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