡽⠜⠁⠀⠀⢀⣿⣤⣸⡀⢀⡇⠀⠀⠀⠀⠀⠀⠈⣧⠂⠀⠀⣼⡿⠁⠀ ⠀⠀⢸⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠗⠷⠅⡏⠀⠀⠀⠀⣰⣿⠷⣮⣿⣷⡾⣀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢸⣹⠁⠀⠀ ⠀⠀⠉⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⣧⡀⠈⡷⢤⡤⠴⠚⡹⣿⠠⠈⠙⠛⢟⢾⣯⡷⣖⢦⣦⣄⣀⣀⣹⣶⣆⠉⠀⠀⠀
⠄⠄⢿⣇⠄⠄⠘⣆⢀⣼⣿⣿⣿⣿⢿⡿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⢧⡲⣿⢷⢦⡀ ⠄⠄⠈⣿⠄⠄⠄⢙⢞⢿⣿⢹⢿⣦⢏⣱⢿⠘⣿⣝⠹⢿⣿⡽⣿⣿⣏⣆⢿⣿⡞⠁ ⠄⠄⠄⢻⡀⠄⠄⠈⣾⡸⡏⢸⡾⣴⣿⣿⣶⣼⣎⢵⢀⡛⣿⣷⡙⡻⢻⡴⠨⠨⠖⠃ ⠄⠄⠄⠈⣧⢀⡴⠊⢹⠁⡇⠈⢣⣿⣿⣿⣿⣦⣿⣷⣜⡳⣝⢧⢃⢣⣼⢁⠘⠆⠄⠄ ⠄⠄⠄⠄⢹⡇⠄⣠⠔⠚⣅⠄⢰⣶⣦⣭⣿⣿⣿⡿⠟⠿⣷⡧⠄⣘⣟⣸⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⢷⠎⠄⠄⠄⣼⣦⠻⣿⣿⡟⠛⠻⢿⣿⣿⣿⡾⢱⣿⡏⠸⡏⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠸⡄⠄⡄⠄⣿⢧⢗⠌⠻⣇⠿⠿⣸⣿⣿⡟⡐⣿⠟⢰⣇⠇⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⣠⡆⠄⠃⢠⠏⣤⢀⢢⡰⣭⣛⡉⠩⠭⡅⣾⢳⡴⡀⢸⣿⡆⠄⠄⠄⠄ ⠄⠄⠄⢀⣶⡟⣽⠼⢀⡕⢀⠘⠸⢮⡳⡻⡍⡷⡆⠤⠤⠭⢸⢳⣷⢸⡟⣷⠄⠄⠄⠄ ⠄⠄⣴⣿⢫⢞⣵⢏⡞⠄⢸⠄⣛⣗⠩⠄⣰⣚⠒⠂⣀⡀⢸⢸⣿⣧⠇⡼⣧⠄⠄⠄ ⢠⣾⢟⡴⢫⡾⣱⢟⠄⠄⢸⠄⢈⡓⡮⡦⡬⠽⡠⠄⠔⠄⢸⠈⣿⣿⡄⣷⢹⣆⠄⠄ ⡿⢁⠞⢀⣿⢣⠇⣿⠄⠄⠸⢀⢳⢣⣗⣿⡇⡔⠄⠔⠄⠄⢠⠄⠹⣿⣷⡝⣧⢻⣆
⣿⣿⣿⣿⣿⠟⠋⠄⠄⠄⠄⠄⠄⠄⢁⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⡀⠭⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠄⢀⣾⣿⣿⣿⣷⣶⣿⣷⣶⣶⡆⠄⠄⠄⣿⣿⣿⣿ ⣿⣿⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠄⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣇⣼⣿⣿⠿⠶⠙⣿⡟⠡⣴⣿⣽⣿⣧⠄⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⣟⣭⣾⣿⣷⣶⣶⣴⣶⣿⣿⢄⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⡋⠘⠷⣦⣀⣠⡶⠁⠈⠁⠄⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣍⠃⣴⣶⡔⠒⠄⣠⢀⠄⠄⠄⡨⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡘⠿⣷⣿⠿⠟⠃⠄⠄⣠⡇⠈⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⡿⠟⠋⢁⣷⣠⠄⠄⠄⠄⣀⣠⣾⡟⠄⠄⠄⠄⠉⠙⠻ ⡿⠟⠋⠁⠄⠄⠄⢸⣿⣿⡯⢓⣴⣾⣿⣿⡟⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣿⡟⣷⠄⠹⣿⣿⣿⡿⠁⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⣸⣿⡷⡇⠄⣴⣾⣿⣿⠃⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⣿⣿⠃⣦⣄⣿⣿⣿⠇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⢸⣿⠗⢈⡶⣷⣿⣿⡏⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄
⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
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⠀⠀⡤⠒⠊⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠙⠛⢿⢿⠿⡿⢷⠼⠷⡄⠀⠀⠀⠀⠀ ⢠⠎⠀⠀⠀⠀⠀⠀⢸⠷⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠿⠿⠿⠏⠾⡋⡡⠼⠿⠿⠿⡦⡴⠖⠒⠒ ⠃⠀⠀⠀⢀⠤⠶⠴⠿⠿⠿⠶⠶⡆⠀⠀⠤⠴⠶⠚⠛⠉⠉⡩⠟⠛⠉⠉⠙⢟⠻⠿⠶⠾⠿⠿⠿⠿⡗⠴⠿⠟⡼⢿⠿⡇⡇⠀⠀⠀ ⠀⠀⠀⢀⠾⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠉⠓⠀⢄⠉⠻⢿⠿⠿⠷⠄⠿⠿⠇⠀⠀⠀ ⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⢻⠿⠿⠿⠿⠿⠿⠿⠿⠿ ⠀⠀⠀⢻⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠈⠻⠿⠿⠿⠿⠿⠿ ⠀⠀⢠⠿⠿⠿⠿⡿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⢿⠿⠿⠿⠿ ⠀⠀⠿⠿⠿⠿⡟⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢻⠿⠿⠿ ⠀⠿⠿⠿⠿⡿⠀⠀⠀⢀⠤⡴⠶⢲⠞⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓⠶⠦⠤⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⢿⠿⠿ ⠀⢸⠿⠿⠿⠇⢰⠀⠈⠁⠀⢀⡴⠋⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠈⠉⠂⢳⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠿⠿ ⠀⠀⠻⠿⠿⠀⢸⠸⠀⠀⠠⠏⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⡷⡀⠘⡄⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠿⠿ ⠀⢀⡴⠉⠿⠀⠘⡏⠀⠼⠃⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⡇⠻⠄⠘⠤⡈⢧⠈⠢⠄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢠⠀⠧⠿⠿ ⢀⡾⠁⠀⡇⠀⠀⠇⠼⡧⠴⠶⠶⢤⠤⠄⠀⠹⠄⠀⠀⠀⠀⢳⠀⠈⠳⢨⠻⠿⢦⠄⠙⢟⡲⢤⠄⡀⠀⠘⢦⡀⠀⠀⠀⠀⠇⢹⠿⠿ ⠼⠁⠀⢸⡇⠀⠀⢏⠀⠀⠀⠀⠸⠿⢟⠉⠳⡄⠈⠣⡀⠀⠀⠈⠦⠤⠤⠤⠤⠭⠳⡈⠙⠢⢽⠦⠄⡏⠉⠒⠒⠉⠆⠀⠀⠀⢸⡼⠿⠿ ⠳⢦⠄⠸⠇⠀⠀⠠⠟⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠈⠳⢦⠀⠹⠄⠀⠀⡀⠴⠾⠿⠿⠦⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠙ ⢀⡞⠁⢹⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠉⠉⠛⠢⠤⠄⡼⠇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠀ ⠏⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⠀ ⠦⠀⡀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢀⠴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠿⢷ ⠁⠈⠙⠿⡇⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⠴⠚⠡⠴⠋⠸⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⡇⡿⠻ ⠀⢀⡼⢁⠿⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠿⠼⠿⡇⠀ ⠠⡞⠁⢸⠿⡄⠀⠀⠀⠙⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠾⠿⠁⠀⠀⠀⠀⢀⠀⢀⡾⠿⠿⠿⠦⡀ ⠹⠁⠀⢸⠟⠇⠀⠀⠀⠀⠀⡄⠉⢳⠦⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠿⠿⠿⠇⠀⠀⠀⠀⠠⠎⢀⠾⠷⠹⠯⡟⠿⠿ ⠇⠀⠀⡾⠀⢻⡄⠀⠀⠀⠀⠿⡄⢸⠿⠿⠿⠿⠿⠿⠷⠶⠆⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⡴⠋⠠⠾⠿⠿⠿⠿⡅⠀⠀ ⠀⠀⠼⠁⠀⠀⢷⠀⠀⠀⠀⢹⠷⠸⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠠⠞⢁⠴⠿⠿⠿⠧⡿⠀⢻⠦⠀ ⠠⠞⠁⠀⠀⠀⠈⢣⡀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⡿⠛⠏⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⢀⠠⡾⢋⠴⠿⠿⠿⠿⠿⡿⠁⠀⠀⠙⠷
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⡿⠉⠄⠄⠄⠄⠈⠙⠿⠟⠛⠉⠉⠉⠄⠄⠄⠈⠉⠉⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿ ⠁⠄⠄⠄⢀⡴⣋⣵⣮⠇⡀⠄⠄⠄⠄⠄⠄⢀⠄⠄⠄⡀⠄⠄⠄⠈⠛⠿⠋⠉ ⠄⠄⠄⢠⣯⣾⣿⡿⣳⡟⣰⣿⣠⣂⡀⢀⠄⢸⡄⠄⢀⣈⢆⣱⣤⡀⢄⠄⠄⠄ ⠄⠄⠄⣼⣿⣿⡟⣹⡿⣸⣿⢳⣿⣿⣿⣿⣴⣾⢻⣆⣿⣿⣯⢿⣿⣿⣷⣧⣀⣤ ⠄⠄⣼⡟⣿⠏⢀⣿⣇⣿⣏⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣟⣿⣿⣿⣿⣏⠋ ⡆⣸⡟⣼⣯⠏⣾⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⡟⠸⠁⢹⡿⣿⣿⢻⣿⣿⣿⣿⠄ ⡇⡟⣸⢟⣫⡅⣶⢆⡶⡆⣿⣿⣿⣿⣿⢿⣛⠃⠰⠆⠈⠁⠈⠙⠈⠻⣿⢹⡏⠄ ⣧⣱⡷⣱⠿⠟⠛⠼⣇⠇⣿⣿⣿⣿⣿⣿⠃⣰⣿⣿⡆⠄⠄⠄⠄⠄⠉⠈⠄⠄ ⡏⡟⢑⠃⡠⠂⠄⠄⠈⣾⢻⣿⣿⡿⡹⡳⠋⠉⠁⠉⠙⠄⢀⠄⠄⠄⠄⠄⠂⠄ ⡇⠁⢈⢰⡇⠄⠄⡙⠂⣿⣿⣿⣿⣱⣿⡗⠄⠄⠄⢀⡀⠄⠈⢰⠄⠄⠄⠐⠄⠄ ⠄⠄⠘⣿⣧⠴⣄⣡⢄⣿⣿⣿⣷⣿⣿⡇⢀⠄⠤⠈⠁⣠⣠⣸⢠⠄⠄⠄⠄⠄ ⢀⠄⠄⣿⣿⣷⣬⣵⣿⣿⣿⣿⣿⣿⣿⣷⣟⢷⡶⢗⡰⣿⣿⠇⠘⠄⠄⠄⠄⠄ ⣿⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡟⢀⠃⠄⢸⡄⠁⣸ ⣿⠄⠄⠘⢿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢄⡆⠄⢀⣪⡆⠄⣿ ⡟⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣻⣩⣾⣃⣴⣿⣿⡇⠸⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⢀⠀⣀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣠⣾⢶⣶⣶⣯⡢⡀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣠⣾⣿⡇⡏⠉⣾⣿⡻⢮⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠫⠉⢭⣾⣿⣾⡄⠙⢦⣄⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣠⡾⢟⣛⣯⠥⠤⠀⠒⠒⠒⠒⠶⠦⠭⣝⣒⡚⠷⣤⡀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⡵⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⡿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢜⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⢸⠋⠉⠁⢒⠒⠚⢻⠒⠉⠉⠉⢡⡇⠀⠀⢨⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⢰⠀⡆⣀⣀⣀⡀⠁⡕⠘⡆⢀⣀⣄⣀⡣⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠜⢀⠈⡦⢾⠛⣻⣿⣿⠁⠙⠀⢩⢙⣿⣯⡏⠻⢲⠀⢠⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠎⠀⣿⠘⠀⠻⠙⠃⠀⠀⠀⠀⠎⠛⠙⠀⢀⣼⠀⠈⠂⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⠀⠀⠀⠀⡏⢢⠀⠀⠀⠀⠀⠀⠀⠀⠪⣂⠀⢀⢾⢿⠀⠀⠀⠀⣇⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠀⠀⠀⡀⣿⣤⣷⣀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣰⣇⣸⠀⠀⠀⠀⢹⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⠀⡆⠀⡇⣿⠇⠈⠙⣿⡖⠤⣀⣀⡠⠴⣾⠛⠉⠀⡾⢰⠀⠁⠀⣾⣿⣟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣿⣿⢀⢰⠀⣷⠸⠀⠀⣰⢻⣟⠲⠤⠤⢴⣞⡿⢳⠀⠀⣙⣼⠀⡇⣴⣿⣿⡟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣾⣄⠸⣶⠀⢠⣏⠈⢿⣷⠀⠀⢽⣿⠇⠘⣇⠀⢡⣃⣴⣷⣿⣿⡿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⠿⣿⣿⣿⣆⣸⣿⡦⣄⠉⠀⠀⢉⣀⡴⣾⣿⣠⣟⣿⣿⡿⠿⣟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⣔⢍⡛⠧⣀⡈⠉⠭⠷⠦⣄⠀⣹⣿⠴⠿⠯⠭⠍⠀⠉⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⡗⠪⣑⠢⣍⠓⠦⣄⡀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡹⠀⠀⠉⠒⢍⠒⢤⣉⠛⠲⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠇⠀⠀⠀⠀⠀⠑⢆⠈⠙⠒⠶⣤⣈⡉⠙⠛⠲⠶⢶⣤⣤⣀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠙⠓⠶⢦⣤⣀⡀⠈⠉⠉⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡴⠁⠐⠆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⡍⠑⠒⠒⢶⡏⠀⣀⣧⣼⣇⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⠻⢹⢿⣻⣿⣿⠟⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⠀⠀⢨⣷⣆⠐⣶⠿⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠃⠀⠀⠀⠀⠀⠘⡗⠒⠒⠒⠒⠁⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⠍⠙⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⣿⣿⣿⣿⣿⣿⣿⠁⠈⢀⡤⢲⣾⣗⠲⣿⣿⣿⣿⣿⣿⣟⠻ ⡀⢙⣿⣿⣿⣿⣿⣿⢀⠰⠁⢰⣾⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⡄ ⣇⢀⢀⠙⠷⣍⠛⠛⢀⢀⢀⢀⠙⠋⠉⢀⢀⢸⣿⣿⣿⣿⣿⣷ ⡙⠆⢀⣀⠤⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⣿⣿ ⣷⣖⠋⠁⢀⢀⢀⢀⢀⢀⣀⣀⣄⢀⢀⢀⢀⢸⠏⣿⣿⣿⢿⣿ ⣿⣷⡀⢀⢀⢀⢀⢀⡒⠉⠉⢀⢀⢀⢀⢀⢀⢈⣴⣿⣿⡿⢀⡿ ⣿⣿⣷⣄⢀⢀⢀⢀⠐⠄⢀⢀⢀⠈⢀⣀⣴⣿⣿⣿⡿⠁⢀⣡ ⠻⣿⣿⣿⣿⣆⠢⣤⣄⢀⢀⣀⠠⢴⣾⣿⣿⡿⢋⠟⢡⣿⣿⣿ ⢀⠘⠿⣿⣿⣿⣦⣹⣿⣀⣀⣀⣀⠘⠛⠋⠁⡀⣄⣴⣿⣿⣿⣿ ⢀⢀⢀⠈⠛⣽⣿⣿⣿⣿⣿⣿⠁⢀⢀⢀⣡⣾⣿⣿⣿⡟⣹⣿ ⢀⢀⢀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣦⣤⣶⣿⡿⢛⢿⡇⠟⠰⣿⣿ ⢀⢀⢀⢀⣿⣿⣿⡿⢉⣭⢭⠏⣿⡿⢸⡏⣼⣿⢴⡇⢸⣿⣶⣿ ⢀⢀⢀⢰⣿⣿⣿⢃⣶⣶⡏⠸⠟⣱⣿⣧⣛⣣⢾⣿⣿⣿⣿⣿ ⢀⢀⢀⣾⣿⣿⣿⣾⣿⣿⠟⢻⡿⡉⣷⣬⡛⣵⣿⣿⣿⣿⣿⣿ ⢀⢀⣸⣿⣿⣿⣿⣿⣿⡿⢰⠘⣰⣇⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⠘⢿⣿⣿⣿⣿⣿⡷⢺⣿⠟⣩⣭⣽⣇⠲⠶⣿⣿⣿⣿⣿ ⢀⠐⢀⣾⣿⣿⣿⣿⠟⢐⡈⣿⣷⣶⠎⣹⡟⠟⣛⣸⣿⣿⣿⣿ ⠠⢀⣼⣿⣿⣿⣿⣯⣼⣿⣷⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣤⣤⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣴⣤⣤⣤⣴⣾⣿⣿⣿⣿⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠠⠾⢿⣿⣿⠟⠋⠁⠤⣬⣽⣿⡇⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⡄⠄⠄⢀⣽⣦⡎⠁⠒⠒⢻⣿⣿⣄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⢀⣧⡀⢀⣾⣿⣿⣧⣦⣴⣾⣿⣿⣿⣿⣧⠄⠄⣠⣴⣆⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡻⣿⣿⣿⣿⣧⢸⣿⣿⣿⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣝⣿⡟⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠸⣄⢺⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⢿⠄⡀⠄⣸⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠸⡆⠄⣀⣛⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠇⠄⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠐⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠿⠽⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠄⠄⠄⠄⠄⠄ ⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⣿⣿⡿⠟⠛⠉⠄⠄⠄⠄⠄⠄⠄⠄
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⢻⣕⢯⢿⣯⡷⣹⣿⣿⣦⠹⣿⡆⢿⣿⡄⡆⢿⣿⣷⣿⣇⣿⣿⣿⣿⣸⣿⣿⣿⣿⡟⣰⠟⠛⠻⢿⣴⣿⠏⣴⣿⣟⣾⠟⢀⣵⣿⣿⣿ ⢷⣝⢷⣱⣟⣿⠋⣌⢿⣿⣷⡹⣿⣬⣿⠿⠿⣛⣛⣉⣭⣭⣭⣭⣭⣭⣝⣛⡻⠿⢿⣴⡟⠀⠀⠀⢸⡿⢣⣾⣿⠟⠛⠙⠛⠛⢷⣿⣿⣿ ⠙⠻⣷⣏⣿⢣⠁⢻⣷⡙⡿⢟⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡇⠀⠀⠀⣾⣵⣿⡟⠀⠀⣴⣶⣦⠀⠀⠙⣯⣵ ⣿⣿⣍⣿⢣⠉⠀⠶⣿⣷⠐⣿⣿⣿⡿⣿⣿⣿⣿⣿⣻⣿⣿⠿⢿⣛⣛⣭⣭⣭⣶⣶⡇⠀⠀⣸⣧⣭⣽⣇⠀⠀⢸⣿⣿⠁⠀⠀⣿⣿ ⡙⠿⣿⠇⠆⠀⢀⣾⣾⡝⠇⢿⣿⡿⣕⣪⣿⡿⢟⣛⣭⣵⣶⣿⣿⣿⣿⣿⡿⠿⠿⢻⡇⠀⢠⡟⠀⠀⠀⠈⡳⠶⣳⠞⠁⠀⠀⣰⣿⡿ ⣿⣷⡿⠀⠀⠀⢸⣿⣿⣿⢮⣿⣷⡿⢟⣫⣵⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⢸⡇⠀⣾⡀⠀⠀⠀⠀⡀⡼⠁⠀⣀⣴⡾⣟⡭⠖ ⠿⣿⡇⠀⠀⠀⣿⣿⡿⢏⡾⢟⣥⣶⣿⡯⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠤⠶⠂⠘⣴⠞⠂⠸⣯⢈⠄⡀⠎⡐⣸⠇⠀⣼⣵⡟⢻⣡⣴⣾ ⣬⣿⢰⣀⣀⣤⣾⠶⠞⣭⣾⣿⣿⣿⠟⠋⠁⠀⠀⢀⠀⠀⠀⠩⠁⠀⠞⣈⣷⠐⣯⠀⠀⠀⣽⠂⣾⣿⣦⣴⠛⠁⠘⣯⠻⣿⣿⣿⣿⣿ ⢾⡇⣾⣿⠟⢩⣾⣿⣿⠇⢬⠛⠋⠀⠀⠀⢠⣤⠄⠀⠀⠀⣿⡶⡤⠀⢀⠻⢿⠀⢸⠳⠶⠞⣷⡀⠛⠿⠿⣯⡀⠀⠀⡼⢷⡹⣿⣟⣛⣩ ⣿⢸⣿⠟⠀⠀⠨⣶⠷⠀⡈⠃⢀⡀⠠⠚⣿⣿⠁⡀⢠⠀⠨⠁⠄⠀⠨⠈⠂⠀⢸⡌⠀⡀⣿⣧⠀⠁⠀⢎⡛⠛⠛⠡⠀⢳⠹⣿⣿⣟ ⣿⠘⣡⣾⡀⡀⠀⣁⣀⣤⣑⠀⠈⠁⠈⠊⠂⠀⠀⣇⣿⠀⠀⣀⣀⣀⣤⣤⣤⣤⣼⣥⣤⣥⠿⢿⠆⠀⠁⠁⠈⠀⠀⠀⠀⠀⠃⢻⣿⣿ ⢣⣾⣿⡿⠋⢀⡘⠻⠟⠛⠁⠀⠀⣀⡤⣀⣤⣶⣶⣬⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣮⡻⣶⡆⠀⠀⢠⣇⠀⢸⣿⣿ ⣿⠿⢁⠀⠀⢸⠀⣀⡀⠠⢰⢰⣿⣟⣾⣿⣿⣿⣿⣿⡿⠷⡽⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⡟⠋⠙⢸⡇⠀⢰⢸⣿⠀⢸⡿⠾ ⠁⠀⢸⠀⠀⣸⠀⠃⠀⠀⣿⡎⣿⢸⣿⣿⣿⣿⣿⣟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣇⠀⠀⣠⡇⠀⠘⣇⢿⠀⢸⡿⣿ ⠀⠀⠸⡀⠀⣿⠓⡇⢘⠿⠹⡿⡸⡼⣿⣿⣿⣿⣿⣿⣶⣤⣖⣿⣿⣿⣿⣿⣿⣿⣿⡘⢿⣿⣿⣿⣿⣿⣿⣟⣼⣇⠀⠀⠈⠪⡠⣿⣿⣿ ⠀⠈⠀⢇⠀⢻⠀⡀⠈⢇⠀⠐⠱⡑⣌⡻⣿⣿⣿⣿⠿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⣛⣛⣛⣻⣵⣿⣿⣿⣶⠲⠂⣆⢦⣤⣉⣻ ⠁⠀⠀⠘⡄⢸⠀⠠⠀⡐⠘⢀⣀⣌⣌⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⡘⣿⣿⣿ ⠀⠀⠀⠀⠐⠘⡄⠀⠀⠠⠅⡈⠉⢩⠉⠉⣤⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⡇⣿⠛⠿ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡀⠀⠀⢡⠁⢌⢻⣿⣿⣿⣿⢏⣦⣭⣭⣮⣭⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⡇⢸⡷⢦ ⠀⢀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠁⢀⠀⠀⠂⠔⢡⠹⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠿⢛⠁⠀⠀⠀⠀⠀⠀⡇⣼⣛⠷ ⢀⠄⠀⣼⣄⣀⣀⡀⠰⡄⠀⠀⠀⡠⠀⠀⣁⠡⠂⢻⣿⣿⣦⣍⡻⠿⠿⢟⣡⣿⡿⠿⠿⢛⣛⣭⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⡇⣿⢿⣿ ⠘⠀⢰⣿⣿⣿⣿⣿⣄⣿⡄⠀⠀⢃⠀⠀⠸⢤⠈⡀⢭⣩⣭⣭⣭⣉⠭⣶⢠⣶⢶⢄⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢰⣿⣷⣎ ⣶⣤⣼⡿⣟⣽⣿⣿⣿⣿⣧⣤⣤⣤⡤⠀⣀⡁⠐⠀⢠⣙⠛⠛⠟⠛⠫⢦⠞⣩⣽⣮⡻⣿⣶⣮⣭⣛⣛⣛⢿⣿⣿⢋⣶⣶⣎⢿⣿⣿ ⣾⣛⢇⣫⣿⣿⢫⣶⣶⡝⣿⢟⣋⣥⣶⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⢟⣧⣬⢱⣮⣝⣿⣿⡸⣿⣿⣿⣿⣿⣿⡎⣛⠟⡨⢹⠻⣋⣾⣿⣯ ⠀⣱⣾⣿⣿⡿⡘⠿⠿⡣⠁⠿⢻⣿⣿⣿⣿⣿⣿⣿⠏⡀⢺⣿⢱⣿⣿⡟⣄⠻⣿⣷⡹⣧⠹⣿⣿⣿⣿⣿⡇⣿⠺⣥⡰⣵⣟⣮⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⣿⣷⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⣿⣇⣿⣀⠸⡟⢹⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣿⣿⣿⡇⠝⠋⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠊⣽⣿⣿⣿⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⠀⢠⣴⣿⣿⣿⠋⣠⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣟⡻⠉⠀⠀⠀⠈⢿⠋⣿⡿⠚⠋⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⡄⠀⣳⡶⡦⡀⣿⣿⣷⣶⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⡇⡿⠉⣺⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⠽⢲⠇⠣⠐⠚⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡐⣾⡏⣷⠀⠀⣼⣷⡧⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣮⠳⣿⣇⢈⣿⠟⣬⣿⣿⣿⣿⣿⡦⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣾⣿⣿⣿⣿⣿⣿⣿⣷⣜⢿⣼⢏⣾⣿⣿⣿⢻⣿⣝⣿⣦⡑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⡷⣥⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣤⣾⣿⣿⡿⠻⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣮⣾⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⡿⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⣫⣿⣿⣿⠋⠀⠀⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢘⣿⣿⣟⢦⡸⠀⠀⠀ ⠀⡰⠋⣴⣿⣟⣿⠃⠀⠀⠀⠈⠀⠀⣸⣿⣿⣿⣿⣿⣿⣇⣽⣿⣿⣿⣿⣇⠀⠀⠀⠁⠸⣿⢻⣦⠉⢆⠀⠀ ⢠⠇⡔⣿⠏⠏⠙⠆⠀⠀⠀⠀⢀⣜⣛⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⡇⡇⠹⣷⡈⡄⠀ ⠀⡸⣴⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡇⡇⠀⢻⡿⡇⠀ ⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⠿⠤⠒⡛⢹⣿⠄ ⠀⣿⣷⡆⠁⠀⠀⠀⠀⢠⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⢷⡀⠀⠀⠀⠀⠀⣸⣿⠀ ⠀⠈⠿⢿⣄⠀⠀⠀⢞⠌⡹⠁⠀⠀⢻⡇⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢳⠀⠀⠁⠀⠀⠀⠀⢠⣿⡏⠀ ⠀⠀⠀⠈⠂⠀⠀⠀⠈⣿⠁⠀⠀⠀⡇⠁⠀⠘⢿⣿⣿⠿⠟⠋⠛⠛⠛⠀⢸⠀⠀⡀⠂⠀⠀⠐⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠕⣠⡄⣰⡇⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⣸⠠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣽⡋⠭⠶⠮⢽⣿⣆⠀⠀⠀⠀⢠⣿⣓⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢹⣶⣦⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣶⣾⠿⢿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⠘⠻⠿⢛⣛⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⠏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋ ⠀⠀⠀⠈⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⠿⠿⠿⢿⣿⡿⠿⢿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣤⡾⠛⠉⠉⠉⠴⠖⠀⠀⠀⢀⣬⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠙⠿⣷⡶⠯⠭⢽⣭⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿ ⢄⠀⠾⢛⣩⣽⠟⠛⠛⠿⣶⣾⣿⠻⣿⣿⣿⣴⣿⠀⠀⠺⣷⠀⠀⣴⢰⠄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠉⠉⠙⠻⠿⠟⠻⢶⣭⣛⠿⣿⣿ ⣧⣴⡿⠛⠛⠀⠀⠀⠀⠀⣸⣿⣇⣄⢹⣿⡿⢫⣤⠄⠀⠀⠀⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣀⣀⠀⠀⠀⠙⣿⣄⠀⠀⢀⣠⣤⡶⣦⣬⣉⠛⢾⣝ ⠉⢀⠔⠂⠀⣀⣀⣀⡀⣰⣿⣿⣿⣿⣿⣿⡇⢸⣿⡀⠲⢶⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠛⠋⠉⠉⠛⢷⣦⣷⠀⠘⣿⠷⠞⠋⠁⠀⣠⣴⣮⣭⣤⣤⡍ ⠀⠈⣠⡀⠸⡟⠁⠉⠙⢻⠟⠉⠉⠉⠛⠿⢷⣤⣜⠿⠷⠆⣴⣾⣦⠀⠀⠤⠀⠷⠄⠀⣀⣤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣤⣿⠀⠀⠀⢀⣼⡿⣿⣿⡿⠉⠁⠀ ⠄⠀⠈⠻⠦⢻⣆⠀⢠⡞⠃⠀⣀⠀⠀⠀⠀⠀⠙⠳⣤⣴⣆⠁⠀⠐⣀⣡⣤⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣹⡇⠀⠀⢠⣿⣏⣾⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⡾⠁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⢸⣿⣿⠃⠀⢀⣿⣿⡟⣗⠀⠀⠀⠴⠀⠀ ⠀⠀⠀⠀⠀⠀⣐⣿⣄⠀⢠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⠛⠁⠀⢸⣿⡟⠀⣠⣾⡿⠋⢰⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣿⣇⠈⢻⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⠁⣴⡿⠋⡄⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣭⣭⣍⣛⢻⣿⣿⣿⣿⣿⣯⣵⣶⣶⣶⣾⣶⣶⣶⣤⡀⠀⠀⢸⣿⣿⠃⠀⠀⢀⣾⣿⠃⣼⣿⡵⠟⠀⣾⠟⠰⡄⠹⣦⡀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⠟⠉⠉⣽⣿⣿⣛⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣭⣵⡄⠈⠙⣿⣶⣄⣸⣿⠃⠀⣠⣶⠿⠿⠷⣴⠟⠁⠀⠀⣰⡏⠸⢦⣽⣦⡘⢿⣤⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠘⣿⣿⡄⠀⠀⠻⢿⣿⣿⡿⠁⠉⣿⣿⣇⠀⠀⠘⠿⠿⠿⠿⠁⠀⠀⣼⣿⣿⠟⠁⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠠⣾⣿⣧⣤⣄⣉⢋⠁⠀⠹⣦ ⣿⣿⣿⣿⣿⣿⠟⠁⠉⠙⠶⠶⣄⣈⣻⣿⣦⣀⠀⣀⣀⣀⡴⠶⠞⠛⠋⠙⠛⠶⠶⠶⠦⢄⣤⣀⣤⡾⠿⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠟⠋⠉⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⢉⣀⠀⠀⠀⠀⠀⠀⣀⣭⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣶⣤⣀⣧⣴⣶⣤⣴ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠳⠀⠀⠀⠀⠘⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⣿⣿⣿⣿⣿⣿⣯⣀⡈⣹ ⣿⣿⣿⣿⣿⣿⡀⠈⠙⢶⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿ ⣿⣿⣿⣿⡿⠛⢡⡄⠀⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠃⢠⠚⣷⡀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⡾⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡀⢺⠀⠹⣿⡄⠀⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣠⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣧⢸⣆⠀⠸⣿⣄⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⢉⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⣿⣿⡄⡝⠀⠀⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠋⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⠟⠛⠁⢀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿ ⢻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢈⡛⠛⠿⠿⣿⣿⡷⠶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣾⣿⠿⠟⠛⠉⠉⠀⠀⢀⣤⡶⣛⣵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠷⣤⡄⠈⠉⠉⠓⠦⠤⠤⠖⠛⠛⠒⠋⠉⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⣁⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⡿⠛⠉⢁⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠉⠛⢻⣿⣶⣶⣶⣶⣶⣿⣟⡛⣻⣿⣿⣿⣤⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠋⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⠃⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣮⣽⣿⣿⣿⣿⣿⣯⣭⣭⣿⣢⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠋⠙⣉⠛⣛⣿⣿⣿⠟⠛⢧⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⠯⠄⠀⠀⠀⠀⣦⣤⣽⣿⣟⣗⣄⠈⢣⡗⠀ ⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⡴⠚⠉⠀⢀⣤⣬⣬⣿⣿⣿⠹⣿⡇⠀⣿⠀ ⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⠋⠀⠀⢠⠴⠟⣛⣿⣿⣿⣿⣿⣶⣾⣰⡀⢹⡢ ⠀⠀⠀⠀⠀⣸⢾⠟⠻⣿⣿⠇⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⡟⢻⢻⣿⣿⣶⡇ ⠀⠀⠀⠀⢀⣾⣏⣐⡄⠀⣯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠄⠘⣿⣿⣿⣷⡅ ⠀⠀⠀⠀⢸⣤⣿⣿⠀⠀⣿⣷⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠇⣄⣀⠸⡾⣷⡄⡇ ⠀⠀⠀⠀⠈⠣⣃⡈⢉⣸⣿⡻⣿⣮⣴⣾⡏⢀⣽⣿⣿⣿⣶⣶⣶⣴⣇⣿⠀⣱ ⠀⠀⠀⠀⠀⠀⡏⡏⠁⣿⢿⣆⣿⣿⣿⣿⣧⣿⣿⣿⣛⣿⣿⣿⣿⡦⣾⡟⢠⣃ ⠀⠀⠀⠀⠀⠀⣧⡇⢠⡏⢂⢹⣿⣿⣿⣿⣿⣿⣿⣿⡷⣬⣭⣙⡛⢳⣼⣿⣿⣎ ⠀⠀⠀⠀⠀⢠⢿⠀⠘⣿⣧⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣥⣿⣿⢿⡿ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣸⣿⢻⡿⠀ ⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⠁⠀ ⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣜⡆⠀ ⣒⠶⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⣠⡟⠀⠀
N   O     O      o      o       o      o      。     。    .    .     .     .
⠀⠀⠀⠀⠀⠀⢰⣰⣿⠟⠛⠛⠻⠟⠙⠉⠉⠉⢿⣿⣿⣦⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣧⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣀⡀⠀⢠⣀⣀⣀⣀⠀⠘⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⢿⢸⣿⣿⣿⡆⢸⣿⣿⣭⣿⠇⠀⣿⡏⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡜⠈⠙⠛⢻⡇⠀⣈⠉⠉⠁⢠⠶⠟⢀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣷⣤⣬⠓⠄⡴⠏⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⣾⣿⣬⣿⣶⣤⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣴⠛⠿⠛⠚⠋⢙⣆⣠⡾⠉⣷⣭⣒⠂⠀⠀⠀⠀⠀ ⡠⠤⠒⠒⠒⠢⠤⣀⣀⣯⢻⣧⣴⣾⣷⣠⣾⣿⠟⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠈⣧⣀⠀⠲⣤⢼⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢉⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿ ⠦⢦⣄⣈⡛⢂⣀⣾⣶⣶⣿⡟⡻⢿⣿⣿⣿⣾⣶⡾⠁⠀⢸⣿⣿⡿⢿⣿⣿⣿ ⠄⠀⠸⣿⣿⣿⣿⡿⣿⣿⣿⡏⢳⣴⣿⣿⠿⢵⣿⠃⠀⠀⣾⠟⠁⠀⠀⠀⠈⠻ ⣦⡀⠀⣾⣿⣿⣿⡇⣿⣿⣿⣇⠘⣏⠀⡴⠆⣼⠇⠀⠀⠀⠛⣆⣠⡀⠀⠀⠀⣾ ⠉⠁⠠⣿⣿⣿⣿⠇⣿⣿⣿⡏⠀⢹⡄⠉⢻⡏⠀⠀⠀⡠⠞⣿⣿⣄⣠⣿⣿⣿ ⠀⠀⢠⣿⣿⣷⣶⣶⣶⣾⣿⣷⠀⠀⢻⣍⡟⠀⠀⡠⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⣯⠽⣥⣦⠶⠉⡘⠃⠙⡈⣭⣍⡙⠿⢛⣛⠓⠒⠶⢤⣀⠀⠀⠀ ⠀⠀⠀⣠⣿⣻⠼⣿⡿⣼⠃⠠⠀⠃⠀⠀⠀⠀⠛⠻⠜⠻⢄⠀⠀⠀⠻⣄⠀⠀ ⠀⠀⣰⣟⢧⢯⣛⣧⢿⣥⣣⣤⣤⣤⣜⠀⠀⠀⢰⡃⢀⣄⣄⣀⡀⠀⠀⢹⡄⠀ ⠀⣼⣟⡞⣯⣞⡽⢮⠿⠿⣿⣽⣿⣿⣿⣿⡶⠘⢿⣿⣯⣿⣿⠿⠟⠀⠀⠀⢻⡄ ⢹⣟⣾⣹⢳⣮⢽⣫⢟⣳⣶⣦⠀⣴⡿⣞⣳⠀⠘⣿⣦⡀⠀⠀⠀⠀⠢⣀⠀⣷ ⠃⣿⡶⣯⣟⢮⡗⣯⣾⣿⡻⣼⣟⢯⣿⣿⣿⣀⠀⢹⣿⣷⠀⠀⢰⣤⣤⣹⢄⡷ ⠀⠹⣷⣻⡽⣮⣷⣿⢿⣫⠷⣿⡝⡾⣿⢿⣿⣻⣶⣾⠟⠉⠲⡀⠘⢿⣭⢻⣼⠃ ⠀⠀⠘⣷⣻⣿⣿⡿⣿⠿⣿⠿⣿⢿⣟⡛⠿⠷⢶⣶⣦⣤⣤⣤⣤⣬⣿⣦⠏⠀ ⠀⠀⠀⠹⣷⣻⣧⢟⡮⣟⢾⣹⢎⡷⣎⡗⠀⣤⢀⡀⠀⠈⠁⠉⠀⠀⠘⣿⠀⠀ ⠀⠀⠀⠀⠈⠻⣽⣞⡵⣻⢮⡝⣯⢾⣹⡛⠒⠠⠄⠠⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⢳⣯⣾⣭⡏⡟⣿⡄⠒⢰⠀⢠⢰⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠿⡵⣿⣶⣦⣀⡀⠀⠀⣀⣀⡴⠋⠀⠀⠀ ⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀
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⣿⣿⣿⢿⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣽⣻⡽⢯⡿⣽⣫⡟⣽⣫⢟⣽⢫⡟⣽⢫⡟⣭⡻⣭⢻⡭⢯⡽⣭⢯⡽⣭⠻⣜⡣⢟⣜⡣⢟⡜⣣⢛⡜⣣⢛⡜⣣⢏⡼⣡⢏⡼⣡⢏⡼⣡⢏⡼⡱ ⣿⣷⣻⣟⣾⣳⢿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⡷⣯⣟⡷⣯⡽⣯⢷⣏⡷⣽⣣⢯⣟⢮⣯⢽⣚⡷⣹⢧⣻⡜⣧⣛⢧⡻⣜⢮⡳⣭⢻⡔⣏⡳⢎⡝⢮⠼⣱⢫⠼⣱⢫⡜⡱⢎⠶⡱⢎⠶⡱⢎⠶⡱⢎⠶⣙ ⣿⢿⣽⡾⣷⣟⣯⢿⡾⣽⣻⢾⣽⣻⢾⣽⣻⢾⣽⣻⣞⣯⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣽⣻⢾⣽⣻⢾⣽⢾⣯⢷⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⢯⣟⡷⢯⣟⡷⣻⣵⡻⣾⣱⢷⣫⠷⣞⢯⡞⣧⢟⡼⣏⢷⣣⢟⡵⣫⢞⡽⣎⢷⡹⣞⢣⡞⣱⢭⡛⡼⣙⡞⣥⣋⢗⣣⠳⣜⡹⢎⡳⣙⢎⡳⣙⢎⡳⣙⢮⡹⣒ ⣿⣯⣷⢿⣳⣯⣟⣯⡿⣽⢯⣿⢾⣽⣻⢾⣽⣻⣞⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢯⣷⣟⡿⣞⡿⣞⣯⡿⣞⣷⣻⣞⣷⣻⣞⣷⣻⣾⣽⣿⣾⣿⣿⣾⣿⣷⣿⣷⣯⣟⣾⣭⢿⡹⣾⣹⢮⣏⢷⣫⢞⡵⣫⢷⡹⣎⢷⡹⣎⠷⡭⢮⡕⣏⠶⣹⢱⢣⠞⡴⣩⠞⡴⣋⠶⣙⢮⡱⣍⢮⡱⣍⢮⡱⡍⢶⣑⢣ ⣿⡾⣽⡿⣽⡾⣽⣳⡿⣯⣟⣾⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣟⣾⣽⣻⡽⣟⣯⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣛⡾⣼⢣⡟⣮⢳⡝⣮⢳⡝⣮⠳⣭⢛⡼⢣⢞⡬⡳⣍⢎⢧⡛⡴⢣⡛⡴⣍⢞⡱⢎⡵⣊⠶⡱⢎⡖⣱⡙⢦⡍⡖ ⣿⣻⣽⣟⡷⣟⣯⡷⣟⡷⣯⢷⣻⣟⣾⣳⢯⡿⣽⢯⣟⡷⣯⢷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⣟⣯⡷⣯⣷⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣫⢞⡵⣏⢾⡱⢯⡞⡵⣛⢦⣛⡼⣍⠾⣰⠳⡜⣎⠶⡹⣜⢣⡝⡲⣍⢮⡱⢫⠴⣩⠞⣡⠳⡜⡥⣚⢥⡚⡜ ⣿⣽⣳⣯⣟⣯⡷⣟⣯⢿⡽⣯⢷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⢯⣷⣻⣞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣞⣯⢿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⡽⢮⡝⣧⡛⣵⡩⢖⣣⠞⣬⠳⣥⢛⡼⣌⢳⡱⢎⢧⡚⡵⣊⠶⣉⢧⢛⡤⣛⠴⣋⠼⡱⡜⣆⢧⡙ ⣿⢾⣽⡾⣽⣳⣟⣯⣟⣯⢿⡽⣯⣟⣯⢿⣽⣻⢾⣽⣻⢾⣽⣻⡞⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⢿⡽⣯⣟⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⢟⠶⣙⢦⡛⡵⢪⡝⢦⡛⡴⣋⠶⣩⢖⡹⢎⠶⡹⠴⣩⠞⡱⢎⡣⠞⡴⢋⡼⣡⠣⡵⣈⠦⣙ ⣿⢯⣷⣟⣯⡷⣯⣷⣻⣞⣯⣟⣷⣻⣞⡿⣾⣽⣻⢾⡽⣻⡞⣷⡻⢷⣛⣾⣳⣟⣾⣳⣯⡿⣽⢯⡿⣽⣳⣟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣿⢻⡽⢺⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⡹⣆⠻⣜⢣⠞⣥⢛⡴⣩⢞⡱⢎⡵⢋⡞⣱⢋⠶⣉⠷⡩⢞⡱⣘⠣⢖⡡⢓⡴⣉⠖⣡ ⣿⣻⢷⣻⡾⣽⢷⣯⢷⣻⢾⡽⣞⡷⣯⣟⣷⣳⢯⣟⢾⣳⢟⣳⣟⣯⣟⣾⣳⡽⣞⡷⣯⢿⡽⣯⣟⣷⣻⣞⣿⣿⣿⡟⢥⠲⡝⣾⣟⣿⣿⣻⣿⣟⣿⣯⢿⣞⣷⣻⣽⣚⠷⣘⢧⡚⡕⢦⢫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⢣⡭⢳⢬⢣⡛⡴⣋⠶⡱⢎⡵⢋⡜⣣⠞⡥⢫⡜⡱⢎⡱⢎⠴⢣⡙⢦⡙⢦⠱⣌⠚⡤ ⣿⣽⣻⢷⣻⢯⣟⡾⣯⣟⣯⢿⣽⣻⢷⣻⢮⣽⣳⢯⣻⣭⡟⣷⣞⣳⣞⡷⣯⢿⡽⣽⣏⣯⣟⣷⣻⣞⣷⣻⣿⣿⠫⠄⣉⣳⣽⣼⣿⣿⣿⢿⣟⣿⢯⣟⡿⣞⣷⡳⢞⡜⢢⠏⡖⡩⢞⡥⣛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⢞⡱⢎⢧⡙⢶⡩⢞⡱⣋⠶⣩⠞⣡⠞⣱⠣⡜⡱⢊⠖⡩⢎⡱⡘⠦⡑⢎⡱⢌⡓⡔ ⣿⢾⣽⣻⣯⢿⣽⣻⢷⣻⣞⣯⢷⡯⣟⣞⡿⣼⢏⣯⢷⣳⣻⣳⣞⢷⣫⣟⡷⣯⣟⢷⣻⢮⡽⣞⣷⡻⣞⣿⣿⠁⠳⢾⣧⣽⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣿⡝⣮⢞⡳⣎⠳⡵⢊⡴⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢮⠳⣍⠶⣙⢦⡙⣎⠵⣊⠗⡱⢎⡱⣊⠥⡓⣬⢱⡉⢎⡱⢊⠴⣡⠣⣙⠢⡑⠦⡱⢌ ⣿⢯⣟⡷⣯⣟⣾⡽⣯⢷⣻⣞⣯⣽⣻⣼⣛⣾⣛⡾⣏⡷⣏⡷⣞⣯⢷⢯⡽⣶⢯⣛⣧⢿⡽⣳⢾⣽⣻⣿⠃⢉⡷⣿⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡿⣯⢟⡞⣞⡳⣜⣫⡑⠳⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⢬⢳⡩⢖⡹⡸⡜⡡⢏⡕⢎⡱⣉⠖⡱⢢⠱⡘⠦⡑⣍⠲⢄⠳⣄⢣⡙⢆⡱⢊ ⣿⣯⢿⡽⣷⣻⣞⡿⣽⢯⣷⣻⢮⢷⣳⣳⠿⣜⣯⢷⣏⡿⣽⣹⢯⣞⣯⢯⣟⡾⣽⣛⣾⣫⡽⢯⣷⣫⣿⡟⢠⣯⣄⢿⣿⣿⣿⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡱⢦⡝⢳⡒⠦⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡱⣋⠶⣙⢎⡵⢱⠱⣙⠲⡘⢎⡱⢌⢎⡑⢣⠱⣡⢣⡑⠦⡙⣌⢃⢆⠣⡜⠢⣅⠣ ⣿⣞⣿⡽⣷⢯⡿⣽⣻⣟⡶⣯⢟⣯⣗⡯⣿⠽⣞⣯⢾⣝⡧⣟⡧⢿⣜⡯⢾⡽⣞⡽⣶⢏⣿⣛⡶⣯⣿⠇⠿⢱⣿⢸⣿⣿⣡⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⠧⡝⢲⠱⣌⡠⢘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠳⣍⢞⡱⢎⠴⣋⢜⣢⡙⡱⢣⠜⡌⠦⣙⢂⠳⡐⠦⣑⢣⠱⡌⠎⡜⢢⡑⢣⠆⢣ ⣿⡾⣽⣻⡽⣯⣟⣷⣻⠾⣝⣳⣟⣞⡾⣽⢞⡿⣽⣺⣝⣮⡽⣞⡽⣏⡾⣝⣯⠾⣽⣹⢞⣟⣮⢿⣱⢯⣿⠀⣐⡊⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣜⢣⠷⢤⡡⠉⠆⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣊⢮⡱⢍⡲⢩⡒⢤⢣⡑⢣⠚⢬⡑⢢⢍⠲⣉⠖⡡⢎⠱⡘⡜⣠⠣⣘⢂⢎⡡ ⣿⡽⣷⢯⣟⣷⣻⢾⣽⣻⡽⣳⢾⣝⡾⣭⢿⣹⢧⢷⢾⣱⡟⡾⣵⢏⣷⢻⡼⣻⡵⢯⣾⣹⢮⣯⣻⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣶⣭⡞⢣⢏⣬⡱⡌⢒⡠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢲⠍⣦⠱⡎⡜⣡⠚⡔⢢⡙⢢⡙⢦⡘⢥⢊⠵⡨⠜⡐⢎⠱⡐⢆⡡⢒⡡⢊⠴⡐ ⣿⣳⣟⡾⣽⢯⣟⡾⣽⣫⢷⣻⣞⣽⣳⣛⣞⢯⣞⠾⣼⢏⣷⡳⡽⣞⡽⣞⢧⡿⣱⠾⣭⡟⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⢞⡩⣇⠣⠌⡑⢺⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⡑⢎⡴⢩⡒⢥⠣⣍⠲⣑⠪⡑⢎⡱⢨⠱⡌⢚⠤⢃⠲⡑⡌⢆⠓⡌⢃⠎⡱⠘⡄⢣ ⣿⡽⣞⡿⣽⣻⢾⣽⣳⢯⣟⡵⣞⣧⢷⡻⣼⢏⣾⢻⡽⣺⢧⢿⣹⢾⣹⡞⣯⠾⣝⡯⣗⢿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣖⣿⢯⢀⢒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡶⡷⣎⠷⣤⢓⡒⣩⢒⣿⣿⣿⣿⡟⡹⠋⢴⣆⡘⣿⣷⣏⢲⡘⢥⡙⢆⠳⣨⠱⠌⡥⣙⠢⣅⠣⢃⠍⡆⠣⠍⠦⡑⠌⡌⠱⡈⠆⡜⢠⠃⡜⢠ ⣿⡽⣯⣟⡷⣯⣟⡾⣵⣻⠾⣽⣻⡼⣳⢏⣷⢻⢮⣏⡷⣏⢿⡺⣽⣚⣧⢟⣧⢿⣹⢾⣹⢾⣹⢟⡿⢥⣼⣿⣿⣿⣿⣿⣿⣿⣿⢳⠚⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣭⡛⠿⡵⣉⠞⣩⠳⢦⡀⢎⣽⣿⣿⣿⣇⢠⣅⠮⠿⢿⠿⣿⣗⠦⣙⢢⡙⣌⠳⣄⠫⡜⡰⢡⠣⡔⢩⢊⠜⡰⢩⠘⡰⢁⠞⡄⢣⠑⡌⠔⡡⢊⠔⡡ ⣿⣽⣳⣯⣟⡷⣯⣟⣳⣽⢻⣳⣭⠷⣏⣟⡮⣟⡽⢮⣗⢯⡯⢷⡳⣏⣾⢫⣞⣳⢯⢾⣹⡞⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⣇⡋⡔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢮⡓⢦⡙⣷⡳⣬⣦⢥⡛⣤⡙⣦⣿⣿⣿⣿⣏⣿⢸⣿⣿⣿⣿⣾⣿⡜⣌⠣⣜⠰⢣⢌⡱⢢⢙⣂⠳⢌⡡⠎⢆⡑⢢⠡⡑⢊⠴⡈⢆⠱⣈⠒⡡⠎⡰⢁ ⣿⣞⣷⣻⢾⣽⣳⢯⣷⢫⣯⢷⣚⣯⡽⣞⡵⣯⢽⡻⣼⣛⠾⣯⢽⡳⣽⢻⡼⣽⡺⣏⡷⣽⢣⣟⡞⣿⣾⣥⣿⣿⣿⣯⣿⡳⢷⡈⡑⠌⢠⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣶⣍⢏⡞⣴⣙⣦⡹⢆⣿⣴⣽⣾⣿⣿⣿⣿⠐⡻⢷⢩⣿⣿⣿⣿⣿⡗⣨⠱⣌⠹⣂⠎⡔⢣⢌⠢⢃⠆⢢⠍⢢⠘⡄⢣⠘⣐⠢⡑⢌⠢⡁⢎⠰⡁⢆⠡ ⣿⢾⣳⣯⢿⡾⣽⣻⣼⣻⢞⣽⣹⢶⣻⢼⣻⢼⣳⡻⣵⣫⢟⡮⣗⣻⡼⣳⡽⣖⣻⡝⣾⡱⣟⢮⣽⡟⢻⣿⣿⣿⣟⣿⣯⢳⣦⣷⣶⣿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣆⢳⣎⠿⣖⣾⣿⣾⣿⣿⣿⣿⣿⡀⣟⢈⣦⣹⣿⣿⢿⣿⠓⡤⢓⣌⢣⠱⡊⢜⡂⢎⡱⢊⡜⢄⠚⡄⢣⠘⡄⢃⠆⡱⢈⠆⡱⢈⠆⡱⢈⠄⡃ ⣿⢯⣟⡾⣯⣟⡷⣯⢶⣏⣟⡮⣗⣻⡼⣏⡾⡽⢶⡻⣵⢫⣾⡹⣞⡵⣫⢷⣹⢞⡵⣻⢖⣻⡝⣾⣿⠁⠰⠟⣿⣯⢸⣿⣯⡧⣴⣠⣴⣶⣦⣄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣮⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠃⢿⣿⠟⣽⣿⣿⠣⡙⡔⢣⠜⣢⠣⢍⠢⡙⢄⢢⠡⡘⢄⠣⡘⢄⠣⡘⢄⠊⡄⠣⡐⢄⠃⡔⢠⠃⡌⡐ ⣿⢯⡿⣽⣻⢾⡽⢯⡷⣞⢧⣟⣭⠷⣝⡾⣱⠿⣭⢗⣯⢳⡞⣵⡻⣼⣛⢮⡗⣯⡝⣧⡟⣧⢻⡞⣿⠀⠀⣦⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣛⣷⠿⣫⣾⢃⠧⡱⡘⢥⠚⣄⠳⣈⠱⡈⢆⠢⡑⢌⠢⡑⢌⠢⡑⠰⡈⢆⠡⢃⠌⡂⠜⡠⢂⠅⢢⠁ ⣿⢯⣿⣳⣟⣯⣟⣯⠷⣏⡿⡼⣞⢯⣻⠼⣏⣟⢮⣻⡜⣯⢞⣳⡽⣣⢯⣳⢻⡼⣽⢲⡟⣼⡳⣏⢿⣆⠀⢿⣿⣿⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢟⣿⢅⠺⡰⢡⡙⠤⢋⠤⠓⡄⢣⠘⡄⢣⠘⡄⢣⠘⠤⡑⢨⠑⠌⡄⢃⠢⡘⠄⡃⠔⣁⠊⡄⢃ ⣿⣻⣞⡷⣿⢮⡽⣞⣿⡹⣞⡽⣞⢯⣳⢻⡝⣮⢟⡶⣻⡝⣞⣧⢻⡵⣫⣗⢯⣳⡭⢷⣫⢷⡹⣎⡯⢿⣆⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢀⢻⡯⢌⢣⡑⢧⠘⡥⢋⠌⡓⢌⠢⡑⢌⠢⡑⢌⠢⢉⠆⢡⠂⡜⡐⢌⠂⡅⠢⡑⠌⢒⡀⠣⠌⡄ ⣿⣳⢯⡿⣽⣏⡿⣽⣲⢟⡽⣞⣭⢷⣫⢟⡼⣏⡾⣳⢧⣛⢷⡺⣝⡾⡵⣞⢯⡖⣯⡳⣝⡮⢷⡹⣞⣻⣿⡄⣿⣿⣿⡟⢛⣫⣿⣿⣿⣿⣿⣿⠟⣿⠛⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣹⡟⣌⠲⣡⠊⡕⢢⠡⢚⠰⡈⠖⡡⢊⠔⠡⢂⠱⡈⢌⠂⡅⢒⡈⢄⠣⡐⢡⠂⢍⠂⡌⢡⠒⠠ ⣿⡽⣯⣟⡷⣯⢷⣳⡽⢾⣹⡞⡽⣎⡷⣫⡽⣞⡵⣛⣮⢟⣮⢽⣣⢟⣵⢫⡾⣹⢖⣯⢳⡝⣧⢻⡜⣷⣿⣿⣿⣿⣿⣴⣿⡿⡏⢻⣿⣟⣤⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠠⢚⡯⣐⠣⢆⠹⣠⢃⠣⢌⠢⡑⠌⠴⢁⢊⠱⡈⢆⠘⡠⢃⡘⢄⡘⢄⠢⢑⢂⠩⢄⠊⡔⠡⠌⡡ ⣿⣽⣳⣯⣟⣷⣛⣶⢻⡝⣧⡻⣝⢾⣱⣏⢷⣹⢞⡽⣎⢿⡜⣧⣛⠾⣜⢯⣳⣛⠾⣜⢧⡻⣜⢧⡻⣜⣿⣿⣿⣿⣿⣿⡟⠳⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⡐⢫⢄⠫⡜⢠⢃⠌⡒⢌⠢⢑⠊⡄⠣⢌⠰⡐⡈⢆⠡⢂⠔⡂⠔⡈⢆⠡⢊⠰⡈⠒⢄⠣⡘⠠ ⣿⣞⣷⣻⣞⡾⣝⡾⢯⣽⢺⡵⣏⡟⣶⡹⣞⡽⣚⡷⣹⢮⡻⣵⢫⡟⡽⣎⠷⣭⣛⢮⡳⣝⢮⡳⣝⡞⡶⣿⣿⣿⣿⡿⠈⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠬⣙⠆⢳⠘⠤⣉⠆⡱⢈⢆⠡⢊⠰⡁⢆⠡⢂⠱⣀⠣⠌⢒⡈⢆⠡⢂⠱⡈⠤⢡⠉⡂⢆⠡⡁ ⣿⢾⣽⣳⢯⣟⡽⣞⡿⣜⣳⡽⣺⡝⣶⢫⢷⡹⣝⠾⣭⣳⢻⣜⡳⣽⢳⣭⣛⢶⣭⢳⡝⣮⢳⡝⣮⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡈⠴⣈⢏⠰⣉⠒⡡⢊⠔⡡⢈⠆⡡⢒⠈⡔⡈⢆⠡⡐⢂⡑⠢⡐⢂⠅⡊⠔⡠⢃⠢⡑⠨⠄⡃⠔ ⣿⣻⢾⣽⣳⢾⣹⣳⢽⡺⣵⢫⢷⡹⣞⡽⢮⣽⣚⢯⣳⢭⣳⢭⣳⢭⣳⢮⡝⡾⣜⢧⡻⣜⢧⡻⢶⣭⢳⢧⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡐⢈⠲⢡⢎⡱⢄⡩⢐⠡⢊⠄⣃⠰⢁⠢⡑⠰⡈⢄⠃⡔⣁⠢⡑⢄⠃⡌⠰⣁⠒⡄⢃⠌⡑⢌⠰⢁ ⣿⣽⣻⢾⡽⣞⣧⢟⣞⣳⡭⣟⢮⢷⡹⣞⣳⢮⡝⣾⣱⢻⡜⣧⣛⢮⡳⣏⢾⣱⢏⡾⣱⢏⡾⣹⢳⣎⡟⡾⣴⢛⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠭⡀⢡⠌⡡⢂⡅⢺⡔⡨⢔⡡⢊⡅⢒⠠⡑⣈⠒⡈⢅⠒⣈⠒⡐⢄⠒⡨⠐⡌⠰⣁⢂⠒⡈⢆⡘⠰⢈⠢⢁ ⣿⢾⡽⣯⢷⣻⢮⣛⣮⢳⣝⣮⣛⢮⢷⡹⣎⢷⣹⠶⣭⣳⣛⠶⣭⡳⣝⡞⣧⣛⢮⣳⡝⣮⢳⣝⡳⢮⣝⡳⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡁⠞⡌⠐⡤⠂⠤⢡⠘⣐⠣⣏⡐⠆⡔⣡⠈⡆⡑⠰⣀⠃⡜⢠⢊⡐⢌⠰⣈⠂⡅⢃⠌⡡⢐⢂⠱⢈⠆⢌⠡⢊⠄⠡ ⡿⣯⣟⡷⢯⢷⣫⠷⣭⢷⣚⢶⡹⢮⡳⣝⢮⣳⢭⣛⢶⣣⢏⡟⡶⣝⢮⣝⠶⣭⡳⢧⣻⣜⡳⢮⣝⡳⢮⣽⣟⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣍⡳⢍⢦⣹⡰⢬⠑⡠⠨⠰⢀⣋⠄⠳⣼⡄⣙⠰⢠⡘⠤⣁⠣⡐⢌⡐⢢⠐⡰⢈⠢⠄⡃⠔⣈⠢⠑⡂⢌⠢⡁⢎⠠⠃⡄⢊⠐ ⣿⢷⣯⣟⢯⢷⣫⣟⢮⣳⡝⣮⣛⢧⣛⢮⡳⣝⡮⣝⣮⢳⣏⣞⡳⣝⠾⣜⡻⢶⣹⢳⡳⢮⣝⡳⢮⣝⡳⣞⢿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⢻⣌⠳⣭⢖⣦⠳⣌⢌⠡⢁⠒⢡⠈⢎⠡⠜⣷⡈⠜⣠⠘⡰⢀⢣⠘⡄⠒⡄⢣⠐⡡⢂⠱⢈⠒⡠⢁⠣⢘⠠⢂⠅⢊⠐⠡⠐⠂⠌ ⣿⣻⢶⢯⣛⡾⡵⣞⢯⢶⡹⣖⢯⡞⣭⣳⢻⣜⡳⣝⢮⡳⣞⡼⣳⢭⣛⣮⡝⣧⢏⡷⣹⢳⢮⣝⡳⣎⠷⣭⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⣽⣳⢮⡳⣎⡳⡼⡞⡴⢫⡜⠌⢦⠉⠈⠄⡐⠂⡜⢨⢽⣿⡔⢂⠱⣀⠃⢆⠱⣈⠱⡈⢆⠱⣀⠣⡘⢄⠣⡐⢡⠊⡄⠣⢌⠘⡀⢊⠡⠌⠡⢈ ⣟⡷⢯⣟⡽⣺⣝⢾⡹⣎⢷⡹⢮⣝⠶⣭⡳⢮⣝⢮⡳⣝⢮⡳⣝⢮⣳⢮⣝⢮⡻⡼⣭⣛⠾⣜⡳⣭⣛⠶⣭⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣟⡳⢞⡥⢯⡽⣭⢳⢧⡹⢜⣣⡙⢾⡀⠎⠡⠀⢄⠡⡀⠣⢎⢿⣿⣧⣖⡠⢉⠆⡒⠤⡑⡈⢆⠱⣀⠣⡘⢄⠣⡘⢄⠣⡘⠰⡈⠆⡁⠢⠐⡈⢂⠁ ⣯⣟⣟⣮⡽⣳⢞⣯⢳⡝⣮⢽⡳⣎⡟⡶⣝⢯⡞⣧⣛⢮⢷⡹⣞⢧⣛⠾⣜⢧⡻⣵⢣⣏⠿⣜⡳⢧⣏⠿⣜⡧⣏⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⢾⡸⣹⡍⣞⣱⠞⣥⢻⢦⡙⣦⠧⡙⢦⡑⢎⠡⡀⠆⠰⢀⢣⠘⡼⣷⣏⡿⣿⣶⣾⣤⣵⣠⡑⣈⠒⠤⢑⠰⡈⢆⠱⡈⢆⠡⢃⠜⡠⠑⣂⠑⡠⠁⠌ ⣷⣻⡼⢶⣻⢵⣫⢞⣧⢻⡜⣧⢻⡼⣹⢳⡝⣮⡝⡶⣭⣛⢮⣳⡝⣮⣝⡻⣜⢧⡻⣜⡳⣞⡽⢮⣝⡳⣎⠿⣜⡳⣝⠾⣭⣛⠿⡿⢿⠿⣿⢿⣿⠋⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣞⡧⢷⡩⡜⠶⣥⢯⡙⣧⣾⠵⣣⠝⣌⠣⡜⢢⠡⡁⠂⠅⣂⠢⠘⢤⢫⡝⣻⣷⣻⢞⣽⣻⣟⣿⡿⣿⣶⣮⣴⣡⣈⠆⡑⠌⢢⠁⢎⡐⠡⡀⠎⢠⢁⠂ ⣷⣳⢻⣏⣞⢧⣛⡾⣜⢧⡻⣜⣧⢻⡵⣫⢾⡱⣏⢷⣣⢟⣮⢳⡝⡶⣭⢳⡝⣮⢳⣭⢳⡝⣞⡳⢮⡝⣾⡹⢧⡻⣜⡻⢶⡍⡷⣍⣛⠮⡵⢎⣽⠀⠀⠀⠀⢮⣿⣿⣿⣿⣿⣿⡿⡞⣥⢳⡉⢳⡜⣦⢿⡻⣌⠷⣢⠝⣠⠒⡌⢠⠃⡔⢁⠂⠴⢈⡑⢎⡳⢼⢯⡷⣯⣟⣮⢷⣻⣾⣟⡿⣽⣿⣻⣿⣿⣿⣷⣾⣤⣉⡤⠘⢠⠁⡌⠂⡄⢂ ⡷⢯⣛⣞⢮⡻⣜⡳⣝⢮⢷⡹⣎⢷⡹⢧⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⢷⡺⣝⠾⣱⢏⡳⣝⢶⣹⢳⡝⣧⣛⢧⠞⡵⢎⢧⡛⣜⢣⢾⡃⠀⠀⠀⠠⣼⣿⣿⣿⣿⣟⣷⡻⣬⢓⣌⠶⣹⣯⣗⣳⣭⠳⡆⣍⠲⠠⠄⠃⡜⠐⡌⡀⢂⠬⠑⡎⡵⢋⡞⣹⢳⣻⣾⣿⢿⣟⣾⣟⣷⣿⣿⣽⣷⡿⣯⣿⣿⣿⣿⣿⣦⣴⣀⠡⠐⠂ ⣟⢯⡽⣎⣯⢳⡭⣗⢯⡞⣧⢻⡜⣯⣝⡳⢮⣏⢷⡹⣎⢷⣫⢞⣧⢻⡵⣫⢷⡹⣎⠷⣭⢻⡥⣏⢷⡹⣎⢷⣫⢞⡵⣭⠺⡭⣝⢮⢣⡝⣬⠓⡾⡇⠀⠀⠀⠐⢼⣽⣿⣿⣿⣿⣷⣿⠶⣏⢬⣛⣷⣻⣞⡷⣊⠷⣉⠦⣁⠣⣘⠐⡈⠱⣀⠖⠡⠀⡝⡘⡔⠫⡔⢣⡞⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣿⣾⢿⣟⣷⡿⣯⣿⣿⢿⣿⣿⣿⣾⣤ ⣯⣛⢾⡱⣏⢷⡹⣎⢷⡹⣎⢷⣛⠶⣭⣛⠷⣎⢯⡳⡽⣎⢷⣫⢞⣧⢻⡵⣫⠷⣭⢻⡜⣧⢳⡝⣎⢷⡹⣎⢷⣋⠾⣜⢫⡵⣚⡬⢳⡜⢦⡛⡴⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣯⡿⣜⡶⣹⣾⢯⣟⣳⡽⢎⡕⢢⠰⣁⠣⡜⢀⠡⡘⢠⠁⢆⠐⡤⢩⠓⣬⢓⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣻⣿⣿ ⡷⣭⡗⣯⠽⣎⢷⣫⢞⡵⣫⡞⣭⣛⠶⣭⢻⡼⣣⢟⡵⣫⢞⡵⣫⢞⣧⢻⡵⣻⡜⣧⢻⣜⡳⢞⡭⡞⣵⢫⡞⣭⢻⢬⡳⣜⡱⢺⡱⢎⢧⡙⡖⣿⠀⠐⠄⢀⠀⠀⠉⣿⣿⣿⣿⣿⣟⡷⣏⣷⣿⣿⢿⣻⡝⢮⡜⣡⠓⠬⣑⠜⣨⠂⡁⢃⡚⢤⡈⢠⢃⡝⢦⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⣿⣽⣿ ⣟⡵⣻⣜⡻⣜⢧⣛⢮⡳⢧⡻⣵⢫⡟⡼⢧⡻⣵⢫⡞⣵⢫⡞⣵⢫⡞⣧⣛⢶⡹⣎⢷⣪⠽⣹⢼⣙⢮⣳⢹⡜⣣⢳⣙⠦⣝⢣⡝⢎⢶⣭⡿⠛⠀⠀⠀⢹⠆⣄⣀⠿⣿⣿⣿⣿⣯⣿⡽⣾⣿⣯⡿⣧⣛⢧⡚⡥⢊⠶⣩⢎⡡⢚⠄⢃⠜⡢⣄⠣⡘⣬⢣⠿⣽⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢞⡵⣎⡷⣹⢎⣯⢳⡽⣳⡝⣮⢳⡽⣹⢧⡻⣜⢧⡻⣜⢧⣻⡜⣧⣛⢶⡹⣎⢷⡹⢶⣩⢏⠷⡮⣝⡞⣬⡓⣞⣱⢫⡜⣹⢬⣳⡾⠟⠋⠁⠀⢀⠀⠀⠀⢸⡅⣦⢉⡉⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣖⡻⢦⡛⣌⢏⡾⡵⢪⡕⢯⣌⢣⣌⡱⢎⡧⣙⣤⢏⡿⣵⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢷⣫⢞⡵⣫⢗⡯⣞⢧⡻⣵⢻⡜⣧⢻⡵⣫⢷⡹⣎⢷⡹⣎⢷⡹⢶⡹⣎⢷⡹⢎⡗⣯⣜⢫⢷⡹⡖⣽⠲⣝⡼⢲⣍⣾⠟⠋⡁⢀⠀⠀⠀⢰⣿⠀⠀⠀⠈⡇⠸⣧⣌⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣥⣋⢷⡙⣞⣮⡽⣽⢳⣚⠷⣜⡲⣬⡳⢯⣶⢻⣼⣻⣞⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣫⢞⡵⣫⢞⡽⣎⠷⣭⢳⡝⣮⢷⡹⢧⣏⢷⡹⣎⢷⡹⢮⡝⣧⢳⡝⡮⡝⣏⡞⢶⢎⡿⢬⡳⣝⠮⣝⣲⣽⠟⠋⠀⠠⠀⢀⡀⢀⡈⢷⣾⣿⠀⠀⢠⠀⢻⡄⢽⣷⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡍⣎⢿⣼⣳⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⣱⣏⣞⡳⣝⢮⣳⢭⡟⣼⢫⡞⣵⢫⣝⡳⣎⢷⡹⣞⢧⣛⢧⢻⡜⣳⠞⡵⣋⢶⡹⣚⢮⡜⢧⣛⡼⣹⣶⠟⢡⣀⠈⢒⠠⣇⢢⣽⣦⣿⣿⣿⣿⠃⠀⠈⢣⠀⢳⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⡼⣣⢟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣻⢯⣟⡳⡽⣎⢷⣛⣾⣳⣿⣿⣿⣿⣿⣿⣿ ⣳⢯⡽⣹⢧⡻⣜⢯⡞⣵⢫⡞⣵⢫⡞⣽⢣⡟⡼⢧⡻⣜⡻⣜⢮⣓⢏⡖⢧⠻⣜⡣⢟⣬⢓⡮⢫⣵⡿⠋⠀⠈⢻⣤⣚⡤⢿⡞⣿⣻⣿⣿⣿⠏⠀⠀⠀⠈⡆⠸⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⡵⣿⣿⣿⣧⣻⣾⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⡿⣟⣿⣯⣿⣟⡿⣿⣻⣿⣽⣟⣷⣿⢾⣟⡾⣽⣳⢧⣻⣼⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⢯⡞⣵⢏⡾⣱⢯⡞⡽⣎⢷⡹⣎⢷⡹⣎⢷⡹⣝⢧⡟⣼⡱⢏⡶⢭⡺⣜⢫⣝⡲⢭⣓⢮⡹⣼⡟⠃⠀⠀⠀⣐⡠⠞⣿⡽⢎⡽⣶⢿⣾⢏⡆⠀⠀⠀⠀⠀⠑⠀⣧⠀⢺⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣝⡮⣝⡾⣿⣳⣿⣟⣿⣿⣽⣷⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣾⣟⣷⣿⣻⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡼⣣⡟⣼⢣⡟⣼⢳⡝⣮⢳⡝⣮⢳⡝⣾⡱⣏⠾⣜⢧⡝⡞⣜⡣⢗⣎⠳⣎⣵⣫⣼⣶⠟⣉⣠⠀⠀⠀⢀⡿⣷⢍⣙⣧⣿⣾⣿⣫⣝⣾⣤⣄⣲⣤⣹⣦⠲⠤⣄⠀⠈⢿⣿⣿⣿⣿⣿⠃⢤⣿⣿⡿⢫⣙⢮⣳⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯ ⣞⡳⣝⢾⡱⣏⣞⢧⡻⣜⢧⡻⣜⢧⡟⣼⢣⡝⣮⣛⡼⢎⣞⡹⡲⣍⣷⡾⠟⢋⢉⣥⣶⣾⣿⣿⣿⣿⠿⡩⢞⣷⠟⠉⡐⢎⠛⡍⢯⡽⣻⣿⡻⢿⣿⣿⣿⣿⣷⣦⣜⣦⡀⠹⣿⣿⣿⣿⠏⢀⣿⡿⠉⢁⠣⣞⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⣿⣟⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠾⣝⢯ ⣯⣝⢾⣣⢟⡼⣎⡷⣹⢎⣯⢳⡝⣮⡝⣮⢳⡝⢶⡹⣜⣫⣖⣽⠿⢋⡡⢴⠶⣞⡾⣞⣷⣿⣾⣿⣿⣟⡶⣡⣿⠋⠀⠀⢁⠢⠕⡚⢡⢎⡱⠭⣽⠿⣟⢿⡻⣝⣮⣿⣿⣿⣷⡧⣿⣿⣿⡋⢥⣿⡏⣠⣄⣠⣔⣫⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣟⡿⣿⣾⣿⣿⡿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣽⣯⢿⡽⣞ ⡷⢮⣳⡝⣮⢳⡝⣾⡱⣏⡞⣧⣛⢶⣽⣮⡷⠿⢛⠛⡫⢍⠋⡅⣎⢱⡙⣎⠿⣜⣻⡽⣿⣾⣿⣿⣿⣿⣿⣿⠏⢀⢠⡐⣠⠉⠒⠬⡁⢎⡰⢿⣬⡻⣜⣯⢷⣻⣿⣿⣿⣿⣿⣷⣉⡟⢦⡑⣮⢯⣴⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣻⡾⣿⣟⣯⡿⣿⣿⣯⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡷⣯⡿⣽⢯ ⣽⢳⢧⡻⣜⢧⡻⢶⣹⢮⣽⡶⠿⠛⠉⠀⠐⠤⠣⡘⠐⢊⠒⡌⢂⠧⣜⡎⣷⣹⡾⣽⣷⡿⣿⣿⣿⣿⠿⣡⠲⣌⢶⡹⢿⣆⣙⣲⠱⣮⢙⠶⣣⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠥⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢷⣯⣟⣷⣿⣳⣯⢿⡽⣷⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⡷⣟⣯⣿ ⣳⢯⡞⣵⣫⢞⣽⣳⠟⠋⠁⠀⠀⠀⠀⠐⠠⠂⢀⠈⠄⢡⠘⡰⣍⡞⣴⢯⡷⣯⣟⣿⡾⣟⡿⡹⣍⢆⡳⢣⡽⣘⣮⡟⣽⣿⣿⢣⠷⣌⣯⣛⣷⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣯⢷⡿⣜⢯⢾⣭⢿⡿⣿⡿⣿⣾⢿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣻⣿⣾ ⣟⢮⣽⢺⣵⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠢⡜⢢⡝⢲⣟⡾⣽⣯⣿⣿⣻⡽⣛⢥⢳⡱⢎⢎⣝⢣⡻⣵⣳⡿⣟⣿⣞⣯⢿⣝⡶⣛⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣟⡾⣞⡯⣝⢿⣫⡗⣾⣯⣿⡽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣿⣷⣿ ⣻⢞⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠔⣠⠒⣭⠳⡜⣧⣿⣟⣷⣯⢷⣫⢇⡧⣙⢎⢣⠳⡞⡼⣌⢷⣻⢽⣯⢿⡽⣯⣟⡞⡿⣮⣽⢳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⢦⡈⢿⣞⣿⣿⣿⣿⣷⡿⣿⣟⡾⣽⣟⡾⣽⢣⡟⣽⣺⢷⣻⢽⣳⣯⣿⢿⣻⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿ ⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢬⡸⣔⢫⢖⣻⣾⣿⠿⣝⡾⣡⠧⣍⠞⣰⠙⢎⡲⢥⣛⣼⣻⡼⢯⡟⣞⢯⣿⣱⢿⡜⣷⡝⣾⢻⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣄⡆⣹⣜⣿⣿⣿⣿⣿⣿⣿⢿⣟⣿⣳⢏⡷⣭⢗⣯⣛⣷⢻⣾⢯⣿⣻⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⡞⠶⣱⣮⣾⣿⣿⢿⡽⣛⡮⢱⡡⣚⡜⡸⢣⢛⣤⡝⣫⣼⠶⡽⢾⡹⡞⡭⢞⠶⢭⢞⡹⣞⡽⣮⢿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⣻⣽⢻⡼⣾⢿⣿⣿⢿⣻⣿⣿⣾⣳⢯⡻⣼⢛⡾⢧⣻⣼⣻⣾⢿⣽⣿⣻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡌⣞⣬⣿⣿⣿⣿⣿⣯⣿⡟⢧⠘⡅⣶⢩⠞⣱⢛⣼⢲⡝⣣⢟⡽⢞⡹⢻⡱⣛⢮⣙⣧⢫⡷⣭⢷⣯⣟⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⣟⣮⢷⡏⣯⢳⣭⢻⡼⣟⣧⣿⣹⣽⣻⣯⣿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡜⣰⣿⣿⣿⣻⣽⣯⢿⣿⣯⠳⡜⢠⢛⡘⢤⡃⣞⡥⢏⡞⡶⣙⢮⣟⡼⡳⣍⣳⣫⡝⣮⣝⣮⣻⡽⢯⣿⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡷⢧⣿⣿⣿⣿⢯⣟⡾⣽⢻⡯⣟⣳⡛⢾⣳⣽⡽⣞⡿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⡼⣼⣿⣻⣷⢿⣽⣿⣽⣿⣿⣦⠃⡄⠙⠦⠸⠀⡗⡌⢲⡛⣜⠶⣙⡞⣼⣱⢯⣝⣣⢿⣝⣯⣟⣾⣳⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣼⣿⣋⢿⡟⣞⣻⣞⡷⣹⢏⡷⣫⢷⣹⣛⣷⣻⣽⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢠⡉⣥⢻⣽⣷⢿⣷⣯⣿⣿⣿⣿⣿⣿⠂⠄⠡⠒⠐⠈⠳⢐⡚⡡⢜⡭⢻⡴⣛⢶⣭⡞⣧⣟⣯⢿⣭⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢿⠙⣇⣿⢫⡝⣭⣓⣮⠷⣳⢾⣱⢟⣯⣟⣯⣷⣻⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣟⡷⣯⣿⣿ ⠀⠀⣀⣄⣠⠌⢦⡱⣯⣿⣻⣾⡿⣯⣿⣿⣿⣿⣿⣿⡏⠙⠀⠀⠀⡰⣃⡤⢋⣜⣍⣫⣜⣣⣷⣻⣟⣶⡿⣟⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡉⠁⡫⢜⠣⢯⣜⣦⠳⣬⠷⣽⣚⣷⣞⣳⣾⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣿⣽⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡟⠀⠀⠀⣀⠀⠀⠀⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⢀⠄⠉⣀⡀⢉⠁⣠⣶⣶⣶⣶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⢁⠔⠀⠀⠪⢂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡇⢀⣴⣿⡿⢀⠀⠀⠉⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣦⠀⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠀⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢉⠡⢀⡀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠐⠂⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⡿⠛⠐⠂⠤⡐⠄⠀⢠⠀⠀⠊⠶⠛⠛⠛⠊⠥⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡏⠀⣀⣴⠶⠶⢾⠰⠀⠀⠀⠀⠀⠠⠤⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠊⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠣⡞⢟⠁⢀⠠⢘⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡹⠂⠀⠀⡐⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠀⠀⡌⠀⡘⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⢰⠀⢈⢃⡀⠀⢠⠐⠀⠀⠀⠁⠀⠀⠀⠀⠑⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⣀⠠⠄⢀⣀⣤⣀⠀⠈⡄⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡄⠀⡀⠀⢀⠤⠒⣈⣩⡤⢶⠞⠟⢙⠉⡋⣛⣿⡆⠀⡇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢄⠐⢄⠠⣿⣿⡋⡁⢁⣀⣤⣷⣾⣿⣿⣿⢿⠃⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⡜⢜⠻⣿⣿⡿⢻⣻⠹⠕⠋⢁⠊⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⢄⠢⢀⣉⡁⠁⠀⠤⠐⠊⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⡁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠐⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠰⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀
⣠⣤⣤⡤⠤⢤⣤⣀⡀⠀⠐⠒⡄⠀⡠⠒⠀⠀⢀⣀⣤⠤⠤⣤⣤⣤⡄ ⠈⠻⣿⡤⠤⡏⠀⠉⠙⠲⣄⠀⢰⢠⠃⢀⡤⠞⠋⠉⠈⢹⠤⢼⣿⠏⠀ ⠀⠀⠘⣿⡅⠓⢒⡤⠤⠀⡈⠱⣄⣼⡴⠋⡀⠀⠤⢤⡒⠓⢬⣿⠃⠀⠀ ⠀⠀⠀⠹⣿⣯⣐⢷⣀⣀⢤⡥⢾⣿⠷⢥⠤⣀⣀⣞⣢⣽⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⢙⣿⠝⠀⢁⠔⡨⡺⡿⡕⢔⠀⡈⠐⠹⣟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⣟⢦⢶⢅⠜⢰⠃⠀⢹⡌⢢⣸⠦⠴⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣇⡬⡌⢀⡟⠀⠀⠀⢷⠀⣧⢧⣵⣿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⢻⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣼⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠛⢻⠉⡉⠍⠁⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⢀⡼⡄⠃⠤⠀⠀⠀⠀⠀⡐⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣸⡎⣀⣷⣤⣶⣶⣶⣦⡀⠀⠈⠓⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣤⣯⣿⣿⣿⣿⣿⣿⣿⣭⣯⡆⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⣿⣼⠀⢹⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢘⣿⠙⠡⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣯⠏⠀⢀⣿⣿⣿⣯⣠⡀⠀⠀⠀⢀⣾⡏⠒⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢘⣏⣺⣤⣬⣭⣼⣿⣿⣯⡉⢻⣦⣌⣦⣾⣿⣿⡚⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⡟⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣧⡞⣻⣩⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣬⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡟⠻⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠓⠲⠤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢯⡁⠀⠀⠀⠉⠹⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀⠹⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠀⢸⡄⢹⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⡄⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡀⣀⣰⣿⠀⠄⠹⣾⣿⣿⡿⣿⠀⢠⣤⣀⣴⣤⣤⡴⠶⠶⠿⠿⠛⠛⠋⠉⠉⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡱⠏⠉⡟⠃⠀⠀⠀⢸⣿⣿⠇⣿⡴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢋⣡⣶⣿⣂⡼⠁⠉⠙⠋⠙⠿⠟⣢⣄⢿⡟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀ ⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⣸⡿⠟⠀⠀⠀⠀⠀⠀⠲⣾⡛⣿⣬⡄⠀⠀⠁⠠⣤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡟⣿⡟⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠆⠀⠀⠀
⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬛⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬛🟩⬛⬛⬜⬜⬜⬜⬛⬛🟩🟩🟩⬛⬛⬜⬜⬜⬜⬛⬛🟩⬛⬜⬜ ⬜⬛🟩🟩🟩🟩⬛⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬛🟩🟩🟩🟩⬛⬜ ⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛ ⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛ ⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛ ⬛🟩🟩🟩🟪🟪🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟪🟪🟩🟩🟩⬛ ⬛🟩🟩🟪🟪🟪🟪🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟪🟪🟪🟪🟩🟩⬛ ⬜⬛🟩🟪🟪🟪🟪🟩🟩⬛🟩🟩🟩🟩🟩🟩🟩⬛🟩🟩🟪🟪🟪🟪🟩⬛⬜ ⬜⬛🟩🟩🟪🟪🟩🟩🟩🟩⬛🟩🟩🟩🟩🟩⬛🟩🟩🟩🟩🟪🟪🟩🟩⬛⬜ ⬜⬜⬛🟩🟩🟩🟩🟩🟩🟩🟩⬛🟩🟩🟩⬛🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜ ⬜⬜⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬜⬜ ⬜⬜⬜⬛⬛⬛🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜
⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠉⣉⣩⠭⠭⠉⠉⠩⠭⠉⠉⠉⠙⠛⠛⠛⠻⢿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⠤⠒⣉⠤⠔⠒⠒⠒⠋⠙⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠮⠙⠻⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⠤⠊⡡⠖⡩⠔⠂⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠠⢒⠒⠒⠀⠒⠢⣄⠀⠀⠀⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠠⠊⠴⠋⠀⣀⣀⣤⣤⣤⣀⡀⠀⠑⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⣠⣾⣟⣀⡀⠀⠀⠀⣀⡀⢠⣶⣿⣿⣿⣿⣿⡋⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠻⣧⣄⠀ ⠀⢠⣾⣻⠋⠉⣡⣤⣤⣤⣌⡉⠔⠈⠛⠛⠉⢉⣭⠉⠛⠻⣶⣶⡿⠃⠀⠀⠐⢾⣿⡿⠿⠛⠛⠛⠋⠉⠀⠀⠉⠉⢍⡳⢌⢻⣦ ⣰⡿⢱⠃⢠⡾⠋⠁⢰⣌⠙⠛⠷⢶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣄⣀⣴⡶⠶⠶⣶⠹⠀⢳⣿ ⢿⡇⢸⠀⣿⠃⣀⣤⣾⠿⢷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣤⡤⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠈⠙⠛⠋⢠⣇⠀⠀⢠⠇⣸⣿ ⢸⣧⠘⡆⢹⣇⠉⠉⢿⣆⠀⠈⠙⢿⣷⣦⣤⣉⡁⠀⠀⠸⣿⡀⣶⡶⠶⠄⠀⠀⠀⣠⣿⠿⠗⠦⣄⠀⠀⣼⣿⡇⢀⣣⠴⣿⠏ ⠀⠹⣧⣘⠲⠅⠀⠀⠘⢿⣿⣶⣤⣸⣿⡀⠈⠙⠛⠿⢶⣦⣭⣅⣀⡀⠀⠀⠐⠷⡾⠟⠁⠀⠀⢀⣠⣴⣿⢿⣿⣷⠈⠀⣼⡟⠀ ⠀⠀⠈⠻⣿⡀⠀⠀⠀⠈⢻⣦⠉⢻⣿⣿⣶⣦⣄⣀⣸⡏⠉⠉⠉⠛⢿⡿⠿⠶⢶⣶⠶⠿⠛⢿⡏⠁⣿⣄⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⢷⣼⡟⠀⠉⠛⠻⢿⣿⣷⣶⣤⣤⣤⣼⣧⣤⣤⣤⣿⣤⣤⣤⣾⣷⣴⣿⣿⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⣸⡟⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⢀⡀⠀⢀⠀⠉⠻⣷⣴⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⣽⡏⠉⢹⣿⠋⣽⡟⢸⣿⡿⠃⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡓⠦⣍⠒⠤⣀⠉⠙⠛⠿⠶⢶⣤⣾⣧⣄⣀⣠⣿⣄⣠⣾⣧⣴⡿⠷⠿⠋⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣉⠒⠦⢍⣑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⡆⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⡉⠑⠒⠩⠭⠍⢐⣒⣒⠒⠂⠐⠒⠒⠒⠒⠒⠉⠀⢀⡤⠚⠀⠀⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀
⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟪⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟪🟪⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬜⬜⬜⬜⬛🟪🟪🟪⬛⬜⬛🟪⬛⬜⬛⬛⬜⬜⬜⬛⬛🟪🟪⬛ ⬜⬜⬜⬜⬛🟪🟪🟪🟪⬛🟪🟪⬛⬛🟪⬛⬜⬛⬛🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬛🟪🟪🟪⬛🟪🟪🟪⬛🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜⬜⬜ ⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬛⬜ ⬜⬛🟪⬛🟥🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛⬜ ⬛🟪🟪⬛🟥⬛🟪🟪🟪🟪🟪🟪🟥🟥🟪🟪🟪🟪⬛🟪🟪⬛⬜⬜ ⬛🟪🟪⬛🟪🟪🟪🟪🟪🟥⬛🟥🟥🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛⬜ ⬜⬛⬛⬛⬛🟪🟪🟪🟪🟪🟥🟥🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛ ⬜⬜⬜⬛⬜⬛⬛🟪🟪🟪🟪🟪🟪⬛⬛🟪🟪🟪🟪🟪🟪⬛⬛⬜ ⬜⬜⬜⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜🟪🟪🟪🟪🟪🟪⬛🟪⬛⬜ ⬜⬜⬜⬜⬛🟪⬜⬜⬜⬜⬜⬜⬜🟪🟪🟪⬛⬛🟪🟪🟪⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟪⬜⬜⬜⬜🟪🟪🟪🟪🟪🟪🟪⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬜ ⬜⬜⬜⬜⬜⬛🟪⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪🟪⬛ ⬜⬜⬜⬜⬜⬜⬛🟪🟪⬛⬛🟪🟪🟪🟪🟪🟪🟪🟪⬛🟪⬛⬛⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛🟪🟪🟪🟪🟪⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🟪🟪🟪⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜
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⠀⣠⠔⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠢⣀⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⣼⣿⣿⠀⠠⢳⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠻⣿⠿⠴⠁⠘⠤⠤⡤⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡡⠔⠐⢄⢸⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸ ⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎ ⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢉⣻⣿⣿⣍⡛⣯⣉⣿⣷⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢛⣿⠟⠀⠀⠈⠛⠛⠳⣬⣭⣍⡐⣶⣤⣉⠛⢻⣽⡳⣦⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣟⡛⠉⠀⠿⢷⣒⣒⣶⠀⠀⠁⠈⢛⣟⠿⠧⠤⣾⢿⡿⠉⠙⠋⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠳⣄⣰⣿⣿⡟⢳⣶⣶⣶⠤⢬⡤⠤⠤⠀⠸⣿⣿⡶⠠⡏⢠⣿⣿⣦⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⣿⢯⣉⣁⣼⠹⣿⡿⠀⢀⡇⠀⠀⠀⠀⠈⠉⠁⠀⣷⢿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡞⠉⠉⠙⢻⢛⠾⢷⣄⣀⣠⡾⢟⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠻⠿⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⡷⢿⣿⠋⠉⠉⠉⢹⣿⠒⠦⣌⡛⢦⡙⠨⡅⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⠀⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⠦⠬⠿⠤⠤⠤⠤⠞⠛⠒⠒⠚⠻⠦⡕⣄⢠⣶⣤⡀⠀⠀⠀⠀⢰⠟⣏⠉⡙⠛⢿⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⣶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣼⡄⠙⠋⠁⠀⠀⠀⠀⠻⣆⠸⣦⡉⠛⠶⣌⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠤⠒⣋⡡⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⣿⡆⠀⠀⣿⠳⢬⡓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⡿⣿⠛⠉⠙⠛⣋⣥⠶⠛⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢿⡀⠈⠙⠁⠀⠀⢻⠀⠀⠙⠳⣍⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠸⢥⡴⠛⣩⠞⠛⠛⠒⢯⠹⡆⠀⠀⠀⠀⠀⠈⠙⣦⢤⣀⣀⣀⣀⣤⣖⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⣸⡇⠀⠀⠀⢿⡧⣸⡇⠀⠀⠀⠈⢙⣮⣷⣤⣄⣀⠀⠀⠀ ⠀⠘⠚⠋⠁⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⢠⠏⢾⠀⢨⣼⣿⣿⣿⣿⣿⠛⠓⠒⠒⠒⠶⠿⡷⠤⠴⣿⠴⠖⠒⠒⠛⠉⢹⡃⠀⠀⢠⠞⣩⠷⠦⣄⢀⣉⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⡼⣿⡿⢦⣙⣻⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢹⡇⠸⣿⠗⠀⠀⢈⣷⠀⠀⢸⡤⠇⠀⠀⠈⣧⢹⣦⠹⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⣫⠵⠚⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⠉⠙⠓⠦⠶⠒⠒⠷⠦⣤⡿⠴⢿⡻⣶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡏⠳⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡍⠉⠃⠀⢀⣾⠃⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠈⠙⠒⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⣄⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⡀⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣽⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⣿⣿⣿⣿⣿⣿⣷⣮⣙⠿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⠃⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠃⠀⣼⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣈⣙⠻⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣸⣿⣿⣿⡟⠀⠀⢠⣿⣿⡟⠀ ⡏⢻⣿⣿⣿⣿⣿⣦⡀⠈⠉⠉⠉⠉⢙⣷⣽⡿⢿⣿⣿⣿⣿⣟⠛⠛⠻⠷⢶⣄⠉⠙⠋⠉⠁⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠷⣶⣿⣿⣿⡋⠀⠀⣀⣿⡿⠋⠀⠀ ⡇⠀⠹⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⠾⠛⠋⠉⠀⠀⠈⠙⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣴⣿⠿⠋⠙⠻⢷⣔⡋⢸⡇⠀⠀⠀ ⡇⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣷⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⠄⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⢀⣼⣿⡿⠋⠁⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⣤⣿⣆⠀⠀ ⡇⠀⠀⠀⠀⣠⡴⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⣠⣾⠟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄ ⡇⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠶⠊⣉⣉⠉⠐⠂⠀⠀⠀⠀⠀⢀⣿⡏⠀⠞⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿ ⣷⠞⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠲⣄⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⣠⠶⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⣄⣾⣿⣿⣿⣿ ⡗⠀⠀⠀⠀⠀⣠⡤⠚⠁⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠈⠙⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡤⠞⢉⣠⣤⣶⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠘⣿⣿⣿⣿⣿ ⡇⠀⠀⢀⡴⠛⠁⠀⢀⣠⣴⣿⣿⣿⣿⠿⠛⠛⠻⣿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⣤⣾⣿⡿⢟⣿⡿⠿⠛⠛⢿⣿⡿⣿⣯⡙⠳⣿⣿⣿⣿⣿ ⡇⢀⡴⠋⠀⠀⠀⣼⣿⣿⢿⠛⠉⠁⠀⠀⠀⠀⠀⠈⢧⠀⠙⣿⣿⣯⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡴⣫⣿⠿⢃⣀⡀⠀⠀⠀⠀⠀⢘⡇⠉⠲⣝⣿⣦⣿⣿⣿⣿⣿ ⣿⠋⠀⠀⠀⣠⣾⣿⠏⢡⡼⠖⠶⡆⠠⠤⣂⣉⠀⠀⠘⣧⠀⠀⠉⠙⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⣱⠃⢰⡏⣉⣹⠆⣠⡤⠶⠒⠨⣿⠀⠀⠈⠈⢹⣿⣿⣿⣿⣿ ⣿⡆⠀⣠⣾⠟⢋⡏⠀⠸⠶⠶⣞⡵⠖⠋⠉⣁⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠘⣋⠉⢐⣩⡥⢶⡒⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣷⣾⡿⠁⠀⣼⡇⠀⠀⠈⠩⠄⠀⠀⠤⠚⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢳⣀⡴⠾⠋⠀⠀⢠⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⡆⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠒⠀⠀⢠⠟⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⠀⠀⣀⡀⠈⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⣴⣋⣀⡤⣖⡫⠏⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡆⠀⠸⠭⣕⣲⣾⠿⣶⣤⣤⣀⣀⡤⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠒⠚⠛⠋⠉⠁⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠙⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⢿⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠘⣿⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣿⣿⣿⣿⣿⣆⣿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠶⠶⠤⠤⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠓⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⣿⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⢷⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣇ ⢿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢧⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠈⠙⠛⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⢿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⠻⢶⣤⡀⠀⠀⠀⠸⠦⠄⣀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⡶⠶⠶⠒⢻⣏⣿⣿⣿⠃⣿⣿⣿⣿⡿⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⣠⣮⠔⠋⠀⣀⣾⣿⣿⣿⡤⠒⠒⠊⠉⠉⠉⠉⠙⠒⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⣿⠞⠁⠁⠀⠀⢠⣿⣿⣿⡯⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠌⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣿⣇⣠⡀⢀⡴⣾⣿⣿⣿⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⣮⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣟⣿⠉⣿⠧⣸⡇⣼⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠈⠛⢦⣄⠀⡀⠀⢀⡞⢓⠄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠛⣿⣶⡻⣷⡌⢷⠿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⠿⣷⢷⣴⡋⠀⠈⠳⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣷⣟⣿⣿⣼⡇⣸⢁⣼⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡿⣟⠏⠉⠀⠀⠀⠹⡄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠻⣿⢿⣿⠛⠻⣾⣵⡿⠁⠀⠀⡀⣠⠋⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢰⠁⠀⣸⢹⣿⣴⠶⢶⣄⠀⠀⢹⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠻⡏⣸⣷⣶⣾⣿⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠏⠀⠀⡟⢸⠻⣆⠀⠸⡆⠳⠀⠀⢳⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠛⠉⢸⣿⣿⡇⠀⠀⢀⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢠⠏⠀⠀⣸⠁⡞⠀⠈⠳⣄⢹⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢿⣿⠃⠀⠀⢸⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⡴⠃⠀⠀⢰⠏⢰⠇⠀⠀⠀⠙⣾⡆⢀⠀⠀⣇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⠀⠀⠀⠀⠙⠳⣤⣀⡙⢧⣀⠀⢸⠀⢀⠀⡴⠃⠀⠀⠀⠀⠀⠚⠁⠀⠀⣠⠋⢠⠏⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣟⡿⠁⢸⡇⡟⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⣿⣶⣶⠤⣀⡀⠀⠀⡇⠸⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⣰⠋⠀⠀⠀⠀⠀⠀⣠⣶⡟⢀⡴⠋⠀⠀⠀⠉⠙⠛⠳⢤⡇⠀⠀⠀⡿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣇⣴⢃⣠⠖⣀⣠⣤⢶⡻⠟⣁⡴⠋⠀⠀⣤⣭⣭⣿⣶⣤⣀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⣟⡧⠀⠀⢸⣿⣥⣯⡷⣛⣻⡿⠛⣉⡤⠞⠁⠀⠀⠀⠸⠿⣿⣿⢻⢿⡿⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⢹⣿⠀⠀⢸⡿⠭⠭⠭⠵⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠭⠾⠴⠿⢻⡇⠀⠀⠀⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢈⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡆⢸⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⢸⠀⠀⠀⡏⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠇⠀⠀⡇⢸⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⢸⢸⠀⠀⠀⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠀⡇⢸⢧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡏⣸⢸⠀⡀⠀⣿⠀⠀⠙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⢸⠀⠀⠀⡇⢸⠸⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡾⠀⣇⢸⠀⡇⠀⣿⠀⠀⠀⢻⡾⣿⡶⣄⡀⠀⠀⠀⠀⢀⣠⠴⣿⠷⣿⠀⠀⠀⢸⠀⢰⠀⢷⣸⠂⢻⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⣼⠃⠀⠈⠻⣄⡃⠀⢹⠀⠀⠀⠈⢳⣌⡛⠶⢽⣳⣦⠤⠚⠋⣠⠞⣡⡾⠋⠀⠀⠀⣺⠀⢸⣤⠞⡅⠀⠀⢧⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢰⡟⠀⠀⢰⠀⠈⢷⡀⢸⠀⠀⠀⠀⠈⣿⣿⣶⣦⣬⣉⠑⢦⣠⢧⣴⣿⡇⠀⠀⠀⠀⣿⠀⣸⠃⠀⣿⠀⠀⠸⡇⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⢸⠀⠀⠈⠛⢾⡄⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡷⢿⣿⣿⣾⠿⣷⣶⣤⣀⠠⡷⠚⠁⠀⠀⣿⠀⠀⠀⣿⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⡘⣆⠀⠀⡿⠀⠀⠀⠀⢀⣠⣿⣥⣿⣿⡿⣿⣿⣿⣿⣿⣄⣿⣯⣼⣿⡿⣸⣿⣅⣿⣦⣀⠀⠀⠀⠀⢿⠀⠀⠠⠏⡼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣳⠿⣤⣤⣧⠴⠶⠞⣿⣹⣿⣤⡿⠋⠁⠀⠀⠀⠻⣻⡿⢋⣽⣿⠿⢿⣿⣿⣿⣿⣦⣿⣿⣹⢓⡶⠦⣼⣤⣤⠷⣾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⣼⣿⡟⢶⣀⣀⣼⣿⣿⠟⠀⣀⣤⠤⢤⣤⣴⢋⣴⠟⠛⠛⠛⠛⠉⠉⠁⡿⣿⣿⣿⣧⠀⠀⢰⢛⣿⣿⣴⡿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠋⠈⣻⣾⣿⣿⣽⣿⣿⣤⣞⣵⠶⠻⠷⢶⣽⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣧⠀⣿⣿⠁⠙⠛⠯⣾⣳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⣼⣿⣿⡿⢿⣿⣿⣿⠋⠉⣙⣦⠤⣤⣴⠋⠛⢾⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⡇⡇⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀ ⣤⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⣷⣿⣿⣷⣾⣿⡮⣿⡓⢿⣾⣿⣉⣹⡿⠿⠦⣞⣠⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣇⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀ ⢹⠘⣦⡼⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣷⡿⣏⠙⣙⣮⣽⡵⢛⡿⣿⣿⣵⣞⢦⣀⣯⣴⡌⣇⢀⠀⠀⠀⠀⠹⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⢷⡠⠎⠀ ⣸⠠⣿⢳⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⡛⡛⠁⣠⢞⣿⠶⠦⠤⠤⠴⠿⠋⠀⠀⠙⢷⢦⣬⣥⠦⠥⠭⠭⠭⢭⡽⣟⣻⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⣼⣵⡧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠙⠲⣄⣠⠴⠖⠒⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣠⡤⠴⠶⢤⣌⣷⡀⠀⠀⢀⣀⣀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠙⠿⣏⠉⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⡿⠀⠀⠀⣀⣀⣀⡤⠖⠛⠉⠉⠉⠙⠻⡷⠖⠚⠋⠉⠉⠙⠒⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡏⠀⠃⠀⠀⠀⠻⠿⣧⣄⡀⠀⠀⠀⠀⢀⣠⣟⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⣯⣝⣓⣚⣛⣩⡵⠋⠉⢻⣻⡿⠛⢚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠠⠞⠋⠁⠀⠐⠒⠾⣿⡗⠚⢿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢻⡀⠀⠀⢰⡟⣏⠹⡞⢷⡀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⡴⠚⣟⣛⣓⣒⠒⠦⠤⠤⣤⣄⣀⣀⣀⣤⣤⠴⢚⡇⢸⣳⣄⣧⠸⡆⢻⢸⡇ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠘⠧⢤⣭⣭⣭⣍⣉⠛⢒⣲⣶⣶⣶⡿⠿⠶⠚⢚⡟⠁⣌⣯⠙⠛⠀⠀⢀⡾⠁ ⠀⠀⢀⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣹⢏⡟⢸⣿⢰⣿⣷⡞⠛⠙⡿⠛⠉⠀⠀⠀⣀⡴⠋⠀⠀ ⢀⡾⠋⠀⠉⠳⢭⣙⡓⠒⠶⠤⠤⠤⠤⢤⣼⣏⢿⠀⠁⠘⠃⢸⠏⢈⡇⠀⠀⡇⠀⠀⠰⢶⡟⠉⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠖⠒⠒⠛⣶⢤⡄⠀⣀⡤⠶⣏⠀⠀⠀⢿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇⠀⠈⠳⣄⠀⠸⡇⠀⠀⠀⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠀⣿⡄⠀⠀⠀⠈⣷⠶⠃⠀⠀⠀⠸⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿name 1⡄⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⢰⣾⢛⣃⣾⣿⣿⣿⣿⠟⠋⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠡⣶⡾⢿⡄⠻⣿⣿⣿⣿⡟name 2⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠄⢸⣇⢸⡇⠱⣌⣛⣛⡛⣉⣤⣤⡤⠤⠭⠭⠉⠻⠿⠿⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⡆⡄⢻⡀⠳⣷⣶⣷⠂⣰⣿⣿⡀⣶⠄⠄⠄⠄⠄⠄⠄⠄⠄⢸⣿⣿ ⣿⣿⣿⡿⣡⣿⣦⣌⠢⡙⠋⠄⢺⡿⠿⣩⣴⣿⠠⣤⣤⣤⣤⣤⣤⣤⣤⢀⣿⣿ ⣿⣿⣿⡇⢿⣿⣿⡏⢠⣄⣙⠂⢈⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⣦⠻⣿⣷⠈⢿⣿⡐⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⣿⣆⠹⣿⡇⠈⢻⣧⢻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⣿⠟⣠⡿⢁⣾⠄⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⡏⢸⡿⢁⣾⣿⣶⡇⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⡇⡾⠄⠬⠍⡙⠄⠑⠿⠿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⡐⠧⣜⡻⢿⣏⡘⠂⠄⠐⣿⣿⣿⣿⠸⢛⣛⣛⣛⣛⣛⣛⠻⢸⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿

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