Sakura Dot Art

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⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⢠⠋⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⡿⣿⣿⠃⣤⣄⣀⡀⠀⠀⣠⠃⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣇⠀⢿⣿⠻⢿⣼⣷⣶⡄⠀⠈⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⡆⠀⠀⠀⠀⠘⡄⠀⠀⢐⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⡿⣿⣧⠀⢩⡶⠟⠋⡏⠀⢀⣔⠀⠘⣧⠀⠀⠀⠀⠀⠇⡆⠀⢧⢀⣴⣷⠀⠀⢱⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠙⠃⠀⠀⠀⢰⠁⠀⠀⠉⠁⠀⢻⡄⠀⠀⠀⢠⠀⠸⡀⢸⠻⣿⣿⠇⠐⠀⢇⠀⢸⡇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⢣⠸⡀⠙⠁⠀⠀⠀⠘⡆⠀⡇⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⠍⣒⣤⣀⠀⠀⠀⢠⢇⠀⠀⠘⡀⠀⠀⢆⡇⠀⠀⠀⠀⠀⠀⠘⡀⡇⠀⠀⠘⡄⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⢮⣽⣿⣦⣀⠈⠙⡆⠀⠀⡇⠀⠀⠘⣾⡀⠀⠀⠀⠀⠀⣠⢧⡇⠀⣀⣀⣽⡀⠀⠀⠨⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠰⡰⡯⠻⣿⣭⣦⣼⡄⠀⠇⠀⣸⠀⠘⣇⠀⠀⠀⢀⣜⣡⣴⣿⣿⡭⣤⠀⢣⠀⠀⢰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢻⣾⢶⣄⣀⠤⠋⠻⡏⢳⣷⠀⢸⡿⠁⠀⠀⠸⣦⢤⣒⠿⣿⣿⣿⠛⠛⡏⢙⡿⠋⡆⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡟⠻⠿⠷⣶⣶⣒⣃⣀⣙⢣⡘⠀⠀⠀⠀⢀⣼⡋⣁⡾⣏⠐⠉⢁⡼⢁⡼⠃⠀⢸⡀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢣⣰⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠳⣇⠀⠀⢸⣯⠥⠤⢼⣠⡤⢽⣿⣿⣿⠟⠃⠀⢠⠃⢣⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣧⢸⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢹⡼⠀⠀⢠⣯⠀⠈⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⡼⢸⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣾⠃⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡼⡏⠀⠀⡼⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣧⢿⡆⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢠⠎⠸⠀⠀⡸⢁⡟⡇⠀⠀⠀⠸ ⠀⠀⠀⠀⡇⠙⢷⣽⡀⠀⠘⣗⡇⠀⠀⠂⠀⠀⠀⠀⠹⣷⣦⣤⢤⣶⠇⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⡏⠀⠃⠄⢠⣷⣼⡅⡇⠀⠀⠀⠀ ⠀⠀⠀⢰⠀⠀⠀⠘⢧⠀⠀⢻⣆⠀⠀⠀⠀⣀⣀⣀⠀⠈⠻⠖⠋⠀⠀⠀⠀⠀⠀⠀⢀⡜⣣⣾⣿⡇⠀⡸⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠘⣿⣷⠀⠀⠀⠉⠀⣀⣉⣉⣀⣀⣀⠒⠚⠒⠂⠀⠀⢠⣾⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⡇⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⣇⣼⣷⡀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠠⠤⠤⠤⠤⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠛⠛⢛⣉⡽⠿⠛⠻⣿⣶⣤⡀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠋⠀⠀⠉⠛⠚⣫⠄⠀⠀⠀⠀⠀⠙⢯⡛⢷⣤⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠠⠞⠁⢀⣀⠀⠀⠀⠀⠀⠀⠙⢦⠹⣿⣄⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡏⠀⠀⠀⣠⣾⣤⣄⠀⣠⣴⣿⣿⠷⡄⠀⠀⠀⠀⠀⠘⣗⣺⣿⡄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⠀⠀⣰⠿⠛⠚⠛⠚⠛⠉⠉⠉⠉⠙⣆⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠠⡄⠀⠀⢿⣿⣿⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣧⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠃⠀⢀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⣾⢀⡤⡒⠲⠤⠞⠀⠀⠻⠤⠤⠖⠚⢓⣲⠾⡆⡯⠀⠀⢰⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢰⣿⣷⣶⡿⢦⣄⠀⠀⠀⠀⠀⠀⣴⡞⢻⡿⢿⣧⣷⠀⠀⢸⣿⣋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⡏⠈⢯⠙⡕⢺⡟⠂⠀⠀⠀⠀⠈⢹⣗⢦⣿⡭⢻⡏⠀⠀⣿⣿⢧⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣸⡇⠀⠸⡄⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢉⣉⡉⠁⢨⡇⠀⠀⣿⢿⡾⠘⣿⠀⠀⠀⢰⣷⣦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⡇⢀⠀⢳⡈⠉⠑⠂⣄⠀⡀⠀⠀⠀⠈⠉⠁⠀⢸⡇⠀⢀⣿⡏⠀⢀⣿⡀⠀⠀⣿⣿⣿⣿⣷⣤⣀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠇⣿⠀⠀⢨⢧⡀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠟⡇⢀⣾⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠸⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⢸⠀⠙⢦⣀⠈⢻⢳⠀⠀⠀⠀⠀⣠⣶⣿⡇⠀⣼⠀⢹⣾⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⠳⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⢸⠀⠀⠀⠈⣷⢮⣏⣀⣀⣤⣶⣟⣿⣿⠿⡇⠀⡏⢀⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⣿⣷⡾⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⢸⠀⠀⣀⠀⢸⠈⢿⣿⣿⣿⣿⣿⡛⠙⢆⡇⢠⡇⣸⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡇⢸⠀⠀⣿⠀⡆⠀⠘⢿⣿⣿⣿⣿⣿⣶⣄⢹⢸⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⠟⠛⠁⣾⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡀⠀⡇⠀⡇⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡛⢿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣧⠘⣿⡀⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣧⣀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⣆⡷⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣿⣟⢽⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡄⠀⠀⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡡⠞⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠤⠤⠤⠤⠾⠇

⠀⠀⠀⠀⠀⢀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣻⣿⣧⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠹⡽⡜⢿⣷⡀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣞⣿⠁⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠙⣷⠈⢿⣷⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⢸⠇⠀⠀⠀⡜⡞⠀⠉⠲⢤⣀⠀⠈⠑⠲⢌⡑⠢⣄⠀⠈⢆⠀⠀⠀⠀⠀⠈⠇⠈⣿⣷⣄⠀⠀⠈⢆⠀⠀⠀⠀ ⠀⠀⢠⠃⣿⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠈⠉⠒⠢⠄⣀⡈⠑⠦⣙⠢⣄⠳⡀⠀⠀⠀⠀⢸⠀⠸⣿⠘⡆⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⡼⠀⡇⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⢼⣿⠂⠀⠀⠀⠈⠉⠐⠒⠿⣦⣝⢷⡀⠀⠀⠀⠘⡄⠀⢿⡇⠸⡀⠀⠀⠘⡄⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢷⠀⠀⠀⠀⠀⠀⢸⣿⣶⣧⠀⠀⠀⢱⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⡶⠶⠛⠉⠉⠉⠀⠈⢇⠀⢀⠀⠀⠀⠈⣥⡃⠙⡇⠀⠀⠀⣇⠀ ⠀⠀⠀⣧⠁⠀⢸⡏⠀⣀⡤⠶⠶⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠘⡆⢸⠀⠀⠀⠀⡿⢷⡄⡇⠀⠀⠀⠸⠀ ⠀⠀⢀⣿⠀⠀⢸⠁⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣺⡿⠿⠿⠿⠛⠀⢃⠀⡇⠀⠀⡀⢹⡞⢸⢻⠀⠀⠀⠀⡇ ⠀⠀⠘⢻⠀⠀⢸⠀⢀⣴⣖⣒⣒⠦⣄⠀⠓⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢸⡞⢀⢿⣼⠀⠀⠀⠀⠰ ⠈⠀⣆⣼⠀⠀⢸⠀⠈⠛⠉⠉⠉⠙⠛⠀⠀⠀⢀⣀⣀⣠⢴⣦⡶⠟⠾⠒⠀⠀⠀⠈⡄⠀⠀⠀⢸⣇⡜⠸⣿⠀⠀⠀⠀⠀ ⠀⠀⣿⡏⠀⠀⣸⡄⠀⠀⠀⠀⠀⢀⣠⡠⣶⣶⠟⡩⠋⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⡀⠀⡇⡇⠀⠀⣾⢷⡄⠀⣠⣶⠷⠟⠻⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⡏⠀⠀⠀⠀⠀ ⡇⠀⣧⡇⠀⠀⢸⢣⣱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⡇⢠⢸⣇⠀⠀⢸⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠂⠀⠀⠀⢀⣶⡇⠀⠀⡞⠀⠘⡏⠀⠀⠀⢀⡞⠀ ⣧⠸⠈⣿⠀⠀⢸⣆⠈⣿⡄⠀⠀⠀⠀⠀⠀⢠⣴⣶⡭⠟⢚⣩⠟⠁⠀⠀⠀⠀⣠⠎⣿⡇⠀⢠⠇⠀⢰⠃⠀⠀⢀⡞⠀⠀ ⢻⡄⡇⠸⡀⠀⠈⡟⡄⢿⡟⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⣠⣞⣡⣾⢿⠀⢀⡞⠀⢠⠋⠀⡴⢀⡞⠀⠀⠀ ⠀⢷⠸⡄⢧⠀⠀⢣⠘⣌⣿⡀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⡘⢀⣮⣠⣴⣃⣴⡾⡠⠊⠀⠀⠀⠀ ⠀⠀⠳⣽⡌⣆⠀⠘⣄⠈⠻⣿⣦⣄⡈⠑⢲⣤⣀⣀⠀⡀⢀⣠⡴⢿⣿⣿⣿⣿⡟⠰⣠⣾⣿⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢿⣄⠀⠹⡓⠴⣮⣽⣿⠼⠉⠙⣿⣿⣿⡉⢹⠁⠘⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣶⣤⣄⣀⣀⣠⠤⠒⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⣄⣳⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⠀⣇⢠⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠐⠒⠲⠾⠷⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀⠸⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠟⣏⠑⠦⣄⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡴⣃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⡆⠀⡃⠄⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠉⠉⠉⠀⠒⠠⠅⡸⣿⣿⣿⣷⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡄⢀⡴⠁⡠⠐⠈⠁⠉⠁⠐⠺⣿⠉⣿⠹⡿⡗ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⡝⠀⡁⡇⡸⢱⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⡆⠡⠀⠣⠁ ⠀⠀⠀⠀⠀⠀⡰⢃⠎⠀⠀⢇⢁⠡⡙⠀⠀⠀⠀⣠⠾⡇⠀⠀⠀⠰⣀⣤⡤⣣ ⠀⠀⠀⠀⠤⠊⠀⠐⠰⡂⠀⣸⢮⠣⠁⠀⠀⣠⠞⠁⠀⢳⠀⢀⠀⠀⣿⣿⡿⠫ ⠀⠀⠀⠀⢖⢀⢶⢢⠤⠌⢵⠿⡏⡄⠀⠀⡴⠡⣄⠀⠀⠛⡆⠸⠀⠀⣸⣿⣷⣆ ⠉⠉⠉⡝⠉⣾⣹⡈⠀⠀⠘⣻⢁⠀⠀⣜⠷⠆⠀⠀⠀⠠⢵⠸⠄⠀⣿⣿⣿⣿ ⠑⠒⠮⢀⠠⠇⠻⡇⠀⣀⢴⢿⢸⢸⡸⠁⠙⠀⣄⠀⠀⢴⣬⡶⡆⢀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢇⢉⡖⠠⣼⢸⣸⠇⠀⠀⠘⠯⠜⠀⠓⣴⡇⠃⣸⣿⣿⣿⣿ ⠀⠀⠈⠀⠀⠀⠀⠈⢼⢣⣠⢿⣸⢿⣄⠀⠉⠥⠂⠀⢀⠎⡼⠣⢠⣿⣿⣿⣿⣿ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣿⡟⢻⠈⢈⣦⣤⣶⣶⠎⢁⣼⢧⡇⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣀⣤⣤⡶⠉⣼⣿⣷⠈⣠⣾⣿⣿⡿⠛⣲⣿⣧⣿⣿⡿⣿⣿⣿⣿⣿ ⠀⠀⠀⣰⣿⣿⡿⠁⣰⣿⣿⣿⣶⣿⣿⣿⡟⠁⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿ ⠆⠀⢠⣿⣿⡿⠁⢰⣿⣿⣿⣷⣿⣿⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⡄⣾⣿⡿⠁⢀⣿⣿⣿⣳⣿⣿⣿⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⠀⠀⠚⠄⠐⠈⠄⠀⠈⠀⠀⢀⣤⡀⠁⠀⢠⠱⡄⠀⠀⠀⡀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠀⠏⢄⢃⠈⠄⠀⡆⠀⠺⡿⠃⣀⠀⠈⠀⠈⢆⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡂⠒⠠⢮⡄⠐⡀⢠⠀⠀⠀⠀⠀⠈⠄⣀⣀⠤⠧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢗⣖⣶⣀⣝⡛⠲⢌⡇⠀⠀⠈⢶⠖⣛⣿⣦⣴⣶⣕⡀⠀⠀⠀ ⢠⠀⠀⠀⠀⠀⠸⠇⢸⠐⢈⠳⠄⠈⢳⡀⠀⢀⠋⣰⠛⣑⣂⢇⠟⠀⢂⠀⠀⠀ ⢀⡀⠀⠀⢀⠀⠀⠻⠳⠛⠲⠚⠀⠀⠀⠑⠀⠀⠀⠙⠓⠒⠒⠋⠁⠀⢠⣦⠀⠀ ⠘⠠⠀⢠⠀⠑⡄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠂⢐⣆⠀ ⠀⠀⢃⠈⠀⠀⠈⡢⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⢠⣿⣿⠟⡄ ⠀⠀⠀⢂⠀⠀⠀⠠⠈⠙⠆⠀⠀⠀⠰⣤⣤⡶⠀⠀⠀⠀⠂⠀⢠⣇⣴⡷⡫⡰ ⢀⠀⢀⣴⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠘⠀⡰⣿⣻⣿⣿⡎⠀ ⠸⠀⠈⢙⠻⢆⠀⠀⠀⢂⠀⠀⠀⠤⠐⠒⠒⠒⠀⠀⠀⢀⣾⣿⡟⠁⡚⠁⣴⠀ ⠀⠀⠀⣽⠐⢻⢣⡀⠀⠀⢂⠀⠀⠀⠀⠉⠀⠀⠀⢀⣔⣽⣿⣿⠀⡾⣇⢲⣿⠀

⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⣶⣤⣶⣖⡀⠐⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠊⠉⠛⠦⢔⡋⠁⠀⠀⠙⢿⡳⣦⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⡀⠀⠴⠋⢀⡀⠀⠀⠀⠀⠙⢮⠿⣦⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⢀⣾⣶⣆⣠⣶⡿⠾⠧⡀⠀⠀⠀⠈⣿⣿⡆⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢹⠀⠀⢿⣿⡆⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⡇⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⡇⢸⠀⠀⢸⣿⠇⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢘⠀⣸⣧⣎⣍⠉⠁⠀⠈⠙⠋⣉⣬⣿⣿⣼⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢀⠟⢟⢻⡭⡷⠄⠀⠀⠀⠘⣿⣌⣧⡻⣿⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣼⠀⠸⡄⢙⠓⠀⠀⠀⠀⠀⠉⣉⡉⠀⡍⠀⢸⣿⠞⢸⡇⠀⠀⣴⣦⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⡄⠀⢳⠀⠉⠀⢤⠄⠀⠀⠀⠈⠀⠀⡇⠀⢸⣏⠀⣰⣧⠀⢰⣿⣿⣿⣷⣦⣀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠈⠀⡇⠀⠀⠱⣄⠀⠰⣤⡀⠀⠀⠀⢀⣴⡇⠀⡎⠸⣴⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⠿⢦⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⠀⠙⡦⣟⣁⣀⣤⣶⣿⡿⣇⠀⠇⣰⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⢁⣶⣶⣽⡆⠀⠀⠀⠀⠀ ⠀⠀⠘⡄⡇⠀⢠⠀⡇⠹⣿⣿⣿⣿⣋⠱⢼⢠⢀⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⡇⠸⣿⣿⡇⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⢣⣷⠀⠜⠀⠀⠀⠙⢿⣿⣿⣿⣷⣼⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣉⣤⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠸⣿⡆⣷⢠⠃⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡝⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠙⢳⣼⣿⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡰⠀⠀⠳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⢎⣀⣀⣀⣰⠁

⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⡄⢒⢹⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠉⡵⠟⡀⢻⣿⣿⣿⣿⣿⣿⣿ ⢸⣀⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣴⡿⣡⣴⡶⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠾⣾⢛⠑⢙⠛⠟⣿⣿⣿⣿⣿⣿⣿ ⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡟⠀⠪⠄⠀⠀⣀⠀⠀⣿⣿⣿⣿⣿⣿⡟ ⠀⣴⣹⣽⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⢣⠃⢨⢿⣿⣿⣿⣿⣿⠃ ⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⡀⣠⠄⠀⠀⠀⡌⢠⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⠤⠵⢥⠀⠖⠈⠐⣠⣿⣿⣿⣿⣿⣽⣿⣿⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠐⠀⡠⢂⣼⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀

⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢢⣀⠤⠶⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣀⣀⣀⡇⢀⢎⡤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣷⠿⠋⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⡏⠙⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⢀⣴⢞⡿⠔⠚⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣅⡠⢸⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢳⣾⡿⣿⣋⣴⣾⣿⣯⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣯⣞⠿⡿⠵⠭⠴⠷⠞⡫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠃⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⠀⠀⢫⠼⠍⣒⠤⠤⣤⠤⠔⠋⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⣿⠏⠉⠑⠣⠄⠀⠀⢀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢚⣿⠒⠒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⡰⡷⢠⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠀⠀⣰⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠐⠁⣇⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⢟⠢⢾⡟⠁⠀⠀⠀⣰⠄⡸⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⣀⠀⠠⠽⠭⠤⣀⡶⠖⠉⠀⡰⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡃⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠉⠉⠉⠉⠉⠁⢀⣀⠄⡠⠊⢠⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡆⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢈⠖⠒⠒⠈⠉⠉⠀⢀⠞⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠺⢉⣁⣀⣀⣀⡀⠀⠀⠀⠉⠉⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⡯⢶⣶⣿⣿⣿⣏⠀⠰⠿⠻⢋⡉⢷⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡿⠃⢐⣺⠿⠿⠿⠿⠯⠧⢤⣀⣰⣫⣿⣿⣿⣷⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⢋⡧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠇⠀⠀⢠⠀⠀⣯⣧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢰⠀⠀⣘⡆⢰⣷⣼⣆⠀⠀⣿⢦⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⢸⠀⢀⣿⣣⢸⡝⣿⣝⣦⠀⣿⣬⣷⡀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣬⡳⣄⠀⠀⠀⠀⠀⠀ ⢰⠇⢸⠀⣸⠙⠻⣾⣿⣿⠋⠉⢦⣻⠛⠿⣿⡄⣇⢷⡀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣀⠀⠈⠻⣾⢷⠀⠀⠀⠀⠀ ⢸⠀⠈⡇⣿⣦⣀⣹⣿⠁⠀⠀⠈⠻⣶⠾⣿⣿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢻⡙⠲⠤⣈⣧⡀⠀⠀⠀⠀ ⢸⠀⠀⣿⠛⣿⡿⣿⢿⣿⣆⠀⠀⠀⠁⢸⣟⣹⣼⣟⡞⢷⡀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⢸⠀⠀⠈⠀⣿⠹⣬⣷⡿⢿⡆⠀⠀⠀⠀⠋⠋⠙⣿⡇⠀⡗⠀⠀⠀⠀⢰⣦⢸⣷⡄⠘⣶⣤⣀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢠⡄⠀⢹⡇⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⡇⠀⠀⠀⠀⠘⡏⣷⣿⢹⣦⣿⣿⠈⠓⠦⢿⣄⡀⠀⠀⠀⠀⠀ ⢸⣶⠇⣷⠀⠠⣿⢻⣿⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⢹⠀⠀⠀⣀⠀⣇⡿⠉⢻⡿⣿⠧⠄⠀⠀⠀⢀⠈⠙⠦⣄⠀⠀ ⠘⠋⠀⢹⠀⠀⣟⣷⣿⡇⠀⠙⠶⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⢰⡿⣦⢿⠇⢀⣿⣱⡏⠀⠀⠀⠀⠀⠀⢀⣤⠴⠛⣿⡆ ⠀⠀⠀⠈⡇⠀⠹⠈⢿⣿⡀⠀⢴⡶⠶⠶⡶⠖⠀⣸⡟⢀⣼⡆⠀⡿⣡⣿⢿⡄⢸⣷⣿⠃⠀⠀⠀⠀⠀⢠⠞⢁⣴⣿⣿⡇ ⠀⠀⠀⠀⢳⠀⠀⣀⢨⡟⣧⡀⠀⠉⠉⠉⠉⠀⢀⣿⣷⣟⣵⣇⢸⣷⡟⠁⠈⠁⣾⠟⠁⠀⣲⠖⠀⠀⡴⠃⣴⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠸⡄⢠⣿⣿⡿⠙⣿⢦⣀⠀⠀⢀⣴⣾⣿⣿⣿⠋⣿⣼⠋⠀⠀⠀⣸⠏⠀⣛⡽⠗⠀⠀⡾⢃⣾⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢿⢸⠻⡿⢿⡄⠸⣎⠈⣹⣿⣿⣿⣿⣿⣿⣿⡄⢻⣇⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⡼⢡⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠘⣿⠀⢧⠘⣷⡀⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⡼⢁⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢠⣿⣦⣘⣇⣻⣧⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢯⡇⣰⠏⠀⠀⠀⠀⠀⠀⢠⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠘⣾⠀⢹⣌⡉⠉⡏⣿⡿⣿⣿⣿⡿⣛⣛⣛⣟⣷⣾⣿⠁⠀⠀⣀⣄⡀⠀⠀⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⣿⡄⠈⠛⠁⠀⣿⣷⢷⡄⠈⢿⣇⠀⠀⣒⣿⠞⢹⠹⡀⠀⠀⠙⠏⠁⠀⢰⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢀⣾⣷⡤⣤⣤⣀⣿⣿⣾⠟⠀⢸⣿⢀⣹⡟⠁⠀⠈⣆⠛⠦⠤⠤⠤⢠⠠⠜⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣛⣉⣙⣁⡠⣤⠀⢿⡄⢠⣄⠀⠀⠀⠙⠛⠛⠛⠒⠒⠒⠠⡴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⡄⠀⠀⢹⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠤⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢻⠈⢷⡄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡀⠀⠈⣇⠀⠘⣆⠀⠀⠀⠀⠀⡇⠀⠉⠁⠀⠀⣠⣾⣧⡀⠀⠀⢳⡀⠀⠀⠸⡆⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀ ⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⡻⡄⠀⢸⡀⠀⠘⣆⠀⠀⠀⠀⢻⠀⠀⠀⠀⣾⣿⣿⣿⣷⠄⠀⠈⢳⡀⠀⠀⡇⠀⠀⠞⢷⡀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠂⠙⣄⠀⢧⠀⠀⠙⣆⠀⠀⠀⢸⡄⠀⠀⠀⠙⢿⣿⠟⠁⠀⢀⡀⠈⢧⠀⠀⢻⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣄⣀⠀⠘⢦⠘⡆⠀⠀⠘⢆⠀⠀⠈⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠈⢧⠀⢸⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣧⠀⠀⠈⠉⠓⠾⢷⣻⣀⠀⠀⠈⢧⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⣄⣀⣤⣤⣤⠶⠾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⢀⣀⣀⣀⡀⠀⠀⠻⣿⢿⣦⢤⣈⣳⡀⠘⣧⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⣠⢤⣾⡜⡟⠛⣉⣀⣀⣀⣀⣈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣶⣜⣺⣯⣍⣑⣲⣬⣧⠈⠉⠓⠯⢿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡾⠋⠁⢀⣿⣿⣿⣷⣶⣶⣯⣤⣼⢞⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠋⠉⢹⠏⢉⠉⠻⣿⣷⣄⠀⠀⠀⠙⣎⣧⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⣴⡿⣿⠋⢁⡈⠻⡄⠙⢿⣿⠋⠀⢻⡄⠀⠀⠀⠀⠀⠀⠘ ⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⡆⠀⢸⠀⠸⠟⠀⣸⠈⢿⣦⡀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⢼⠋⠀⠀⣼⡟⠁⢷⡀⠙⠋⢠⠇⣰⡿⠃⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣧⠿⢤⣈⠳⠦⠤⠞⣁⣀⣸⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⠀⢸⣿⣄⣀⣈⣛⣓⣒⣁⣴⣿⣥⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⢰⡄⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠹⣖⡿⠛⠏⠹⠛⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡏⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⣞⣿⡄⠀⠀⠀⠀ ⢸⢹⡀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠟⢻⡀⠀⠀⠀ ⡜⠀⢧⠀⠀⠀⠀⣠⠀⠀⠈⠳⣄⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⢎⣷⠀⠀⠀ ⡇⠀⠘⣆⠀⠀⢰⣿⠀⠀⠀⠀⠙⢦⡀⠀⠈⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⠀⣼⡧⡴⣫⣯⢞⣧⠀⠀ ⡇⠀⠀⢹⡄⠀⠈⠁⠀⠀⠀⠀⠀⠈⡟⢦⡀⠘⣧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣰⡿⣽⡵⣷⣷⣻⠛⡆⠀ ⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠙⢦⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⣟⣿⢟⣜⢟⡽⡵⣫⢹⡄ ⡇⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠉⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠠⣴⣦⣤⣄⣀⣠⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⣰⣯⠏⣸⣷⣻⣫⢮⠞⡵⠃⢧ ⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡯⣯⣼⣽⣟⡵⡵⢋⠞⣠⠆⠘ ⡇⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⠿⣯⣿⢿⣿⣿⣿⣳⢥⡼⠁⠀⠀ ⣇⠀⠀⠀⣰⣟⣛⣾⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣑⣿⡵⣮⣭⣟⡿⣾⢽⡿⢵⡀⠀⠀ ⢸⠀⠀⠀⡇⠙⠿⣿⣻⣿⣦⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⣽⣶⣿⠟⠀⢀⡴⣡⠎⠀⣸⡇⠀⠀ ⢸⠀⠀⠀⡇⠀⢤⠀⠀⠉⡟⣧⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣀⣀⣀⣀⣀⣀⠈⠉⠀⠀⠀⠀⠀⣠⣾⣿⣷⣿⣿⡟⠁⠀⣠⡞⢰⠃⠀⢰⣿⡇⠀⠀ ⠘⡄⠀⢀⡇⠈⣿⡆⠀⢱⡇⡏⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⣿⣿⣿⣿⢿⠁⠀⣰⣟⡇⣼⠀⡉⣾⣿⡇⠀⠀ ⠀⡇⠀⠘⡇⠰⣾⡇⠀⠀⡇⣧⠀⣝⢦⡀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣵⣾⣿⣿⣿⣿⣿⣿⠀⢸⡿⢻⠁⡧⠄⢀⣿⣿⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠉⠉⠉⠙⠛⠒⠒⠲⠤⠤⣄⣀⡀⠀⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⡀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⣶⠃⠀⠀⠀⠀⣀⣤⠤⠒⠦⡤⠖⠒⠦⢤⣄⣀⣉⣙⢿⣿⡇⢸⣿⣿⠙⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢀⣠⠞⠀⠀⢀⣼⡿⠁⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣻⣿⡇⠀⣿⣿⠀⠘⣿⣿⢿⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡟⠀⢀⠏⠀⣾⠀⣠⢞⡿⠁⣠⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡅⠀⢸⣿⠀⠀⠘⣿⠈⢻⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢁⡾⠀⠀⢸⡀⠀⡿⠀⠉⡾⠁⢠⠿⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠻⠀⠀⠀⠸⡆⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣄⡞⠁⠀⠀⠈⣇⠀⡇⠁⣼⠃⣰⢯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣴⠏⠀⠀⠀⠀⠀⢿⢸⡇⢀⡁⣰⠟⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣀⣤⣤⣤⡶⢋⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠘⣿⡆⡼⢡⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣯⣠⡟⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠐⠲⣔⠒⠂⠠⠤⠤⠤⣹⣿⣥⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠼⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⢀⣾⡵⣦⣼⠀⡞⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⢠⣬⣿⠀⠀⢀⣷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠐⢀ ⠈⠁⠈⠉⠉⠉⠉⠉⠙⣶⠛⠉⠙⡶⢶⣦⣔⣊⡉⠁⠀⠀⠉⣻⣋⡵⣻⡇⢠⠇⠀⠀⠀⠀⠀⣰⣿⣅⣀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣆⠀⠸⡟⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣼⣆⡘ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡆⠀⣼⣡⣾⠁⢠⠏⠉⠉⠉⠛⠋⣿⠉⢉⣿⠀⣼⠀⠀⠀⠀⠀⣴⡟⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠸⣿⠀⠀⡇⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠹⣾⣷⠏⣽⠀⡿⠀⠀⠀⠀⠀⠀⣿⣷⣯⡏⠀⡇⠀⠀⠀⠀⣼⣿⣟⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⠹⡇⠀⣧⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣿⠧⣄⣿⢠⡇⠀⠀⠀⠀⠀⠀⢸⣌⣿⠁⢸⠀⢀⠀⠀⣼⡿⣌⠉⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⠀⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⠲⠦⢤⣤⣤⠼⠁⠀⠀⠀⢸⢇⣀⣹⣿⢸⡇⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⡘⠀⣸⠀⢸⡿⠁⠻⠽⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠻⡇⡇⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠉⠉⠛⠶⠤⠤⠖⠛⠋⠉⠀⠹⣼⡇⠀⠀⣀⣤⠾⢟⣫⠼⢻⠀⢡⠀⢻⠀⡿⠁⠀⠀⠀⠀⠀⢀⡴⣶⠀⢀⡀⠀⡙⠳⢶⣯⣽⣿⡇⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⠺⣯⣀⡀⠈⠀⢀⣿⠀⡇⠀⣸⢰⠇⠀⠀⠀⠀⠀⠰⣯⣷⡿⠀⣾⠀⠀⢳⣶⣆⢉⣽⢿⠇⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣾⠁⠉⠙⠛⣿⢹⠀⣿⢀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠙⠚⠰⠚⠁⠀⠀⠀⠁⢀⡾⣽⢸⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡟⣆⠀⠀⠀⡇⢸⠀⡏⣸⣿⡟⠀⠀⠀⠙⠒⠶⠦⢀⣀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡇⡏⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⡇⠹⡆⣠⠾⠟⢻⡆⣿⡟⢸⡿⡄⠀⠀⠀⠀⠸⠷⠦⠈⠉⠁⠀⠀⢀⡼⠋⢠⣾⡇⢧⡖⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢹⣿⣷⣄⡿⣷⢹⡇⢸⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠾⠋⠀⠀⡾⣿⠀⣼⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⠸⣾⠃⠀⠀⠀⣀⣽⣶⣴⣶⣾⣿⣿⣿⣿⠁⠀⠀⢀⣾⣧⠃⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠞⢛⣿⣿⣿⣿⡄⠀⠹⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣠⣴⣿⣿⠈⣴⣿⡇⣸⣇⢻⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣠⣤⣤⣴⣾⣿⠋⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣯⣻⢿⣿⣿⣾⣿⣿⣷⣿⣿⣸⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⡀⢀⣴⣿⣿⣿⣿⣿⡿⣻⣭⡟⠁⠀⢀⣾⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⡇⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡇⠀⠁⠀⢰⣿⣿⣟⣿⣿⣿⣿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣵⣿⣿⠟⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣿⣧⢹⣿⣿⣿⣧⣾⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣿⣿⣿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⢟⣷⣿⣿⡟⣿⣿⣿⣿⢹⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿ ⣇⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿ ⠘⡄⠀⠀⠀⣸⣿⣿⣿⣇⣿⡿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⢚⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣼⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿ ⠀⢹⡄⠀⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠏⣤⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣼⣿⣿⣿⢟⣽⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣷⣻⣿⣿ ⠀⠀⢻⠀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢯⣶⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢀⣼⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡰⠇⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⡈⠰⠀⠀⠀⠀⠠⠁⢠⡇⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠃⠘⠀⠀⢀⠃⢀⠈⣇⠰⠗⠑⢄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⣬⣀⠀⢀⠘⡄⠀⠀⠀⢀⣢⡀⠀⠀⠀⠀⡄⡀⠀ ⠀⠀⠀⠀⠀⣴⠁⠀⠆⠀⠀⢏⣝⡳⢦⣤⠖⠐⣬⡖⣍⢝⢯⠀⠀⠀⠀⣇⣧⠀ ⠀⠀⠀⠀⢀⢃⢴⡀⡂⠀⢸⠀⠀⠉⠊⠉⠀⠘⠉⠉⠀⠀⢨⠀⢠⠈⡄⠊⠇⡀ ⠀⠀⠀⢀⣜⣁⣼⠀⢹⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⡿⠤⠧⠤⠴⢰ ⠀⠀⠈⠀⠀⠀⠀⣹⣿⡀⢸⣿⣆⠀⢀⡈⠕⠫⢤⠂⡠⣹⣿⢠⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⢻⣿⣿⡵⡠⠊⢉⣉⣉⢎⣾⣿⣿⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠠⣀⠀⠀⣾⣿⣿⣿⣾⣿⣿⡊⡀⠞⠉⣉⣈⡋⢿⣿⣿⣿⢿⣷⣀⣀⣀⡀ ⡀⠀⠀⠈⠙⢾⣿⣿⣿⣿⣿⣿⡿⠀⠠⠐⠊⢐⢒⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢰⢻⣉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢸⣋⣣⣧⣬⣥⣶⣶⣾⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀

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

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡍⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣭⣷⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠖⠚⠛⠛⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠉⡁⠀⠀⠙⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⠷⢿⣦⣤⣈⡙⢿⣿⢆⣴⣤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⡀⣸⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣟⣩⣤⣴⣤⣌⣿⣿⣿⣦⣹⣿⢁⣿⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⣿⣯⣼⣿⡿⠟⠃⠀⠀⠀⣿⣿⣿⣿⣿⡛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣧⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢁⣀⣀⣀⣀⣀⣠⣀⣀⢀⢀⢀ ⠀⠀⢿⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠛⠛⠙⢻⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡇⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢿⣿⣆⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡼⠁⢀⣀⡀⠀⠀⠀⣦⣄⠀⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣷⣬⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣿⡿⠿⠦⢤⣴⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠒⣿⣿⣿⡿⠟⠹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡖⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣾⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⣀⣀⣤⣴⣶⣶⣾⣿⣷⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡇⣿⣿⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠻⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠓⢁⣬⣿⠇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡿⣻⠇⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢐⣯⠞⠁⠀⠀⠀⠀⠀⠀⣄⠱⣄⠀⠀⠀⠀⠸⡧⠟⠆⠀⠀⠀⠀⠘⠿⢿⠿⠿⣿⡿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠂⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣦⣼⡏⠳⣜⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣷⣦⣤⣀⣀⣀⣴⣿⣿⣿⣿⣿⡿⠻⠆⠸⣎⣧⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣠⡄⠀⣿⢹⡇⢸⡀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿

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⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣼⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠛⢻⠉⡉⠍⠁⠁⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⢀⡼⡄⠃⠤⠀⠀⠀⠀⠀⡐⠸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣸⡎⣀⣷⣤⣶⣶⣶⣦⡀⠀⠈⠓⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣤⣯⣿⣿⣿⣿⣿⣿⣿⣭⣯⡆⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣻⣿⣿⣼⠀⢹⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢘⣿⠙⠡⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣿⣯⠏⠀⢀⣿⣿⣿⣯⣠⡀⠀⠀⠀⢀⣾⡏⠒⢻⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢘⣏⣺⣤⣬⣭⣼⣿⣿⣯⡉⢻⣦⣌⣦⣾⣿⣿⡚⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⢿⡟⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣧⡞⣻⣩⣽⡽⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣇⣬⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⡟⠻⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣍⠓⠲⠤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⡏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢯⡁⠀⠀⠀⠉⠹⠶⢤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀⠹⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢩⠀⢸⡄⢹⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣤⡄⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡀⣀⣰⣿⠀⠄⠹⣾⣿⣿⡿⣿⠀⢠⣤⣀⣴⣤⣤⡴⠶⠶⠿⠿⠛⠛⠋⠉⠉⣠⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡱⠏⠉⡟⠃⠀⠀⠀⢸⣿⣿⠇⣿⡴⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⢋⣡⣶⣿⣂⡼⠁⠉⠙⠋⠙⠿⠟⣢⣄⢿⡟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀ ⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⣸⡿⠟⠀⠀⠀⠀⠀⠀⠲⣾⡛⣿⣬⡄⠀⠀⠁⠠⣤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡟⣿⡟⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠠⠤⠤⢤⠤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⢀⠠⣒⠨⠅⢀⡀⠉⠭⠄⠐⠀⠈⠭⠭⠓⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⢂⢕⠜⠊⠁⠀⠀⠈⠆⠀⠀⠀⡌⠉⠉⠐⢂⠀⠈⣇⠀⠀ ⠀⠀⣠⣾⠥⠄⠀⢤⢄⣶⣿⢿⣿⣉⠳⣄⠀⢀⣀⣥⣶⣶⣶⠄⠤⠀⣘⢦⡀ ⠀⡞⡍⣠⠞⢉⡝⠲⠤⠤⠴⠊⠀⠈⠙⠁⠀⠀⢹⡏⠀⠀⣀⣠⢤⠦⠕⠡⣿ ⠘⣇⠃⢿⠰⢻⡉⠓⢦⣤⣀⠀⠀⢲⡚⣃⣄⠀⠀⢉⣷⠄⡀⠁⣸⡄⢐⣱⡟ ⠀⠙⢮⡂⠀⠈⢻⡶⢤⣧⣉⠙⠓⡶⠥⢤⣀⣀⣳⣋⣀⣠⡤⢾⢻⣷⠁⡞⠀ ⠀⠀⠀⠹⡄⠀⠀⠙⣤⡏⠙⠻⢿⣧⣤⣤⣼⣤⣤⣿⣤⣤⣧⣼⣾⡿⠀⡇⠀ ⠀⠀⠀⠀⠻⣄⠀⠀⠈⠛⢦⣄⡞⠀⠀⠉⡟⠛⢛⡿⢛⡿⣻⢿⣿⠇⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠓⢮⣔⡩⢐⡨⢉⠛⠒⠶⠷⠶⠾⠷⠾⠷⠛⠛⡉⢀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣅⠘⠓⠰⠄⢀⡀⡀⠀⠒⣒⣈⠠⠘⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⢤⣀⣀⡀⠀⠀⠀⢀⣀⡴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠉⠉⣉⣩⠭⠭⠉⠉⠩⠭⠉⠉⠉⠙⠛⠛⠛⠻⢿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣀⠤⠒⣉⠤⠔⠒⠒⠒⠋⠙⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠮⠙⠻⢷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⠤⠊⡡⠖⡩⠔⠂⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠠⢒⠒⠒⠀⠒⠢⣄⠀⠀⠀⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠠⠊⠴⠋⠀⣀⣀⣤⣤⣤⣀⡀⠀⠑⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⣠⣾⣟⣀⡀⠀⠀⠀⣀⡀⢠⣶⣿⣿⣿⣿⣿⡋⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠻⣧⣄⠀ ⠀⢠⣾⣻⠋⠉⣡⣤⣤⣤⣌⡉⠔⠈⠛⠛⠉⢉⣭⠉⠛⠻⣶⣶⡿⠃⠀⠀⠐⢾⣿⡿⠿⠛⠛⠛⠋⠉⠀⠀⠉⠉⢍⡳⢌⢻⣦ ⣰⡿⢱⠃⢠⡾⠋⠁⢰⣌⠙⠛⠷⢶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣄⣀⣴⡶⠶⠶⣶⠹⠀⢳⣿ ⢿⡇⢸⠀⣿⠃⣀⣤⣾⠿⢷⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣤⣤⡤⠀⠀⠀⠀⠀⠘⠻⣦⣄⠀⠈⠙⠛⠋⢠⣇⠀⠀⢠⠇⣸⣿ ⢸⣧⠘⡆⢹⣇⠉⠉⢿⣆⠀⠈⠙⢿⣷⣦⣤⣉⡁⠀⠀⠸⣿⡀⣶⡶⠶⠄⠀⠀⠀⣠⣿⠿⠗⠦⣄⠀⠀⣼⣿⡇⢀⣣⠴⣿⠏ ⠀⠹⣧⣘⠲⠅⠀⠀⠘⢿⣿⣶⣤⣸⣿⡀⠈⠙⠛⠿⢶⣦⣭⣅⣀⡀⠀⠀⠐⠷⡾⠟⠁⠀⠀⢀⣠⣴⣿⢿⣿⣷⠈⠀⣼⡟⠀ ⠀⠀⠈⠻⣿⡀⠀⠀⠀⠈⢻⣦⠉⢻⣿⣿⣶⣦⣄⣀⣸⡏⠉⠉⠉⠛⢿⡿⠿⠶⢶⣶⠶⠿⠛⢿⡏⠁⣿⣄⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠙⢷⣼⡟⠀⠉⠛⠻⢿⣿⣷⣶⣤⣤⣤⣼⣧⣤⣤⣤⣿⣤⣤⣤⣾⣷⣴⣿⣿⣿⣿⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠛⢷⣤⡀⠀⠀⣸⡟⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⢀⡀⠀⢀⠀⠉⠻⣷⣴⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠈⣽⡏⠉⢹⣿⠋⣽⡟⢸⣿⡿⠃⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡓⠦⣍⠒⠤⣀⠉⠙⠛⠿⠶⢶⣤⣾⣧⣄⣀⣠⣿⣄⣠⣾⣧⣴⡿⠷⠿⠋⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣉⠒⠦⢍⣑⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⡆⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣀⡉⠑⠒⠩⠭⠍⢐⣒⣒⠒⠂⠐⠒⠒⠒⠒⠒⠉⠀⢀⡤⠚⠀⠀⣹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣠⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⣠⣮⠔⠋⠀⣀⣾⣿⣿⣿⡤⠒⠒⠊⠉⠉⠉⠉⠙⠒⠒⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⣿⠞⠁⠁⠀⠀⢠⣿⣿⣿⡯⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠌⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣿⣇⣠⡀⢀⡴⣾⣿⣿⣿⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⣮⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣟⣿⠉⣿⠧⣸⡇⣼⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠈⠛⢦⣄⠀⡀⠀⢀⡞⢓⠄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠛⣿⣶⡻⣷⡌⢷⠿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⠿⣷⢷⣴⡋⠀⠈⠳⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣷⣟⣿⣿⣼⡇⣸⢁⣼⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡿⣟⠏⠉⠀⠀⠀⠹⡄⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠻⣿⢿⣿⠛⠻⣾⣵⡿⠁⠀⠀⡀⣠⠋⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢰⠁⠀⣸⢹⣿⣴⠶⢶⣄⠀⠀⢹⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠻⡏⣸⣷⣶⣾⣿⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢠⠏⠀⠀⡟⢸⠻⣆⠀⠸⡆⠳⠀⠀⢳⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠛⠉⢸⣿⣿⡇⠀⠀⢀⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢠⠏⠀⠀⣸⠁⡞⠀⠈⠳⣄⢹⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢿⣿⠃⠀⠀⢸⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⡴⠃⠀⠀⢰⠏⢰⠇⠀⠀⠀⠙⣾⡆⢀⠀⠀⣇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⠀⠀⠀⠀⠙⠳⣤⣀⡙⢧⣀⠀⢸⠀⢀⠀⡴⠃⠀⠀⠀⠀⠀⠚⠁⠀⠀⣠⠋⢠⠏⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⣠⣾⣿⣿⣟⡿⠁⢸⡇⡟⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⣿⣶⣶⠤⣀⡀⠀⠀⡇⠸⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⠀⣰⠋⠀⠀⠀⠀⠀⠀⣠⣶⡟⢀⡴⠋⠀⠀⠀⠉⠙⠛⠳⢤⡇⠀⠀⠀⡿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢸⣇⣴⢃⣠⠖⣀⣠⣤⢶⡻⠟⣁⡴⠋⠀⠀⣤⣭⣭⣿⣶⣤⣀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⣿⣟⡧⠀⠀⢸⣿⣥⣯⡷⣛⣻⡿⠛⣉⡤⠞⠁⠀⠀⠀⠸⠿⣿⣿⢻⢿⡿⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡟⢹⣿⠀⠀⢸⡿⠭⠭⠭⠵⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠭⠾⠴⠿⢻⡇⠀⠀⠀⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢈⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡆⢸⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⢸⠀⠀⠀⡏⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⠇⠀⠀⡇⢸⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⢸⢸⠀⠀⠀⡇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠀⡇⢸⢧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡏⣸⢸⠀⡀⠀⣿⠀⠀⠙⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠀⠀⢸⠀⠀⠀⡇⢸⠸⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡾⠀⣇⢸⠀⡇⠀⣿⠀⠀⠀⢻⡾⣿⡶⣄⡀⠀⠀⠀⠀⢀⣠⠴⣿⠷⣿⠀⠀⠀⢸⠀⢰⠀⢷⣸⠂⢻⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⣼⠃⠀⠈⠻⣄⡃⠀⢹⠀⠀⠀⠈⢳⣌⡛⠶⢽⣳⣦⠤⠚⠋⣠⠞⣡⡾⠋⠀⠀⠀⣺⠀⢸⣤⠞⡅⠀⠀⢧⠈⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⢰⡟⠀⠀⢰⠀⠈⢷⡀⢸⠀⠀⠀⠀⠈⣿⣿⣶⣦⣬⣉⠑⢦⣠⢧⣴⣿⡇⠀⠀⠀⠀⣿⠀⣸⠃⠀⣿⠀⠀⠸⡇⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⢸⠀⠀⠈⠛⢾⡄⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡷⢿⣿⣿⣾⠿⣷⣶⣤⣀⠠⡷⠚⠁⠀⠀⣿⠀⠀⠀⣿⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⡘⣆⠀⠀⡿⠀⠀⠀⠀⢀⣠⣿⣥⣿⣿⡿⣿⣿⣿⣿⣿⣄⣿⣯⣼⣿⡿⣸⣿⣅⣿⣦⣀⠀⠀⠀⠀⢿⠀⠀⠠⠏⡼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣳⠿⣤⣤⣧⠴⠶⠞⣿⣹⣿⣤⡿⠋⠁⠀⠀⠀⠻⣻⡿⢋⣽⣿⠿⢿⣿⣿⣿⣿⣦⣿⣿⣹⢓⡶⠦⣼⣤⣤⠷⣾⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⢿⣦⣼⣿⡟⢶⣀⣀⣼⣿⣿⠟⠀⣀⣤⠤⢤⣤⣴⢋⣴⠟⠛⠛⠛⠛⠉⠉⠁⡿⣿⣿⣿⣧⠀⠀⢰⢛⣿⣿⣴⡿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠋⠈⣻⣾⣿⣿⣽⣿⣿⣤⣞⣵⠶⠻⠷⢶⣽⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣧⠀⣿⣿⠁⠙⠛⠯⣾⣳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠉⠁⠀⠀⠀⣼⣿⣿⡿⢿⣿⣿⣿⠋⠉⣙⣦⠤⣤⣴⠋⠛⢾⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⡇⡇⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀ ⣤⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⣷⣿⣿⣷⣾⣿⡮⣿⡓⢿⣾⣿⣉⣹⡿⠿⠦⣞⣠⡇⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣇⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀ ⢹⠘⣦⡼⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣷⡿⣏⠙⣙⣮⣽⡵⢛⡿⣿⣿⣵⣞⢦⣀⣯⣴⡌⣇⢀⠀⠀⠀⠀⠹⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⢷⡠⠎⠀ ⣸⠠⣿⢳⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⡛⡛⠁⣠⢞⣿⠶⠦⠤⠤⠴⠿⠋⠀⠀⠙⢷⢦⣬⣥⠦⠥⠭⠭⠭⢭⡽⣟⣻⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⣼⣵⡧⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢉⣻⣿⣿⣍⡛⣯⣉⣿⣷⣦⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢛⣿⠟⠀⠀⠈⠛⠛⠳⣬⣭⣍⡐⣶⣤⣉⠛⢻⣽⡳⣦⡤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣟⡛⠉⠀⠿⢷⣒⣒⣶⠀⠀⠁⠈⢛⣟⠿⠧⠤⣾⢿⡿⠉⠙⠋⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠳⣄⣰⣿⣿⡟⢳⣶⣶⣶⠤⢬⡤⠤⠤⠀⠸⣿⣿⡶⠠⡏⢠⣿⣿⣦⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⣿⢯⣉⣁⣼⠹⣿⡿⠀⢀⡇⠀⠀⠀⠀⠈⠉⠁⠀⣷⢿⣿⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡞⠉⠉⠙⢻⢛⠾⢷⣄⣀⣠⡾⢟⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠻⠿⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⡷⢿⣿⠋⠉⠉⠉⢹⣿⠒⠦⣌⡛⢦⡙⠨⡅⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⠀⣿⣷⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠙⠦⠬⠿⠤⠤⠤⠤⠞⠛⠒⠒⠚⠻⠦⡕⣄⢠⣶⣤⡀⠀⠀⠀⠀⢰⠟⣏⠉⡙⠛⢿⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⣶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⣼⡄⠙⠋⠁⠀⠀⠀⠀⠻⣆⠸⣦⡉⠛⠶⣌⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠤⠒⣋⡡⠼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⣿⣿⡆⠀⠀⣿⠳⢬⡓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⡿⣿⠛⠉⠙⠛⣋⣥⠶⠛⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢿⡀⠈⠙⠁⠀⠀⢻⠀⠀⠙⠳⣍⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠸⢥⡴⠛⣩⠞⠛⠛⠒⢯⠹⡆⠀⠀⠀⠀⠀⠈⠙⣦⢤⣀⣀⣀⣀⣤⣖⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇⠀⣸⡇⠀⠀⠀⢿⡧⣸⡇⠀⠀⠀⠈⢙⣮⣷⣤⣄⣀⠀⠀⠀ ⠀⠘⠚⠋⠁⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⢠⠏⢾⠀⢨⣼⣿⣿⣿⣿⣿⠛⠓⠒⠒⠒⠶⠿⡷⠤⠴⣿⠴⠖⠒⠒⠛⠉⢹⡃⠀⠀⢠⠞⣩⠷⠦⣄⢀⣉⣿⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⡼⣿⡿⢦⣙⣻⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢹⡇⠸⣿⠗⠀⠀⢈⣷⠀⠀⢸⡤⠇⠀⠀⠈⣧⢹⣦⠹⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⣫⠵⠚⠉⠀⠀⢠⣿⣿⣿⣿⣿⣿⠉⠙⠓⠦⠶⠒⠒⠷⠦⣤⡿⠴⢿⡻⣶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡏⠳⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡍⠉⠃⠀⢀⣾⠃⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠈⠙⠒⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⣄⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣠⠔⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠑⠢⣀⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣶⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⣼⣿⣿⠀⠠⢳⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠻⣿⠿⠴⠁⠘⠤⠤⡤⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡡⠔⠐⢄⢸⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸ ⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎ ⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠔⠁⠀

⣿⣿⣿⡀⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡇⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣽⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣎⣻⣿⣿⣿⣿⣿⣿⣷⣮⣙⠿⣿⣿⣿⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⠃⢸⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⠃⠀⣼⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣧⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⡿⠁⠀⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣈⣙⠻⠿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣸⣿⣿⣿⡟⠀⠀⢠⣿⣿⡟⠀ ⡏⢻⣿⣿⣿⣿⣿⣦⡀⠈⠉⠉⠉⠉⢙⣷⣽⡿⢿⣿⣿⣿⣿⣟⠛⠛⠻⠷⢶⣄⠉⠙⠋⠉⠁⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⡿⠿⠾⠿⠷⣶⣿⣿⣿⡋⠀⠀⣀⣿⡿⠋⠀⠀ ⡇⠀⠹⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⠾⠛⠋⠉⠀⠀⠈⠙⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣴⣿⠿⠋⠙⠻⢷⣔⡋⢸⡇⠀⠀⠀ ⡇⠀⠀⠀⠈⠙⠛⠻⠿⠿⢿⣿⣷⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠦⠄⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⢀⣼⣿⡿⠋⠁⠀⠀⠀⠀⠰⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⣤⣿⣆⠀⠀ ⡇⠀⠀⠀⠀⣠⡴⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⣠⣾⠟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄ ⡇⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠶⠊⣉⣉⠉⠐⠂⠀⠀⠀⠀⠀⢀⣿⡏⠀⠞⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿ ⣷⠞⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠲⣄⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢀⣠⠶⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⠦⣄⣾⣿⣿⣿⣿ ⡗⠀⠀⠀⠀⠀⣠⡤⠚⠁⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠈⠙⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡤⠞⢉⣠⣤⣶⣿⣿⣿⣿⣿⣷⣶⣤⣄⠀⠘⣿⣿⣿⣿⣿ ⡇⠀⠀⢀⡴⠛⠁⠀⢀⣠⣴⣿⣿⣿⣿⠿⠛⠛⠻⣿⠿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⣤⣾⣿⡿⢟⣿⡿⠿⠛⠛⢿⣿⡿⣿⣯⡙⠳⣿⣿⣿⣿⣿ ⡇⢀⡴⠋⠀⠀⠀⣼⣿⣿⢿⠛⠉⠁⠀⠀⠀⠀⠀⠈⢧⠀⠙⣿⣿⣯⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡴⣫⣿⠿⢃⣀⡀⠀⠀⠀⠀⠀⢘⡇⠉⠲⣝⣿⣦⣿⣿⣿⣿⣿ ⣿⠋⠀⠀⠀⣠⣾⣿⠏⢡⡼⠖⠶⡆⠠⠤⣂⣉⠀⠀⠘⣧⠀⠀⠉⠙⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⣱⠃⢰⡏⣉⣹⠆⣠⡤⠶⠒⠨⣿⠀⠀⠈⠈⢹⣿⣿⣿⣿⣿ ⣿⡆⠀⣠⣾⠟⢋⡏⠀⠸⠶⠶⣞⡵⠖⠋⠉⣁⠀⠀⠀⢸⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠘⣋⠉⢐⣩⡥⢶⡒⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣷⣾⡿⠁⠀⣼⡇⠀⠀⠈⠩⠄⠀⠀⠤⠚⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢳⣀⡴⠾⠋⠀⠀⢠⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿ ⣿⣿⡆⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⠒⠀⠀⢠⠟⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⠀⠀⣀⡀⠈⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⣴⣋⣀⡤⣖⡫⠏⣹⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡆⠀⠸⠭⣕⣲⣾⠿⣶⣤⣤⣀⣀⡤⠤⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠒⠚⠛⠋⠉⠁⠋⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠙⣿⣿⣿⡟ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⢿⣿⣿⠃ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠘⣿⡏⠀ ⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣿⣿⣿⣿⣿⣆⣿⠁⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠶⠶⠤⠤⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠓⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡄ ⣿⣿⣿⣿⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⢷⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣇ ⢿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢧⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠈⠙⠛⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⢿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⠻⢶⣤⡀⠀⠀⠀⠸⠦⠄⣀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⡶⠶⠶⠒⢻⣏⣿⣿⣿⠃⣿⣿⣿⣿⡿⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠉⠉⠙⠲⣄⣠⠴⠖⠒⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣠⡤⠴⠶⢤⣌⣷⡀⠀⠀⢀⣀⣀⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠙⠿⣏⠉⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⡿⠀⠀⠀⣀⣀⣀⡤⠖⠛⠉⠉⠉⠙⠻⡷⠖⠚⠋⠉⠉⠙⠒⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡏⠀⠃⠀⠀⠀⠻⠿⣧⣄⡀⠀⠀⠀⠀⢀⣠⣟⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⣯⣝⣓⣚⣛⣩⡵⠋⠉⢻⣻⡿⠛⢚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠠⠞⠋⠁⠀⠐⠒⠾⣿⡗⠚⢿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢻⡀⠀⠀⢰⡟⣏⠹⡞⢷⡀ ⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⡴⠚⣟⣛⣓⣒⠒⠦⠤⠤⣤⣄⣀⣀⣀⣤⣤⠴⢚⡇⢸⣳⣄⣧⠸⡆⢻⢸⡇ ⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠘⠧⢤⣭⣭⣭⣍⣉⠛⢒⣲⣶⣶⣶⡿⠿⠶⠚⢚⡟⠁⣌⣯⠙⠛⠀⠀⢀⡾⠁ ⠀⠀⢀⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣹⢏⡟⢸⣿⢰⣿⣷⡞⠛⠙⡿⠛⠉⠀⠀⠀⣀⡴⠋⠀⠀ ⢀⡾⠋⠀⠉⠳⢭⣙⡓⠒⠶⠤⠤⠤⠤⢤⣼⣏⢿⠀⠁⠘⠃⢸⠏⢈⡇⠀⠀⡇⠀⠀⠰⢶⡟⠉⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠖⠒⠒⠛⣶⢤⡄⠀⣀⡤⠶⣏⠀⠀⠀⢿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇⠀⠈⠳⣄⠀⠸⡇⠀⠀⠀⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠀⠀⠀⣿⡄⠀⠀⠀⠈⣷⠶⠃⠀⠀⠀⠸⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣧⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⠿⢋⢧⡀⠀⠀⣰⡟⣡⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢶⣽⣦⣴⠏⣸⠛⡉⠙⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⣀⣽⡀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣰⣿⢀⣚⣛⣻⣶⣿⣷⣄⠀⣀⣤⣤⣾⣿⠿⢿⣀⣠⠴⣿⣿⣿⣿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠉⠻⢿⣼⣿⣇⣹⣿⠟⠋⠉⢻⣿⣿⣿⡿⣄⠀⢈⡴⠋⠉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⢉⣩⠙⠆⠀⠀⠀⠀⠙⠿⢽⣓⡛⠑⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⣾⣶⣶⣶⣿⣯⣴⣷⣄⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢤⠶⢾⡿⣿⣄⠀⠈⠉⠙⠻⠿⢿⣶⠶⠶⠛⠛⠿⣦⣄⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⢀⣀⣴⣿⡇⢸⠀⢸⡇⠸⣯⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠻⣿⣿⣿⣿⣿⣧⠸⣄⢀⣿⠛⠛⢷⡝⠲⢤⡈⠉⠑⠒⠒⠒⠒⠒⠛⠉⠘⠃⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣧⠙⠚⣿⡆⠀⠈⢷⡐⠆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣶⣶⣦⡀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣴⣿⠇⠀⠀⢸⣇⣀⣀⡴⠂⠉⠀⠠⣄⠈⡆⠀⢀⣴⣿⣿⣿⣿⣿⠛⠁⠀⠈⠁ ⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⣀⣬⠿⠁⢠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣹⣿⣿⣏⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⠟⠋⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣀⣀⠀⢀⡰⠞⠛⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣤⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⢀⡠⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣟⣷⡆⠀⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠃⠀⡀⠀⠀⠀⠀ ⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠖⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣶⡟⠛⠛⠿⠿⠿⠿⠖⠒⠛⠓⠦⣄⡀ ⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠐⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⣶⡾⠿⠟⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⣠⡄⢢⣰⡜⠿⣿⠁⠉⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⡾⣟⣿⡶⣌⡞⠀⠀⠀⠀⢸⣿⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠉⠉⠉⠛⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣶⣶⣶⣤⣤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀ ⠀⠀⢀⣼⣿⠛⢿⣿⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢠⡟⠁⠀⠀⠹⣇ ⠀⢀⣾⣿⠃⠀⢘⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡇⠀⣏⡱⠀⣿ ⠀⢸⣿⣿⠀⠀⣸⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⠀⠀⠀⢠⠏ ⠀⢸⣿⣿⣷⣶⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡤⠀⣀⡀⠘⣆ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⡇⠀⢅⡔⠀⡿ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⢷⣄⣀⣠⡼⠃ ⠀⣀⡴⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠻⠿⣿⡟⠀⠀⠀⠀⠙⠛⠉⠀⠀ ⣸⠏⠀⠀⠈⠙⠿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⠀⠀⠀⠀⠀⠀⠉⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠶⠶⠶⠶⠶⠶⠞⠛⠳⣦⣤⣤⣤⣤⣤⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠀ ⠀⠀⣠⡴⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀ ⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠈⠻⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠘⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀ ⠀⠀⠀⠹⡄⠘⢷⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀ ⠀⠀⠀⠀⠈⠢⣈⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠮⢽⣛⡷⡶⢶⡶⠾⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠢⠤⠤⠤⠤⠤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠔⠒⠒⢋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠛⠛⠛⢿⣿⣶⣦⣄⠀⣠⣴⣶⣿⠿⠛⠛⠛⠛⠻⢿⣷⣶⣤⡀⠀⢸⣿⣿⣿⡛⠛⠛⠛⠛⢛⠛⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠀⠻⣿⣿⣿⣄⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⢸⣿⣿⣿⡟⠛⠛⠛⠛⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣉⡛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠈⢉⣙⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠚⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀ ⣾⡟⠉⢻⡄⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⢳⡄⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠈⠉⠳⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠻⣇⠀⠀⠀⠀ ⠀⠈⣷⡀⠀⢳⡀⠀⠀⢻⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠘⣷⠀⠈⢧⡀⠀⠀⢘⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠈⣧⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⣸⡏⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠈⣧⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⡀⢘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠘⠿⡾⠏⢀⣠⣤⣤⣀⣸⡇⠀⠀ ⠀⠀⠀⢠⡶⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄⠀⠀⠀⠘⠿⣧⣀⣀⣀⣽⡇⠀⠀⠀⠀⠀⠛⠷⣤⣤⠿⠛⣇⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⢠⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣶⠾⣦⡀⠀⠀⠀⠀⠀⡿⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⣸⠇⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⢿⡀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠈⠻⣆⠀⠀⠀⣿⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠘⢧⡄⠀⣿⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣸⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⣴⣄⣠⣿⣤⣄⠀⣤⣀⣀⣀⣀⣀⣀⢀⡿⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⣄⣀⣀⣀⣄⣀⡀⠀⣧⣀⡀ ⠀⠀⢸⠇⠀⠀⠀⣼⣧⣠⣿⣦⠺⠀⣹⣿⣤⣿⣯⡙⠯⠉⣽⣿⣾⣁⣠⡶⢿⣏⣹⡟⠿⣦⣄⣤⣿⣿⡙⠯⣹⣿⣧⣠⣿⣟⣿ ⠀⠀⢸⡆⠀⠀⠀⢻⣏⠉⣿⠙⠳⠞⠋⣿⠁⣿⠌⠛⠶⠞⠉⣿⠉⢹⡟⢰⡿⡏⢸⠟⡆⢹⣏⠉⣿⠈⠛⠛⠋⢸⡏⠉⡇⠉⡿ ⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⣿⡐⣿⠃⠀⠀⠀⠀⣿⣀⣸⡇⠸⣷⣿⢸⣷⡇⢸⣟⣆⣿⠀⠀⠀⠀⢸⡇⣸⡇⢀⡇ ⠀⠀⢸⡇⠀⠀⠀⠸⡟⠛⣿⣀⣀⣀⣠⣿⠋⣿⣆⣀⣀⣀⣠⣿⠉⠙⠻⣆⣈⠉⠉⢩⣠⡟⠋⠙⣿⣄⣀⣀⣀⣸⡟⠙⣧⣼⠇ ⠀⠀⢸⣇⠀⠀⠀⠀⣷⠀⠈⠉⠉⣟⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢰⡏⠀⠀ ⠀⠀⠀⢿⣆⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠿⣿⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⢶⣿⠁⠀⠀⣿⠓⠒⠶⠶⠶⠒⠛⠛⠉⠉⠉⣩⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣄⣄⣀⣤⣤⣤⡿⠀⠀⠀⢻⣦⠤⠶⠶⠶⠶⠶⠶⠶⠟⠛⢻⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⣿⣤⣄⣄⣠⣤⣤⣤⣤⣤⣤⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢤⣤⣤⠶⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⢤⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⣤⣤⣧⣤⣤⣤⣴⢴⣟⣛⣯⣅⣷⣠⣤⡀⠀⣠⣤⣀⣤⣤⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢾⣻⡯⡟⠏⠹⠀⠟⠸⣼⠿⠀⠹⠇⢟⢻⡿⠓⠎⢻⡴⠛⣷⡞⢻⠇⡿⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣀⠀⠀⠹⠇⠀⠙⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⢖⡋⠁⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⢤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣫⡶⠋⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣴⡟⠁⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⠋⢠⡾⠃⠀⠀⠀⠀⠀⢀⠄⣼⢃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠋⠀⣠⡟⠁⠀⢀⠀⠀⠀⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠀⠀⢠⠏⠀⠀⣴⢿⠀⠀⠀⠀⢐⠀⣿⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⠁⠀⠀⠀⠀⠋⠀⠀⣼⠃⢸⡆⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⢀⣀⡀⠀⠀⠀⢸⠀⣿⡇⠀⠀⠀⠀⢸⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⣿⡴⠚⢀⣠⡄⢸⣿⣄⠀⠀⠀⠀⠀⠀⠈⡇⢹⡀⠠⣤⣈⣙⠷⣦⣀⢸⡆⣿⣿⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠠⠚⣩⣷⣾⡏⠉⣿⣤⡀⠻⣦⡀⠀⠀⠀⠀⠀⠙⠀⢁⣦⠿⠿⣿⣿⣶⣽⣿⢀⡟⣿⠀⠀⠀⠀⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣠⣾⡿⠋⣿⠃⠀⠀⢸⣻⡆⠈⠛⠦⠤⠀⠀⠀⠀⠀⣿⡏⠈⠉⠸⣿⣟⢿⣿⣾⠁⣿⠀⠀⠀⠀⠀⠸⡆ ⠀⠀⠀⠀⠀⡤⠀⢠⡇⠀⢰⣿⠏⠀⠐⠻⡆⠀⠀⠈⢙⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⣿⠀⠀⠀⠁⢿⡆⠹⣿⣧⣿⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⣼⡏⠀⠀⠀⣾⠁⣀⡀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⡂⠀⣀⣀⣸⡇⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⠀⣼⠇⠀⢾⣇⠀⠀⠀⠙⢧⣽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⣹⣿⠏⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⢀⡟⠀⠀⠀⢉⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⣀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠆⠀⣼⠟⠀⢸⡇⠀⠀⠀⠀⢲⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡬⠍⠁⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣼⡟⢀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸ ⣸⡏⢸⠃⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢀⡞ ⡿⠀⡟⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⡾⠁ ⠃⢸⠇⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⣼⠁⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠻⢦⣄⣀⣀⣀⣀⠀⠀⠀⣀⣤⡶⣶⠀⠀⠉⠉⠉⠛⠶⢶⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣟⣁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡲⠾⣿⡍⢿⡏⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣠⡴⠞⠛⠉⠀⠀⠈⠉⠉⠑⠲⠦⣄⠀⠀⠀⠀⠀⢳⣿⠉⠹⣾⡆⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⠆⠈⠙⢦⣀⣠⢴⣶⠖⠒⠒⠶⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠾⢿⡟⠁⠀⠀⢠⡀⠀⠀⠀⢠⡄⠀⠀⠈⣷⣄⠀⠀⠀⠈⢻⢀⡀⠈⢿⣰⢠⠀⠀⠀⠀⢀⣿⠀⢀⢆⠞⠀⣀⠴⠚⠁⢠⠞⡅⠀⠀⠀⠀⠀⠀⠀⠉⠟⣦⣄⣀⡀⠀⠀ ⠀⠀⡆⠀⠀⠹⣦⡤⣄⠀⠹⣦⡀⠀⠀⠳⣄⠀⠀⠘⣯⢷⠀⠀⠀⣼⢸⢷⠀⠀⣿⣿⠀⠀⠀⠀⣼⠞⠀⡼⡾⣀⠞⠁⠀⠀⠀⡟⡼⠁⠀⠀⠀⠀⠁⠀⣰⣦⣾⠿⠛⠛⠿⢶⡄ ⠀⢠⡇⠀⠀⠀⠈⠻⣿⡷⣄⠈⠹⣶⣄⠀⠻⣧⠀⠀⠈⣿⣷⡀⠀⢹⠸⣸⠀⠀⢹⢸⠀⠀⢠⢀⡏⠀⢠⢣⣷⠃⠀⠀⠀⠀⣼⡿⠁⣠⠎⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⢀⠸⠍ ⠀⢸⡇⠀⠀⠀⠀⠀⠙⣿⣮⡳⢦⣙⢯⡃⠀⠈⢷⣄⠀⢸⠹⣷⡀⠈⣇⡅⠀⠀⠸⢸⠀⠀⣿⢸⢰⠀⠘⣾⠃⠀⠀⠀⠀⣰⡽⢁⡾⠁⢀⣴⠋⢡⡞⠀⠀⠀⡀⠀⠀⠀⢈⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⢦⡀⠈⠻⣿⣦⡉⠳⣝⣦⡀⠈⢻⣷⡠⡀⠻⣿⡵⢝⣧⠀⠀⠀⢸⠀⠀⡏⢸⣾⠀⢠⡟⠀⠀⠀⠀⢠⣿⣡⡟⠀⣠⡟⠁⠀⣾⠃⠀⠀⠀⠁⠀⠀⢀⡆⢀⡀ ⠀⠀⠘⢇⠀⠀⠀⠀⠙⢦⡀⠈⠻⢿⣶⣈⠛⢿⣄⠀⢳⡿⣇⠀⠹⣟⠈⣿⣆⣀⣴⡾⣦⣴⣷⣶⣿⣦⢿⡀⠀⠀⠀⠀⣾⣿⠟⢀⣼⠏⠀⠀⣸⠇⠀⠀⢀⠀⡀⢰⣠⡞⠋⣹⠃ ⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠙⠦⣄⠀⠙⠻⣷⣄⠻⣆⠀⠻⡿⡄⠀⢻⣶⣿⣿⣿⣿⣷⣿⣿⣿⣷⣻⣿⣤⣇⣾⠂⣀⣾⣿⣫⣾⢿⡟⠀⠀⣰⡇⠀⠀⠀⠈⡇⡇⣾⢏⢀⣼⡇⠀ ⣴⠊⠉⠉⢳⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠻⢦⡈⣧⠈⢹⣿⣤⡿⣿⣿⣏⢿⣿⣿⡟⠿⠿⠿⢿⣧⣽⣏⣹⣿⣿⣿⡾⠛⣡⠞⠀⡠⣪⣾⠀⠀⠀⠀⢠⣷⣿⠃⣄⣸⠏⠀⠀ ⡅⠀⠢⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢄⠈⠻⣷⣄⣀⠙⢮⡳⣄⠙⠿⣿⣟⣿⣿⣿⣿⠇⠀⣶⣜⡛⠀⢹⣿⣿⣿⣿⠿⣿⣷⠞⠁⠀⢞⣿⡿⡇⠀⠀⠀⣀⣸⡿⠃⣸⣿⠏⠀⠀⠀ ⡷⠀⢀⣙⢦⣠⢬⣳⣄⡀⠀⠀⠀⠀⠉⠲⢬⣑⡿⣷⣦⣽⣯⣳⣾⣷⣿⣿⣿⣿⣿⣶⣀⠙⠾⠟⣁⣾⣿⣻⣿⣷⣿⢿⡟⠀⠀⣠⣾⠿⣻⡧⣶⣶⡿⠿⠿⠷⣾⠟⠁⠀⠀⠀⠀ ⣇⠀⠈⠉⠑⠺⢧⣌⣙⠻⠷⣤⣠⡤⣤⣤⣄⣈⣉⣳⣾⣍⣉⣙⣿⣷⣿⣿⣿⣿⣋⣽⣛⣿⣿⣿⣿⣿⣿⣟⣿⢿⣧⣸⣀⣴⣞⣯⠷⠟⣿⠟⠉⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠹⣦⠀⠀⠀⢀⣀⣈⠉⠳⣶⣤⡬⢝⣲⢦⣤⣄⣀⣉⣩⣭⡿⣿⣿⣿⣿⣿⣟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⡿⣿⣿⣿⠗⠀⠀⡇⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢆⣀⡘⣇⠀⠉⠁⠀⠉⠉⠲⢶⣾⣉⣉⣉⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣿⠿⠋⠁⠀⢠⡾⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⡟⠉⠁⠀⠀⠀⣀⣼⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠽⠿⠿⣏⣿⣿⣿⣿⣿⣿⠀⠈⡇⢻⣿⣿⣻⠏⠀⣀⡀⠀⠀⠀⣿⠏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⠶⣶⣾⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⣿⡿⠉⣿⠛⠀⣀⣿⠬⠿⠿⠿⠖⠋⣩⣿⣷⣶⠾⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠶⠶⢶⣦⣤⣤⣄⣄⣀⡀⠀⢀⣀⣾⣉⣀⣀⡿⠞⠉⠁⠀⠀⠀⢀⣤⣶⢾⣿⠟⠲⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣶⡶⢾⣍⠛⢶⣿⢾⣭⣻⣏⠉⠉⠉⣁⡀⠀⠀⢀⣀⣀⣠⡶⣿⡟⣩⠋⢀⣴⢖⣻⣏⣉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⣖⣋⣠⠀⢉⣿⣉⣿⠻⠃⠀⣼⣧⠀⠉⠳⣍⢫⠛⢳⠾⠿⠾⠿⠶⣶⢾⣿⠋⠉⡰⠉⣼⠃⣼⣿⣗⣚⣭⡉⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢋⣴⡋⢀⡴⣿⡯⠎⢻⣦⡶⢶⡇⠈⠉⠲⠶⢿⣄⠁⠈⢷⠀⠀⠀⠀⣿⣾⣿⠴⠂⠁⠸⣿⠞⢩⠭⠿⠿⠿⢽⣲⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠩⠶⣿⣷⣿⡴⠂⠀⢻⣀⣾⣄⣤⡶⠾⢟⣒⣛⣳⣄⠈⠳⢄⡀⠀⣿⣿⣿⣀⠠⢤⣾⣩⣅⡀⠀⠶⠶⢦⣶⣮⣝⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢩⡿⢿⡁⢀⣸⣿⡿⠟⠉⠉⠻⣍⠀⠀⠈⠉⠷⠛⣦⣽⠿⠋⣹⠁⠀⠀⢠⠉⢷⠙⣿⣶⢤⡀⠀⢮⡙⠺⢝⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠓⠙⠛⠉⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣠⠶⠋⣿⢀⡶⣿⣀⣶⠀⠈⣧⠈⣧⣹⡄⠈⠉⠁⢮⡏⠀⠀⠙⣯⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣿⣋⣶⣿⡟⠉⣧⠀⡾⠀⢸⡿⡝⣦⠀⠀⠘⣿⠀⠀⠰⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⡇⠀⢙⠾⠁⠀⢀⣧⠹⣼⣷⡀⠀⠈⠀⠀⠀⠀⠹⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢳⠁⣰⡿⠶⣾⠃⣸⠙⣆⣿⡟⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠉⢀⣾⡧⢰⣿⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⡇⠀⠀⣿⣥⠟⠛⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢹⣿⣿⣿⣿⡸⣿⢿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣧⠻⣯⡻⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⢿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣷⡙⣿⣟⢿⣿⣿⣼⣿⣿⣿⣯⣻⣿⣿⢸⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣿⣿⣿⣾⣿⣮⣻⣿⣿⣿⣿⣿⣿⣧⢿⣿⡀⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⣿⣿⣿⢹⣿⣿⣿⣿⠋⠙⠿⣝⢿⣿⣿⣿⣿⣷⡹⣿⣿⣿⢿⣿⣿⡼⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣧⣿⣿⣿⢸⣿⣿⣿⣿⡄⠀⠀⠈⠋⢿⣿⣿⣿⣿⣿⡜⣿⣿⣯⢿⣿⣇⢻⣧⣿⣿⣿⣿⣿⡧⣿⣿⣿⣿⡟⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢸⣿⣿⠿⣿⣷⡀⠀⠀⠀⠀⠙⢿⣿⣿⠻⣿⣬⣿⣿⡼⣿⣿⣸⣿⣿⣿⣿⠏⣿⣇⣿⠏⣿⣿⢡⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢿⢸⣿⣿⠀⠈⠙⠻⠤⠀⠀⠀⢀⣠⣬⣿⣷⣬⣿⢿⣿⣷⣿⣿⡇⣿⣿⣿⡟⢠⡿⣻⠋⢠⣿⣟⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠘⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⠾⡎⣿⣿⡄⠀⠀⢀⣠⠴⠖⠋⠉⠉⠀⠀⠈⠀⠀⠀⠈⢿⣿⣿⡇⣿⣿⣿⠿⣿⡿⣧⣄⣾⡿⢙⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡄⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣷⠸⣿⡧⠔⠋⠁⠀⠀⣀⣀⡤⠶⠒⠒⠀⠀⠒⠀⠀⠀⠙⣿⣧⣿⡿⠃⠀⠉⠀⢀⡾⠟⠦⣼⣱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⣿⣷⡹⣿⠀⠀⠐⢚⣩⢥⣖⣲⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⢻⢺⠟⠁⠒⠒⠒⠒⠋⠀⠀⣀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⣿⣿⣿⣿⡟⣿⡇⢸⣿⣿⡄⣿⣿⣷⡙⢧⡀⢔⣿⣿⣿⢿⡿⠿⢿⡿⢻⠟⠿⠈⠓⠀⠀⠚⠀⠀⢠⣴⣶⣶⣶⣶⣦⣤⢬⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡇⣿⣿⣿⣿⡇⣿⡇⢸⣿⣿⡇⣿⣿⣿⡇⠀⠉⠀⠈⠀⡎⠨⣽⣍⠉⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⠿⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⡇⣿⣿⣿⣇⠀⠀⠀⢀⣀⣑⡀⠀⠀⠀⢰⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠈⠁⠀⣸⢣⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣿⢻⣿⣿⣿⡇⢸⡇⢸⣿⣿⣷⢻⣿⣿⣿⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠤⢤⣠⣾⡅⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣟⢸⣿⣿⣿⣿⢸⡇⢸⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣸⢸⣿⣿⣿⣿⢺⣷⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⣿⢸⣿⣿⣿⣿⣸⣿⡘⣿⣿⣿⣿⣿⣿⣿⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣦⠀⠀⠀⢠⢰ ⠀⢸⣇⣿⡏⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡿⢏⢹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⡦⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡿⠿⠇⠀⠀ ⠀⠸⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡟⠌⢿⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⣿⣿⣿⢿⣿⣿⣿⣾⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⢦⣀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢇⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀ ⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⡇⢹⣦⡀⠀⠉⠳⣤⡈⠙⠛⠶⢤⣄⣀⣀⣀⣠⡴⣶⡿⢹⣿⣿⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠛⢸⡇⠀ ⠀⢸⣿⣿⣿⠘⣿⣿⣿⣷⣿⣿⡄⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣶⣤⡀⠀⠌⣙⠲⠦⢄⣀⣈⣉⣩⠴⠖⠋⢀⣼⡏⣿⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀ ⡀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣶⣤⣈⣉⠒⢦⣾⠀⢄⢈⣉⣭⣶⣿⣿⡇⣿⢸⡿⢸⣿⢹⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⡇⢘⢸⣿⣿⣿⣿⢿⣇⣿⢸⡇⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⣿⡇⣿⣿⣿⡟⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⡇⣾⠀⣿⣿⣿⢋⣷⣷⣟⣸⢳⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⣿⣿⣿⢻⣷⣿⣿⣿⣷⡿⢾⣿⣾⣿⣿⣿⢻⣿⣿⡿⣷⣯⡻⢿⣿⣿⣿⣿⣿⣿⠘⠀⡇⠟⠀⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⡇⣿⣿⣿⣼⣿⣼⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿⣷⣮⣹⠿⢿⣿⣿⣶⣶⣶⣖⣫⣽⣾⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⣿ ⣧⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡟⣼⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⢻ ⡿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣟⣶⣬⣽⣟⣻⣿⣿⡇⣿⣿⠀⠀⠀⠹⣻⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡴⠶⠶⠟⢛⡿⢻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡴⠶⠶⠞⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⡴⠋⠀⣸⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠶⠶⠞⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣼⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡶⠶⠶⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣴⢟⠁⠀⠀⠀ ⠀⠀⣀⣀⣀⣀⣤⣤⣴⣶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⣠⡾⣩⣟⡀⠀⠀⠀ ⠀⣿⣯⠉⠛⠻⠿⢿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⡾⣯⠞⣫⢏⣷⣀⣀⣤ ⠀⠹⣿⣄⡄⠀⠀⠀⠀⠉⠉⠛⠛⠶⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠟⣾⢃⠜⣡⠟⠉⠉⠈⣽ ⠀⠀⠉⠙⠛⣿⡶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣰⠟⢁⣼⢋⣵⠟⠁⠀⠀⣠⣾⠋ ⠀⠀⠀⣠⣴⢿⣷⠶⠾⡟⠙⣛⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⢶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢠⣾⣫⡴⢞⣵⠿⠁⠀⠀⣠⣾⠏⣹⠀ ⠀⠀⠀⢿⣝⠒⠒⠤⠤⢿⣛⡋⠀⠉⠙⣿⡉⠙⠛⠻⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣦⣤⣄⣀⠀⣠⠟⠁⢀⣴⡿⠋⠁⣠⡿⠋⠀⣠⣴⣿⡿⠋⣠⣟⡀ ⢠⣤⠴⠶⠿⠟⠛⠶⢶⣤⣤⣉⣉⡒⠂⠘⠿⠶⣤⣤⠶⢶⣦⠉⠉⠛⠻⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠈⠉⠻⣿⠁⠀⣰⣿⣿⠁⣠⡾⠋⠀⣠⣾⠿⠛⠉⣠⣾⣋⣽⡇ ⠀⣧⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠶⠦⣤⣈⣉⡓⠻⠷⠶⠶⣶⣶⣄⠈⠉⠙⠛⠳⠶⣤⣄⣀⡀⠀⢿⣤⡾⠛⠛⣡⡾⠋⠀⣠⡾⣯⣠⣤⢶⣻⣍⣻⡏⣽⡇ ⣾⢿⣍⠙⠛⠛⠻⣷⣶⣶⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⢤⣬⣿⣆⠀⠀⠀⠀⠀⢀⣼⠟⠛⣻⣿⠏⢀⣠⠞⠋⠀⣠⣾⣻⠁⣽⢡⣴⡿⠋⠩⣹⡿⠋⠀ ⢻⣆⠉⠛⠶⢤⣤⣤⣍⣉⣥⣬⣭⣭⠿⠿⠛⢛⣶⠶⣶⣤⣄⣀⣀⠀⠀⠀⠈⠻⣦⡀⣀⣠⣴⣿⣅⣉⣉⣡⣤⡶⠛⠁⠀⣠⣾⣿⡿⢃⣴⠏⠀⣹⣷⣠⡾⠋⠀⠀⠀ ⢸⣟⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡾⠟⢻⣆⠈⠻⣷⣬⡙⠿⡟⢶⣶⣤⣤⣉⣉⠉⠀⠈⠉⠉⠉⠉⠁⠀⠀⣠⣾⠿⠛⣡⣴⣟⣁⡤⠾⣻⡿⠋⠀⠀⠀⠀⠀ ⠘⣿⣬⣍⡉⠉⠉⠙⠿⣟⡛⠉⠉⠉⠉⠀⠀⠀⠀⠙⢷⣄⠈⠙⠻⢷⣦⣄⣙⠛⠻⠿⠿⠿⠛⠶⣦⣤⣀⡀⠀⢀⣼⣯⣤⣶⠿⢋⣿⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠛⠻⠶⣦⣤⣈⡛⢶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣽⣿⣦⣄⣀⠀⠉⠙⠛⠓⠒⠲⠶⠒⠒⠚⠋⢉⣿⡿⠛⠋⠉⠁⢀⣠⣾⠃⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣬⣭⣉⡉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⠶⢶⣤⣤⣤⣤⣠⣤⣤⣴⡶⠟⠋⠀⠀⠀⠀⢠⣿⠋⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣦⣄⣀⠀⠀⠀⠀⠙⠻⣦⣤⣀⣀⣈⣩⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣾⢃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⠶⣤⣤⣀⡀⠀⠈⠉⠉⠉⠛⠻⠿⢿⣦⣀⣀⣠⣴⢿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣀⡀⠀⠀⠀⠈⢿⡏⢉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀ ⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⡇⠂ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⡇⠀ ⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⣸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⣸⣿⡿⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⣀⣼⣿⡟⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⢀⣼⣿⡟⠁⠀⠀ ⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣛⣉⣠⣤⣴⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣟⣛⣁⣠⣤⣴⣿⣿⡿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⢸⣿⠀⠀⣀⣤⣤⣤⣶⣶⣄⠀⠀⠀⠀⢀⣴⣶⣤⣤⣤⣄⡀⠀⢸⡏⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠙⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⣿⡏⠀⠀⠀⠀⢀⣠⣴⣤⡀⠀⠀ ⠀⠀⢸⣿⡟⢿⣿⣆⠀⠀⠀⠀⣿⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⣠⣤⡀⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⢸⡇⠀⠀⠀⢠⣿⡿⠻⣿⣷⠀⠀ ⠀⢀⣿⣿⠃⠀⢻⣿⣦⣄⡀⠀⣿⡄⠀⠀⠀⠉⠉⠉⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⣾⠇⠀⣀⣴⣿⡿⠁⠀⣿⣿⣄⠀ ⣰⣿⡿⠋⠀⠀⠀⠙⠻⢿⣿⣷⣾⣷⣤⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣶⣿⡿⠟⠋⠀⠀⠀⠈⢻⣿⣦ ⢿⣿⣶⣶⣶⣶⣶⣤⣄⠀⠈⠙⠻⢿⣿⣿⣿⣷⣦⡀⠀⠀⢻⣿⠟⠻⣿⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠋⠁⠀⣀⣤⣶⣶⣶⣶⣶⣿⡿ ⠀⠉⠉⠉⠉⠉⠙⠻⢿⣿⣷⣦⣄⡀⠈⢻⣏⣿⣿⣷⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⣸⣿⣿⢳⡿⠉⠀⣀⣤⣶⣿⡿⠟⠋⠉⠉⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣿⠘⣿⣿⢳⡦⡤⢤⠤⡤⢤⢤⡴⣶⢻⣿⡏⢸⣷⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⠀⣿⣿⣿⣷⣷⣾⣴⣧⣼⣾⣷⣿⢿⣿⠃⢸⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡿⣿⡀⠈⠻⣼⣇⣏⢻⠙⡏⢹⢹⣇⣿⠾⠋⠀⣼⡿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣿⡿⠟⠋⠁⢀⣿⣧⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣰⣿⡀⠀⠉⠛⠿⣿⣿⣶⣶⣶⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⢿⣿⣏⠉⠉⠉⠉⠁⠀⣀⣴⣾⣿⠿⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠿⣿⣷⣦⣄⡀⠀⠉⠉⠉⠉⢉⣿⣿⠇⠀⠀ ⠀⠀⠀⠈⠻⣿⣷⡄⠀⢀⣶⣿⡿⠟⠋⠁⠀⠀⠀⠙⠻⠿⢶⣶⣦⣶⣶⣶⠾⠟⠋⠁⠀⠀⠀⠉⠛⢿⣿⣷⣄⠀⠀⣴⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⢀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⠀⢠⡤⠤⣴⣦⡤⠤⠤⢤⡄⠀⡤⠤⠤⠤⣤⢠⡤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⣤⡀⠈⢷⢸⠆⠀⣿⢸⠀⠀⠀⠀⣧⢸⠃⠀⠀⠀⡇⢸⠀⠀⣤⣄⠀⠘⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⢿⡓⠒⠚⢻⠀⠀⣻⢸⠀⠀⣶⠀⢸⡿⠀⢰⠀⠀⡇⢸⠀⠀⣿⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠈⠳⡄⢸⠀⠀⣿⢸⠀⠀⣿⠀⠘⡇⠀⣿⠀⠀⣧⢸⠀⠀⠉⠉⠀⢠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡶⠒⢺⢷⡄⠀⢹⣼⠀⠀⣿⢸⠀⠀⣿⡇⠀⠃⢀⣿⠀⠀⡿⢸⠀⠀⣶⠒⢚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠶⠃⠀⢸⢿⠀⠀⣿⢸⠀⠀⣿⢷⠀⠀⢸⢿⠀⠀⣇⢸⠀⠀⣿⣀⠈⢳⣄⠀⠀⠀⢰⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⣀⣀⡴⠋⠸⣤⣤⡿⠸⣤⣤⡿⠸⣤⣀⡾⢸⣤⣤⡿⢸⣤⣤⡿⠉⠛⠒⠿⣦⡀⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⡸⠀⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⣆⠉⠐⢦⠃ ⠀⠀⠀⠀⠀⠀⠀⢰⢃⠎⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠈⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠁⠀⠀⠀⠀⢀⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀ ⠀⠀⠀⠀⠀⠰⣟⣤⣶⣿⣿⣶⣶⣤⣈⡹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠐⢊⣉⣤⣴⣶⣾⣿⣿⣿⣿⣶⣄⡈⠣ ⠀⠀⠀⠀⢠⣾⣿⣿⠿⠻⠛⠙⣿⣿⡿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣄⠀⢹⡀⠀⣸⣿⣿⠿⠟⠻⣿⠛⠋⠉⢻⡿⣿⣿⣶ ⠀⠀⠀⠀⠀⡿⣿⠁⠀⢰⣤⣴⣿⣿⣗⣤⣿⠉⠳⡄⠀⠀⠀⠀⡏⠑⢄⢣⠐⠉⠁⢱⣤⣤⣞⣿⡇⠀⠀⣺⡇⠈⣻⡿ ⠀⠀⠀⠀⠸⡇⠈⠁⠀⠸⣿⣿⣿⣿⣿⣾⣿⠀⠀⠘⢦⡀⠀⠀⢸⠀⠀⠙⢧⠀⠀⢸⣿⣿⣿⣿⣿⡦⢶⣿⠁⠀⠁⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠠⡀⢻⡀⠛⠛⠛⠀⡟⠀⠀⠀⠀⠙⢆⠀⠈⡇⠀⠀⠀⠀⠀⠀⢇⠀⠓⠦⠟⠁⣠⠃⠀⠀⡔⠀ ⠀⠀⠰⠀⠀⠀⠱⡀⠀⠀⠀⠳⠤⠤⠶⠞⠀⠀⠀⠀⠀⠀⠀⠑⢤⣹⡀⠀⠀⠀⠀⠀⠘⠓⠲⠶⠶⠞⠁⠀⢀⠞⠀⠀ ⠀⠀⠀⠳⣄⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀ ⠀⠀⠀⠀⢠⠈⠑⠒⠷⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⢠⠖⠛⠋⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⠤⠔⢒⡟⠀⠀ ⠀⠀⠀⠀⠀⠁⡄⡎⠀⠒⠒⣠⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀ ⠀⡆⠀⠀⠀⠀⣿⠇⠞⠉⠉⣻⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠈⢳⣤⣀⣠⣴⡟⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢸⠁⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⣼⡷⣤⠟⢹⡇⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡀⠀⠀⠀⢀⣼⣿⣿⣯⢶⣈⣷⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢤⡀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠉⠑⠢⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡟⣦⣼⣸⣄⠴⡿⠁⠀⠀⢀⡴⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣝⣳⡟⠁⠀⠀⠙⢻⡥⢀⣀⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣠⠴⠒⠒⠾⠖⠉⠀⠀⠉⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠼⢿⠀⠀⠀⠀⠀⠘⣷⠚⠁⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀ ⠀⠀⠈⠉⠉⣻⢆⡀⠀⠀⢀⣼⠬⢳⣤⠀⠀⠈⠒⠤⠤⠤⢄⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢰⡷⠚⢻⣉⠟⢧⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠉⠁⠈⠢⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠙⠂⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣀⡉⠒⠤⠤⠖⠦⣀⣀⠀⣀⡠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⢀⡠⠤⠄⠐⠒⠒⠒⠒⠒⠒⠂⠠⠤⣀⠈⠑⠢⢄⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⡠⠔⠋⠁⣀⡠⠤⠐⠒⠒⠒⠒⠒⠒⠢⠄⣀⡀⠉⠒⢄⡀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⠔⠉⢀⡠⠒⠁⠀⣀⠤⠔⠒⠒⠒⠒⠒⠒⠤⢄⡀⠈⠑⢤⡀⠈⠲⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡔⠁⢀⠔⠉⢀⡠⠒⠉⢀⡠⠄⠐⠒⠒⠒⠒⠠⠤⣀⠈⠑⠢⡀⠈⠢⡀⠈⢦⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠎⠀⡠⠃⠀⡠⠋⢀⡠⠒⠁⢀⡠⠤⠔⠒⠂⠤⠤⣀⠈⠑⢦⡀⠈⢢⡀⠘⢆⠀⠱⡀⠈⢆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⢠⠃⠀⡜⠀⢀⠎⠀⡠⠊⠀⣠⠞⠁⣀⠤⠔⠒⠲⠤⣀⠀⠙⢦⡀⠙⢄⠀⠑⡄⠈⢢⠀⠱⡀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⢀⠎⠀⡜⠀⢀⠎⠀⡴⠁⢀⠜⠀⡠⠊⠀⡠⠤⠤⠤⢄⡀⠙⠢⡀⠙⢄⠈⢣⠀⠘⡄⠈⢧⠀⢱⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⡞⠀⣸⠁⢀⡎⠀⡼⠁⢠⠎⢀⠞⠀⡰⠋⠀⠀⠀⠀⠀⠙⢆⠀⠱⡀⠈⡄⠀⢧⠀⠸⡀⠈⡆⠀⢇⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢰⠁⢀⠇⠀⡸⠀⢰⠁⠀⡎⠀⡜⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠱⡀⠘⡄⠈⡆⠀⢣⠀⢱⠀⠸⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⡌⠀⢸⠀⠀⣇⡠⠮⣄⣸⠀⢰⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢣⠀⣱⡀⠼⣄⡘⡄⠀⣇⠀⡇⠀⡇⠀⠀⠀ ⠀⣀⠴⠚⠓⠦⠓⠉⠉⠁⠊⠁⠀⠀⠀⠈⠑⣧⣀⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣀⡼⠋⠀⠀⠀⠀⠈⠙⠉⠉⠉⠻⠔⠛⠒⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠙⠢⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⠁ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠑⠢⠤⣀⠤⠔⠊⠁⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠈⠒⠤⠄⡀⠤⠔⠊⠐⠂⠀⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠳⡀⠀⠀⣰⣫⣴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⢬⡖⠒⠁⢉⣠⣤⣬⣿⣶⡀⠀⠀⠀⣀⣴⣾⣇⠀⠀⡜⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠐⢶⣯⣿⣶⡾⣿⣿⠷⠶⣿⣿⣿⣷⡦⢈⠒⢊⠤⠾⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣄⡀⢀⣀⣠⡾⠁⠀⠀⠈⠉⢉⡽⠋⠀⠀⠀⠈⠻⢿⣿⣽⡾⢶⡁⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⢹⠿⣿⣿⠁⠀⠀⣤⣶⣾⣿⣿⣿⣦⣀⠀⠀⢀⣰⡄⠀⠀⠀⢹⣷⢿⣿⣿⠀⠀⠀⠀⠀⣠⠔⠒⠒⢄ ⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣸⣸⣿⡇⠀⢀⡾⠋⠁⠀⠀⠉⠙⠻⣿⡿⠛⠋⠙⠻⣶⣄⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠉⠳⠤⠊⠁⠀⠉⢦⠀⠀⣿⣯⣿⣿⣿⠃⠀⢸⠑⢶⣾⣿⢻⠶⣶⣤⣀⣀⣀⡀⠀⠀⠙⣿⠀⢸⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠏⠀⠀⣿⣿⣿⣿⣿⡄⠀⠘⢠⠸⣿⣿⣿⣶⣧⣀⣏⣉⣏⣽⣿⠗⠀⠁⠀⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄ ⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠈⢧⠙⣿⣍⠙⠛⠿⠿⠿⣿⡿⢋⡔⠀⠀⢠⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠳⢌⡙⠓⠶⠤⠴⠞⢋⡤⠋⠀⠀⣰⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣷⡄⠀⠀⠀⠉⠓⠒⠒⠒⠋⠁⠀⠀⣠⡾⢃⣾⣿⣿⡟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⣾⣿⣿⣿⣧⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⣀⣠⠤⢤⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠠⠶⠤⠶⠛⣉⣴⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠒⠉⠉⠙⠒⠢⠤⣠ ⣡⠖⠊⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣯⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠻⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⠿⠟⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢙⣿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣤⣤⣶⠟⠋⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀

⣼⠀⠀⠀⠀⠀⠀⠅⣾⣿⢻⣿⣿⣿⢖⣰⡿⣼⡇⣟⣾⢰⠲⢶⣶⣬⣟⢷⣾⣾⡄⣿⣿⢚⡻⣿⣿⡟⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⣾⣿⣽⡿⣼⣏⣿⣿⣿⣾⣿⣿ ⠁⣱⠆⠀⠀⠀⢀⡄⣿⣿⠸⢟⣭⣾⠟⣽⠇⣿⡇⣸⡏⣿⣶⣤⣘⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡾⣫⣷⣽⢧⣿⣧⡿⢸⣿⣿⣿⣿⣿⣿ ⣼⡀⠠⢀⣦⣶⣿⠇⣿⣿⣾⢿⣫⡶⣴⢯⡆⡿⡁⣿⢿⣷⣤⣉⠛⢿⣷⣶⣩⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⣾⣿⣱⢯⣿⡿⣸⣇⣿⡟⡵⣿⣟⣭⢻ ⡱⠁⠀⣠⡿⣛⣥⣾⣿⢫⣴⢏⡿⣹⢏⡾⢿⣿⣧⣫⡟⠀⠀⡉⠛⢿⣿⣽⢿⣿⣿⣿⣿⠿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣿⡇⣿⣹⡟⣼⣧⠾⣿⢏⣾ ⠃⠀⢐⣵⡿⣛⣯⢆⡟⣀⢈⡿⣽⢏⡾⠙⢶⣉⣻⣿⣿⣿⣶⣤⣄⣓⢻⣿⣿⣿⣿⠟⢷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠉⠛⢿⣿⣿⢹⠏⣶⣲⣯⣾⣿ ⠣⢐⣛⣵⣾⣻⣯⣾⢻⡏⠞⣽⢟⣾⣿⠾⢿⣫⣭⢻⣿⣿⣿⣽⡻⢿⣿⣿⡿⠟⢉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣷⠀⠀⠉⠲⣄⠙⢧⣿⣸⣏⣿⣼⣿⣿ ⠀⣿⣿⠿⣵⢏⣾⣯⣿⡅⣼⡟⣾⣿⢫⣷⠟⣹⣏⡿⢷⣽⣿⣯⠻⣷⣌⡙⠿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⢸⠃⠈⢧⠀⢿⡿⣼⣿⣿⣿⣿ ⢸⣿⣿⠀⢸⣼⣿⣾⣿⡇⣿⢇⣿⡏⣿⡽⣳⣟⣼⡃⠀⢻⣷⡿⣷⣌⠙⢿⣦⡈⠙⢿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠲⣁⡴⠶⠸⡀⢸⢃⣏⣿⣿⣿⣿ ⢺⣿⢸⡄⠀⠘⣿⣿⣿⢻⡿⢸⡂⣿⣷⢷⣿⣹⣿⣷⣸⠾⠋⣳⣼⣿⣆⠀⠈⠻⣦⠚⠙⠻⣿⣿⣿⣿⡿⠆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⡇⠀⢸⠃⢸⣼⣿⣿⣿⣿⣿ ⡿⣿⡎⣷⠂⢀⣿⡞⣿⡸⣧⣿⣧⣽⢏⣿⢯⣿⣿⢿⣧⣤⣾⣿⣿⣿⣿⣧⡀⠔⠉⢷⡀⠀⠘⢿⣻⣟⠀⠀⣀⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢯⢡⡼⢹⢸⣿⣿⣿⣿⣿⣿ ⠃⣿⠀⢹⡗⠦⣼⣿⣻⣷⣻⣿⣿⡿⣾⡏⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣤⣤⣶⠷⠿⠛⠛⠛⠛⢿⣿⡞⢿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢹⠃⢸⢸⣿⣿⣿⣿⣿⣿ ⠀⣿⡇⠀⣷⡄⠈⣽⣿⡿⣧⡹⣎⢳⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣶⣿⠟⠋⠁⣀⣀⣀⡀⠀⠀⠀⢸⠏⣷⡘⣿⣿⣿⣿⣿⣿⣿⢻⣧⣸⢰⢸⡜⣿⣿⣿⣿⣿⣿ ⡹⢻⣇⠀⠸⣿⡄⢠⢿⣯⣻⣷⡹⣾⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⡾⣿⠃⠀⢠⠋⣀⣤⣤⡉⢳⡀⠀⣸⠄⣸⣇⠹⣿⣿⣿⣿⣿⣿⠈⢿⣟⠘⣿⣷⣿⣿⣿⣿⣿⣿ ⡇⢸⣿⣴⣀⢻⣷⡄⢇⣻⡟⠙⢷⡸⢷⡄⠙⢿⡯⠻⢿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠸⡀⢟⢿⠁⢹⠄⢳⠘⠁⠀⢸⣿⠀⢹⣿⣿⣿⣿⣿⠀⠈⠻⠷⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣾⣿⣿⠟⠉⠹⣦⣾⣷⡌⢻⣦⡀⠙⢦⡄⠙⢻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠓⠶⠞⢀⣾⠞⠀⠀⠀⣿⡇⠈⣿⣿⡟⠙⠁⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⡿ ⢸⣯⣿⣿⣿⣿⠟⢻⣧⠀⣴⣿⣿⣿⣿⣦⠙⢷⣦⡀⠈⠓⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠀⠀⠀⠀⠀⠈⣷⠀⠻⣿⣗⡆⠀⠀⠠⠀⢸⢸⣿⣿⣷⠻⣿⡿⠁ ⢸⣿⣿⡿⣿⡁⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⡁⠙⠲⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠸⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⢿⠀⢸⠃⠉ ⠀⣿⠁⢿⣻⣷⣸⣶⣿⣿⣼⣿⣿⣿⣿⡿⣿⣿⣦⣴⠶⠿⢭⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠃⠀⠀⠀⠀⠀⢸⣿⠀⢉⣰⡇⠄⠀⠀ ⢃⢹⡇⢈⣿⣿⣿⣿⣿⣿⢧⢻⣿⣿⣿⣿⣮⣻⣿⠁⠀⡞⢉⣭⢽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣠⣿⡧⠀⠀⠀ ⠘⠾⣿⣿⣿⣿⣿⣿⣿⡟⠺⡾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠻⡼⢍⣈⣷⢹⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣿⣿⠃⢀⠐⠀ ⠐⠀⢻⣿⣿⣿⣿⣿⣿⡇⢰⢳⣿⣿⣿⣿⣿⣇⠘⡿⠦⠄⠈⠓⠶⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠷⠊⠁⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⢸⣟⣹⣿⣿⣿⣿⡎⠳⢦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⠟⠉⠀⠈⠙⣿⣷⡄⠀⠀⠀⢰⡿⠟⠋⠀⠀⠀⠀⡀⠀ ⢀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣦⣄⠙⢦⣀⠀⢦⠀⠀⠹⣄⠀⠷⠄⠒⠀⠀⠀⠀⠀⣠⣿⣿⡿⢿⡏⠀⠀⠀⠀⣰⣿⣿⣷⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡼⠃⠀ ⠈⠢⠀⠠⢿⣿⣿⣿⣿⣿⣿⡏⡌⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⢷⣎⢷⣄⠀⠈⠱⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡌⢿⠀⠀⠀⢰⣿⣿⣿⡛⢠⠋⠀⠀⠀⢀⣀⡀⣴⡿⠁⠀⣀ ⠀⠰⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣌⠃⠀⠀⣾⣿⡟⠁⢠⣋⡤⠔⠒⠋⠉⢉⣼⣿⣴⠞⢋⣽ ⠀⠐⡤⠀⠀⠀⢻⣿⣿⣿⣿⢿⣼⣾⣷⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣷⣤⣿⢡⡤⠖⠋⠁⠀⢀⣠⣶⣿⣿⠟⠉⠀⣰⡾⠁ ⠀⠠⣀⠀⠀⠀⠀⠙⢟⠿⣿⣧⡉⠻⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠞⠉⠀⠀⣀⣤⡾⠿⠋⣹⡿⠁⠀⣰⣿⠋⠀⠸ ⠀⠀⢀⠗⠀⠀⠀⠀⠈⠁⡼⠻⣿⣆⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡤⠞⠋⠘⠋⠀⢀⣼⡿⠁⠀⢠⣿⠃⠀⠀⠀ ⠀⠰⠃⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠙⢷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢯⠁⠉⠉⠓⠒⠘⢧⠀⠀⠘⡄⠀⠀⠀⣰⣧⠞⠉⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢀⣿⡏⠀⠀⠀⠀ ⠀⠃⠀⠀⠀⠀⢀⣠⣾⡥⠴⠒⠒⠚⠉⠉⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠙⣄⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⣸⠟⠀⠀⢠⡶⠚ ⢰⠀⠀⢀⠴⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⣿⣿⣿⣿⠏⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⣸⠏⠀⠀⠀⠀⢀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⡿⠁⢀ ⠀⠀⠈⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⣾⡏⣿⣿⣿⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠽⡶⠃⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⢀⡟ ⠀⠇⠀⠀⠀⠈⠙⠓⠲⠤⢤⣤⣄⣀⣀⠀⢰⠏⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢾⡉⠛⠷⣤⡀⠀⠀⣿⠷⢤⡀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠶⣤⡀⠀⣾⠉⠉⠛⠳⢤⡀⠘⣧⠀⣄⠈⠛⠦⣄⠸⣆⠀⠙⢦⡀⠀⢰⡏⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⡀⠀⠈⠙⢦⣿⡄⠀⣦⡀⠀⠙⠷⣽⣦⠘⢷⡄⠀⠉⢳⣿⡞⣦⠈⠹⣆⢸⡇⢀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠙⢦⡀⠀⠀⠙⣷⡀⠈⠻⣆⠀⠀⠈⠻⣆⠀⠹⣆⠀⠀⠙⢿⡌⣧⠀⠈⢿⣇⠘⡄⢹⡄⠀⣀⣴⠞⠛⢻⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣽⣶⣶⣶⣾⣷⣄⡀⠀⠀⠀⠀⠀⢈⣧⣠⣤⣄⣀⡀⠀⠁⠈⠃⠀⠀⢿⣌⡇⢀⣿⠞⣋⣥⢶⣆⣠⣴⣿⠁ ⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣻⣹⣤⣄⡀⠀⠉⠻⢿⣦⡀⢀⣤⡾⠿⢛⡋⠙⠛⠛⠿⣷⣦⡀⠀⠀⠀⠀⠘⣣⡾⢃⡾⢋⣴⠟⠋⣡⡾⠃⠀ ⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⣼⣿⣿⣿⣿⣿⣦⠀⠀⠈⢻⣷⣿⣫⣴⣾⣿⣿⣷⣦⡀⠀⠈⢿⣷⡀⠀⠀⠀⠈⠉⠀⠀⣾⢋⣀⣤⠾⠋⠀⠂⠀ ⠀⠸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⠁⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣷⠀⠀⠠⡄⠀⠀⠀⠛⢻⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⠙⣿⣟⡶⠶⠤⣤⣄⣀⣀⣀⣀⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣸⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⡿⠀⠀⠀⢻⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⡈⠳⣤⣄⡒⠂⠀⠀⣀⣀⠉⢿⣧⠀⠈⠻⠿⠿⠿⠛⠁⠀⠀⣰⣿⣿⠀⠈⠻⣿⣿⣿⣿⠿⠃⠀⠀⣴⣿⠇⠀⠀⠀⠘⣧⠀⠀⠠⡄⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠳⡄⠈⠻⢿⣛⠦⠀⢀⠈⠉⠈⠻⣷⣄⡀⠀⠀⠀⠀⢀⣠⣾⡿⠋⢻⣷⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠹⠀⠀⠀⢿⠀⢸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠉⠛⠦⣤⡉⠓⠂⠀⠉⠛⠿⢷⣶⣶⣶⡿⠛⠋⠀⠀⠀⠙⢿⣷⣦⣤⣤⣤⣶⣿⠿⠋⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠘⡇⢠⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠙⠒⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣠⣠⣠⣤⣄⣀⣀⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⠀⠀⠀⠀⠁⠀⣹⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠲⠶⣄⡀⠀⠀⠀⠀⢩⡶⠋⠀⢸⡀⠀⠀⠀⢹⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣾⠇⠀⢀⠀⣇⠀⠀⡀⠈⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣿⠀⡆⢸⠀⢻⡀⠀⢷⠀⢹⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⡇⢸⠀⠸⡇⠀⢸⡀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⠃⢸⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠙⠸⣿⠀⠀ ⠀⠀⠀⣤⣴⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄⣼⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣿⠀⠈⣷⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠹⣿⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠀⣸⡇⠀⠀⠀⠀⠀⢠⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⣿⠀⠀⢿⠀⠀⢸⠀⠀⡇⠀ ⠀⠀⠀⠀⢹⡏⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿⡇⠀⠀⠀⠀⠀⢿⣿⠍⠙⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⡿⠀⠀⢸⠀⠀⢸⡆⠀⡇⠀ ⠀⠀⠀⠀⠀⣇⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠇⡇⠀⠀⠀⠀⠀⠘⣿⣷⠂⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⣸⢣⡇⣾⣷⠆⠀⢸⠀⠀⢸⡇⠀⣷⠀ ⠀⠀⠀⠀⠀⢻⡆⠀⢻⡉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⡏⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⣤⡻⣦⡀⠀⠀⠀⠀⣰⡿⠞⢠⡿⢸⡇⠀⠀⠀⠀⠀⠃⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠇⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠻⢮⠛⠲⠶⠶⢚⣋⠀⢠⡿⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣼⠋⠈⣠⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠒⠒⠋⢁⣴⠟⠁⣿⠀⠁⠀⢠⠀⠀⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠰⠉⠛⠶⠶⠶⠶⢞⣋⠁⠀⣰⡿⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⠁⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣀⣀⠀⠘⢛⣉⣡⡼⠟⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⢸⠀⠀⢸⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀

⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠈⢷⠀⠰⡆⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⣟⠀⠀⠈⠀⠀⢹⡄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⠛⠀⣠⡞⠀⠀⢀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠻⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⡼⠃⢀⡴⠋⢀⣤⣾⣿⠟⣁⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿ ⣷⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⣀⠀⢼⡷⣄⠈⠳⣤⣀⠀⠀⠀⠀⣰⣿⣿⣟⣡⠴⠯⠴⠿⠿⢿⣿⣟⣋⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾ ⠛⢧⠀⠀⠀⢤⣻⣦⣀⠀⠀⠀⠈⡛⠒⠤⢤⣙⣻⣭⣿⡿⠿⠛⠛⠛⠲⠬⠭⠟⠛⠛⠛⠩⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⣿⡿⠿⠟⠛⠒⠒⠀⠀⠀⠈⠛⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣀⣀⣈⣉⣑⣲⡶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⡀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠐⢶⡄⣤⣀⣀⡀⠉⠙⠻⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣿⣧⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡟⣶⡽⣯⣭⣽⣿⣿⣿⣿⣿⣿ ⠷⠄⠀⠀⠀⠀⢀⡶⠚⠋⠉⣩⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠰⡆⠘⠇⠀⣇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣤⣤⠀⠀⠀⣴⡟⢁⣴⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣿⡀⠀⢠⣿⠿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⢠⣾⣿⣴⣿⣿⣷⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠉⢻⠃⠀⠈⡇⠀⠀⠉⠃⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢁⣴⣿⣭⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⣀⣤⣤⡶⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣵⠿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠷⠿⠿⢿⣶⣀⠀⠁⠀⠀⠀⢀⡼⠛⢉⣠⡤⢶⣶⣖⣒⣲⡭⢵⣶⠶⠀⠀⣸⢡⢷⠘⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠱⢟⣿⣿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣒⣚⡳⢦⣄⠀⠀⠀⠀⢀⡞⣤⣿⣿⣷⣾⠿⣟⣿⣶⠋⠁⠀⢰⡆⠀⠀⣷⣿⠸⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠸⢿⡇⢀⡀⠙⠻⣿⡇⠀⠀⠀⠀⢀⡠⢤⣤⣶⡿⢷⣾⣿⣿⣷⣆⠙⠾⠏⠀⠀⠀⠀⠀⠀⠘⠋⣽⡟⠁⠀⠻⠿⠟⠀⠀⣠⡿⡤⢀⣴⣿⡙⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⣧⢸⡟⢦⡀⠹⣿⠀⠀⠀⠀⢦⢦⡀⠁⠀⠀⠀⣿⣿⡟⠉⠙⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠹⠄⢀⣀⣀⣀⣠⣴⣶⡿⢳⠃⣼⢠⠉⣧⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠘⠇⣌⠿⣆⠸⣆⠀⢀⡀⠨⣻⡙⢦⡀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠂⠀⢀⣤⣤⣾⣧⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢚⡟⠛⣠⡏⡜⣼⡿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⡄⠀⡇⠀⢸⡇⠉⠀⠀⢳⡄⢳⠹⢦⡭⠷⠶⠖⠚⠉⠁⠀⠀⠀⢀⣴⡿⠟⠛⢹⠿⠿⠷⠦⠤⠤⠤⠄⠀⠀⠀⠈⠙⠋⠙⡿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⣇⠀⢿⣄⠈⢷⡀⢀⠀⠸⣿⣘⢛⣛⠧⠀⠀⠀⠀⠀⠠⠤⠤⠴⠛⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⢦⣀⠙⢾⣄⣴⡿⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠉⠛⠿⡜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡏⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⢹⡽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠁⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣴⣾⣷⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠀⠀⠰⣼⣟⠏⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣷⣿⣷⣄⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⣒⣻⠽⠛⠁⠀⠀⢀⣾⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠙⣯⠻⣟⠻⣷⣄⠀⠀⠀⠉⠉⠛⠛⠻⠯⠭⠥⠤⠤⠤⠴⠚⠋⠀⠀⠀⠀⠀⣠⣾⣯⠏⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⢹⡆⠈⠳⣍⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠆⠀⠀⠀⢀⣴⡟⣵⠇⠀⢸⣏⢳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⠳⣌⠙⢿⣦⡀⠀⠀⣀⡀⠉⠉⠙⠋⠉⠁⢀⣀⣠⣿⣿⠿⢏⣾⡿⠀⠀⢸⠈⢷⣝⢷⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⣿⢦⡙⠿⣿⣿⣿⣷⡀⢻⣇⠀⠀⠀⢸⡏⣸⠋⠀⣠⠟⢈⡇⠀⠀⢸⠀⠀⠙⢶⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⣤⣿⣿⣿⣿⣁⡠⠤⠖⠒⠚⠛⠲⢤⣤⣿⡆⠀⠀⠀⣿⡄⠙⠷⣬⣁⠀⠀⠙⢦⠻⡄⠀⠀⠸⠠⠇⣀⡼⠃⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠈⠛⠧⠀⠀⠀⠀⠀⠀⠀⣠ ⣠⣤⣼⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⣤⣿⣿⡀⠀⠀⠉⠳⠦⣤⣤⣤⣤⣤⣤⡴⠶⣻⠟⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠽⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠏⢻⣿⣧⠀⠀⠀⠀⠀⠈⢻⣟⠂⠈⠁⢠⣶⠋⠀⠀⠀⢀⣼⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⢸⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⡿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢹⣾⠀⠀⠀⢻⣿⡄⡀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠙⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⡶⠟⠁⣆⠀⡆⠈⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠋⠀⢀⣴⣾⣾⣤⣤⣀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠆⣰⠿⠋⠁⠀⠀⡈⠙⠳⠦⡇⠀⠀⠀⠀⠀⠀⠀ ⡠⢲⣏⠐⡀⠈⡅⣠⠖⢂⠀⡈⠈⠢⣀⠀⡅⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠿⠀⣇⠀⢋⣡⢤⠾⠀⠹⣤⣠⠄⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⠢⣀⠀⠀⠀⠀⠸⡀⢀⣀⠀⣀⠤⡖⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⢄⠐⠠⠔⠋⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠈⢩⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣴⡉⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⢛⣿⠋⠉⠙⠛⠿⠷⠶⢶⡶⠂⠀⠀ ⠀⠀⠀⠀⡾⠟⠋⠁⡀⠀⢸⣷⠀⠀⠀⠀⠠⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠀⢠⠳⢆⡆⠀⠀⠀⢸⣿⠀⢨⠭⠭⠶⠆⠀⠃⠸⡀⠀⠀ ⠀⠀⠀⡈⠀⠀⡇⠀⠈⠀⢸⣿⡄⢌⠀⠀⢠⠀⢸⠀⠃⣧⠀⠀ ⠀⠀⢠⠁⠆⠀⡇⠀⠀⠀⢸⣿⡇⠈⠢⠠⠚⠀⡈⢠⢰⢸⡀⠀ ⠀⠀⡆⠸⠀⠀⡇⠀⠀⠀⣾⣿⡇⢸⠀⠀⠀⠸⣷⠀⠆⠄⣧⠀ ⠀⢸⠃⠄⡐⣼⢹⠀⡄⠀⣿⣿⡇⠸⠀⠀⠀⢰⠈⡄⠸⣸⢇⠀ ⢀⠏⠀⠈⢰⠇⠘⡀⠀⠰⣿⡿⠁⢰⠀⠀⢠⠋⡄⡇⠀⠰⢸⠀ ⣾⠀⠀⠀⣍⠀⡰⠁⢂⢂⢨⠇⢠⠉⠄⠠⠁⡐⢉⢏⠠⠀⠘⡄ ⠙⢗⠀⠀⠁⠡⣘⣬⣤⡥⠤⢴⣦⣴⣶⣷⣶⠗⠁⠀⢀⠠⠘⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⠈⠉⠑⠒⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠔⠒⠒⣻⡟⠉⡉⠉⠉⠉⠉⢻⡉⠉⢻⣏⠉⠉⠉⠑⠒⠚⠫⢶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣾⠟⠁⠀⠀⠀⠀⢰⣿⠁⠀⡇⠀⠀⠀⠀⠈⣷⠀⠀⣟⣆⠀⠀⠀⠀⠀⠀⠀⢆⠈⠉⠙⠲⠦⣄⣀⠀⠀⠀⠈⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⣸⣻⠀⠀⠀⠀⢀⡇⢸⢻⠀⠀⣧⠀⠀⠀⠀⠀⢿⣇⠀⢸⡻⡄⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠘⡄⠀⠉⢓⣦⢤⣀⡀⠀⠈⠙⠢⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⡿⢹⠁⠀⠀⠀⡏⢸⠀⠀⠀⠀⢸⡆⡇⢸⠀⠀⣽⣿⠀⠀⠀⠀⠈⣿⡀⠀⢧⠹⡄⠀⠀⢆⠀⠀⠀⠘⣆⠀⠀⢠⠸⡄⠀⠈⣟⣆⠈⠉⠓⠲⠤⠤⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⡟⢀⣇⡏⢸⠃⠀⢸⠃⢸⡀⠒⠋⠉⣹⣷⡇⠀⢧⣠⡯⢿⣦⣤⣤⣄⣀⣸⡷⣄⠈⡦⠙⡦⠤⠈⣆⠀⠀⠀⢻⣆⠀⠀⢧⢹⡀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤ ⠀⠀⠀⢰⡇⣼⢸⠇⡿⠀⢀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣷⣶⣿⣤⣀⠀⠘⣿⡄⠀⠸⣇⢷⠀⠀⢿⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⣀⣀⣻⣿⠀⡏⢸⠀⣿⣴⣿⣿⠛⡍⠙⢿⣿⣷⣦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⢿⣿⣭⣛⠿⣿⣿⣶⣾⣳⡀⠀⣾⡌⡇⠀⢸⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡿⠃⢰⠃⢸⠀⣏⢙⡟⠃⣼⣧⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣼⣿⣿⣿⣷⡄⠈⠙⢿⣿⠧⢤⣹⣻⣷⠀⠈⣿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⣿⠋⠀⠀⢸⠀⢸⣶⢿⠋⠃⠀⣿⣿⣿⣿⣟⣿⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠘⠸⡆⠀⠀⠀⠀⠀⠀⢹⡇⠀⢿⢤⡀⠀⠀⠀⠀⠀ ⠽⢻⣶⠶⣾⠀⠈⠙⣸⠀⠀⠀⢻⡿⠉⠛⠛⠛⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⢿⣿⡿⠛⢿⣿⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⢷⡉⠓⠂⠀⠀⠀ ⣄⠈⠟⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠙⠦⣤⡤⠤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠦⢤⣀⣀⣀⣾⠋⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠈⣿⢧⠀⠀⠀⡆ ⣀⠀⠀⠀⡇⡀⠀⠀⡿⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠈⢻⡳⡀⠀⠀ ⠀⠀⠀⢀⡇⡀⠀⢠⠇⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⠀⠘ ⠀⠀⠀⠀⢻⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⣏⠉⣰⡟⢹⣟⠉⠉⠉⠻⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠰⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠘⢿⣾⡟⠀⡼⠛⠛⠛⠷⣶⣤⡘⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⡇⠀⠀⠈⢻⠀⡼⠃⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡆⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢹⡂⢀⠞⡫⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢹⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢷⡀⡆⠙⢦⡀⠀⠀⠀⠀⠈⣏⠀⠀⠀⢻⣾⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡰⠋⠘⡆⢸⠀⠀⠀⢰⡌⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠱⡀⠘⣿⢦⣀⠀⠀⠀⠹⣦⣤⣴⠞⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣴⠊⠱⣄⠀⡇⢸⡀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⡄⢱⠀⠸⣆⢻⣿⠶⣤⡤⠞⠁⠀⠀⢀⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⣠⠴⠚⠉⠈⣧⢀⡈⠳⣷⢸⣷⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀⢷⡞⢻⡘⢻⣠⠞⠀⠀⠠⠤⠖⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⢿⣖⣿⠉⠀⠀⠀⠀⠀⢿⢧⣉⠙⣿⢸⣿⠀⠀⢸⣿⡇⠀⣎⣤⣴⣾⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⢰⠛⣧⡞⠀⠈⣿⠞⠁⠀⠀⠀⠀⠀⠀⢀⡼⢏⠉⠉⠻⣏⠙⠉⠉⠉⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⣠⠏⠀⣸⠇⠈⠛⣿⣸⣽⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣦⣤ ⠀⠀⠀⠀⣀⣀⣤⡟⠀⣿⠃⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⣸⡀⠀⠀⠘⢣⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⢀⠔⠁⠀⡾⠁⠀⠀⠀⢸⣿⣾⡆⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⡴⠚⠉⠉⢸⡇⢠⣿⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⡇⠀⠀⠀⠀⠉⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⣿⠀⡷⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢰⠏⢠⠴⠖⠒⠀⣧⣸⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⡞⢠⠏⠀⠀⠀⠀⢹⡁⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠹⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿ ⡷⠋⠀⠀⠀⠀⣀⡤⢧⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⠀⠀⠈⠙⡶⣲⣄⣀⡠⠤⠤⣶⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⠞⠁⠀⠈⢷⣄⠘⣧⣄⣀⣀⠀⠀⣀⡴⠋⢀⣸⣿⣆⠀⠀⠀⣧⡏⠳⣄⣠⠔⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⡻⣇⢹⣯⣿⣿ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢻⣷⡷⠒⠦⠩⣭⣻⣯⠛⠒⠿⣅⣸⢿⣧⠀⠀⣿⣁⡴⠊⠓⢤⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡎⠹⡝⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡔⠓⠶⠶⠶⠽⣿⣿⠯⣬⣻⡾⢿⣷⣄⣿⠋⠀⠀⠀⠀⠉⢲⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⠸⣄⠀⠙⣆⠿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢹⣿⢶⠇⣰⢃⡾⢩⣝⣿⠦⣀⠀⠀⣀⡴⠉⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⣁⠘⢧⡘⣦⠘⠆⠀⡼⠰⠁⣨ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⣼⠏⣧⡰⠃⡜⢀⠏⠘⣿⡆⠈⠳⢞⡋⠀⠀⢸⣳⠂⠀⠀⠀⠐⠚⠛⢛⠋⢁⡀⣀⣠⠴⠛⠙⡇⠈⢧⡈⢣⠀⣰⣡⠃⠀⠹

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⠀⠀⠀⠀⣿⣿⣯⡙⣾⠏⣿⣿⣿⣻⠏⢩⣿⣽⠁⢸⣧⣿⠁⢀⣹⡏⢀⣨⣿⣮⣍⡒⣤⡇⢠⣼⡇⢈⣭⣶⣞⠁⣠⣤⣴⠟⠀⠀⠀⣹⡟⠉⠻⣿⡿⣿⣿⣿⡟⣛⣿⢿⣿⡋⠀ ⠀⠀⠀⣠⡟⢰⣿⡇⢹⣿⣿⣿⣏⣿⠀⣠⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⡏⠀⢀⣾⡿⠁⢹⣿⣿⣿⣙⢡⠟⠹⡇⠀ ⠀⢀⣴⣿⣧⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣾⣿⣿⣿⢻⢸⡛⣇⡟⠈ ⢀⣼⣿⣿⣿⣾⣼⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣼⣯⠟⠁⠀ ⣼⢻⣿⣿⣿⣿⡿⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⠞⠉⣿⣿⣧⠀⠀⠀ ⠁⡾⣼⢿⣿⣿⣿⣆⠀⠙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠵⡞⠁⢀⣴⣿⣿⣯⣇⠀⠀ ⡿⢣⡿⢰⡟⡿⣿⣿⣦⣄⡀⠉⠀⠈⠉⠿⠿⡛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⢯⣿⣿⡽⠿⠛⠋⠉⠁⠀⠀⠀⠁⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣧⠀⠀ ⠇⢸⡇⠨⡇⡇⣿⣿⢿⣿⣿⣿⣶⣶⣦⣾⣦⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣂⣀⣀⣀⣤⣤⣶⣶⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣇⠀ ⠀⢸⣿⣇⡇⣧⣿⡏⣘⣿⣿⣿⣿⣿⣷⣿⣿⣿⡋⠛⠛⠛⠛⠛⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠋⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠻⡄ ⡀⠸⠃⣿⣿⣧⣿⡇⣾⡏⣿⣿⣿⣿⣿⣿⡿⣿⣧⣄⣀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣧⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⣿⠃⠀⠙ ⡇⠀⣸⡟⢻⣾⣿⡇⣿⠇⣿⣿⣿⣿⣿⢻⡇⣿⠀⠈⠉⠛⢻⣞⢾⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⡷⣤⣤⣤⣤⣶⠶⣿⣿⢻⣿⡏⣿⣿⣿⣿⡇⢸⣿⣿⡿⣷⣿⠀⠀⠀ ⠃⢸⡿⠀⡟⠛⣿⣧⣿⠀⣿⣿⣿⣿⣿⢸⡇⣿⠀⠀⠀⠀⠀⠈⠳⣿⢹⢿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢻⡿⠈⣿⡇⣿⣿⣿⡏⡇⢸⣿⣿⣥⡈⣿⣇⠀⠀ ⡇⣼⡇⢸⠀⣀⣿⣿⣇⡀⣿⣿⣿⣿⣿⣸⡇⣟⠐⠀⠀⠀⠀⠀⠀⡿⠶⠀⣿⡿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣏⣀⣀⣀⣀⣀⣴⣾⠷⡶⣾⣇⣛⣿⣿⣿⡇⡎⣿⡏⠀⠙⣎⣿⡄⠀ ⡁⢻⣇⢹⡜⠁⠈⡿⣟⣿⣿⣿⣿⡛⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠇⢿⣧⠏⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠿⣿⣿⣿⣿⣧⡿⠁⠲⣄⡿⣿⠃⠀ ⡄⠈⢿⡄⢧⡀⠀⠇⢿⣿⣿⣿⣿⡇⠀⠸⣷⣄⠀⠀⡛⠻⠛⠁⣠⡟⠀⠀⠘⠛⠀⣿⡿⣿⣿⢸⡏⢹⠇⠈⢿⡈⠉⠛⠛⠛⠁⠀⢈⣿⡇⠀⣿⣿⣿⣿⢻⠇⠀⠀⢸⢇⡟⠀⠀ ⠁⠀⠈⢻⡈⠙⠢⣄⣈⣉⣿⡟⡇⠳⣄⠀⠈⢿⣟⣎⣍⡉⢁⣴⠟⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠁⠀⠀⠀⠈⠳⣤⣌⠈⠀⣠⣀⣿⠟⠀⢀⣿⠛⣻⠋⠀⠀⢀⡴⣫⠟⠁⠀⠀ ⠀⠀⠀⠀⠹⢶⡆⠈⠉⠉⢻⣷⠀⠀⠈⠳⢄⣀⡀⠁⠉⢀⣈⣀⡴⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⠈⠙⠓⠒⠛⠉⠀⣀⣴⠟⠉⢰⡿⠖⠒⠚⣩⣾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣄⣀⣀⣹⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⠴⠾⠛⠉⠀⠀⢠⡟⠀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⣚⡛⠋⠉⠩⣭⡍⢙⣄⣿⡿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⣿⡿⢖⣶⣶⣿⡿⢿⣼⠟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣿⡟⠃⢸⣿⡇⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⡽⢿⣿⠿⠟⣷⢺⣿⣴⣟⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢠⣅⣼⣿⠟⢁⣤⣾⣿⠁⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⠋⠉⠉⠉⠉⣻⣷⣤⣤⣤⣤⣤⣤⣤⠤⠴⣿⣮⣿⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣋⣀⣴⣾⣿⣿⠏⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⣐⣲⡤⢤⣄⣉⠉⠉⠁⠉⠉⠉⣿⣿⠙⢷⠄⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⣿⠃⣼⠟⠁⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣤⣀⡀⠙⢽⡲⢦⣀⠀⠀⠹⠿⢤⣼⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠶⠿⠿⠿⠟⠛⠿⠞⠃⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⣮⡳⢮⣙⣶⡆⠀⠀⠀⢿⣿⡟⠛⠻⡟⣷⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠻⣿⣦⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣸⣿⡽⣆⠀⢹⡋⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣟⣦⣈⢿⣄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣠⡆⣀⣀⣀⡉⠻⣿⣿⣶⣌⡛⣿⣆⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣦⡸⣿⣿⣿⣿⠀⠸⣟⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦⣄⡀⢙⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡤⢻⠀⡇⠀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⡞⢰⠃⠰⠗⠺⠤⢀⣀⣀⡤⠴⠒⠚⠉⠙⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠸⠧⠋⠀⠀⡀⢠⠀⠀⠈⠀⠀⢀⡤⢴⠟⣲⠃⠀ ⠀⠀⢀⡠⠖⢲⠞⠋⡹⠀⠀⠀⢀⣴⣧⡟⠀⠀⠀⠀⣀⠉⢦⡎⡰⠃⠀⠀ ⠀⢠⠏⠀⣴⣃⡴⠋⣀⡠⠤⠒⠉⠀⠋⣇⠀⠀⠀⠀⠉⠳⡀⠙⢧⠀⠀⠀ ⢠⣎⢀⡼⠉⠉⡹⠋⣿⣮⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢇⣀⣸⡆⠀⠀ ⠘⢟⠉⠀⠀⡼⠁⠀⠙⠋⣀⠀⠀⠀⢠⣴⣾⢧⡀⠀⠀⠀⠘⣅⠈⠉⢳⠀ ⠀⠀⠑⠒⠒⡇⠀⠀⢠⣆⣿⠙⠀⢠⡀⠉⠃⠀⠙⢦⡤⣤⠤⠞⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⣧⡀⠀⠀⠉⠉⠓⠒⠊⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⢹⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢦⣀⣀⡤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⣶⠈⠙⢶⠀⠤⠤⠴⠦⢶⡖⠉⠀⠀⢠⡈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠹⣀⡧⡞⠳⠤⠤⠤⠖⠋⠙⢆⢀⣶⣺⣷⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠃⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⡖⠀⢀⣶⠀⠀⡆⠀⠀⠀⢸⡀⠀⢀⡤⠒⠓⢲ ⠀⠀⠀⠀⠀⣠⡔⠋⠁⠘⣇⡀⣼⡼⠀⢀⣇⣤⠔⠊⢹⠧⠖⠋⠀⠀⢠⠞ ⠀⠀⠀⠀⠀⠛⠒⠒⠒⢺⣀⡽⠃⣏⡩⠟⠋⠉⠀⢠⠿⣀⣀⣀⠤⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⢠⣴⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠏⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣧⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣦⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⣠⣴⠶⠞⠛⠛⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣤⠖⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⣀⣤⣤⣤⣀⣠⣾⠿⠋⠉⠉⠁⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠘⣿⣷⣤⣾⠟⠛⠉⠙⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⠿⠿⠿⠿⠿⢷⣦⠀ ⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠈⢿⣿⡏⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽⠁ ⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⢀⣴⡾⢿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⡄⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣠⣶⢿⡯⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡴⠛⠉⠀⠘⣷⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢿⣷⠀⠀⢀⣾⣿⣏⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⡀⠀⠀⡟⠀⠀⠀⠈⣿⣤⣴⡿⠋⠈⢻⣦⡀⠀⠀⠀⢀⣾⢯⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⣷⠶⠖⠚⠉⠀⠀⢀⡇⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠙⠁⢀⣀⣠⣿⣟⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢻⡄⢀⣀⣠⣤⠴⢿⣇⢀⣀⣀⠀⠀⢸⡇⣀⣠⣴⡾⢻⡅⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⢿⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠘⣧⡀⠤⣤⡤⠴⠛⢻⡀⠀⠀⠀⠀⠈⣿⠟⠛⠛⢧⢠⣿⠿⠟⠛⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⣴⡾⣿⣄⣤⣶⠶⢶⣜⣧⣄⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⡟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣾⣤⣤⣾⣿⣧⣀⣀⣤⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⢠⣿⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⢿⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠷⠶⣶⣶⣦⣦⣦⣴⣶⣿⣿⠫⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⣀⣀⣀⡤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢹⣿⡇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢛⠕⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠻⣿⣿⣿⣷⣶⣶⣶⣶⡾⠿⢛⢙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣿⣶⣶⣶⣶⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣶⣶⣶⣾⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⣴⡌⣏⣱⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢣⣿⣿⣳⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⠁⠀⠀⠀⠈⠑⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠸⡿⣿⣿⣿⣿⣿⣿⣿⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⡿⠿⣷⠀⠀ ⠀⠁⢸⣿⠻⢿⣿⡿⡟⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠈⢻⣿⠅⠀⠈⠈⣧⠀ ⠀⠀⠘⡯⠁⠈⣿⣇⠁⠀⣴⣾⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⢿⡀⠀⠙⠀⣿⣇ ⠀⠀⠀⠉⠢⠀⣿⣿⣷⣆⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⢻⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠂⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣄⣀⣀⣀⣤⣶⡟⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠙⠿⠦⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠲⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣻⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠳⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⣠⠏⣠⠞⣆⠀⠀⢀⠀⠀⠀⡽⠉⠋⠉⠁⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠷⣄⡀⠀⠀⠀⠈⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⢀⡰⠖⠋⠀⠀⠀⣰⠷⠊⠁⠀⢻⠀⢀⡞⠳⠶⣀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠉⢹⡀⢀⣤⣤⡤⠞⠀⠀ ⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣷⠏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⠻⣯⡁⠀⣠⣤⢤⡄⠀⠀⠀⠀⠀⢳⡌⠉⠀⠀⠀⠀⠀ ⠰⠞⠁⠀⠀⣠⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣅⣹⣦⡴⠿⣟⢿⣷⡿⣥⣬⣇⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡺⡿⠀⠸⣧⣞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣺⣿⡿⠟⠛⠛⢧⢸⣾⡏⠉⠛⠛⠾⢭⣟⡓⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⢻⣇⠀⠀⠛⠃⠈⠛⣦⡀⠀⠀⠀⠀⠀⢠⣤⠤⢤⣀⣠⡖⣿⡽⠛⠋⠁⠀⠀⠀⠀⠀⢸⠀⠁⣧⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⡙⢷⣤⣤⣄⠀⠀ ⠀⠜⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⢹⣦⠀⠀⠀⠀⢸⣇⣘⣿⣿⠁⣿⠁⠀⠀⠀⠀⠀⢀⣀⣤⡤⢿⣷⣶⣿⢾⣶⣤⣄⣀⠀⠀⠀⠀⠈⡇⠘⣿⣯⣼⡇⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⡀⠀⠀⢩⣟⣫⣾⠀⢿⣀⣠⡤⠖⠛⠋⠉⠀⠀⢀⡼⣹⠟⡉⠉⠳⡑⡄⠈⠙⠓⠢⣤⣤⡇⠀⣿⠶⣥⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣤⣄⣼⣿⡏⢸⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⡀⢿⠀⢀⡿⣿⠀⠀⠀⠀⠀⠈⠙⠶⣼⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⢸⡇⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡛⢲⡶⣋⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡏⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣍⡙⢉⣡⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⢽⡏⣧⠀⠀⠀⣸⠇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣭⡭⠽⠧⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⣀⣶⡇⠘⠦⠶⠚⠁⠀⠀⡇⢀⣤⣶⡦⣤⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⣶⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⣠⣤⠾⠛⣻⡧⠴⠖⢋⣉⣁⡇⠀⠀⠀⠀⠀⠀⢠⣿⠟⣋⣷⡇⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠻⣻⣧⣹⣷⠀ ⠀⢀⣀⣴⡾⢉⣹⣀⡤⣿⡇⠀⠃⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣯⣿⠿⠗⠋⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣀⣀⣀⣩⣿⡿⠛⠀ ⢰⣿⠋⠀⣿⢹⢹⢃⣾⣿⡇⢿⠃⢿⠛⠛⣿⠀⠀⠀⠀⠀⣀⣀⣿⡠⠤⠤⠶⠖⠒⠒⠒⠦⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡖⠉⠉⠉⠀⠈⠛⡇⠀⠀ ⠀⣿⠀⠀⡟⠿⢸⠼⠿⢻⣷⣒⡒⡛⠉⠉⣿⣠⠤⠶⠒⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣵⣄⠀⠀⠀⠀⠀⠀⣰⣳⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⢴⣿⣴⣀⣧⠀⢸⠀⠀⢸⡏⠿⠷⠶⠦⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⢳⠀⠀⠀⠀⣰⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠨⠯⣩⣝⡿⠿⣝⣳⣶⡴⢧⣀⣀⡀⠐⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣧⣷⣀⣀⣠⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀ ⠀⠀⠈⠉⠒⠦⢄⡉⠛⠷⢶⣤⣉⠉⠑⠒⠾⣶⣶⣶⣶⡶⠶⢦⣼⡷⠶⠒⠒⡉⠉⠉⠉⠉⠉⢩⡭⠿⠭⠾⠿⠿⠿⠾⠿⢿⣯⡉⠀⠀⠀⠀⣀⡀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠉⠙⠻⢶⣤⣀⠀⣧⡸⣯⡽⣷⣾⣿⡇⠀⠀⠀⡯⠭⠭⣭⢭⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢹⣿⣿⣿⣿⣿⡉⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠉⠛⠷⣿⡉⣳⡇⣿⡇⢹⡇⠀⠀⠀⠉⠉⠉⠉⠉⠙⢻⡏⠉⠉⠹⡟⢻⢟⣟⠉⠙⢹⠈⠉⠉⠉⠉⠀⠀⢠⡇⠀ ⠀⠀⠰⣦⡦⠀⠀⠀⢀⣴⠖⠷⢤⠈⠙⠲⣄⡀⠈⠙⢿⣿⣿⡇⢸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣷⣼⣼⣿⠀⠐⣿⡃⠀⠀⢀⣀⣠⣤⢾⡇⠀ ⠀⠀⠀⠉⠀⢀⣴⡿⠙⢻⣤⡄⠈⣧⠀⠀⠈⠙⠶⡄⠀⠀⠙⢦⣿⡀⢻⠛⠛⠛⠓⠒⠒⠓⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⣾⠁⠀ ⠀⠀⠀⠀⢀⡿⢸⡇⠀⢸⣷⣽⣾⠛⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠙⠻⣄⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⠀⣿⡵⠾⢧⣤⣿⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⠀⢸⣯⣻⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠃⠈⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⣀⣀⣀⣘⣿⣿⣿⣯⣤⣤⣤⣴⢶⣶⣾⣯⣿⠄⠀⠀ ⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⢰⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⡿⠟⢿⣟⢿⣛⣛⡛⣻⣛⣿⣿⣋⡉⠭⠭⠭⠭⣷⡝⢿⡷⣆⣖⢦⠀ ⠀⠀⠀⠀⡟⠈⠀⠀⠀⣤⣼⡁⢸⡀⠀⣿⣤⣤⡀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢿⣭⣯⣿⡟⣧⡤⠤⠤⠤⠤⠴⠖⠒⠒⠚⠛⠛⠛⠛⢦⠙⢮⢯⡋⠀ ⠀⣶⣄⠀⣷⠀⠀⠀⠀⠀⢈⣧⡀⠳⣄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢸⡤⠤⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠈⠉⠉⢳⡈⢷⡻⠄ ⠀⠙⢿⣟⣻⣛⣶⣒⣢⣾⣯⣽⠟⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⡷⠶⠾⣿⣿⣿⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠈⢻⡀⠻⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⢰⡖⣚⣛⣻⡇⢿⡆⠀⠀⠀⠀⠈⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣛⣿⣛⣛⣻⡇⢸⡏⠉⢉⣉⣉⣉⣀⣀⣈⣉⠉⠉⠉⠉⠉⠉⠉⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣴⣉⣉⣉⣨⣽⡇⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀

⣶⣶⣶⣴⣤⣤⣤⣤⣟⣥⣼⣿⠿⣿⠏⡇⠀⣤⡌⢦⣌⢳⣴⠁⠀⠀⠀⢹⡴⠋⠉⠙⡏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⣟⣰⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡷⠞⢻⣿⠻⡿⡟⢿⣿⢻⣿⡿⣿⣿⣿⣿⣿⣿ ⣿⣻⣿⣻⣿⣿⣿⣿⡿⣇⠀⠉⣿⣿⣿⣿⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣷⣿⣾⣾⣿⣦⣭⣯⣼⣯⣽⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣤⣾⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣀⡿⠿⠿⠿⠟⠿⠿⢟⡿⠿⠿⣿⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣈⠙⠙⠻⢿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠒⠤⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣟⣷⣦⣄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⡀⠀⢀⣠⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⡟⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡏⢰⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣠⠾⠿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⠇⡀⠀⠀⠀⠀⠀⣷⢤⡀⠀⠀⠀⠀⠠⡀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢭⣿⣿⠿⠟⣻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⣴⠀⠀⠀⠀⠀⠘⡄⠙⠢⡀⠀⠀⠀⠱⡄⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⢰⠈⠣⡀⠀⠀⠀⠀⠱⡀⠀⠈⣑⠦⢄⣀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠈⠀⠀⠈⠲⢄⡀⠀⠀⠱⣤⠚⡁⣠⣾⣤⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠔⠊⠁⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⡇⠀⠀⢇⠀⢉⡉⠉⡢⠈⠉⠒⠒⠚⠺⣿⣿⣿⣿⡆⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠘⢆⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⠇⠀⠀⠈⢷⣶⣿⣿⣿⣇⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢣⡀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⡺⠀⠀⠀⡰⠉⢿⠸⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠇⠀⠘⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠀⢸⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠳⣼⣦⠀⡇⠀⠀⠉⡒⢒⣦⣤⣤⠀⠀⠀⣀⡀⣼⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣡⠃⠀⡇⠀⠀⠀⢘⡌⠻⣿⣿⡧⠔⢉⡴⢶⡿⠃⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⡗⠀⠠⣧⠀⣠⣴⣿⣿⡀⠻⣋⣀⠀⢀⣴⠊⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣶⣧⣤⣴⣿⣿⣿⣿⣿⣷⠀⠉⠁⠀⠀⢀⠏⢱⣶⣤⣤⣴⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠏⢻⣿⣿⠿⢹⣿ ⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣧⠿⢿⣿⠿⠛⠉⣀⣿⣿⡀⠀⠀⠀⡼⣤⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⡘⠀⢰⠈⠙⠷⣶⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⣟⣻⣿⡿⠖⠋⠀⠀⣰⠟⠁⠀⠀⠷⣀⣠⢴⣿⣿⣿⣿⣟⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⡴⠁⣠⠃⠀⠀⠀⠈⠙ ⣦⣈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣠⣴⢦⠀⠀⣿⠀⠀⠀⢀⡠⠟⣿⢦⡉⢻⣿⣿⣿⣷⠤⣄⡀⠀⠀⣀⣠⠴⣚⡴⠊⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⢀⠆⠀⣰⢿⠁⠀⠀⠀⠀⠀⠆⢣⠀⡆⢱⡀⠈⠻⣷⡺⠀⠀⢀⠂ ⠀⠀⠀⠀⠠⠎⠀⣠⡏⠈⢸⠀⠀⠀⠀⠀⠀⢸⠆⢰⡀⢧⠀⠑⢷⠵⡿⠐⠄⠀ ⠀⢀⠀⠀⢰⠄⡜⣸⠀⢶⢸⡇⡀⠀⠀⠀⡀⢼⢸⠘⠑⢌⢧⠸⣌⢲⡿⠀⡀⠠ ⠀⠀⠑⢄⢸⡰⠀⡟⢰⡀⢾⠺⡧⢀⠀⢂⡇⢆⣸⣧⣤⣈⢺⠆⢃⣧⢹⠒⠼⠀ ⠀⠀⠀⠀⢛⡇⡀⡁⠘⠀⣈⣧⣁⣹⣴⠾⠋⠐⣿⣟⡷⡈⡟⠀⠘⡇⢫⡇⠀⠂ ⠀⠀⠀⠀⠈⠃⡇⣧⢰⡼⢙⣿⣽⡏⠁⠀⠀⠀⠑⠭⠴⠅⢰⠀⠀⡇⠈⠀⠀⠀ ⠀⠀⠀⠀⢀⡆⡆⠀⣾⡕⠈⡫⠍⠃⠀⠀⠀⠀⠀⠀⠀⠀⡬⣶⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠰⡌⠇⣤⢹⡀⠀⠀⠀⣔⡪⠁⠀⠈⡇⠀⠈⡰⢻⡌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠁⠀⠸⡸⢟⠑⣄⠀⠀⠈⠢⢀⠠⠔⠀⡠⠐⠁⢻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠁⠀⠀⠀⠙⠀⠀⠀⠁⠒⢢⠤⠄⠀⠔⠊⣧⠀⠀⠘⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠤⠤⠤⣀⣀⣀⣠⡴⠓⢇⠀⠀⢀⠔⠁⢳⣤⡃⠀⠀⠀⠀⠀⠀ ⠠⠀⣀⡰⢓⣀⠠⢤⠄⢾⣿⠿⢿⡃⠀⠀⡹⡮⡁⠀⠀⢸⣿⣻⣿⣶⢢⠀⠀⠀ ⠫⡁⢀⠔⢁⢔⡡⠌⠡⢈⣿⢿⡛⣇⠀⢊⡰⣓⢌⣀⠀⡌⢸⡿⠿⠿⢚⣃⡤⡀ ⠀⢐⠁⢠⠃⢃⢾⠗⠫⡜⠉⣲⡇⠀⠈⠙⢣⣰⠖⠉⠈⠀⢸⢣⠋⢑⣇⠀⢩⡀ ⠀⠀⠩⠋⠑⡶⣴⣶⠴⢭⠖⠳⡧⠀⣀⠀⠀⠛⠀⠀⢀⠀⠀⠧⡝⠙⣟⠁⢹⡁

⠀⠀⠀⡠⠒⠉⢉⣑⠢⣄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠀⠀⠎⢦⠀⣨⠞⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⡀⠀⠀ ⠀⢸⠀⠀⠀⢂⠈⡟⢡⠎⣀⣤⠀⠀⡇⠀⠀⠀⠀⠀⡀⠀⡠⠊⢠⠞⢁⡽⡄⠀ ⠀⡇⠀⠀⠀⠀⣜⣤⡷⠉⠘⡠⠱⡴⠀⠀⠀⠀⠀⡏⠈⠳⠁⠀⠁⠠⠃⢀⠇⠀ ⠀⡇⠀⠀⠀⡸⢸⠁⠔⠒⣄⠃⢸⠜⠊⠉⠑⡄⠀⠈⡆⠀⡀⡀⠀⠀⠀⠎⠒⢢ ⠀⡼⠀⠀⠀⡗⠉⠀⠃⠀⢿⠄⠉⠀⠀⠀⠀⡸⠀⠀⣥⠀⠁⠡⠂⠀⢀⠤⠴⠊ ⢸⠀⠀⠀⢀⠑⠤⠤⢄⠀⢉⠀⢀⣀⣀⣀⣴⡇⠀⠘⣄⠀⠀⠀⢀⡤⠃⠀⠀⠀ ⠀⠣⢄⡰⠊⣑⠢⠄⠴⠁⢸⣿⣿⣿⣟⡛⡟⠀⢀⠎⠀⠑⠢⡤⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠊⠑⠀⣀⠀⠀⠈⢟⠁⠲⡇⣧⡔⠁⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠒⠒⠊⢣⠙⠦⡀⠀⠐⠂⡰⢻⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⡀⢸⣀⠦⢞⡖⠊⠹⠀⠸⡀⠀⠐⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠉⠉⠉⠐⠃⠀⢱⡀⡠⠔⢏⠱⡀⡇⠀⠀⠙⠦⣀⠀⡘⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⡯⠀⠠⠇⠈⡽⠋⠀⠀⠈⢢⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⡼⠂⠀⠈⠀⠈⣄⠀⢀⡤⠊⢉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⢸⣀⡠⢄⡀⠀⠀⠀⢉⠥⠓⠒⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠈⠉⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠊⢇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠸⡂⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢏⢆⠀⠑⠦⢀⣀⡀⠴⢻⠈⡇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⢕⡢⢤⣀⣀⣀⡠⡞⢠⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠔⠚⠁⡜⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⣁⣀⡀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠤⢄⡀⠉⠲⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠈⠑⢌⢢⠀⠈⢦⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣀⣇⢣⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢣⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡏⡆⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣴⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠳⢤⣀⢀⠀⣀⠀⣸⢦⡞⠀⠻⢦⣤⡴⣆⡠⣤⣤⠞⠁⢠⡇⢀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⣈⣧⠀⠈⠙⠙⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠛⢻⣤⠶⣧⣠⡴⣺⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣝⠲⠤⣄⣀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠡⣴⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⢀⣠⣤⣴⣦⠤⢠⣶⡞⠂⠿⢦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⠀⠀⠀⣠⣾⠟⠿⣿⣿⣷⡄⠀⣠⣶⠟⠉⠻⣿⣿⣷⡀⣿⣿⡏⠋⠙⢁⣾⣾⠃⠀⢲⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡷⠋⠀⢀⣶⣿⠃⠀⠀⠈⣿⣿⣏⣾⣿⡏⠀⠀⠀⢸⣷⡿⢡⣿⣿⣷⣶⡶⢸⣿⡏⠀⠀⠀⠉⢙⣷⡶⠶⠒⠀ ⠉⠉⠛⠻⠭⢍⣉⠉⠀⠀⠀⣿⣩⣿⠀⠀⠀⢠⣿⣿⠁⣿⣿⡇⠀⠀⠀⣼⣿⠃⢸⡿⡿⠉⠉⠁⢿⡛⠇⠀⠀⠠⣾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⡀⢻⣿⣿⣆⣀⣀⣾⡿⠁⠀⣿⣿⣾⣦⣤⣼⡿⠃⠀⣿⣿⠇⠀⠀⠸⣿⣿⠶⠀⠀⠠⣾⠛⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠼⣇⡀⠈⠻⠿⣿⠿⠻⠋⠀⠀⠀⠈⠛⠿⠟⠋⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣈⡓⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⠉⠉⠉⠛⠓⢦⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠴⠞⠛⢿⠀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⣀⠀⠀⠀⢳⡿⠟⠓⠪⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣼⠋⠈⡇⠀⢀⡴⠛⠏⠙⡆⣰⠟⠛⢢⡟⠓⢾⡏⠹⠏⠉⠛⢶⣌⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡰⠋⠀⠀⠀⠀⠛⠃⠀⠀⠀⠋⠀⠈⠳⠀⠀⠀⠀⠀⠈⠳⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠑⢌⢢⢔⠗⢁⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⢳⢔⠕⠁⣠⡏⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢜⠕⠁⠀⠀⠫⠯⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠚⣳⠁⠀⠀⡠⡄⠀⠀⠈⣖⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢺⣤⠞⢁⠔⢠⡎⣴⣮⢢⡈⠢⡘⠷⡤⠓⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⢊⣴⣇⠀⠔⢁⡔⠓⢻⡌⢡⡟⠛⠂⣄⠀⠀⠨⣦⡑⢤⣀⠀⠀ ⠀⡾⠫⠺⡿⡿⢋⠀⢰⣟⠣⣀⡬⠓⠚⢧⣀⠜⢹⡆⡀⡑⢌⣿⡖⠝⢿⠀ ⢰⣁⡀⠠⠿⡎⠠⠄⢁⠉⣿⣪⠃⠀⠀⠐⣽⢿⢭⡼⠠⡄⢱⡽⠄⢀⣈⡦ ⠀⠀⠨⣄⠎⠐⡀⠀⠀⢡⣧⢻⣄⠀⣀⣰⡏⣼⡔⠀⠀⠀⠆⠘⢤⢇⠀⠀ ⠀⠚⠒⠉⠉⠳⡱⠀⠀⠀⠹⢯⢩⠱⠮⣩⡜⡸⠀⠀⠀⣼⠞⠉⠉⠒⠚⠁ ⠀⠀⠀⠀⠀⠀⢳⢃⠀⠀⠀⢡⠹⡢⠖⡞⠰⠁⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣏⡄⠀⣄⢀⣷⡇⠸⣶⣅⠠⠄⢀⢳⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣞⣤⣴⡿⠋⠀⠀⠘⢿⣷⣤⣨⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠈⠉⠐⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠾⠶⠖⣢⡀⠀⢛⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⢒⠒⣄⣀⣈⠚⠀⢸⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢧⡈⣀⡏⠠⠤⣳⠀⠸⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠰⡟⢿⣵⡥⠙⣆⡴⠁⠀⠇⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢧⣄⡛⢻⠿⡋⣿⠀⠰⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣏⠀⠀⠉⠙⠻⠿⡿⠟⠀⠃⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⣖⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠃⢠⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠎⠀⠀⠀⠀ ⠀⠀⠀⢰⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠌⢠⠁⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⢠⠋⠀⢰⡖⠁⠀⠠⠀⠀⠀⡌⢠⠃⠀⡜⠀⠀⠀⠀⠀⠀ ⠀⢀⠻⡍⠀⠀⠀⠀⡀⠁⠀⢀⠌⠠⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⢰⠁⠀⠀⠀⡀⠀⠀⠠⠃⢔⠁⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀ ⢰⢀⠃⠀⠢⠠⠐⠀⠀⡠⠀⠈⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣼⠀⠀⠀⠀⠀⠀⠜⡀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠣⣤⠀⣀⢔⠡⣊⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣳⢦⡀⠀⠀⢠⣾⡿⠛⠒⠒⠒⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡖⠒⣤ ⠀⠀⠀⢀⡤⠴⣄⢠⡇⣸⠁⢀⡗⠀⠀⣾⣿⠀⠀⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⠀⠀⡇⠀⢸ ⠀⢠⠞⢉⡴⠒⢻⣿⠀⢹⡶⠟⠁⠀⢰⡏⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⣶⣾ ⢀⡏⠀⣸⣤⡴⠟⠉⣇⢸⡇⠀⠀⠀⠸⣧⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣷⣴⣼ ⢸⠀⣼⠁⠀⠀⠀⠀⢸⣾⣽⡇⠀⠀⠀⢿⣿⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿ ⠺⣭⡿⠁⠀⠀⠀⠀⠀⠈⠹⣽⡄⠀⠀⠈⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡏⣿ ⠀⠹⣟⣦⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢸⣿⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡿⠿⢿ ⠀⠀⠈⠑⣿⣦⡀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠘⣿⣷⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠈⠳⣽⡄⠀⡼⣷⠃⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣀⡤⠤⡖⢲⡦⠤⣀⠀⠀⠀⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠀⠀⢻⣷⣾⡟⠁⠀⠀⠀⠀⠀⣸⣿⠏⠀⢠⠞⠁⠀⢀⣿⣿⡇⠀⠈⠳⣄⠀⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠀⠀⡟⣿⠋⠀⠀⠀⢀⣀⣤⣶⣿⠏⠀⢠⠏⠀⢀⡴⠋⠁⠈⠙⢳⡄⠀⠘⡆⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠀⡼⣵⠃⠀⢀⡴⣺⠟⠛⠉⠁⢰⠀⠀⢼⠰⣶⣺⠀⠀⠀⠀⠀⠀⡓⣶⡦⣿⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⢸⢳⠃⠀⠀⠸⣿⣧⣄⣀⠀⠀⠸⠀⠀⠸⡆⠀⠘⢧⡀⠀⠀⠀⣰⠃⠀⢀⡏⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠻⣿⡄⠀⠀⠀⠀⠹⣆⠀⠀⠉⢑⣞⠉⠀⠀⣠⠞⠀⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠘⣾⣆⠀⠀⠀⠀⠀⢀⣴⡿⠃⢀⠀⠀⠀⠀⠈⠑⠦⠤⣈⣋⡠⠴⠚⠁⠀⠀⠀⠀⡇⠀⢸ ⠀⠀⠀⠀⠀⠘⠺⢽⣒⣒⣲⣾⠿⠋⠁⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣃⣀⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠛⠛⠿⣶⣄⠀⠀⠀⠀⣠⣴⡾⠿⠛⠿⣶⣄⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢡⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⢀⣾⡟⠁⠀⠀⠀⠀⠈⢻⣧⠀⣠⣾⠿⠛⠉⠀⠀⠉⠛⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⣀⢻⣷⣄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣾⠿⠛⠛⢿⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣶⠿⠟⠛⠛⠛⠛⠻⠿⠿⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀ ⠀⢀⣴⡿⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⣿⡏⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀ ⢸⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣶⣦⣄⡀⠀ ⠀⢿⣧⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⠀⠈⠻⣷⡄ ⠀⠈⢻⣷⣄⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿ ⠀⠀⠘⣿⣿⣿⣶⣶⣶⣾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿ ⠀⠀⠀⠘⠿⣿⣿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⣿⡏ ⠀⠀⠀⠀⢠⣿⢫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣦⣴⣿⣿⠇ ⠀⠀⠀⠀⣿⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⣿⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⠀⠙⢦⣀⠀⠀⠀⠀⣀⣠⠤⠺⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠉⠙⠛⠉⢀⣴⡆⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣫⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣧⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⣴⣾⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⡀⠀⠈⠙⠒⠶⠶⠚⠉⣰⣿⡿⣿⡄⠀⠉⠓⠶⠤⠤⠤⠤⠶⠚⢹⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠛⠋⠉⠀⠀⢻⣿⣦⣄⣀⣀⣀⣠⣴⣾⣿⣿⠃⠘⣿⣦⣄⡀⠀⠀⢀⣀⣠⣾⡄⠀⢣⡀⠀⠀⠀⠀⢠⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⢦⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣦⡀⠀⠑⢦⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢻⣿⣷⣦⡀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣤⣈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣠⣴⣾⣿⠿⠛⠉⠉⠹⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⠿⠾⣷⣤⣄⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⣀⠤⠤⠷⣀⡠⠤⠟⠛⠛⠛⠚⠿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠟⠛⠛⠒⠒⠒⠒⠒⠉⠉⣁⠀⠄⠀⠀⠐⠢⠤⠽⣛⣒⠦⢤⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢰⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣠⠤⠤⠔⠒⠠⠖⠋⠀⠀⠀⣈⣙⠒⢄⡀⠀⠀⠈⠉⠲⢤⡉⠑⠲⣖⠋⠁⠀⠀⠀⠀⠈⠠⡸ ⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡤⠒⠉⠉⣀⡀⠀⠀⠀⠀⠀⠠⣤⠒⠻⠏⠉⠑⠢⢝⢦⡀⠀⠀⠀⠀⠈⠑⠦⡈⠳⣄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⣠⠞⠁⡠⠚⠁⢀⣠⠶⠛⠉⢀⣴⡆⣖⣆⠀⠀⢿⢧⠀⠀⠀⠀⠀⣄⠳⡝⢆⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⡄⠀⠀⠀⠀⠁ ⠀⠀⠀⢀⡴⠁⣠⠊⠀⠀⣠⡟⠁⠀⢀⠔⠉⢸⡇⢹⢸⡀⠀⠘⣯⣳⠀⠀⠀⠀⠀⠑⢼⣆⠳⡀⠀⠀⠀⠀⠀⠀⠈⠳⡈⢦⠀⠠⠀⠀ ⣀⣀⡴⠋⢀⠞⠁⠀⠀⣰⡿⠀⣠⡴⠁⠀⠀⠸⡇⠸⣾⡇⠀⠀⠘⣷⡅⠀⠀⠀⠀⠀⠀⠻⡄⠹⡄⠀⠀⠀⠀⠀⠀⢀⠱⡌⢷⡆⠀⠀ ⢙⡟⠀⣠⠋⠀⠀⠀⣰⣻⠁⢠⡟⠁⠀⠀⠀⢰⡇⠀⣿⠇⠀⠀⠀⣿⢹⣦⡀⠀⠀⠀⠀⠀⠘⣆⢹⣄⠀⠀⠀⠀⠀⠀⢳⢱⡘⣇⠀⠀ ⠈⠀⣰⠃⠀⠀⠀⢠⢏⡏⠀⣼⠁⠀⠀⠀⣠⠏⣧⠀⢷⠇⠀⠀⠀⡟⠀⣯⠙⢦⡀⠀⠀⠀⠀⢸⣆⢿⢧⠀⠀⠀⠀⠀⠈⣧⢧⠸⡆⠀ ⠀⠰⠁⠀⠀⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⣰⠃⠀⣿⠀⣿⠀⠀⠀⠀⡇⠀⣿⡀⠀⠙⢦⡀⠀⠀⠀⣿⡾⡎⢧⠀⠀⠀⠀⠀⢹⣏⣆⢳⡞ ⠀⠂⠀⠀⠀⠀⠀⠀⠸⠀⣸⠁⠀⠀⢰⠃⠀⣰⣿⠀⣿⠰⠀⠀⣸⡇⠀⣿⢙⢦⡀⠀⠙⠀⠀⠀⠈⢻⣇⠘⣆⠀⠀⠀⠀⠘⣿⠸⡜⣷ ⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⢀⡟⠀⢠⡟⢸⡀⣇⠀⠀⢀⣿⡇⢠⡿⠀⠁⠙⠢⣄⠀⠀⠀⠀⠀⢿⡀⢹⡄⠀⠀⠀⠀⡏⡀⢇⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⠀⠀⡼⠀⢠⠟⠈⢈⡿⣿⠀⠀⠘⢸⣀⣾⡥⢄⣀⣀⣀⣀⣙⣢⣄⡑⣄⠸⣷⠀⢿⡄⠀⠀⠀⢿⢹⠸⡾ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⢰⠃⢠⠟⠀⡴⠟⣧⣿⠀⠀⠀⣸⠄⡟⠈⠉⠉⠀⠀⠀⠀⠀⠀⠑⢮⡻⣿⡄⠘⣿⠀⠀⠀⢸⢸⡄⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⣠⡏⣠⣋⡤⠊⠀⠀⣿⣿⡆⠀⢀⣿⣿⠃⠀⠤⠀⠀⠀⠀⣀⣀⣠⣀⣀⡘⢿⣇⠀⢿⡆⠀⠀⢨⢘⡇⠸ ⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡴⣿⣴⠋⠁⠀⠀⠀⠀⣿⠛⡇⠀⢸⢹⡟⠀⠀⠀⠀⣰⠗⣫⠟⠛⠉⠛⠛⠿⣿⣿⡀⢸⡇⠀⠀⠀⠘⢣⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣱⠃⠀⠀⠀⠀⠀⠀⣸⠀⣇⢀⡿⢸⡇⠀⠀⠀⠀⢫⣾⠃⡾⠛⡛⢦⠀⠀⠘⣿⡉⢹⣷⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⢀⣀⣀⣒⣒⡶⢶⡀⢻⣼⡇⠘⡇⠀⠀⠀⠐⢩⠿⠈⣷⣿⡿⠿⣇⠀⠀⠙⡇⠀⠻⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣠⣾⠟⠉⣠⣬⣉⠛⢷⡓⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣐⡡⢃⣴⠾⢫⣷⢰⡀⠀⠀⠀⡇⣼⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡿⠁⠀⢸⣏⣁⣹⣦⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⢸⢸⠁⠀⠀⠀⠃⢿⠀ ⠀⠀⠀⠀⢠⡄⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣟⣋⢹⡆⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡆⠀⠀⠀⢘⠘⠀ ⠀⣄⠀⠀⢸⣧⣆⠀⠀⢸⣿⡙⠢⣀⣀⡙⠲⠤⠚⢰⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⢀⡾⠀⠀ ⠀⢻⣇⠀⢸⣿⣿⠀⠀⠸⡍⣧⡀⠉⠉⠿⢋⡩⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⣿⡧⠀⠀⢸⠡⠀⠀ ⠀⣸⣿⡄⠀⡿⣿⡆⠀⠀⡇⢻⣷⡀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣒⣲⣤⡀⠀⠀⠀⠀⠀⠀⠐⠋⠈⣼⡷⠀⠀⣾⠀⡂⢸ ⡄⡟⠹⣿⠀⠟⣿⣷⠀⠀⠧⠘⣿⡿⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⢠⣿⠀⢸⡀ ⣧⡇⠀⢻⡆⠀⠸⣾⣧⠀⠀⠀⢻⡷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠟⠋⠁⠀⠙⣆⠀⠀⠀⠀⣴⢿⢹⡇⠀⣾⣿⠀⠀⣡ ⠣⢭⡳⡄⢳⡀⠀⢻⡟⣇⠀⠀⠈⣿⣮⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣼⣏⢸⡈⣷⢠⡇⢿⢠⣾⣄ ⠀⠈⠓⡹⡌⢷⡀⠸⣧⢹⣆⠀⠀⠹⣿⠈⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣀⣀⡤⠋⠀⣰⣿⣿⣿⠸⡇⢿⣸⣷⠸⣻⣿⡿ ⠀⠀⠀⠁⢹⡀⢳⡀⢻⡷⢿⣆⠀⠀⢻⡀⢁⠀⠉⢳⣦⣄⣀⠀⠀⠀⠑⠒⠒⠒⠋⠉⠁⠀⠀⣠⣾⣿⡿⢿⣻⡄⢿⢸⣿⡟⠀⣿⣭⡤ ⠀⠀⠀⠀⠀⣧⠈⢿⢌⣧⠀⠙⢦⠀⠈⣇⢸⠀⠀⠀⠃⢹⣿⣿⣷⣶⣤⣤⣀⣀⠀⠀⢀⣠⣾⣿⣿⠝⣧⡀⠀⠉⠛⢿⣿⢹⡀⣿⣿⣇ ⠀⠀⠀⠀⠀⠘⡆⠈⣏⢿⣆⠀⠀⠑⢄⢸⣾⡇⠀⣰⠖⠊⠉⢉⡙⣆⠉⠙⠻⣿⣿⣿⣿⣿⣿⠟⠉⠀⣿⣿⣆⠀⠀⠀⠈⠳⡱⡙⣿⣷

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠋⣶⡖⠒⠒⠤⢀⣀⠀⠀⠙⢄⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⣀⣴⣶⣆⠀⡼⠟⠀⠀⠀⠀⠀⠀⠉⠒⢤⡈⢆⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣶⣿⣦⣠⣤⣾⣿⣿⣿⣿⠙⣏⠛⠳⠦⣤⣀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⢋⣿⣿⣿⡿⠋⠉⠉⠛⠋⠉⠀⠈⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⣠⠞⠹⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⢄⣠⣗⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣆⣾⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢀⢣⠀⠻⣯⡁⠀⢀⣀⢀⣄⣶⣾⠟⠳⡄⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⣬⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢱⠀⠀⠀⠀⢱⠀⠀⠀⠈⡘⡆⠀⠹⡿⣳⣦⢩⣾⣿⡟⠁⠀⠀⠘⡄⠀⠀⠀ ⠀⢸⠀⠀⠀⢰⣿⠃⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢧⠀⢧⠀⠀⠀⠈⡶⠀⠀⠀⡇⢣⠀⠀⢻⣡⣼⣿⣿⡿⡄⠀⠀⠀⠀⠸⡀⠀⠘ ⠀⠀⢇⠀⢀⣿⠇⠀⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⣆⢸⡆⠀⢀⠜⢻⠈⡄⠀⢸⠘⡄⠀⠸⡆⠹⣷⡱⣁⢀⡀⠀⠀⣀⠀⠁⠀⡀ ⠀⠀⠈⢢⣸⣿⠀⠀⢀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢻⡄⣿⡔⠁⠀⠸⡆⣇⠀⠘⡄⡇⠀⠀⣿⡀⠈⠑⠚⠒⠋⡏⠁⠀⠀⠀⠀⣇ ⠀⠀⠀⣼⣿⣿⠀⠀⢸⣀⠀⠀⠀⠘⣧⠀⠀⠘⡀⠀⠀⢸⣷⢻⣧⠀⠀⠀⣧⢹⠀⢀⡗⠃⠀⠀⢸⣇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠑ ⠀⠀⣸⠉⢸⣿⠀⠀⢸⣿⡤⠤⠤⢤⡯⣆⠀⠀⢣⠀⠀⠈⣽⡞⡏⣆⣀⣤⣾⠾⣯⣥⣿⠃⠀⠀⠘⠾⡀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀ ⠀⠀⠸⠀⠘⣿⡄⠀⠈⣿⣇⠀⠀⠀⠧⠚⢦⠀⠈⢧⠀⠀⣇⣷⠿⢛⣩⣷⡾⠻⠿⢿⣿⡄⠀⠀⠀⡇⣇⠀⠀⠀⢰⠀⠉⠙⢄⠀⠀⠀ ⠀⠀⠆⠀⢀⣾⡇⠀⠀⢻⣿⣄⣀⣀⣸⣤⣬⣧⣀⡼⠗⠋⠁⠙⠒⢻⡟⠉⢣⣠⠀⠀⣝⡇⡄⠀⠀⠈⢹⡄⠀⠀⠸⡄⠀⡀⢸⠀⠀⠀ ⠠⠮⠤⠒⠁⢸⡇⠀⠀⢸⣿⠛⣿⣭⣽⣷⠾⢿⣿⡀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠉⣀⠴⠉⠇⢂⠀⠀⠀⢸⠘⡄⠀⠀⡇⢠⢇⡜⠠⠄⣀ ⠀⠀⠀⠀⠀⢸⢻⠀⠀⠈⡿⢿⡁⠙⣿⠛⢆⣰⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢰⢸⠀⠀⠀⢸⠀⠰⡀⣰⣤⣾⣿⡁⠀⠀⢰ ⠀⠀⠀⠀⠀⠸⡟⡆⠀⠀⢣⠀⢳⣄⠈⠦⣀⣉⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢸⡄⢠⠀⢸⠒⣒⣾⣿⣿⣿⣯⣿⣦⠀⠈ ⠀⠀⠀⠀⠀⠀⣧⢱⠀⠀⢸⠀⠸⣏⣦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠋⢨⣼⣧⣀⡧⢮⣉⠔⠙⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡌⠀⠀⠈⡇⠀⣿⡟⠳⢄⣀⣀⣀⣀⣀⣀⣀⡬⠥⠲⢾⡛⡵⠃⠀⠀⣀⠝⠉⠁⠀⠀⠘⢄⠀⠙⢿⣿⣿⣿⣿⣭⣿ ⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⢇⠀⢸⣿⣧⣇⣤⣼⣋⣼⣏⠀⠀⠑⠤⢄⣀⣿⣧⡤⠔⠚⠁⠀⠀⠀⠀⢀⡠⢼⡆⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⣄⢸⡶⠧⠴⣿⣿⣷⣿⣍⣷⣿⣢⡀⠀⠀⠀⣿⣯⣼⠂⠀⠀⠀⠀⣀⣴⡮⢿⣶⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠜⠉⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣾⣓⣤⡀⠀⣿⣿⣿⠃⣀⣠⣴⣾⢿⡿⣽⣿⣟⡺⢿⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠉⠻⢿⣿⣯⣽⣿⢿⣷⡧⣿⠿⣿⠿⢿⣯⡿⢿⣿⡽⠓⠚⢹⠃⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠟⠋⠙⠡⠁⡌⠡⢉⡉⠛⠳⣦⡄⠌⠠⢉⠉⡙⠛⠳⠿⣟⣦⢤⡀⠀⠀⣠⣴⣾⠿⠟⠛⠻⠴⣄ ⠀⠀⠀⠀⠀⠀⠀⣠⢶⡿⠚⠉⠀⠀⠀⠠⠁⢂⠡⣀⢁⠂⡄⢃⠂⠌⡉⠄⢃⠂⢌⠠⣁⠃⢆⡈⠙⠻⣾⣳⣾⠿⠉⠀⠀⢀⣠⣤⠶⠾ ⠀⠀⠀⠀⠀⢀⣼⡿⢋⠞⠀⠀⠀⣔⣒⣥⣭⣦⣵⣬⣬⣵⣬⣦⡥⠒⣐⠈⠄⠌⡀⠆⠙⠻⣦⣌⡡⢃⠠⠙⢿⣤⣧⣄⡐⠏⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⢁⠎⣰⣮⣶⣿⠿⢛⠩⢄⠡⢂⠴⠠⢌⠡⣾⡁⠰⣿⠀⢊⠐⠠⠈⠄⠡⢀⠙⢷⣦⡀⠡⠈⠻⣯⣛⣿⣎⢀⡀⢄⡀ ⠀⠀⠀⠀⠀⣿⡏⢰⠾⣻⣴⣟⣁⠊⣄⣳⠞⠋⠉⠉⠉⠸⡆⢻⣇⠐⣿⣆⠀⠌⠀⠡⠈⡐⠀⢂⠀⠹⣷⠀⠁⠀⠘⣿⡜⣿⡇⠈⠀⠀ ⠀⠀⠀⠀⠀⣿⣷⠈⣶⡿⢉⡻⠛⠛⠛⠋⠀⠀⢀⠀⠀⢀⣿⠄⡹⢷⣼⢻⣆⠀⠀⠐⠀⠀⠈⠀⠈⠀⢹⡇⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣼⡟⢡⡞⠁⠠⠀⠄⠠⠀⠂⢀⠠⠁⠈⠻⢿⣦⣤⣌⡂⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⢻⡅⠬⡑⠢⢄ ⠀⠀⠀⠀⠀⣀⣿⣿⣷⣿⠿⣿⣶⣅⠈⡄⢁⠂⠄⠂⡐⢀⠀⡀⠀⠉⠙⢿⡂⢿⡆⠀⠀⠀⠸⡄⠀⠀⢀⣿⡄⠀⠀⢀⣿⣯⣰⣁⣋⣤ ⠀⠀⠀⢀⣴⣿⡟⠁⢾⣀⠐⡢⢻⣿⠇⡐⠂⣌⠠⠡⠐⣀⢂⣀⣄⣂⣀⠀⢷⡘⣿⡀⠀⠀⠐⡇⠀⣘⢨⡗⡧⢀⣤⠿⠁⣿⡗⠋⠛⠒ ⠀⣠⣼⠟⢡⡿⢀⠃⠌⠻⣤⠙⢧⣔⠘⣦⡡⠘⣧⡁⢃⣼⡿⠟⠿⠻⢿⣷⣄⠣⢹⣧⠀⠀⡘⡄⢰⠃⣿⢘⣷⠞⠁⠀⢸⣗⡇⠀⠀⠀ ⣴⡿⠋⠀⣿⡇⠠⢈⠂⠅⠨⢁⠂⡉⢓⠈⠳⣦⠘⣷⡈⢳⣄⠌⡰⣀⠢⡻⠿⠀⠹⣿⠀⢀⡧⢡⠏⣼⠏⣸⡇⠀⢀⡴⣿⣿⡇⠀⠀⠀ ⡿⠁⠀⢸⣿⠀⠐⢀⠈⠠⠁⢂⣡⣾⣟⡛⠶⣌⠡⠘⣷⡀⠻⣦⡀⢿⡄⢳⡄⢊⠰⣿⠁⣼⠁⢎⡾⢡⢂⣿⣃⣔⣭⡞⣽⣾⠀⠀⠀⠀ ⡇⠀⢀⠾⣿⡀⠈⠀⡀⠄⢬⣾⡹⢲⠬⣝⡛⢻⣦⠁⠄⡁⢂⠙⣧⡘⣷⠈⣷⠠⢸⡿⢸⠃⣬⡿⠁⡏⣼⡟⠹⣿⠐⣰⣿⠋⠀⠀⠀⠀ ⡇⢠⢋⡐⣿⡇⠀⢀⠀⠀⣾⢣⠕⡫⢜⠢⣍⢣⠜⣇⠀⡀⠂⡐⢀⠡⢉⠡⠘⠓⣼⡏⢱⣸⡟⠁⣸⢱⡿⠁⢰⣿⣹⣏⠏⠀⠀⠀⠀⠀ ⢁⠒⣤⣿⣿⣿⣦⣀⠀⠀⢻⡜⢬⡑⢎⡱⢌⠖⣩⣟⠀⠀⠐⠠⠀⠂⠄⢂⠡⣸⣟⣰⡿⠋⠀⢠⢇⣿⠃⢀⣾⣟⣧⠞⠀⠀⠀⠀⠀⠀ ⡄⣽⢫⠏⠀⠹⣻⣯⡲⣄⠈⠳⣆⡙⢢⡑⢎⡜⢡⡞⠀⠀⠈⠀⠀⡁⠐⠀⣴⣿⠏⠁⠀⠀⣰⢏⣾⢃⣴⣿⣛⡜⠁⠀⠀⠀⠀⠀⠀⠀ ⣷⣣⠏⠀⠀⣴⣿⠟⣻⣷⣟⡲⢬⣙⡓⠮⠶⠼⠋⠀⠀⠂⢀⣈⣤⣤⣶⠿⠋⠁⠀⠀⣠⠞⣱⣾⣟⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⠃⠀⠀⣾⡿⢡⣾⣟⣯⢿⣿⣿⣦⡍⢫⠙⣉⢋⠥⣩⣾⠟⠋⠉⠀⠀⢀⣀⣠⠴⣋⣵⡿⢟⡛⠟⠿⢻⠿⣿⣖⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣿⣿⠰⣿⣞⣭⣟⣾⣳⣿⣿⣄⣃⣐⣬⡾⠋⢀⣠⣐⣮⣽⣭⣯⣶⡾⢟⡛⣍⢖⡣⢞⣩⠝⣦⠳⣌⠻⣿⠆⠀⠀⠀⠀⠀⠀ ⣴⣿⠿⣻⡹⢿⣷⡹⣾⣳⣾⣿⣿⣿⡿⣿⣿⣿⢟⣴⡿⠟⡛⣍⠳⣌⣦⡽⣶⢶⣧⢿⡼⣮⡽⣏⣾⣻⣼⣻⣼⢻⣿⡃⠀⠀⠀⠀⠀⠀ ⣿⡏⡽⣱⣭⣿⣿⣷⡽⣿⣟⣷⣻⢾⣿⣷⠟⣯⠏⣥⣶⣽⣾⡾⢿⢟⣟⣻⢛⣛⡛⠿⣿⣽⣻⣽⣷⣟⣾⣳⣿⣟⠏⠁⠀⠀⠀⠀⠀⠀ ⣿⡿⣽⣻⡿⡯⠒⢽⣿⣿⢿⣾⣽⡿⣋⣴⣾⣾⢿⣿⢿⡿⣽⣞⡹⣎⡞⣜⣫⠞⡽⢶⡄⠹⣿⣷⣻⣌⠻⣿⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠱⡻⣷⣟⠝⠀⡌⠠⠙⣯⣿⣿⣷⣾⣿⣿⣽⣾⡿⣩⢞⣿⣷⣻⣟⣿⣿⡿⢿⠿⣿⣯⣿⣦⢹⣷⡿⣿⢦⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠛⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⢤⡉⠲⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠓⢦⡀⠀⣰⠋⠁⠀⣴⠛⢦⣬⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢦⡀⠙⢾⣅⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠙⠳⣅⠈⠻⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⣷⣦⣄⠙⢲⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⢠⣤⠲⣦⣹⠟⠲⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢀⡀⢤⣭⢻⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢦⡀⠀⠀⢀⡀⣈⡛⢶⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠉⠳⣄⠘⠿⢮⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠰⢦⣝⣷⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⣇⡐⢦⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⡆⠰⣬⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠃⠀⠀⠀⠀⢀⣛⣳⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡆⠀⠀⢀⠈⡻⢦⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⢯⡀⠀⠐⣿⣼⣻⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡙⠳⣴⡿⣽⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡷⠉⢻⠑⢙⠱⣄⠂⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿ ⣿⣿⣿⠁⣎⠔⠀⠔⣅⢴⣈⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⣿⣿ ⣿⣟⠋⠄⠋⠴⠚⡋⠀⠀⠀⠀⠀⠀⠉⠲⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⢿ ⣿⡛⠧⢨⠋⡜⡄⣱⠄⠀⠀⠀⠀⠀⠀⠀⠈⠻⡍⢉⠔⠋⠉⠃⠤⡀⠀⢠⣾⣿ ⣿⣟⢂⠃⠈⢃⢠⠁⣠⠲⠒⠂⠀⠀⠀⠀⠀⠀⢹⡁⢕⡄⠔⢀⠀⠀⠀⢈⣺⣿ ⣿⣿⣼⠐⠢⢄⠀⠀⠀⠀⠎⢉⣀⣀⣠⠤⣤⠀⠀⣿⠟⢛⣛⣿⣿⣶⣶⣿⣷⡉ ⣿⣿⡿⠄⠒⠢⢦⠀⠀⠀⠻⠭⠅⠒⠛⢋⣡⢄⢤⠇⠸⠄⡐⡉⣿⣿⣿⣿⣿⠓ ⣿⣿⣿⣖⠒⡖⣶⣧⣄⣀⣀⠀⠀⠀⠉⠥⢀⠧⠁⠀⠀⣅⡜⣱⣿⣿⡏⠘⠉⠠ ⣿⣿⣿⣇⡩⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠆⠀⠚⢈⣾⣿⡿⡇⠀⠀⠀⠀ ⣿⣿⣿⣽⠊⠈⠂⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⢰⠀⠰⠋⠹⣿⣿⣇⣀⣀⣀⣤⣤ ⣿⣿⣿⣿⡆⠀⢴⣪⣥⣤⡶⠾⢿⠟⠁⠀⡠⠊⡠⠁⠀⠀⣙⣿⣿⣿⠿⠛⠛⠛ ⣿⣿⣿⣧⢿⣦⡀⠏⠀⠀⠀⡠⠂⢀⡤⠊⣠⡾⠀⠀⠀⠊⣉⣽⢋⣁⣤⣴⣶⡶ ⣿⣿⣿⣞⣿⣿⣷⣾⠀⢀⡎⡄⠖⢉⣴⣾⠿⠃⠀⣠⣴⣾⣿⣾⣿⣿⣿⣿⣶⣾ ⣿⣿⣇⡈⠙⠻⠿⣿⣷⣭⣁⣤⣾⠟⠋⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣉ ⣿⡟⣿⣿⣿⣶⣦⣤⣬⣭⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀ ⡇⡔⢒⣆⡤⠤⣔⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢠⢸ ⡇⠧⣾⠃⣠⠤⡴⠃⠁⠀⠀⠀⡤⠤⠤⠴⠲⢀⡠⠶⠤⢄⣀⣠⠤⠤⢰⡶⠦⠦⠄⢄⠀⠰⠤⡀⡀⠔⠢⢔⠺⢸ ⡇⡇⡻⣄⠙⠢⣄⣸⠉⣽⡼⠉⣿⠏⠙⢉⠉⠳⣼⠉⠙⣉⣷⠚⣉⡙⢮⡽⠉⢋⡉⠙⣋⡉⠳⣹⠞⣉⡉⢳⣡⢸ ⡇⡁⣙⡈⠓⡆⢸⡏⠀⡇⡇⠀⣿⠀⢸⢉⡇⠀⡏⠀⡾⢹⠃⢨⣉⣁⣨⡇⢀⣏⡇⢠⢿⠇⢰⡇⢠⣉⣉⣀⡏⢸ ⡇⡻⣅⠉⠋⢀⡼⢇⠀⠛⢁⡼⡏⠀⡈⠋⢀⡼⡇⢠⢳⡘⢆⠈⠛⢉⢿⠁⢸⢸⠀⢸⣸⠀⣸⢧⡈⠛⢉⡽⣸⢸ ⡇⡙⠺⠭⠭⠑⠉⠲⠭⠍⠭⢲⡇⢠⢯⠭⠑⠪⠩⠩⠄⠈⠢⠭⠭⠕⠊⠩⠭⠬⠩⠭⠌⠭⠱⠓⠩⠭⠭⠊⢸⢸ ⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠞⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⣴⠞⠉⠙⠛⠶⠋⠙⠳⠷⠶⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⡟⠃⠀⡀⠀⠀⢀⣄⣴⠋⠓⠚⠛⢿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠋⠙⠒⠒⠻⠂⠁⠀⠀⠀⠀⠀⢻⣿⡈⠹⡸⣿⣷⣿⣧⡀⠀⠀⠀⠀⠈⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠗⣿⣿⣿⣿⣿⣇⣠⣤⡀⠀⠀⣹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡀⢻⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣇⠀⢹⣿⣿⣿⡿⢿⣿⣷⡀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⡇⠘⣿⣿⡿⠀⠀⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⠋⢓⠀⣼⣿⣟⠃⢠⠛⣿⡟⠀⠀⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⠇⠀⠀⢸⣶⣿⣿⡇⠀⢸⣷⣿⣷⣤⡄⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⡏⠀⠀⢀⣿⣿⣿⣿⣧⠐⣿⣿⣽⣿⡿⢁⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⢀⣾⣯⣿⠏⣼⣧⣿⠉⢻⣁⣿⣷⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢀⡴⡠⠀⣼⣿⣿⡟⣰⣿⣿⠃⠀⣤⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣏⡼⡵⠁⡼⣵⣿⡟⣁⡟⢁⠏⠀⣼⢿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠟⣹⣎⣿⣟⣾⣿⣿⡿⢴⡿⢠⣶⣤⣴⡯⢿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⡠⠂⣼⣿⡿⢋⣾⣿⣿⣿⠗⡞⢁⣾⣿⣿⠟⣿⣾⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠋⣳⣿⣠⣾⣿⣿⡱⢩⣿⣿⢿⠏⠘⡝⣺⣿⣿⣯⣴⡿⠃⠀⠀⠀⠀⠀ ⠀⣀⣠⣤⣶⣾⠿⠛⠉⠁⡀⢞⣿⣿⣿⣿⠏⢉⣴⣿⠟⡰⠃⣠⣾⠿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⠈⠈⠉⠛⠫⠤⣀⣴⣗⢍⢤⣪⣴⣿⣿⡡⣶⣿⢟⣡⣊⣠⡾⣻⡯⠼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡤⣒⢾⣟⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢫⢎⠔⠁⢫⣉⡉⢛⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⣿⡁⢀⠔⠉⣄⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡀⣇⣸⣧⣀⡞⢹⣿⡟⠁⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡟⠁⠀⠈⠙⢶⣿⣇⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣟⢦⣤⣠⡼⢻⠛⠛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡌⣆⠏⠑⢺⣶⣾⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢾⣗⠦⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡾⢾⣏⣉⣻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⢾⣫⢏⣈⠟⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠿⠿⣯⣽⣟⡢⢄⡜⣉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⣀⠀⠀⠀ ⣉⠀⡔⢁⣿⡿⠛⠞⠒⠒⠟⠻⠿⣿⣻⡟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣼⣭⣿⣯⣉⡹⠒⠒⢸⠢⠤⣀⣿⣿⣿⡁⣘⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇

⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡆ ⠀⡆⠀⢙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡍⠀⡆ ⠀⡇⠀⢸⣾⣿⣷⣶⣶⣶⣶⣶⣴⣿⣿⣿⠃⠀⡇ ⢀⢧⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣠⡇ ⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⣿⣿⣿⡿⡏⢹⢹⣿⣿⡿⢻⠉⣿⣿⣿⣿⠀ ⠀⡼⢿⢿⣿⣧⣥⣤⡄⠻⣿⢁⣬⣤⣼⡿⠛⡿⢆ ⠀⠀⢨⢆⡻⡏⠘⠿⠁⠀⠈⠈⠿⠛⣿⣃⢾⠀⠀ ⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀ ⠀⠀⣴⣾⣿⣿⢫⡂⢄⣈⣁⡠⢲⢻⡻⢿⣷⣦⡀ ⠀⠀⡿⠉⠀⠈⣧⢣⠂⠇⢸⠀⣘⣯⠀⠀⠈⣿⠇ ⠀⠀⣿⡐⠒⢥⣽⣿⠈⢿⡿⠖⣼⣷⡒⠤⢐⣿⡆ ⠀⢠⣿⣷⣴⣿⡛⢿⣆⣸⣿⢠⡿⣻⣿⣶⣿⣿⡁ ⠀⢰⣿⣿⣿⣿⣿⣷⣽⣿⣿⣫⣾⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠙⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⡟⠉⠉⠉⠉⠙⠃⠀⠈⠙⢿⣿⣿⡈⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠚⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠹⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠈⢷⣦⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⢦⡀⠀⣦⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡏⣀⣀⣀⣼⣧⣤⣤⣤⣤⣤⣤⣤⣿⣶⣧⣤⣄⣀⣀⣀⣀⣀⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠻⢿⣿⣿⣿⡛⠋⠉⠉⠉⠉⠉⠉⢉⣽⣿⠟⣿⣯⡉⠉⠉⠉⠉⠉⢹⣿⠿⢤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⠒⠢⣄⠉⠁⠹⣿⣶⣤⣀⣠⣤⣴⣾⡿⠋⠁⠀⠘⢟⣿⣷⣦⣤⣤⣴⣿⡏⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⡋⠙⣆⠀⠀⠀⠙⠛⢿⠛⠛⠛⠉⠀⠀⠤⠀⢀⡠⠟⠈⠙⠛⠛⠛⠁⡇⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠙⠦⣈⣢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⡷⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⢳⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⢦⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡟⠻⢆⡀⠀⠠⠒⠋⠉⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢸⠁⠀⠀⠉⠑⡦⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⡗⠦⣄⣸⠀⠀⠀⠀⢀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣭⡉⠉⠉⣩⣼⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⡿⠟⠛⠛⠹⣿⠿⢿⣿⣿⡿⣻⣿⣍⣙⣿⣿⣿⣿⣆⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠛⠉⠀⠀⠀⠀⠀⠙⢦⣸⣿⣿⡿⣿⣿⣿⣹⡿⣿⣿⣿⣿⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠤⠔⢒⡒⠋⠁⠉⠉⠉⠉⠑⠒⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢀⣤⣶⣿⣇⠀⠀⠀⠀⠀⢀⡤⠚⢉⣠⣤⣌⣙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⣊⣀⡶⢛⠉⠉⠙⣿⣇⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⡏⠉⣟⠒⠛⠖⢹⣠⡘⣿⠀⣿⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣆⠀⠀⠀⠀⢣⣽⠀⡿⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⠔⠒⢲⠶⣋⠉⡏⠉⠉⠉⠉⢹⠙⢦⠀⠻⣷⣶⣶⠶⠋⢉⡽⠃⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠞⠁⠀⠬⢵⣷⠀⡀⠀⠀⢸⠀⠀⠙⠲⠧⣄⣤⣤⡖⠋⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠠⣴⣾⢿⣧⣿⡿⠽ ⣿⣿⣿⣿⣿⣿⡿⠃⢀⡴⠁⣾⠛⢻⣿⣟⣹⣤⠻⡄⠀⢸⣗⠒⠒⠒⠒⠺⡄⠀⠈⠓⠤⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⢷⣮⣽⣿⡿⣿ ⠏⠠⠖⠀⢈⡟⢁⡴⠁⡇⠀⠉⠁⠉⠙⠋⢠⣟⠀⠘⡄⢸⢿⣯⣃⠀⠀⠀⢳⢀⣴⢦⠀⢈⣵⣲⣄⡠⢤⡜⠉⠓⠀⠀⠈⢿⣿⣻⣇⣿ ⠀⠀⠀⠀⣼⡴⢻⠇⢰⠁⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠸⣼⠈⠻⠝⠻⢶⣤⣨⣿⠀⠈⢧⣸⠈⠀⣿⢲⠀⡟⠲⠤⣄⡀⠀⠈⢷⣶⣿⢳ ⠀⠀⠀⠀⠉⢀⡞⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄⡀⠉⣧⠀⠈⢾⣼⣇⠀⠀⣿⣿⣿⣶⣾⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣇⡾⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠞⠀⢠⢋⠇⠀⢀⡇⠘⢧⡀⣿⣿⣏⣽⣿⣶⣾⣿ ⠀⠀⠀⠀⠀⠘⠏⠀⢠⣸⣦⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠒⠋⠀⢠⣧⠎⠀⣠⠛⣦⣀⣀⣳⣿⣿⡟⢿⡁⢹⣿⣟ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⢄⡈⠑⠢⢄⡀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣠⣿⠀⡾⠙⣿⣿⡧⣾⣇⢸⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⣗⠀⢻⣷⡙⢦⡀⠀⠈⠲⡄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢣⢞⡽⠃⣶⠃⠀⠈⠿⣿⡋⢹⣷⣟⢹ ⠀⠀⠀⠀⠀⢀⡼⠃⠀⠘⣄⠀⠙⢿⣷⣿⣦⣤⣤⣤⣴⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡿⢋⡴⠁⠀⠀⠀⠀⠈⢷⣾⣿⣿⡿ ⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠈⠓⠤⣀⠀⠹⡏⠙⠛⢛⠻⣆⢹⡀⠀⠀⠀⠀⠐⢦⣀⡤⠤⢤⠖⣁⣴⠞⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷ ⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣾⡟⠉⠳⠘⡿⡇⢀⡠⠔⠚⢉⣉⣉⣻⣶⣶⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⡼⠋⣀⣴⡾⠟⠋⣉⠽⠛⠛⠛⠓⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣶⣶⣧⣾⠟⢉⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿ ⠐⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿

⠀⠀⠀⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣙⣿⣶⣄⡀⢻⣮⣿⣿⣿⣿⣿⣿⣥⣾⣷⣶⡀⠀⢹⣿⣿⣿ ⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣿⣿ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣏⣿⡇⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢿⠿⡝⣿⣿⣿⣿⣿⡿⢉⣽⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣿⢿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠙⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣴⣽⣿⣿⣿⣿⣅⣼⠀⢻⠙⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠘⡟⣿⣿⣿⣿⡿⣿⣿⡆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⠃⠀⠳⡘⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠹⣽⣿⣿⣿⣷⢻⣧⣹⠀⠀⣠⣾⡿⢿⣿⣯⡻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠁⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⡀⢹⣿⣿⣿⣿⣇⢻⣿⣧⡾⠋⠁⢀⣠⡿⢿⣿⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠁⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣀⡖⢛⢱⣴⢻⣿⣿⣿⣿⡌⢿⣿⡇⠀⣴⡟⠋⣠⠔⠻⣿⣶⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⡾⣾⣧⠀⠈⢿⣿⣿⣷⡾⢿⣿⣸⡏⠀⠀⣇⠘⣷⠊⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠄⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣋⣩⣌⣀⠀⠈⢿⣿⣿⣷⠈⢿⣿⡇⠀⠀⣨⣟⡥⣺⣿⠿⡛⢿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠻⣦⡈⢻⣿⣿⣧⡈⢿⣿⣴⡾⠟⠡⠚⠉⠀⠀⠈⠳⣝⣷⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⡞⠋⠉⢛⢿⣿⣆⣹⣿⣿⣷⡈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⢣⠐⢿⣙⡇⠘⢿⣿⣷⡹⣿⣆⠀⠀⠀⠀⠀⣀⣠⢴⣿⡏⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢣⣹⣿⣿⣿⣿⣿⣿⣷⣶⠾⠛⢉⠉⣻⡇⠀⠈⢿⣿⣷⡌⢿⣆⠀⠀⠀⠀⠀⢠⣾⡏⠡⠀⠀⠀⠀⠹⣿⣿⣿⡗⠘⣿⣿⣿⡟ ⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣃⡤⠀⠹⣿⣿⣆⢻⣆⠀⠀⠀⡰⠛⢻⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠈⣿⣿⣧ ⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠈⢹⣍⠀⠀⠀⠀⠈⠻⣿⣧⡻⣦⣠⠞⠀⠀⡘⠀⠀⠀