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⠀⠈⠳⣄⠀⢷⡦⠽⠻⣿⣿⣼⣷⡸⣿⣿⣷⣿⣯⢻⣿⣾⣿⣿⣿⣿⣖⠚⠿⢾⡿⣾⣯⡴⠦⣭⣻⣶⣤⣐⠓⢘⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣷⣿⣿⣷⣾⣿⣆⢦⡠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢻⣿⣷⠀⠀⠈⠻⣿⣿⣧⢿⣿⣿⣿⣿⣷⣻⣿⣝⠻⣿⢿⣿⣷⣟⠚⠛⠾⣿⣟⡿⠀⠀⠀⠈⠙⠳⣦⣜⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢷⡀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣆⠀⠀⠈⢿⣿⣯⡉⠈⠻⣯⢻⣿⣿⣿⣦⠈⠿⢻⣿⡻⣦⡀⠀⠉⠈⢷⣄⠀⠀⠀⠀⠐⠀⠙⢿⣦⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⡆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡜⠻⣷⣦⡀⠀⠻⢿⣿⣶⣶⡏⠻⢮⣻⣿⣿⣷⣄⠘⢾⣿⣾⡿⣦⣀⠀⠀⠙⢦⡀⠄⠀⠀⠀⠀⠀⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⣨⡇⠀⠀⠀⠀⣠⡤⠾⣫⠄⠐⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢉⠓⢻⡀⢤⠘⠛⢾⣔⣿⣿⣿⡿⢷⣦⡀⠙⠻⢿⣿⣿⣷⣦⣙⢿⣿⣿⡻⣷⣄⠀⠀⠙⢮⠀⠀⠀⠀⣀⣀⣻⡀⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡀⣠⡴⢞⡉⣴⡾⣡⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣖⡞⠀⢈⣳⣀⠀⠀⠀⠉⠻⣷⣬⣹⣶⣉⠛⠷⣦⣠⡽⣿⣿⣿⣿⣷⣮⣿⣟⢷⣝⡿⣦⣀⢈⠳⣖⣚⣻⣿⣾⣿⣷⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⣿⡃⣠⠏⢀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠌⣼⠀⠀⠀⠁⣝⠃⢤⣀⠀⠀⠘⠻⣿⣿⣿⣷⣤⡈⠙⠻⢦⣽⣿⣿⡿⣿⣿⣿⡶⠿⣿⣾⣿⣷⣿⣿⣿⣿⠿⠿⢛⡿⣿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠏⠉⢧⣏⡽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠈⠐⠆⠀⡀⠛⠛⠟⠻⢿⣿⣷⣧⣄⡈⠙⠛⠿⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⣤⡬⠆⠙⢧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⡀⠀⢚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣴⣿⣿⣿⣷⣤⣄⣈⢷⡀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣧⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠻⠟⠋⠙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣄⠀⡘⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢄⡖⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⠏⣹⣿⣿⣿⣯⣽⣿⡁⠙⠘⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣾⣷⣾⣿⣿⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢰⡂⣿⣿⣿⣿⠟⠹⣿⣽⣿⣿⣶⣿⣿⣿⣿⡛⠂⠀⠀⠁⠙⢯⡀⠘⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣶⣿⣷⣿⣿⣿⣿⣿⣿⡿⠟⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⣾⣠⣿⣷⣿⣷⣴⡶⠾⢿⣿⠿⠻⣿⠟⠿⠈⠇⠀⠀⠀⠀⠀⠀⠙⠶⣽⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠛⠙⠻⠿⣯⣿⣿⣿⣿⣽⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢄⠀⠐⣿⠛⠼⠛⠉⢉⠐⣤⡅⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⣀⠟⢀⠂⠀⠀⠀⠀⠀⠈⠿⣃⣹⣷⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠾⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠹⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⡛⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡓⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⡿⠿⠀⠐⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠴⠖⠋⠁⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢷⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡈⢹⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⠿⣼⣿⡶⢬⡴⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⣿⣷⣼⣇⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣁⣼⡿⡿⣿⣿⣿⣿⠟⡿⠛⠙⠀⣠⡟⠈⠀⠈⠁⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣼⠏⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣍⠀⠃⠘⢿⣇⠻⠀⠀⢀⡴⠞⠋⠀⠐⢠⠤⢠⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢶⡾⠋⠀⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠳⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣦⡀⠀⠀⠉⠳⣷⣶⠋⣧⠀⠀⠀⠀⠀⠀⣼⣯⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠋⠄⠀⢠⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣿⣿⣶⡶⠶⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⣆⠀⠀⠀⠀⠛⠷⣤⣤⣈⠀⠞⠀⠀⢛⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣠⡀⠀⠳⣾⣿⠿⣷⣇⡀⠰⠄⡴⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⣷⡙⠻⣕⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⣻⣷⠀⠀⣹⣿⠛⠋⢻⣿⢮⣛⠃⠀⠀⣆⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣤⢄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡀⠙⢿⣷⣈⠛⢿⠦⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡄⠀⠀⠀⠀⡍⠈⣹⣿⡛⢻⣄⣴⢎⡉⣖⠺⢷⣤⣔⡁⢸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢀⡀⣴⠋⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡿⣿⣿⣿⣿⣌⢿⣯⣙⠗⠒⠒⢒⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣄⠀⠀⢀⣼⠄⣹⢿⣗⣾⠋⢀⣴⠿⠟⢻⠻⠞⠻⣿⣻⡄⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⣘⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣷⠦⣤⣀⢼⠃⣈⠉⣻⣿⡿⠏⠁⠀⠀⠀⠀⠀⠈⠙⣿⣾⠷⣿⣍⠁⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣧⡠⡀⠘⠓⠚⢠⡏⢧⡁⣏⠐⠚⠀⠀⣤⠉⠀⠀⠀⠀⠀⠈⠛⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢄⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠛⢿⣿⣿⣿⣿⣦⡀⠀⠻⠟⠘⠳⠘⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣟⠻⢿⣿⣿⡛⠻⠻⣿⣿⣟⡋⢷⡈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⢤⣢⡌⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⠀⡀⠀⢀⠠⣀⡴⣾⠋⢡⣿⣿⣿⠋⢛⠀⠀⠀⠀⠀⠀⠀⢀⡄⣰⠇⠘⢧⠈⠻⣿⣧⣯⡑⠁⢿⣿⣷⡄⠰⡘⣿⣿⡃⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡉⣹⣿⣿⡿⢿⣿⣿⣿⣶⣠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣡⡆⠀⣀⣼⢶⡞⠋⠁⠀⣹⣿⣿⠿⢻⣶⣶⡟⠀⠀⠀⡄⠀⠀⠀⠘⢠⠏⠀⠀⢸⠀⠀⠈⠻⣿⣷⣿⣦⣽⣿⣧⠀⠛⣟⣿⣷⡝⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⣮⣹⣿⣿⣿⣿⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣯⣷⣾⡋⠉⠀⢀⣷⣤⡶⢿⡿⢛⢁⠀⠲⣽⠿⡀⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣿⣿⣟⠛⢻⣅⣀⡛⠛⢿⣷⠀⣈⠙⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠟⣿⠻⠿⣆⠈⣯⠷⣠⠿⠉⠁⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡈⠉⠳⡄⠚⣿⣷⣉⠀⠀⠘⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠛⠿⢿⣿⣄⣀⠀⠀⠙⠿⠿⣿⠿⠟⠟⠋⢹⠏⢈⡇⡀⠀⠘⡆⢀⠈⢀⣴⣚⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠸⣿⣬⣁⢷⡀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠿⣾⣿⣿⣿⣿⣯⡻⢾⣿⣿⣿⣿⣦⠀⠀⠀⠈⠙⠛⠷⢤⣤⣀⠀⠀⠠⠶⣧⣼⣿⣀⠘⠋⠇⠀⠀⡼⠷⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠘⠃⢀⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣅⣀⡈⠻⠉⠀⠻⣄⠀⠀⠀⡈⠙⠲⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣅⠀⠲⠰⣄⠈⠻⢦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡐⢾⡧⠀⠀⠙⠶⣄⠈⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡿⠻⣿⣽⣿⣿⣿⣿⣿⣿⣿⡿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡙⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣞⡵⠋⠀⢀⣾⠋⢛⣿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠈⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⠀⢠⠟⠁⢨⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⡀⠀⠈⠻⣶⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣦⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣀⠀⠲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣼⢿⣿⣿⣿⣿⣿⡟⣿⣿⣷⣄⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⣾⣿⣿⣿⡟⢿⣿⣦⡙⢿⣿⣷⣮⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣿⡗⣿⣿⡻⣶⣯⠈⠙⠆⠘⠿⢿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣽⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⣿⣿⣧⠘⢿⣦⡀⡀⠀⠀⠀⠈⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⢸⣿⣿⠀⠈⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⣿⡿⠀⠀⠀⠀⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠰⢇⠈⡟⣿⢸⣿⠇⠀⠀⠀⠀⠘⠊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢸⠀⡏⠈⡧⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀