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

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