⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢸⡀⠀⢀⡤⠖⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⣴⣃⡤⠤⠚⠓⠒⠛⠲⠤⣼⡇⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠛⢦⡀⠀⣀⡀⢠⡇⠹⣄⡤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣞⡉⠉⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⡀⠹⣴⢻⠁⢸⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠙⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠲⣄⠀⠀⠀⠈⢳⠀⠛⡏⠀⡼⠋⠀⠀⠀⠀⢀⣤⠖⠊⠉⠉⠉⡏⢹⠶⣤⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⡄⠘⣆⠀⠀⠀⠈⡆⠀⣧⡞⠁⠀⠀⠀⢀⡴⠋⠘⢶⠒⢦⡀⠀⣿⢸⠀⠈⠳⡄⠀⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢽⡀⢸⣿⠁⠀⠀⣧⣸⣏⠀⢀⣤⡄⣰⠏⠀⠀⠀⠘⣇⢸⡧⢖⣻⠞⠀⠀⠀⢹⡀⠀⠀⠀⢸⡌⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⡄⠹⣧⣤⡾⣿⡟⠙⣦⡾⣿⣳⢗⣶⠖⠀⢀⣴⠏⡄⢻⡋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⣀⣀⣳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⡴⠒⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⠀⠹⣿⠁⠉⠛⠒⠛⠃⠙⠃⣼⢷⡾⠿⣽⡤⢾⠇⣼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢠⡏⠉⠈⠉⠃⠀⠀⠀⠀⠀⠀⡴⠋⣳⣤⠴⠒⠛⠒⠚⠓⠒⠶⣄⣀⣤⣀⡀⠀ ⠀⠀⠀⠘⣷⠞⠉⠀⠀⠀⣠⣄⡀⠀⠀⠀⠈⢧⠀⢤⡴⠿⠞⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠚⠁⠀⠀⠀⣀⣤⣤⣄⠀⠀⠈⠙⣦⠖⠛⠙ ⠀⠀⠀⢸⠟⠀⠀⠀⠀⣾⣛⣿⣽⡇⠰⣄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢠⡏⠀⠘⣆⠀⠀⠀⠀⣄⠀⢠⠟⠀⠀⠀⢠⠔⠋⠁⠀⠀⠀⠙⢦⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠈⠻⣆⢀⣀⠀⠙⢶⣽⡵⠃⠀⢸⣧⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡾⠉⠓⠲⣼⠀⠀⠀⢸⡏⢉⡏⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⣄⠀ ⠀⠀⠀⠀⠀⢸⡟⡽⣷⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠄⢱ ⠀⠀⠀⠀⠀⠀⠙⠛⣧⠀⠀⠀⠀⠸⡇⠹⣧⡀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⣴⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⣟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡇⠀⠹⣿⡇⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣠⢾⡀⠀⡇⠀⠀⠀⠀⠀⠀⠨⣿⠓⢿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡎⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⢶⡤⠧⢤⣾⣿⠁⢠⠞⠁⠀⠀⠀⠀⢀⣠⣶⠋⠁⠀⠙⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⠋⠙⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡎⠉⠀⣠⠟⠋⠁⣴⠃⠀⠀⠀⠀⣠⠖⠉⠀⠘⣦⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⣼⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣹⢁⣸⠟⠁⠀⠀⡼⠁⠀⠀⠀⢀⡾⠉⠉⠳⣦⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡲⠶⠶⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⠁⠀⠀⠀⢠⠟⠳⢄⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⣸⣆⠀⠀⠀⢀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⢠⣏⡠⠤⠤⢷⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠑⠶⡇⠀⠀⠀⠀⡇⠀⠀⠀⢧⠈⠳⠦⠴⠚⣡⠇⣠⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⡀⠀⠀⠀⣼⣇⠀⢸⡷⠦⣄⡇⠀⠀⠀⢠⠷⠤⣀⠀⠀⣹⠟⣀⣘⠛⢓⣺⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡷⠤⠤⣄⡀⠀⠀⠀⠀⠀⠸⣄⠹⢆⡙⡦⢴⠋⢁⡿⠀⠀⢣⠀⢸⠁⠀⠀⠀⢸⠦⢤⣀⣙⣻⣡⠞⠁⠈⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⣤⠖⠛⠃⠀⠀⠀⠀⠀⠀⠻⣟⣚⣛⣣⣼⣻⣍⠀⣀⣠⠼⠷⡾⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣛⣡⠤⠤⣴⠇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠘⢧⠖⠒⢒⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢛⡟⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠳⣾⠉⠀⠀⢀⡠⣤⠖⠀⠀⠀⣠⡖⠀⠀⠀⠘⣤⡞⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠙⠲⠴⣋⣀⢻⡀⠀⠀⣴⠃⠳⣄⠀⣀⡴⠋⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠛⠒⠒⠛⠋⠁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠤⠤⣄⣀⣀⣀⣀⣠⠤⠤⠔⠚⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠒⠛⠿⢿⣗⠶⣤⠀⠀⣠⠶⣛⡿⠿⠓⠒⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠖⠛⠛⠿⢿⣭⣛⠻⢷⣶⣦⣌⠁⠈⢳⡟⠁⠊⣡⣴⣶⡿⠟⣛⣭⡿⠟⠛⠛⠲⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠀⢀⣀⡀⠀⠀⠀⠈⠙⢷⣦⠙⢳⡌⠻⣦⠈⢁⣴⠏⢡⠟⠁⣤⡾⠋⠁⠀⠀⠀⠀⣀⣀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⡾⠋⠉⠉⠉⠻⢷⣦⡀⠀⠀⢻⡷⣄⠹⠀⠸⣧⣸⠃⠀⠈⣠⢾⡟⠀⠀⢀⣴⡾⠛⢉⡉⠉⠻⣦⠀⠹⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⣆⠀⠀⠀⠀⢻⡇⠀⣷⡀⢰⡿⠛⣧⠀⢻⣇⠀⠀⠈⢿⡈⠀⠀⠀⣿⣿⠀⠀⠀⢡⡿⠀⠀⠀⣸⡏⠀⣼⠛⢿⠀⢀⣿⠀⣰⡇⠀⠀⠀⢀⣰⢿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⡌⠳⢦⣜⣶⡦⣿⣆⡈⠻⢦⣭⡾⠏⣀⣾⣿⣤⣤⣤⣼⣧⠤⠴⠶⠿⠿⠶⠤⠤⣼⣧⣤⣤⣤⣿⣧⣀⠹⢦⣭⠴⠟⠁⣰⣿⢴⣶⣢⠴⠟⢁⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢻⣤⣀⠀⠀⠀⠀⠙⢿⣦⣤⣤⣶⡟⠋⠀⠀⠀⠉⠛⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠉⠀⠀⠈⠙⢻⣶⣤⣤⣴⡿⠋⠀⠀⠀⠀⣀⣴⡏⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⠈⣧⠉⠛⠲⢤⡀⣠⡤⠿⣿⣟⠛⠛⠳⠤⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠤⠒⠛⠛⢻⡿⠿⢤⣄⣀⡤⠖⠚⠉⡾⠁⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠘⢧⡀⠘⢦⣽⡿⣤⠄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠠⣤⣽⣏⡴⠂⢀⡼⠁⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢧⡀⠈⢳⡄⢨⣿⡄⠻⠴⠶⢿⣤⣤⡿⡄⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⣠⣿⣤⣼⡿⠶⠤⠟⢰⣿⡄⣠⠞⠁⢀⡼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄⢹⡿⠈⣿⣦⣤⣴⣦⣤⣤⣁⠉⠛⢦⡀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠸⢋⠀⠀⠀⢠⡶⠛⠉⣈⣥⣤⣤⣤⣤⣶⠏⠈⢿⡏⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⠀⠈⣿⢛⣹⠋⠀⠀⠉⠳⣆⠘⣷⡀⠀⠀⠘⣄⠀⠀⠀⠀⣰⠃⠀⠀⢀⡾⠃⣰⠟⠁⠀⠀⠹⣏⠋⢹⠀⠀⢸⣿⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢿⣷⣻⢻⠀⠐⣄⡇⣸⡇⠀⠀⠀⠀⠀⢹⣇⠈⠳⣤⡟⠉⣙⢷⠀⢀⡾⣉⡍⢳⣴⠟⠁⣼⡇⠀⠀⠀⠀⠀⢹⡇⣼⢠⠀⠀⣟⣿⣼⡹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⣱⠏⢠⣿⠀⠀⢀⣙⣿⣿⣅⡀⠀⠀⠀⠀⣸⢿⣧⣄⠈⠳⠶⢋⡼⠀⠈⣧⡙⠶⠟⠁⣠⣾⡻⡇⠀⠀⠀⠀⢀⣸⣿⣿⣃⡀⠀⠘⣿⡄⢳⣜⠷⣄⠀⠀⠀⠀ ⠀⠀⢀⡴⢛⣡⠞⠁⢠⠟⣿⡴⠚⠋⠁⠀⠀⠀⠉⠛⢦⣄⢠⡟⣈⣤⡬⠿⠿⠿⠛⠒⠒⠒⠚⠛⠿⠿⠿⢥⣤⣁⢳⣀⣠⠶⠛⠉⠀⠀⠀⠈⠙⠻⢦⡏⠹⡀⠙⢷⣌⠛⢦⡀⠀ ⠀⢰⡟⢀⡞⢁⣴⠧⢤⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠛⠋⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠙⠛⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡤⠼⣦⡘⢷⡀⠻⡄ ⠀⡟⠀⣾⠀⡏⠀⢠⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⣴⠞⠉⠉⠙⠲⢤⣀⠀⠀⠀⢀⣠⡤⠞⠋⠉⠉⠳⣄⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢀⡄⠀⢻⠀⡇⠀⣧ ⠀⡇⠀⠘⣧⣳⣤⡼⢃⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⠖⠒⣤⠀⠉⠉⢓⠚⠉⠁⠀⣴⠖⢲⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠸⣧⣤⣞⡴⠃⠀⣼ ⠀⠹⣆⠀⠀⠉⠉⣠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣉⣥⠾⢷⣄⠀⢈⡇⠀⣠⡼⢧⣬⣉⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⢳⡈⠉⠁⠀⠀⣰⠇ ⠀⠀⠈⣳⣶⣶⠞⢋⣾⡏⠹⣿⣦⣄⣀⣀⣠⠤⠴⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠶⠤⣄⣀⣀⣠⣴⣿⠃⢻⢧⡙⠷⣶⣶⣋⠁⠀ ⢀⡴⠏⠁⠉⠀⠀⠘⢸⡇⠀⠘⢿⡓⠲⠶⠿⣿⣿⡟⠛⠿⣾⣽⣳⣦⢤⣀⣀⣤⢴⣾⠟⠿⣗⡶⢤⣀⣀⡤⣶⣞⣽⣷⠿⠛⢻⣿⣿⠿⠾⠗⣛⡿⠃⠀⢸⡎⠃⠀⠀⠉⠈⠙⣦ ⣸⠁⢀⡴⠛⠉⠙⠻⣾⡇⢰⠀⠀⠻⡛⠲⢤⡈⠙⣇⠀⠀⣿⣿⣷⣯⣽⣿⣻⣿⣩⣤⣾⣶⣤⣍⣿⣟⣿⣯⣽⣶⣿⣿⠀⠀⡼⠛⢀⡤⠖⢻⠏⠀⠀⡇⢸⡷⠚⠋⠙⠛⣦⠀⠈ ⣿⠀⢸⠁⠠⠚⢳⡆⠸⣇⢿⡆⠀⠀⠹⣦⡀⠙⢦⡘⢆⠀⣿⠛⡿⣿⠛⠛⠛⠻⠿⠿⣿⣿⠿⠿⠟⠛⠛⠛⡿⣿⠛⣿⠀⣰⣡⡾⠋⢀⣴⠋⠀⠀⢸⡇⣸⠁⢠⠞⠓⠀⢘⡇⠀ ⠸⣆⠘⠳⠦⠤⠞⠁⢠⡟⠾⣿⣄⠀⠀⡈⢻⣦⡀⠙⢮⣷⣼⣶⣇⠈⢳⣄⡴⣦⣴⣦⣼⣧⣖⣦⡤⢦⣠⠞⠁⣸⣶⣧⣾⡿⠋⢀⣴⠟⠁⠀⠀⣰⣿⠟⢻⡀⠈⠳⠤⠤⠚⠁⣰ ⠀⠙⠲⢤⣄⣀⣠⣴⡿⠖⠒⠛⠿⣧⠀⢳⡀⠙⢷⡀⠀⠉⠻⢵⣉⠙⠒⠛⠋⣉⣉⣉⣉⣉⣉⣉⣉⡙⠛⠒⠋⣁⡮⠞⠉⠀⢠⡾⠋⢠⠖⢀⣾⠿⠓⠒⠲⢿⣦⣄⣀⣀⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⢀⡤⠀⠀⢸⡄⠀⢿⡄⠸⣇⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀⣾⠃⢠⡏⠀⢸⠇⠀⠀⢤⡀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣄⠀⢀⡼⠁⠀⢸⡷⢰⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡆⣾⡇⠀⠘⢷⡀⠀⣸⡇⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⠉⠉⠀⠀⢀⣾⣷⠏⠀⠘⢦⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠻⣿⣷⡀⠀⠀⠉⠉⠁⠀⢀⣼⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠦⠴⠶⠟⠋⠀⠀⡴⠏⣉⣭⣙⠳⣶⡞⠋⠉⡏⠀⠀⣿⡇⠀⠈⢹⠉⠉⢳⡶⠞⣫⣍⣉⠻⣆⠀⠈⠉⠻⠶⠦⠤⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡾⠃⣦⣹⠀⣽⡇⠀⢰⣷⠃⣄⡿⢷⢠⠸⣾⡀⠀⢸⣇⠀⣇⣼⠘⢧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢧⣄⣠⡤⢞⠟⠀⢀⡾⢃⣼⡽⠁⠘⢧⣧⡘⣷⡀⠀⢻⠷⢤⣀⣠⡾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣤⣴⣻⣴⢟⠋⠀⠀⠀⠀⢙⣻⣮⣿⣦⣤⣀⣀⣀⣠⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⠀⡠⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⢄⢀⠀⠳⡠⠚⠈⠉⠉⠁⠓⢄⢒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⡄⠀⢃⢻⡸⠋⠀⡠⣐⡂⢰⡂⢄⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⡜⡇⣸⡼⣠⣄⣎⠀⢰⠰⠾⠃⠀⡆⠀⢨⠐⡄⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀ ⠀⠰⡸⠃⢁⡉⠁⠻⡛⡳⠷⠀⠀⠀⠇⠀⠸⡁⠁⠀⠀⢰⠝⠒⢈⣈⡀⠢⡀⠤ ⠀⠘⢅⣀⠸⠿⠋⣦⠄⠀⠀⠀⠀⡜⠀⢀⠃⠼⠀⠠⢢⠁⠀⠎⠀⠀⠈⠆⠘⡀ ⠀⠀⠘⠻⡁⠀⠐⢣⡀⠀⢀⠄⠊⠀⢀⢦⠀⠀⠀⢀⡃⠀⠰⠀⠀⠀⠀⡀⣰⠉ ⠀⠀⠀⠀⣃⠤⠐⡼⢇⠄⠁⢀⠠⡖⠉⠾⠀⠀⠀⠘⢼⠀⠈⡀⠀⠀⢠⠗⠙⠀ ⠀⠀⠀⠀⠻⠕⠉⢠⠃⠀⡔⡉⢢⠜⠀⠀⠀⠀⠀⢖⢺⠀⠀⡇⠀⡀⠁⢀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⠂⠘⠀⠀⠀⣄⠀⢀⡀⡤⢹⠀⠀⠇⡀⠢⢄⡴⡥⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⢨⠕⠂⠀⠀⠳⣑⡫⡷⣁⠰⡌⠀⢠⠁⠐⠃⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⢦⣀⠤⠀⠀⠀⢀⠈⢰⢻⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠁⠒⠭⠅⠀⠋⠄⠔⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⢀⣀⣀⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣬⣿⣿⣤⣶⣶⣾⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣶⣶⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠋⠉⢻⣯⣭⣭⣥⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠉⠉⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣶⡀⠀⣠⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⣠⣾⣿⣿⡿⠟⠃⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⢨⣟⠿⣿⡷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣠⣴⣿⡿⠟⣛⠁⠀⠀⠀⠀⠈⠙⠻⠟⢀⣀⡀⠀⠀⠀⢻⣷⣤⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠘⠿⠃⠀⠚⠋⠉⠁⠀⢸⣿⣷⣄⣀⣀⣤⣤⣴⡶⠿⠿⠟⠛⠃⠀⢠⣿⡟⠋⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠁⠉⠉⠉⢉⣠⣤⣶⣶⣦⠀⠀⣠⣿⠋⠀⣸⣿⣦⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁⠀⣤⣀⣀⣀⣠⣶⣷⣦⡀⠀⢀⣼⡿⠁⠀⣾⣦⡈⠉⠉⠉⣉⣉⣥⣄⡴⣿⣿⣷⣶⣾⣿⠟⠁⠐⣶⣤⣀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⠛⠙⣿⣿⡟⣶⣿⣿⣤⣦⣼⣿⠟⠙⠛⠛⠛⠛⢛⣉⡁⠀⠘⠋⢀⣼⡟⢡⣄⠀⠀⢹⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠈⠛⠉⣠⣿⠟⣅⠀⢰⣤⡤⠴⠞⠻⣿⣿⠗⢀⣴⣿⣋⣀⣤⣿⣷⠀⠈⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⣿⣿⠀⠀⢀⣴⡿⢉⣀⣹⣿⣌⣿⡇⠀⠀⣠⣿⣇⠸⣿⣿⡿⠛⠉⠁⠈⣿⠀⠀⣿⡏⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⡀⠀⠀⠀⣿⣿⣿⣿⠟⣿⣿⠀⣶⣿⣿⠿⠛⠉⠁⡿⠋⠸⣿⠒⠛⠻⠉⡉⠀⢻⣦⣤⣤⡶⠾⠟⠛⠀⠀⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⠆⠀⣿⣿⠀⠀⠀⣿⣿⠀⣮⣏⣁⣤⣴⡶⠿⠗⣶⣤⠾⠶⣿⡿⠟⠛⠉⠀⣿⣷⣤⡴⠾⠿⠂⠀⢰⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠛⠻⠿⠿⠿⠛⠛⠉⣿⣿⣿⠟⠁⠀⠀⣿⣿⣠⣄⠀⣿⣿⠀⠙⣿⣇⣀⣤⡶⠆⠀⢸⡷⣤⣴⣿⡷⠾⠛⠀⠀⢸⣿⣤⣴⠶⠞⠀⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⣿⣿⠛⠛⠛⣿⣿⠀⠀⣿⣧⣠⣤⣶⠆⠀⢸⣇⣠⣤⣿⣷⡾⡗⣀⣀⣈⣿⣤⣤⣤⣶⡶⠀⠸⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⣿⣿⠀⠀⢹⣯⣉⣥⣤⣤⣤⢾⣧⣀⣭⣿⣦⣿⣷⣯⡟⢻⣿⠻⣯⡀⣼⠟⠂⠀⠉⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⣾⣿⠇⠀⠀⢸⣿⣿⠿⢿⣿⠿⣯⡉⣿⡆⠀⠹⣏⠩⣅⠰⣦⠀⣿⡿⠁⢸⡟⠀⢈⣿⣷⣤⣀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⢠⣿⡟⠀⠀⠀⢸⣿⣿⠀⢠⣿⣀⣽⢿⣦⣄⣀⣿⠹⣷⣸⣧⠹⢷⣿⠇⢀⣿⣷⣾⠟⠁⠈⠻⠿⡟⠋⠁⠀⢸⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⣼⡿⠁⠰⣶⣤⣾⣿⣿⠠⣿⡿⠟⠀⠀⠉⠛⢻⡿⠀⠉⠙⢶⣤⣾⡿⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠙⢿⣶⣤⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⣴⡟⠁⠀⠀⠈⠻⣿⣿⡟⠀⠉⣵⡆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⢀⡉⠀⠀⠀⠲⣶⣦⣤⣄⡈⠻⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠛⠀⠀⠀⠀⠀⠀⠛⠛⠀⢀⣴⣿⣿⠀⢻⣶⡄⠀⠀⠀⠻⣶⣶⣦⣄⠀⠀⠈⢷⣄⠀⠀⠀⠉⠻⣿⣿⣿⠀⠹⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠻⣿⣦⣄⡀⠀⠈⠙⠿⡿⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⠈⠙⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠘⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠋⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣠⣿⡷⢚⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣽⣿⡏⠻⠟⣋⣉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠀⠻⣿⣡⣤⣽⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠿⠛⠛⣹⠉⠅⣼⠏⢀⣀⣀⠴⠚⠻⠿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡟⠀⢠⣾⢀⣿⣿⣼⡏⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⠇⢀⣿⣿⠏⢛⣿⢏⣀⣤⣶⡆⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋⣸⣿⣿⡛⠛⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⢀⣼⠟⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠴⠋⠁⣀⣀⣤⡶⠛⠁⠀⠀⠙⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣋⣩⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⢿⣦⡹⣤⠞⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⢷⣲⠯⣯⣻⣬⠟⠻⠤⠟⠉⠳⣄⠀⠀⠀⢀⣀⣀⡤⡄ ⠀⠀⠀⠀⢶⢦⣀⣤⣇⣧⡀⢀⣀⠀⠀⠀⠀⠀⠀⢸⠛⣆⠀⢠⠞⣻⠀⠛⣻⣿⣻⠽⣶⡮⠽⠇⠀⠀⢀⣀⠀⠋⠉⠉⢉⣽⣧⠌⠀⣹ ⠀⠐⣖⣦⣾⣻⣗⣞⣓⣖⢻⣭⠟⠀⠀⠀⢸⡖⢦⣼⢷⡞⠉⠙⠶⣇⠀⣀⣨⠉⡴⢒⣚⣢⡤⣄⠀⠀⠘⠈⠀⠀⠀⣀⣤⢟⣿⣀⣼⠿ ⢶⣶⢿⣻⠿⠚⠉⠻⡗⣎⡻⣸⣷⡤⣤⣀⣀⣿⠖⢫⡋⣬⠛⢺⣉⣹⡋⣡⠾⣤⣹⣦⣀⣠⣽⣶⣒⣲⣶⢤⣠⣶⣿⣿⣯⠟⠀⠳⠏⠀ ⢰⣧⠞⠁⠀⠀⠀⠀⢻⡬⡗⠺⠿⣶⠉⢳⣭⡟⢒⠎⢹⡽⠳⣈⣫⣀⣉⣯⠻⣝⡿⣟⣿⣷⡿⣥⢀⠈⠙⠻⢶⣿⡟⣿⣿⣷⣀⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢏⣑⡧⢾⣶⡯⠼⠓⢺⠉⣟⣽⠉⣧⠬⣵⣀⣹⣆⡟⣨⠛⠻⣽⣿⣷⡟⠙⠒⡒⠲⠯⢍⣛⣛⣿⠿⢛⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠚⡤⠹⢏⣾⣉⣱⢒⡏⠉⣯⡿⡍⠺⠔⠬⣅⣧⢼⡭⢼⢤⡞⠛⢾⣿⢀⣰⢿⣿⡄⠀⠀⠀⠉⢹⢿⠟⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⢾⡝⠉⠉⠙⠛⢯⣽⠋⠀⠹⣽⠗⢤⢽⡥⡼⠂⡼⠛⢳⡀⢸⣭⠽⠃⡾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢥⣗⣶⣶⣺⡇⠸⣷⣾⣿⠀⠹⣧⠼⢦⡛⢤⡤⠓⢲⢋⡷⣄⡤⠚⢦⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣖⣁⣺⣷⡼⢥⡞⠉⠿⠋⠀⠀⠈⠳⢤⣟⣙⣤⡴⠞⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⠉⢸⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠉⠀⠀⣀⣠⣤⣴⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠁⠀⠀⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣛⡛⠓⠦⠄⠀⠀⠀⠈⠙⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠐⢋⣡⣤⣶⡆⢹⣿⣿⣿⣿⣿⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⠟⠀⠠⠤⣤⣤⣤⣾⣿⠟⠋⣉⡀⢸⣿⣿⠋⢿⣿⣿⡀⠀⠙⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀ ⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⣥⣶⣿⠟⢁⣾⣿⠏⠀⠀⢻⣿⠇⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀ ⠀⣼⣿⣿⠏⠀⠀⠀⠀⢠⣿⠏⣿⣿⣿⣿⠏⢀⣾⡿⠋⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄⠀ ⢰⣿⣿⡟⠀⠀⠀⠀⠀⢸⠃⣼⣿⣿⣿⠇⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀ ⣸⣿⣿⠃⠀⠀⠀⠀⠀⠁⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣦⠀⠀⢸⡄⠀⠛⠋⠉⠉⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠀⠀⠀⠀⠰⠟⠋⠁⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠆⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃ ⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀ ⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠟⠉⠲⠶⣶⣶⣶⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀ ⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣨⣿⣿⣡⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀ ⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⣀⣴⣾⠟⢻⣿⡄⠀⠀⠀⠐⠛⠋⢙⣿⡿⢋⣼⠆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⣴⣾⣿⠟⠁⠀⠀⢻⣿⡄⠀⠀⢀⣠⣴⡿⢋⣴⡿⢻⣶⣄⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣈⠛⠁⠀⠀⠀⠀⠀⢻⣿⡀⢚⢛⣉⣡⣶⠟⠋⠀⠀⠙⠿⠗⠀⣠⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣦⣄⡈⠙⠛⠿⠿⣿⣧⠈⠉⠉⠁⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢧⠀⠀⠀⠀⢠⣶⡟⠲⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⢙⡃⠀⠀⠀⠀⠀⠀⢙⡉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣷⣄⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⣰⣤⣴⡿⣯⠚⠧⠛⢠⣀⣀⣀⢠⢄ ⠀⡠⣸⡷⡾⢾⣄⡄⠀⠀⡤⣠⠽⠤⠎⡇⢈⡛⡷⠿⢑⡁⠀⠆⠈⠀⢀⣿⣀⣼ ⢲⣻⠟⠊⠹⡾⣇⣷⡠⡤⣽⣋⠭⣑⠨⠹⡽⣧⣷⣬⣽⠖⠶⣦⣴⣾⣿⡆⠑⠁ ⠈⠁⠀⠀⠀⢩⡆⡯⣧⣿⠇⡇⣼⠌⠾⢆⡳⣜⡹⢻⣽⣷⠃⣀⠹⠟⣛⣷⢛⠀ ⠀⠀⠀⠀⠀⠸⡵⢜⡼⠺⢭⣀⡞⢯⣇⣺⡇⣃⡲⣎⠹⣇⣾⣿⠀⠀⠀⠘⠋⠁ ⠀⠀⠀⠀⠀⠀⠑⢺⢦⠶⡆⣯⣶⠀⢣⡱⢝⡤⠃⡾⠢⠑⠺⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠕⠸⠿⠝⠀⠁⠀⠀⠉⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⡟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣦⠄⠀⠀⠀⠀⠈⠛⢿⣿⣿⣇⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⣿⡿⠿⠛⠋⠉⠉⠁⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠘⣿⣿⣿⣷⠀⠀ ⠀⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⣄⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠸⣿⣿⣿⡆⠀ ⠀⣸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠙⣷⣶⣶⣾⣿⣿⡆⠀⠀⠀⣸⣿⣿⣤⣶⣾⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢻⣿⣿⣿⠀ ⢀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢸⣿⣿⣿⡆ ⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠀⣴⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡻⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⠇⠈⠉⠉⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⣿⡇ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣬⣙⣛⣛⣛⣫⣵⡷⠈⠁⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⣿⣿⠀⠀⢀⣿⣿⣿⡇ ⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⣠⡾⠃⠀⠀⠀⠀⣾⣿⡿⠀⠀⢸⣿⣿⣿⡇ ⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢤⣴⣶⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⣀⣤⣾⣿⠋⠀⠀⣠⣴⣿⠃⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣸⣿⣿⣿⠀ ⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⣀⣀⣀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣋⣀⣠⣴⣾⣿⡿⠃⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⢠⣿⣿⣿⡟⠀ ⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠈⠻⠿⠿⠟⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢀⣠⣾⣿⣿⡿⠁⠀⢀⣾⣿⣿⣿⠁⠀ ⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⣀⣴⣾⣿⣿⠏⠀⠀⠀⠀⢠⣿⡿⢿⣟⣭⣭⣬⣼⣿⡇⣤⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠀⠀⠠⡿⠋⠀⠀⠈⠙⠛⣻⠏⠉⣤⠀⠀⠀⠀⢀⣿⠁⠀⣸⣿⣿⣿⣿⣿⡿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄⠀⠀⢨⣶⣶⣶⣶⣶⣶⣿⠟⠀⠀⣿⣷⣤⣤⣶⣿⠇⠀⢠⡿⠿⠿⠛⠛⠉⠀⠀⠀⠘⢿⣿⣿⡿⠿⠛⠛⠋⠁⠀⢠⣾⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣦⠀⠘⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠹⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣽⣗⣯⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⢫⣟⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡤⠖⠒⠒⠲⢤⣄⡀⠈⢻⡝⠳⣆⠀⠀⢀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⢀⣠⣴⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠳⠦⣄⠀⠀⠀⠉⠳⣦⣹⠀⠈⣧⣰⠋⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠹⣆⠀⡠⠊⠉⢰⠋⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠙⠃⠀⠸⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡿⠀⠀⢰⣇⣤⠔⠋⠁⠀⠀⠀⢀⣸⡿⠟⠀⠀⠀ ⠀⠀⠀⣦⡄⢀⣠⣶⡛⠛⠛⠓⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠁⠀⠀⠾⠋⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠙⢯⣍⠉⠙⠶⣄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠷⠖⠶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⢿⡀⠀⠈⠙⠒⠶⢾⠿⠶⠀⠀⠀⣀⣠⠤⠤⣤⣀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⡤⠶⠞⠻⠃⠀⣠⣿ ⠀⠀⠀⠈⠻⣆⡀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⣀⣨⣿⣦⡀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⣀⣤⠴⠶⠦⣄⣀⡀⠀⠀⠀⠐⠛⠳⠶⠦⠤⠴⠖⠋⠁⣸ ⠀⠀⠀⠀⠀⠀⣉⣛⡒⠛⠛⠙⢧⡀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⢦⣄⠀⠘⣦⡀⠀⠀⠀⢰⠇⠀⢀⣴⡾⠋⠁⠉⠳⡆⠀⠀⠈⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋ ⠀⠀⠀⣠⡴⠊⢉⡏⠀⠀⠀⠀⠈⣷⢤⡀⠀⠀⠀⢻⡄⠀⠀⠀⣸⠀⠉⢓⣦⣽⣦⡄⠀⢠⣯⣤⡖⠋⠀⡇⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣠⡟⠈⠉⠓⣶⣒⡒⠒⠒⠋⠁⠀ ⠀⠀⡾⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠙⣆⠉⠒⠦⣤⣀⡙⠒⠒⣛⣡⡤⢖⡿⠟⠉⠁⠀⠀⠀⠈⠉⠻⣷⣤⣝⠦⣤⡤⠞⠁⠀⠀⢀⣠⢞⡿⠀⠀⠀⠀⢳⠈⠙⠲⣤⠀⠀⠀ ⢀⣾⠁⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣀⣀⣉⣉⣩⡧⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢭⣓⣶⣶⣶⣶⣖⣫⠴⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠈⢳⡀⠀ ⢸⡏⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢷⠀ ⢸⡇⠀⠀⠹⣇⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⣸⠃⠀⠀⢸⠀ ⢘⢿⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⢀⣼⡟⠀⠀⠀⡞⠀ ⠛⢾⣷⣖⣉⣉⣉⣷⣄⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣰⠯⣟⡀⠀⠀⣴⠃⠀ ⠀⠀⠙⢷⣍⠉⠁⠉⠻⣷⢄⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣤⡾⠧⢤⣀⣉⣙⣾⠷⠀⠀ ⠀⠀⠀⠀⠈⠻⣆⠀⠀⠈⠳⢽⡶⣄⡀⠀⠀⠙⠳⢤⣀⣠⠤⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠦⢤⣠⡴⠚⠁⠀⠀⢀⣠⡾⠟⠋⠀⠀⢠⣤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠙⠛⠿⣷⡤⣄⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⣠⣤⡾⠛⠉⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠉⢺⠁⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⢻⠋⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠁⠀⠀⢀⣾⠁⠀⠀⠀⠀⢰⡶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠛⠃⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⢀⣧⣀⡀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢴⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⣸⣧⣙⠳⠦⠤⠤⠤⠴⠛⠀⠈⠙⠛⠓⠚⠛⠋⠙⢷⣄⣀⣀⣀⣠⣾⡷⣄⣀⣀⣀⡤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⢻⡉⠓⠢⠤⣤⣄⣀⣠⣠⡤⠤⠤⠦⠤⠤⣤⣀⣀⣉⣉⣋⡭⠟⣹⢣⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠳⣄⠀⠀⢸⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⡟⠀⡴⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡘⢧⠀⠈⠻⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⢠⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⢸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢃⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠸⡎⢳⡀⢀⡀⠀⠀⠀⠀⢀⣀⠀⡞⢡⠃⣼⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣷⡀⣧⠈⣷⠋⠹⡄⠀⠀⠐⡟⠉⢹⠁⣸⠼⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠉⠛⠒⠛⠒⠛⠛⠋⠛⠉⠉⠉⠉⠉⠁⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⣀⣠⡤⠤⣤⣀⣀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣩⠆⣼⡋⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⢏⣾⣿⠀⠻⣷⣤⣀⣹⣦⡀⠀⠀⠀⠀⠀⠀ ⣠⠴⠶⠦⣄⡀⣀⠾⠋⠾⠿⠛⠳⠦⠈⠙⣛⣻⡭⠗⡒⢦⠀⠀⠀⠀ ⠘⡄⠿⢤⡀⠉⠁⠀⢀⠀⠀⠀⠀⠀⡀⠀⠉⠁⣤⡴⠟⡼⠀⠀⠀⠀ ⠀⢻⣜⠶⠏⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⣋⣴⠃⡄⠀⠀⠀ ⠀⠀⣿⣇⣀⣀⣀⣀⣧⠀⠀⠀⠀⢀⣾⣄⣀⣀⣠⣿⡇⠀⢳⡀⠀⠀ ⠀⠀⣿⡏⠉⠁⣄⣀⡙⡇⠀⠀⠀⡾⢋⣀⡀⢉⠉⣿⠇⠀⠸⣷⡀⠀ ⠀⠀⠘⣿⠀⢆⡘⠒⠷⠀⠀⠀⠀⠠⠧⠗⢁⡾⢸⡏⢰⠀⠀⣿⣿⡄ ⠀⠀⠀⠹⣧⠀⢱⣦⠀⠀⠀⠀⠀⠀⢠⣾⠋⣡⡟⢁⡿⠀⠀⣼⣿⣷ ⠀⠀⠀⢸⣾⣷⣴⡏⠀⡀⠀⠀⢀⠀⠸⣿⣾⠋⣠⡾⠁⠀⣰⣿⣿⠇ ⠀⠀⠀⢸⣿⡟⢿⡇⠀⠻⢿⡿⠟⠀⠀⣿⠏⣼⡏⠀⢀⣾⡿⠛⠁⠀ ⠀⠀⠀⠈⢿⣷⡌⠳⣤⠤⠼⠧⢄⣤⡴⠋⣠⣿⠃⠀⢻⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣌⠢⣀⣀⠴⠋⣠⣾⡿⠃⠀⢨⡜⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣴⠾⠛⠋⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣅⣠⣼⠇⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠙⠋⠁⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⢀⣀⠀⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣶⡌⡏⣴⡆⢩⠘⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗⠓⠺⡗⠊⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣚⡛⠻⠿⡶⣄⢀⡴⢞⠿⠛⣛⣓⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠉⠉⠛⢿⣍⡛⢿⡶⣄⠈⠟⢀⡴⢺⡿⢋⣭⠟⠋⠉⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⡶⠒⠒⠶⣦⣀⠀⠙⣿⣄⠱⠈⢷⣠⡏⠀⠋⣴⡟⠁⠀⣠⡴⠖⠒⠲⢦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⢧⡀⠀⠀⠸⡇⢸⣄⢰⡞⣶⠈⣿⡀⠀⠘⣏⠁⠀⢸⣿⠀⠀⠈⡾⠀⠀⢸⡏⢠⡞⢷⠀⣸⠇⣸⠁⠀⠀⢠⠾⡄⠀⠀⠀ ⠀⠀⠀⠀⡏⢠⠙⠲⠿⠟⠿⣤⡙⠓⠞⣋⣴⠿⠷⢶⣶⡿⠒⠒⠛⠛⠛⠒⠲⣷⣶⠶⠾⠷⣤⡛⠶⠚⢁⣴⠟⠺⠷⠚⢁⡄⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠈⡟⠦⢤⡀⠀⢈⣿⣿⡿⠯⣄⡀⠀⠀⠈⠙⢇⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⣀⣬⠿⣿⣿⣟⠁⠀⣀⡤⠖⡿⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠸⣄⠀⢯⣿⣏⡄⠙⣧⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⡾⠁⢠⣹⣏⠵⠀⡼⠁⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠘⢦⣠⣿⡘⠒⠺⠿⠤⡿⣄⠀⠀⠀⠀⢤⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⣰⣷⠴⠿⠒⠚⣰⣿⣀⠞⢁⡰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣤⡟⠀⢿⡶⣾⠶⠲⠦⣄⠙⣆⠀⠀⢠⠀⠀⠀⠀⢨⠀⠀⠀⡼⠉⣠⠴⠒⢶⣶⢾⡏⠈⣿⣰⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠇⢀⣸⢡⡎⠀⠀⠀⠘⣧⠙⢦⣠⠖⢳⡄⠀⣰⢗⢲⣀⡼⢁⡞⠁⠀⠀⠈⢷⢈⣇⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⢺⠟⣱⡇⠀⢀⣿⣾⣇⡀⠀⠀⠀⡾⣧⣀⠙⠶⢃⡏⠀⢧⡻⠴⠋⣠⣾⡇⠀⠀⠀⢀⣸⣿⣏⡀⠀⣿⡌⢯⡳⣄⠀⠀⠀ ⠀⢀⡔⢫⠔⡁⠐⢉⡷⠋⠁⠀⠀⠀⠉⠓⢦⣴⡥⠴⠚⠛⠛⠋⠁⠁⠉⠙⠛⠛⠳⠦⢽⣤⡔⠋⠁⠀⠀⠀⠉⠓⣿⠑⠀⡙⢮⡙⢦⠀ ⠀⡟⢰⠃⡞⠛⠓⣾⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠘⡖⠛⠛⢦⢱⠈⢧ ⠸⡇⠘⣜⣦⣠⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⡤⢤⡈⠓⠲⡤⠒⠋⢁⡤⢤⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢺⣀⣼⡼⠀⢸ ⠀⢷⡀⠀⠉⣁⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣡⠴⠷⣄⣀⣇⣀⡤⠻⢤⣩⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⡉⠁⠀⣠⠏ ⠀⣀⡽⠿⠟⢁⣾⠃⠹⣷⣦⣤⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⢀⣸⣿⣄⠀⠀⠀⠀⢀⣠⣤⣶⣶⣷⣶⣦⣤⣴⣿⠃⢹⢧⠙⠻⠿⢥⡀ ⣰⠃⢀⠴⠒⠦⣼⠀⡄⠘⢶⠬⣉⠛⢿⠀⠉⣿⣿⣿⣿⣶⣿⣛⣋⣬⣙⣻⣷⣾⣿⣿⣿⡟⠁⢸⠿⠋⣩⢴⡞⠁⢠⢸⡤⠴⠲⢤⡀⠹ ⡇⠀⡇⠠⠲⣤⢸⡄⣧⠀⠈⢦⡈⠑⢌⢧⠀⡿⢿⣿⠛⠛⠿⠿⢿⣿⡿⠿⠟⠛⢛⣿⡛⡏⢀⣎⡴⠋⣠⠞⠀⢀⣷⣸⠁⡴⠒⠀⢳⠀ ⠸⣄⠑⠲⠖⠁⣰⣛⣿⣦⡀⢀⠙⣦⡈⠻⢷⣿⡾⣌⣳⣴⣶⣾⠶⡷⢾⣦⣶⣤⣏⣠⢷⣷⡿⠋⢠⡾⠃⠀⢀⣾⣟⢻⡀⠙⠲⠒⠉⡰ ⠀⠈⠑⠒⠒⣺⠟⠉⠉⠉⢷⠀⢧⠈⢷⠀⠀⠙⠳⠤⣤⠤⠴⠶⠒⠒⠒⠦⠤⠤⡤⠴⠚⠁⠀⢠⡏⢀⠎⢠⡟⠉⠉⠉⠻⡗⠒⠒⠋⠀ ⠀⠀⠀⠀⢠⡇⠀⢾⠀⠀⡼⠀⢸⣧⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣾⠀⠘⣆⠀⢈⡇⠀⣻⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⣀⠀⠉⠉⠀⢀⣼⡿⠃⠈⣦⣄⡀⠀⠀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠀⠀⢀⣠⣞⠀⠹⢿⣆⠀⠈⠉⠉⠀⣠⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠋⠁⠀⣰⢋⡴⠾⡍⢻⡏⠁⣸⡀⢈⣿⠀⣀⡇⠉⢹⠏⡽⢣⢬⠳⡀⠀⠉⠛⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢼⡀⢓⣣⡾⠁⢀⡟⣰⡿⠘⣷⡜⣷⡀⠸⣧⣙⠛⢈⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⣉⣉⣀⣠⣴⣯⡾⠋⠀⠀⠈⣻⣮⣷⣤⣀⣈⣉⣩⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⢹⠀⠀⠀⠀⡾⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⡉⠉⢲⣖⠉⠙⡟⢏⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⣄⠀⢠⠤⣼⡯⠼⠁⠙⢲⠁⡈⢓⠊⣅⠙⠧⠼⣇⡤⢄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠞⠒⠛⠒⠋⠀⠀⣠⠔⠁⠈⠇⠀⢧⠈⠓⢄⠀⠈⠢⠞⠓⢴⡋⠁⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡺⡏⢼⢯⠒⠒⠁⠰⠋⠙⢀⣀⣀⣀⣀⣀⣃⣀⠘⠳⡄⠶⠶⣶⣄⠉⢶⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⠬⡿⠛⠁⠘⠄⠁⠀⣀⢴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢤⡀⠈⠁⡏⠰⣏⣉⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠉⢳⡞⠳⣚⣀⣀⠤⠴⠊⡡⠊⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⠳⡀⢧⡀⠀⠸⠥⢾⡖⠒⢲⡄⠀⠀⠀ ⠘⠿⠤⣾⣙⢾⡥⠤⠄⠀⢀⠞⢆⡀⠀⠀⠀⠈⠙⠢⠤⠄⣀⣀⡠⠤⠚⠁⠀⠀⢀⡼⢦⠛⠲⣤⡄⠙⢦⣀⡶⠃⠀⠀⠀ ⠀⠀⠘⠧⣼⠀⠙⡆⠀⢀⠾⣀⡀⠉⠑⠒⠒⠢⠤⢄⡀⠀⠀⠀⠀⣀⡤⠤⠒⠊⠁⢀⡨⢇⠀⠁⡟⢠⡔⢣⡀⠀⠀⠀⠀ ⠀⠀⠀⣾⣹⠖⡆⠀⢀⣎⣀⣀⣉⡉⠉⠐⠒⠢⢄⡀⠈⠓⠒⠒⠊⢀⡠⠤⠒⠒⠋⠁⠀⣈⣦⣀⠃⠀⢽⠟⡲⠀⠀⠀⠀ ⢀⡤⠖⢾⡁⠀⢁⠴⠊⠉⠁⠀⠀⠉⠑⠲⢄⡀⠀⠈⣶⢤⣀⡤⢶⠋⠀⠀⢀⣠⠔⠒⠉⠉⠀⠈⠉⢢⠈⠑⢳⡎⠉⢳⡀ ⣏⠀⠀⢠⠿⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣆⣀⣠⠃⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⡀⢈⣷⡤⠞⠁ ⠈⠙⢺⣅⡤⠿⢨⢧⡀⢴⠶⠾⣭⣍⡙⠒⠦⣄⠀⢱⡀⢧⢀⡟⢀⡜⠁⢀⡤⣖⣎⣭⡭⠭⡶⠆⢀⣾⠀⢹⠰⡏⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⣎⡀⠙⢦⡑⠦⣿⣿⣿⣯⣷⣮⢷⡤⣧⠸⣩⠃⡞⣠⣶⣵⣯⣽⣿⣿⠷⠊⠀⣠⠎⠀⢇⢸⠀⡇⠀⠀⠀ ⠀⢳⡸⣇⠙⠀⡗⢿⢶⡄⠈⠓⣮⣍⣉⣉⡉⠉⠉⠉⢿⠀⠈⢸⠐⠋⠉⠉⠉⠉⠉⠀⠀⠐⠋⡡⣼⠯⢿⠀⢠⠇⠀⠀⠀ ⠀⠀⡇⠈⠦⣄⣿⣌⠹⡞⢹⠄⡠⠟⠉⢀⣠⠼⢛⠿⠚⢠⢧⠈⠳⣼⠮⣉⠉⠹⢟⡋⠳⡖⠲⡷⠚⢁⣾⣴⠟⠀⠀⠀⠀ ⠀⠀⡇⠀⡤⣾⣿⠘⣆⠉⢡⠎⠁⠀⡴⠋⢠⠞⠁⠀⢠⠏⠈⡇⠀⠈⠳⡄⠙⢦⠀⠉⠣⡈⠛⠁⡠⢪⡿⣗⣦⠀⠀⠀⠀ ⠀⡜⠀⠀⠳⠽⢿⡇⠈⢷⡇⠀⠀⡜⠀⠀⠈⠉⠙⢧⡘⠤⢤⣇⠖⠒⠒⠚⠀⠀⢱⡀⠀⠹⣤⠎⢀⣾⠧⠽⠝⠀⠀⠀⠀ ⠀⡷⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⢸⠃⢀⡠⠤⠄⠀⠀⠈⣉⣉⠉⠛⠛⠓⠲⠤⣀⠀⢧⠀⠀⠃⢀⡞⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠀⠀⠀⠀⢸⣧⠀⠀⢀⡏⣰⠁⠤⠒⠊⠉⣉⡭⠭⠭⠭⣉⡉⠉⠒⠲⢤⡑⣜⣆⠀⢀⠞⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠓⠀⠀⠀⠀⢸⠋⠓⡒⠋⠀⣇⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⣹⡈⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡇⠀⠀⡟⠢⠖⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠤⠤⠃⡇⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⢧⠀⠀⣇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⡇⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⢸⠀⠀⣼⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⣿⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠀⠘⡖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡞⢸⡟⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⡆⠀⠈⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠁⢸⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢺⠀⠀⠀⣧⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⢸⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⢻⡟⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⡿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠛⣇⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡾⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠤⠴⣄⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⣼⡿⣤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣿⣷⣶⣶⣾⡿⠿⠿⠿⠿⠿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠛⠛⠛⣿⣏⠉⠉⠉⠉⠀⠀⠻⢷⣶⣶⣤⣀⠀⠀⣸⣿⣿⣿⠿⠿⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃⠀⠀⣠⣾⣿⡿⠗⠀⣠⣀⣀⠀⠀⠀⠉⢻⠿⣿⡆⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠸⣿⡿⠃⣠⣴⡿⠟⣛⡁⠀⠀⠀⠈⠛⢛⣀⣀⡀⠀⢈⣷⡦⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⣿⡿⠢⠶⠶⠶⠛⣛⣉⡉⠁⢀⣼⠟⢡⣄⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⢀⣀⠀⢀⣠⣤⡀⠀⢀⣼⠟⠀⣦⡀⠒⠚⠛⢛⣋⣁⣴⣿⣧⣤⣾⠟⠃⣤⣀⠀⢸⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⢹⣿⡿⢶⣿⣯⣤⣾⡿⠛⠒⠛⠛⣋⣍⡁⠈⠋⣡⡿⢣⣄⠀⢸⣿⡿⠸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠉⣠⡾⠛⣦⡐⣷⡖⠋⠉⣿⠟⣠⣾⣯⡴⠶⢿⡇⠀⣿⡇⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⣿⣿⣶⣾⣿⡇⣠⣾⣿⠶⠖⢻⡿⠻⣧⠤⠾⠿⠃⢻⣏⣁⣠⣤⠾⠇⠀⣿⡇⠀⣿⡇⠀⠀⠀ ⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⡖⠀⣿⡏⠀⢸⣿⡇⢼⣏⣠⣤⠶⠞⢢⡤⠷⢶⡞⠛⠛⠀⢻⣧⠤⠶⠗⠀⢰⣿⡇⠀⣿⡇⠀⠀⠀ ⠈⠉⠛⠛⠋⠉⢨⣿⡿⠋⠀⠀⣿⣷⣶⣼⣿⡇⠈⣿⡦⠶⣛⠂⢸⡿⠒⣿⣟⣻⡁⠀⢸⡷⠒⠛⣃⡀⢸⣿⡇⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢠⣿⡇⠀⢸⣿⡇⠀⢿⡓⢛⣋⣀⣸⣟⠛⣻⣟⣿⣴⣶⣾⣿⣟⠛⣹⡧⠈⠛⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⣿⡀⠀⠀⢸⣿⠁⠀⢸⣿⡷⢶⣿⢿⣋⣿⠍⢸⣟⢋⡉⣥⡈⣿⠃⢸⡇⢈⡿⣧⣄⣀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⣾⡏⣀⠀⢸⣿⡇⣰⣯⡴⠛⢷⣦⣼⠛⢷⣿⠘⣻⡟⢠⣾⣿⠋⠀⠈⠙⢫⣉⠀⢠⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⣼⠟⠀⠙⢻⣿⣿⠇⠛⣯⠀⠀⠀⠀⠛⠀⠀⠙⣿⡿⠁⠈⠟⠁⠀⢤⣀⣀⡀⠹⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⠀⠻⠋⠀⣰⣿⡇⢹⣦⡀⠀⠀⠲⣶⣬⡄⠀⠀⢷⣄⠀⠀⠙⢿⣿⣧⠈⣿⡿⠃⠀⠀⠀ ⠀⢀⣀⣀⣀⣤⣤⣾⣿⣧⣄⣀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠹⣿⣦⣄⣀⠈⠛⠛⠀⠀⢈⣿⣷⣤⣀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣿⣿⣿⠿⠛⠛⠛⠛⠻⠿⣿⣷⣶⣤⣤⣘⣋⡀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣷⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⣀⣀⣀⣠⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠦⠶⠶⣖⠒⠚⠛⠻⢯⣭⣉⠉⢩⣿⣿⡷⠀⠀ ⠀⠀⠠⣤⣤⣀⠀⠀⠀⣾⡟⢀⣠⡾⠟⠃⠰⣤⠀⠀⠹⣟⠃⠉⠁⡀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⡇⠀⠀⠋⠀⠉⠀⣼⠆⠤⢖⣚⣛⠁⣰⠋⣄⠀⠀⢻⣷⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⢰⣶⠖⣷⢦⣼⣁⡾⠦⠭⠷⡒⠻⢓⡿⡁⠸⣶⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⠀⣠⣞⣱⡼⡏⣉⣟⢵⠿⠒⣻⠀⣿⢸⣿⠀⠀ ⠀⣀⣤⣴⣿⣿⡶⠀⣿⠉⣿⠸⡯⠤⡖⢤⠷⣶⣒⠈⣯⢽⡂⢀⣿⢸⣿⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⢀⡟⠛⣿⠀⣯⠽⣂⣸⠭⣿⣖⣤⣿⡽⢲⠈⠟⢸⣿⠀⠀ ⠀⠀⠀⠀⢸⣇⠀⣸⠇⠀⣿⠛⡟⣯⣃⡸⣽⡴⣼⠃⣏⡼⠳⡤⠄⢸⣿⠀⠀ ⠀⠀⠀⠀⠈⣿⣦⠏⠘⢲⡿⠘⣏⢀⠉⠃⠈⢳⠟⠘⠋⠠⣤⣈⡳⣾⡿⠀⠀ ⠀⠀⢀⣀⣠⣽⣅⡀⠀⠀⠁⣾⡟⠘⢷⣄⡈⠻⠆⠀⢳⣄⡈⠛⠃⠙⠁⠀⠀ ⠈⠛⠿⠛⠉⠉⠉⠛⠻⠶⣶⣭⣤⣀⣀⣉⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣶⣶⣶⣶⡿⠿⠛⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⣶⣤⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⡾⠿⠛⠉⢉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢁⣠⣤⣶⣿⣿⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃⠀⠠⠴⣶⣶⣶⣤⣶⣿⣿⠿⠛⠉⢀⣀⢠⣿⣿⣿⡏⠙⣿⣿⣿⣇⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣁⣴⣶⣿⡿⠁⣸⣿⣿⡟⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⡟⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀ ⠀⢀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣾⡟⢁⣼⣿⣿⣿⣿⠏⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀ ⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠀⣾⣿⣿⣿⣿⡏⢀⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇ ⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠚⠁⢰⣿⣿⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢀⣠⣤⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠘⣧⠀⠀⠿⠿⠿⠿⠟⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠿⠛⠂⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿ ⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿ ⠀⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠟⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇ ⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁ ⠀⠀⠻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠟⠁⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀ ⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⡿⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⡄⠀⠀⠀⠀⢀⣠⣴⡿⠿⢿⣿⣿⣿⠋⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠛⠁⠹⣿⣿⡄⠀⠀⠀⠈⠁⠀⠀⢀⣴⣿⠟⢡⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣄⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⣀⣴⣾⡿⠟⢁⣴⡿⠋⢾⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⡈⠛⠛⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠛⠛⠛⣛⣁⣤⣾⠿⠋⠀⠀⠀⠙⢿⡿⠆⠀⣀⣴⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠓⠲⢶⣶⣶⣿⣿⣧⠀⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠉⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡷⣲⣾⠃⠀⠀⠀⠀⠀⠀⣀⢸⣧⡄⠀⠀⠀⠀⠀⠀⠐⢶⡲⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢻⡟⠶⠀⠀⠀⠀⠀⠘⢿⣽⡆⠙⠀⠀⠀⠀⠀⠀⠻⣻⢿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⠻⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⣠⣾⠟⠋⠁⢀⡀⠈⢻⣿⣷⣄⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀ ⠀⢀⣾⡿⣿⣿⡇⠀⠀⢰⣿⠃⠀⠀⠀⠻⠟⠀⢠⣿⣿⣿⣇⠀⠀⢸⣿⣿⢿⣧⠀⠀ ⠀⣾⣿⠁⠘⣿⣷⠀⠀⣾⡇⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⠀⠀⣸⣿⠇⠈⣿⣧⠀ ⢰⣿⣿⡆⠀⢻⣿⡀⠀⢹⣷⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣿⡟⠀⢀⣿⡟⠀⢠⣿⣿⡆ ⢸⣿⠘⣿⡄⠈⢿⣷⡀⠈⢻⣷⡀⢿⣿⣦⣼⣿⣿⣿⣿⡿⠁⢀⣼⣿⠁⢀⣿⠋⣿⡇ ⢸⡏⠀⣿⣷⡀⠈⢿⣿⣦⣀⠙⠻⣿⣿⣿⣿⣿⣿⠿⠋⢀⣴⣿⡿⠁⢀⣼⣿⠀⣿⡇ ⢸⡇⠀⣿⣿⣷⣄⡀⠙⠻⢿⣿⣶⣤⡀⠉⠉⢁⣤⣶⣿⡿⠟⠋⠀⣠⣾⣿⣿⠀⣿⡇ ⢸⣷⠀⣿⣿⣿⣿⣿⣶⣶⣤⣄⡙⠻⣿⡆⢠⣿⡟⢋⣀⣤⣴⣶⣿⣿⣿⣿⣿⠀⣿⡇ ⢸⣿⠀⣿⣿⣿⣿⣿⣉⠉⠉⠛⢿⣶⣿⡇⢸⣿⣴⡿⠛⠉⠉⢉⣽⣿⣿⣿⣿⠀⣿⡇ ⢸⣿⠀⠘⣿⣿⣿⣿⣿⣷⣶⣤⣴⣿⡟⠀⠀⢻⣿⣦⣤⣶⣾⣿⣿⣿⣿⣿⠏⠀⣿⡇ ⢸⣿⡄⠀⠀⠉⠉⠉⠉⠉⠀⠉⠿⠋⠀⠀⠀⠀⠙⠿⠋⠀⠈⠉⠉⠉⠉⠀⠀⢰⣿⡇ ⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁ ⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀ ⠀⠸⣿⡆⠀⠀⠀⠀⠀⣠⣼⣿⣿⣦⣤⣾⣷⣤⣤⣿⣿⣷⣄⡀⠀⠀⠀⠀⢸⣿⠇⠀ ⠀⠀⢿⣿⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣿⡟⠀⠀ ⠀⠀⠈⢿⣷⡀⠀⣿⣿⡿⠋⠀⠛⠿⠿⠛⠛⠿⠿⠋⠀⠙⢿⣿⣿⠀⢀⣾⡿⠁⠀⠀ ⠀⠀⠀⠈⢿⣷⡀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣦⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣀⡀⠀⠀⠀⠀⢀⣀⣤⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠛⠛⠓⠛⠙⠋⠋⠛⠟⠛⠟⠂⠚⠻⠛⠋⠂⠀⠃⠙⠙⠛⠛⠒⠒⠒⠺⠒⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣌⠻⣦⠀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢰⣾⣿⣿⠛⣷⣬⣿⠋⢠⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣿⣿⣿⣟⣛⠿⢦⣽⣦⡞⠉⠛⠶⠞⠁⠀⠙⢷⡄⠀⠀⢀⣀⣀⣤⣤⣴⢳⡄ ⠀⠀⠀⠀⠀⢰⣶⣄⣀⣀⣾⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⡀⠀⢀⣴⠛⡇⠀⠙⠛⣻⣽⣟⣫⣿⣶⣦⣭⣿⠆⠀⠀⠀⠀⠀⠀⠸⠉⠉⠉⠉⢩⣽⣦⡌⠁⠈⢻ ⠀⠀⢤⣤⣀⣠⣷⣿⣯⣥⠿⣯⡽⣿⡞⣻⡟⠀⠀⠀⠀⢰⣤⣄⣀⣸⣇⣬⡿⠶⢿⣅⣸⠇⠀⠀⠈⢻⠛⣋⣥⣤⣿⣄⣀⠀⠀⠀⠀⠀⠿⠙⠀⠀⠀⠀⠀⠀⣻⣿⡿⠀⠀⣼⣿ ⣀⠀⢘⣿⣿⣿⣗⣿⣶⣿⣶⠚⣧⣸⠛⢿⡀⠀⠀⠀⠀⠘⢷⡈⣻⡿⣼⠿⢤⣄⣀⡤⠽⣷⣤⠶⢚⡿⠀⣯⡀⠒⠒⠺⢿⣝⣃⣀⣀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡾⠛⣶⢛⡟⠉ ⠻⣿⡿⢻⣽⠟⠋⠁⠀⠈⢿⣹⣇⣸⠦⣿⣷⠶⣿⣦⣤⣤⣾⡟⠉⢸⣅⣰⡏⠉⠹⣄⣀⣼⣄⣰⣟⠳⣶⣼⣿⣦⣤⣤⣾⣻⡯⠭⣭⣿⣻⣶⠤⣾⣿⣿⣿⣯⣾⠁⠀⠙⠿⠁⠀ ⢠⣯⡴⠋⠁⠀⠀⠀⠀⠀⠘⣿⢤⡟⠲⣿⣷⣾⠋⠘⣷⣈⣿⠛⢺⠋⠰⣯⠟⢻⠉⠹⣄⠀⡉⢿⡙⢿⣍⣿⣿⣛⣿⣿⣿⣧⡀⢀⡀⠉⠛⠻⢿⣿⣿⡿⣿⣿⣿⣧⣀⣴⣄⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣹⠒⢾⣖⣼⣧⣴⢏⣹⠷⠤⣾⠒⡾⢛⡗⠚⣏⠉⠙⡏⠉⠙⣧⢀⡟⠑⣿⠿⢻⣫⣿⣿⣷⡿⠓⠶⠤⠤⣤⣽⣉⠛⠿⠿⣾⣿⣿⡿⠿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⡛⠺⣇⡼⣟⡿⠯⣏⣀⣠⠷⠴⢷⢿⣿⢭⣹⡉⠉⢻⠒⡾⠛⣿⠧⢺⡇⠀⣸⣿⣟⣿⣿⠁⠀⣠⣶⣆⠀⠀⠉⠙⠓⠲⠶⣯⣥⣴⣦⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⡉⢉⣳⣼⣷⣤⣾⣀⣯⣀⣠⣾⡟⢻⣄⣈⡏⠉⢻⣦⡷⠖⢿⠖⠚⡟⢿⠋⠀⢹⣿⣇⣤⣼⠟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠿⠻⠏⠘⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠙⣯⡿⠁⠀⠀⠉⠛⠻⣶⣾⠋⠀⠀⢿⣌⡿⠲⡼⢿⡦⣤⠾⠒⡶⠋⠛⣷⡀⠈⣯⣥⠾⠋⣼⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣉⡷⣤⣤⣴⠒⣾⠀⣿⣥⣶⣶⡆⠀⠻⣧⣀⣳⣤⠽⢧⣀⣠⠷⠤⡶⢛⣷⡀⢁⣠⠴⢦⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠟⢻⣿⡛⣻⡟⢀⣼⠿⣿⣿⠇⠀⠀⠙⢧⣀⠘⣳⡤⣞⠁⠀⣘⣷⠟⠁⠛⠋⠁⠀⠈⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⣧⣤⠤⣿⣽⣏⣙⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⠾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⠠⠤⢀⡐⠦⣄⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢈⣰⡀⠈⠚⠈⠊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⢰⠤⠒⠀⣀⠶⠀⠀ ⠀⢰⡓⠎⣓⣄⡑⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⡠⠃⠀⠀⠁⠀⠀⠎⢠⣄⠀⡀ ⠀⠀⠑⠄⣀⠠⡔⠊⠉⢨⠕⢦⡀⢣⠀⠀⢠⠊⣀⠤⢔⠂⠤⢀⠀⠛⠂⠒⠈⠇ ⠀⢠⠒⠙⠀⠀⠱⡢⢀⡱⠄⢔⣨⡶⠗⠀⠳⢎⣡⣀⡰⠀⢀⣠⠋⠁⡲⢄⠉⠀ ⠀⠇⠀⠙⡄⠀⠀⠈⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⠉⠛⠛⠚⠃⠁⠀⢠⠃⠀⠱⠀ ⢀⡆⢘⣄⠀⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⣰⠃⢠⠀ ⠀⠙⢇⡈⠳⣄⡀⠑⢄⠀⠀⢀⠔⠂⠉⠉⠑⢢⣀⠀⢀⡠⠊⢀⡠⠮⠭⡲⠇⠀ ⠀⠀⠀⠱⣄⠈⠙⠲⢤⠊⠉⠁⠀⠀⠀⠀⠀⠀⡀⠈⠱⠤⠒⠉⠀⢠⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⠤⠀⢸⡀⠀⠀⠐⡀⠀⠀⢠⠁⠀⠀⢰⠁⠀⣠⡊⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠒⢺⡮⠔⣒⣈⡀⠩⠉⣁⣑⣀⠶⣷⠂⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠄⠰⠼⠀⠀⠀⠀⠡⠜⣬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⡀⠀⠀⠀⠀⡠⢆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠼⠰⠰⠀⠰⠑⠵⢊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠄⠒⠒⠠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠉⠉⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⢰⣶⡆⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢀⣾⣿⠟⢿⣿⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠛⠁⠀⢀⣿⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⣿⢻⣿⣧⠀⠀ ⠀⣾⣿⡏⠀⠈⣿⣿⣧⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠃⠀⢹⣿⣧⠀ ⢰⣿⣿⣷⡄⠀⢹⣿⣿⠀⠀⠘⣿⣧⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣿⣿⡟⠀⠀⣼⣿⣿⡆ ⣼⣿⠛⢿⣧⠀⠈⢿⣿⣇⠀⠀⢻⣿⣦⠀⢰⣿⣿⡏⠀⣹⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⣿⣿⠃⠀⣸⣿⢻⣿⣇ ⣿⣿⠀⢸⣿⣆⠀⠈⣿⣿⣧⡀⠀⠙⣿⣷⣄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣴⣿⣿⠃⠀⢠⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⡄⠀⠈⢻⣿⣿⣦⣀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣀⣴⣿⣿⡿⠁⠀⢀⣾⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣦⡀⠀⠉⠻⢿⣿⣿⣶⣦⣄⠈⠉⠉⠉⠉⣠⣤⣶⣿⣿⡿⠟⠋⠀⢀⣴⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⣶⣦⣄⣀⡈⠉⠛⢿⣿⣷⡆⠀⢠⣾⣿⡿⠛⠉⠁⣀⣠⣤⣶⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣷⣦⣄⡙⢿⣿⠀⣸⣿⠋⣠⣴⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿ ⣿⣿⠀⠸⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠙⢿⣿⣿⡟⠀⢸⣧⣾⡿⠋⠉⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⢰⣿⡿ ⢻⣿⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⡿⠁⠀⠈⢻⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⡇ ⢸⣿⡇⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠙⢿⣿⠟⠀⠀⠀⠀⠀⠙⢿⣿⠋⠉⠉⠛⠛⠛⠛⠛⠛⠁⠀⠀⢸⣿⡇ ⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣤⡀⠀⠀⣤⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇ ⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀ ⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣧⣄⣀⣤⣿⣦⣀⣠⣼⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀ ⠀⠀⢻⣿⣇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣼⣿⡟⠀⠀ ⠀⠀⠈⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⠀⠀⠀⣰⣿⡿⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⡄⠀⠀⣿⣿⣿⠏⠁⠀⠈⠛⠻⠟⠋⠉⠙⠻⠟⠛⠁⠀⠀⠹⣿⣿⣿⠀⠀⢠⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣆⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⣰⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣶⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢡⣾⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⢿⣿⡿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣰⣄⡀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⢀⣀⣀⣀⣀⠀⠀⠀⡄⡤⣤⡄⢠⢠⠤⠠⡄⢤⢠⡠⠤⠀⠀ ⠀⠀⠘⢛⠛⠓⠛⠃⠚⠒⠁⠘⠛⠚⠛⠓⠛⠒⠛⠚⠚⠃⠓⠉⠀⠀⠓⠘⡁⠚⠓⠛⠒⠓⠛⠒⠓⠓⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠋⢀⣱⣀⣠⣊⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣶⢤⡀⠀⠀⠀⡟⢇⣀⠴⠛⠉⠁⠀⠀⠀⠈⠉⠓⢤⡔⠒⢋⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⡄⠙⣾⡇⢸⣤⠞⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⠳⡀⠀⠀⠸⡄⢹⢁⠞⠁⠀⠀⢀⡴⣚⡉⠀⠀⢣⢹⠓⢄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⡆⠹⣶⠀⠀⣇⢸⠏⠀⣀⠀⡴⠋⠀⠘⡆⢱⣠⢼⡿⠀⠀⢣⠀⠀⠀⢿⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⡄⠻⣄⣴⣿⡟⢧⣼⣿⡾⣷⠆⠀⣀⠞⡙⡿⠉⠀⠀⠀⢸⠀⠀⠀⢸⣄⣈⣧⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⠴⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡀⣻⠇⠈⠉⠉⠁⠉⠰⢿⡟⠻⠷⣺⣣⠇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠉⠀⠀⠀⠀⠀⡜⣉⠧⠒⠊⠉⠉⠉⠓⠢⣤⠤⢤⣀ ⠀⠀⢀⡿⠁⠀⠀⣠⣶⣦⡄⡀⠀⠱⡀⠛⠉⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⡏⠳⡄⠀⠀⠀⠀⠀⣰⠏⠁⠀⢀⠤⠒⠒⠲⢄⠀⠈⢻⠉⠀ ⠀⠀⠘⠣⡀⠀⠀⠻⣿⣿⠇⠈⣦⡴⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡸⠒⠤⣼⠀⠀⠀⡟⢲⠃⠀⠀⡰⠁⠀⠀⠀⠀⠀⢣⠀⠀⣇⠀ ⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠱ ⠀⠀⠀⠀⠀⠉⢳⡀⠀⠀⠘⠀⢿⣦⡀⠀⠀⣠⠔⠊⠁⠀⠀⠀⡴⠋⡇⠀⠀⠀⠀⠀⣤⣀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠀⡼⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣠⣄⣠⣿⠀⣠⠞⠁⠀⠀⠀⣀⡤⠊⠑⣄⡇⠀⠀⠀⠀⠀⠹⡄⢃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣆⠜⢣⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⣮⠛⢁⡼⠛⢁⡜⠁⠀⠀⢀⡔⠋⠈⢦⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⢱⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣧⠼⠋⠀⠀⡞⠀⠀⠀⣴⠋⠉⠑⣤⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⢺⠀⠀⠀⢸⠀⠀⠀⠀⠋⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡼⢁⣉⣢⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣸⠀⠀⠀⢸⠀⠀⢰⠓⢄⣀⡠⢊⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢰⠋⠁⠀⠈⠁⠀⠀⠀⢠⣧⡀⠀⠀⣰⡄⠀⡶⢄⣸⠀⠀⠀⡸⢄⡀⠀⢳⠶⣀⠲⠯⣴⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠒⠢⣄⠀⠀⠀⠀⠰⣄⢣⣙⡒⣞⣡⠇⠀⠸⡀⡍⠀⠀⠀⡷⠤⠬⢝⡥⠊⠁⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡖⠉⠀⠀⠀⠀⠀⠀⠙⠯⠭⠔⢯⡷⡤⠴⠚⣹⠇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠸⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠋⡟⠿⡟⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⢶⡎⠉⠁⣠⡤⠂⠀⠀⣴⡂⠀⠀⢳⡼⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⠑⠫⠤⢷⣀⣀⣘⣀⣳⣀⠤⠊⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠤⣄⣀⣀⣀⣀⣀⣀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⠋⠁⣀⣤⣶⣾⣿⣷⡶⠦⢄⡀⠈⠙⠿⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣾⡿⠋⠀⠀⢚⣩⣴⠌⣿⣿⣿⣟⠿⣦⡀⠀⠀⠀⠈⢻⣿⣆⠀⠀ ⠀⢠⣿⡟⠀⠈⢻⣿⣟⣡⡴⢢⣿⠃⠹⣿⠀⠈⠻⣆⠀⠀⠀⠀⠹⣿⣦⠀ ⢀⣿⡟⠀⠀⠀⡟⣹⣿⡿⢡⡿⠃⠀⠀⠋⠀⠀⠀⠘⡆⠀⠀⠀⠀⠹⣿⡆ ⣸⣿⠁⠀⠀⠐⢠⣿⣿⠁⠉⠀⠀⠀⠀⠐⡀⢀⣤⣀⠁⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠸⠿⢯⠀⠀⠀⣴⠾⠂⠀⢣⠈⠉⠀⠐⠀⠀⠀⠀⠀⢸⣿ ⢿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⢀⠆⠀⠀⠀⠀⠀⣸⣿ ⢸⣿⡆⠀⠀⠀⠀⠀⠳⣶⣄⠀⠀⠀⠀⠐⠛⢁⡠⠊⠀⠀⠀⠀⠀⢀⣿⡿ ⠀⢿⣷⡀⠀⠀⠀⠀⠀⣨⣿⠟⠉⠒⠶⠶⣾⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃ ⠀⠈⢿⣷⡄⠀⠀⠀⣈⣽⢿⣦⠀⠀⠤⠚⣻⡾⣤⠀⠀⠀⠀⢀⣼⣿⠃⠀ ⠀⠀⠈⠻⣿⣦⡀⢾⠟⠁⠀⢻⣇⢠⡤⠞⣫⠞⠱⣦⡀⠀⣠⣾⡿⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⠒⠶⠿⠄⠊⠉⠁⠀⣀⣠⣶⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣶⣶⣶⣶⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠄⠀⠀⠉⣍⠁⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠁⠀⠀⠹⠃⠀⠀⠀⢛⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡿⠿⠿⠿⠿⠿⢿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⣴⣶⣤⠄⠀⠘⠿⣿⠀⢀⣀⣀⡀⠀⠀⠀⠀⠈⢿⣷⡀⠀ ⠀⢰⣿⠏⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠘⣿⡟⠉⠀⠀⠀⠈⠐⢄⠀⠈⢿⣷⠀ ⠀⣾⡿⠀⠀⠀⠀⣼⠀⠀⠲⣤⣾⡇⠀⣸⣧⣤⠶⠒⠂⠀⠀⠀⢳⡀⠘⣿⡇ ⢰⣿⡇⠀⠀⠀⠀⢻⣧⣀⠀⣹⣿⣧⢰⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣇⠀⣿⣧ ⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠉⠀⢠⡇⠀⠀⣠⠀⠀⡄⠀⢠⡿⠀⣿⡟ ⠀⣿⣇⠀⠀⠀⠀⣾⡇⠴⢾⣿⠀⠀⠀⣼⣇⣤⡶⢁⣠⡞⠀⢀⣾⠇⢠⣿⡇ ⠀⢹⣿⡄⠀⠀⢀⡿⠐⠒⣻⡿⠀⠀⣰⣿⠿⢿⡾⠿⠋⣀⣠⣾⡟⠀⣼⣿⠁ ⠀⠀⢻⣷⡀⠀⢘⣁⣀⣻⠋⣅⠀⣠⠉⣼⣿⡿⠃⢻⣿⣿⣿⠿⠁⣼⣿⠃⠀ ⠀⠀⠀⠻⣿⣆⠛⠛⠛⠁⠀⠛⠟⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣾⡿⠃⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣤⣤⣀⣀⣀⣠⣤⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⢲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⢖⠑⣶⠚⡖⡅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢎⣩⠦⠮⠝⠈⢀⠔⠀⠨⠐⢉⠉⠆⠦⣠⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⠏⠟⠀⠁⣊⠡⠄⠀⠀⠂⠤⢑⠐⠲⡌⡰⠌⠀⠀⠀⠀⠀ ⣴⠒⡜⣓⣁⠤⠔⠔⠈⠠⡀⠀⠀⠀⠀⠀⡸⠑⢄⢇⠉⠫⡦⠒⢄⠀⠀ ⠈⢸⣳⠋⠁⢀⡎⠑⠠⠄⢀⣈⠀⠒⠂⢁⠀⠤⠊⣣⠈⠳⢈⢖⠁⠀⠀ ⠀⣰⠽⠰⢀⠦⠤⠍⢁⡀⠒⢄⡁⠒⢈⠤⠒⠀⣉⠀⠧⠄⡈⢏⣂⢀⠀ ⡋⢈⠇⠰⠁⠀⠀⠀⠀⠈⠢⡀⢫⣉⠏⢀⠔⠈⠀⠀⠀⠀⡱⡀⢳⠤⠃ ⠀⣿⡆⢡⠃⠜⢍⣷⣯⣱⣢⣘⡸⡸⡰⣡⣴⣿⣶⡯⠋⡠⠣⠘⢩⠀⠀ ⠐⡸⡁⢸⢷⣆⡑⢯⡭⠍⢉⣉⡇⡁⡊⣉⠉⢉⣁⣀⣪⣴⠛⢆⡌⠀⠀ ⠀⠇⢨⣾⠣⡑⡗⠉⡠⢊⠕⠁⡘⢡⠈⠫⡑⢌⠑⢌⠚⡀⣾⣮⡄⠀⠀ ⢸⠀⠈⠛⡇⠙⠀⡰⠀⢀⡀⠑⠱⠾⠮⠭⢁⠀⢂⠀⠗⢠⠛⠚⠁⠀⠀ ⠈⡄⠀⠀⢸⣀⣀⢣⠃⠐⢈⠩⠉⠉⠭⡁⠒⠪⢪⢄⠠⠁⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⢀⠀⢸⠤⢴⠃⠀⠀⠀⠀⠈⢢⠤⠜⣄⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠘⡆⢘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⡸⢸⡇⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⡇⠀⡆⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡆⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⢹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠘⡀⠈⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣀⣈⣀⣀⣀⣸⣆⢀⡀⠀⠀⣀⣀⣀⣸⣆⡸⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢶⡮⣭⣋⠲⡔⢊⣫⠭⣶⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⠔⢒⠢⣄⠙⢦⡡⢱⡰⠁⣡⠎⢀⡤⢖⠒⡌⢆⠀⠀⠀⠀⠀ ⠀⠀⠸⡑⠤⠬⢆⡳⠽⣇⠼⢤⣼⠤⠼⠧⠤⢼⣤⠼⣄⠯⠴⣣⠧⠤⠔⢱⠀⠀ ⠀⠀⢰⠘⡒⠢⣠⠽⣟⠓⠤⠀⠈⠣⠀⠀⠀⠉⠀⠠⠐⢛⠿⢥⡠⠒⡘⢸⠀⠀ ⠀⠀⠈⠢⡐⢬⢏⠃⡺⠴⢄⡀⠀⢀⠀⠀⢠⠀⠀⣀⠴⠼⠂⣫⢇⠜⡠⠋⠀⠀ ⠀⠀⠀⢠⣿⠏⢈⢫⠋⠉⠲⡸⣄⠴⡄⢀⣼⣄⡜⡰⠉⠉⢏⡃⠈⣾⣇⠀⠀⠀ ⠀⢀⢔⠝⣼⡠⠼⠛⠤⢀⢠⢓⣬⡾⠜⠘⢴⣯⣘⢇⢀⠠⠜⠫⠤⡹⡙⢕⢄⠀ ⢰⢱⡑⢓⠞⠀⠀⠀⠀⠔⢉⠤⠤⢄⠀⠀⢀⠤⠤⢌⠑⠄⠀⠀⠀⠸⢒⠳⢡⢡ ⠸⡈⠓⣪⣶⡀⠀⠀⠀⠀⠸⢔⣉⢦⣈⣏⡠⢎⣁⠜⠀⠀⠀⠀⠀⣰⣎⠚⠊⡸ ⡠⠚⣋⡑⡇⠻⣲⠶⣾⠲⣶⣤⣀⣀⡴⠷⣤⣀⣤⣴⠶⢾⡷⢶⡺⠃⡗⣉⡛⢢ ⡇⡎⠔⡌⣧⡄⠑⣍⠪⣆⠟⡿⡛⠻⡿⡿⡟⠛⡻⡟⢂⡢⢊⠕⠀⣆⡏⡔⠈⡆ ⠘⠢⠭⡴⠓⠛⡄⢎⢣⠈⠻⢕⣛⠻⠬⠭⠜⢛⡒⠽⠋⢠⢋⠂⠞⠓⠳⡬⠥⠊ ⠀⠀⠀⡅⠨⠤⠂⢸⡾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣾⠀⠦⠼⠀⡇⠀⠀ ⠀⠀⠀⠈⠐⠒⠒⠋⢠⡪⣩⢲⡊⣉⢉⣏⢹⠁⣖⢺⣭⢢⠈⠓⠒⠒⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣑⣐⣊⣠⡷⠋⠈⢯⣣⣘⣒⣐⡹⠀⠀⠀⠀⠀⠀⠀⠀