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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡿⠗⠀⠠⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠑⢶⣶⡄ ⢀⣶⣦⣸⠀⢼⣟⡇⠀⠀⢀⣀⠀⠘⡿⠃ ⠀⢿⣿⣿⣄⠒⠀⠠⢶⡂⢫⣿⢇⢀⠃⠀ ⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⣀⣂⡠⠊⠀⠀ ⠀⠀⠀⠃⠀⠀⠉⠙⠛⠿⣿⣿⣧⠀⠀⠀ ⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀ ⠀⠀⠀⣷⣄⡀⠀⠀⠀⢀⣴⡟⠿⠃⠀⠀ ⠀⠀⠀⢻⣿⣿⠉⠉⢹⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠉⠀⡀⠄⡒⠈⠭⠭⠥⠈⠐⣚⣛⠛⠛⠛⡲⢦⣀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠔⡨⡢⠑⠈⠉⠁⠉⠄⠀⠀⠀⡲⠀⠀⠐⢄⠀⠈⢷⠀⠀ ⠠⣤⣿⣛⡛⠛⣻⢿⣛⣟⡻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⢿⣿⣿⣿⡟⢦⡀ ⡴⠛⢡⡶⠒⡖⠦⢭⣿⣮⣱⣎⣿⣿⡿⠏⠀⠙⡿⠷⠿⣾⢿⣿⢭⡞⡐⣷ ⡇⠀⢺⠠⢾⡟⠲⢤⣀⡀⠠⠤⠄⡖⢂⣀⠀⠀⠙⣦⣄⠉⠉⢰⡄⠠⢃⣿ ⠹⣎⡪⠀⠀⢷⡦⣄⣯⡉⠓⠲⣤⣵⣉⣀⡀⠶⠞⠁⣀⣨⣴⢿⣷⠈⣰⠃ ⠀⠈⢳⡀⠀⠀⠻⣌⡟⠛⠷⣶⣧⣄⣀⣹⣏⣉⣻⣉⣉⣧⣸⣷⣿⠀⣿⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⠳⢤⡀⣸⠉⠉⠛⡿⠻⠿⡿⠿⣿⢿⡿⣿⡟⠀⣿⠀ ⠀⠀⠀⠀⠈⠳⣅⡪⢔⡠⢉⡛⠲⠦⠤⠧⣤⣤⣧⡴⠧⠾⠖⠛⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣅⡒⠡⠶⠀⣠⡤⠤⠤⠤⠤⠤⠐⢁⠠⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⡀⠀⠉⠉⠉⠉⠀⢀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠚⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠉⢉⠍⣉⡉⠉⠉⠉⠓⠲⠶⠤⣄⠀⠀⠀ ⠀⠀⢀⠎⠀⠪⠾⢊⣁⣀⡀⠄⠀⠀⡌⠉⠁⠄⠀⢳⠀⠀ ⠀⣰⠟⣢⣤⣐⠘⠛⣻⠻⠭⠇⠀⢤⡶⠟⠛⠂⠀⢌⢷⡀ ⢸⢈⢸⠠⡶⠬⣉⡉⠁⠀⣠⢄⡀⠀⠳⣄⠑⠚⣏⠁⣪⠇ ⠀⢯⡊⠀⠹⡦⣼⣍⠛⢲⠯⢭⣁⣲⣚⣁⣬⢾⢿⠈⡜⠀ ⠀⠀⠙⡄⠀⠘⢾⡉⠙⡟⠶⢶⣿⣶⣿⣶⣿⣾⣿⠀⡇⠀ ⠀⠀⠀⠙⢦⣤⡠⡙⠲⠧⠀⣠⣇⣨⣏⣽⡹⠽⠏⠀⡇⠀ ⠀⠀⠀⠀⠀⠈⠙⠦⢕⡋⠶⠄⣤⠤⠤⠤⠤⠂⡠⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⣄⣀⣀⣀⣠⠔⠁⠀

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⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀ ⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀ ⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀ ⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀ ⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁ ⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃ ⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⡱⠖⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠆⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠒⢴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢨⠀⣰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢹⡀⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⢠⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⣀⡠⠋⠀⠀⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⣄⠊⠁⠀⠀⠀⠀⠀⢀⡨⢦⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠔⠊⠁⢀⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⡀⠄⠂⠉⢀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢊⠠⠒⣁⠤⠐⣀⡁⠤⢤⠃⢀⣀⡠⢄⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡪⢐⡡⢐⠩⠐⠊⠁⠀⠀⠀⠚⠉⠉⠀⠀⠀⠙⠢⣀⡇⠀⠀⠀⠀ ⠀⠀⢠⡪⡪⡲⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⠀⠀ ⠀⣰⣿⠞⠉⠀⠀⠀⠀⠀⡄⡰⡆⠀⠀⠀⠀⠀⠀⢐⣌⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⡐⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣦⣠⣴⣾⡿⢿⣷⣦⣄⣴⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠙⢻⣿⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⡟⠀⠀⣴⡿⠿⣤⡀⠀⢻⣿⣷⡀⠀⠀ ⠀⢀⣾⣿⣿⡇⠀⠘⢿⣤⣤⣿⠃⠀⢸⣿⣿⣿⡄⠀ ⢠⣾⣿⣿⣿⣷⡄⠀⠀⠉⠉⠀⠀⢀⣾⣿⣿⣿⣷⡄ ⢸⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇ ⣼⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⠟⣿⣿⣿⣿⣟⠁⣀⡀⢀⣀⠈⣻⣿⣿⣿⣿⠟⣿ ⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣿ ⢻⡇⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠀⠀⢰⡿ ⢸⣇⠀⠀⢸⣿⠀⠀⠀⠉⠉⠀⠀⠀⣿⡇⠀⠀⢸⡇ ⢸⣿⣆⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣰⣿⡇ ⢸⣿⡘⠂⠀⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠀⠐⢃⣿⡇ ⠀⠙⢛⣂⣀⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣀⣐⡛⠋⠀ ⠀⠀⠿⠛⡿⡟⡟⠃⠀⠀⠀⠀⠈⢻⢻⢿⠛⠿⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁

⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣋⡉⠀⠀⢀⣤⣀⣉⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠀⠀⠸⢿⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠛⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠤⠒⠺⠿⣷⡀⠀⣏⠀⠀⠀⠻⠿⠿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⢀⠞⠋⠀⠀⠙⣄⠀⠀⠀⢀⠜⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠒⠒⢺⣰⠘⡆⠀⠀⠀⠉⠉⠉⠁⠀⢸⣿⣿⣿⠟⠉⠀⠈⠙⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠘⠿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠉⠉⢲⣄⠀⠀⠀⠀⠀⠈⠲⣤⣴⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⣖⠿⣅⣠⡤⠤⠒⠂⠉⢁⣨⠇⠀⠀⠀⠀⠀⠀⡟⠛⢿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠓⠒⠛⠒⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⡆⠀⢹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢴⠇⠀⢈⡇⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⠦⠤⣤⠤⠤⠤⠒⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠘⠁⠀⡿⣆⠀⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠒⠒⣲⣾⠁⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⠉⠓⢦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⡆⠀⣹⠀⢸⣀⣀⠀⠀⠀⣀⣀⣤⡟⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠹⡄⠀ ⠀⠀⠀⠀⠠⣄⠀⠀⢀⡼⠁⠀⠀⠀⡇⠀⢿⠀⡏⠀⠀⠉⠉⠉⠀⢀⡞⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠀⠀⠀⢹⠀ ⠦⠀⠀⠀⠀⠨⠷⠤⣼⠑⠀⠀⡆⠀⢇⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣇⢀⡠⠴⠒⠒⠒⠒⠒⠢⢤⡀⣸⠂⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣼⠁⠀⠸⡄⢀⠇⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⠊⣸⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⡈⢣⣄⡀⠀⠀⠀⡇

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⣿⣁⢈⠉⠉⣉⣉⡧⠀⠀⣼⠋⠁⠀⠘⠢⡾⠋⠉⠉⢳⠀ ⠐⠛⢻⣯⠀⢠⠋⠉⠀⠀⢸⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇ ⠀⠀⢸⡿⠀⢸⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀ ⢴⣯⣉⣁⣀⡈⠒⠒⡀⠀⠀⠈⠻⣧⡀⠀⠀⠀⢀⡠⠊⠀⠀ ⠈⠉⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠉⠢⡠⠒⠁⠀⠀⠀⠀ ⢰⣖⠒⡀⠀⢠⣴⠒⡂⢀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀ ⠀⠙⣦⠈⢄⡾⠃⡜⣴⠟⢉⢥⡈⢢⢶⣯⢀⠁⠀⢰⡯⠉⡇ ⠀⠀⠈⢿⡬⢁⠌⢠⡿⠁⠆⠈⡇⢸⣿⣇⢸⠀⠀⢸⡇⠀⡇ ⠀⠀⠀⢸⡯⢻⠀⢸⡇⠀⡀⢸⠇⢸⣿⠃⢈⠀⠀⣿⡀⠀⡇ ⠀⠀⠀⣾⠁⠘⠀⢸⣧⠀⠈⠁⢀⠎⣿⠀⢺⠀⣰⡿⠀⢠⠁ ⠀⠀⠀⠛⠒⠃⠀⠈⠛⠳⠶⠖⠋⠀⢿⣄⡀⠉⠁⠀⡠⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀

⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀ ⠀⠀⠀⣰⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⣇⠀⠀⠀ ⠀⣠⡀⣿⠑⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⣿⣀⣄⠀ ⠀⡟⢳⣿⡀⢣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡸⢀⣿⡟⢻⠀ ⠀⡧⠀⢻⣧⠈⢆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢠⠃⣸⡟⢠⢸⠀ ⠀⣷⠘⠀⢻⡆⠘⢆⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣰⠃⢠⡿⠀⠇⣼⠀ ⠀⢹⣇⠀⡈⢻⣆⠈⠳⣜⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠞⠁⣰⡟⢁⠄⣴⡟⠀ ⢻⡶⣿⣆⠈⢢⡙⠳⣦⡈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢁⣤⠾⢋⡴⠃⣰⣿⢿⡟ ⠀⢻⡄⠙⢷⣄⠙⠦⣈⠙⢶⣜⣿⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣃⡶⠋⢁⡴⠋⣠⣾⠟⢁⡞⠀ ⢀⠀⢳⡀⠀⠙⠳⣦⣈⠳⢦⣹⣿⣧⡰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢇⣼⣿⣏⡤⠞⣁⣴⠞⠋⠀⢀⡞⠀⠀ ⠸⣿⢦⣿⣄⠀⠀⣀⠙⠳⣤⣙⣏⢙⣻⣿⡏⠛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢹⣿⣿⡋⣹⣏⣠⠞⠋⣁⠄⠀⣠⣾⡵⢻⠇ ⣄⡹⣆⣬⡙⢷⣄⡈⠙⠲⢬⣿⡿⣦⣹⣿⣷⣄⣙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣋⣠⣾⣿⣏⣴⢿⣿⡥⠖⠊⢁⣠⡼⠋⣡⣠⢏⣠ ⢻⡟⠻⢿⣟⡀⠉⠛⠶⣦⣤⣽⣷⡈⢭⣻⣿⡈⠭⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠉⢁⣿⣟⡭⢁⣼⣯⣤⣴⠶⠟⠋⠀⣪⡾⠟⢫⡟ ⠀⢻⣆⡀⠉⠻⠦⣄⡒⠦⣽⣷⡈⢿⣾⣿⣿⡟⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢻⣿⣿⣿⡿⢁⣾⣫⠤⢒⣠⡴⠟⠉⠀⣠⡟⠀ ⠀⠀⠙⣷⣄⠑⠦⣄⠉⠛⠲⢿⣿⠿⠛⢻⣿⣿⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢧⣾⣿⡟⠛⠷⢿⡿⠖⠛⠉⣀⠴⠊⣀⣾⠋⠀⠀ ⠀⠀⠀⢻⣿⠷⢦⣄⣉⠓⠲⠦⣽⣷⣶⣾⣿⠃⠈⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠀⠘⣿⣷⣶⣶⣯⠴⠖⠚⣋⣡⡴⠾⣿⡗⠀⠀⠀ ⠀⠀⠀⠀⣙⣶⣄⠀⠉⠹⣻⣶⣿⣏⣀⠙⢿⣿⡿⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⢿⣿⡿⠟⣀⣹⣿⣶⣞⠉⠉⠀⣀⣶⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣟⠛⢶⡦⢤⣶⣾⡿⣿⣿⠛⠿⢿⣿⣿⠋⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠙⣿⣿⣿⠿⠛⣿⣿⢿⣗⡲⠦⢴⣶⠞⣫⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣙⣷⠦⠤⠤⠤⠴⣖⣯⣿⣿⣷⣾⠟⣿⣶⣿⡇⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠘⣿⣶⣿⠻⣿⣶⣿⣿⣿⣗⡦⠤⠤⠤⠤⣾⣋⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⡥⢞⡿⣿⣿⣧⣬⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣥⣼⣿⣿⢿⣳⢤⣅⣀⣀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣋⣛⣁⣀⣴⠾⠋⠐⣻⣿⣿⣶⣿⣿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣶⢿⡿⣿⡃⠙⠳⣦⣄⣘⣛⣙⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣁⣄⣤⡾⣫⢏⡴⢛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢧⡙⣜⢿⣦⣤⣈⣿⡯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠶⢿⣿⠷⢿⣥⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣿⢾⣿⣷⡶⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣤⠟⡇⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⣿⡃⠀⠀⢀⡾⡃⠀⣿⠀⠀⠀⠀⢠⡼⠋⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⠟⠋⠁⣰⡟⣠⡇⠀⢻⡀⠀⢀⣴⠏⢀⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⣶⣿⡇⠠⠸⣧⣠⠟⠁⢀⣾⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠐⣧⡀⠀⠀⠀⣸⠏⢾⠿⣿⡇⠀⠀⠙⠃⠀⢠⣾⣿⡇⠀⣿⡆⠀⠀⢀⣀⠀⠀ ⠀⠀⠙⢦⣀⡾⢿⣶⣮⣅⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠅⠀⢹⣇⣠⠶⠛⠛⠀⠀ ⠀⢠⣄⣀⣹⡇⠘⣿⣿⣿⠿⠆⠀⠒⢻⣾⣶⣶⣤⡀⠀⣠⣼⡟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣸⣧⠀⠀⠀⠀⠰⡆⠀⠀⠈⠿⣿⡿⡟⠻⠞⢯⣼⣇⣀⠀⠀⠀⠀⠀ ⠀⠠⡾⠛⠁⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣶⣶⣶⣶⣶⠶⠛⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠛⠛⠛⢻⣇⠀⠀⠀⠀⠉⠳⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡆⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢸⠇⠀⠀⠀⣷⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠞⠛⠛⡆⠀⠀⠀⢸⣆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣋⢀⣀⣠⣴⣾⠇⠀⠀⣰⠟⠙⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⢁⡴⠋⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⠟⢛⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⡄⠀⣀⡀⠨⣙⣏⣉⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⢿⣿⣿⣿⡿⣟⣿⣯⣿⣷⣿⢾⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣒⡛⢫⠤⣠⢤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣯⣿⢿⣿⢯⣿⣯⣿⣿⣻⣞⡷⣿⣽⣻⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢮⣭⣉⡓⠺⠊⢉⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣻⢿⡿⣯⢿⣷⢯⡷⣯⣟⠷⣯⡗⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣩⣿⣿⢿⣷⣄⡙⢮⠭⡁⢠⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣯⢿⣽⡿⣾⣻⣽⣳⣞⣟⡧⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⡴⠹⢿⣿⣀⣿⣿⣯⣍⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡿⣯⣿⡽⣟⡾⣵⢫⣾⡱⢯⡜ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣞⣰⣀⣾⡷⠘⣿⣿⣟⣩⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⢷⣟⣿⢯⡷⣏⡟⣶⡹⢇⡞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣰⢯⣾⣿⣿⡿⠁⠀⠀⠼⢿⣿⠥⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⡾⣟⣯⢿⡼⣹⢶⡹⢣⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⡽⣯⣟⢾⡱⣏⠵⣋⠎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣳⢯⣏⡗⣎⠳⡌⠆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡗⣮⡝⣬⢳⠉⡎ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⣯⢷⣫⢗⡭⢎⢧⡙ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⢛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣯⣟⣧⡟⡼⣉⢆⠣ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⢿⡟⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡂⠭⢊⠻⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣻⣞⡽⣲⢍⡎⢇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⠒⠐⢀⠀⠠⠐⡆⢯⡹⡹⢛⡯⢭⡹⣿⣿⣿⣿⣿⣿⣿⡿⣾⢯⣷⣻⣜⡳⢎⡜⠦ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢎⢦⡹⢄⡄⣌⣩⣝⠾⣡⢃⠡⠃⡘⢧⠿⣽⣻⣿⣿⣿⣿⣿⣽⣿⣟⣷⣻⡼⣝⢮⡙⡖ ⣿⣿⣿⣿⣿⣿⣿⠃⣾⣷⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢉⣩⣁⣳⣶⣦⣤⣤⣈⣥⢛⡞⣶⣿⣜⣫⢝⣶⣫⢞⣡⣀⣒⣀⡴⣨⡽⣎⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⢷⣻⡜⣮⢱⢣ ⣿⣿⣿⣿⣿⣿⣿⡇⣿⢻⠇⠛⢧⠀⠀⠁⠀⠀⠀⠾⠛⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⢾⣯⢷⣻⣼⢣⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⠀⣶⣿⠃⠀⠂⠀⠀⢰⣶⡾⠟⠫⣈⢿⡿⠟⣨⣿⣿⣿⢿⡆⠀⠈⣿⣿⣿⣿⣿⡟⢹⣯⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⢯⣿⢯⡿⣟⡾⣏⣞ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⡀⢿⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣉⣛⠶⣿⣿⣿⣿⠟⣿⠃⠀⢠⣿⣿⡏⢿⣯⣭⠷⣭⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣿⣿⣯⣟⣯⡿⣽⣻⢞⡵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠱⡈⠹⡄⠀⡁⠀⠀⠀⠀⠀⠈⠙⠋⣙⣹⣿⣿⡿⠋⠀⠀⠀⠀⢺⣿⣿⣿⣆⢻⣿⣻⣶⣷⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣟⣾⢯⡿⣽⡷⣯⢿⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢲⡾⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠜⡹⠟⠉⠀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣞⡽⢿⣿⡿⢿⡟⢶⣡⣿⣿⣿⣿⣿⣿⣿⣳⣯⢿⣯⣟⣷⣻⣽⡳⣏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⣀⡆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠱⠂⠄⣙⢣⣟⣮⣿⣿⣿⣿⣿⣿⣿⣟⣷⣻⣟⡾⣽⣞⡷⣯⡽⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⢈⣿⣿⣿⣿⣍⠣⡉⠴⣌⢷⣾⣻⣿⣿⣿⣿⣿⣿⡿⣞⣯⢷⣯⡟⣷⣫⡽⢶⡻⣵ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢺⡿⢏⢀⣠⣀⠀⣦⣀⢻⣿⣿⣿⣿⣣⣝⡳⣎⣿⣽⣿⣿⣿⣿⣿⣿⣟⣿⡽⣯⣟⢶⡻⣵⢣⡟⣯⢳⢧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⢰⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣟⢢⣏⣷⢿⣭⣻⢷⣿⣿⣿⣿⣽⣾⣳⣟⣷⣫⢯⡷⣭⢳⡝⣮⢛⡼ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣞⡿⣎⡶⣿⣿⣿⣿⣿⣿⣞⡷⣟⣾⡳⣏⡷⣹⢎⡷⣙⢦⣋⠖ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣽⢳⢏⣾⣿⣿⣿⡍⣉⣛⣻⡿⢿⣾⣽⣝⣳⣝⢮⠳⣍⠶⣉⠞ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠿⠾⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣞⢿⣺⣿⣿⣿⣿⣿⡉⢿⣿⡙⠲⣤⣈⡙⠻⠮⣽⣙⡌⢣⠱⣊ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⣆⠠⡀⠀⠀⠀⠀⠘⠉⠁⠀⠀⢀⣠⣶⣿⢿⡛⣴⣿⣻⢻⡽⣷⢯⣞⣿⣿⣷⣿⣿⣿⣿⣿⣿⣡⡄⠀⢢⠉⠱⣄⠀⠉⠈⠐⠃⠄ ⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⠹⣄⠙⣄⡀⠀⠀⠜⢢⠳⣾⣿⣿⣿⣿⣿⣷⣯⡷⢭⡷⣯⢿⣯⣿⢾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠉⠢⠈⢦⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢱⡙⢧⡈⠻⣦⣄⠘⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⢌⢧⡻⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⠀⠀⠃⠈⣷⡀⠀⠀⠀ ⣿⣿⣧⣿⣿⣧⣿⠟⠀⠀⠀⣠⠀⠀⢀⣠⠀⠀⢿⠛⠻⢤⡘⠻⣤⡀⠀⠀⠀⠀⢀⣀⣠⣤⡼⣼⢧⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡄⠀⠀⢀⠸⡇⠀⠀⠀ ⣿⣷⡿⣿⣽⠟⠁⠀⣠⡏⢰⡇⠀⠀⢸⣿⠀⠀⠘⣧⠤⠄⠙⢶⣌⠛⢶⣤⣶⣶⣿⣾⣿⣯⣟⣯⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣳⢯⣿⡄⠘⠤⢂⠙⢦⡀⠀ ⣟⡾⣽⠟⠁⠀⠀⢠⡿⠀⣾⡇⠀⠀⠹⢿⣀⣤⡀⠙⢆⡰⣳⣦⣈⡛⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣿⣿⣿⣿⣿⣿⣷⢫⣞⢿⡃⠄⢂⠀⢣⢳⡀ ⣯⡟⠃⠀⡰⠀⠀⣿⠃⢸⣿⡇⢀⠀⡀⠀⠈⠻⢿⣷⣮⠵⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⣿⣿⣟⡿⣷⣿⠿⣝⡷⣎⠲⣅⠀⠀⠈⠀⠡⢓ ⠋⠀⣀⠔⠁⠀⢀⡇⠀⣾⣿⡄⠈⣆⠘⡀⠀⠀⠀⠹⢿⣿⣿⣟⣯⣙⣌⣙⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⣿⢯⣟⣿⣿⡿⣿⡽⣾⣽⣻⣿⡹⣌⢳⣍⡒⠈⠄⠀⠀⠀⠀⠈ ⠀⠀⠀⠠⣆⠀⢸⠀⢠⠿⣿⡇⠀⢸⣧⠑⢦⠀⠁⠀⠀⢈⠛⢿⣿⣽⣶⣯⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣻⣞⡷⣿⢯⣟⣷⢳⣿⣯⡕⢎⠲⡡⠌⠐⠠⡀⠀⢀⠀⠀ ⠀⠀⠀⠀⠈⢆⡇⠠⠊⠀⣿⡇⠀⠀⣿⡷⣄⠳⣤⠀⢠⠀⠀⠀⠘⠻⠿⣿⢿⡿⠟⢉⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣟⣾⢿⣽⡻⢾⡭⣟⣿⡗⢮⡡⠂⠑⣂⠀⡲⢱⠀⠄⡁⠀ ⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣿⣷⠀⠀⢸⡷⠜⢧⡈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡾⡽⢧⠿⣜⣿⡟⢢⠑⡤⠘⢤⠣⢌⢣⠘⠠⠀⠂ ⣾⣦⡀⠀⠀⠀⠀⢙⣦⠀⣿⣿⠀⠀⠀⠀⠆⠐⠛⣦⣄⠠⣄⠀⠰⠀⠀⠀⠀⠀⡐⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⡿⣷⣿⣻⠯⣷⣎⡿⡍⢦⡙⠴⡁⠎⣇⠫⢄⠊⢀⠁⠀ ⠀⠀⠉⠲⣭⣯⣿⣾⣿⣷⣽⣿⡀⠀⠀⠀⠁⠀⣨⡇⠸⣷⣄⠁⠄⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣿⣿⡣⢿⡱⢎⡝⠻⠶⣾⡽⣙⠦⡙⠤⠃⢘⠀⢳⡈⡐⠀⠀⠀ ⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣇⢠⠐⡁⢰⣿⠿⡷⠀⠹⡙⣶⣄⡀⠀⢠⡄⢀⣾⡿⣟⢣⠟⡼⢫⣿⢿⣿⣿⣿⡿⣿⣷⣏⠂⢜⡱⣌⡄⢣⣝⠂⡉⠒⡁⠀⠀⠂⠐⠈⠀⠠⠀

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣹⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠷⢶⣤⣀⣀⡀⠀⡾⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣷⠾⣿⣄⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡉⠻⢧⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡿⠛⠦⣈⠙⢷⡀⠈⠳⣄⠀⢀⣠⠤⣤⢤⡄⠀⠀⠀⠀⠀⢀⡏⠻⣆⣀⡾⠃⠀⢀⡠⠔⠒⠒⠒⠒⠢⢤⣀⠀⠙⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣦⣄⠈⠓⠖⠈⣄⠀⠈⠓⠛⠁⢀⣼⠟⠀⠀⠀⠀⠀⠀⠈⣇⢀⡾⠛⠁⢠⣖⠭⠖⠚⠛⠉⠉⠙⠛⠛⠛⠷⣄⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⢶⣄⠀⠈⠉⢳⡀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⠀⠀⣰⠋⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠈⠙⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢠⠇⠀⠀⠀⢠⡖⠉⣠⣄⣈⠙⢦⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣾⠀⠀⠀⠀⡞⠀⣾⣿⣿⣙⡇⠈⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢻⡀⠀⠀⠀⢷⠀⢿⣿⣿⣿⠇⢠⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠘⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢻⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠳⣤⣈⣉⣠⡴⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠈⠷⢤⣤⣤⣤⣤⠴⣿⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠚⣹⡏⠙⠀⠀⠀⢰⡶⠶⢤⣤⣀⣀⠈⠙⠳⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠀⢀⣀⣠⠤⠞⠁⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠙⣷⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠷⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⡴⣿⣿⡿⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠦⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠔⢚⢉⡼⢁⡼⠁⠀⠀⠀⠀⣼⠃⠀⠀⡀⠀⠀⠀⢸⠀⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠈⠻⣍⣩⣍⠉⢉⣍⡉⣩⠥⢤⠔⢩⠟⣲⠞⠁⠀⠀⠀⢀⣼⠏⠀⠀⢰⡏⠉⠙⠓⠛⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠈⠁⢈⡽⢿⣿⠿⢦⡴⠋⣉⡽⠞⠁⠀⠀⠀⠀⣠⡾⠃⠀⠀⢀⣸⣷⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⢀⣠⡾⢿⡇⠀⠀⠀⢸⡑⠃⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⡋⠀⠘⣧⠀⠀⠀⠘⠷⠤⢾⣀⣤⠤⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢈⣿⠟⠻⠷⠶⠶⠶⠶⠶⠿⠟⠛⠋⠁⠀⠙⣷⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⢷⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣭⠿⠯⢽⡓⠶⠤⠼⠇⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⣧⠤⠴⣒⣫⠭⢯⣳⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⠋⣨⠷⢿⠛⠛⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠐⠒⠒⣦⡜⠙⣯⣹⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣏⣀⣨⣇⣤⣤⡤⠤⠤⠶⠶⠶⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠦⣤⣤⣀⣀⣀⡀⠀⣞⠁⠹⣦⠼⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠁⠀⠀⠀⠀

⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⡈⠀⢀⣴⣦⢶⣴⣴⣦⢶⣴⢦⣶⡴⣦⡶⣴⣦⢶⣴⣤⡀⠀⠠⡀ ⠀⠀⣿⣟⣾⠗⢀⢸⣾⢿⣽⣻⣾⠻⠝⠛⢉⡈⠛⠻⢾⣿⠀⠀⠀ ⠀⠀⣿⣾⠷⠞⣹⡿⣯⢿⡞⠋⣡⣴⣾⢿⣟⡿⣟⣷⣄⠹⠀⠀⠀ ⠀⠀⣿⣯⣤⣼⡿⣽⡛⢁⣴⣿⣻⣽⡾⣯⡿⣽⣟⣷⣻⡆⠀⠀⠀ ⠀⠀⣿⣽⣻⢯⡟⠃⣴⣿⣻⢾⣽⣳⡿⣽⣻⣽⡾⣯⣷⢿⠀⠀⠀ ⠀⠀⣿⣳⡿⠏⣠⣿⣟⣷⣻⣯⣟⣷⣿⣻⣽⣷⣻⢷⣯⣿⠀⠀⠀ ⠀⠀⣿⣽⠃⣴⣿⣳⢿⣞⡿⣿⠆⠀⠀⢠⣿⣞⣯⣿⣳⡏⠀⠀⠀ ⠀⠀⣿⠃⣼⣻⢾⣽⣯⣿⠟⠁⠀⣠⣄⣸⣿⢾⣽⣞⣯⠅⠀⠀⠀ ⠀⠀⡇⣸⣷⣻⣯⣷⣻⣿⡀⣠⠞⠹⣿⣿⢯⣿⣞⣯⠏⢸⠀⠀⠀ ⠀⠀⢁⣿⣽⣯⢿⣽⡟⢿⠗⠉⠀⢠⣿⣽⢾⣯⣟⡿⢀⣾⠀⠀⠀ ⠀⠀⢸⣟⣾⡽⣯⣿⠀⠀⠀⣠⣶⣿⣻⢾⣟⣾⡽⢀⣾⣻⠀⠀⠀ ⠀⠀⣿⣟⡷⣿⣻⣿⣤⣤⣤⣬⣿⣷⣻⣯⢿⠞⢠⣾⢯⣿⠀⠀⠀ ⠀⠀⣿⣽⣻⢷⣟⣿⣻⣟⣿⣻⣟⡾⣷⡻⠋⣰⣿⢯⣿⣽⠀⠀⠀ ⠀⠀⢻⣷⣻⢿⣾⣳⡿⣾⡽⣷⣻⡽⠛⣠⣾⢿⡽⠿⢾⣽⠀⠀⠀ ⠀⠐⡌⢳⣿⣻⡾⣽⣻⢷⣟⠏⢃⣤⣾⢿⡽⡟⣁⣤⣾⣿⠀⠀⠀ ⠀⠀⣿⢦⣈⣑⠛⠛⣋⣁⣤⡾⣿⡽⣾⣻⡏⠛⣡⣾⣟⣾⠀⠀⠀ ⠃⠀⠙⢿⣯⣟⣿⣻⣯⣿⣽⣻⣷⣟⣯⣷⣷⣶⣿⣳⡯⠋⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣼⢿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡝⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠈⣿⣿⣮⣛⢿⣿⡿⠿⠿⢿⣿⣿⣿⢿⣿⣿⣿⢧⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣹⣧⣽⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡟⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⡟⠁⠀⠀⠀⣤⣴⣶⣶⢸⣶⣶⣄⣘⣿⢳⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠇⠀⣠⣶⡾⢿⣿⣿⣿⠀⢺⣿⣿⡿⣿⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠙⠁⠀⠘⣿⣿⣦⣈⣼⣿⡿⠀⠀⠹⣤⣥⣿⡇⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠉⣿⣿⣿⡿⠟⠁⠈⣲⠃⠘⢻⣿⠷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢰⣦⡈⠋⠁⠀⠀⠐⠊⠀⠈⠂⢀⠁⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠒⠓⠀⠀⠀⠀⠀⠀⠀⠶⠋⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿ ⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣆⠀⠀⠀ ⠀⠀⠀⠘⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠃⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀ ⢀⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣤⣤⡀ ⠘⠷⠤⠤⠤⠤⠤⢤⣤⢤⣤⠤⠤⠤⠤⠤⠤⣤⡤⣤⡤⠤⠤⠤⠤⠤⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠶⠶⠶⠿⠶⠷⠶⠶⠶⠶⠶⠶⠾⠶⠿⠶⠶⠶⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣾⠋⠀⢀⣠⡄⠙⣷⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣧⠀⠀⠿⠟⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀ ⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀ ⠀⠀⠀⠈⢿⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⣦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠋⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠉⠳⣶⣄⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⡻⣧⠀⠀⢀⣀⡤⠶⠒⠒⠉⠉⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⣽⣶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠹⡄⢀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣟⡒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠲⠶⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⣂⣠⡤⠤⠿⠒⠚⠋⠉⠉⠉⣤⣾⣿⣿⣿⣿⣿⡏⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡉⠉⠛⣶⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣾⡭⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢻⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⠀⠀⣧⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⣿⣿⣿⣿⣟⠛⠛⠛⠲⠦⣄⣈⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡋⠀⣀⣀⣀⡏⢹⠀⠀⠀⠀⠀⠀ ⣤⣖⡿⠷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠓⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⡄⠀⠀⠈⠉⢸⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠛⠛⠋⠉⠙⠓⠲⣾⣀⠀⣄⠀⠀⠀ ⠀⠀⢠⡟⣴⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⢀⣼⡠⢼⣿⣿⣷⣌⠳⠀⠀ ⠀⠀⡼⢰⠇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⡀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢀⣠⠶⠋⠋⢠⢏⣼⠯⠛⣿⣧⠀⠀ ⠀⠀⡇⢸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢭⣛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⠏⠀⠀⠀⠀⠤⠖⠛⠉⠀⠀⣠⣴⣿⠟⠓⠀⠀⠈⢹⡆⠀ ⠀⠀⢳⢸⡆⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠓⠢⠤⣍⣻⣦⡙⠲⡄⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡞⠋⠁⠀⠀⠀⠀⠀⢠⣼⠁⡇ ⠀⠀⠸⣾⣧⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣹⠳⣽⣦⡘⢦⣀⣠⡴⠋⠁⠀⠀⠀⠀⢿⡟⠓⠶⠾⠛⠛⠛⠉⠁⠀⠐⠀⠀⠀⠀⠀⠀⢸⣿⢏⡄⠀ ⠀⠀⠀⠹⣾⣆⢂⠀⠈⢷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠈⠻⣷⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣞⢂⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⣀⢒⣾⣾⠟⡡⠎⠀⠀ ⡇⠀⠀⠀⠘⢿⣎⠃⠀⠈⢷⡀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢦⣤⣤⣤⣤⣤⣤⡤⠶⣾⠛⠋⠴⠛⠁⠀⠀⠀ ⠹⣄⠀⠀⠀⠀⠙⠷⣄⠀⠌⢳⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠫⣷⠲⠤⢤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠀⠀⠀⣸⢃⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⣝⢷⣦⣄⠀⠀⠀⠈⠙⠲⠤⠿⣆⠀⠀⠀⠈⠳⣄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⢉⡟⠀⠀⠀⠀⠀⠀⠀⣰⢃⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠣⣙⢿⣍⠓⠶⠦⠤⠤⠤⠤⠾⢷⡄⠀⠀⠀⠈⠳⢄⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡾⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠌⠙⠶⢦⣄⣀⣀⣀⣀⣀⣹⡷⣄⡀⠀⠀⠀⠈⠙⠲⠦⢄⣀⣀⣀⡀⠀⣿⣀⣀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣠⡶⣋⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠁⠀⠀⠀⢨⡙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣛⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢈⡝⣳⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣴⣖⠒⠋⠉⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢇⠀⠀⠀⠀⠉⠑⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠽⢦⣀⠀⠀⠀ ⠀⠀⠀⠀⠈⡧⢴⡒⠋⠉⣀⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⢧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣗⢋⣭⣍⣁⠈⠁⠀⠀⠀⡤⠞⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⡰⠃⠫⣧⣿⣽⠽⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⠀⠀⠀⢸⠃ ⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠧⠛⡆⡇⠀⠀⡾⠀ ⠀⠀⢰⣇⠀⢈⣉⠳⠀⠀⠀⠀⠀⠀⠀⢹⣆⠘⢯⣡⠃⠀⣰⡇⠀ ⠀⠀⠀⠈⠉⣩⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⢤⠀⠐⠁⣇⠀ ⠀⠀⠀⠀⠸⡥⠤⠤⢿⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⢸⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠳⡖⠊⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀ ⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠸⣄⣀⠀⠀⠀⣠⠴⠚⠙⣏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡆ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠙⡆⠀⢀⡴⠋⠀⡀⠀⠀⠰⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠐⠋⠐⠊⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣦⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⢀⣤⠄⢾⣿⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⣸⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠐⠶⠾⠛⠉⠀⠀⠀⠀⠀⢀⡼⠃⠀⢈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠒⠒⠒⠋⠀⠉⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠻⣦⡼⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠘⠉⣿⠛⠶⠤⣄⣠⠤⠴⠶⢤⣄⡀⢀⣠⣤⠤⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠹⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀ ⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢀⣤⠞⠉⣿⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠛⠁⠀⠀⢹⡄⠀⠀⠀ ⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⣦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢻⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠛⠲⣄⢷⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣿⣿⣿⠆⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢠⡿⣄⠀⠀ ⠀⠀⠀⢸⠀⠙⢦⣄⠀⠀⠀⣀⣴⠏⠁⠀⠀⠀⠀⠈⠻⣷⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⣿⠀⠙⣆⠀ ⠀⠀⠀⠸⡆⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⢦⡀⠀⠀⠀⠀⠀⠸⣦⣠⣄⡀⠀⠀⠀⠀⠀⠀⠛⠻⠂⠀⠀⠀⠀⠀⣸⣋⣀⡀⠀⠀⢠⡾⠁⠀⠀⢻⡄ ⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠉⠛⠻⣏⡀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣧⠀⠀⠀⠈⠙⢶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⡶⠛⠉⠉⠙⢻⡟⠁⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⡀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠘⠳⣦⣄⠀⢀⡾⠂⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⡅⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠚⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣀⣀⣀⣀⣤⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠿⠛⠛⠻⠿⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⢸⡆⢀⣀⣀⣤⡀⠀⠀⢀⣤⣀⣀⡀⠀⡟⣸⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⠁⣿⣿⣿⣿⡟⠀⠀⠸⣿⣿⣿⣿⠆⣿⠟⠀⠀⠀⣀⠀⠀ ⠀⢰⡟⢿⣆⠀⠀⣿⠀⠙⢿⣿⠟⠀⣠⣄⠀⠹⣿⣿⠟⠀⢹⠀⠀⣠⡿⢻⣇⠀ ⣠⡾⠃⠈⠻⢷⣦⣽⣄⡀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⢀⣠⣿⣤⡶⠟⠁⠘⢿⣆ ⠻⠷⠶⠶⣶⣤⣈⠙⠻⣿⣷⣦⠀⠸⠋⠙⠟⠀⣠⣾⣿⠟⠋⣁⣠⣴⠶⠶⠾⠟ ⠀⠀⠀⠀⠀⠉⠛⠿⣶⣼⠿⣿⣲⡤⡤⡤⢤⢰⣿⡏⣿⣶⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡄⠻⣹⡟⡟⡟⣻⣻⠽⠁⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣶⠾⠶⠾⠟⠋⣁⣼⣷⡀⠀⠉⠉⠉⠉⠀⢀⣼⣧⣀⠉⠛⠷⠶⠿⣶⡄⠀ ⠀⠀⠙⣷⡄⢀⣴⠿⠛⠁⠀⠙⠳⠶⠤⠴⠶⠞⠋⠀⠈⠙⠻⣶⡄⠀⣾⠟⠁⠀ ⠀⠀⠀⢸⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⡿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⢰⡄⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⢀⡆⠀⠀⠀⠀⠀ ⠀⠀⢹⣷⣤⣀⢸⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⢀⣠⡆⠀ ⠰⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠀⠀ ⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡄⠀ ⢷⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⠖ ⠈⢿⣿⣿⣿⣿⣿⠿⠿⣟⠻⣿⣿⣿⣿⣿⠟⣻⠿⣿⣿⣿⣿⠏⠀ ⠀⠈⢿⣿⣿⣿⣍⢀⢤⠀⠀⠀⠉⠻⠋⠁⠀⠀⢈⣹⣿⣿⡟⠀⠀ ⠀⠀⠸⣿⣿⣏⠁⢁⠤⠵⣄⠀⠀⠀⠀⠀⡠⠎⡘⠈⣿⡿⠀⠀⠀ ⠀⠀⢠⠫⢽⡅⢀⠃⢠⢲⣾⠆⠀⠀⠐⣯⢲⡄⢱⠀⣝⡗⡆⠀⠀ ⠀⠀⢸⠀⣔⢱⠀⠂⢸⣿⡿⠀⠀⠀⠀⣾⣾⡇⠀⡰⠇⠘⡁⠀⠀ ⠀⠀⠀⠑⢄⢹⡄⠀⠈⠙⠁⠀⠀⠀⠀⠙⠛⠀⢠⢋⡠⠔⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠤⡀⠀⠀⠀⠐⠆⠀⠀⢀⠠⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣰⡉⢵⠢⢀⣣⣃⢠⡶⢙⣆⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠔⠒⠒⠒⠛⠓⠒⠒⠚⠋⠛⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡄⠉⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⡈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠙⢦⡘⠻⣦⡀⠀⠀ ⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⣷⡀⠀ ⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠹⣧⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠹⡆ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧ ⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸ ⢿⡇⠀⠀⣤⡀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⣴⠋⠀⠀⠀⢸ ⢸⣇⠀⠀⠙⢿⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠃⠀⠀⠀⠀⡘ ⠈⣿⡄⠀⠀⠈⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⡇ ⠀⢻⣿⠀⠀⠀⢻⠀⢻⣀⣤⣀⡤⠤⠤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⠀⠀⠈⠓⠲⠤⣄⡀⣏⢸⡀⠀⠀⠀⢰⠀ ⠀⠘⣿⡤⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠐⠟⠋⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⠁⠘⣧⠀⠀⠀⡜⠀ ⠀⠀⠸⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣘⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣧⣴⣶⣶⣶⣶⣤⣄⣀⠀⢸⡇⠀⡼⠁⠀ ⠀⠀⠀⢿⡆⢰⡏⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢳⣸⠁⠀⠀ ⠀⠀⠀⢸⣧⣾⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⡠⠄⡶⢤⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⡟⠀⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⡇⠀⠙⠓⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣄⠀⠀ ⠀⢰⣶⡿⠃⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢱⡄ ⠀⣿⡄⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣶⠇⣾⡇⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⣸⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀ ⠀⠀⢿⣖⠀⠀⠀⠀⠀⣴⠊⠁⠀⠀⢀⡴⠾⠃⠀⠀⠀⠀⣰⣿⣿⡀⣿⣿⣧⠀⠀⠀⠀⠀⣴⠶⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⣠⠇⠀ ⠀⠀⠈⠻⣆⣀⣀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⣠⡤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⣏⠙⠓⠢⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣿⡀⠙⣧⡀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢀⡘⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡿⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠸⣷⠀⣿⡀⠀⠀⣀⢀⡀⢠⠄⠀⠀⠘⡗⢀⠀⢰⡆⠰⣧⠠⡄⠀⣾⠇⡸⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⣆⠸⣧⠀⠀⣗⡞⢀⠟⠀⠀⠀⢨⡇⠈⠀⠸⣇⢀⣈⣀⠃⢸⡟⣼⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣴⢿⣿⡛⡞⡟⠛⡷⢴⡾⠿⣶⠞⢻⡷⣶⡚⢿⡝⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠙⢾⣾⣥⣷⣧⣠⣇⢸⡇⠀⣿⠀⠈⣷⢸⣧⣸⡷⣿⢿⣍⡟⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠸⣿⣷⡇⡏⢾⢩⣿⢻⠛⣿⠓⡟⠹⡏⢻⠀⣿⣼⠾⠏⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠾⢿⣾⣷⣿⣰⣿⣴⠷⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡘⠚⠛⠀⠀⠀⠀⠀⢀⡴⠀⢰⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠠⠖⠉⠀⠀⠈⠻⠲⠤⢤⠀⠀⠀⠀⣀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣤⣀⣀⣤⠤⠤⠤⠤⠴⠚⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⡄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⠀⠣⢸⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡏⢰⠃⠘⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⢁⠃⢠⠃⠘⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢀⠌⢀⠂⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⢃⠂⠠⠃⠀⠀⡐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⢁⠔⠁⠀⢀⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⢾⡾⠁⠀⢀⠔⠁⠀⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢁⡼⠋⡀⠔⠁⠀⠀⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⣁⢴⢻⠀⢹⠟⠉⠀⠀⠀⢀⠤⠒⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⡠⠖⠉⠀⣼⢊⣴⣯⠤⠤⠀⠒⠉⠀⠀⣠⠃⠀ ⠀⠀⠀⠀⠀⡠⠊⣠⠖⠉⠀⠀⣠⠞⠁⢀⣿⠉⠛⠲⠤⣤⣀⣤⣖⠁⠀⠀ ⠀⠀⠀⢠⠞⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡔⠁⠑⠂⠄⣀⠀⢀⡤⠋⠀⠀⠀ ⠀⢀⡔⠁⠀⡾⠀⠀⠀⠀⠀⢀⣠⠶⢇⡀⠀⠀⠀⠀⢀⡀⠝⠀⠀⠀⠀⠀ ⢠⠎⠀⠀⢀⣇⣀⠀⠀⢴⠺⠉⠳⣄⠀⠈⠐⠠⠄⡀⠔⠁⠀⠀⠀⠀⠀⠀ ⠘⣄⣀⣀⠜⠁⠀⠈⠉⠛⠅⡀⠀⠸⣙⠲⡤⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢔⣒⠂⣀⣂⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣟⣼⣷⠼⣞⣽⢏⣿⣆⠱⣄ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣆⠛⠢⠐⡍⡉⣾⣾⣽⣟⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⠀⠤⢶⣿⠿⢋⣴⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣺⡙⢻⣿⣿⣧⣽⣉⣁⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡔⡉⣩⢋⡋⠩⠯⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣘⣶⣁⢙⢐⣄⡴⠪⠓⠁⠉⠃ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⣿⣿⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠫⣿⠉⠻⣇⠘⠓⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣿⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⢶⣾⣿⣿⣿⣿⣿⣶⣄⠀⢐⢝⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⠈⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⢿⣿⣿⠿⢛⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⡀ ⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢈⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣷ ⠀⠀⢀⡔⠁⠀⠀⠀⢀⣴⡿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠁ ⠀⣠⡟⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⣰⣾⣶⣆⠀⠀⠀⠀⡄ ⣿⣿⡀⠀⠀⠀⢸⣿⣿⣧⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⢿⣿⣿⣿⡆⠀⠀⢸⣧ ⢿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠁⠀⢠⣿⣿ ⢸⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠲⣶⣶⣶⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿ ⢰⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⣬⣅⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⠻⣿⣿⣿⣿⣿⡎⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠙⠻⠿⣿⣿⠗⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⡿⠇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⡜⠻⠿⢾⣷⠹⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡎⠁⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⡠⠞⠛⠛⠻⢽⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⡀⠀⢀⠀⢂⠀⡀⠀⠀⠀⠜⠀⠀⠀⠀⡀⠸⠀⠤⢄⠀ ⠀⠀⠀⠀⠙⣗⣄⠀⠠⡀⢢⠃⠀⢸⠌⠀⡠⢊⠀⠊⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⣀⣀⣈⣲⣕⣦⡈⠢⣻⡀⡎⢀⣴⡢⠑⠂⠁⠀⠀⠀⠀⡠⠃ ⠀⣴⠿⠽⠏⠀⠀⠀⠈⠉⢒⣺⣷⣗⣉⣁⣀⣀⣀⠀⠠⠤⠐⠈⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⢀⠠⡖⠁⣿⢳⡬⡁⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀ ⠈⢦⡀⠀⠀⡀⠄⠂⠁⠊⠀⢰⣯⡏⠎⢌⠑⠀⠀⠀⠈⠑⢄⠀⠀⠀ ⠀⠀⠉⡻⠀⠀⠀⠀⠀⠀⣲⡟⡟⠀⠀⠀⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢧⣤⡄⡀⠀⢀⡔⣽⠃⢧⡄⠀⠀⠀⠰⣀⠀⠀⣀⠞⠀⠀⠀ ⠀⠀⠀⠈⠳⠬⠥⠔⠋⡜⡌⠀⠘⣿⣦⣀⠀⡀⡇⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠀⠀⠀⠈⠛⠯⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⡠⠤⣄⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠴⠦⡏⠀⠀⠉⠀⠀⠘⠋⠀⣷⣤⡀⠀⠀⠀ ⢀⡔⠉⠁⢀⣉⡲⠴⠒⠣⢄⠀⢀⡠⠄⣀⡀⠀⠀⠀⠀⠀⢀⣟⣀⠀⠀ ⠈⠓⠒⠂⣹⡟⠋⡑⣤⠤⠤⣻⡵⢤⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠀⠀⣰⠃⠑⠬⠗⢟⠇⢀⠇⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀ ⠀⠀⠀⢧⠰⠂⡦⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠟⠀ ⠀⠀⠀⠈⠓⠦⠤⠴⠒⢯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢶⠂⢠⡀⠀⡀⠀⡀⠀⣄⠀⣦⣤⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡟⠓⠚⠧⠜⠙⠒⣿⡛⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣟⢼⢃⠀⠀⠀⠀⢠⣔⠿⠃⡏⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢁⡸⢸⠀⠀⠀⠀⠀⠀⣠⣒⡯⠓⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠓⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⡀⠀⢣⣄⠀⠀⠉⠛⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣄⠀⠹⣿⣷⣶⣦⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡿⢛⡙⢻⠛⣉⢻⣉⢈⣹⣿⣿⠟⣉⢻⡏⢛⠙⣉⢻⣿⣿⣿ ⣿⣿⣇⠻⠃⣾⠸⠟⣸⣿⠈⣿⣿⣿⡀⠴⠞⡇⣾⡄⣿⠘⣿⣿⣿ ⣿⣿⣟⠛⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡄⠀⢿⠀⠘⠃⠀⢼⡏⢸⡷⠀⠘⠃⠀⡿⠀⢠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⣆⠀⠋⠀⣠⡴⠶⠖⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⡀⠘⠁⢠⡶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⣾⡿⢻⡟⢻⡟⢿⣿⣶⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⢾⡃⢘⣷⠈⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣶⡀⠀⠀⢠⡀⠀⢀⣄⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀ ⠰⣶⣤⠶⠞⠃⠀⢀⣤⠄⢸⡟⢷⡀⠀⢸⡿⣦⡀⠉⠁⣄⡀⠀⠈⠻⠶⣤⣴⠆ ⠀⠈⠙⢻⡟⠛⠃⠈⠁⠀⣿⣀⡈⠛⢶⣤⣿⣌⣻⣦⡀⠈⠙⠛⠛⢻⡟⠋⠁⠀ ⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣿⠋⢻⡆⠀⠀⠉⣿⠉⣿⣧⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⣿⠀⢰⡇⠀⠀⣿⠙⠳⠞⣡⣤⣤⣤⠛⠶⠋⣿⠀⠀⢸⡇⠀⢿⡄⠀⠀ ⠀⠀⠀⣿⠀⠘⣧⠀⠀⢻⣆⠀⠀⢻⣄⣠⡿⠀⠀⢠⡿⠀⠀⣸⡇⠀⣸⠇⠀⠀ ⠀⠀⠀⠹⣆⠀⠹⣦⣀⠀⠙⣷⣶⣤⣀⣀⣠⣴⣾⠛⠁⣀⣴⠟⠀⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣤⣀⡙⠿⣿⣭⡅⠀⠉⠋⠁⢀⣭⣿⠿⠋⣁⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀

⢠⣶⣿⣿⣿⣶⡄⠀⣶⣶⣶⡆⢰⣶⣶⣶⡆⠀⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⡄ ⣿⣿⣿⠉⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣧⢸⣿⣿⣿⣿⠀⢸⣿⣿⡏⢻⣿⣿ ⢿⣿⣿⣦⣉⠉⠁⠀⣿⣿⣿⡇⢸⣿⣿⢻⣿⢸⣿⢻⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿ ⠈⠻⢿⣿⣿⣷⣄⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟ ⣤⣤⣤⠙⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⡏⠉⠁⠀ ⢿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀ ⠘⠿⢿⣿⣿⠿⠋⠀⠿⠿⠿⠇⠸⠿⠿⠀⠹⠿⠇⠸⠿⠿⠀⠸⠿⠿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⠲⠦⣤⣤⣴⠶⠛⣋⣉⠉⠉⠛⠶⠶⢤⡤⠶⠚⠛⠉⠉⣁⣍⡙⠓⠶⣤⣤⣤⣤⣵⠶⠶⠶⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠈⣉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡍⠙⠇⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣠⡄⠘⠛⠋⠀⠀⠀⣀⣼⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠻⢿⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠋⠀⠀⠀⠀⣀⣤⣾⣟⣉⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡶⠶⣶⣶⣿⣿⣿⢿⣿⣿⣿⣶⣄⠀⠙⢶⡀⠀⠀⠀⢠⡴⠋⢁⣤⣶⣶⣿⣿⣿⣿⣷⣶⡶⢶⣶⡶⠞⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⣿⣿⣹⣷⣾⣿⣷⣿⣏⢹⣿⣷⡄⠀⢻⡄⠀⣴⠋⢀⣴⣿⡿⢋⣽⣷⣿⣯⣭⡿⢻⣿⣦⠀⠙⢦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀⣿⡿⣠⣾⣿⣿⣿⣿⠃⠀⠀⢹⣯⣻⣿⡄⠀⣿⣰⠃⢰⣿⡏⣻⣾⣿⣿⣿⣿⠋⠉⠙⣿⡙⣿⣷⡀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣿⠁⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⡿⢿⣿⠀⢸⡏⠀⣿⣿⢀⣿⣿⣿⣿⣿⣿⣄⣀⣠⣿⣿⠛⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⠀⢸⡇⠀⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣿⣟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣸⣿⠃⢀⣿⡇⠀⢻⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⡽⣿⣷⡏⢻⣿⣿⣿⣿⡿⠟⢷⣌⣿⠏⢀⣼⠟⢿⡄⠈⢿⣷⣤⡿⢿⣿⣿⣿⣿⣿⣿⠋⣠⣿⠏⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⠻⠿⣦⣾⣅⣀⣩⣤⣶⡿⠟⢁⣰⡟⣻⠀⢸⠻⣄⠀⠙⢿⣶⣄⣹⣟⣋⣉⣿⣬⣷⠿⠃⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠳⣤⣀⡀⠈⠉⠉⠉⠉⢁⣠⡴⠟⠋⠀⣿⠀⢸⠀⠘⠷⣤⣀⡈⠉⠛⠛⠛⠛⠛⠋⣀⣠⡴⠟⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠛⠛⠛⠛⠋⡍⠉⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠉⠛⠓⠲⠶⠶⠶⠶⠞⠛⠉⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⠀⢸⠿⣄⡀⠀⠀⠀⠀⢀⡞⠉⢻⣆⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠋⣿⠀⢸⠀⠈⢷⡀⠀⠀⢀⡾⠀⠀⠀⢻⡀⢸⡇⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⣴⣶⣤⡄⠀⠀⢀⣼⠃⠀⠀⠀⡟⠀⢸⡇⠀⠈⡇⢠⠀⢸⠁⢀⣠⣄⣸⡇⠈⢀⡾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠀⠀⠙⠻⠟⠃⠀⠀⢿⣍⡴⠀⠀⢀⡇⠀⢸⡇⠈⢷⣴⠟⠀⠘⢦⣌⠛⠿⠛⠀⠀⢀⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡷⠶⠚⠓⠲⠶⠶⢶⣶⠛⠓⠲⢶⣾⡇⠀⢸⣿⡦⢤⡤⠶⣾⡶⠶⣤⣤⣤⠶⣤⣀⣼⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢻⡿⢿⣀⣀⣀⠀⠀⠀⠀⠀⠉⠳⠤⠜⣹⡇⠀⢸⡇⠱⣦⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⢹⢿⡶⠶⠋⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⣯⣿⣿⣿⣿⠛⣿⣿⣿⣷⣾⣿⠃⠀⠈⣿⣶⣿⣾⡿⠶⣾⣷⣶⣶⣶⣶⢶⣾⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠾⣧⢸⡀⠈⠉⠉⠉⠁⠀⠈⠙⠉⠙⠛⣿⣄⠀⣰⡿⠛⠛⠛⠃⠀⠙⠛⠛⠛⠛⠋⠀⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠸⣷⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣯⣀⣀⣀⣀⣀⣤⣠⣤⣄⣤⣤⣄⣰⣧⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠀⣿⠀⢰⣿⣤⣀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣽⣟⣛⡛⠛⣿⣿⠉⠉⣽⠇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡌⣇⣿⠀⠀⠈⠉⢹⠛⢻⡋⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠛⣟⠛⠋⠀⠀⣿⣰⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣹⡟⠀⠀⠀⠀⢸⡇⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⡏⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠃⠀⠀⠀⠀⢸⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡃⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣧⡀⣠⣾⠁⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⢸⣷⡄⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣷⣾⣿⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣿⣛⣛⣛⣙⣛⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣛⣻⣿⣿⣿⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣧⣸⣿⣧⣤⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⢀⡀⣠⣤⣦⣴⣿⣿⣿⣿⠛⠉⠁ ⠀⠀⠀⠀⠀⣿⣿⣿⢿⠿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⠂⠀⠀ ⣠⣄⣶⣤⣿⠋⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀ ⠉⠛⠿⢿⠃⠀⠀⠀⠀⠀⠀⣠⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠛⠻⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠿⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⡀⢀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⣴⣾⣶⣶⣿⣿⣷⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠻⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣤⣄⣴⣶⣿⣿⣶⣶⣦⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣀⣶⣆⣶⣦ ⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠈⠛⠛⢿⣿⣿⣿⣿⣿⠛⡟⠛⢿⡿⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣧⣀⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠙⠛⠿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠁⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣰⡏⣠⠟⠀⠀⠀⢠⠤⠤⠤⠤⢴⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⢤⣼⣾⣾⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⣿⡔⢳⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⣿⣥⣴⣿⣿⣿⣿⣿⣿⣀⣶⡒⢦⡿⠀⠒⡿⠯⢹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠽⠆⠀⠀⠀⠀⠰⠤⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠂⠀⠀⠀⠀⠐⠲⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡁⠀⠀⠀⠈⢹⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⠁⠀⢸⡑⡄⠀⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⢧⠀⠀⠀⡇⠈⢢⡀⣠⠇⠀⣿⣿⣿⡟⢿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡤⠜⠀⠀⠀⠹⡾⣟⣯⣝⣦⡼⢻⣿⡏⡇⠸⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⣿⣿⣿⡿⡆⠀⠀⠀⣄⠀⢣⠀⠀⠀⠀⠀⠹⣖⠲⠽⠿⣧⢀⡏⢹⠁⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀ ⢈⣿⣿⣿⣿⣿⠁⢇⠀⠀⠀⠸⡀⠈⢧⠀⠀⠀⠀⠀⢻⢍⣉⡓⣾⠸⡇⢸⠀⠸⡀⡎⢹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⠀⠘⡄⠀⠀⠀⡧⠀⠈⠣⣀⠀⠀⠀⠘⡦⠬⢭⣿⠀⢹⠉⠀⡴⠁⡆⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣿⣿⣿⣿⡏⠀⠐⠚⠀⠀⢀⠇⠀⠀⠀⠈⠓⢤⣀⠀⢹⣿⣿⣯⡀⢸⢀⡞⠀⠀⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢨⣿⣿⣿⡇⠀⢀⣀⣀⣠⣸⠤⣀⠤⠒⠲⠖⠋⠉⡏⠁⠀⢛⣒⡟⢿⡟⠀⠀⠀⡇⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣿⣿⡠⠚⠉⠠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠤⡾⢀⣾⠀⠀⠀⠀⡇⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣘⣷⡒⢲⣻⣧⠎⣹⠀⠀⠀⢸⠀⠘⢻⠉⠓⠦⢄⣀⢞⣇⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⠀⣀⣀⠤⠤⠼⠿⠞⠛⠁⠑⣤⡖⢶⠀⣼⠀⢠⣀⣸⠀⠀⠀⠀⠀⠀⡎⠁⢾⠁⠀⢠⣽⣿⣶ ⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠼⡄⣿⠀⠘⠛⣿⣶⠤⢄⣀⠀⠀⢳⣤⣀⣀⣀⣼⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⣷⡿⠀⠀⠀⢻⠀⠀⠀⠀⠈⠑⠚⠷⠤⠋⠙⠿⠈⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠐⠒⠒⠒⠉⠉⠉⠉⠉⠛⢶⠾⠗⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠀⠀⠉⠉⢦ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁⠀

⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⡿⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⠧⠿⠶⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⢀⣀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡀⠛⠉⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢻⣦⣤⣤⣤⣤⢤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⡿⡄⢀⣠⣤⣀⢻⡁⠀⠈⢧⠀⠈⠻⣦⠀⠀⠀⠀ ⠀⠀⣰⣿⣛⣀⣷⠘⠫⠟⠛⠀⢣⠀⠀⠀⢣⠀⠀⠘⢷⡀⠀⠀ ⢀⣾⣿⠟⠃⠀⠘⣇⠀⠀⠀⠀⠈⢧⠀⠀⠀⢧⠀⠀⠈⢻⣄⠀ ⢸⡇⡇⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⣆⠀⠀⠘⣧⠀⠀⠀⢻⡄ ⠈⣷⢹⡀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⡄⠀⠀⠋⠀⠀⢀⣿⠁ ⠀⣿⠈⢇⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⠃⠀ ⠀⣿⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⡿⠃⠀⠀ ⠀⠙⠳⣦⣽⡄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣸⡶⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⣄⣀⣤⠴⠷⢤⣤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀ ⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀ ⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢹⡄ ⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇ ⣿⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⡇ ⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⠀ ⠈⢷⡀⢸⡇⠀⢀⣠⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣄⠀⠀⣿⠀⣼⠃⠀ ⠀⠈⢷⣼⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡾⠃⠀⠀ ⠀⠀⠈⣿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⢠⠀⣄⠀⠀⠙⢿⣿⣿⣿⡿⠏⠀⠀⢘⡇⠀⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣴⣿⠀⣿⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⠳⣦⡀⠀⠀⠀⠸⣿⡿⠀⢻⣿⡟⠀⠀⠀⠀⣤⡾⢻⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⢻⠻⣆⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢀⡾⢻⠁⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⢹⠒⡦⢤⠤⡤⢤⢤⡤⣤⠤⡔⡿⢁⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⢸⠦⣧⣼⣀⡇⢸⢀⣇⣸⣠⡷⢇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⠺⣄⣇⢸⠉⡏⢹⠉⡏⢹⢀⣧⠾⠋⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠉⠙⠓⠚⠚⠋⠉⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⣤⣤⣤⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣾⡿⠿⣷⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠉⠉⠀⠀⠀⠙⢿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢡⣦⠄⠀⠀⣴⡤⠀⠀⠀⠘⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⢰⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢾⣦⣀⣤⣶⠆⠣⡀⡀⠀⣾⣿⠁ ⠀⠀⣀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠉⠉⠉⠁⠀⠀⠐⣀⣼⣿⠋⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠈⠻⠿⣶⣦⣤⣤⣤⣶⡶⠿⠟⠋⠀⠀⠀ ⢰⣶⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠛⠿⣷⣦⣤⣄⣀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣷⣶⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠛⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⣠⣯⣀⠀⠀⠀⠀⠀⠀⠀⠈⣣⡀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣦⣄⠀⠀⣼⡟⣛⣛⠻⣦⡀⠀⠀⣠⡶⠛⠛⠳⡄⢀⣠⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⢿⣿⠻⣿⣿⡆⠸⣿⣿⣿⡿⣶⡄⣰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣾⣿⡤⠞⠋⠀⠀⠙⢿⣿⡗⠋⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢀⣴⣦⣦⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣶⣶⡿⠿⠿⠿⠷⠶⠶⠖⠛⠋⠳⣄⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢀⣿⣿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣟⣷⠾⣭⣵⣶⣒⠒⠒⠒⠊⠉⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡾⣿⣾⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣸⣯⣹⡟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠤⠾⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠤⠴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡏⠁⠀⠀⠀⠀⠸⡿⠟⠋⠉⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣯⣴⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣾⣿⣿⣻⣿⣶⣦⣴⣦⣿⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣄⣀⣀⡀⣀⣀⢀⣰⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣿⣿⣟⣛⣛⢿⣿⣿⡚⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣻⣿⣿⣿⣿⠿⠷⣇⣌⣽⣿⠿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣯⣝⣹⠟⠃⢠⡟⣿⣷⣮⡏⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⠻⡏⠐⠖⠛⠲⠻⣯⣤⣄⠀⠀⠀⠀⠀ ⠀⢀⣠⣾⣿⣿⠿⠿⠞⠁⢀⣴⠋⢀⣿⣿⣿⣿⣷⣿⣄⣤⠀⣀⠀⠀⠀⠀⣠⣴⡶⢿⣿⣿⣿⣿⡽⣤⢠⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇⡀⠙⣦⡀⠈⠲⢶⣿⣿⣿⣦⡀⢰⠀⠀ ⣾⣿⣿⣿⣟⣿⣷⣄⠀⣴⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣟⣽⡁⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣿⡀⠈⢷⣄⠀⢀⣼⣿⣿⣿⣿⣷⣦⡀ ⣿⣿⣿⣷⣮⡙⢿⣿⣿⠏⠀⢠⣿⣿⣿⣷⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⢻⣾⣩⣷⡄⠀⠙⣶⣿⣻⢟⣿⣽⣿⣿⣿⡷ ⡟⣾⣿⣿⣿⣿⢸⣟⡟⠀⣴⣿⣱⣿⣿⣿⣿⣆⠨⠿⢿⣿⣿⣿⣿⣿⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⢹⣻⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⣿⣿⣿⣏⣷⡄⠀⢸⣧⡇⣼⣿⣿⣿⣏⢻⣧ ⣿⣽⣿⣿⡿⢟⣼⣿⡏⠀⣸⣿⣽⣿⣿⣿⣿⡛⠂⠀⠈⢻⡟⡿⣿⠟⠋⠉⠉⠁⠀⠀⠁⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⠏⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣧⢻⣿⣿⣿⣧⣾⣿ ⢹⣿⣷⣶⣷⣿⣿⡿⠃⣴⠏⢉⣛⣿⣿⣿⠇⠀⠀⠀⢀⡾⣿⣧⠡⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠈⠙⠉⠿⣧⠀⠀⠀⠀⣿⣿⣿⠿⠛⠿⢷⡘⢿⣿⣷⣷⣾⣿⣿⣿⠋ ⢸⣿⣷⣦⣝⣿⣿⠁⣾⣇⠀⠀⠀⢉⣿⡿⠀⠀⠀⣴⣿⣷⣤⣿⣷⣿⣿⣿⣧⣀⠀⠀⣿⣧⣤⣤⣴⣴⣶⣠⡀⠀⠀⣹⣷⡄⠀⠀⢹⣿⡍⠀⠀⠀⢸⣷⡄⢿⣿⣿⣿⣿⣿⣯⠀ ⣸⣿⢿⣿⣿⣿⣿⣾⡿⣸⠾⣿⣤⡼⣿⠃⣀⠀⢀⡏⠛⠯⢿⣿⠛⠛⠋⠉⠙⠛⠳⡄⠈⠉⠁⠉⠉⠙⠻⢿⣿⣦⣶⣛⣿⣧⠀⢀⣼⣿⠾⣤⣼⡯⣿⣿⣿⣸⣧⢿⣿⣿⣽⣏⠀ ⢿⣝⡮⣭⣽⣿⣽⣿⡿⠉⠀⠀⠀⠀⠉⠀⢿⣿⣿⠇⡀⠀⢨⣿⡄⠈⢧⡀⠀⠀⠀⢮⡇⠀⠀⠀⢀⡆⣀⢛⡇⠀⠀⠉⡉⠻⡷⠻⣟⠉⠁⠀⠀⠀⠈⠹⣿⣿⣿⣿⣭⣿⣿⡿⠀ ⠘⣿⡟⢿⣿⣿⣿⡋⠀⠀⠀⢀⠀⠀⠀⠀⠏⣿⣻⣧⣅⠀⢸⣿⣿⣿⣾⣷⡀⠀⠀⢸⣷⡄⠀⠠⢼⠬⢵⣿⠁⠀⠀⠀⢱⣤⡇⢸⣻⡀⠀⠀⠰⠖⠀⠀⢈⣿⣿⣿⣿⣿⣿⡇⠀ ⢰⣿⠷⣿⣿⣯⣿⣿⠷⠿⠶⠾⠶⠖⠚⠁⣾⣿⣟⣿⡎⠀⢠⣿⠿⠿⠿⠿⠿⣍⠉⣹⠿⢿⣿⣶⣶⣾⣿⣿⠀⠀⢀⣴⢿⣿⠀⠈⣇⠈⠙⠒⠒⠶⠾⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀ ⣷⢿⣷⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⢯⣿⠇⢀⣸⣿⣷⣀⣀⠀⠀⠸⠟⠃⠀⠀⠈⣹⣿⣿⣿⠇⠀⠀⠸⣿⣿⡟⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⡇⠀ ⠀⠉⠙⣿⣻⡿⠿⠿⠦⠄⠀⠀⠀⠄⠀⢸⣿⣷⣼⣿⡄⠀⣿⣿⣿⣯⠯⡵⢦⡀⠀⠀⠒⠂⢤⣿⣿⣿⠋⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠻⡞⠚⠒⠶⠶⠿⠻⠻⣻⢿⡿⣿⣿⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀ ⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀ ⠀⢸⣿⡿⠁⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢹⣿⣷⠀ ⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⡀⠀⠀⠀⢀⣤⣦⣤⣀⣿⣿⣿⣿⣿⣇⣠⣴⣤⡀⠀⠀⠀⢀⡀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣴⣿⣿⣷⣦⠀⣾⡿⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡆⣠⣾⣿⣿⣷⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠏⠉⠉⢿⡿⣿⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⣿⡇⣿⠋⠈⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣆⠀⠘⠁⠈⠁⠀⢿⡟⠙⣿⣿⣿⠟⠙⣿⠀⠀⠁⠀⠛⠀⢠⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠙⣿⠀⠀⠀⠀⠀⠀⠈⠛⠆⣹⣿⣿⠀⠛⠋⠀⠀⠀⠀⠀⠀⢾⡏⠉⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇ ⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀ ⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢻⣛⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣄⣀⣀⣀⣉⣉⣉⣉⣉⣙⣻⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀ ⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀ ⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⡿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠐⠂⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣊⡁⣀⡀⠀⣠⢾⣿⣿⠿⠛⠳⢮⣳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⣺⣷⣿⣿⣯⣝⠳⣿⣿⢡⣴⣦⡀⠀⢻⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡼⣸⡿⠛⢁⣤⣄⠈⢳⣌⢧⠘⠿⠟⠁⠀⣼⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⣆⣼⣇⠀⠸⣿⡿⠀⢸⣿⣬⣧⣄⠀⣀⣼⣽⠉⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣷⣹⣄⠀⠀⠀⢀⣾⣿⠿⠷⠿⠿⠟⠋⠁⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠉⠙⠻⢽⣛⣷⣚⡿⠟⠁⠀⠀⢀⡠⠆⠀⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⣠⣤⣀⠀⢿⠲⣄⡀⠀⠀⠈⠁⠉⠓⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⣠⣿⡆⠀ ⠀⢀⣴⡟⢛⣿⣿⣷⡄⠑⠦⡙⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣼⣿⢟⢳⠀ ⢰⣿⣥⣿⣯⣞⣻⣿⣿⠀⠀⠈⠻⣿⣿⣷⠿⠛⣛⣉⣋⣋⣹⣿⣿⣿⣿⣿⣇⣸⣄⡇ ⠈⠻⣿⣤⡴⣬⣿⣿⣿⣆⠀⠀⠀⢸⠻⠏⠀⠰⠀⠀⠀⠀⠠⣼⡿⣿⣿⣿⣿⣿⣿⡷ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⠶⢤⡼⠣⠄⢀⠈⢦⣀⣀⣀⣀⣾⣉⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣗⠚⠀⠀⠀⣂⠀⠂⠀⠀⠨⠥⠀⢉⡭⢾⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⠛⣿⣿⡿⢧⣀⣀⣀⣉⠳⠶⣶⠐⠆⠀⠒⠋⣷⣈⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠋⠁⠀⠀⠹⣿⣿⣷⡞⢻⣷⣾⣶⡿⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⠤⢀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢉⠅⠊⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⢤⣒⠢⣄⠀⠀⠀⠀ ⡔⠁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣌⢳⡀⠀⠀ ⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡗⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⣼⠄ ⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⡟⠀ ⠀⠀⠈⠑⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢾⣿⣟⣀⠀⠄⠁⠀ ⠀⠀⠀⠀⠀⠙⠉⢷⣄⠀⠀⢸⣟⣿⢿⣿⡝⢝⢝⢕⢕⢕⢝⠟⠅⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣈⣿⡅⠔⠛⠐⠐⠑⠑⠑⠁⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠝⢝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⣶⡛⠉⣷⡶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣞⣿⡿⢟⣇⣽⣷⣮⣛⣙⡛⠾⢿⣗⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣯⣿⠏⣡⠞⠋⠉⢸⣿⣿⣿⠈⠉⠓⢮⡉⣿⡿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠏⣩⣴⣿⠏⣼⠷⠖⠚⠓⢾⣿⣿⣿⠒⠒⠒⠦⣿⡌⢿⣦⣮⡉⠿⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡟⣠⡾⠷⣿⠿⠠⢇⡀⠀⣀⣀⡾⣿⢯⡿⣄⣀⡀⠀⣨⠧⠿⣯⠷⢿⣦⠙⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢥⠏⠀⢠⡏⢺⣿⠄⣷⣏⠀⣹⣧⡳⠾⣧⣿⠁⢹⣾⡃⣿⣿⠈⡇⠀⠘⣇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⡘⣶⠋⠙⣷⠖⣴⣾⠛⣉⣶⣦⣭⣾⣿⣌⣁⣲⣞⡛⢫⣶⠰⠾⠏⠉⢷⣯⣼⣏⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣞⣶⡃⠿⠃⠾⣀⣤⠶⣿⣟⣉⣹⣏⢩⣾⣿⣮⢉⣿⡉⣛⣻⡶⢦⣄⡲⠒⠻⢋⣷⣟⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣯⣿⡆⠾⣥⣞⣩⡭⠿⠤⠿⠿⠿⠬⢽⣌⣛⣾⠽⠂⣶⣉⣿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡶⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⢀⣀⣠⠤⠴⠒⠒⠒⠒⠒⠒⠲⠤⢤⣄⣀⠀⠀⠀⠙⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⣠⡴⣾⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢀⡴⠛⠁⠀⠀⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⢀⡴⠉⠀⢀⡴⠚⠙⢦⡀⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠦⣀⠀⠀⠑⣄⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⡼⠁⠀⠀⣰⠋⠀⢀⡴⠋⠀⠀⠀⠀⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠈⠳⣄⠀⠈⢳⡀⠀⠀⢳⡀⠀⠀ ⠀⠀⡼⠁⠀⢀⡼⠁⠀⣰⠋⠀⠀⣠⠖⢦⡀⠀⠀⠙⠊⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⢀⡴⠛⢦⠀⠀⠈⢦⡀⠀⠹⡄⠀⠀⢹⡀⠀ ⠀⣸⠃⠀⢀⡾⣧⡀⡴⠃⠀⠀⡴⠃⠀⣠⠟⠀⠀⠀⠀⠀⣠⡤⢤⡤⠀⠀⠀⠀⠐⠻⡤⠀⠈⢳⡄⠀⠈⢳⡀⠀⠹⡄⠀⠀⢣⠀ ⢠⡏⠀⠀⡼⠁⠀⢹⠃⠀⢀⡞⠁⠀⡴⠁⠀⠀⣠⢦⡀⠀⠀⠙⠋⠀⠀⢀⡴⢦⡴⠊⠀⠀⠀⠀⠹⡆⠀⠀⢧⠀⠀⢹⡀⠀⠈⡇ ⢸⠀⠀⢰⠇⠀⠀⡏⠀⠀⣼⡀⠀⡼⠀⠀⢀⡞⠁⠀⠙⢦⡀⠀⠀⢀⡴⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⡇⠀⠀⡇⠀⠀⢱ ⡟⠀⠀⢸⠀⠀⢸⠁⠀⢰⠏⠻⣶⠇⠀⠀⡞⠀⠀⠀⠀⠀⠙⢦⡴⠋⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⣇⠀⠀⢷⠀⠀⢹⠀⠀⢸ ⡇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⠃⠀⠀⠀⢸⠋⠉⠉⠉⠉⢹⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢹⠀⠀⢸⠀⠀⢸⠀⠀⢸ ⡇⠀⠀⢸⠀⠀⢸⠀⠀⢸⠀⠀⢸⡀⠀⠸⣧⡀⠀⠀⢸⠀⠀⠀⣠⡤⣼⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣼⠀⠀⣸⠀⠀⢸⠀⠀⢸ ⢷⠀⠀⢸⡀⠀⠸⡆⠀⠈⣇⠀⠈⣧⠀⠀⢹⡻⣦⡀⢸⠀⠀⠀⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡇⠀⠀⡏⠀⠀⡾⠀⠀⢸ ⠸⡄⠀⠈⣇⠀⠀⢳⠀⠀⠹⡄⠀⠘⣦⠀⠀⠹⢮⡻⣾⡆⠀⠀⣀⣀⡧⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣸⠁⠀⢠⠇⠀⠀⡎ ⠀⢷⠀⠀⠸⡆⠀⠈⣧⠀⠀⠹⣄⠀⠈⢷⣄⠀⠀⠙⠺⠇⠀⠀⣏⣀⡤⠶⠋⠁⠈⠳⡄⠀⠀⢠⠞⠀⠀⢠⠿⣦⣀⡞⠀⠀⢰⠁ ⠀⠈⣇⠀⠀⠹⡄⠀⠈⢦⠀⠀⠈⢦⡀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⡴⠋⠀⠀⣠⠏⠀⢈⡿⠀⠀⢠⠏⠀ ⠀⠀⠘⣆⠀⠀⠹⣆⠀⠀⠳⣄⠀⠀⠙⣆⠀⠀⠀⠈⢹⠆⠀⠐⡶⠶⣶⠚⠉⠁⠀⠀⢰⠋⠀⠀⢀⡴⠃⠀⢠⠟⠀⠀⢠⡏⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠈⢧⡀⠀⠈⠳⣄⡀⡟⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠈⠳⣄⠀⠀⠀⢸⠀⢀⡴⠋⠀⢀⡴⠃⠀⠀⣠⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢦⣀⠀⠀⠙⠃⠀⠀⠀⠀⢸⡀⠀⢠⡇⠀⠀⠀⠈⠳⣤⡀⠘⠚⠁⠀⢀⡴⠋⠀⠀⢀⡴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠻⣄⣀⡤⠞⠉⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠈⠙⠒⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠖⠚⠁⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⢉⠁⠀⣀⠀⠀⣀⡤⢖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠤⢤⣀⣉⣹⠁⢉⡇⢹⡏⠙⠛⣯⣫⣳⣱⢳⢄⢛⡛⠙⢁⠀⡀⠀⠀⠀⠀

⠀⢄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣿⠟⢻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠋⠀⠀⠸⣿⣿⣿⣿⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⣿⣷⡄⠀ ⠀⠀⢀⣠⣶⡿⠿⠿⣿⣿⠛⠿⠿⠟⠛⠛⠙⢿⣿⣯⠁⠙⢿⣿⣧⠀⠙⠛⠁⠀ ⠀⢀⡾⠋⠁⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠄⠀⠈⠻⣷⣄⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⣴⠾⠋⠁⠀⠀⠀⠀⠈⢻⣆⠀⠀ ⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠶⠶⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠖⠶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠒⢺⡟⠉⠀⠈⣷⡦⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣠⢴⣿⠀⠀⠘⡇⠀⠀⠀⣿⣱⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠋⢁⠀⠀⢹⡀⠀⠀⡇⠀⠀⠀⡿⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀ ⢸⠶⠼⣧⠀⠀⡇⢀⣠⡇⠠⠤⠀⡇⠀⣀⣿⡀⠀⢀⣠⣴⡞⠁⠀⠀⢀⣴⡇ ⢸⠀⠀⠘⣆⢠⣿⢀⣠⣿⡤⣤⣠⡇⠶⢼⣿⡷⠞⠋⠁⠀⠀⢀⣠⡴⠋⠁⠀ ⢸⠀⠀⠀⠈⠛⠿⢿⣯⣿⡶⠾⠟⠀⠀⠀⢹⣷⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀ ⠘⡇⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠻⣆⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡀⠀⠀⢀⣀⣰⣿⣄⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡿⠿⠿⠿⡿⢻⠟⢻⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⢸⠁⡏⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⡀⠀⢠⡿⣸⠀⢀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠿⠷⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠙⠛⠓⠒⠲⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠹⣿⠀⠀⠀⣾⠏⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠟⠋⠀⠀⢻⡇⠀⢸⡟⠀⠀⠙⠻⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⠿⠟⣻⣽⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣤⣤⣬⣉⠛⠻⠿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠘⣇⠀⠀ ⠀⠀⣿⠀⠀⠀⢀⣴⡾⠿⠟⢿⡏⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣼⡇⠀⢸⣷⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⢹⣿⠻⠿⠿⣦⡀⠀⠀⠀⣿⠀⠀ ⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⠀⠀⠀⣸⡿⠀⠀⠀⢿⣇⠀⠀⠀⠀⣿⣿⣿⠛⣿⣿⣿⡇⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⣿⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⡿⠁⠀⠀⠀⠈⢿⣦⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠶⣤⡈⢿⣿⣿⣿⣿⣿⠟⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠿⣿⣿⣿⡿⠋⢀⣤⠶⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣹⣶⣌⣉⣉⣉⣥⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⣀⣀⣤⣴⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢤⣀⣀⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏ ⠸⡄⠀⠀⠀⠀⠀⣀⡤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣈⠳⣤⡀⠀⠀⠀⠀⢠⠇ ⠀⢷⡄⠀⠀⣠⡿⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⢿⣆⠀⠀⠀⡾⠀ ⠀⠈⢻⡄⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⡞⠁⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠶⠚⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⣿⣿⣿⣶⣶⣿⠿⠟⠛⠛⠻⠿⣿⣶⣶⣿⣿⣿⣶⣄⠀ ⣼⣿⣿⣿⣿⣿⣿⣿⠃⠛⠛⠀⠀⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⡶⠀⠀⢾⡧⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⢿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠐⠂⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠉⠛⠛⠛⠉⢉⣻⣿⣿⣿⣿⣿⣿⣟⡉⠉⠛⠛⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠏⠀⠀⠹⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⠁⣿⣿⠀⠀⠀⠀⣿⣿⠈⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⣤⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠙⢷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣧⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠈⡿⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⣟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣰⡄⠀⠀⠀⠀⣤⡀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡄⠀⠀⠀⢸⡀⠀⠀⠀⠙⠁⡾⠛⠶⢤⣉⠁⠀⠀⠀⣸⠀⠀⠀⠀⢀⡆⠀⠀ ⢀⠀⠈⣧⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢹⠓⢶⠦⠬⠿⠀⠀⣰⠏⠀⠀⠀⠀⣼⠁⠀⠀ ⠘⠳⢤⣸⡆⠀⠀⠀⢈⣷⣄⡀⠀⠀⠈⠑⠋⠀⠀⠀⣠⡾⢷⡄⠀⠀⠀⢰⣏⣤⠞⠃ ⠀⠀⢀⣬⠿⠶⣤⣴⠞⠳⣌⠙⠲⠤⣤⣀⣤⠤⠖⠚⠁⠀⠀⢹⣄⣠⠶⠿⣥⡄⠀⠀ ⠀⠀⠈⠀⠀⠀⡼⠋⠓⠦⣈⡛⠶⢤⣀⣀⡀⠀⠀⢀⣀⣀⡤⢶⠿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠉⠓⠒⠶⣯⠭⠽⠿⠛⢛⣇⠀⠘⣇⠹⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠈⣿⠀⠀⢹⡄⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡅⠀⠀⠀⠀⢹⡄⠀⠀⢳⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠂⠀⠀⠀⠘⡧⠖⠚⠉⣹⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠸⢧⡿⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⡀⠀⠀⢀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀ ⠀⠘⠚⠛⠚⠛⠻⠟⠛⠛⠟⠻⠛⠐⠛⠟⠛⠃⠀⠈⢐⠟⠓⠛⠛⠊⠐⠀⠂⠐⠓⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣷⠀⣿⣿⣿⣿⣿⣷⠀⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⡄⠘⣿⣿⣿⣿⠏⢠⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⣿⣿⣿⣷⠀⠀⠀⠀ ⣀⡀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⢀⣀ ⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏ ⠘⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⢤⠤⣧⢤⡀⢀⡤⣼⠤⡤⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠈⢹⠗⠋⠀⠀⠙⠺⡏⠁⠀⢸⣿⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⢿⡄⠀⡏⠐⠶⢶⡶⠶⠂⢹⠀⢠⡿⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠉⠛⣦⣤⣤⣴⠛⠉⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠈⠛⠛⠁⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⠁⠀ ⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣼⣿⣿⣿⣿⣇⠀⠀ ⣴⣿⣿⣿⣿⣿⡏⠉⠻⣿⣿⡿⠏⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠛⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠘⠻⢿⣿⣿⣿⣿⣿⣿⣦⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠾⣿⠛⠋⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠿⠛⠛⣿⣀⢼⡇⠀⠘⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣤⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⠿⠛⠛⠉⠁⣀⣠⡴⠂⠀⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⣤⣴⠾⠿⢻⣿⢠⣿⠋⠀⠀⣿⣇⣤⣤⣤⣶⣾⠿⣿⠛⢻⡇⠀⢻⠀⠀⣶⠀⢸⡿⠁⢀⡄⠀⣿⠀⢸⠁⠀⣦⣀⣤⣧⣤⣶ ⠀⢠⣿⠇⠀⠀⢸⣿⣿⡏⠀⠀⢰⣿⡟⠋⠁⠉⣿⠀⢠⡿⠀⢸⡇⠀⠈⠀⢰⣿⠀⢸⡇⠀⢸⡇⠀⡏⠀⢸⣠⣴⡿⠟⢹⣿⣿⡇ ⠀⣸⣿⠀⠀⠀⠸⣿⣿⠁⠀⠀⢸⡟⠀⢰⡆⠀⢸⠀⢸⡇⠀⢸⠁⠀⠀⠀⢸⣿⠀⢸⡇⠀⠈⠀⣠⣷⣶⣿⣿⡇⠀⠀⢸⣿⣿⡇ ⠀⣿⡏⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⠀⢸⡇⠀⢸⠀⠀⠀⠀⢸⡏⠀⢸⣷⣤⣶⠾⢻⣿⠿⠛⢹⡇⠀⠀⢸⣿⣿⠀ ⠀⣿⡇⠀⠀⠀⠀⢿⠁⠀⠀⠀⣾⡇⠀⢸⡇⠀⡿⠀⢸⡇⠀⢸⠀⠀⡄⠀⢸⣧⣴⣿⣿⡏⠀⠀⢸⡇⠀⠀⢸⠇⠀⠀⢸⣿⡿⠀ ⢸⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⡇⠀⢸⡇⠀⣾⠀⣀⣷⡾⠟⠋⠉⠉⢻⡇⠀⠀⢸⠇⠀⠀⢸⠀⠀⠀⢸⣿⡇⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠃⠀⡇⠀⠈⠁⣰⣿⣿⠟⠉⢀⣠⡄⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⣿⣿⠃⠀ ⢸⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠿⠀⢰⣿⣶⣶⣾⣿⣿⠃⠀⠀⣿⣿⠃⠀⠀⢸⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀ ⢸⣿⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⢸⣧⣀⣠⣴⠿⠋⠁⠀⠀⢹⡟⠀⠀⠀⣿⠿⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣿⡟⠀⠀ ⢸⡿⠀⠀⠸⣧⠀⠀⣼⠀⠀⠀⢸⣿⠛⠉⠀⢠⣶⡆⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣤⣶⣾⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀ ⢸⡇⠀⠀⠀⣿⡀⠀⣿⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⡇⠀⠀⠀⣾⣿⠿⠟⠛⣿⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⣀⣿⠃⠀⠀ ⢸⣧⠀⠀⠀⣿⣧⠀⣿⡆⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⢀⡇⠀⠀⢠⣿⡿⠀⠀⢀⣿⠀⠀⠀⣰⣿⠻⣿⣶⠾⠿⠛⠛⠀⠀⠀ ⢸⣿⠀⠀⠀⢻⣿⣾⣿⡇⠀⠀⢀⣹⠀⠀⠀⢸⣿⡇⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣠⣾⣿⣶⡾⠿⠟⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣀⣤⡶⠟⠋⠁⠸⣿⣴⡾⢿⣿⠀⠀⠀⠼⠟⠀⠀⢀⣾⡿⢶⣶⣴⣶⡶⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠿⠛⠉⠀⠀⠀⠀⠀⠋⠁⠀⢸⣿⠀⠀⠀⣀⣠⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣍⣉⡉⠀⠁⣄⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢾⣧⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡷⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠺⡇⠀⢸⣧⡀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣞⣠⣤⠶⣿⣥⠶⡞⠋⣿⠀⣰⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⢸⠉⣷⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⠟⠉⢳⠀⣿⡿⠀⡇⠀⣿⣴⠏⢻⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠇⠀⡟⠀⡟⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇⠀⠀⢸⠀⠀⡇⠀⡇⡾⠟⢹⠀⢸⠀⣾⡄⠀⠀⣼⠀⠀⠀⠿⠤⠾⠃⢠⡇⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠧⣄⣀⣤⣀⡠⠃⠀⠳⣄⣀⣸⣀⣸⣾⠛⣷⣾⡆⢹⣤⡟⠛⡦⠀⠀⠀⢸⣧⡏⠘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⣿⣿⣇⣼⠏⠀⣼⠃⠀⠀⠀⣾⡟⠀⠀⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡾⠛⠁⣠⡾⠓⠒⠒⢶⡾⠋⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⢦⡄⠀⢰⣶⠛⠛⠛⠛⠉⠉⢀⣀⣤⠞⠋⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣀⣀⡀⠀⠳⠦⠤⠽⠓⠒⠒⠒⠚⠛⠋⣿⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣽⢿⣯⣛⣻⣿⡶⠒⠶⣶⣤⡤⢤⣤⣿⣀⣤⠾⠋⢀⣤⠤⢤⣄⡀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠹⣇⠀⠀⠈⣹⢹⡿⠶⣾⡿⣯⡙⢻⠟⠛⠉⠀⠀⠀⠛⠁⠀⠀⠈⠙⠳⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢻⡄⠀⠀⣿⠀⡇⠀⡟⠀⣿⠙⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠘⣇⠀⠀⢹⠀⡇⢰⡇⢰⡇⠀⠀⠘⣧⠐⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀ ⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⣼⡏⠘⢷⡀⠀⠀⣿⠀⠀⢸⡆⣿⢸⡇⢸⡇⠀⠀⠀⢹⡆⠀⠈⠙⢧⡀⠀⣠⡴⠞⠛⠋⠛⠛⢿⡄⠀ ⠀⣼⠋⠙⢷⣤⣀⣤⡴⠞⠉⢿⡄⠈⠻⣄⠀⢸⡇⠀⠈⣟⢻⠀⣷⠘⣇⠀⠀⠀⠀⣧⠀⠀⠀⠈⢿⡾⠁⠀⢀⣀⣀⣀⣀⣀⣿⡀ ⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢻⡾⡇⠀⠀⠻⠾⠇⠹⢧⡿⠆⠀⠀⠀⢻⡀⠀⠀⠀⠀⣿⣠⠞⠋⠁⠀⠀⠀⠘⡿⠃ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⣧⠀ ⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠉⠛⠲⠶⠤⠴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⠃⠀

⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠈⠹⡇⠀⠀⠟⠋ ⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠳⡀⠀⠀⠀⢢⡀⠈ ⠛⠛⠛⠛⢻⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠙⢆⠀⠀⠀⢻⣶ ⠀⠀⠀⠀⡎⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⡀⠀⠈⠎⠓⢄⡀⠈⠓⠦⣄⣀⣹ ⠀⠀⠀⣰⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⣉⠓⠦⣄⣀⣀⣠ ⠀⠀⠀⡟⠀⢀⡄⠀⠀⣿⡄⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣾⠁⠘⣧⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠠⣄⠹⡄⠀⠀⠀⠘⡏⠙⠛⠛⠉⠁ ⠀⠀⢠⠃⣠⠎⠀⠀⢸⡏⢳⠀⠀⠀⠀⢸⡄⠀⠀⠀⣸⡏⠀⠀⠈⢿⣦⠀⠀⠀⠉⠛⢦⣤⣀⡀⠀⠀⠙⠻⠤⢄⣤⡀⡏⣆⠀⠀⠀⠀ ⠀⠀⢘⣴⠏⠀⠀⠀⣿⠁⠈⢇⠀⠀⠀⠀⣷⡀⠀⢠⣿⠁⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠷⠶⠖⢶⡋⠀⡇⠸⡆⠀⠀⠀ ⠀⠀⠘⡏⠀⢀⡀⢸⣿⠀⠒⠚⣆⠀⠀⠀⠸⣷⡀⣾⠧⠤⠖⠒⠉⠉⠁⠈⢛⢦⣄⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣷⡀⢳⣆⠀⠀ ⠀⠀⠀⡇⢀⡾⠁⣾⣿⣦⣤⣤⣌⣧⡀⠀⠀⠹⣿⠇⠀⠀⣠⣶⣾⣿⣿⣶⣾⣧⣬⣿⣦⣈⠻⢷⣦⣤⣄⠀⠀⠀⠀⠀⠈⠓⠾⣿⣇⠀ ⠀⠀⢰⣇⡘⣷⣸⠟⣿⣿⣏⢻⣿⣿⣷⣦⣀⠀⠙⢆⠀⠀⠘⠛⠁⢻⣻⠟⣿⡿⣩⡿⠟⢏⠙⠲⠾⢿⣶⣮⣤⣀⣠⣶⣦⣤⣶⣾⣿⣷ ⠀⠀⠘⠻⠿⠻⢿⡀⢿⣿⠙⠮⠯⠤⠛⠈⠻⠳⢤⣈⠳⡀⠀⠀⠀⠐⠛⠒⠚⠛⠁⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⡀⠀⢈⡏⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠸⡇⢸⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡼⣼⠁⠀⢰⡇⢹⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠇⢸⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⣿⠋⠀⠀⢸⡇⢸⡿⢩⣿⣹ ⠀⠀⠀⠀⠀⠀⢠⣿⠘⠏⡏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣿⣷⡇⠀⠀⢸⠀⣾⣷⣾⣿⣟ ⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⣾⠃⣰⠁⠀⠀⢾⠀⢿⣿⣿⣿⠿ ⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣷⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢹⠃⠀⣠⡾⠁⢠⠇⠀⠀⠀⣼⡄⠸⣿⣿⣿⣷ ⡀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡿⢧⢸⡃⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⢠⠇⠀⣠⡿⠃⢠⡏⢠⠀⠀⢀⡇⠱⠀⢻⣿⡿⠻ ⣿⣿⣿⠛⠛⠛⠛⣿⠏⣧⢿⠘⣾⡇⢸⣿⣿⣦⡀⠀⠀⠀⣀⣠⣶⣭⣤⣤⣤⣤⣶⠋⣠⠞⠛⡇⠀⡾⠀⢸⠀⠀⢸⢡⡀⠀⠘⣿⠁⠀ ⣿⣿⣿⣦⣤⣤⣴⣿⠀⢾⠿⡇⢸⣧⣿⣿⣿⣿⣏⠙⠚⠉⠁⠀⠀⠀⠀⠀⠀⡰⠷⠊⠁⠀⢰⠃⠀⠁⢀⡏⠀⢀⡏⠀⢣⠀⠀⢻⣷⣄ ⣿⣿⣿⣿⡇⣿⣿⣿⠀⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡞⠀⣠⡾⠀⠀⠈⢧⠀⠘⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣯⠀⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠃⢀⡤⠋⢀⣰⡿⠁⠀⠀⠀⠘⣆⠀⢹⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣴⡿⠀⠀⢸⣿⣿⠿⠛⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣧⠴⢋⣰⠾⢛⡟⠓⠦⣄⡀⠀⠀⠸⣆⠈⣿ ⣿⣿⣏⠉⠉⠁⠈⠉⢹⡇⠀⣠⣾⠉⠀⠀⣠⠊⣴⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⡿⠛⠛⠉⠀⣰⠟⠀⠀⠀⠀⠈⠑⠢⣄⣻⡀⠸ ⣿⣿⣿⣿⣿⣟⣛⣛⣛⡇⠀⣿⠇⠀⢀⣴⣃⣾⠝⢚⣿⠀⠀⢠⠞⣿⡓⠶⠛⠋⣡⠞⠁⠀⣀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⠁⣠⠤⢤⠉⠈⡠⠤⡃⠀⠤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⡐⠁⠸⠉⠉⠓⠓⠥⣀⠀⠀⠑⠄⠈⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠂⡜⠀⡠⠓⠂⠀⠰⢤⣀⡈⢒⠄⠀⠈⡄⠀⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⢀⣼⣴⣀⠀⠀⠀⠀⠀⠈⢂⢊⠂⠀⠰⠀⠈⡄⠀⠀⠀ ⠀⠀⠀⠀⡐⢀⣴⠿⠛⠿⠿⠀⠀⢰⣿⣯⠳⡀⠈⡌⠀⠀⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⡰⠡⢁⠋⡆⠀⠀⠄⠀⠀⠀⠁⠈⠁⠀⠀⢿⢄⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⢀⠃⠀⡌⠀⠰⠀⢈⣐⣀⠀⠀⠀⠀⠀⠀⡀⢊⢴⠱⡀⠸⡆⠀⠀⠀ ⠀⠀⢸⡀⠀⠃⠀⠀⠡⠘⡿⠥⣿⠟⠁⠀⢀⠔⠀⠀⠄⠀⠀⠀⠗⡀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⢡⠀⠀⠀⢀⠠⠔⠹⡀⠀⠀⠰⠀⠀⠀⠀⠡⠀⠀ ⠀⠀⢸⠃⠀⠀⡀⢠⢤⡤⠭⠋⠉⠀⠀⠀⠀⠀⣢⠖⠂⠓⠠⡀⠀⠀⠑⡀ ⠀⠀⢸⠀⢀⣊⣠⣲⠏⠀⣀⡀⠀⠀⠄⠀⠀⣞⠃⠀⠀⠀⠀⠈⢄⠀⠀⠡ ⠀⠀⣈⡴⠋⠁⠀⠉⢳⡔⠃⠌⣢⠀⠀⠀⢸⠟⡸⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⢠⠃⠀⠀⠀⠀⠀⢰⠒⠒⠂⠨⡄⢀⠠⢼⡢⠁⠀⠀⠀⠀⠀⠄⠘⠀⠀ ⢠⠏⠀⠀⠀⢀⠠⠐⢰⢈⢁⠀⠀⠫⠒⠈⠁⠀⠰⠐⠈⠉⠈⡎⠀⠆⠀⠀ ⠟⠀⠀⠀⠠⠁⠀⠀⠀⢹⠈⢆⠀⠘⡄⠀⠀⠀⣠⠀⠐⠈⠉⡁⡘⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠲⡀⡴⠋⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⣀⣀⡞⠙⢾⠀⠀⢹⠃⠀⠀⢸⡠⠚⠛⡄⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠙⣦⣤⣤⠞⠀⠈⢧⣀⣼⢤⣤⣼⣦⣤⣀⣾⠀⠀⢰⣧⠤⡄ ⢠⣄⣀⡼⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⢿⣿⠟⠲⣏⠀⢀⠇ ⠰⠶⢾⠁⠀⠀⠿⠂⢠⢷⠀⠰⠆⠀⠀⠭⠭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡋⠀ ⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⢀⣠⣄⠀⠀⢀⡞⠀ ⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣸⣴⡛⠉⢿⣿⣦⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⣺⡗⠋⠹⣿⣷⣀⣠⠽⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢖⢺⠋⠛⢥⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣸⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣾⣦⢽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢯⣙⣯⣿⣛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠖⠋⡾⢿⡟⠳⠀⠀⠀⠉⠑⠲⣤⡀⠀⠀ ⠀⠀⢸⠃⠀⠀⠀⠀⠠⠃⡠⠁⠀⠀⠀⣸⠇⡈⣷⡀⠀ ⠀⠀⡏⣴⡀⠀⠀⠀⠀⠐⠁⠀⠀⠤⢤⣯⡸⠁⢰⡇⠀ ⠀⢠⠇⠘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⠀ ⢀⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⡇ ⢸⣶⡶⣾⣧⡀⢀⣰⣶⣶⣄⡀⠀⢀⣠⣾⢿⣷⣶⣤⣽ ⠀⠻⣷⣴⣿⣿⣝⣻⣚⣿⣿⣿⣿⣿⣿⣾⣾⣿⡿⠿⠃ ⠀⠀⠈⠉⢹⣿⠻⣿⣿⡿⠛⠛⠛⢛⠛⣿⣍⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣟⡀⣠⠀⡁⡀⢀⣀⣨⣤⣽⡏⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠈⠛⢿⣶⣿⣿⠹⠟⠛⠉⠀⣷⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠟⢦⡤⢤⠄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⡇⢠⡀⠉⠳⣷⣀⣈⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠉⠒⠂⠘⣧⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢾⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⡏⢧⡀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠷⣤⣀⣀⣠⣴⠃⠸⣇⠐⠄⠀⢠⡷⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⡍⣿⡀⠀⠹⣿⣶⣶⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⢸⡇⢸⡇⠀⠀⣿⣟⠋⢻⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠃⠀⠀⢸⣯⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣾⡿⠀⠀⠀⠘⣿⣧⣾⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠇⣸⡇⠀⠀⠀⠀⢸⡟⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⢹⣧⠀⠀⠀⠀⣸⠁⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣯⣈⣿⣿⠆⠀⠀⠀⣟⠀⢹⣄⠀⠀⠀ ⠀⠀⣶⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⠟⢁⡀⠀⠀

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⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⣦⣄⠀ ⠀⣷⡀⢀⣠⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⠾⠻⣿⡟⠁⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢀⣿⡆ ⠀⠈⢷⡀⠀⠀⠙⢷⣄⣠⡶⠟⠛⢿⡇⠀⠀⢹⡆⠀⠀⠀⢀⠈⣧⠀⠀⠀⣰⡿⠁⠀⠀⢀⣴⠟⠛⠁ ⠀⠀⠈⢷⣄⠀⠀⠀⠹⣇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠒⢻⡇⢹⡆⠀⣼⠏⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠹⣦⠀⠀⠀⢻⡄⢀⡤⢼⣇⠀⠐⠉⢿⡄⠀⠀⣿⠁⠈⣿⡾⠃⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠻⡄⠀⠀⢹⡄⠀⠀⢸⣇⣤⣀⢹⣧⡾⠟⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠻⣄⡴⠚⢿⣾⠛⢻⣯⣀⣿⠾⠋⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠻⣧⣀⣰⠿⣦⣤⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠉⠁⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠙⠷⠤⠤⠤⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠶⢦⠶⠒⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠤⠖⠋⠀⠀⠙⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⢸⠁⠀⠀⠀⣠⠀⠀⢀⡔⠁⠈⠳⡄⠀⠀⢠⠀⠀⠀⠀⢇⠀ ⠀⢸⠀⠀⠀⢠⠇⠀⢠⠞⠀⠀⠀⠀⠹⣄⠀⠈⡆⠀⠀⠀⡸⠀ ⠀⢸⡄⠀⢀⡞⢀⣴⠋⠀⠀⠀⠀⠀⠀⠘⣦⡀⢹⡀⠀⠀⡇⠀ ⠀⠈⡇⠀⣼⣡⣏⠙⢷⣄⠀⣀⢀⠀⣠⡾⠋⢹⣦⣳⠀⢰⡇⠀ ⠀⢰⡇⢠⣿⣏⠻⢷⣶⡿⠛⣡⣄⠙⠿⣷⡶⠟⢩⣿⡇⢸⣧⠀ ⢀⡏⠇⡾⣴⢋⣷⣦⡀⠀⢠⣿⣿⡇⠀⢀⣤⣾⣉⢧⢻⡘⠻⡄ ⢸⠁⢰⡇⠳⣈⠙⢿⡉⠂⠈⠉⢈⠁⠀⢋⡿⠟⢉⡼⠀⡇⠀⢷ ⠸⡀⠈⣧⡀⠈⠳⣄⠈⠻⢶⡧⢤⡧⢿⠋⢠⠖⠉⠀⣰⠇⢀⡞ ⠀⠙⢦⡙⠛⢦⡀⠈⢣⠀⠘⠀⠀⠃⠀⣰⠃⢀⡠⠞⣋⡠⠊⠀ ⠀⠀⠀⠉⠓⢤⣉⠓⠮⣷⠶⠚⠓⠲⢴⡧⠖⣉⡤⠞⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣲⠤⣠⣴⣯⠴⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⣿⣿⣿⠀⢰⢸⣿⡿⢿⡃⠀⢀⣠⣶⡿⠟⢛⣭⠵⠒⡆⠉⢹⣏⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡳⠒⢤⣄⠤⡀⠻⣿⡇⠀⣿⡴⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡘⠟⠿⠿⡆⣿⠀⠀⢀⣬⣿⡶⠟⣋⡥⡶⠊⠉⠀⢀⣠⢷⣴⡞⣸⡆⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠒⠬⢥⡀⠀⠄⠙⠳⣤⣹⢷⠀⣿⡇⠑⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀ ⠀⠰⡿⠋⠁⠖⣲⣤⣴⣾⣷⣿⠟⢋⡠⠖⠋⠁⢀⡀⠀⣐⣲⣶⣾⣿⣛⣰⣿⡇⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⣠⣼⢿⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀ ⠀⠀⠀⣠⣤⣾⣿⠿⠛⢻⣏⠁⠀⠉⠀⠀⠴⠺⠥⠶⠿⣿⣿⡿⠟⠛⠉⠁⡀⠀⠀⢀⠀⠀⠀⠀⠉⠛⠓⠦⢤⡤⠤⠤⠒⠚⠋⠁⢸⡟⢿⣄⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠉⠻⣿ ⣠⣴⣶⣿⡿⠛⠁⣠⣴⡿⠛⣿⣦⣀⠀⣀⣀⣀⣠⣤⠼⠋⠁⠀⠀⠀⠀⠀⠈⠳⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠽⡀⠈⠓⠦⣄⡂⠀⠀⠀⠈⠀⠀⠀⠙⠛ ⡿⣼⡿⠉⠀⣠⣾⠟⠁⣀⣾⣿⣾⣿⣷⣶⣶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⢻⡀⠀⠀⠀⠙⠲⣤⠀⢀⠀⠀⠀⠀⠀ ⡇⢿⡇⣠⡾⣟⣡⣴⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠈⠳⣄⠀⠰⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣦⣀⠀⠈⠳⣄⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠘⠋ ⣿⣧⡘⣿⣿⣿⣿⣿⡟⡟⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⢸⠷⣄⠀⠀⠀⠀⠴⢾⣿⣿⣿⣿⣿⣿⠃⠀⢬⠳⢯⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⡦ ⣿⣿⣷⣿⠛⣿⣿⣿⠃⣇⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣧⠀⠀⠀⠀⠀⠀⠀⢸⠀⡈⠳⣄⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⠀⠀⠈⡇⠀⠉⠒⠤⢄⣀⣀⡀⠀⠀⠠⠀⣈ ⣿⣿⣿⣿⠀⣿⣿⡿⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢦⣄⠑⢦⣀⠀⠀⡀⢹⠻⣿⣯⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢿⣿ ⣿⣿⡉⠙⠃⠉⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣠⠴⢶⡚⢧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠙⠦⡈⠙⠦⣷⣸⡀⠙⢿⠀⠀⠀⠀⣧⠘⣆⠀⠀⠀⠀⠀⣠⣦⣀⣸⣿ ⣼⣿⣿⣄⣀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠑⠈⢣⡀⠀⠀⠀⠀⠸⡄⢀⣤⢴⣄⣤⣤⣀⡒⠈⡹⣧⠀⠈⠁⠀⠸⡄⢸⡀⠘⡦⠄⠀⠀⠀⢻⣿⣿⣿⣉ ⢻⣿⣿⣿⡷⣷⣦⣶⣶⣾⠁⠀⠀⠀⠀⠀⢀⠀⢀⣾⢏⣤⣤⣤⣤⣤⡀⠰⣿⣦⣀⠀⠀⠀⢳⡀⠹⠛⣫⣿⣿⣯⡻⣶⡀⢻⠀⠀⠀⠀⠀⣧⠀⣇⠀⠸⣆⠀⠀⠀⠀⠙⣿⣇⡟ ⡼⠿⠿⠿⠯⠿⠿⣿⣯⡏⠀⠀⠀⠀⠀⠀⣾⠀⢸⣿⣾⠋⣿⣿⣿⣿⡛⠀⠈⠙⠻⢵⣖⣦⣤⠷⠄⢸⣿⣿⠿⣿⣷⠈⠻⣼⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠻⡄⠀⠀⠀⠀⠈⠛⠣ ⠀⠀⠀⠀⠀⠀⠀⢤⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⢿⣾⠃⢰⣿⣿⠛⣿⣷⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⣿⡿⠒⢿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢀⣠⠴⢢⠇⠀⠀⠀⠀⠀⠀⠀⣹⣄⡟⠈⠀⠸⣿⠿⢚⣿⡿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠙⠷⠾⠟⠋⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀ ⠄⠙⠦⣀⢸⠁⠀⡼⠀⢰⠃⠀⠀⠀⠀⢰⢿⠻⡇⠀⠀⠀⠙⠳⠖⠛⠁⠀⠀⠀⢀⣀⡠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣶⣦⠀ ⣆⠀⠀⠈⠓⠆⣸⠁⠀⡞⠀⠀⠀⠀⠀⣸⣯⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⢀ ⣿⣿⣶⣤⣤⣴⠃⠀⢸⡇⢰⠀⠀⠀⢀⡇⠈⢳⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠻⣿⣷⣼ ⢿⣿⣿⣿⡇⠏⠀⠀⡾⡇⢸⡀⠀⠀⣼⠀⠀⠀⠙⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿ ⣿⣿⣿⣿⣇⠀⠀⠀⠇⠇⠘⡇⠀⠀⡏⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⣀⣠⣤⣤⣤⣭⣭⣭⣥⣤⣤⣤⣀⣀⣀⣀⣰⠟⡅⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠀ ⣾⣿⡿⠿⠿⢶⣄⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣿⣿⡿⠿⠛⠛⠛⠛⠛⡋⠀⠀⠀⠀⠀⠀⠉⢙⣿⠃⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢰⣥⡀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠐⠢⢤⣈⣙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⣤⣤⣴⣶⣶⣿⣿⣿⣿⣇⣀⣀⠀⠀⣠⣿⠃⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡷⠠⠍⣹⢷⣦⣄⠤⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠁⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢲⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⣿⣦⣽⣿⣝⣶⣤⣀⢀⣀⠀⠀⠁⢀⣸⣿⣿⠟⠻⠿⠶⠿⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠺⡖⠀⣀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠠⢾⣾⣿⣿⢿⣿⣿⣿⣻⡿⣿⣷⣟⣻⣷⣶⣾⣿⣟⣀⣀⣀⠀⠀⣀⣴⡿⠋⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⡀⠀⠉⠳⣷⣶⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⡃⠈⠛⠻⠿⣿⠿⠛⠛⠛⠻⠭⢟⡛⠛⠛⠻⠿⠛⠛⠋⠁⠀⠀⢀⡴⠋⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠀⠀⠈⠙⢶⣦⣤⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣦⡴⠚⠁⠀⠀⢀⡔⠀⣠⠀⠀⠀⠀⠀⠀⠬⣷⣦⣀⣒⣚⣭⠤⠶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠱⡄⠀⠀⠀⠀⠀⠀⠈⠻⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⢠⠟⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠈⣀⣀⣀⣀⣑⣀⡀⠀⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢀⡴⣰⠃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠲⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⠟⠻⠛⠛⠉⠉⠉⠋⠛⠩⠹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠉⡸⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠲⠆⠀⠀⠲⠦⢤⣤⣭ ⠀⠀⠀⣀⣀⠀⣀⣀⣽⢞⠰⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠉⠀⠀⠀⠀⢠⣤⣤⣄⣀⣀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⡤⠶⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣶⠞⠁⠀⠀⠀⠀⠈⠑⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣇⡀⠀⠀⠀⠀⠀⣠⠴⠒⠳⢄⠀⠀⢙⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣴⡇⠀⡀⠀⠀⣷⠚⠉⢈⡷⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠈⢧⡀⠛⢀⣠⢏⣠⠔⠋⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣦⢄⡀⠉⠉⢉⡿⠋⢀⣠⢴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣤⣿⠀⢠⣿⣴⣺⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⢹⡦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠘⠚⣿⣯⡴⢾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⣹⠋⠁⠀⢷⠋⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢹⡄⠀⠀⠀⠀⠀⠈⠙⣇⠸⡿⣿⣟⠘⣿⣟⣳⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠙⢓⣦⠀ ⣶⠓⢲⠖⠛⠁⣄⣧⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠮⣝⣲⣯⣧⠿⣽⡟⢦⣀⣀⣀⡀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣠⠖⠚⠉⠀ ⠛⢷⢸⡀⣟⣿⣁⡝⣧⠀⠀⠀⠀⠀⠀⢀⣧⠤⠖⠊⠁⠸⣏⠙⠛⠛⢯⡉⠁⠀⠙⣦⠖⠚⠉⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀ ⠀⠸⣆⠉⠁⠈⠁⠰⠧⣄⣀⣠⠴⡶⠶⠼⣅⡀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠙⢆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡄⠀⠀⠙⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢀⣿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠧⣄⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣰⠏⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣷⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠈⠙⠦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠣⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠈⠺⣿⡗⠒⠒⠲⠶⠖⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⢉⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠚⠉⠉⠉⡿⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⢁⡼⡅⠈⠲⣄⡀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠒⠋⠉⣹⠃⠀⠀⠀⠈⠉⠙⠛⠛⠋⡿⠁⠀⠀⠀⣿⠀⠘⠢⣄⡀⠉⠓⠲⠤⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠻⣷⠀⠀⠀⠉⠓⠲⡶⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⣀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢰⠟⠀⢰⠋⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠸⡆⠀⠘⢧⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢠⡏⠀⢠⡏⠀⠀⠀⣼⡿⡀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠘⡆⢀⠀⠀⠀⢹⡀⠀⠈⣆⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣿⠀⠀⣸⠀⠀⠀⠀⣯⡇⡇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣇⠀⣧⠀⠀⠘⣧⠀⠀⠸⣇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡏⠀⢀⡇⠀⠀⠀⢠⢿⠀⡇⠀⠀⠀⠀⠀⢀⢨⡁⠀⠀⢸⡄⠸⡄⠀⠀⣿⡄⠀⠀⢻⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⣿⠇⠀⢸⡇⠀⠀⠀⣼⣼⠀⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⣇⠀⡇⠀⠀⠸⣇⠀⠀⠘⣧⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠠⣤⣀⠀⠀⣹⠀⠀⠀⠀⢰⡿⠀⢀⣾⠀⢰⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⠀⢐⢸⢿⠀⠀⢸⣿⠀⢸⠀⠀⠀⣿⡀⢀⠀⣿⡀⠀⠀⠀⠀⢸⣁⣀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠑⡇⠀⠀⠀⠀⢸⣷⠀⢸⣿⠀⢸⠤⠶⣿⣿⠛⡟⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⢺⣿⡙⢿⠁⠒⠢⣼⣇⢸⡄⢸⡇⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⣾⣿⠀⡼⠀⠀⣿⠹⠀⣿⡀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡾⡇⢸⠀⠀⠀⣿⣿⠘⡇⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢹⠿⡄⣇⠀⠀⣿⠀⡇⡿⡇⠀⠀⠀⠀⠀⢠⣿⡄⠀⢸⠃⣧⢸⡆⠀⠀⢸⣿⠀⣧⢸⠃⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣼⡷⠀⠀⠀⠀⢸⢻⠀⢸⡀⡇⢻⠀⠀⣿⣤⣷⣿⣱⡀⠀⠀⠀⢀⣿⣿⡇⠀⣼⡤⣼⣤⡇⠀⢀⣟⣘⡇⠛⢸⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠐⠚⠉⢀⣧⠀⠀⠀⠀⢸⣼⣆⣾⣷⣿⣿⣿⣿⣿⣷⣿⣿⡍⠛⠒⠒⠒⠒⠛⠉⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣄⣀⠉⠒⠀⠀⠀⠀⠀⠐ ⠀⠉⠙⠓⠒⣶⠖⠋⠉⢸⠀⠀⠀⠀⠸⣿⡇⢹⡇⣧⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣴⣿⣭⣿⣿⣿⡏⣸⠉⣿⡀⠀⠀⠀⠀⢸⡄⠈⠉⠙⢷⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⡾⠀⡼⡄⠀⠀⠀⠀⡏⡇⠀⠣⢻⡿⢿⣿⣿⡟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡿⠿⠟⠉⣿⠃⠃⠀⣼⡇⠀⠀⠀⠀⣼⣇⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡃⢸⡇⠀⢷⣧⠀⠀⠀⠀⢷⣧⠀⠀⠀⠻⢿⣀⣀⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣤⣴⠛⠁⠀⠀⠀⣿⠁⠀⡇⠀⢀⣏⣿⠀⢀⣷⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣅⡿⠀⠀⢸⣽⡄⠀⠀⢻⠸⣿⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⠇⠀⢸⣿⡇⠀⢸⠏⠀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⡀⠀⢸⡟⣧⠀⠀⢸⡀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡟⠀⣼⠀⠀⣾⣿⠇⢠⠏⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⣧⢸⡀⠀⠀⡇⠹⣯⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢸⠇⠀⡟⠀⢠⣿⢟⣴⡿⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣧⠀⠀⢷⠀⢧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢸⠀⢰⠃⠀⣾⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⡆⠀⠸⡇⠸⡆⠀⠀⢹⡳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠻⣯⠀⠀⢀⡏⠀⣼⠀⢰⣿⣿⣿⡀⣻⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣄⠀⢿⡀⢳⠀⠀⠀⢳⠀⢌⠉⠓⠲⠤⣤⣀⠀⠀⢀⣀⣤⠤⠖⠚⠉⣵⢁⡼⠁⠀⠀⢸⡇⢸⡏⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠁⠹⡄⠈⣧⠘⣇⠀⠀⠈⢳⡈⠳⣤⡀⠀⠀⠀⠙⢯⡽⠋⠀⠀⠀⣠⠞⢁⡾⠁⠀⠀⠀⡾⠀⣿⠁⣾⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠻⡄⠀⢹⡄⢸⣆⢹⡄⠀⠀⠀⠙⣦⣀⠈⠲⠠⠤⠀⠀⠀⠀⠠⠴⢋⣡⣾⡟⠀⠀⠀⠀⢰⡇⣼⠇⢸⠃⠀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡷⢠⡸⢦⠀⠻⡄⢹⡄⢳⡀⠀⠀⠀⠀⠻⣝⢻⠛⠻⢿⡛⣛⡿⢲⢶⣿⡵⠋⠀⠀⠀⠀⢀⡾⣸⢿⢠⡏⠀⡼⣽⢿⣿⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢛⣇⠈⡷⣸⠳⣄⠻⣶⣿⣾⣷⠀⠀⠀⠀⠀⠈⡇⢠⣠⠴⠚⠛⠦⣼⠛⡏⠀⠀⠀⠀⠀⠀⣼⣷⠋⣾⡿⢠⣾⣡⡀⠼⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡜⣟⣶⢧⠏⡆⠈⠳⣽⣿⣎⠻⣧⠀⠀⠀⠀⠀⡇⠘⢧⣄⠀⢀⡴⢻⠀⡇⠀⠀⠀⠀⠀⣰⡿⠃⠘⣻⠷⣫⡌⢳⣷⣼⣿⣠⣼⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆⡸⣿⡟⢰⠃⣼⠓⢦⣉⢳⡦⣀⡀⠀⠀⠀⢀⠃⡇⢀⣨⠿⠯⣀⠀⠀⠇⠀⠀⠀⠀⠀⢉⣠⣴⠛⠁⢸⡇⠹⡌⢷⡿⠋⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡿⠁⠀⢹⠞⢧⡸⣆⠉⠀⢠⠇⢸⠁⡆⠉⠙⠲⠦⣼⢰⣿⡉⠀⠀⠀⣠⠟⠃⢦⡤⠤⠴⠖⠛⣉⡀⢹⡀⢲⠈⢁⣴⢧⣾⣷⠊⠈⢿⣿⣿⣿⣽⣧⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠘⠶⠤⣿⣮⡛⢦⡞⢠⡏⢰⠃⣾⠉⠓⡦⡼⢸⠀⠙⣦⣴⠋⠁⠀⡄⢸⠀⣆⠀⣞⡋⠉⡇⠀⣇⠘⣶⢟⡵⢋⣸⠁⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠈⣇⣙⣲⣤⣼⠁⢸⣄⡁⠀⢠⠇⡄⢸⡠⠞⠉⠈⠙⢦⣜⡇⢣⠀⣿⠀⠛⠃⣀⡇⠀⢸⣧⠞⢫⡞⠉⠁⠀⠀⠀⠀⣟⠉⠙⢿⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⣟⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠉⠙⢻⣏⠓⠦⣬⣉⠓⠚⢀⡇⠘⠳⣄⠀⠀⠀⣠⠽⡇⢸⠀⢸⡶⠒⣋⣩⠴⢲⣿⠗⠒⠛⠀⠀⠀⠀⠀⠀⠀⡼⢠⣀⡞⠁⠀⠀⠀ ⣀⣀⣀⣀⣀⣿⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⣏⣹⣾⡇⡆⠀⠀⣙⠶⣏⡁⠀⠁⢸⡿⣏⣹⠿⠛⠒⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠙⣦⣀⣀⣀ ⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣧⠖⠋⠁⠀⠀⠉⢳⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠐⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⠙⢤⣀⣀⡤⠞⠋⣹⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⣿⣻⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢒⠒⠢⡄⡀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⢀⠠⠤⠀⢤⡄⠀ ⠀⠀⠈⣄⠑⠄⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠂⠀⠀⠔⢁⢾⠁⠀ ⠀⠀⠀⠹⣄⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⢀⠔⢃⠎⠀⠀ ⠀⠀⠀⠀⣈⠶⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⣾⣤⣤⣤⡶⢥⢔⠁⠀⠀⠀ ⠀⠀⠀⢾⡀⠀⠈⢇⠀⠀⠀⠀⠀⠀⢀⢜⡴⡹⣿⡿⢹⡟⠛⠁⠀⣨⡆⠀⠀ ⠀⠀⠀⠀⠁⠒⡲⠘⣦⠀⠀⠀⡠⠒⡡⠣⠁⠚⠛⠟⣏⠉⠺⡋⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣛⣥⣑⣄⠀⢀⣾⠮⠵⣦⡠⠜⣄⢘⠗⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠊⠁⠀⠀⠉⠺⣗⠂⠀⣝⡗⠒⢎⠉⠁⠢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡌⠉⠢⠀⠀⠀⠀⠀⠘⠆⠀⣿⠋⠀⠀⠈⠁⠢⣣⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⢱⢀⠀⠈⢄⠀⠀⠀⡀⢸⡼⠁⠀⠀⢀⠄⠊⢩⠹⠡⡀⠀⠀⠀ ⠀⠀⢀⠾⣀⡏⢀⠼⡆⠀⠑⠠⢐⠀⡌⠀⠀⣀⠔⠁⠀⡠⢣⠒⢇⠑⡀⠀⠀ ⠀⡔⠁⠀⠈⠃⡊⣠⡧⠤⠤⢤⡀⢉⣁⡈⠉⠀⠀⠠⢪⣖⠈⢢⢈⡇⠙⠠⠀ ⠰⠀⠀⠀⡜⠀⠉⢿⠁⠀⠀⠀⢱⢸⠀⠀⠉⠁⠒⡠⢄⡄⠑⡜⠋⠀⠀⠀⠁ ⠀⠢⣀⣊⡀⠤⠊⠀⢑⣤⣠⣐⣁⠼⡄⡀⢀⡀⠔⠁⢀⠃⠒⢅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠸⠁⠀⢹⠂⢤⠀⠠⠔⠁⠁⢄⠀⠈⠁⠈⠁⠀ ⠀⠀⢀⡀⠀⠤⠇⠐⠒⠒⠒⠊⠀⠀⠈⠁⠘⠐⠒⠒⠒⠀⠤⠧⠀⢀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠻⠶⠶⠶⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⣀⣤⠶⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠺⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠙⠛⠶⢤⣤⣄⣀⡀⠀⠀⣿⠁⠀⠀⠈⣷⡄⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠾⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠿⣦⣄⣀⣀⠈⠃⠀⠀⠙⠷⠾⢦⣤⠄⠀⠾⢷⡟⠀⠀⠙⣦⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠦⢤⣤⣀⣀⠀⠀⠀⢸⣇⠀⠀⠀⠸⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠲⠿⠦⣤⣀⣀⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⣭⣿⣿⣿⣦⠀⣀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⣾⠟⣩⠟⣽⢯⣿⠏⢉⣥⣶⠿⣻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⢠⡟⠀⢀⡞⠛⠁⣀⣥⣈⡁⠚⣾⣞⡙⠋⠁⠚⢩⠞⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢿⡷⠯⣷⣦⣠⣞⠁⢠⣏⢀⡴⠋⠁⠀⠀⠉⠻⣏⠉⠉⠓⢦⡀⠀⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠟⠛⠛⠛⣻⣿⣿⣇⠀⠛⢹⠟⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠱⣶⣏⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣻⡆⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⣿⣿⣛⣖⣻⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⠘⠉⠓⠻⠃⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⠛⢿⡄⠉⠙⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡿⣿⡄⢀⣤⠶⢶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⢸⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⣷⣯⣾⠈⠀⠈⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⠧⢿⡿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡿⠏⠙⣮⡀⣶⠀⢻⡛⠲⠤⣤⣀⣀⣀⠀⠀⢰⠏⠀⠀⠀⢠⡾⠀⠀⢻⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⡇⣀⠀⠀⠈⣽⠇⠀⠀⠑⢄⠀⠀⠉⠉⠉⠉⣹⡛⠛⠛⠉⢉⡽⢁⣤⣨⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠿⣆⠀⠀⠀⠀⠙⠒⠶⠶⠶⣏⠉⠉⢱⡦⠖⠉⠀⢸⠏⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⠏⠀⠈⠳⢤⣀⣀⠀⠀⠀⣀⣀⣈⠽⠿⣍⠀⠀⢀⡴⠋⣠⣤⣿⣃⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣶⣦⣦⠌⠉⠉⠉⠉⢉⡥⠶⠦⣄⣈⣓⡛⠉⠀⢘⡿⠋⠉⠉⠉⠙⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡿⣷⡶⢶⡶⢰⡏⠀⣠⠚⠉⢀⡹⠗⠒⢾⡿⠁⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠳⠤⣇⠀⢀⡎⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⣤⣀⡿⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋⠁⠀⢀⡀⠀⠀⠈⠓⠒⠳⣤⣤⠼⠃⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡀⠀⠀⠀⠳⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠀⠀⢀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⢻⡏⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⠻⢸⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣿⡆⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⡇⠀⠀⢸⣟⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠟⣿⠀⠀⠀⢸⠋⠉⢉⡿⠉⠉⠉⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣄⡏⠀⠀⠀⣸⠀⢀⡞⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡟⢹⠇⠀⠀⠀⣿⢀⡾⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣿⡇⠀⣿⠀⠀⠀⠀⣿⡾⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣟⠛⢋⣿⣿⣷⡶⣾⣿⠿⢲⡇⠀⠀⠀⠀⡿⠁⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣿⣯⣭⡍⠀⠀⣛⣛⠟⠰⠛⠁⠀⣾⠁⠀⠀⠀⢸⡇⠀⠀⢀⣸⣇⡀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣠⣉⣄⡀⠀⠀⠀⠀⠀⠀⣠⣿⡈⣿⣦⡀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⣿⠀ ⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⢸⡄⠉⢨⡇⠀⠀⠀⠀⠀⣰⠟⠈⢳⡘⡞⢧⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠄⢸⠀⠀⣿⠀ ⠀⠀⠀⠀⢸⠈⢳⡄⠀⠀⠀⠀⠀⠙⠴⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠈⣿⣹⡜⢧⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣷⣦⢸⡄⠀⣿⠀ ⠀⠈⠀⠀⢼⠀⠈⠻⣦⡀⠀⠀⢀⣠⣤⣶⠟⠻⣦⡶⣟⠁⠀⠀⠀⠀⢸⣧⢳⠈⢧⠀⠀⠘⢿⣤⣤⣶⠖⢾⡟⠉⠉⢯⠉⢿⡷⣶⣤⣤⣶⣶⣆⠀⣼⣽⣿⡀⢸⣿⣿⡇⠀⢹⠀ ⠀⠀⢀⡄⢸⠀⠀⡷⠀⠙⣆⠀⢸⠁⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣿⣟⣆⣈⣧⣀⣘⣿⣿⠤⠾⢷⡶⡷⠦⠤⠼⣦⠀⠹⣿⣏⠉⠙⣮⣝⣷⣿⣻⣿⣷⣈⣻⣿⡇⠀⢸⠀ ⠀⠀⠋⠀⠸⡄⢠⡇⠀⠀⢻⡆⠘⡇⠀⠀⣷⠀⠀⠀⣾⡄⠀⢸⡀⠀⠈⢹⣿⣯⠉⠙⣯⠁⠈⢛⡇⠀⠈⢷⡁⢶⡄⠀⠸⡄⠀⠈⠻⣆⠀⢸⣿⣷⣍⠙⣿⣿⣿⣿⣿⡇⠀⢸⡀ ⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⣿⡆⣧⠀⠀⣸⣆⠀⠀⢹⣇⠀⠀⣇⠀⠀⠀⢿⣿⠀⠀⠈⣧⡀⢸⣽⠀⠀⠈⢳⣎⢷⣄⡀⢻⡀⠀⠀⠈⢷⠀⢻⣷⡙⣷⣼⣿⣿⣿⣿⣿⡀⢸⡇ ⠀⠀⠀⠀⠀⢻⣸⣷⠀⠀⠀⠙⢿⣿⣠⠾⠁⢹⣦⠀⠀⣿⡆⠀⢸⡆⠀⠀⠸⣿⡆⠀⠀⠸⣧⠈⣿⡇⠀⠀⠀⢿⡄⢻⣧⠸⡇⠀⠀⠀⠀⢷⡈⢿⣿⢿⣿⣿⣿⣿⣿⣿⡇⢸⡇ ⠀⠀⠀⠀⠀⠸⣿⣿⠀⢀⣠⣴⣿⣿⠁⠀⠀⠀⢻⣧⠸⢹⣷⠀⢀⣷⠀⠀⠀⣿⣧⠀⠀⠀⢹⡰⣯⣧⣀⢤⣤⣤⣷⣤⣿⣶⣿⠀⠀⠀⠀⠀⢳⡹⣿⣧⣽⣿⣿⠿⠻⣿⣷⢸⡇ ⠀⠀⠀⠀⠀⠀⢳⣿⣾⡏⠁⠀⢹⣿⡆⠀⠀⠀⠀⢻⣦⣱⣿⣷⡈⣿⣧⢠⡰⣼⣿⡀⠀⢀⡼⣷⣿⣿⣿⠿⠿⠿⠿⣿⣿⡛⠿⣿⣶⣤⣀⡀⠈⢷⣿⣿⠶⠟⠁⠀⢀⡈⢿⡌⡇ ⠀⠀⠀⢀⡤⠚⠙⣿⡇⠳⡀⠀⠈⢿⣷⠀⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣻⣼⡇⢻⣿⡇⠀⢀⣴⢿⣿⣿⣥⣤⣤⣶⣯⠬⣽⣷⡀⠀⠈⠛⣿⡛⠛⠛⣿⣿⡇⠀⠀⣰⡟⠙⠈⢿⡇ ⠀⠀⠐⠉⠀⠀⠀⠻⣽⡀⠻⣄⠀⠈⢿⣇⠀⠀⠀⠀⠀⠱⡝⢿⣷⡹⣷⡹⡇⠀⢻⣇⠀⠺⠃⢸⣿⠻⢿⡉⠛⠉⢹⡇⠀⠙⢧⠀⠀⢰⡟⠛⠓⠒⠚⣿⣧⠀⠀⣿⠓⠀⠀⠈⡇ ⡄⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣨⠷⠶⠶⣾⣦⠀⠀⠀⠀⠀⠙⢦⡙⢿⡌⠻⣄⠀⠀⠛⠀⠀⠀⠘⣿⡀⠀⠙⢦⣀⠏⠀⠀⠀⢸⣄⡴⠏⠀⠀⠀⠀⠀⢻⣿⠀⠀⠘⣆⠀⡀⠀⡇ ⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠙⠀⠙⠂⠈⠓⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠻⠛⠒⠲⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣰⠃⢠⡇⠀⡇ ⠀⠀⠀⠀⠀⣠⣾⡿⣿⡟⠉⠀⢀⣀⣤⠾⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⣠⠎⠀⢰⢃ ⠄⠀⠀⢀⣾⡿⠋⢠⡟⠀⣾⡛⠛⠋⢹⡟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡿⠁⠀⠀⡾⠋ ⢰⡀⣤⣿⡿⠁⠀⢸⣇⢰⣿⠓⠢⠔⠋⣀⡤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣸⠁⠀⠀⠀⠒⠞ ⠀⣿⣿⣿⡀⠀⠀⠈⣿⣼⠃⢀⣠⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⡇⠀⠀⠀⠀⠀⣁ ⠋⣼⣿⣻⡷⢤⣀⠀⠸⢧⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⡇⢀⣀⠀⠀⠀⠰ ⠀⠀⠸⣿⣷⡀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠀⠀⠀⠀⢸⢿⢯⣀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⠘⠆⠀⢱⣤⡀⠀ ⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣦⠌⠙⠻⣷ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠖⢒⣲⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠙⢦⣴⠛⣦⡀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣯⡤⠤⠖⠛⠉⠀⠀⠀⠈⠉⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠙⣦⡈⠿⣶⣄ ⠠⠤⣤⣠⡀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣤⠟⠀⠈⠳⣤⣌⠛ ⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢠⣄⣱⣄⠀⠀⠀⠀⠉⠙ ⠓⢤⣀⠀⠀⠈⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⣠⣄⠈⠀⠀⠀⠄⢀⠜ ⣤⣀⠈⠉⡉⠉⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣠⠞⣿⠁⠀⢀⡼⠳⢬⡳⣄⠀⠀⠀⠂⠀ ⠿⣿⣄⣀⣿⠀⠀⣿⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⠞⠁⠀⣿⠀⣤⣿⠀⠀⡆⠙⢾⣳⣄⡀⠐⠀ ⢀⣿⣿⣿⣿⣀⣀⣼⣦⠀⠙⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡴⠋⠀⢠⣦⢻⣿⣿⣿⠟⠛⣧⠀⠀⠉⠛⠻⢦⡀ ⣼⡿⢻⣿⡟⠋⢹⣿⣿⠓⠶⠋⠙⠻⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣤⣤⣤⣤⠖⠋⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⠉⢷⣯⣿⣷⣦⡇⠀⠀⠀⠀⠀⠀⢹ ⠉⢠⣿⡟⠀⢤⣿⣿⡟⠀⠀⢠⡀⠀⣀⣈⠉⠛⠿⣗⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠄⠀⠈⣿⠀⣿⣐⣿⢀⣀⡥⠀⠀⠀⠀⠀⠀⠠ ⣴⣿⠋⣰⣷⡿⣿⣿⡇⠀⠀⢸⣧⠞⠉⠉⠛⠂⠀⠈⢳⡀⠀⠀⠉⠉⠓⠲⡆⢠⣤⣀⣀⠀⠀⠈⡇⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠹⣷⠭⠿⠳⣄⡀⠀⠀⠀⠀⡀ ⠟⣠⣮⡿⢫⡾⣿⣿⠇⠀⠀⣾⠃⠀⠀⢠⡶⢦⣄⠀⠀⢳⡄⠀⠀⠀⠀⠀⠈⢉⡀⠀⠈⠉⠉⠉⢻⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⢇⠀⠀⣀⡽⠶⠆⠀⠀⠀ ⡚⠛⢉⣰⣟⣻⣿⡿⠀⢀⡼⣁⣄⠀⠀⢸⡿⠀⢻⣟⡶⠤⢿⣄⠀⠀⠀⢠⣄⣈⣿⣿⡃⠀⠀⠀⢸⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔ ⢧⣄⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⠀ ⠘⠿⣿⣗⣦⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣤⡶⣻⣿⡿⠏⠀⠀ ⡄⠀⢿⣿⣟⢦⣽⣶⡶⠟⠍⠉⠉⠙⣿⣿⠏⠙⠚⡯⠯⠕⠒⠿⢯⡿⠁⠀⠀⢠ ⣅⡤⠈⢻⣿⠉⠉⠉⢉⠀⣄⡀⠀⠀⢻⢷⠀⠀⠈⡗⠀⠀⠀⠀⠈⣇⡀⢀⣂⢰ ⢅⠀⠀⠘⠃⠀⠀⠆⢸⣧⠃⢰⠀⠀⠨⠐⠀⠀⠀⠈⢷⡄⡄⠀⠀⠀⠐⢶⣾⠁ ⢸⣇⡀⠀⠀⠀⠸⠀⣿⡏⠀⠈⣆⡄⠀⠀⣦⠀⠀⠀⠈⣷⡏⠀⠀⠀⣀⠀⠹⡃ ⣼⣯⡷⡶⣶⣶⣾⣷⣶⣍⠀⢠⢿⣇⣆⠠⠳⢀⠀⢠⢀⣽⣾⣿⣿⣿⡿⡀⠀⠘ ⣿⠃⠁⠧⡘⢿⣿⣿⣿⣿⡂⠀⠃⠻⢿⣟⣴⠁⠀⠁⣿⣿⣿⣿⣿⠟⣠⠇⠀⠀ ⣿⣄⡄⠀⠈⠑⠌⠙⣿⣿⣷⠀⠀⠀⠀⢱⠁⠀⠀⣰⣿⣿⠛⠋⠡⠒⠁⠀⠀⠀ ⣇⠃⠙⢾⡀⢀⣀⣠⠟⢿⣻⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⠀⠀⣄⣤⠀⠀⠀ ⠸⣇⡀⠈⠙⠻⣿⡗⠀⢲⣿⣻⣖⣀⣀⣀⣀⣠⣾⣿⡯⢧⣰⢿⡿⠛⠀⠀⠀⣠ ⠀⠈⠳⡀⠀⢰⡎⠋⠀⠀⠙⢿⣿⣿⣿⣽⣿⣿⣿⠟⠁⠀⢭⣯⣀⣀⣤⣶⣿⣿ ⠀⠀⠀⢉⣦⣜⣧⣣⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠁⠀⠀⡶⢲⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⡷⠖⣶⠒⣬⣿⡟⠤⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⣾⣿⣿⣿⣿⡟⠓⠢⣄⡉⠉⠈⠉⠉⣁⣴⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠭⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠒⠒⠒⠒⠒⠒⠒⠒⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⠀⢠⡤⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⢤⡄⠀⣀⣀⣀⡀⠀ ⡰⠕⠀⠐⠂⠍⡆⠙⣭⣛⡀⠤⠤⠤⠤⠤⠤⠤⠄⢐⣛⣭⠋⢰⡩⠐⠂⠐⠫⢆ ⢣⢄⠀⠀⢀⢠⢛⠞⠁⠀⠉⠉⠁⠒⠒⠒⠒⠈⠉⠉⠀⠈⠳⡛⡄⡀⠀⠀⡠⡜ ⠈⠳⣕⠀⣰⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣝⣆⠀⣪⠞⠀ ⠀⠀⠀⠉⢠⠇⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠸⡄⠉⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢠⡾⠿⠿⠿⣿⣄⠀⠀⣠⣿⠿⠿⠿⢷⡀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠈⢀⣶⠛⠛⢦⠙⠀⠐⠋⡶⠛⠛⣷⡀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠃⠀⠀⠸⣷⡈⡃⣸⠇⠀⠀⠸⣇⢹⠁⣾⠇⠀⠀⠘⢇⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⠀⠀⢀⣩⠿⢿⡭⠤⢶⣶⣤⣭⡿⠿⣉⣀⠀⠀⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠘⢆⡀⢀⡞⠁⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⠈⢳⡀⠀⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⢷⣀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⡾⢠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠈⠫⣹⡒⠚⢉⠉⢉⡉⠉⣉⠓⢒⣏⠝⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠒⠛⠤⠼⠧⠤⠛⠒⠋⠁⣀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣤⣀⣠⣄⣀⣠⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⠾⡇⠈⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣮⣦⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡍⠻⠐⣦⡉⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣄⠈⣿⣿⣿⣿⣧⠙⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠈⠉⠛⠻⣦⣼⣟⢻⣿⣟⢀⡤⢽⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⢄⡙⠻⣿⣿⠈⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠀⠀⢀⡴⠉⡼⠁⣷⠀⠀⠹⣄⠹⣿⠀⠀⠀⣧⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⣠⡞⠀⡼⠀⣀⣿⣧⣄⡀⠘⣆⠀⠀⣠⣾⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡸⠟⠻⡟⠀⠈⣱⣾⣿⣿⣿⣿⣿⣦⠸⡆⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠀⠀⠀⠀⠒⠻⢿⣿⣿⣿⡾⠧⢤⠜⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣧⡔⠸⡆⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢧⠀⠹⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿⠿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠹⡄⠀⠹⣦⣄⣀⣀⣀⣀⣻⣢⠇⢘⣧⣬⣉⣀⣤⡾⠁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠢⡀⠈⠛⠿⣿⣿⣿⠿⠋⠀⠀⡇⠙⠛⣿⠉⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠲⢄⣀⠀⠻⠀⠀⠀⠀⠀⣿⠀⠀⠛⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠤⢿⠦⠤⣤⣄⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⣀⣬⠭⠷⢶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠋⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛ ⠉⠉⠛⠓⠲⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣠⣖⣋⣁⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⠿⠛⠉⢀⠀⠀ ⠒⠶⠦⣤⣤⣀⣀⡀⠀⠈⠉⠉⠛⠛⠻⠿⠿⣿⣿⣝⣳⣶⠴⣿⣿⣯⡉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣤⣮⣴⡾⠟⠋⠁⢀⢀⣠⣾⣿⡃⠀ ⢓⡶⠶⢦⣤⣄⣉⣉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠿⠶⢤⣤⣄⣀⣀⣀⣤⣶⠿⠟⠋⠁⡀⢠⣶⣿⢻⣾⣿⢩⣽⠇⠀ ⠀⠉⠉⠛⠒⠒⠯⠭⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠖⠂⠀⠀⠉⣹⠛⠉⣀⠀⠀⠀⢸⣷⣼⣽⣯⠀⠟⠃⠀⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠿⠛⠛⠛⠉⠉⠛⠛⠛⠿⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠿⠟⠛⠛⠻⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⢀⣤⣤⡀⠀⠀⠙⢿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⡀⠀⢸⣿⣯⡀⠀⠀⠀⢾⣿⣿⡷⠀⠀⠀⢀⣽⣿⡇⠀⢀⠀⠀ ⠀⣴⣧⠀⠘⢿⣿⣿⣦⣀⠀⠀⠉⠉⠀⠀⣀⣴⣿⣿⡿⠃⠀⣾⣆⠀ ⢰⣿⣿⣷⡀⠈⠙⠿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠿⠋⠁⢠⣾⣿⣿⡆ ⠈⢿⣿⣿⣿⣷⣄⡀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⢀⣠⣾⣿⣿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⢀⡀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣾⣏⣹⣿⣦⣧⠈⠛⣹⣟⣿⣷⣟⡿⣶⣦⣤⣤⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣾⡿⣼⠛⣇⣽⣿⡿⠿⣣⣾⣿⡿⣽⣿⣿⣿⣖⣹⣿⣷⡙⣿⡀⣌⣛⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢱⡿⠉⣠⣿⡿⣄⡟⠉⣠⣾⠿⢋⣡⠴⢿⡟⣹⣿⢉⣡⣴⢿⣿⣿⣿⠿⢿⣄⢺⡉⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢻⡟⢀⡜⢁⣾⣿⠃⠠⠋⠀⢸⣧⡤⠞⣩⣽⣶⣶⣦⣤⣇⣸⣿⣿⣿⣿⣿⠋⣴⣿⣿⣿⣿⣷⣾⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⣫⣿⣶⡟⢡⢈⣛⡯⣖⣤⣦⣠⣾⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⢀⡴⠟⣰⢳⣯⢏⠟⣰⠋⢸⡟⣹⡟⠙⠛⢻⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⡞⠀⣸⣇⡟⢡⢾⡴⢷⠄⣸⣿⠟⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⢀⣇⡴⠋⠉⢰⠏⠈⢁⣿⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠁⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⣼⡟⢹⣆⠀⣿⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣧ ⠀⣿⣿⣹⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿ ⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⠟⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡻⣄⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢙⣿⡛⣿⡮⠙⠛⠳⠄⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿ ⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡯⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿ ⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣼⢿⡿⠿⠷⢤⠄⠀⠀⠀⠀⢀⣠⣳⣆⣤⣶⣶⡶⣄⣿⡀⠈⣿⠃ ⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠴⠚⠉⠉⣁⣠⣴⣖⡦⣄⡀⠀⠀⠀⠀⠀⢀⣬⣭⣼⣿⣷⣷⣾⣤⡉⢙⠛⠀⡿⠀ ⠀⠀⣿⡷⢦⣈⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣶⣠⡶⠿⠛⠻⠿⠟⠈⠛⢲⣽⠃⠀⠀⠀⠀⠘⣏⠚⠛⠛⠛⠋⠘⠛⠻⠇⠀⠸⡅⠀ ⠀⠀⣿⣧⠀⠉⣁⠻⢿⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠶⠶⠖⢒⡿⠋⠀⠀⠀⠀⠀⠀⢻⠀⠉⠑⠒⠒⠒⠂⠀⠀⠀⠀⡇⠀ ⠀⠀⢰⡀⠀⣴⠟⡷⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠈⢳⡀⠻⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠙⠶⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡀⠀⠀⠀⠀⠀⣠⣷⡀⠀⠀⠀⠀⠀⡸⢿⡇⠀ ⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠳⢦⣠⣤⣴⣿⡏⠀⠀⠀⠀⠀⠛⠃⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢳⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣉⣁⣭⣤⡴⠀⠀⠀⠀⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠛⢛⠛⠛⠛⠛⠛⣿⣿⠟⠛⠉⠀⠀⠀⠘⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⣰⠋⡀⠀⠀⠀⢠⣤⣈⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⣿⣹⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠀⢀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⢄⣀⣀⠀⢀⣄⠀⠀⠀⢀⠀⠀⢀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣼⠁⠀⠀⠉⢢⣄⡉⢙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣶⣶⣿⠿⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⣏⣠⣴⠾⠛⠁⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⡿⠉⣿⡀⠀⠀⢿⠱⡀⠀⠀⠀⢀⠀⢠⠄⢸⠀⡇⠀⢸⠋⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⡟⠀⠀⢹⡇⠀⠀⠘⣠⡧⢒⡁⠀⠁⣠⠏⢠⠇⠀⠁⡰⠃⠀⠀⠀⠀⢀⡴⣪⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⢿⣿⣿⠁⠀⠀⠸⡇⠀⠀⣰⣥⠛⠁⠀⠀⡰⠃⢠⠋⠀⢱⣀⣇⠀⠀⠀⠀⠀⠈⢻⢿⡿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⢧⢀⡔⡛⠁⠀⠀⠀⣼⠁⢠⡧⢴⣄⠈⢯⠙⠦⠀⠀⠀⠀⠀⠁⠘⣇⢹⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠀⠀⢨⠏⡐⠀⠀⠀⠀⠠⠃⢀⣏⢳⣴⣊⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⡰⢁⠜⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⣟⣒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠑⠋⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⠏⢰⣸⡋⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⡌⠀⡆⢠⠁⢀⡠⠤⠐⠒⢎⠉⢫⢠⣾⡟⠙⡄⠀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⢠⠁⠀⣄⠞⠊⠁⠀⠀⠀⠀⠀⠳⡄⢻⣿⡇⠀⠈⠓⠠⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀ ⢀⠎⠀⣰⣯⠀⠀⢧⡀⠀⠀⠀⠀⠀⠈⠸⢿⣟⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⠀⠘⠀⠀⠀⠀⠀⠀⠒⠛⠒⢶⠀⠀⠀ ⡣⠤⠊⠁⢻⠀⢠⢸⣧⠀⠀⠘⣆⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣳⠏⠉⠉⠉⢳⣶⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠘⡇⠸⣦⣧⣇⠀⢠⠈⢧⡀⠀⠀⠀⣀⠀⠀⠉⠙⠒⢒⣲⠶⠋⠁⠀⠀⢀⡼⠁⠀⣶⡿⠭⢍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡀⣇⠙⣿⣆⠀⢣⡀⠙⢆⠀⠀⠀⠈⠑⠲⣶⡚⡩⠭⠭⡽⠲⣾⣭⣿⠀⠀⠚⠁⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀ ⠀⠀⠀⠀⠀⠀⠑⢼⣆⠈⢿⣆⠈⢿⡒⠤⠽⣦⣄⡀⠀⠀⠈⠛⠦⣀⠀⢸⣄⣸⣏⡇⠀⠀⠀⠐⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢀⠿⣗⣌⢣⡀⠀⠀⠀⠉⢳⠲⢷⡶⠤⠄⠉⠹⣿⡻⢿⡇⠀⠀⠀⠀⣠⠖⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠛⢷⡑⣄⣠⠴⠶⠿⠿⢿⡁⠀⠀⠀⢀⣸⣿⣿⡀⠀⠀⠀⠀⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠈⢻⡿⢄⡀⠀⠀⠈⢳⣄⣤⣴⠃⠀⠀⠀⠉⠢⡀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⡿⠋⡍⠀⠀⠀⠀⠀⢀⠙⣆⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⠀⠀⠀⠠⣿⠀⠀⠀⠀⢠⣾⣿⠆⢀⣧⣄⡀⠀⠀⠀⡜⢀⠟⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⣿⣤⣆⣀⣠⠾⠿⢻⣧⡿⠿⣿⣿⣆⠀⢠⠁⡞⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠀⢀⣀⣿⡿⠟⠻⣿⠀⠀⠀⣻⠀⠀⠘⣿⣿⣇⠘⡸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⡽⠋⠉⠸⡄⠀⠀⠙⢧⡀⠀⣇⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣤⡤⠤⠤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢔⡇⣀⣤⡴⠊⠀⠀⠀⠀⣇⠀⠀⠀⠀⠉⢦⣿⣦⣀⣀⣼⣿⣿⢿⣤⡀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢙⣶⠄⠀⠀⠀

⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡖⢫⡽⠛⠿⠥⣶⣒⠛⠛⠭⢭⣶⣖⣦⢤⣄⣼⣽⢧⣌⠩⢭⡭⣩⣿⣿⣿⣟⣾⣆⣴⣿⣿⠟⣫⣿⡇⢸⡟⡆⠃⠀⣠⣶⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠁⠀⣤⣀⠀⠀⠀⠀⠈⠉⠲⢿⣝⠒⠦⣌⣩⠟⠉⠛⠛⠺⢭⣭⣙⣿⣿⢽⠋⠑⠻⢿⣟⢯⣷⣻⡇⢿⢧⠸⣿⣹⢼⣿⣿⣿⣿ ⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠀⠸⡄⠀⠀⣌⠉⠲⢦⣀⠀⠀⠀⠀⠉⠳⣌⢻⠋⠀⢀⣰⣶⣝⣲⣶⠞⠉⢠⡟⠉⠓⠒⠒⠿⠷⢛⣿⣧⡘⢿⣧⣌⣩⣾⠿⡏⠁⢸ ⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠃⠀⠀⠙⣄⢠⡈⠳⣄⠀⠈⠳⢦⣀⠀⠀⠀⠈⠻⣦⡀⠀⠙⢮⣙⠛⠋⠀⢠⣞⣶⢤⣤⣤⡲⢴⣚⠏⣹⣿⡿⣿⣿⣿⠋⠁⠀⣧⠖⠋ ⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣼⡇⠀⠀⠘⡇⣤⠀⠀⠈⢢⡳⣄⠈⠓⢦⡀⠀⠻⣷⣕⢦⡀⠀⠈⠻⣦⠀⠀⠀⠀⢀⣴⠯⠬⠭⠭⠝⠛⠋⠉⣠⠞⣱⡿⢿⡟⠹⢸⠀⣠⠞⠃⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⢀⣾⡾⠁⣰⠄⠀⣿⡘⣆⠀⠀⠀⠙⢮⡻⣦⣀⠉⠓⢤⣈⠛⢷⣝⢦⡀⠀⠈⢳⣤⣤⡴⠋⠁⠀⠀⠀⠀⠀⣀⡴⠚⢡⠞⡽⠃⣸⢹⠂⢸⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⣿⢫⠇⢀⢧⠀⢸⠉⢷⡈⢷⣄⠀⠀⠈⠙⢮⣻⣽⣶⣦⣌⣙⠲⠿⢾⡵⣄⠀⠀⠹⣷⣯⡉⠓⠒⠒⠒⠒⠋⣁⣠⠖⢁⠜⠁⢀⡿⢸⣾⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣾⠃⡾⠀⢸⢸⠀⣿⠀⠀⠙⢦⡻⣟⠦⣄⠀⠀⠈⠙⠻⢦⣄⠈⠉⠙⠓⠿⣎⢧⠀⠀⠙⣎⠙⣶⠤⣀⣀⣀⣴⠟⠉⠻⣦⠀⢀⡼⡇⢸⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⣼⡇⢸⠇⠀⡇⣿⡀⡏⠀⠀⠀⠀⠙⠯⢷⣤⡙⠓⠶⠶⠒⠋⠁⠀⢀⣠⡤⠤⠈⢿⣳⡀⠀⠸⣦⣌⠙⠓⠚⢻⡇⢰⠟⣧⠘⣧⠞⣹⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣯⣴⣯⠤⡟⠀⢸⡇⡇⣷⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠈⢳⣵⡀⠀⠹⣮⡓⠦⣄⣸⡀⡾⠀⠘⡆⠸⡴⠃⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⠓⠀⡇⠀⢸⣷⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣴⣾⣯⠭⣽⣧⣼⣷⣻⡀⠀⢻⣯⣲⢤⣹⠀⡷⠦⠖⠃⠀⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣿⣿⠟⢁⣰⡇⠀⢸⣿⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡽⢿⣿⣾⠿⠿⣿⡙⠛⢿⣿⣳⠀⠈⣷⠨⣷⣽⡆⣷⠞⢶⡄⢀⡇⣸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⡷⡋⣤⣼⣿⡇⠀⠸⣇⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠻⠛⣿⡟⣿⢙⣿⣷⣸⣷⢀⡾⠛⢧⣧⠀⠘⡆⠈⢻⡇⠈⣳⠂⡇⣼⡸⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣫⢿⣋⣜⡿⡽⠁⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣿⠁⢻⣏⡻⠟⣰⢏⣼⡋⠁⠘⡎⡆⠀⢹⡀⠀⠳⠚⢁⣼⢡⠏⣱⡻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣀⡈⠑⠋⠚⠁⠀⡇⠀⢸⣵⠀⠀⠀⠀⠀⢀⣠⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣬⣽⣿⣿⠽⠛⠀⠀⠀⠀⢻⣱⠀⠈⣇⠀⠀⡶⢻⣵⣏⣴⡟⣡⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣍⠉⠉⣩⣿⣿⣷⠀⠸⣿⣴⡶⢶⣾⣿⣿⣿⣶⣾⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣇⣧⠀⢸⡀⠀⣆⡼⣿⣯⣝⢿⣿⡾⣻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣶⣿⣿⠿⡿⡼⡆⠀⢧⣏⠘⣿⣷⡿⢯⣙⣷⡀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⡀⠀⡇⠀⣿⢸⠁⣾⠙⡆⢹⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡏⠁⢀⣹⡙⢧⠀⢸⣿⣸⣿⠟⣿⡾⠿⣿⡇⣼⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⢸⣄⣿⠸⣸⢹⢸⡇⢸⠰⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣶⣿⡿⠛⢾⡄⠀⣿⡟⣻⢦⣙⡻⣿⡯⡞⠁⢸⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢣⠀⠸⣿⣿⣆⠙⠾⣞⣃⡼⣰⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠛⠁⠀⠈⢧⠀⢻⣹⣧⠸⠋⡟⠙⠀⠀⠀⠀⠉⠓⠒⠁⠀⣠⡤⠖⠒⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⣿⣽⣻⣷⡾⠿⡟⠀⡏⢸⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠘⡇⠈⣏⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⣀⣤⣶⣶⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⡿⣹⣧⣤⡇⠀⣇⢸⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡀⠸⡜⣷⣽⣦⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⣴⣾⣿⣿⣿⣫⠿⠿⢳⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⣷⣿⣼⣷⣿⣿⣇⠀⣿⡜⡄⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢷⠀⢷⡹⡍⢻⠷⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠋⠁⣀⡤⠖⣻⠀⠀⠀⠀⢀⣴⣿⣿⡇⢀⣿⣼⣧⣿⡜⢿⣿⡄⣿⣷⣳⡀⢿⣧⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣀⣀⠄⠀⠀⠀⠈⣇⠈⢧⠹⣧⡜⠙⢧⡀⠀⠀⠀⠀⠀⠘⣿⣿⣡⠔⠋⠁⢀⡴⠃⠀⠀⠀⣠⣾⣿⣿⣿⡇⢸⡿⣿⢻⣽⢣⠈⣿⣷⣜⣿⣿⣷⣬⣿⣿⣷⣦⣤ ⠀⠀⠀⠀⠀⢀⡜⠋⠀⠀⠀⠀⠀⠸⡄⠸⣷⡹⣧⠀⢀⡟⢦⣀⠀⠀⠀⠀⠘⢿⣤⣤⡤⠖⠋⠀⠀⠀⣠⣾⣿⣿⡟⣿⣹⠀⣸⣾⣻⡿⠛⠋⠀⠘⣿⣿⣿⣿⣿⣿⣟⣿⢿⣿⢻ ⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠹⣄⠘⢷⣽⣏⢩⣠⣾⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣾⣿⡇⠀⣷⣹⣿⠑⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠋⢈⣿⢿ ⠀⠀⠀⠀⠀⣠⠇⠀⠀⢠⡾⠿⠛⢿⣿⠿⠿⡶⢸⣿⣿⣙⣻⠀⠀⠀⣯⠙⢷⣶⢤⣀⣠⣤⣾⣿⣿⠿⠿⠛⠻⢿⡿⡟⠀⢰⠇⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⣾⠋⢠ ⠀⠀⠀⠀⣴⠃⠀⠀⣰⡟⠀⠀⠀⢸⡇⠀⠀⣷⢸⠇⠀⢹⡟⠀⠀⣼⡟⠀⢸⣿⡄⢸⣅⣿⢣⣿⣿⡄⠀⠀⠀⠀⣿⠁⠀⠸⡆⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⢀⣾⠃⠀⣸ ⠀⠀⠀⠀⡸⠀⠀⣰⠏⠀⠀⢀⡄⠸⣧⠀⢀⡟⢸⡀⠀⣿⢗⢦⣰⣿⠃⠀⣸⣿⡇⢸⣿⣿⣿⣿⠟⣧⠀⠀⠀⠀⣿⠀⠀⠀⠹⣆⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⣼⠃⠀⣰⣿ ⠀⠀⠀⣠⠃⠀⣼⠏⠀⠀⢀⡾⣷⡀⠛⠛⢿⣷⢚⡛⡶⠿⢮⣳⡹⣟⠀⢠⣿⣿⡇⣾⣿⡇⣿⠃⠀⢻⠄⠀⠀⠀⠹⣷⡀⠀⣘⣾⣦⣴⣿⣿⠋⠀⠀⠀⠀⢀⡴⣿⠏⠀⠰⠟⠁ ⠀⡠⠔⠁⠀⣴⠏⠀⠀⠀⡾⠃⠘⣷⡄⠀⠀⠹⣷⣸⣿⠃⠀⢳⡹⡝⣦⣾⣟⣿⣾⠟⣡⡾⠁⠀⠀⡾⠀⠀⠀⠀⠀⠈⠻⣷⣽⣾⣿⣿⠟⠁⠀⠀⠀⠀⣰⠏⢰⡟⠀⠀⠀⠀⠀ ⠿⠤⠤⠄⣸⠋⠀⠀⠀⣼⠇⠤⠴⠾⢿⣄⠀⠀⠘⢷⣝⠶⠤⠴⠧⠷⠿⠿⠾⠿⠧⠾⠿⠤⠶⠶⠾⠧⠤⠤⠤⠤⠤⠤⠤⠿⠿⠿⠿⠧⠤⠤⠤⠤⠤⠾⠧⢤⣿⠀⠀⠀⢠⣿⡄ ⠀⠀⠀⠀⠙⠷⢦⣤⣼⣿⠀⠀⠀⠀⠀⢻⣶⡴⠿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⠿⠉⠿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠒⠀⠀⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠐⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠉⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠘⣷⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠸⡀⠀⠀⠀⠀⣀⣀⠀⠀⡄⠀⠀⢿⡇⠀⡀⡄⠘⠉⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀ ⠀⢳⡀⠀⠀⠀⢠⡀⣞⡗⣿⣷⣿⠸⣇⠀⣟⡟⣷⣿⡆⢸⣀⠀⠀⠀⠀⢠⠇⠀ ⠀⠀⢳⡀⠀⠀⠈⠁⠈⠁⠁⠁⠉⢠⡿⠀⠉⠁⠀⠉⠀⠈⠉⠀⠀⠀⣠⠏⠀⠀ ⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠤⣀⣀⣀⣀⣀⡠⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀