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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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⢸⡟⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⣀⠤⢊⠜⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠭⠄⠂⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡤⠤⠤⠶⣦⡀⠀⠀⠀⠀ ⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢯⡉⠉⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠀⠀⠰⣏⢹⡄⠀⠀⠀⢳⡀⠀⠀⠀⠹⣄⠀⠀ ⠀⠀⠀⣠⢿⡄⠀⠀⠀⠹⣏⠹⣄⡠⠎⠁⣻⣤⣤⣀⣀⡘⢦⠀ ⠀⢀⡴⡣⠃⢻⡀⠀⠀⣀⠼⣆⠹⣆⣠⠞⠋⠳⣄⠀⠀⠉⠉⠁ ⠀⠀⢻⡀⠀⠀⢻⡉⠁⠀⣀⣸⣧⠘⣇⣠⢔⡿⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⡿⣞⠋⠁⣀⡬⣧⡘⣿⢋⡀⠙⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⣸⠃⠹⣶⠽⠖⢋⠉⠋⠁⠀⢈⣱⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⢳⡟⠀⠀⠀⠀⡇⢈⠀⢀⡀⠐⡞⠃⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⢴⠁⠑⢤⠇⠀⢰⠲⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡞⠓⠦⡄⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠞⠋⠑⢀⣴⢾⡿⣟⣶⣶⣶⣾⣿⣿⡀⠀⣠⡀⠀⠀⠁⠖⠀ ⠀⢀⡴⠋⠢⣄⣴⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠁⠈⢢⡔⠁⠀⠀ ⠠⠞⠠⠀⣠⠟⠹⣿⣻⡿⠛⠁⠉⠙⠋⠀⠈⣿⣿⡗⠤⡀⠈⠀⠐⠄⠀ ⠀⠀⣠⡿⠃⡀⢀⢿⣟⠀⠀⢀⣀⣀⣠⣴⣶⣿⣿⡣⠂⠁⠠⡀⠀⠁⠀ ⠀⡴⠁⠀⠀⡴⠃⠈⢿⣿⣿⠿⣿⡿⠛⢿⣽⠿⠟⣟⠇⢀⠔⠁⠀⢀⠀ ⠈⠀⠀⣠⢎⠀⠀⢠⣯⣯⠙⢗⠞⢡⡄⠾⠌⠀⠀⣟⡴⠓⠀⠀⡀⠊⠂ ⠀⢀⠞⠁⠀⠑⣖⠁⠈⢢⣆⠀⠈⣠⣬⣯⣭⠀⢰⠯⡀⠀⣠⠞⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣢⠋⠈⢣⡀⠈⠟⠛⠋⠀⠘⣦⣀⡰⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢻⡝⡕⠈⠉⠀⠀⢠⡇⠐⠊⠉⠀⠀⠂⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⡀⢸⣇⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡾⣷⣟⣻⣾⢿⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⣛⣂⣑⣛⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣦ ⠸⣿⣿⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⣿⣿ ⠀⠈⠛⠛⠒⢶⣄⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣽⣛⣳⣶⣷⣶⡄⠀⠀⠀⠀⠀⣠⡶⠚⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⡿⠁⠘⢿⣿⣿⣿⣿⡟⠁⠘⣿⣿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⣀⣴⣾⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠈⢿⣷⣦⣄⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⢸⠛⠛⣻⣿⣿⡿⠟⠋⠀⠀⢀⣴⢿⣯⣾⣿⣿⢿⣦⡀⠀⠀⠙⠻⢿⣿⣿⡛⠛⠛⡟⠀ ⠀⠀⢸⣴⣿⡛⠉⠀⡇⠀⠀⠀⢠⣿⢳⣿⣿⣿⣿⣟⣿⡿⣿⡀⠀⠀⠀⢸⠀⠉⢻⣦⡈⣧⠀ ⠀⠀⣸⣿⣿⣇⠀⠀⡇⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⢸⠀⠀⣾⣿⣷⣿⠀ ⠀⠈⣹⡿⠁⠛⠀⠀⣷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠃⠀⠀⠀⡿⠀⠐⠃⠘⢿⡁⠀ ⠀⠀⢻⠀⠀⠀⠀⠀⣿⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣀⣀⣀⣀⡇⠀⠀⠀⠀⠐⣧⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⢿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⢸⣀⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⢨⣿⡿⣽⠏⢀⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⣴⣿⣟⣿⢏⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣤⣄⠀⠀⠀⠀⣿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣡⠤⠒⠂⠀⠀⠒⠒⠦⢬⡙⠻⣿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢿⡒⠚⠉⠉⠉⠉⠉⠉⠉⠑⠒⠚⠓⠦⢄⡀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⣒⣒⣒⣒⣒⠒⠛⠷⣄⠀⠀⣀⡠⠤⠤⠖⠒⠒⠲⠦⠤⠭⣷⡄⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣠⠴⠚⣩⠴⠚⠉⠁⠀⠀⠀⠉⠙⠓⠦⣬⣟⣉⡥⠤⠖⠒⣚⣛⣛⣛⣓⣶⣦⣤⣉⣆⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣴⠾⠧⠖⠚⠉⠀⠀⣀⢤⣴⡖⣿⣿⣿⣿⣆⠈⠉⢻⠷⠒⠚⠉⠉⣸⣿⠛⣿⣿⣿⣧⡉⠙⠻⣇ ⠀⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠓⠒⢲⣶⣒⠊⠉⠀⢸⣿⣶⣿⣿⠛⠛⣿⣧⠀⣸⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠻⣿⣇⠀⢀⡿ ⠀⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣈⠳⠤⣄⣼⣿⣿⣿⣿⣦⣤⣿⡿⠛⡻⠒⠤⠤⠤⠾⣿⣧⣿⣿⣿⡾⠿⢛⣿⠟⠀ ⡰⠉⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠮⠭⠍⣛⣛⣛⣉⡥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀ ⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠋⠁⠀⠀⠀⠙⠲⢤⣀⣀⣀⡤⠤⠴⣶⠋⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⠈⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣆⢀⣾⣿⣷⣶⣤⣤⣀⡀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠦⣼⠋⠁⣄⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣏⠀⠓⠧⠤⣀⣸⣆⠀⠀⠀⢻⡙⠛⠓⠾⠯⠭⢭⣉⣉⣛⣊⣛⣋⣉⣉⣉⡭⠥⠒⠋⠉⢀⣽⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠈⠙⠦⣄⣀⠀⠈⠉⠉⠓⠒⠲⠽⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢤⣴⠛⠁⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⡀⠀⠀⠈⠉⠓⠒⠒⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀ ⣘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⣲⠶⠒⠚⠉⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣶⣬⣉⡉⠓⠒⠒⠦⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢰⡖⢤⡀⠀⢀⣀⣀⣀⣀⡴⠒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣦⡈⢿⣿⣷⣿⣿⡟⢠⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣹⣻⠿⣆⠻⣿⣿⡿⢣⢿⠹⡞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠬⠳⣌⠛⢱⡏⠊⠀⣧⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⣻⣾⠗⠀⠠⣽⡖⢲⣦⠀⠀⣹⣄⣤⣵⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⢹⢹⣿⣶⣦⡄⣨⣷⣿⣧⣖⣿⣿⣿⢿⢀⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣠⡞⢸⣿⡏⠙⠛⠉⠀⠀⠀⠉⠈⣿⣿⢸⡘⣿⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⣿⡇⣼⣿⠀⠀⡀⠀⠀⠀⠀⣄⣀⢿⣿⠘⣷⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⢣⣿⣿⣓⣾⣷⡀⠀⠀⣸⣿⣧⣾⣿⡇⠸⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⢸⣿⢻⣿⣿⣿⣷⣄⣰⣿⠿⠿⠟⠉⢿⡀⢻⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣼⣿⠈⠁⠀⠁⠙⢿⡟⠈⠀⠀⠀⠀⠈⣧⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢠⡀⠀⠁⠀⣠⣴⣿⡀⠀⢸⡀⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡤⡀⠀⠙⢷⡐⣦⣾⣿⣦⣠⣦⣿⡿⢿⣧⡄⣸⡇⡟⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⡵⡀⠀⠀⠙⢿⡿⠋⠉⢿⣿⠋⢀⡀⠹⣧⣿⣿⡇⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⢷⡑⡀⠀⠀⢠⠇⢀⠀⢸⣧⣴⣿⣷⣄⣿⣦⣭⣍⣉⣛⡓⠦⢤⡀ ⣸⣍⠒⢄⡀⠀⢳⢱⠀⠀⢀⠀⢸⣄⣸⡿⢛⣩⣽⣿⣛⣩⣝⣛⡿⠿⢿⣷⣤⡇ ⠓⠮⡻⢦⣈⠓⠿⠧⠧⢴⣿⣦⡼⣿⣾⠿⢿⠻⣿⣿⣿⣿⡿⣿⣿⠉⠓⠾⠿⠃ ⠀⠀⠈⠳⢝⠿⠶⠶⠶⠿⠿⠿⢟⡼⠁⠀⠀⠑⢝⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⠿⠙⠻⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀ ⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠻⣿⣟⠛⢻⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀ ⠀⠀⠙⢿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣤⣶⣤⣤⣿⣿⣿⣿⣿⠟⠉⢹⣿⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀ ⠈⣿⣿⣟⠿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿ ⠀⠈⢿⣿⠀⠀⠀⣠⣴⡿⠛⢻⡟⠉⠀⠀ ⠀⠀⠈⣿⡄⠀⠘⠛⠻⣿⣶⣾⡇⠀⠀⠀ ⣠⣴⣾⣿⠧⠀⠀⠀⠀⠀⢸⢿⣷⣤⡀⠀ ⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠹⠝⠋⠀

⠀⠀⠀⠀⠀⢀⢴⣊⣉⠱⢲⡶⠖⢾⣃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡰⠅⠁⠁⠘⠓⠀⠀⠀⠀⠁⠋⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢃⠄⠀⠀⢀⠀⣠⢀⠀⣠⠀⠀⠀⠀⠘⢛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣧⠆⣀⡤⠛⠋⠉⠱⣾⣷⣿⣿⣯⣠⣆⣠⣿⡟⠉⠀⠀⠀⠀⠀ ⠀⠸⡡⢚⡛⠁⠀⢀⣤⣾⣿⣿⡿⠁⢒⣿⡻⠻⣗⠁⠀⠀⠀⠀⠀⠀ ⠀⣽⣧⠟⠁⣴⣶⣿⣿⣿⣻⣿⡇⠀⠀⠀⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀ ⠸⡍⡅⠀⣠⣿⣿⡿⠿⡟⠉⠉⣮⣖⡀⠀⠀⠀⠀⣀⡀⣀⣀⡤⠖⠀ ⠀⢇⡧⢾⣟⣿⠛⠀⣾⣤⣿⣻⡫⢵⢽⣫⣄⡪⣿⣥⣿⣿⣗⣒⠊⠁ ⠀⠀⢫⣸⣿⢋⣀⣄⣿⡿⣷⣿⢞⡚⠋⠭⢯⡿⠋⢼⣾⣿⠏⠑⠂⠀ ⠀⠀⠀⠘⠙⢜⡿⣿⣻⣯⣈⣙⡿⢺⡒⠚⣡⠄⠛⠛⣿⣶⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⢷⠽⠏⠋⠹⠗⠾⠿⠗⠛⠒⠈⠉⠉⠉⠁⠀⠀

⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡿⠋⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠿⢿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⢣⣶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣸⠃⠀⠈⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⢿⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⢸⣇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡌⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣷⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢈⣿⣿⣷⡘⢿⣤⠀⠀⠀⠠⣖⠚⠛⠛⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠙⠻⣷⣄⠙⢷⣤⡀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⣸⣿⠀⠀⠀⠈⠁⠀⠉⠻⠶⢦⣤⡾⠃⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀ ⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠈⠙⠿⢿⣿⣷⣄ ⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠉⣿⣿ ⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⡿ ⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⢿⣿⣷⡄⠀⢸⣿⡇⠀⠀⢀⣿⣿⠃ ⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠦⠀⠀⢀⣠⣶⣶⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠹⣿⣿⡄⠸⣿⡇⠀⢀⣾⣿⠁⠀ ⠀⠀⠈⣿⣿⣆⣀⣀⣀⣀⣀⠀⠠⠤⠶⠶⣶⣶⣤⣀⠀⠀⠀⢠⣾⡟⠉⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⢀⣠⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⢰⣿⣇⣠⣿⠟⠁⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⡿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠙⠓⠂⠀⢸⣿⠀⠀⠰⣦⠀⠀⠀⠹⣿⡆⠀⠀⢸⣿⡄⠀⠈⠙⣿⡄⠀⠀⠀⠀⠀⠀⠿⠋⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⣰⣿⡿⠋⠉⠀⠀⠀⠙⢿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠸⣿⣄⠀⠀⢿⣆⠀⠀⠀⠙⣿⡄⠀⠀⠹⣿⣦⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠛⠻⠿⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⠘⢿⣄⠀⠀⠀⠙⢷⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠉⠻⠿⣾⣿⣷⣤⣠⣤⣼⣿⡿⢿⣏⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⣤⣾⣿⣥⣀⡀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠀⠘⣿⣦⣤⣤⡶⠟⠀⠀⠀⠀⠀⠀⣠⣿⡿⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠘⢲⣾⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠐⢾⣿⣭⡀⠀⠀⢀⣠⣼⣷⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣾⡿⠟⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣆⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⢿⣯⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠙⠛⠻⠿⣿⡿⠿⠿⠿⠛⠛⠉⠉⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣶⣶⣶⡶⠾⠛⠻⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⣀⡀⠀⢀⣀⣠⣶⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠎⠀⠎⡜⠁⢠⠃⣰⠏⠀⠀⠀⠀⠹⣆⢸⢃⠸⡀⢡⠀⠀⠠⠀ ⡆⠀⠀⢠⠁⡘⠀⠸⡌⠀⢀⠇⣰⢋⠠⢄⠀⠀⠀⠀⢻⡀⡞⡀⢧⠈⡄⠀⠀⠆ ⣶⣼⠀⡜⠀⠇⠀⣶⠀⠀⡞⠐⡎⢃⠒⠸⠀⢀⠤⠂⠈⠇⠇⡇⢸⠀⡇⠀⠀⠀ ⠿⠟⠀⡇⠀⠀⠀⠏⡀⢸⡇⢰⠀⢆⠉⣡⠴⠥⠥⢖⢄⢸⣠⠀⢸⠀⠀⠀⠀⠀ ⠀⢸⠀⡇⠀⠀⠀⠀⡇⠀⡇⣇⠀⢠⣮⠇⢠⣦⠀⠀⠡⢸⠿⡄⡄⢀⠃⠀⠀⠀ ⡀⣼⡄⢃⠀⠀⢀⠀⢣⢀⣧⡿⠀⠀⠀⠢⣀⠀⢀⡠⠰⠋⠀⣇⡗⣸⠰⡀⠀⠀ ⢻⣿⠋⠌⠆⠸⡘⢸⢸⢴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠎⣧⢻⡧⣟⡶⣀ ⣿⣿⠀⠈⢼⣠⣇⡟⢏⡈⠲⠄⠀⠀⠀⣀⡀⠤⠐⠂⠁⣹⠊⠰⠃⣯⠔⢋⡔⠀ ⡉⠁⠀⠀⠈⠿⣼⡇⠀⢃⠈⠉⠉⠉⠀⠀⣀⣀⣠⣴⣶⡏⠀⠀⢰⡟⠒⡏⡀⣆ ⠟⠉⠀⠂⠀⠄⢈⣼⣄⠀⢻⣿⣿⠿⡫⠕⠒⠒⠒⢄⡝⠀⠀⣠⠟⠀⠀⡛⠐⣿ ⠀⠀⠀⢀⣤⣾⣀⣹⡿⢆⡚⠭⢻⣊⣀⣀⣀⡀⢤⠎⠀⢀⠔⠁⢀⡇⡌⠈⢢⠏ ⡀⠀⢠⣴⣿⠿⠿⠟⠚⠉⠱⡈⠠⠄⠀⠀⠤⠔⢁⡠⠚⠁⠀⢠⢺⡺⠀⣠⢛⣒ ⠝⠦⡉⠁⠀⠀⠀⠀⠀⢀⣀⣼⣺⣾⣿⣾⣾⡯⡁⠀⠀⠀⠠⠁⣗⣡⣚⣰⣿⣿

⠀⠀⠀⠀⠀⢉⡟⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠹⠏⠉⠉⠉⠙⠻⢍⠉⢯⡙⠯⣍⡉⠉⠉⣹⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⣀⠠⠀⠈⠉⠁⠠⠐⢄⠀⠁⠀⠙⢷⣄⠙⣆⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⠉⠀⠀⢀⠔⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡇⠀⢀⠀⠀⠀⠀⣅⠀⠱⠀⠀⢆⠀⠻⡷⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠟⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇⢸⡇⠀⠸⠀⠐⡆⠀⢹⠀⠀⡇⠀⢸⠐⡄⠹⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠄⠀⠀⢠⡟⠀⠀⢀⠀⠀⢀⣾⠀⡄⢠⡇⣼⡇⠀⠀⡇⠀⣷⠀⢸⠃⣤⡇⠀⢸⠀⠸⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⠀⣾⠋⠀⠀⡜⣹⢰⠁⡸⠃⣿⡇⠀⢠⡇⢀⣿⠀⣞⣼⣿⡀⠀⣸⠀⡄⢧⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⡜⠀⠀⠀⣼⢿⣿⡟⣤⡇⢰⣇⢻⠀⣼⠀⣼⠻⣶⣿⠏⢻⣇⣰⢿⡸⡇⡘⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣼⣿⡿⠛⣻⣟⣿⣟⡛⠚⠳⣿⣠⠃⡠⠛⠓⣒⣿⡟⠓⣾⠃⣷⠃⢸⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⣠⠞⠀⠀⣠⣎⠈⣧⠀⡾⠋⢻⣿⡿⠛⠀⠀⠘⠇⠀⠀⠟⢺⣿⡿⠙⣿⠟⣼⠏⠀⣾⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢀⣴⠏⠀⠀⡰⠁⢻⠀⠈⢣⡀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃⠰⢫⣾⣿⣞⣼⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣿⠀⠀⣠⠃⠀⠈⣇⠈⢷⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⣾⣿⣻⣿⣿⢿⣿⣿⣿⣿⣿⣷⣀⣤⣄⣀⣠⣴ ⠀⠀⠀⠸⣆⠀⢻⡀⠀⠀⠘⣆⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠁⠀⢀⣴⣎⣴⠟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠹⡿⡈⢷⡈⢆⠀⠘⣿⣽⣷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣼⣿⣯⢿⡆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠛⠛⢦⣳⣬⣳⡄⠹⣦⡁⠉⠃⠀⠀⠀⠀⠉⠋⠉⠀⠀⣠⣾⣿⠏⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠄⠀⠒⠒⠒⠧⣄⠀⢙⣷⣷⡿⣦⣵⣾⣂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠙⠺⣭⣿⡕⠀⠉⠉⠈⠳⣦⣄⣀⠀⢀⣠⡞⣿⣿⣿⣿⣿⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡽⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⡿⡟⣿⣯⡿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣰⢿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⠛⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠠⠤⣤⣤⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⣵⡄⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣀⢬⣬⣩⣥⡄⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⢇⠀⠻⡇⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢈⠈⣉⣩⡜⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠦⡤⠄⣈⠀⣀⡇⠀⠀⠀⠀⠀⢀⡤⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠁⠙⠈⠁⠀⠀⠀⠀⠀⣷⣤⣄⣀⣀⠀⠈⠢⡀⠀⢰⠃⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣⠀⠀⠈⠻⣿⣦⡙⣤⠏⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⠀⠈⠻⢿⣧⣤⣾⡿⠛⡆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⢰⣴⣿⡁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡎⠀⡀⠀⢘⣄⣴⣿⣿⡿⢻⣿⣿⣧⠈⣿⠟⠁⠀⠀⠀⢸⡏⢻⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⢀⣤⡖⠲⣏⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀ ⠀⠀⠘⣿⣧⡖⡤⠍⣾⠿⠉⠻⠧⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⡸⠻⣿⣿⠟⠉⠀⠀⠀⠀⠸⢄⣀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷ ⠀⠀⣴⠁⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠈⢧⠀⠇⠀⠀⢰⡟⡦⣦⠀⢠⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢿⣯⡛⢷⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠈⢣⡘⣶⠞⠁⠀⣠⣿⣧⣾⣆⣧⠀⠀⠀⠀⠀⠀⢀⣨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾ ⠀⠙⠻⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢿⣿⠀⠀⢠⣟⣿⡿⠃⠈⡽⣄⠀⣀⣀⣴⣟⡋⢹⣦⠀⠀⠀⠀⠀⢀⣶⡶⢾⣿⠀⠀⢻ ⠀⠀⠀⠀⠉⠣⢬⣿⣶⠀⠐⣄⠀⠀⢀⡱⠀⣼⢛⢀⢰⡏⠉⣁⡠⠴⢊⣡⣶⣾⠛⠉⢀⣙⡿⠦⠽⠷⣄⣀⡀⣤⠈⠉⠀⢰⡇⠀⠠⣼ ⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣙⠳⣤⣜⣧⡼⠻⣸⣾⣷⣷⠞⢃⠄⣰⣟⢿⣟⣹⠦⠖⠋⠁⠀⠀⠀⠀⠉⠑⠙⠧⠤⠤⠴⢿⢃⠀⢲⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠉⠙⠻⠥⠼⠧⠊⠙⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠐⢤⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⢁⣠⢶⡶⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⢶⢲⢺⡙⣤⣽⣿⡼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢩⣁⣦⠴⠶⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀�