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