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