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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠂⡄⠘⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢇⠘⠁⢏⣁⠁⢂⠀⠉⡱⠂⠀⠀⠀ ⢀⣤⣴⣲⡄⠤⠄⣀⡃⠀⠀⢁⡖⢆⡁⠀⡸⡸⡎⠀⠀⠀⠀⠀ ⣾⣾⣇⠠⠄⠀⠤⠄⣀⢱⣦⠀⠈⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀ ⠘⡇⠑⠢⢄⣀⣀⣀⣀⡽⡟⡇⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠈⠢⣀⠀⠀⠀⢰⡉⠁⠘⠣⠤⠤⠞⠁⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠀⢻⠳⢤⡀⠀⠀⠀⠀⣀⠄⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⠀⠀⠈⠑⠒⠒⠋⠀⠀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⢹⠀⠀⠀⠀⠀⠀⡴⠋⠉⠃⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⣖⡚⠛⢆⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠘⠳⢤⡀ ⠀⠀⠀⠀⠀⠙⢇⣀⢤⢗⡢⢄⣠⣎⠉⠉⠃⠀⠀⣠⢻⡄⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠋⠚⠉⠙⠦⢤⣤⣖⠪⠥⠊⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠋⠉⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣴⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⣾⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⠫⣱⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⠿⣿⣿⣷⣄⠀⠀⠀⣀⣀⣈⠀⡔⠀⢀⣴⠿⠋⠀⣴⠏⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠘⢷⣶⣿⡿⠟⣋⠉⠉⠉⠙⠓⠲⢿⣷⡤⣤⣼⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⣈⣹⣶⡞⢋⠁⠀⠀⠀⠀⠀⠀⢀⡀⣹⣿⣷⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⣷⡟⢿⣮⣣⡱⡶⣴⢳⡀⠀⣾⣿⡿⣿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢨⣿⣻⣶⣝⣿⣿⣯⣿⢻⡏⣷⠠⣿⣿⣿⣿⣿⡾⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⡟⢀⣿⣃⣘⣿⢻⣻⡟⣿⠟⠻⣿⣿⡆⠙⣿⠿⠋⢿⣇⢈⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢿⣶⣟⣉⣿⣷⣄⠙⠛⢀⣴⣿⠟⠀⣠⣈⣳⣄⢈⣩⣾⣿⡇⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠻⣷⣞⣓⠻⠿⢛⣶⣿⣿⠋⠀⠚⠳⣼⠟⠛⠿⣝⣲⡾⠑⠊⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠙⠙⠆⠈⠳⢤⣔⣺⣽⡟⠉⠀⠀⣠⠴⠚⣿⠲⣆⠀⣠⡿⡏⠓⠶⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢳⣤⠦⣒⣠⣠⠼⢛⡛⠃⠀⣰⣺⣃⣸⣻⣵⣤⣿⡎⠁⠀⢹⠀⠀⠀⠙⢦⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠙⠛⠛⠛⠛⠙⠉⠁⠀⠀⠧⠥⠏⠙⠋⠉⠸⠿⠃⠀⠀⠸⡇⠀⠀⠀⠀⠀⠉⠙⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢠⡔⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣼⣇⣶⡶⡶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡒⣿⣋⢉⣻⡟⠀⠀⠀⠀⣠⣼⠻⣿⣶⡶⡟⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢠⠞⣻⡿⣼⣷⣦⡽⣗⠀⠀ ⠀⠀⢀⣬⠟⠋⢽⡟⣽⡻⠟⣿⣷⣼⣿⠀⠀⣀⠀⣾⠟⢳⣾⠛⠀⠀⣷⡀⠘⠻⡆⠀⠈⣇⢀⠀⠀⠀⠀⠀⣠⣾⠏⠀⢰⠏⠀⣾⠃⠀⠈⢿⣆⣾⡇⠀ ⠀⢠⡾⡁⠀⠀⢀⠜⠷⢙⣓⠐⠿⣿⣿⣦⡀⠀⠙⠓⢦⠞⠋⠀⠀⠀⢹⣇⢄⢇⢻⠀⠀⠘⠪⣿⣠⣤⣴⣾⠛⠁⠀⢠⠏⢀⣼⠃⠀⠀⠀⣼⠿⠟⠃⠀ ⣰⡿⠂⠛⠒⢺⣿⣶⣶⠟⢛⣒⣶⣿⡿⣿⣟⣦⠀⡀⠘⢦⡀⠀⣠⢤⣈⣿⠈⠎⣎⡇⠀⢀⣀⢻⡏⠉⢁⣿⠀⠀⣰⣿⣠⡾⠋⡰⠲⣤⡾⠃⠀⠀⠀⠀ ⠿⠿⣯⣩⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣆⡙⢦⠐⢷⡄⢸⡀⣨⢿⡀⠘⡄⢹⠋⠀⠈⢻⠑⢦⡘⣿⠛⠀⠀⠈⠉⢻⣦⠧⣴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣉⣉⣻⣿⣿⣿⢿⣛⣿⣿⣏⣻⡹⢭⣉⣉⡟⡚⣛⡒⠛⠲⠭⠥⠞⠉⠙⠧⠼⠤⠤⠴⠾⠷⠾⠋⠛⠒⠒⠒⠒⠒⠒⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⠛⠻⠟⠿⠟⠳⠿⠁⠸⠟⢻⣧⢀⡿⠺⠟⠿⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠤⢤⣼⠏⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡴⠛⠛⠲⣤⡴⠒⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢼⠀⠀⠓⠀⣽⡘⠀⢀⡏⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠁⠀⠈⠳⠤⠤⢞⣻⡋⠉⢉⣠⡤⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠸⣥⣴⢷⡄⠈⠹⢦⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡷⠄⠀⠀⠙⢿⣘⣆⠀⠀⢹⡎⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠈⠁⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠶⠛⠛⠳⣄⠀⠀⠀⠀⢲⠀⠀⠀⠀⣠⣟⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢀⡿⠀⢠⠀⠀⠸⡇⠀⣠⡾⣻⠇⠀⠀⠀⣀⣀⣤⠤⠤⠤⠴⠦⠤⢤⣄⡀⠀ ⢰⡟⠁⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⣠⡾⠧⢤⡘⡇⠀⠀⠹⣟⠁⣿⣿⡆⠀⠀⣼⡛⠛⠓⠒⠒⠒⠒⠒⠒⠋⢽⣧⠀ ⠈⠳⠦⢤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣶⡶⢿⣦⣤⣤⣆⢰⣾⣿⣿⣿⠀⠀⡀⢺⣟⡿⠿⠟⢀⣼⣯⣅⣀⡀⠀⢀⣀⣀⣀⣀⡤⠾⠟⠂ ⠀⠀⠀⠀⠀⠀⠘⠋⠋⠙⠉⠈⠁⠁⠉⠀⠈⠉⠙⠃⠈⠉⠉⠁⠉⠙⠳⠚⠛⠚⠉⠀⠀⠀⠈⠙⠑⠋⠙⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣠⣤⡾⠿⠿⠿⠛⠛⠻⠿⠶⠶⣿⣥⣄⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀ ⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣆⠀⠀⠀⠀⠀⠀⢰⣶⣶⡀⠀⠀⠀⠀⠙⣷⣄⠀⠀ ⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡀⠀⠀⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀ ⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣼⠇⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⠀⠀⣨⣿⣷⣄⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠟⠁⠀⢹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢙⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⢉⣿⡿⠶⣶⣤⣤⣄⣀⣀⣠⣤⣤⣴⡶⠾⣿⣏⠁⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣸⣇⢠⣿⣿⣷⣤⣿⣀⣀⣀⣀⣉⣉⣀⣀⣸⣧⣼⣟⣻⣧⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀

⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⡙⢷⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡪⢫⠇⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⠀⠙⠦⣙⠲⡤⠔⠂⠉⠉⠁⠀⠀⠉⠓⠎⡡⠎⢀⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢆⠀⠀⡸⠋⠀⠤⠠⠤⠤⠠⠄⠀⠀⠀⠀⠈⢦⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⡼⠁⠀⢀⡤⠐⠒⠈⠐⠂⠤⠤⠤⠤⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡅⠀⠒⠉⠀⠉⣄⠀⠀⠀⡔⠈⠉⠐⠄⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠁⢀⠝⣛⡯⣍⡗⠛⢺⢉⢭⡥⢄⠈⠉⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⣀⣈⣑⣛⣓⣨⠇⠀⠸⣌⣚⣉⠉⢀⣀⢿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡁⠀⡇⠉⠉⠀⠀⠠⣤⠤⠤⠤⠴⡤⠀⠐⢊⣉⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢁⠠⠀⠈⠒⠤⠔⠋⠀⠀⠄⢀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠥⠀⠀⠀⡠⢂⡴⢲⢲⣄⣠⡐⠄⣀⠀⠈⢙⡯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠼⣿⢥⡀⢰⠁⣰⣯⣧⣼⣼⣀⣇⣿⡆⢸⢀⣠⣼⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣶⡎⠂⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⡎⢼⣏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⢴⠿⡯⢼⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⢩⣿⣿⡀⠀⠀⠀⠀⠀ ⠄⠒⠉⠉⠁⠀⠈⣤⡻⡫⡇⢹⣿⣿⣿⣿⣿⣿⣿⡇⢸⣼⡇⣸⠉⠒⠢⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣷⡇⠀⠻⣿⣿⣿⣿⣿⠟⠀⢸⠷⡮⠎⠀⠀⠀⠀⠉⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡦⠄⣈⣿⣛⡯⡁⣀⣠⣯⠆⠐⠒⠒⠠⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣴⠿⡷⣧⣗⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⢓⠄⡄⠂⠈⠑⡄⠀⠀⠀ ⡠⠒⠒⠀⠤⠔⡢⠉⢀⢀⠀⣆⣢⠁⠀⠀⠀⠷⡀⠀⠀ ⡇⠀⠀⠀⠀⠌⣀⠠⠤⠭⠩⠤⢀⡑⠠⠄⠊⠀⠈⢆⠀ ⢸⠀⢠⠔⠊⠁⣄⡀⠀⢀⣴⠖⠃⠀⠑⠠⡀⢀⡠⠬⠆ ⠘⡄⡏⠛⢶⢦⡎⣱⠀⠙⠚⠉⠀⠀⠀⠀⠈⣇⠠⠤⢼ ⠀⢹⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⡼ ⠀⠸⡀⠀⡆⠀⠀⡕⢄⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡰⠁ ⠀⠀⠳⣄⠈⠢⡜⠀⠀⠈⠐⠒⠁⢀⡠⠐⢁⠤⠊⠀⠀ ⠀⠀⠀⠀⠉⠲⡈⠥⠤⠤⠄⠐⣈⠥⠐⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⡿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠁⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠐⣆⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢏⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠘⣎⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⡞⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⣎⣿⣆⠀⣀⣠⣤⣤⣤⣶⣶⣶⠶⡶⢿⣶⠷⣶⣶⣦⣾⡏⢼⣁⣀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣈⡏⠿⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣨⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⢦⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠿⠿⢿⣿⣟⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⢴⣾⡿⠛⠛⠛⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢀⣼⣇⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⣠⣾⣿⣿⡇⠀⠀⣀⣠⣴⣦⡄⠘⣿⣦⠾⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀ ⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠙⣿⣿⣿⣿⠃⠀⠀⠘⢿⣿⡟⠁⠀⠘⢿⣶⣤⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣿⣦⣤⣤⡄ ⢀⣀⣤⣿⣧⣤⣤⠄⠀⠀⠀⠀⠀⠀⠐⣿⣿⣶⣿⣿⢿⡇⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣁⣸⣿⡉⠙⠃ ⠘⠛⠛⣿⠉⣩⢡⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠄⣿⡛⠁⠀⠀⠀⠀⠀⣿⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡿⠛⠿⠆ ⠀⣤⣼⣿⣷⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠘⠻⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀ ⠀⠙⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⢽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣥⣶⠶⠿⠛⠛⠿⢶⣦⡶⠾⠛⠛⠻⠷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⢠⣤⣴⠿⠛⠻⣷⣤⣄⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⢠⣿⠃⠀⠀⠀⣠⣦⣤⣤⣤⣶⠿⠁⠀⠀⠀⠀⠻⣷⣦⣤⣤⣴⣦⠀⠀⠀⠈⢿⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⠀⠀⠀⠀⣾⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣉⠀⠀⠀⠀⢙⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠁⠀⠀⠀⢘⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣄⣄⣀⣀⣀⣀⣠⣠⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⣀⣤⣀⣀⣀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⡿⠟⠛⢻⣟⠛⠛⠛⠛⠛⠛⠿⠿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠉⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⢿⡆⠀⠀⠀⠀⠀⣾⠀⠀⢰⡟⠀⠀⣰⡿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⣿⠁⢸⣧⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⠀⣴⡿⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⠀ ⠀⠀⢠⡏⠀⢸⡟⠀⠀⠀⣀⣀⣿⣀⣀⣸⡀⢰⡿⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠈⣿⠀⠀⠀⠀⣰⣿⠋⠀⠀⢹⡆ ⠀⠀⢸⡇⢀⣴⣿⡿⠿⠿⠿⠛⠛⠛⠻⠿⢿⣿⣤⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣻⠀⠀⠀⣰⡿⠁⠀⠀⠀⣸⡇ ⠀⠀⣼⠇⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣹⣀⣠⣾⡟⠁⠀⠀⠀⢠⣿⠀ ⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣿⠙⠛⠉⠀⠀⠀⠀⣠⣿⠃⠀ ⢀⣿⠃⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢸⣯⡀⠀⠀⠀⣀⣤⣾⠿⠃⠀⠀ ⢸⠇⠀⠿⡇⠀⠀⣤⢄⡀⢤⡄⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⣿⠻⢿⣶⡾⠿⠿⠛⠁⠀⠀⠀⠀ ⢸⡀⠀⠀⠀⠀⠀⢿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⢀⣼⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠃⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣍⣛⡛⠿⢿⣷⣶⣶⣿⣿⠿⠛⠋⢀⣀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⢿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠟⢉⣼⠟⠻⢿⣶⠀⠀⠀⠀⠀⢠⣶⡿⠿⠛⢿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣿⡿⠿⢿⣿⡿⠿⠟⠛⠉⠀⣠⣾⠏⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⣸⣿⣿⠿⠿⠿⠿⣿⡿⠋⠀⣠⣾⡿⠿⢿⣿⣿⡿⠿⢿⡿⠿⣷⣆⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣡⣴⣶⡿⠟⠋⠁⠀⠀⢀⣼⠟⠁⣠⣾⠟⠉⠀⠀⠀⠀⢻⣧⠀⠘⣿⠀⠈⠻⣷⣄⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⢻⡇⠀⠀⠈⠻⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠇⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣀⡀⠀⢀⣀⡀⠀⢀⣀⡠⠤⠤⠤⠄⣀⣀⠠⠴⠄⢒⡉⡅ ⠑⢄⡀⠀⠀⠀⠉⠁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠐⢶⢇⠔⠁ ⠀⠀⢣⡠⠀⣉⡀⠀⠀⠁⠀⠀⢀⣀⡀⠀⠀⢀⡔⠁⠀⠀ ⠀⠀⠀⠃⣾⣻⡎⠄⠀⠀⠀⠈⡸⣯⣿⠀⠀⠀⢣⠀⠀⠀ ⠀⠀⠘⡄⠈⠛⠉⡤⠒⣖⠀⠀⠈⢉⠁⠀⠀⠀⠐⡇⠀⠀ ⠀⠀⠀⠡⡀⢀⡀⠳⠜⠈⠀⠀⣐⠀⡤⢀⡀⠀⡴⠀⠀⠀ ⠀⠀⠀⠔⢉⠷⣸⠺⡖⣦⣀⠪⢶⠉⠢⢀⡰⠊⠂⠀⠀⠀ ⠀⠀⠀⠀⠡⠊⠀⠑⠏⠜⢜⠄⢀⠡⠐⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣈⣿⣷⣤⣤⣴⣴⣶⣦⣤⣤⣀⣀⣼⡿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⡾⠿⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⣶⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀ ⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀ ⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⣾⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀ ⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠘⣿⣿⣏⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⣀⣀⣴⣿⠟⠿⣷⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡛⠁⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏ ⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁ ⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀ ⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀ ⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠉⣻⣿⠷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⣿⣿⠉⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣰⣿⣿⣆⠀⣿⡟⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⢻⣿⡀⣰⣿⣿⣧⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣠⣠⣴⣤⣶⣿⣧⣼⣿⣷⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣷⣾⣿⣿⣿⣿⣤⣤⣄⣀⣀⣀⠀⠀ ⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀

⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⡿⢹⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠙⠷⣌⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣤⠞⢋⣴⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠈⠷⣄⡈⠙⠲⣤⣀⣤⠴⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠳⢶⡋⢀⣰⠟⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠈⠛⢷⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣅⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⡼⠁⠀⠀⠤⠤⠔⠒⠒⠒⠒⠒⠢⠤⣀⣀⣀⣀⡀⠀⠀⠀⠈⢷⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠟⠀⠀⠀⠀⣖⣲⣋⡉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠒⠒⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠞⠉⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠉⠑⢦⡀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢷⣄⣀⣀⡀⢀⣾⣀⣠⠤⠤⠤⠤⠥⠤⣤⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⢀⡴⢛⣛⡷⣤⣀⣿⠋⠉⠉⢹⡍⢀⣤⣤⠴⢶⣄⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠻⣄⣾⣿⣷⣤⠽⣿⠀⠀⠀⢸⡇⢯⣰⣿⠷⠶⠛⠂⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣆⣀⣀⣀⣠⣤⣤⣤⣤⣴⠿⠀⠀⠀⠀⠷⠴⠤⣤⣀⣀⣀⣀⣀⣀⡿⢸⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⢼⠌⣉⠉⠉⠉⠉⠉⠉⠉⢉⣁⠀⠀⠀⠀⠀⢀⣀⣠⡀⠈⣉⠩⠭⠛⠛⠓⢺⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠤⢼⡄⠠⠄⢀⣀⡀⠀⠀⠀⠛⢿⡍⠉⠉⠉⠉⢉⣡⡿⠁⠠⠤⠤⠤⠔⠒⠒⣿⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⢁⣀⡠⠀⠀⠙⠷⣤⣤⠾⠛⠉⠀⠀⠠⢄⡀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣾⠆⠒⠒⠒⠒⠉⠁⠀⣀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠑⠒⠤⢼⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡣⠖⠀⠀⠀⠀⠀⣠⠞⠁⣰⡿⠋⡏⠙⣷⣤⣤⣤⣌⠓⠦⢄⣀⠀⠀⠀⠀⢹⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣴⣂⡀⠀⠀⡴⠋⠁⣠⡾⢹⡃⠀⡇⠀⣿⠀⢸⢸⡿⣧⡀⠀⢸⠁⠀⠀⣔⣷⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⣿⣿⢛⡷⠀⠀⣇⠀⢰⣿⣿⣾⣿⣿⣿⣿⣿⣶⣾⣾⣿⣿⣿⠀⡟⠀⡦⣿⣻⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣠⢃⣆⠘⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠇⡼⠁⣼⣼⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣾⡵⢻⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⡇⢤⣴⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣿⠿⢿⡗⠒⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠀⢾⢿⣟⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠶⠶⠚⠛⠋⠉⠀⠀⣇⠀⣺⣿⣒⢺⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢈⣿⣟⠉⢸⡓⠦⣤⣄⡀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢫⠙⣆⠺⡆⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣏⢽⡯⠆⣠⣸⡇⠀⠀⠉⠛⢷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣣⡾⣆⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣧⢟⣤⡚⣱⠏⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⢀⡟⠉⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠞⣦⣤⠀⣀⣽⣭⡍⣹⢻⡀⢄⠀⠀⣠⣼⣧⠞⠀⠀⠉⠉⠙⠒⠦⢤⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣮⡼⢱⡺⢉⡼⣿⡿⡹⡎⣹⡀⢿⣷⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⣿⣧⣞⡃⡟⣧⢇⢷⣟⣍⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⢤⠏⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⠡⠙⡾⠉⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠊⠀⠙⠒⣺⡏⠉⣄⣸⠤⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠻⡳⡀⢹⠜⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠔⠢⡀⠀⠀⢀⠀⠀⢠⡖⠂⠒⠊⠀⠀⠀⠀⠀⠀ ⢀⠤⠀⠤⠄⠀⠀⠀⠸⠆⠀⠀⢀⣇⡀⡀⠘⣤⢴⣿⠀⢀⡤⠤⠐⠒⠒⠒⢦⠀ ⠘⠦⠤⠤⣤⣤⣤⡤⣴⠶⡦⡤⣍⣼⣿⡇⢀⢸⡾⠿⠂⣼⢇⣀⣀⣀⡀⠤⠼⠃ ⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠁⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡤⢦⠀⢈⣿⣌⣽⣷⣶⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣁⣴⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣶⠚⣩⡾⠋⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⠾⠋⠁⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡚⡝⣇⣀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣴⣶⣾⣻⠿⢯⣍⡀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣽⠃⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⣾⣿⡿⠛⢿⣿⣷⣦⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⢙⣳⣶⠶⣶⣤⣤⣄⣀⠀⠀⢻⡅⠀⢰⡇⠀⠀⢀⣤⡄⣀⣤⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣷⣤⣾⣿⡿⣿⣧⠀⠘⣧⠀⠀⠀⢀⣤⣾⣿⣿⣶⣦⣄⡈⠉⢻⣭⡉⠀⠀⢿⡀⢸⠃⠀⠀⢸⡏⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡟⡾⣿⣿⣿⣿⣿⣿⡿⠟⠀⢸⣿⠀⠀⣿⠀⢀⣴⣿⣿⣿⠟⠛⣿⣿⣿⣿⣦⡀⠙⣷⠀⠀⠘⣧⡟⠀⠀⠀⠘⣷⣜⣽⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⡇⠸⣿⣿⣇⠀⠀⠀⣀⣴⡿⠋⠀⣰⡏⢀⡾⠁⣿⣿⣿⣶⣴⣿⣿⠿⠁⠹⣿⡀⢸⣧⠀⠀⢹⠇⠀⠀⠀⠀⠸⡿⠋⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⢸⠃⠀⢷⠀⠈⠻⠿⠿⠿⠛⠋⠉⠀⠀⣰⡟⠁⣼⠇⠘⣿⣿⡿⠛⠿⠛⠁⠀⠀⣰⣿⠁⠀⣿⡄⠀⢸⡀⠀⠀⠀⠀⣀⣁⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⢦⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠋⠀⠀⢹⡇⠀⢻⣿⣿⣄⣀⣀⣀⣤⣾⡿⠃⠀⠀⢹⡇⠀⢸⡇⠀⠀⢠⠞⠋⣉⡽⠃⠀⠀⠀ ⠀⢀⣀⣠⠤⣼⣄⠙⠒⠛⠛⠶⣤⡤⢤⠤⠴⠚⠋⠀⠀⠀⠀⠈⣷⡀⠀⠙⠿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⣾⡇⠀⢸⡇⠀⢰⡇⠀⢰⠋⠀⠀⠀⠀⠀ ⠈⠉⢁⡠⠔⢻⣇⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀⣸⠁⠀⠘⢧⠀⠈⢧⡀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠀⢿⡆⠀⠀⠀⠀⢠⠾⠃⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠙⢳⣦⣤⣀⣀⣤⣤⣤⡴⠞⠉⠀⣀⡤⢤⣿⣀⠀⠀⠈⠳⣄⠀⠱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢻⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠻⢧⣐⠊⠁⠀⣼⠇⠀⠀⠀⠀⠀⠙⣆⠀⠙⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠈⠓⠒⠒⠋⠳⢤⣀⠀⠀⢀⣼⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⣿⠿⣤⡀⠀⠀⠀⠀⠀⠘⢧⠀⠈⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢦⡀⠉⠳⠄⠀⠀⠀⠀⠈⡇⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠛⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠶⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠻⣯⣛⡿⠿⠿⣿⡛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⣿⠀⠀⠀⠘⣷⠒⠒⠓⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⢦⡤⠖⣯⣀⣀⣀⣤⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣸⡇⠀⠈⠉⠉⠁⠀⠈⠛⢷⣦⣤⣀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣶⣤⣀⠀⣿⡄⠀⠀⠀⠀⢀⡼⠁⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⣇⣀⣀⣴⠶⠋⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠉⠁⠀⠀⢀⣀⠤⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡾⢿⡟⠲⣄⡀⠀⠀⠀⣠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⠈⣷⠀⠈⠙⣦⣤⣞⣁⣠⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⠀⢀⡏⠀⠀⠀⠈⠀⠛⠛⠛⠛⠛⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠠⣲⣿⣄⠀⠀⠀⠀⠀⠀⢠⠞⠻⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⣠⡼⠡⡦⢈⡧⠀⠀⠀⠀⠀⠹⣤⣀⣤⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠈⠙⠲⠶⠚⠁⠀⠀⠘⣻⡤⠶⠶⠷⢦⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢭⣿⠁⣴⠞⠛⣷⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢰⡏⠁⠀⢠⡏⡏⠀⠀⢠⡆⠀⠀⣤⡤⣤⠀⣶⠀⠀ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇⠀⠀⢸⠀⡇⠀⠀⢸⡇⠀⠸⣏⠀⣸⡇⣿⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇⡞⠀⠀⠀⢸⠀⡇⠀⠀⠘⠿⠾⠆⠙⠿⠛⠀⠻⠶⠇ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣿⠀⣇⠀⠀⢀⡾⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣍⣛⣛⣭⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢷⠀⠀⠀⠀ ⠀⠀⢸⠌⠢⣙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⠀⢸⠀⠀⠀⠀ ⠀⠀⠸⡖⠀⠈⠻⡳⣄⣀⣀⣤⢶⣴⠤⠴⠶⠶⢶⠤⡴⣣⢎⡀⠤⡝⠀⠀⠀⠀ ⠀⠀⠀⢩⠄⠀⠀⠑⡌⠢⣀⣁⣀⣀⣀⡠⠤⠤⢰⣾⠞⢁⡀⠫⡽⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⡦⠂⣤⣤⣼⣦⣤⣁⣀⡀⠀⢰⡤⡴⠟⣿⣿⡟⢷⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⢶⡇⢸⣶⣷⣦⡉⢸⡗⠚⠋⢷⣡⣾⣿⣿⣿⣸⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⣧⣘⣿⣿⣿⣻⣾⡷⠀⠀⠾⠗⠒⠛⠋⠉⠁⣆⡠⠔⠚⠀⠀⠀ ⠀⠀⠀⠦⢰⣄⡀⣀⡀⠀⠀⢀⠰⣦⡤⢤⣾⠃⠠⣀⣠⠖⠉⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣰⣛⣆⣀⣉⣽⠶⣾⠀⠈⢻⢩⠇⠀⠀⡞⣭⡭⢭⣽⣁⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⠁⠀⣿⡤⠔⢺⣯⣤⣷⣶⣾⣾⣿⣿⣿⣿⡟⠀⣤⣿⡄⠈⠙⠀⠀⠀ ⠠⠞⠁⡇⠀⠘⢩⣷⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⣴⣿⠮⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⠀⠘⢿⣿⣵⠀⠘⢿⣿⣿⣿⣿⣿⡿⠁⠀⣿⡘⠂⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠣⡀⠈⣿⣿⠀⠀⢻⡿⣿⣿⣿⠃⠀⢶⣿⠃⠀⠀⣀⠈⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢆⢿⢻⣿⣆⢠⢙⠛⠛⢣⣀⣿⣟⠙⠀⡠⠊⠁⠀⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⡙⠻⡿⠿⠷⢖⢾⡟⠇⢁⠴⠋⠀⠀⠀⠀⠀⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣋⡁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡿⠋⠁⠀⠉⢳⡄⠀⠈⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡼⠁⠀⣰⣦⠀⠀⣧⣤⠴⠲⠤⣄⠉⠉⠛⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢷⡀⠀⠈⠁⠀⣰⡟⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠈⠳⣄⡀⠀⠀⣿⠐⢺⣿⡶⠀⠀⠀⢹⡀⢦⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⣴⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠇⣸⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣶⠟⣛⣿⡿⠷⠾⠛⠛⠛⠛⠛⠛⠛⠓⠶⢤⣄⡀⠀⠀⠀⢀⣤⠾⣧⡀⠙⠳⣤⣀⣀⣠⡴⠋⠰⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣶⡟⣧⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠈⠷⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣻⡟⣧⣘⡤⠖⠛⠉⠉⠉⠉⠉⠉⠙⠒⠶⣤⣀⠀⢸⡏⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⡇⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣔⠇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣇⠀⠀⠀⠉⠻⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣼⠟⢻⡏⠈⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⣭⡽⢯⣿⠀⠀⢻⣾⠇⠀⠀⠀⠀⠀⣀⣼⠗⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢶⣤⣤⣄⣀⣀⣤⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡏⠻⠿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠿⢦⣄⡀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠙⢿⠆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⢤⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⠀⠀⠈⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⠇⠀⠀⠀⠀⠙⣶⣤⡀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠾⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⢸⣷⣦⡀⠀⠀⠉⢻⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣠⣶⡿⣯⣍⡙⠶⣦⣀⣀⣀⣿⡋⣠⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣾⠃⢹⣧⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣄⡙⠶⣝⡻⢶⣤⣈⣭⣭⣿⣿⡇⢠⠆⠀⠀⠀⠀⠀⠀⣀⣠⣶⠟⠁⢀⣾⠇⠀⠀⠀⠀⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠈⠛⠃⠉⣿⠁⠀⠀⠉⠛⢿⣶⣤⣤⣤⣴⣾⣛⣋⣁⣠⣤⡾⠟⠁⠀⠀⠀⠀⢀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⠿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠶⣶⣶⣶⣶⣶⣶⣾⣿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀ ⠀⠀⠀⢸⡈⠓⢄⠀⠀⣠⠄⠒⠊⠉⠉⠉⠉⠉⠒⠢⠤⣀⠀⠀⣠⠔⠊⡽⠁⠀ ⠀⠀⠀⠀⢇⠀⠀⣩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⡀⠀⡜⠀⠀⠀ ⠀⠀⠀⠀⠸⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠃⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⠺⠽⠷⠂⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠀⡔⠭⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠈⢄⠀ ⠀⡘⠐⠒⠒⠒⠀⠀⠨⠂⢰⣶⡶⠀⠀⠀⠐⢉⡉⠤⠤⠤⠤⠀⠀⠀⠤⠀⠈⡆ ⠀⡇⠐⠈⡉⠄⠤⠤⠁⠀⠀⠀⠀⠀⠀⠈⠡⠀⣂⣒⠒⠂⠀⠐⠒⠠⠄⠀⠀⡇ ⠀⢳⠀⠈⠠⠂⠉⢀⣀⣤⠶⠶⠾⠶⠿⢶⣦⣅⠀⠀⠀⠉⠉⠀⠂⠄⠀⠀⠀⠇ ⠀⠈⣦⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠲⡀⠀ ⠀⠀⢀⡤⠒⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠘⢄ ⠔⠊⠁⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠙⣆⠀ ⠀⠀⠀⠀⡦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠸⡄ ⠀⠀⠀⠀⣧⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⢻⡄⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠙⣿⣧⣀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡴⠋⢀⠔⡀⠀⠀⠀⠀⠀⢰⡏ ⠀⠀⠀⠀⠀⢹⣆⠀⠐⢆⠘⢌⣻⣿⣿⣿⣿⠟⠋⠙⠻⣿⣿⣿⣦⣴⣧⡊⢀⠤⠂⠀⠀⠀⡞⡇ ⠀⠀⠀⠀⠀⠀⢻⠣⡄⠀⢷⣞⣿⣿⡿⠏⠋⠀⠀⠀⠀⠀⠀⢩⣿⣿⣷⣏⠳⣄⠀⠀⠀⡼⢰⠃ ⠀⠀⠀⠀⠀⠀⠘⡆⠘⠦⠋⠘⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢹⠿⢿⣆⠀⠀⡞⢀⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠂⢀⣀⣀⠀⠈⢳⠀⠀⠀⠀⠀⢀⡴⣶⣎⠙⣾⣉⣀⣀⡀⠀⠸⠀⢸⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⡀⣾⡟⣶⡾⠀⠀⠀⠀⢀⢼⣆⠻⣿⣆⡿⠁⠀⠀⠑⡄⠀⠀⢸⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⣉⠽⠋⠹⢁⣀⣀⠀⠀⠋⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢷⡀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡗⠲⣼⡇⠀⠀⢰⠋⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣣⣀⣘⡇⠀⠀⠘⢷⡀⡿⠛⠁⠀⠀⢀⡀⠤⠤⢀⡀⠀⠀⡀⠀⠀⠀⢸⠀⠀ ⠀⠀⠤⠒⠊⣉⠡⠼⣖⣺⣷⠄⠀⢀⣀⣹⣥⣀⠀⠀⠈⠉⠩⣹⡒⠤⣌⡤⠚⠁⠀⠀⠀⢸⡀⠀ ⠀⣀⠤⠒⠉⡀⠔⠊⢻⠀⠈⠓⢤⡽⠦⣀⣀⡴⠏⠑⠢⠔⠚⠁⠙⠢⡀⠉⠒⢄⡀⠀⠀⠘⡇⠀ ⠈⠀⢀⠴⠊⠀⣀⡠⠊⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠂⠀⢀⣷⠀ ⠀⠘⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡤⠚⠛⠛⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⢀⣀⢰⣄⣄⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣦⣴⡶⣶⠟⠿⠟⠟⢿⣿⣦⣆⣀⣀⣀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣶⡤⠹⣷⣦⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣿⣷⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣿⣧⣌⠻⣄⣽⣯⣤⣀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⣼⠏⣰⡿⢟⣩⣌⡉⢻⡆⢠⣶⡊⢉⣹⣗⣿⢿⣼⡿⠿⠛⠁⠘⢿⣿⣍⣛⣖⡂⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢄⠀⠀⠀⠀⣼⣯⠄⠸⣇⣿⣿⣽⠷⠊⠀⠺⠿⢿⡞⣻⠛⠁⠀⠀⢰⠀⠀⠀⠀⠀⠘⢿⣖⠚⣻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠈⠱⡀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡘⠀⡠⢤⣐⣒⣒⣚⣻⣗⢻⣿⣶⠂⠤⠤⠤⠀ ⠀⠀⠀⠀⢉⠶⡠⠛⣻⡿⠁⠀⣀⣤⣴⡶⠉⠁⠀⠀⠀⡔⠛⠲⣄⠀⠈⠀⠀⠙⠦⢧⣘⣒⠒⠤⢽⣿⣹⣟⠓⠒⠤⣄⡀ ⠀⠀⠀⣰⢃⣾⢃⣼⣿⣴⠶⢛⣿⣛⢉⡡⠆⠀⠀⠀⣼⠖⠒⠓⠚⢦⣄⠀⠀⠀⠈⠓⠶⢦⣍⣁⠒⢻⣤⣙⡗⠒⠠⢄⣀ ⠀⠀⠀⢿⣞⣷⡿⢟⣯⣴⡾⠛⣩⣷⠟⠉⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢍⣲⡿⣧⣙⡒⠀⠀⠀ ⠀⠀⠀⠸⢋⣿⣿⣿⣿⡥⣴⠟⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠳⣿⣯⣿⡦⡀⠀ ⠀⢀⡠⠒⣹⣿⣿⣿⡯⠊⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡂⠀⠀⠀⠀⠀⠙⢯⠁⠀⠀ ⠐⠉⠠⠊⣽⣟⣹⠋⠀⠴⠗⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀ ⠀⠀⠐⠁⠘⠈⠁⠀⠀⠀⠀⠉⠛⠿⠿⠶⠤⣀⣀⠀⢀⣰⣄⣤⣄⡀⣠⡤⠜⠛⠉⣁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣹⠇⡏⠋⢳⡀⠠⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡿⣿⣿⣍⠙⠛⠳⢦⣤⣤⣤⡤⠶⠶⠶⠚⠛⠚⠓⠒⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⠉⢿⣆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀⣠⣴⠶⠶⠿⣿⣶⣶⣄ ⣾⠇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣰⠟⠉⠉⣿ ⣿⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣿ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⣠⠖⠚⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣄⡀⠀⠀⠀⠀⠀⢠⡟ ⢸⣧⠀⠀⠀⠀⠀⣾⣥⣤⣤⣤⣤⣤⣤⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⢸⠇ ⠀⣿⡀⠀⠀⠀⠀⣷⠈⠛⠃⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⢻⣿⠒⠒⠒⠒⢚⡇⠀⠀⢀⣿⠀ ⠀⠸⣇⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⡴⠟⠀⠀⠰⢶⣾⣷⠖⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢸⣧⠀ ⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠋⠀⠀⠀⠀⢸⡿⠀ ⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⠀⠘⢿⣄⠀⠀⠐⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡙⠻⣦⣄⢀⣀⡆⠄⡠⠞⡱⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⣙⣿⠟⡀⠀⠈⣙⣶⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⡿⣽⣿⣾⣯⡤⣿⣿⡷⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⣵⣿⣝⣃⣼⢃⣜⣌⣳⡇⡀⠔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡓⠙⠤⣶⡟⢁⢄⡻⣄⡹⡗⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠙⠛⠛⠂⠀⠋⠛⠉⠛⠀⢁⠀⠈⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⠀⠀ ⠀⢠⠤⣴⣶⣎⣴⠁⢀⣴⡱⠶⡓⢄⠀⡀⠀⠀⢀⡴⢠⢺⠟⢶⢣⠀ ⣰⠅⢠⣚⡦⢙⣿⣄⠙⢒⠁⠀⢧⢎⡄⠙⡧⠴⠏⢠⢂⢎⡀⡜⠛⠀ ⠛⠻⢿⣿⣿⣿⠿⣿⠮⢢⠧⣣⡻⠴⣉⣈⣃⡮⠏⠀⠙⠶⠎⠀⠀⠀ ⠀⠉⠉⠋⠉⠈⠙⠘⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⡾⠿⣯⠓⠲⢤⡤⠤⠴⠒⠒⠒⠲⠦⠤⣄⡀⠀⠀⠀⢀⡀⠀⠀ ⢸⠃⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠚⠉⢉⡿⠻⡆ ⢸⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡇ ⢸⡆⠀⠀⠀⡠⠖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠀⠀⠀⢰⠃ ⠀⡇⠀⠀⢸⠳⠶⠒⠒⠚⡇⠀⠀⠀⠀⢰⠥⡤⠤⠤⢵⠀⠀⡼⠀ ⠀⢹⡀⠀⠀⠓⠤⠤⠤⠚⠀⠐⠶⠖⠀⠈⠦⣀⣀⣀⠜⠀⠀⡇⠀ ⠀⠀⢧⠀⠀⠀⢀⣀⣀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠈⢳⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠀⠙⢦⣄⠀⠀⠀⠀⠀⣀⡤⠴⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⢩⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⠳⣤⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣠⠴⠚⠉⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣰⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⠋⠀⢀⣀⣀⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠿⠴⠿⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠼⠿⣯⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀ ⠀⠀⠀⡴⠋⠒⠒⠒⠤⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⣸⠁⣴⠖⠒⠒⠒⠒⠤⠤⠄⣀⣙⠆⠀⣶⣲⡶⣲⠦⠀⠀⠀⢀⠤⠔⠒⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⣄⡀⠀⠀⠈⢳⠀ ⠀⢰⡇⠀⠀⢀⣀⡤⠤⠤⠒⠒⠤⢤⡄⠀⠀⠈⠋⡇⠛⠃⠀⠀⠀⠀⡤⠤⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢸⠀ ⠀⢸⡇⠀⠘⠁⠀⣀⡠⠤⠤⠤⠤⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠑⠒⠢⠤⡄⠀⠀⠀⢸⠀ ⠀⠀⣷⠀⠀⠐⠊⠀⣠⠴⠒⠊⠉⠉⠁⠀⢀⣠⣤⣤⣴⣶⣶⣶⣴⣤⣄⣀⠐⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⢹⡇⠀⠀⠠⠊⠀⠀⠀⢀⣀⡴⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠷⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠹⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠳⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠳⣦⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠴⠚⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠘⣦⠀ ⠀⠀⣀⡴⠞⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹ ⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⣀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠉⠉⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠛⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡽⠃⣀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡁⠀⠙⢦⣳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣠⠏⡰⠁⠀⠤⡾⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣏⠁⠀⠀⠙⣏⠳⣤⠤⠤⢶⠞⠿⠿⠓⠚⠛⠛⠛⠛⠻⣛⡶⣣⠞⠡⣀⡘⢲⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠤⠀⠀⠀⠈⢳⡘⠶⣄⣈⣁⣀⣀⣀⣀⡤⠶⠶⠔⣺⣿⠞⠁⣀⡀⠲⣬⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣆⡤⢄⣀⣀⣀⣷⣤⣀⠉⠁⠀⠈⠉⠁⣤⣤⣤⣾⢿⣶⣿⣿⢿⣧⣴⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣦⣰⡏⠹⣯⣽⣿⣟⠻⠟⢻⣧⣤⣴⠿⣧⠋⢠⣾⣿⣿⣿⡆⢿⣽⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠈⢹⡇⠸⣿⣿⣿⣿⣦⣀⢸⣇⠀⠀⠀⣹⣆⠛⢿⣿⣿⣿⡷⠾⣻⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⣷⣤⣽⡿⠿⠿⠯⠽⠿⠿⠀⠀⠐⢛⡋⠉⠉⠉⠁⠀⠀⣀⣷⠴⠒⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢦⣈⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠰⣦⢤⣤⠴⣾⠃⠀⢤⡀⣀⡴⠊⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⢿⡄⠀⠉⠓⢲⣤⣤⡇⠀⠈⢿⡒⢻⠇⠀⠀⢀⡿⣟⣉⣙⡓⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢉⡟⠓⠚⣟⠛⠉⣉⣽⣴⠚⠳⣄⣀⣀⣧⣸⣤⣤⣤⣼⣶⣾⠋⠀⢩⣿⡓⠒⠶⢤⠀⠀⠀⠀ ⠀⠀⣠⠔⡿⠀⠀⢀⣿⡿⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀ ⠠⠞⠁⠀⣧⠀⠀⠈⢰⣿⣦⣀⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢤⣿⣿⠓⠦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠀⠀⠀⠘⠿⣿⣯⢷⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣺⣇⠙⠄⠀⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠉⢻⣾⣷⠄⠀⠈⢿⣿⣿⣿⣿⣿⡿⠀⠀⣤⣽⡿⡄⠀⠀⠀⠀⠘⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⣿⣿⣦⣄⡀⠈⢿⣽⣿⣿⡿⠃⢠⣴⣬⡿⡇⠀⠀⢀⡴⠋⠀⠈⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣻⢹⣿⣿⣧⣰⣄⣌⠉⠉⢰⣷⣼⡟⣿⠀⠀⣠⠞⠁⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⠋⠛⡿⠿⠿⠚⢛⠿⣿⠙⠆⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣀⣀⠈⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡇⠈⠀⠈⠉⣆⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠠⢄⠀⠀⠀⠀⢰⣀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣿⣿⣦⡉⠒⠉⠉⠀⠀⠀⠀⠉⠑⠤⠐⢂⠭⣥⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠈⢸⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠃⡸⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠀⠉⠀⠠⣄⠐⣦⣦⣦⣄⠀⢸⢦⡤⣴⣄⠀⠀⠰⠁⠀⠀⠀ ⠀⠀⠀⢀⣔⡿⠀⠀⠀⡀⢈⠀⢴⢿⢤⡁⠀⠀⠀⣀⣀⣀⡀⢠⠃⠀⠀⠀⠀ ⠀⠀⣠⣿⠋⠁⢠⠀⠀⠁⠛⠆⠓⠘⠏⠁⢀⠊⠐⠼⠐⠞⠂⠆⠀⠀⠀⠀⠀ ⠰⡟⠏⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢄⠀⢰⠌⣀⣒⣁⡠⠊⠀⢀⠠⢤⡤⠠⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠒⠋⠁⠀⠀⠀⠨⣘⡀⠘⢀⣒⠲⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⡀⢀⠀⠀⢀⠁⠀⡘⠀⠀⠀ ⠀⠀⠀⠀⠀⢯⠂⠣⠁⠀⠈⠂⠑⠈⠂⠘⠘⠙⠃⠓⡋⠀⡼⠀⠀⡇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠠⠬⠦⠙⢌⠳⣄⠀⣠⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⣙⣤⠒⠋⠀⠀⠈⢇⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⣈⡆⠈⠛⢋⡉⠉⠉⠉⠉⠈⠉⠒⠒⠤⣄⡀⠀⣠⠔⣺⠟⠽⠛⡁⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠈⠓⠢⢤⡤⢴⡏⠀⠀⣁⢀⡠⠔⠋⠁⠀⢀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢤⠞⠁⠀⠀⠈⠉⠉⣑⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡖⣾⠇⠀⡰⠋⡾⠃⠀⢀⠀⡴⢁⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠈⢢⣤⠀⠀⠀⠀⣿⠄⠀⠀⠀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣿⣠⠊⣠⠞⠁⠀⡰⠃⡜⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡜⢀⠀⠀⠀⠀⡀⠳⣄⠀⠀⢈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⣰⠛⠁⡰⢁⠀⠀⢠⠃⠈⢀⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡇⠘⠀⠀⠀⠀⢣⠀⠈⢢⣰⣼⡏⠀⠀⠀⠀⠄ ⠀⠀⠀⠀⠀⢀⠜⠁⣠⡾⠁⡞⠀⢠⡏⠀⢀⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢳⢾⡄⠀⢠⠀⢻⡇⠀⠀⠁⠘⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⣠⠟⢡⠃⡸⠁⢠⠋⠀⢠⡞⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠲⢄⣸⢸⣇⠀⠈⡆⠀⣿⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⢠⢞⠟⣱⠋⠀⡎⢀⡇⢠⠃⣀⢴⣾⠋⠉⠁⠈⣇⠀⠀⠀⠀⠀⣶⡜⠀⠀⠀⠀⠙⣾⡿⡄⠀⢡⠀⢻⡇⠀⠀⠀⠀⠇⠠⠀⠀⠀ ⠀⠀⣿⠏⢰⡟⠀⢠⣇⡞⡇⡎⠉⠀⠀⠉⠃⠀⠀⠑⠚⣦⡀⠀⠀⣰⣿⠁⠀⠄⠒⠀⠀⢻⡇⢻⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠋⠀⢻⡇⠀⠘⣿⢠⣷⡁⠀⢀⣀⣀⣀⣀⣠⣄⡀⠈⠓⢄⣠⡃⡏⠀⠠⠤⣄⣀⠀⠈⢿⠈⣆⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤ ⠀⠀⠀⠀⢸⠁⠀⠀⠉⡸⣨⣵⣾⠟⠉⠉⠈⠉⠉⠛⠃⠀⠀⠀⠈⠈⠃⠀⠴⢶⡚⠷⠿⢧⣄⣧⣸⣼⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⡏⠀⠀⢀⠆⡇⠙⠷⢬⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢙⣦⡴⠒⢺⣿⣿⣇⣇⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⢸⠀⠀⠀⡎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡈⠁⠐⠛⣿⠀⢀⠎⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢸⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡞⠀⠀⠀⣾⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⣿⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡜⠀⠀⠀⠀⠛⠀⠀⠀⣾⣿ ⠀⠀⢸⠀⠀⠀⣿⣇⢹⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢱⣶⣶⣦⣤⣝⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢠⠞⠀⠀⠘⠀⠀⠐⢂⠀⠀⣿⣿ ⠀⢰⣿⡀⠀⣼⡿⣿⢾⡄⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣠⠋⡰⠋⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠹⡇ ⠀⡾⢻⣿⠸⣿⣧⣿⠀⢳⡀⠀⠀⢀⣠⣄⠀⠸⣿⣿⡿⠿⠿⠿⠿⣿⡏⠀⠀⠀⠀⠀⢀⡞⠁⠞⡱⠋⠳⠄⠀⣠⠴⣺⠋⠀⢠⠧⠀⠀ ⠀⠇⢸⣿⠀⢹⡟⢻⡇⠀⣷⡀⠰⡋⠀⠀⡅⠀⢿⡋⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⢀⡴⢫⠄⠀⠀⠀⣀⡝⢃⣼⣡⠞⠁⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⢿⣆⣺⡇⠈⣧⣠⡿⣿⣆⠈⠒⠒⠁⠀⠀⠛⠻⢿⠟⠛⠉⠀⠀⠀⢀⡴⢋⣴⠃⠀⠀⠀⢸⣈⠃⣾⠏⡼⠀⠀⢢⣾⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⢇⢠⣿⠉⠀⠀⠈⠳⣄⠀⠈⠀⠀⠀⠀⠀⢷⠀⠀⠀⣀⠴⢋⡴⢻⣿⠖⣺⣿⡿⠈⠀⣼⢃⡞⠀⠀⢀⡾⡟⣆⠀⠤⠤ ⠀⠀⠀⠉⠙⣷⣼⡿⢅⡀⠀⠀⠀⣀⣾⣿⡦⡀⠀⠀⠀⠀⢸⣀⣤⣺⠥⠚⣁⣠⣾⠃⠀⣯⡍⠀⠀⣼⣿⡞⠀⢠⣿⢛⡇⠘⢾⡆⠀⠀ ⠠⠀⠀⠀⠀⠘⠿⡷⠄⠈⠓⢴⣿⣿⣿⣿⣷⣌⠳⠤⢀⡀⠀⠩⠙⠒⠋⠉⠁⡼⠃⠀⠀⠿⠧⢀⣾⣟⣿⠃⣰⣿⣏⣸⠧⠜⠓⠛⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣤⣶⣤⣤⣶⣶⣦⣤⣤⣴⣾⠃⠀⠀⠀⢀⣠⣿⣿⣿⢃⡼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠎⠀⠀⠒⠘⠅⠠⠔⠡⠤⠤⠀⢀⡀⠀⠀⢉⢡⢵⠊⠀⠀⢡⠀ ⠀⠀⠑⠠⠤⡜⠀⡠⡠⠐⠈⢉⢀⠎⠀⠀⠀⠀⠀⡀⠁⠊⡔⠁⠀⠁⡰⠀⠀⠀ ⠀⠀⠀⠀⢠⣇⠔⡕⠁⡠⡐⣡⠋⠀⠀⠀⠀⠀⠊⡰⠀⠀⢈⠢⡀⠈⢃⠀⠀⠁ ⠀⠀⠀⢀⠜⢁⢎⠀⢠⠁⡐⢱⠀⠀⠀⠀⠀⢀⠔⠁⡅⠀⠀⡆⠈⠔⢟⠀⠀⠀ ⠀⠀⣠⢃⠖⡍⡌⡠⢹⢰⣁⠼⠀⠀⠀⠀⢐⠟⠠⢰⣧⠀⠆⢹⠀⠀⠘⡆⠀⠀ ⠀⣼⢪⡏⢠⡰⢠⠓⠈⠣⠀⠀⢧⠀⠀⣸⠆⠀⠄⠈⣏⡆⢰⢸⡇⠀⠀⠁⠀⠀ ⠀⠃⢘⠅⠘⢧⠦⣠⠤⠤⠤⢦⠀⠑⠠⢽⠀⣒⣆⣤⡘⡘⣸⠀⠇⠀⠀⠀⠀⣴ ⠀⠀⡈⠀⢠⡈⠛⠹⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠴⢔⢻⡿⣏⡀⠀⠂⠀⠀⠀⣿ ⠀⠀⠁⠀⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢡⠁⠌⠀⢠⠀⠀⣿ ⠀⢠⠀⢸⡟⡇⠀⠀⠀⠀⢀⠤⣒⣂⠄⡀⠀⠀⠀⠀⠀⢀⠇⠌⠀⠀⠈⠀⠀⣿ ⠀⣿⣀⣼⢳⠇⠀⠀⠀⠀⢸⣤⣿⣿⣿⣾⠆⠀⠀⠀⡠⢢⢊⠀⠀⠀⣀⠇⡀⠟ ⠸⢸⡏⣻⢾⠈⣄⢠⠒⢐⠘⡟⠉⠉⢉⠏⠀⠀⢀⢔⠁⠁⢁⠅⣐⠙⠁⢰⠁⠀ ⠀⠀⢧⢸⢸⡦⠛⠢⡁⠈⠀⠈⠛⣏⠉⠀⢀⢔⣵⣃⢠⡄⠊⡸⡱⠀⢨⣇⠀⣀ ⠀⠀⠚⣧⡿⢅⡀⣀⣸⣦⢀⠀⠀⠸⣠⢪⣑⢡⡞⠀⣟⠁⣰⣗⢀⡶⣻⣩⣆⠀ ⠁⠀⠀⠈⠉⠁⠈⠛⣿⣿⣧⣩⣀⣤⣭⣀⣠⡜⠀⠀⢉⣾⡿⢣⠾⠓⠉⠁⠀⠀

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⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠ ⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⣶⣾⣷⣾⣟⠝⠈ ⠀⠀⠀⡈⢺⣿⣦⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⣿⣯⡿⠯⠀⠀⠀ ⠀⠀⠀⠙⣄⠹⣿⡿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⢡⣾⢁⣸⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣳⣿⡇⠁⠹⣻⣷⣌⣩⡛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⡇⣰⣿⠏⣸⡿⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡟⡄⠀⠹⡍⠉⠻⣷⠀⠀⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⣿⢻⡀⠀⠈⢓⠂⠼⣧⡀⠀⠀⠻⣿⣶⣤⣵⣤⣄⣤⣄⣀⣀⣴⣶⣦⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⡗⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠤⣿⡆⠃⠀⠀⠀⢱⡦⣹⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠟⠛⠻⠿⣿⣿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⣿⣿⡖⡲⠄⠀⠀⢯⣒⣿⣾⡄⠀⠀⣶⣿⣿⣿⣿⣿⣿⣟⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⣳⡏⠀⠟⠃⠀⠙⠻⠿⠿⢿⣿⣷⣤⡄⠀⣿⣻⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠲⣿⢿⣌⠂⠀⠀⠀⠛⢿⡇⡿⣀⠀⠹⣿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣿⠀⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⡽⢹⡖⠀⠀⠀⠀⣼⣿⣧⣾⣿⡿⠾⠽⠿⠿⣟⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣷⣿⣥⣈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠽⣇⣇⣿⠛⣳⣤⣾⡿⣿⢛⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⣾⣿⣿⠿⠿⣯⣿⣏⣩⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⢙⢹⣼⣿⣿⡟⠛⢻⡿⣟⢻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠓⠞⢶⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠰⣿⣿⡿⣵⡇⠀⠈⠁⠩⢿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣿⣿⣷⠽⠆⠀⠈⢿⣽⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⣿⣿⣿⠋⠀⠀⠀⠀⢰⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⢿⣿⣯⡁⠀⠀⠀⠀⠉⠻⣶⣶⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠙⠻⠏⠁⠀⠀⠀⢀⢂⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢨⣿⠉⠀⣄⡀⠀⠀⠀⠀⠀⠉⠀⢣⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣺⡗⠀⠀⠀⠀⠀⠀⠙⠒⢦⣴⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢯⣿⣿⣽⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣐⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣟⡳⢦⣀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⣀⣀⣀⣀⣀⣩⣶⡛⠃⢽⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠻⠷⠬⣭⣒⡂⠈⣉⣉⡉⠙⠲⢤⣀⠀⠿⣶⣦⣀⢠⡾⣟⠻⡩⠭⠤⠄⢠⡾⣋⡀⠉⢩⣿⠓⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠀⠀⠀⠀⢀⣀⡤⠔⠒⠋⠉⠀⠀⠀⠀⠀⣉⢻⣶⡂⠉⠉⠉⠙⠂⠐⠀⠀⠻⡟⢿⡞⠿⠃⣀⢈⣑⠒⢦⣿⣀⡀⠈⠑⣿⣿⣖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠏⠀⠀⠻⣯⠉⢉⠀⠀⠀⠁⠀⠀⠀⠀⣠⣶⣆⠀⠙⠢⢄⡈⣻⡿⢄⡙⠓⢼⡇⣿⠀⠙⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⣠⠝⠷⢤⣄⣀⣈⣤⠤⠶⢚⡋⣍⠙⣛⡹⠲⣤⣀⣩⡿⠥⣀⠉⠳⢼⡏⣿⠤⣀⠀⠈⠳⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠞⠙⠻⢶⣄⠀⠀⠁⠉⠙⠺⠋⠀⠁⣠⡾⠟⠀⠀⠈⠑⢦⡀⢻⣿⣆⠉⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣹⣿⣻⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡴⠁⠀⠀⠀⠀⠙⠻⠷⢦⣤⣤⣴⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠘⢦⡀⠘⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣺⣷⡏⠀⡴⠁⢠⠣⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡀⢄⠈⢿⣠⠀⠑⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢏⠀⠌⢀⡴⠃⣡⠆⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢷⢌⠓⢘⣿⡀⠀⠀⠀⠀⠀⠀ ⢀⣀⣀⣀⣀⣠⣞⣀⣁⣐⣐⣋⣀⣀⣀⣈⣀⣀⣀⡆⡁⡃⣸⣀⣒⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣠⣱⣣⣳⣀⣘⣧⡆⢀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣷⣶⣦⣴⡿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠛⠉⢉⠙⠛⠿⣿⡌⢿⣿⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣤⣀⣀⡀⠀⢠⣾⣿⡿⠃⠀⠀⠀⣿⣿⣦⡀⠀⠙⢦⡀⠁⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠿⠗⠀⠀⠈⣟⠢⣄⣀⣼⣦⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⣿⣿⣿⣿⡟⠀⠀⢀⣠⡿⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠻⠿⠿⡏⠀⢀⣀⠈⠉⠘⠛⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⠶⠖⠒⠉⠀⠀⠀⠀⠀⠀⢠⠇⣀⣼⠉⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⢦⠙⠉⠀⠀⣰⣾⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡴⢁⠞⡐⠒⠂⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠓⠒⠋⠠⡈⠉⣀⣼⣿⣿⣿⣿⡟⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣹⣿⣶⣦⣤⣤⣤⣤⣶⣶⣫⣁⣀⣀⣀⣀⣤⣼⣾⣿⣿⣿⣿⣿⣿⢿⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡆⠀⣠⣴⣶⣶⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⣀⣀⣀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇ ⢠⣾⣿⣿⣷⣶⣤⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠖⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢋⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠙⢿⣿⣦⣄⣠⣤⣤⣄⣰⣁⣠⡞⠋⢀⠞⡹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠻⣿⣿⠗⠂⠀⠀⠀⠈⠙⠻⣿⣏⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⢿⡟⢷⣔⣔⣴⣤⣄⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠏⢰⡿⣿⣿⣿⣿⣾⣿⣼⡄⣿⣿⣿⣿⠟⣯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢠⣿⣤⢿⣟⠛⣿⠏⢹⣿⠇⠈⢿⡉⠹⢇⣼⡄⠀⠀⢀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡈⢿⣿⠯⢿⠷⣤⣴⣿⠋⠰⢾⡷⠿⢶⣿⣿⠃⠔⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⠆⠙⠧⣴⣶⣿⠋⠁⢀⠴⠚⡗⢦⠀⡨⢿⠒⠢⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⢶⣲⣴⣶⣞⠩⠉⠀⣼⢿⣴⣿⠶⣾⡏⠀⠘⡄⠀⠀⠑⠤⢄⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠁⠀⠀⠀⣰⡊⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣼⣷⣶⠶⣄⠀⠀ ⠀⠀⠠⣤⠤⣶⣶⣿⣿⣧⣠⡿⠁⠀⠀⣴⣎⣹⡿⠛⣏⠙⣤⡀⠀⢄⠀⠀⠀⠀⠀⢀⣴⠃⢠⠎⢻⡟⠛⣿⡛⣧⠀ ⠀⢠⠞⠁⠀⠩⣶⠮⠘⣿⣿⣿⡀⠐⠲⢥⡼⠋⠀⠀⢻⡀⢠⢣⠀⠘⢶⣦⣀⣠⣴⠟⠁⢀⠎⢠⡟⠀⠀⢸⣿⠿⠀ ⣰⣏⣙⣒⣲⢷⣶⣟⣓⣰⣿⣿⣿⣆⠀⠀⢣⡀⢀⡤⣈⣇⠡⠎⣆⡀⢀⣿⠉⠉⣏⠀⢠⣾⣠⠟⠡⢢⡤⠋⠀⠀⠀ ⠛⠛⠦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⣑⣄⣳⣄⣆⡜⣻⣤⡆⣟⠀⢀⣩⡑⣆⣟⠁⢀⡀⢈⣷⣗⡞⠁⠀⠀⠀⠀ ⠀⠀⢰⡶⣾⣿⣿⢿⡟⢛⡷⣷⠙⣶⣶⢴⣿⡦⠈⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠚⠋⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠟⠉⠈⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠈⠉⠷⢦⡀⠀⢀⣠⠖⠋⠉⠉⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠀⢠⠞⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⡤⠤⣤⣄⣀⣀⠀⢀⣠⣤⠶⠚⠋⠁⢰⡇⠀⢠⠀⠀⠀⡏⠀⠄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢀⣴⠞⠀⠀⠀⢧⡀⠸⡄⠀⢀⣿⣤⣠⣽⠃⠀⠀⠀⠀⠀⠄⠀⣠⠇⠙⣦⡀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⢀⡴⠋⠀⢸⠈⢳⣄⠀⠀⠀⠀ ⠰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣀⡤⠤⠶⠒⠒⠒⠛⠛⠓⠒⠲⠶⠤⣄⣀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⢸⡆⠀⠀⠀⠀⠀⢀⣀⡼⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀ ⠀⢸⣿⠀⠀⠀⢠⣶⠞⠉⠀⠀⠀⢠⣼⢀⡀⠀⠀⠀⠀⢀⡤⣲⡿⡿⠋⠁⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⣀⣤⡶⠞⢻⡄⠀ ⠀⠈⣿⡆⠀⢠⣿⣽⣦⣀⡀⠀⠀⠈⢛⡿⣿⡇⠀⠀⠠⣿⣉⣉⣻⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡴⠛⠉⠀⠀⠀⠀⣷⡀ ⠀⠀⠹⡇⠀⣼⠃⠙⠓⠶⣿⣿⡶⣴⣏⠀⢠⡮⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣀⣀⣤⢤⣼⡇ ⠀⠀⠀⢿⠀⡟⠀⠀⠀⠀⠶⠛⠁⠻⠷⣦⡼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠉⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠘⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣠⣤⣼⠃ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠄⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠀⠀⢹⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠘⢷⠀⠀⠀⠀⢀⡞⠁⠉⠳⣄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡼⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⢀⠀⠀⠚⢷⣄⠀⠀⡾⠀⠀⠀⠀⠀⠙⠦⢄⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠋⠉⠓⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⠀⠈⠳⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠋⠁⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡉⠓⠲⠶⠶⠤⠭⡷⡴⣶⠊⠉⠁⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠤⠤⢤⣄⣀⣀⡼⣆⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠀⠺⢯⡀⠀⠀⡠⠔⠒⠚⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣾⠀⠀⠀⠀⡰⠋⠑⣏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀ ⠀⣠⠖⠒⠒⠒⠠⠤⠤⠖⠚⣩⠀⠀⢿⠀⡆⠀⠀⡇⠐⢠⡇⠀⠀⠀⠀⠀⢀⡿⣄⠀⠀⠀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠲⠾⠔⠚⠉⠉⠙⢦⡀⠀⠀⠀⣠⠞⠀⠏⢧⡀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠐⢁⡀⠤⠄⠒⠒⠒⠒⠀⠒⠒⠢⠤⣀⡈⠁⠒⠈⠁⠀⠀⠀⠀⢳⡄⠀⠀ ⠀⣧⠀⠀⠀⣀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⢀⣱⡀⠀ ⠀⣿⡀⠀⣼⣯⣀⠀⠀⠀⠻⣷⣦⠀⠀⢠⣾⢛⣿⣁⡀⠀⠀⠀⠀⠀⠙⠢⣀⡠⠖⠊⠉⠀⢳⠀ ⠀⠘⡇⢠⡏⠙⠓⢿⣷⡆⣾⡁⢨⣅⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣀⣀⡤⠤⢼⡇ ⠀⠀⢻⣾⠀⠀⠀⠘⠉⠀⠛⢳⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⢸⡇ ⠀⠀⠘⣿⠁⠀⠀⢀⠄⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠓⠒⠒⠛⣿⠀ ⠀⠀⠀⣿⠀⠀⠀⣜⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡼⠁⠀ ⠀⠀⠀⢹⣄⠀⠀⢹⡄⠀⠀⢠⠏⠀⠙⠢⣀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠻⣤⡀⠀⠙⠦⣤⠏⠀⠀⠀⠀⠈⠙⠒⠊⠁⠀⠀⠀⣀⠴⠋⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠈⠳⠄⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠋⠀⣠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡉⠓⠒⠚⠛⠳⢲⡉⠁⢀⡠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠒⢦⡀⠀⠻⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⠃⠀⣶⠆⠀⣷⠖⠒⠢⣌⠉⠉⠒⠒⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠈⢧⠀⠀⠀⢸⢁⣤⡀⠀⠀⢳⡀⡀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡶⣦⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠙⠒⣶⣾⡄⠉⠁⠀⠀⢨⡇⣷⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⢻⣻⠿⠗⠛⠛⠉⠉⠉⠓⠒⠦⢤⣀⠀⠀⠠⠴⢿⡄⠙⠦⣤⣤⠤⠊⠐⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⡹⡄⣀⡤⠤⠤⠤⠤⢤⣀⡀⠀⠈⣿⣦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣿⠈⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣿⢙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣆⠀⠀⠙⠲⠦⢤⣤⣀⣀⣀⣀⣠⣼⠛⣿⢹⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣴⡞⠓⠛⠀⠘⢿⣄⡀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⠀⠀⣨⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠛⠿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠛⠦⣄⣀⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠷⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⠉⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⢀⣤⠤⠼⠿⣦⡄⠀⠀⠀⠀⠀⣶⣦⠀⠀⠉⢻⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡶⢿⣿⣬⡓⠶⠤⣤⣾⣥⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢸⡇⠀⠀⠀⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡉⠻⠟⠳⡾⠛⠛⠿⣤⣇⣀⣀⣀⣤⠴⠞⠋⣁⣤⠞⠁⠀⠀⢀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣀⣤⣤⣤⡶⠾⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢱⣿⡜⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠇⠻⠛⠃⠉⠉⠉⠉⠉⠉⠛⠶⣦⣤⡶⢋⣵⣆⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠻⠿⢻⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠀⠀⠀⠠⣖⢲⡶⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠙⠓⢻⡄⠀⣠⠾⠭⠯⠽⠓⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣭⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⣹⡟⠁⠀⢲⡄⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⣹⡛⠛⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⣿⠂⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠉⠁⢺⡅⠀⠀⣴⣦⠀⠀⠀⢸⣧⣤⣄ ⡷⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣠⠞⠀⠀⠀⢀⡴⠃⠀⢀⡇⡏⠀⠀⠀⠸⡇⠀⣽ ⣯⠀⠀⠀⠀⠀⢠⣇⣠⠴⠋⠁⠀⠀⢀⡴⠋⠀⠀⡴⠛⠁⠻⣦⠀⠀⠀⡇⢠⡇ ⢃⠀⠀⠀⠀⠴⠚⠉⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣇⠀⠀⠀⣸⠂⠀⢠⡇⣾⠀ ⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡏⠀⠀⢸⣿⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠳⢶⣾⠃⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣴⠟⠋⠉⠻⣦⣴⠶⠚⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⠀⠖⠀⢸⡗⠾⠀⠀⢸⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠸⣦⣀⠀⢀⣠⣾⣿⠶⠶⠶⠛⠁⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠉⠁⠀⠀⠀⠀⠉⠙⠋⢩⣴⣿⠀⠀⢀⣶⠟⠛⣛⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡀⠀⠈⠻⠶⣾⢻⣷⡀⠀⠘⠛⢷⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⠆⠀⠀⠀⠙⢿⣇⣸⣆⠀⠀⠀⢻⡆⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢦⣤⣤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠘⠉⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣤⡤⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣆⠀⠀⠀⢿⡀⢀⣠⡾⣫⡿⠃⠀⠀⠀⢀⣠⣤⣤⠴⠶⠶⠒⠒⠚⠓⠒⠒⢶⣦⣄⠀ ⣾⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣤⣤⡀⢿⡄⠀⠀⠈⢿⡟⠉⣸⣿⣻⡖⠀⠀⢀⣾⡛⠛⠻⠷⠶⠶⠶⠶⠶⠒⠒⠛⠋⣡⣿⡄ ⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣴⣶⣆⣀⣀⠀⡍⠉⣤⢰⣾⣿⣿⣧⠀⠀⠀⠈⣿⡶⣿⣿⣿⡷⠀⢀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡷ ⠀⠀⠉⠉⠛⠛⠛⢛⡿⢿⠿⣻⡿⢻⡿⠛⠿⠻⠟⠉⠼⠟⣽⣿⠟⠻⢶⠿⠿⡿⢻⠟⣿⣀⣀⣶⣄⣽⡷⠛⠉⠀⠀⠀⢿⡿⢛⣿⠷⣶⢶⣶⣶⣶⣶⠶⠚⠛⠛⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠁⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⢿⣯⠉⠻⢦⣄⠀⠀⠀⢀⣴⠾⠋⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⢿⡆⠀⠀⠙⢷⣤⣴⡞⠁⢀⣀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⠀⠀⠘⠃⠙⠿⠿⠿⠶⠿⠿⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⡀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣒⡬⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠇⠃⠀⠀⠠⢔⣾⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠹⠿⢷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠀⠀⠀⣠⡟⢩⣄⠉⣿⡀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠐⠛⢿⣤⣈⣃⣨⡿⠁⠀⠀⠠⣶⣶⠀⣀⣉⣛⣛⠋⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣀⣀⣀⣤⡶⠟⣛⣉⣉⡉⠛⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⣴⡏⢀⣾⡟⠉⠉⡿⣆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢸⡇⠃⠀⠀⢀⡟⢸⠃⠀⠀⠀⢠⡄⠀⠀⢀⣤⣤⣤⡀⢠⣤⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢸⠃⣿⠀⠀⠀⠀⢸⡇⠀⠀⣾⡏⠁⢹⣷⠸⣿⠀⠀ ⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⠃⠀⠀⠀⢸⠀⢻⠀⠀⠀⠀⢸⣇⣀⡀⢻⣧⣂⣼⡟⠀⣿⣀⣀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢰⡏⣰⡏⠀⠀⠀⠀⢸⡆⣼⠀⠀⠀⠀⠘⠛⠛⠛⠀⠙⠛⠉⠀⠀⠛⠛⠛ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣍⣿⡀⢸⡆⠀⠀⠀⢀⡾⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡈⠻⠶⠴⠾⣛⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⢶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⣷⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⢹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣧⣀⣤⣴⠿⠿⠟⠛⠛⠛⠛⠿⠿⠷⢶⣦⣤⣄⣴⡿⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡀⠀⠀⠘⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠈⠻⣷⣄⠀⠀⠘⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢠⣦⣤⣴⣾⣟⠁⠀⠀⠈⠛⠿⣶⣶⣶⣦⠀⠀⠀⢰⣶⣶⣿⣟⡁⠀⠀⠘⠛⢿⣶⣤⣽⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⢿⣆⠀⠀⣠⣾⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⡀⠀⣴⡿⠛⠉⠉⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣸⡿⠁⠀⠀⢠⣤⠀⠀⠀⠀⢠⣦⠀⠀⠀⢿⣇⣾⡟⠀⠀⠀⠀⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠘⢿⣦⣴⣿⣤⣼⡿⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⢠⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⢀⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⣠⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⣠⣶⠿⠻⠿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣾⡟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠛⢿⣿⠿⠶⠶⠶⠶⣶⡾⠷⠿⠿⠿⠿⣿⣟⡋⠁⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠹⣿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠘⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢈⣿⠆⠀⠀⠀⢹⡇⠀⠀⠀ ⢠⣾⠿⠛⠻⠿⣷⣶⣤⣴⡿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣾⠇⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⡟⠀⠀⠀⠀ ⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣰⡿⠀⠀⠀⠀⠀ ⠀⠈⠙⠻⣷⣤⣄⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣴⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠿⠷⠶⠶⠶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⢰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠆⠀⠀ ⠀⠸⡀⠑⢧⣀⢠⠤⠦⠴⠴⢤⣴⢊⡠⠇⠀⠀ ⠀⠀⢣⢀⣀⣦⣀⣀⠀⣠⢤⣿⣶⣦⡜⠀⠀⠀ ⠀⠀⠸⢺⢸⣿⣦⣸⡉⢙⡦⠿⠿⠿⠃⠀⠀⠀ ⠀⠀⠬⡌⠉⡉⠁⠱⣤⣄⠃⢄⣤⡊⡃⠀⠀⠀ ⠀⢀⡜⢹⡀⢼⣿⣦⣬⣦⣄⣾⡗⣰⡇⠐⠀⠀ ⠐⠀⠄⠈⣷⣄⠹⣿⣿⣿⣿⡟⢰⢿⠂⢀⠀⠀ ⠀⠀⠀⠐⠌⢻⣆⠈⢿⣿⡿⢀⢾⠃⠀⠀⠢⠀ ⠀⠀⠀⠀⠀⠸⢙⠷⠶⠭⣵⠟⢃⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣂⣠⣴⠶⠟⠋⡅⢀⡇ ⢠⡤⠖⠚⠛⠛⠛⠛⠛⠓⠶⠤⢤⣀⣀⣀⣤⡤⠶⠞⢻⡛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠚⠛⠉⠉⠁⠀⠀⢀⣤⠞⠁⣼⠃ ⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠐⢒⣾⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⣴⣾⠯⠀⢀⣼⠏⠀ ⠀⠀⠈⠓⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣳⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣹⡿⢃⣴⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠠⠿⢷⠇⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡴⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡆⡾⠀⠀⢀⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⡼⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠃⢀⣼⣿⣿⣮⡙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣸⣿⠟⣿⣿⡄⠀⠀⠀⠀⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣹⣿⣧⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠘⢿⣿⣿⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣿⣿⡿⢃⣀⠈⠀⠀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠾⣇⠀⠀⠀⠉⠉⠉⠁⢀⣠⠴⠶⠻⣿⡛⣷⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢻⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠺⣿⠀⠀⢰⡿⢿⡿⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠠⢻⣿⣀⡾⠁⠀⠀⠀⠀⠀⠀⠰⠦⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣤⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣀⣠⠴⢲⣄⠘⠙⠋⠁⠀⠀⠀⠀⠀⢀⠀⠢⣤⠀⣠⠾⠉⠙⠒⠶⢤⣀⠀⣰⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠙⢦⣤⠊⢳⣜⣧⡶⢶⣤⡀⠀⠀⢠⣌⡳⣄⣤⠟⠳⣤⡀⠀⠀⠀⣰⣄⡽⠓⠦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⢀⠴⠋⢙⣶⣯⡈⠛⣷⡀⣿⣿⣷⣦⡤⠈⠉⠙⣆⠀⠀⠀⠈⠓⢦⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⡰⠋⠀⠙⠹⣦⣿⡟⠉⢹⠏⢠⠇⠀⠀⠀⠈⢧⡀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢹⡇⠰⠟⣴⠋⡴⠃⠀⠀⣀⡤⠿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⢾⣷⣾⣥⡤⠖⠋⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀ ⠀⠀⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢡ ⠀⠀⣇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠀⠀⠀⢘ ⠀⠀⠸⡀⠀⡀⡻⣦⣤⣄⡤⢤⣤⣤⣊⣐⠅⠀⠀⠀⣼ ⠀⠀⠀⢻⢄⢰⢖⢽⠿⠋⠀⠀⠉⢩⢿⢿⣎⠄⠀⡠⠙ ⠀⠀⠀⠈⡤⣁⠈⠘⠄⠀⠀⠀⡠⣄⢠⡜⢉⠃⠰⠐⠁ ⠀⠀⠀⢀⠃⠠⢾⠵⠆⠀⠀⡔⠧⠻⠜⠁⠀⢱⠀⢰⠀ ⠀⠀⠀⠸⠒⢼⠀⢠⡊⣉⡆⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀ ⠀⠠⠄⡐⢗⣾⡀⠀⣑⣎⡀⠀⠐⢀⠄⣂⠠⠂⠀⠸⠀ ⠔⢊⠡⠂⡹⠀⠑⢚⠂⠔⠊⠁⠂⠁⠁⠀⠀⠢⠀⠀⡆ ⠐⠁⢀⠏⠀⠀⠀⠀⠁⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃ ⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀

⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⣀⡤ ⠀⠀⠰⣿⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁ ⠀⠀⠐⡘⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⣹⠛⣻⠟⠁⠀⠀ ⠀⠀⠀⠙⣮⣿⠉⢻⣿⣭⣿⡒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣇⣼⡟⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⢦⠀⠣⣈⠙⣇⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣻⡜⠄⠀⠈⣤⡙⣷⡀⠀⠙⢿⣿⣷⣶⣷⣶⣶⣾⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣷⡤⠤⠀⠈⢯⣿⣷⠀⠀⣼⣿⣿⣿⣿⣿⣿⠇⠈⠉⠀⠀⠀⠀⣿⠋⠹⠇⠙⠻⠿⠿⣿⣿⣤⠀⢼⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢿⣧⡕⠀⠀⠈⢻⣿⠇⣄⣹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣿⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣏⢻⡅⣀⣀⣼⣿⡿⠿⠋⠙⠛⠛⠫⠷⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣠⣼⣿⣿⣿⡶⢾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠩⡟⠞⣴⣿⣿⠿⢿⣶⣶⣤⡀⠀⠀⠀⠀⠈⠑⠽⢦⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣼⣽⣟⡟⠀⠘⠻⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣇⣼⣿⣯⠗⠀⠘⣯⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⢿⠄⠀⠀⠀⣿⣿⡟⠁⠀⠀⠐⢻⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⠙⣿⠧⠀⠀⠀⠀⠉⠻⠿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⠙⠀⠀⠀⢀⣤⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠋⠀⠀⠲⢤⣀⡀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣶⢿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢻⠇⠀⠀⠀⠀⠀⠀⠙⢿⣿⡦⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣀⣀⣀⣉⣵⠟⢹⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢽⡀⠀⠀⠀⠀⠀⠀⢀⣀⠍⠛⠒⠿⣤⡈⠉⣉⣉⣑⠢⡄⠘⢶⣦⣄⣾⡟⠋⡁⠀⠀⡴⠋⠀⣈⣿⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⠆⠀⠀⠠⠤⠒⠈⠁⠀⠀⠀⢀⣠⠄⢻⣧⠠⠄⠀⠁⠀⠀⠈⠋⢛⡉⠀⢦⡀⠭⣿⡗⠤⣀⡸⢿⠧⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⡹⢦⣀⡀⢐⣀⣠⢤⠖⠛⠿⠲⣄⡈⣳⡿⡉⠓⢤⣝⢺⣀⠀⠙⠦⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠔⠉⠀⣠⠚⠛⠧⣄⠀⠀⠙⠓⠋⠀⢀⡼⠟⠀⠈⠑⢤⡘⣿⣆⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡕⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠖⠁⠀⢀⠔⠁⠀⠀⠀⠈⠛⠓⠶⠶⠚⠋⠉⢁⠀⠀⠀⠀⠀⠈⢧⠈⠢⡀⠁⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠁⠜⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣄⠢⠸⣶⠀⠙⠀⠀⠀ ⢀⠀⡀⣀⣠⣋⠁⣀⣐⣁⣀⣉⣀⣀⡠⠀⠀⢀⣠⣠⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣠⣀⣨⣻⣷⣀⢹⣦⠀⢀⡀⠀

⣿⣿⣿⡐⠂⠓⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣎⡀⠀⠀⢀⣀⣠⡄ ⣿⣿⣿⣷⠀⠀⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣙⢁⢀⡴⡫⠁⠀⢹ ⣿⣿⣿⡇⠀⠀⠀⠀⢎⢻⣿⣿⣿⣿⣿⣿⡀⠉⠃⠉⢿⠛⢻⢴⡵⠃⠀⠀⠀⢸ ⣿⣿⣿⣧⢠⡄⠀⠀⢈⠁⠉⠉⠉⠛⠛⠛⠟⢚⣷⣶⣯⣦⣼⡏⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⠀⠈⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣏⠀⠀⠀⠀⠀⢀⠆ ⣿⣿⣿⣧⠀⠀⠀⢀⣡⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣿⣷⡄⠀⠀⠀⡞⠀ ⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⣿⣿⠃⠀⢀⣇⠀ ⣿⠏⠀⠀⠀⠀⠈⠛⠻⠿⠼⠁⠀⠀⠀⠀⠀⢸⣽⣿⣿⡏⡟⢻⣿⣿⣶⡿⠓⠒ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠁⠈⠰⡄⠀⠁⠈⠉⠉⠁⠻⠿⢻⣿⣷⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⢰⡶⠛⠁⠀⠀⠀⠀⠠⡀⠀⠘⢿⣿⡇⠀ ⣿⡆⠀⠀⠀⠀⠀⢠⣶⣀⣀⣀⣀⣶⡀⠀⠀⠀⠀⠀⠠⣀⠀⠙⠀⠀⠀⠉⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣶⣶⣶⣾⡶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⠿⠿⣿⣿⣆⠀⠈⠙⠛⠿⣶⣤⣤⣶⠾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀⣀⣠⣤⣶⠾⠿⠿⢿⣿⣷⣶⡄⠀ ⢰⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠛⠋⠁⠀⠀⠀⣠⣿⠿⠛⠻⣿⡄ ⢸⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣿⡇ ⢸⣇⠈⠁⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⣿⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃ ⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠖⠛⠓⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⠛⢳⣶⣶⠒⠒⠒⠒⠒⠒⠚⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠸⣿⡀⠀⠀⠀⠀⠀⢸⣇⠈⠉⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⣿⡟⠉⠉⠉⠉⠉⠉⣻⠀⠀⠀⠀⢸⡟⠀⠀ ⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢶⣶⣶⣶⣶⡦⠄⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⢿⡇⠀⠀ ⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣀⣠⣤⠾⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⠶⠦⠤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠐⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⡇⠤⠄⠳⣮⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠇⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣶⡄⠀⠀⠀⢀⣠⡤⠶⠚⢿⡦ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣋⢙⠉⣀⠀⢀⡴⢛⡥⠀⠀⠀⠀⢳ ⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⣘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠹⠿⣿⡿⡿⢿⣿⣿⣿⣿⠇⣻⡾⣫⡕⠋⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣄⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⡙⠉⢸⡾⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠛⠛⠛⠛⠻⠿⠿⢻⠿⢿⣿⡶⢾⣶⣤⣤⣾⣈⣥⠀⢨⣽⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣿⡧⠘⠿⢤⠀⠀⠀⠀⢠⠀⠀⡄⡄⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿ ⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠈⣆⡴⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣠⣶⣿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⡟⠀⠀ ⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣌⣿⣿⣿⣿⣷⠖⠀⠀⠀⠀⡟⠀⠀ ⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣏⣿⣿⣿⣿⣿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣄⡀⠀⢀⣾⣷⠄⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠥⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⣿⣿⣿⣿⠙⡟⠛⢿⣿⣿⣿⣿⣯⡽⠿⠟⠛⠉ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠰⢤⡀⠀⠀⠙⠟⠉⠻⠿⠿⠿⠾⠃⢠⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠤⡀⠀⠀⠀⠀⢛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⠟⢹⣿⣿⣿⣧⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠅⠀⠀⢠⣮⣭⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀ ⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠌⠙⠂⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⠛⣿⣿⠁⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣉⠀⠀⠀⠀⡀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠶⠶⠶⢶⣤⣤⣤⣤⣤⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⣦⣤⣀⡀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣤⣴⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠐⠫⠻⢿⣟⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡹⡍⠀⣀⣴⣶⣿⣿⣿⣿⣶⣦⣀⠀⢫⢏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡍⣠⣾⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣷⣄⢫⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣰⣿⣧⣙⣫⣿⠟⠀⠀⠻⣿⣌⣋⣽⣿⡆⢸⠀⠀⠀ ⠀⠀⠀⠈⠉⠁⡗⢛⣿⣿⣿⠏⢁⢔⡟⣫⢄⠈⠹⣿⣿⣿⣛⢺⠃⠉⠁ ⠀⠀⠀⠀⠉⠁⠙⣄⡡⡝⠻⣷⡇⠀⠀⠁⢞⣦⡾⠟⢫⢌⣠⠋⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⡱⠁⠈⠒⢄⢀⠎⠡⣔⡊⠤⠊⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠄⡀⠀⢠⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡰⡀⠀⠀⣠⡀⠀⠀⠀⡰⡶⠀⠀⠀ ⠀⢀⠎⠀⠈⠉⠉⠁⠱⣄⣀⣀⡅⣇⠀⠀⠀ ⠀⢸⠀⠤⠄⠀⠀⠀⠀⡇⠀⠀⠀⠈⣗⡶⠆ ⣠⣊⡱⠤⠤⢤⡤⢤⡾⠕⠒⠊⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀