Lmao ASCII Art

⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⢋⣩⡽⠿⢿⡭⠭⣍⣉⠡⠾⠛⠛⣿⣶⣤⣄⡀⠀ ⠀⣠⠟⣡⡾⠟⣡⠖⠛⠛⠻⣍⠉⠉⠉⠀⡴⠋⠉⢨⣿⢻⡏⠀ ⢠⡟⠀⠀⠀⣸⠁⣤⣄⠀⠀⢸⡄⠀⠀⢸⠁⠀⠀⠀⠀⣸⡇⠀ ⢸⠃⠀⠤⠚⡿⢦⣛⠋⠀⣀⡾⠀⠀⠀⠈⠓⢲⡶⠒⠚⠧⣧⠀ ⣿⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠤⠤⠤⡤⣲⠋⣴⣛⠛⢦⠘⣧ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠭⠭⢲⡏⢸⠭⠯⠿⠿⡆⣿ ⢹⡀⡄⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠘⡇⢸⠀⠀⠀⢰⢣⠇ ⠈⣇⠹⣼⡄⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⡏⢸⠀ ⠀⠸⡄⠹⣷⠀⠘⡄⠀⠈⢽⠷⣦⡀⠀⢀⡇⣞⣀⠀⠈⡇⢸⡆ ⠀⠀⢱⡀⢻⣧⠀⢧⠀⠀⢀⣉⡓⢯⡂⣼⢀⡇⠀⠈⢢⣻⢸⡇ ⠀⠀⠀⢷⡀⠻⡧⣄⡑⢤⡀⠀⠉⠲⣍⡇⠘⣏⠯⣏⣇⡏⢸⠇ ⠀⠀⠀⠀⠙⢦⡈⠒⠭⣶⣬⣂⣀⠀⠈⢿⡀⠙⠲⠶⠚⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣈⠙⠛⠻⠭⠯⠙⠒⣦⡶⠾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⠤⠴⠟⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠶⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠛⠻⠶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀ ⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀ ⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠈⠉⠤⠤⣤⣤⣤⣤⣤⣤⣠⣄⣀⣤⣤⣤⣀⠤⠄⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀ ⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣀⣀⣀⣠⣄⣴⣤⣄⣀⡛⣻⣶⣻⣯⠉⠉⠉⠀⠀⠈⣿⣟⡓⣰⣰⣰⣴⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⠀⠀⠀⠀⢻⡀ ⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢰⣿⣿⡛⠉⠋⠁⠁⠁⠩⢍⢛⣿⣿⡀⠀⠀⠀⢀⣾⠀⠀⠀⢸⣿⣿⠟⠋⠉⠁⠈⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⢸⡇ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⡿⣿⣍⡇⠀⠀⠀⠀⢨⣽⣿⣯⠁⠀⠀⠀⣾⣿⠀⠀⠀⢸⣿⣞⡅⠀⠀⠀⠀⣶⣿⠆⣿⠀⠀⠀⠀⠀⠀⢸⠁ ⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣴⣾⣿⣿⣷⣎⡉⠀⠀⠀⠀⢒⠀⣴⣿⣿⠀⠀⠀⢠⣿⣿⡄⠀⠀⠘⣿⣿⣷⡀⢀⡀⠀⢈⣙⣴⣿⣀⡀⠀⠀⠀⠀⣸⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣦⣬⣿⣾⣿⡿⣇⠟⠀⠀⠀⠀⣜⣿⣧⠀⠀⠀⠘⢿⣿⣿⣦⣤⣾⣿⣿⣿⠁⠙⠧⠀⠀⠀⢐⡏⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠽⣿⣿⣷⣽⣿⣿⣿⣯⣿⣿⠟⠁⢀⡤⣤⠀⢀⣼⣿⣿⣦⡀⠀⠀⣠⣿⣿⣟⣿⣭⣻⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⠀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣿⣻⠟⠋⠁⣤⣴⣿⡛⣲⣶⣶⣿⣿⣿⣿⣯⣶⣶⣶⣿⠋⠙⠛⠛⠉⠁⢀⣠⡤⢤⣄⡀⠀⣾⡇⠀ ⢿⣇⠀⠀⠀⢠⡶⠟⠉⠁⠈⠉⠉⠓⠦⠀⠀⠀⠀⠀⠉⡛⠉⢁⣠⣴⣿⣷⣿⣿⣿⣿⣿⣯⣿⡿⡟⠻⠿⢿⣿⠿⢋⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢿⠃⠀ ⠘⣿⡄⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠶⠶⠿⠿⣟⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣹⠛⣻⢷⣬⡷⠿⠞⠛⠛⠿⠿⢿⣿⣿⣶⣔⣦⣤⡀⠀⢀⠸⢨⣿⠀⠀ ⠀⠾⣿⡀⢸⡀⠀⠀⠀⣤⣾⣚⣯⡵⡶⠛⠻⠟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣏⢉⣉⣉⣉⣉⣽⣿⣿⣟⣛⣛⣛⣉⣉⣵⣿⣿⠿⠿⠛⠿⣟⣯⣇⣿⡄⢸⡟⠀⠀ ⠀⠈⠙⣿⣦⠇⠀⠀⠀⣿⡝⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⡟⢿⣿⣿⣿⣛⣻⣭⣿⡿⢿⠟⠛⠋⠁⠀⠀⠀⠀⠀⢀⣉⣍⡼⢃⡾⠁⠀⠀ ⠀⠀⠀⠘⢿⣆⠀⠀⠀⠋⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⡿⣿⠛⠻⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠋⢀⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠘⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣍⣠⡿⢿⢻⣿⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⣠⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⡽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠻⠿⢶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠶⠶⠶⠶⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠟⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⠿⠿⠿⠶⣾⣿⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⢀⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⣀⣠⣤⣶⣿⠿⠿⠟⢻⣷⣶⣤⣤⣤⣄⣀⣀⣀⣀⣠⡾⠿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠋⠀⣀⣴⣿⣿⠿⠛⢉⣀⣤⣤⣤⣬⣭⣥⡤⠤⠥⠬⠭⠭⠭⠥⠶⠖⠂⠀⠀⣀⣤⣾⠿⠟⠛⠿⣿⣿⣿⣿⣿⢷⠄⠀⠀ ⠀⠀⢀⣾⣿⠋⢀⣴⣾⣿⡿⠟⠁⣠⣾⡿⠛⠉⠉⠉⠙⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⢠⣴⣿⣿⠛⣿⣿⠀⠀⠀⠀ ⠀⢀⣾⡿⢁⡴⠿⠿⠿⠋⠀⠀⣼⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠙⠿⠿⠿⠀⣹⣿⠀⠀⠀⠀ ⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀ ⠀⣿⡟⠀⠀⠀⠀⠀⠀⣀⣠⣿⡇⠀⢸⣿⣿⣿⣷⠄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣿⡆⠀⠀⠀ ⢠⣿⡇⠀⠀⠀⠀⣀⣴⣿⠿⣿⣷⣄⠸⣿⡿⠟⠃⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣤⣤⣶⣶⣿⣟⡀⣿⡇⠀⠀⠀ ⣸⡿⠀⠀⠀⠀⠈⠉⠁⠀⣴⡿⠛⠻⣷⣦⣄⣀⡀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⠟⠋⠁⠀⠀⠉⠙⠻⣿⣿⡄⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⡿⠁⢀⣤⣶⣶⣶⣶⣄⠀⠈⢻⣿⡄⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠶⠶⠶⠶⠟⣛⠛⢋⣿⡟⠀⢠⣿⣿⣁⣀⠀⠈⠻⣷⡀⠀⢹⣿⡀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣶⣶⣶⡶⠿⠿⠛⠁⣠⣿⡟⠀⢠⣿⠟⢻⡿⢹⣿⢿⣶⢿⣧⠀⠸⣿⡇ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⢶⣶⣶⣶⣶⠖⠉⣿⣿⠃⠀⣼⣿⣤⣾⣥⣬⣯⣼⣿⣼⣿⠀⢸⣿⠃ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣤⣤⣤⣤⣤⣤⣤⡄⢻⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⣸⡟⠀ ⢸⣧⠀⢹⣄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡿⢰⣿⠁⠀ ⠈⣿⡆⠈⢿⡄⠀⣿⡄⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⡟⠀⠀ ⠀⢿⣧⠀⠘⣿⡄⢻⣇⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⠇⠀⣿⠃⠀⠀ ⠀⠘⣿⡄⠀⠘⣷⡈⣿⡄⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀ ⠀⠀⠸⣷⡀⠀⠘⣿⣿⣷⠀⠀⠀⠘⣷⡄⠀⠀⠀⠈⠋⣉⣩⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣷⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠘⣿⣿⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⣮⣉⣉⠛⢿⣿⣦⡀⠀⠀⠀⢸⣿⠀⣼⣿⣤⣤⣄⣀⠀⠀⠈⣿⡆⠀⢸⣿⠀⠀ ⠀⠀⠀⠈⢻⣆⠀⠀⢹⣿⣿⣆⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣌⡛⠻⠄⠀⠀⣿⠃⠀⣿⠇⠀⠀⠀⠙⠻⣦⡀⢹⣷⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠈⣿⡆⠀⠀⢿⡟⢿⡄⠀⠀⠻⣦⠀⠀⠀⠀⠤⢤⣤⣄⣀⠀⠙⢿⣦⡀⠀⣼⡟⠀⢠⣿⠀⠀⠀⠀⠀⠀⠘⢷⣈⣿⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⢻⣎⣿⡄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠉⠙⠳⣦⣄⠉⠛⠶⣿⡇⠀⢸⣿⠛⠻⡿⠛⣿⠻⣟⠛⣿⡟⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠻⣿⣿⣶⣄⣀⠀⠈⢷⣦⡀⠀⠀⠀⠀⠀⠀⠙⢷⣆⢀⣿⡇⠀⠈⣿⣧⣸⣿⣦⣿⡀⣿⣠⣿⠇⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠈⠻⣦⡈⠙⠷⣦⣀⠈⠻⢷⡀⠀⠀⠀⠀⠀⠀⠘⢷⣿⡇⠀⠀⠻⣿⣅⠀⠀⠉⠙⣻⣿⠏⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠈⠛⠷⣦⣬⣻⣿⣦⣄⡙⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠈⠻⠿⢿⣿⠿⠟⠃⠀⢀⣼⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣀⠀⠀⠉⠛⠻⢿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣤⣀⠀⠀⠀⠉⠙⠛⠛⠿⣶⣮⣭⣭⣭⣭⠉⠛⠿⣷⣶⣶⣤⣶⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢀⣀⣀⣀⣠⣼⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⣦⣄⣀⣀⣀⣀⣀⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣴⣾⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣦⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠛⠿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠿⣿⠿⠟⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠐⠛⠉⠉⠉⠉⠙⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⡤⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣀⣠⣠⣠⣤⣤⣠⣠⣠⣤⣄⣤⣄⣄⣤⣀⣀⣠⣠⣠⣤⣤⣤⣤⣀⣠⣠⣠⣀⣠⣠⣤⣤⣤⣀⣤⣄⣄⣄⣤⣤⣤⣤⣠⣀⣤ ⢸⣿⣿⣿⠟⠛⢿⣿⡟⠛⣿⣿⠛⢻⡟⠻⣿⣿⠛⢻⣿⣿⣿⠛⢻⣿⣿⣟⠛⢻⣿⣿⡟⠛⣿⣿⡟⠛⢻⣿⣿⠛⠛⠛⠛⠛⣿⣿ ⢸⣿⣿⣿⠀⡆⢸⣿⣿⠀⢹⡟⠀⣾⣧⠀⢿⠇⢀⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⠘⣿⡿⠀⠀⣿⣿⠁⠀⠸⣿⣿⠀⢸⣿⡇⠀⣿⣿ ⢸⣿⣿⡇⢀⣇⠈⣿⣿⣇⠈⠃⢸⣿⣿⡆⠘⠀⣼⣿⣿⣿⣿⠀⢸⣿⣿⣿⠀⡀⢻⠇⡀⠀⣿⡟⠀⣷⠀⣿⣿⠀⢸⣿⡇⠀⣿⣿ ⢸⣿⣿⠃⠸⠿⠀⢻⣿⣿⡄⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣟⠀⣇⠀⠀⡇⠀⣿⠇⠀⠿⠄⢹⣿⠀⢸⣿⡇⠀⣿⣿ ⢸⣿⡿⠀⣤⣤⡀⢸⣿⣿⠇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠀⠸⠿⠿⣗⠀⣿⡄⣸⡇⠀⣿⠀⣠⣤⡄⠘⣿⠀⠸⠿⠇⠀⣿⣿ ⢸⣿⣧⣤⣿⣿⣧⣤⣿⣿⣤⣴⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣤⣤⣤⣤⣿⣤⣿⣿⣿⣧⣤⣯⣤⣿⣿⣧⣤⣿⣦⣤⣤⣤⣴⣿⣿ ⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀ ⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀ ⠀⢀⡟⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠘⡄⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⣄⣀⣈⣁⣀⢴⣶⠒⠒⠒⣶⢢⣀⣀⡀⠀⠀⠀⢳⠀ ⢠⡏⠀⠀⠀⠀⠉⣉⣿⣟⡛⠛⠟⣿⡏⠀⣰⠀⢹⣿⠛⠛⢛⢻⠀⠀⠀⡇ ⢸⠃⠀⠀⠀⠀⠤⢼⣿⣏⡁⣀⣈⣿⠀⠀⢿⠀⠘⣿⣄⢀⣩⡼⡄⠀⢀⠁ ⢸⠀⠀⠀⠀⠀⠀⠘⠻⣯⣿⣿⠟⢈⡤⣀⣿⣷⣄⣸⡿⠯⠿⠃⣀⠀⢸⠀ ⠸⡄⢠⠊⠉⠈⠁⣀⣀⣬⣭⣤⣾⣿⣿⡿⢟⣉⠿⠿⣵⣤⣀⣀⠀⢱⡙⠀ ⠀⠳⡼⠀⢰⡿⠛⠉⠉⠉⠉⠛⠻⢯⡴⣶⣿⣿⡭⡵⠞⠛⠉⢙⣛⢇⠇⠀ ⠀⠀⠙⢤⡀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠎⠽⢿⡉⠂⠀⠀⠀⠠⠊⢡⠊⠀⠀ ⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣀⣀⠀⠀⠀⠀⠈⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣫⣭⣍⣉⣉⣁⣈⣉⣉⣉⣉⠛⠛⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⣀⣠⣴⣾⡿⠷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣼⠿⠿⠛⠿⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⢁⣠⣴⣿⠟⢋⣡⣤⣤⣤⣯⣵⡶⠚⠚⠛⠛⠓⠒⠂⠀⢀⣠⡶⠟⠛⠛⢻⣿⣿⣿⡷⠀⠀ ⠀⠀⣼⡿⢃⣴⣿⡿⠟⠁⣴⡿⠋⠁⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⢴⣿⣿⠙⣿⡇⠀⠀ ⠀⢸⣿⠁⠉⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠉⠁⢠⣿⡇⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⢠⣤⣿⠀⢸⣿⣿⣷⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣾⢻⡇⠀⠀ ⢀⣿⠀⠀⠀⠠⠖⠛⢻⣿⣷⣜⡛⠛⠁⠀⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣶⡶⠚⠛⠻⢷⣼⣿⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠟⠁⠀⠉⠛⠷⠶⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠁⣀⣤⣤⣤⡀⠈⠻⣧⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⣒⡚⠋⣿⠏⠀⣼⣿⣁⣀⡈⢻⣆⠀⢹⣇ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣛⣛⣉⡤⣾⡟⠀⣼⡏⣹⠋⢿⢻⡟⣿⡀⢸⣿ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⣉⣉⣙⣋⣁⡀⣿⠁⠀⣿⠛⠛⠛⠙⠛⠛⢻⡇⢸⡇ ⠘⣧⠀⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⢻⡇⠀⣿⠀⠀⠀⠀⠀⢀⣾⢁⣿⠀ ⠀⣿⡄⠸⣧⠀⣧⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⣼⠇⣸⡇⠀ ⠀⠸⣷⠀⠹⣆⣿⡄⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⢰⡿⠀⣿⡄⠀ ⠀⠀⢻⡇⠀⠹⣿⣷⡀⠀⠘⢷⡀⠀⠀⠈⢛⣛⣷⣶⣤⡀⠀⠀⠀⠀⢸⡏⢰⡟⠀⠀⠀⠀⢸⣇⠀⢸⣧⠀ ⠀⠀⠈⢿⡄⠀⠹⣿⣧⠀⠀⢸⡇⠀⠀⠀⠀⠰⢤⣭⣙⠿⣦⡀⠀⠀⣾⠁⣸⠷⠶⠦⣤⡀⠀⣿⡄⠀⣿⠀ ⠀⠀⠀⠈⢿⡀⠀⢻⣿⣆⠀⠘⣧⡀⠀⠀⠀⣀⣀⠈⠙⠷⣦⡉⠀⢸⡇⠀⣿⠀⠀⠀⠀⠙⣦⢸⡇⠀⣿⠀ ⠀⠀⠀⠀⠘⣷⡀⠈⢻⣽⣆⠀⠈⠳⣄⠀⠀⠀⠉⠙⠳⢦⡈⠛⠦⣿⠁⠀⣿⠶⣶⠶⡶⢶⠛⣿⡇⠀⣿⠀ ⠀⠀⠀⠀⠀⠹⣷⡀⠀⠹⣿⡷⢦⣄⡈⠳⢦⡀⠀⠀⠀⠀⠙⠳⣄⣿⠀⠀⣿⣧⠿⠶⣷⣸⣶⡟⠀⢠⡟⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠈⠛⢦⣌⡙⢶⣄⡙⠢⠀⠀⠀⠀⠀⠘⢿⡆⠀⠈⠻⣦⣤⣤⣴⠟⠁⢀⣾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠈⠙⠻⠿⣿⣷⣦⣤⣤⣤⣄⣀⣸⣿⣄⡀⠀⠀⠉⠉⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠈⠉⠛⠛⠷⠶⣮⣿⠍⠉⠛⠿⢶⣶⣶⣿⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣀⠀⠀⠀⠀⢠⣶⣶⡶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣶⣾⣧⣄⣀⣴⣶⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⣠⠤⢬⠀⠈⠙⣮⣉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢀⣸⣉⣆⠘⡇⠀⢰⢃⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠉⡿⢭⠙⠇⢀⣸⠓⢞⡲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠅⣸⣯⣏⣉⣹⣽⠏⢣⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠁⣿⠿⣿⣿⣿⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠹⡄⠈⣻⠇⣠⠃⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠲⣄⣀⠀⠀⠀⠙⢛⣡⠴⠃⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠙⣷⠀⠀⣠⣤⠶⢾⠏⣉⡙⠚⠋⢹⢁⣀⣀⠀⠀ ⠀⠀⢀⣀⣀⣈⣇⠀⢿⢀⡾⠋⠀⠀⠈⢰⡇⢹⡄⠀⠘⠉⠉⠉⠓⣆ ⢠⣾⣛⣋⣉⣛⣋⡀⠘⣿⠃⣀⣀⣤⣤⣼⡇⠘⣧⠀⠀⠀⠀⠀⠀⢸ ⠈⠛⢻⣟⠉⠉⠉⠙⣷⡗⢿⣭⣤⣤⣤⡄⠀⠀⢹⡆⠀⠀⠀⠀⠀⡼ ⠀⠀⠈⢿⣦⣄⣠⠴⠃⠸⡄⠀⠹⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠈⠉⣻⠀⠀⠀⢧⠀⠀⠓⠶⠒⡟⠁⠀⢹⠀⠀⠀⠀⡏⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⡆⠀⠀⠀⠰⠃⠀⠀⠘⠧⠀⠀⠰⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢻⣿⣿⣿⣷⡄⠀⠀⢠⣾⣿⣿⣿⠏⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢆⠀⠙⠻⠿⠿⠃⠀⠀⠘⠿⠿⠛⠁⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠐⠂⠀⠐⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⠶⢶⡶⢶⣶⢶⠶⣶⡶⣶⣶⡶⢶⣶⠶⣶⣶⠶⣶⡶⢶⣶⡶⠶⠶⣶⡆ ⣿⣿⢠⢸⣿⡈⡏⣸⣇⢹⢁⣿⣿⡇⢸⣿⡇⢸⡏⠀⣿⠃⠘⣿⠀⣿⠂⣿⡇ ⣿⡏⠸⠈⣿⣧⢠⣿⣿⡄⣼⣿⣿⡇⢸⣿⠇⡆⢡⠀⡿⠰⠇⢿⠀⣿⠀⣿⡇ ⣿⣁⣷⣆⣻⣟⣸⣿⣿⣇⣿⣿⣿⣇⣈⣹⣆⣷⣼⣀⣇⣰⣦⣸⣆⣉⣀⣿⡇ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣬⣝⣶⣄⡀⠀⣀⣀⣀⣀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣛⣯⣷⡿⢿⢛⣫⡭⠭⢟⣿⠿⢿⡿⠟⢻⣿⣶⣶⡒⠒⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣵⢞⣽⣿⢽⣅⡞⠉⠁⣠⠖⠋⣠⡞⠋⠀⠀⠀⠹⣏⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣴⣯⣟⡽⠋⣾⠒⠲⠬⡳⣦⡀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠹⡆⠘⣿⣿⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣼⣿⣫⠏⠀⠀⠾⢦⣀⠀⠈⢫⡳⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⠼⣟⣧⠹⣿⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⣻⣿⡋⠀⠀⠀⠀⠀⠉⠳⣄⠀⢣⢹⡀⠀⠀⢀⡠⠴⠒⢊⣉⣉⠽⠷⡞⢻⠙⣇⢹⡎⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⢱⢣⠿⣇⠀⠀⠀⣾⣿⣦⡀⠈⢧⣸⣾⠃⠀⡴⢋⡤⠖⠋⠉⠀⠀⢀⣴⠃⠈⠟⢫⡭⣽⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⢁⠏⣸⠀⣿⣄⠀⠀⢻⣿⣿⣿⣦⣌⡁⠀⠀⠀⠻⠯⣀⣠⠤⠖⠒⠋⠉⠉⠀⠀⠀⢸⡇⣿⣼⠷⢤⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⡇⢠⠇⢹⣦⡀⠈⢻⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣬⣤⣤⣤⣴⣾⣿⠀⠀⠀⠀⢸⡇⣿⡿⣀⢨⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠼⠀⣼⠉⠻⣶⣄⠙⠿⣿⣟⠉⠉⠻⠿⠛⠙⠛⠿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣼⠃⣿⠷⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣍⡛⠻⠷⠶⢦⣤⣤⣤⡿⠿⠛⠉⠀⠀⣀⠴⢋⣯⣾⠏⠀⢀⠀⠀⠀⠀ ⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⢶⣤⣤⣤⣀⣀⡀⠀⠀⠐⣊⣁⣤⡾⠟⡿⠀⣠⡿⠁⣤⠀⠀ ⢠⣿⣤⡞⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣻⠋⣹⠋⣸⠃⠼⠃⠐⠛⢙⡿⣡⣾⠇ ⠈⠀⠿⠞⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠰⠏⠀⠁⠀⠀⠀⠀⠀⠈⠛⠉⡿⠀ ⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠖⠚⠛⠛⠛⠛⠛⠛⠲⠶⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠟⠛⠛⢋⣉⣉⣉⣉⣛⣉⣉⣉⣉⣉⢉⡓⠚⠛⠋⠀⠀⠀⠀⠀⠀⢷⡀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣤⣤⣤⣤⣤⣤⣐⣾⣿⣿⠉⠉⠀⠈⢹⣿⣇⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⣷⠀ ⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣿⣿⣿⢿⡿⠿⠿⠿⣿⣿⡟⠋⠀⠀⢠⠀⠘⠛⣿⣿⣿⠿⠟⠿⠿⣿⠗⠒⠀⠀⠀⢹⡄ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣿⣿⣶⣦⠀⠀⠀⠀⣺⣿⡃⠀⠀⢠⣿⠀⠀⢠⣿⣏⠀⠀⠀⢀⣤⡘⡇⠀⠀⠀⠀⢸⠁ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⣿⣿⣷⣏⡉⠀⠀⠒⣀⣼⣿⡇⠀⠀⢼⣿⡄⠀⠘⢿⣿⣆⠀⠀⣈⣉⣼⣧⡀⠀⠀⠀⣸⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣾⣿⣿⣿⠞⠀⠀⠀⢰⣿⣧⠀⠀⠈⢻⣿⣷⣾⣿⣿⣏⠀⠉⠀⠀⠀⡇⠀ ⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⡿⠛⢁⣴⡾⢧⣤⣾⣿⣿⣷⣤⣠⣺⡿⠿⠿⠿⠛⠁⢀⣀⡀⠀⢠⡇⠀ ⢸⣇⠀⠀⢠⠶⠚⠉⠉⠑⠒⠆⠀⠀⠀⢈⣛⣉⣁⣠⣾⣿⣿⣿⣿⣿⣿⡿⡟⠻⠿⣿⣟⣳⣄⡀⠀⠀⠈⠁⠀⠉⡆⢸⠇⠀ ⠀⣿⡄⢠⡏⠀⠀⠀⣀⣀⡤⣶⣶⣟⣻⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠭⣭⣿⣾⣿⣋⣩⠍⡟⣻⣿⣿⣶⣶⣦⣀⣤⠑⣾⠀⠀ ⠀⠘⢿⣌⡇⠀⠀⢾⡿⠿⠏⠉⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⡶⠾⠛⠋⠉⠁⠉⠛⢻⣻⢠⡏⠀⠀ ⠀⠀⠈⠻⣆⠀⠀⠘⢷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡼⣿⣿⡿⠻⢯⠁⠈⠀⠀⠀⠀⠀⠀⣰⠿⠛⢡⡟⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⣄⠀⠀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠴⠛⠟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⣤⣤⣤⣄⣀⣀⣠⣤⠤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⣾⣿⣿⣿⣷⣤⣀⡀⣠⣾⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠼⠋⠉⠉⠙⠛⠉⠉⠙⠿⣿⡛⠛⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣠⣶⠛⠻⢶⡄⠀⠀⠀⠀⣹⠷⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠏⠹⡆⠀⢸⡇⠀⠀⠀⢸⢧⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢰⡶⢿⡷⠶⢿⣤⣠⡇⠀⠀⠀⣿⣸⠃⣸⣇⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⣦⡀⠙⠿⠀⠀⢀⡟⠛⠙⠟⣩⡿⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⡀⢸⣷⠖⡾⠛⠛⠛⣟⠙⣷⡟⠻⢆⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣾⣿⣷⣿⣶⣶⣶⣿⣾⣿⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠙⢿⣿⣿⠁⠀⣰⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⢈⣿⠏⠀⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠟⠁⣀⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠻⣿⡀⠀⠀⠀⣀⣤⣶⣾⣷⣾⡿⠀⢀⣈⠉⠉⠉⠉⠁⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⡇⠀⣠⣾⡿⠋⠁⠀⠀⠈⠃⢠⡿⠛⣿⡆⠀⠀⠀⢸⡿⠛⠛⠛⠛⢷⣦⡀⠀ ⠀⠀⢀⣀⣀⣠⣀⣀⣠⣿⣧⠀⠀⣿⣇⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄ ⢠⣶⣿⠟⠛⠛⠛⠛⠛⠛⠋⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⢀⣀⣀⣀⣸⡇⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⢸⣿⣷⣶⣶⣶⡶⠶⠶⠶⠶⢶⣤⡀⢹⡏⣠⣴⠶⠟⠛⠛⠛⠛⠛⠛⠿⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟ ⠀⠈⠉⢻⣿⡇⠀⠀⠀⠀⠀⠀⠉⣿⣿⡏⢿⣷⣶⣤⣤⣴⣶⣶⣦⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃ ⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⣀⣴⠟⠈⢿⡀⠈⠉⠉⢻⡏⠉⠉⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣿⠋⠁⠀⠀⠘⣇⠀⠀⠀⠸⣧⠀⠀⠀⠀⣀⣀⣀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢻⡄⠀⠀⠀⠻⠷⠶⠶⠟⣿⠋⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡋⠀⠀⠀⠀⠀⠐⣛⡃⠀⠀⠀⠀⠀⠀⢙⡃⠀⠀⠀⠀⠀⢘⠛⠀⠀⠀⠀⠘⠛⠀⠀⠀

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⠤⠤⠶⠶⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠶⠾⠛⠛⠛⠋⠉⠋⢉⣥⣄⣀⣀⣀⣀⣀⣀⣀⣻⣛⣿⢿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⠛⢉⣉⣁⣀⣤⣤⣤⣶⣶⣶⠶⢾⡿⠿⠿⠛⠛⣿⣿⢻⡏⠉⠙⠛⠛⠛⠿⠿⣿⣿⣷⣿⣧⣷⡀⠀⠀⠀ ⠀⠀⣴⣿⣯⣿⣷⡶⢶⡿⠿⠛⢻⠛⠋⠉⢹⣿⣿⣯⣧⣿⠀⢼⠁⠀⠀⠀⠘⡗⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠉⠛⡟⠛⠻⣿ ⠀⣸⣿⠋⠀⣽⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⣿⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢳⠀⢸⣿ ⠀⣿⣿⠀⠀⣿⠀⠀⣸⡁⠀⢀⣾⣀⣀⣀⣼⣿⣿⣿⣿⣟⣀⣿⣀⣠⣤⣤⣤⣿⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣿⣆⣀⣀⣀⠘⡄⣼⣿ ⠀⡿⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡍⠋⠛⣿⣿⣿⣿⣿⠻⠿⠟⣻⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⠋⠹ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⢿⠀⠀⢸⡏⠀⠀⠀⠀⢹⡧⠀⠀⠀⠀⢬⣿⠛⣿⠀⠀ ⠀⣇⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢹⣿⢽⣿⠀⠀⠀⣏⣉⣉⣁⡾⠀⠀⢸⣇⠀⠀⠀⠀⣸⣿⡏⠉⠉⠉⣿⣿⡀⡸⠀⠀ ⡾⡏⠉⠉⠉⣹⠛⣩⣿⣛⠿⢿⣿⡟⠒⠶⢿⡇⢸⣿⢻⣿⡶⠋⠛⠛⠛⣧⠀⠀⢀⣤⣤⣿⣟⣿⣿⣿⣿⣿⡟⠛⠛⠛⣻⣿⣿⣷⣤⣀ ⠀⠻⢦⣀⣠⣿⣾⣯⣿⣿⣦⣸⡏⠁⠀⠀⢸⡇⠈⢻⠀⣿⠃⢀⡴⣿⡛⢿⣧⠀⢸⣉⣿⣿⣿⣿⣾⣿⣿⡟⠳⣤⣤⣶⣿⣿⣿⣿⡟⢻ ⠀⠀⠀⠀⠀⢸⣿⠟⣿⣟⠛⣿⣿⣦⡤⢤⣾⣷⣶⣦⣤⠹⣆⣼⣿⣿⣿⣿⣿⡀⠀⠰⣶⣟⣿⣿⣿⣿⣿⡿⠖⠛⢟⠛⣿⣿⣿⣿⠀⠐ ⠀⠀⠀⠀⠀⠈⢿⢷⡿⢻⢀⣿⣹⠏⠉⠉⠉⢻⣟⣛⣿⣶⣿⡿⣿⣿⣿⣿⡏⡏⢹⣟⣟⣛⡟⠛⢿⣉⣉⣻⣿⢛⡏⣿⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠴⠷⠾⠿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢿⠸⣿⣫⡿⢠⠃⣸⠋⠉⠙⠻⠶⢿⠻⣿⣿⠟⣾⣷⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣌⣉⣠⣎⡴⠋⠀⠀⠀⠀⠀⠀⠑⠲⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡀⡀⠤⠒⢉⠥⠐⠉⠀⠀ ⠐⠒⠒⠀⠄⠀⠀⠀⡀⠀⠀⡖⠉⠉⢉⣇⣀⣤⠘⠈⡁⠠⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠂⠠⠄⠐⠛⣷⣿⣶⣿⣻⣿⣯⠤⠬⣧⣧⣤⣤⣤⣤⣤⣤⣤⣤⣄ ⢀⣀⣤⣤⠤⣒⣂⡀⠩⠥⠋⠉⢙⡓⢿⡁⣈⣁⡉⢯⣯⠉⠭⠭⠿⡍⠉⠉⠉⠉ ⠒⠊⠉⠉⠀⠀⠀⠀⢠⠴⡒⡹⠙⡿⡿⠖⠉⣤⡀⡀⢸⠈⠉⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⡿⠀⢘⣷⡌⣀⠸⡟⠳⢫⠿⠀⣤⣤⣀⡄⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡤⠤⣖⣂⣸⠃⠐⠘⠃⡍⡐⢀⢸⠒⢲⡞⡿⠹⣋⣟⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⣝⡉⣧⡧⢋⠀⢀⣀⠘⡐⢀⠂⠨⡤⢼⣿⡉⠸⣿⠦⠃⠀⠀⠀⠀ ⠀⠀⠀⠸⡿⠦⠙⢿⠔⡏⣆⡞⡚⠉⠀⠋⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⣿⡿⠛⣿⣼⡗⠘⢷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡅⠀⠻⡿⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠫⣦⡤⣄⣩⠤⠬⣁⠀⠈⠉⠑⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣶⡆⠀⣤⠑⠦⠤⠼⠁⠀⢠⠖⠒⠢⢄⢈⣽⡦⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣿⣏⠉⠑⢄⠀⠀⠀⠀⣘⠢⠤⣠⠼⠃⠉⣁⠀⠍⠢⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢲⡟⠲⢤⣄⣀⡙⠓⠲⠶⠀⠀⠘⠧⣬⣞⠒⣻⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢉⢿⣿⣿⣭⡟⠛⢁⠤⡀⠀⠀⢨⠟⢿⠒⠶⢶⣾⣾⢿⣾⢛⣾⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣻⣦⣻⣿⣿⣁⠀⢻⣤⣇⣸⡄⠘⠶⠞⠁⢸⣁⣸⣿⣿⡿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢧⡸⣮⠛⠛⠻⠿⢿⣿⣿⣙⣿⠋⠉⠓⣾⣦⣿⠚⠙⣿⣿⣿⣷⠏⠀⠀⠀ ⠀⠀⢀⣤⡶⢶⣾⠟⢉⣿⡿⢩⣇⠀⡼⣿⢾⡶⢄⠀⠀⠀⠈⠙⣛⣭⣷⣤⡴⣿⣿⣿⣶⣶⣿⣿⡿⠋⢳⡀⠀⠀ ⠀⢠⠟⣅⣠⣿⣃⡴⣯⣾⡿⣿⠻⢿⣅⣠⡾⠽⠒⠤⣀⠀⠀⠘⢧⣀⠈⠉⠛⢭⠉⢉⠟⠛⠛⢍⠀⣠⠜⡇⠀⠀ ⠀⢸⣀⣼⠞⢉⡥⣾⣿⢸⣵⣿⣴⣿⠿⠻⢤⣠⡴⣏⠭⣉⡳⠶⣤⣄⣭⣍⣚⡉⠀⠈⠑⠒⣶⣭⣶⣽⡾⠁⠀⠀ ⠀⠀⠉⢀⠴⡏⠀⣻⣿⣾⡿⠟⠉⠀⠀⠀⠀⠉⠒⠦⢶⣉⡴⠚⠁⣠⣾⠋⣩⡿⠶⢶⡟⢛⣿⠟⠛⣿⠀⠀⠀⠀ ⠀⠀⢰⠋⠳⣧⣴⣿⡿⠋⣀⠤⠠⡴⠒⣔⣲⣤⣤⣤⣤⣌⣉⣛⠛⠤⠥⢼⣋⣴⣶⣛⣄⣶⣷⠶⠞⢻⣆⠀⠀⠀ ⠀⠀⣼⣄⡠⢋⣿⣿⠒⢧⣼⣶⣶⣿⣟⠉⠉⣻⣿⣧⣽⣿⣿⣿⣿⣿⣶⣶⣲⡤⣤⣍⣁⠉⢯⣦⠀⠀⠹⣆⠀⠀ ⠀⣼⠃⠀⢠⣿⣿⣀⣟⣶⠟⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣤⣼⣇⣼⣿⣿⣿⣧⠀⠣⢹⡆⠀ ⢰⡟⠀⠀⣎⣿⣿⠟⠻⣿⣤⣤⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣩⣿⣿⣿⣿⣻⣿⡆⢱⡇⣿⡀ ⣼⠃⠀⢸⣽⣿⣷⣀⣀⣼⠿⣤⣿⣿⣯⣬⡇⡀⠀⠀⢘⡿⠿⣿⣿⡟⠛⢿⣿⠿⠟⠉⢹⣿⣞⣿⣿⣼⣼⣿⢸⡇ ⣿⠀⠀⡏⣿⡟⣿⣿⣿⣿⣾⣿⣿⡿⢿⣿⡟⠙⢲⠖⢻⡧⣤⣿⣿⣧⣀⡜⢻⣿⣷⣶⣿⣿⢿⣿⣿⡏⡏⠹⣜⣷ ⣿⠀⠀⡇⣿⣿⣿⡿⣿⠋⠉⣙⠻⡷⣾⠋⠉⢲⣾⢷⣾⠿⠛⠒⠒⠻⣭⣟⣿⣿⣿⡟⠉⠙⣾⡿⣿⡇⡇⠀⢛⡿ ⢿⡀⠀⢷⣿⣇⡿⢷⡬⣽⠧⡀⢳⣸⢸⣦⣴⣿⠟⠉⠀⠀⣠⣴⡞⢛⠛⡛⠿⣯⡻⣿⣦⣾⣿⣿⣿⢷⠃⠀⢸⡇ ⢸⣷⡄⠘⣿⣿⡿⣦⡘⠾⣶⣷⠞⡼⢸⣻⣿⠋⡠⠊⠀⢲⡯⠀⣸⡟⣿⣧⡄⠈⢻⣿⣧⣿⣿⠛⡿⡼⠀⠀⣾⠃ ⠀⢿⣿⣄⢳⣿⣧⢻⣿⣤⡄⣿⠠⡇⡆⢿⡇⢰⣅⣀⣤⣼⣗⠒⠻⣿⣿⣿⠃⢀⣿⢧⢻⡏⠈⣹⣿⠃⠀⢰⡏⠀ ⠀⠈⣿⣧⣃⢻⣿⣷⡙⣿⣷⡘⡄⠻⠯⢼⣷⠀⢙⡏⠀⠀⠹⣗⢤⡀⠑⠘⢠⡾⠃⢸⢸⣿⣾⣿⠃⠀⢠⡿⠀⠀ ⠀⠀⠘⢿⣿⡣⡹⣿⣿⣮⣿⣷⡘⣄⠀⠀⢏⠓⡻⠁⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⣠⡎⣸⡿⡵⠁⠀⣠⡟⠁⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣮⠻⣿⣿⠉⢹⣌⠻⢷⣜⣦⡘⠦⠴⡺⣵⡤⠀⠀⠀⠀⠀⢀⣽⣵⡿⠋⠀⣀⣼⠋⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠋⠉⢻⣿⣧ ⢸⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿ ⠸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⢹⣿⣿⣿⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉⠀ ⠀⠀⠻⣿⣿⣿⣦⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⢻⣿⣷⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠻⣿⣿⡇⠀⠀

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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣦⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡈⠙⠛⠻⢿⣿⣿⣿⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣉⠙⠛⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢠⣿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⢿⣿⣿⣦⣤⣿⡟⠀⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⣀⣸⣿⠋⠉⣿⣿⠿⣷⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⢿⣿⣿⣦⣴⣿⡃⠀⣸⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⣿⣿⣅⣀⣾⡟⠁⢸⣿⡿⠻⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⠟⠛⣿⣿⣿⣶⣾⣿⣀⣀⣿⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⡟⠀⢠⣿⠏⠀⣹⣿⠟⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⣀⣀⣼⣿⣿⣿⣁⣀⣿⣟⣀⣠⣿⣏⣀⣰⣿⣿⣿⣃⣀⣀⣀⣀⠀ ⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⢠⠀⠐⢴⣄⠀⠀⢀⣤⣴⣶⣶⣦⣤⣀⡀⠀⢢⠄⠈⠏⠀⠄⠀⠀⠀ ⠀⢠⣠⡨⣆⠀⠈⠀⢢⣿⣿⣿⣿⡟⢻⡙⡿⣿⣿⣦⣘⠃⠀⣶⠆⠆⠀⠀⠀ ⠀⠜⣿⣯⠘⡆⠀⢴⡿⣯⡿⣭⣧⣤⢳⣿⡼⣾⣼⣿⣷⢁⠈⣻⠃⠀⠀⠀⠀ ⣤⠤⢻⣿⡇⠀⢀⣿⢹⣻⣷⣿⣿⣷⡿⢿⣷⣿⣿⣿⣿⣷⢧⡅⠈⠁⠀⠀⠀ ⠀⠀⢸⡏⠙⠄⣞⡟⣾⣿⠏⠉⢏⠿⠅⠘⠛⢘⣛⠸⣿⡿⠈⠧⠶⠂⠁⠀⠀ ⠀⠀⢸⣯⠀⢘⡻⣷⣧⡇⠀⠫⠭⠽⠁⠀⠴⡖⢒⡦⣿⡇⢀⡏⠐⠀⠀⠀⠀ ⠀⡇⠀⡿⠀⣜⢫⢿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢘⡧⠀⠀⠀⠀⠀ ⠀⡇⢀⡿⣱⡏⣾⣾⣷⣵⡀⠀⠀⠀⢀⣀⠀⠀⠀⢰⣿⣧⠈⢰⠀⠀⠀⠀⠀ ⠀⡇⠀⣼⡿⣼⣿⣳⣿⣿⣷⣄⠀⠀⠐⠂⠁⠀⣠⣿⣿⡟⡀⡄⡄⠀⠀⠀⠀ ⠀⢀⣾⣿⣽⣿⢣⣿⡿⣿⣿⠀⠑⠤⣀⣀⡤⣾⣿⣿⣿⣇⠀⢃⡇⠀⠀⠀⠀ ⣮⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡇⢸⠐⠀⠀⠀⠀ ⣿⣟⣿⣿⡿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠢⡀⠀ ⣟⣾⣯⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠩⠀ ⣿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢃ ⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⡏⠁⣀⠄⢀⣀⣤⡤⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠷⠊⡼⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣡⢔⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⢀⣠⡚⠍⡂⡽⠫⡕⣰⣄⠅⢸⣷⣶⣶⠶⡆⠀⠀⡠⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⢂⠜⣱⢊⠔⡳⢱⣿⡿⠃⠀⠘⢿⠟⠛⠈⠉⠙⢃⢳⡀⠃⠀⠀ ⠀⠀⠀⢀⠎⡰⢑⢎⡁⠕⠊⢀⠞⣞⣿⣦⣀⡶⠂⠀⠀⠀⣀⡀⣤⡜⠁⠀⠀⠀ ⢀⠆⠒⢅⡿⡻⠡⠘⠀⠀⠀⢸⠀⠈⠛⠟⠉⠀⠀⠀⣰⣿⣿⠁⢟⣿⣿⣆⠀⠀ ⡪⢁⠔⡿⡀⠁⠀⠀⠀⠀⠀⠀⠹⣿⡀⣄⣶⣴⣰⣀⣿⡟⠀⠀⣼⣿⠁⠀⠀⢀ ⡵⢋⣌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠂⠒⠁⠙⠋⠀⠔⢁⣿⡏⢳⠛⠋⠁ ⣰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⢀⣀⣠⡼⠶⠛⢻⠦⠥⠀⣀⠀ ⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠚⠉⠉⢙⢯⣀⠔⠂⣯⣁⠒⠈⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⣴⡤⣾⣷⠎⠁⠚⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣔⣖⡒⠒⠤⢂⠯⠢⡈⠑⣼⠗⠛⡫⠭⠓⢖⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⠣⢹⢢⣀⠙⣖⠠⠬⣛⢱⠒⢁⢘⣛⠴⠶⠦⢉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣿⣤⣤⣤⣤⣼⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣄⣀ ⠿⠿⠻⠿⠿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠙⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠶⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⣠⣾⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⣰⡿⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠹⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠤⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡟ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢻⠀⠻⣿⣿⣿⣯⣝⢢⣌⣙⣿⣛⠛⠛⣿⣯⠀⠀⠀⠈⢿⠀ ⠀⠀⠙⣿⣿⣿⣿⣿⣿⠋⢀⣀⠼⢧⣤⡙⢿⣿⣻⠿⢿⣟⣁⠀⠈⡇⠀⣾⢻⠂⡄⠀⠀⢸⠀ ⠀⠀⠀⠈⠀⢸⠈⢻⣿⣯⢁⣠⠤⣴⣬⠇⠸⠉⠙⠓⠻⠟⠚⠛⠋⠀⠼⠃⠀⠼⠦⠀⠀⡎⠀ ⠀⠀⠀⠀⠀⠘⣄⠀⡏⠑⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⣾⡷⠒⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠴⠒⠊⠉⠉⣙⡳⡄⢀⣤⣶⡭⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⢿⠀⠀⠀⠀⠀⢹⠁⡇⠀⠿⢄⡠⠀⠙⠢⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡀⠀⠀⠿⠇⠘⠃⢧⠀⢠⠊⠀⣠⠶⠖⠙⢆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡥⠴⢧⣄⠀⠀⠀⠀⢀⣸⠤⣇⡀⠚⠀⡼⡅⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠘⠉⢣⠀⠀⡴⠛⠃⠀⠀⠹⡀⢠⡿⠁⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡇⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⠀⠀⠀⢠⡷⣾⡑⢤⡀⠀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢛⠟⢳⠀⠀⢀⡠⠾⢷⠒⢺⠛⢤⣀⡀⣄⡸⠀⠃⠑⠄⠁⢀⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⠈⡇⢻⡁⠀⠀⣿⠀⢸⡄⠀⠀⢰⣻⠁⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⣀⣓⡠⠼⠞⠃⠀⠀⢽⠄⢸⡇⠀⠀⠀⠀⠉⠲⠤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠒⠒⠒⠒⠲⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠀⣋⣀⡀⠀⠀⠀⠶⠄⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠁⢀⣠⡄⠀⠙⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⣠⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣧⣆⠀⢀⣾⣤⣀⡀⠀⠀⣤⣾⣰⡀⡀⠛⢰⣤⣤⣴⣿⡀⢻⣿⣧⣾⣿⣀⣤⣶⣦⣤⠀ ⢰⣶⢶⡾⣿⣿⢿⣻⣿⣿⣿⣽⣿⣿⣿⣦⣭⣿⣿⣷⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⠿⢯⣩⣽⡿⠟⠁⠀ ⢰⣿⣿⡦⢬⣉⣸⣦⣍⣀⣬⡍⢸⣯⣀⠀⣉⣉⠙⠋⣡⠤⣴⣖⣾⣿⣯⣽⡟⣻⣷⣶⣧⣽⠃⠀⠀⠀ ⠀⠀⠹⣷⣶⣯⣭⣿⣤⣼⡿⣧⡾⢿⣿⣷⣤⣼⣷⣶⣿⣶⣿⡿⠛⠛⢿⠛⠿⣿⣿⣿⠿⢿⡇⠀⠀⠀ ⠀⠀⢰⡟⣿⠛⣻⢋⢉⣻⠛⠋⢀⣠⣿⡿⠾⢿⣿⣿⠿⠛⠛⠷⣄⠀⠀⠀⢀⡿⢁⣿⣶⣿⣷⠀⠀⠀ ⠀⠀⠈⠳⣼⣿⡿⡿⣿⢿⣷⣶⣿⣿⣿⣦⣴⣶⣇⣼⣶⣿⣿⣤⣘⣿⣷⣶⣿⠿⣾⡶⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣛⠋⠉⠛⠛⢿⠉⣩⢿⣿⣿⡿⠟⠉⠉⠉⠙⠋⠉⣻⣿⠿⠁⣀⣞⣿⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣽⠛⣷⣧⣦⣀⣻⠀⠁⠈⣯⠟⠁⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⠿⠿⠛⢁⣴⣿⣦⡀⣀⠀ ⠀⠀⢀⣼⣿⣿⣿⣽⡟⢻⣿⣿⣄⠀⢀⣿⣾⣿⣿⣿⠛⣛⣉⣠⣤⣄⣀⣴⣦⣶⣶⣿⣿⣿⣯⠹⣟⠁ ⠀⠀⠸⣧⡭⡄⠽⣿⢿⣿⣤⣟⠛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⣿⣿⣿⢿⣭⣥⠥⠤⠿⠇ ⠀⠀⠀⠘⣦⢳⡞⠻⣄⡈⠉⢉⣉⣩⣿⣿⣿⣏⣭⣿⣮⣶⣀⣴⡾⠿⠿⠿⠋⣁⣠⣤⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣷⣶⣼⣏⣉⡉⠉⠛⠛⠛⢻⣿⣿⣿⠟⠋⠁⢀⣀⣀⣶⣾⣿⣻⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣶⣶⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⢷⣒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢸⠹⣟⠲⣍⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢧⢸⡆⠙⣆⠈⠙⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢯⣀⢠⠟⢷⡾⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⡄⠈⠳⣄⡴⠚⠷⠚⠋⠉⠉⢻⡄⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⢸⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⢣⠤⢼⠳⢤⣀⣠⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠈⢇⠀⡇⠀⠀⠀⠀⠀⠀⢀⠎⢨⣆⣼⠀⠀⠀⢠⠇⠀⠀⠀⢀⡟⠒⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⣸⠖⢷⡀⠀⠀⢠⠤⠐⠋⠀⠉⣇⡇⠀⠀⠀⠘⣆⠤⢶⠠⣾⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⢀⣼⠁⠀⠘⡷⠤⠤⠾⠄⠀⠀⠀⠀⡇⣇⠀⠀⢀⣀⡤⠶⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⢰⠃⣠⢤⠏⠸⣄⠀⠀⢹⡀⠀⠀⠀⢸⠓⢲⠞⠁⠉⢻⠉⠉⠙⢦⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀ ⣿⠎⠀⢸⠀⠀⠈⠳⣄⢸⡇⠀⠀⢀⡏⠀⢸⣠⠄⢀⡎⠳⡀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⡸⢷⡀⠀⠀⠀ ⢿⠀⠀⢸⡀⠀⠀⡼⣿⠋⠳⠤⠤⠾⠁⠀⡼⠁⠀⡼⠀⠀⠙⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣤⠔⠋⠀⠀⠳⡄⠀⠀ ⢸⡄⠀⠀⣇⠀⠀⢹⠀⠀⠀⢀⡤⢤⣄⡼⠁⠀⢰⡇⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠈⠣⡀⠀⠀⠀⠙⣦⠀ ⠀⠻⢦⣄⣸⡄⠀⠀⣇⣠⠖⢉⡇⠀⠙⡷⡆⢀⡟⢣⠀⣠⠴⠒⢧⣀⣠⠖⠛⢷⣾⣳⡚⠁⠀⢀⡠⠟⠒⠁⠀⠀⢘⡄ ⠀⠀⠀⠀⠀⢷⠋⠉⠀⠀⣀⠾⠥⠠⠾⠵⣧⠞⠀⠘⣟⠁⠀⠀⠀⠹⣍⡀⠀⠀⡏⠙⠛⠋⠉⠁⠀⣀⣠⠤⠖⠚⠉⠀ ⠀⠀⠀⠀⠀⠘⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠒⠒⠛⠛⠓⠒⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣴⣦⡦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢯⣿⣿⣿⣧⣿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠇⢸⣿⡿⠝⠛⠡⣶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠻⠟⠋⠀⠀⠙⡏⣧⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠈⡷⠦⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣠⠶⠒⠚⢹⠻⣄⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⠁⢀⣤⣤⠘⢦⠙⢦⣸⠙⣝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣀⣤⡴⠒⠉⢹⣿⣁⣼⠄⠀⠈⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣇⠈⣿⠉⠀⠀⠀⠀⠀⢻⣿⠒⢶⣤⣄⠀⢀⡼⣆⠀⠀⠀⠀⠀⠀⣠⣾⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠸⡄⠀⠀⠀⠀⠀⠈⢯⠣⠀⠀⠡⠶⣿⣧⠘⣇⣀⡠⠤⠶⠚⣻⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢇⠀⠀⠀⠀⠀⠀⣾⠀⡠⠄⠀⣠⠏⢿⡷⢉⣁⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠒⣦⡀⠀⠀⣸⣿⣿⣾⠟⠓⡇⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⢛⣦⠗⢴⣿⣿⣿⣗⣲⢄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢰⣿⣿⣿⣿⣿⣿⣷⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣿⣿⣿⣿⡙⠢⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⣩⡿⠙⢿⣦⡈⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⠟⠁⠀⠀⠙⠿⣦⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⡾⠟⠋⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣠⣴⡶⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠞⠋⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⢰⡞⣶⣺⢿⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡇⢛⣦⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠸⡄⠀⠀⠀⠀⠀⠀ ⢰⣿⢃⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡐⢻⠀⠀⠀⠀⠀⠀ ⠸⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⢧⣀⠀⠀⠀⠀ ⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣿⣻⣤⡤⢌⣛⣓⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠚⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠋⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣾⣿⣿⣟⡿⠛⣩⠟⣉⠽⠛⡂⣀⠀⠀⠀⡀⠬⣍⣓⠦⣈⢢⡻⣯⠳⣄⢺⡦⠙⢷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢋⣵⠏⢠⠀⣠⣯⠞⠁⢠⣾⠿⡿⡄⣾⣯⡙⣷⡌⠻⣷⡜⢳⣵⡈⢷⡈⢦⠙⣿⣦⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣵⣻⠇⡰⣁⡼⢉⠏⠀⢠⢣⡟⠀⠸⢀⡿⣿⡿⣯⠙⣖⡜⢿⣶⡟⢿⡄⢳⡘⣧⠈⢟⢷⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣷⡳⢰⢁⣽⠁⡎⠀⢠⠇⣸⠀⠀⡿⠘⠀⢻⠁⢹⡆⢻⡾⡌⢻⣿⣌⢧⠀⢳⢸⣧⠈⢧⠳⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣧⣇⢇⣿⡇⢰⠀⠀⣸⠀⡏⠀⠀⠀⢠⠀⠸⡀⠀⣷⠀⢿⣿⣄⠛⢿⣇⣧⠀⢧⣿⡳⣎⣧⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⡾⡼⣿⠀⣼⠀⢸⡇⢠⡇⠀⠀⠀⢸⠀⡆⡷⡆⠹⡆⢸⣿⣿⡆⠈⢿⣷⠀⠘⣿⣇⢸⣿⣧⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⢷⣷⡇⠀⡿⠀⣿⡇⢸⡇⢰⠀⠀⢺⠀⡀⡗⡁⢸⡗⠀⣿⡈⣿⡄⠈⣿⡇⠀⠉⣿⣮⣿⣷⣈⣷⠀⠀⠀⠀⠀⠀⠀ ⣿⢻⣾⣿⡇⢰⠁⠀⣻⡇⢸⡇⢸⡇⠀⣿⠀⡇⣿⡇⠸⢯⠀⣿⡇⠸⡇⠀⣿⣿⡀⠀⢹⣷⡟⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣾⣿⣿⡅⡈⠀⢸⣿⠃⢸⡇⣾⡇⢀⣿⡀⢿⣿⡇⠀⡄⠀⣿⡇⠀⢿⡆⣸⣿⣿⣼⠈⣿⡇⣿⣋⠹⡇⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣿⠃⡇⢠⢸⣿⠇⢸⡇⣿⣿⣸⣿⣷⣶⣿⣿⠀⠇⣽⢿⠃⢀⣰⣿⣿⣿⢻⡿⡄⢿⣷⣍⣉⢋⡇⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⡇⡇⢸⡜⢿⢰⣾⣷⣿⠻⣿⣿⣿⣿⠉⣟⠀⣆⣿⣾⡾⢟⣯⣴⣿⣿⣾⣿⡇⢸⡇⣿⡿⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣽⡇⡇⢸⡇⢸⣿⣿⠻⣿⣠⣿⣿⣿⣿⠀⢿⣼⣿⣿⠏⢰⣿⣿⣿⣿⡿⣹⣿⢱⡾⣇⡟⢹⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⢛⡇⣷⢈⣿⣾⣿⣿⣆⣿⣿⣿⣿⣬⣿⠀⣸⣻⠿⠋⠀⠘⠉⠽⠿⠿⡾⠟⢹⣸⠀⣿⡷⣻⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⣷⣿⣸⣿⣿⣿⣿⠿⣿⣿⣿⣿⢧⠄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡏⢹⡟⠋⠙⢶⠌⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣻⠿⢤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡃⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢀⡇⠀⠉⠒⠤⡀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡇⠈⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣿⣤⠃⠀⠀⠀⠀⠈⢦⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⢹⠋⠉⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢀⣷⢸⣿⢁⣀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⢀⡿⣷⠘⢸⡇⠀⡀⣏⠳⣄⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⠋⡀⠀⠀⢀⣿⠏⣼⠁⠈⠈⠉⠙⠲⢤⣠⡄⢸⠄ ⠀⠀⠀⡰⠋⠀⢻⡀⢿⡇⠀⢡⢿⠀⠀⠑⢦⣄⠀⠀⠀⠀⠠⠤⠤⠴⠊⠀⠀⣠⣿⣿⢠⡿⠄⠀⠀⠀⠀⠀⢠⠿⢉⣿⠀ ⠀⢠⠞⠀⠀⠀⢆⢇⢸⣷⠀⢺⣌⡇⠀⠀⠘⢿⣿⢷⡦⠤⣄⡀⠀⠀⠀⣀⢼⡏⣽⣇⣿⠂⠁⠀⠀⠀⠀⠀⠘⠀⣸⣏⠀ ⢀⡇⠀⠀⠀⠀⠈⣞⡄⣿⡶⡈⠙⣿⠀⠀⠀⠈⢿⡳⣄⠀⠀⠈⠉⠉⠉⠁⡸⢹⣿⣿⡏⡖⠀⠀⠀⠀⠀⠀⢀⣼⠏⠘⠄ ⢸⠁⠀⠀⠀⠀⠀⠘⢷⣼⣷⠹⣄⠘⢷⢄⡀⠀⠀⠙⠾⣆⠀⡀⠀⠀⠀⣴⡷⢿⡟⣿⠆⡇⠀⠀⠀⠀⢀⠆⣾⣿⡴⡴⠁ ⢸⡀⠀⠀⠀⠀⣠⡤⠈⢻⣿⣆⠈⢳⠘⢧⠉⠲⣄⡀⠀⠈⠙⠻⢆⣀⡜⠉⠀⠋⡰⠋⠀⣇⠀⠀⠀⠀⠸⠀⣿⣽⣾⡗⠀ ⢸⣇⠀⠀⣠⠈⠉⠀⠀⠀⠹⣟⢆⣀⣧⠀⢷⡀⢀⠉⠓⠦⢤⠀⣠⣿⣿⢿⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⢸⣷⠎⠀⠀ ⠀⢫⠳⣞⡁⠀⠀⠀⠀⠀⠀⠈⢣⠱⠜⣧⠘⣟⣄⠑⠢⠤⠄⣠⣿⣟⠉⠀⢹⡟⠲⢤⣀⠀⠀⠀⠀⠀⠓⠀⠘⣿⡀⠀⠀

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⠆⠀⣼⢀⡞⣼⣿⣼⠀⠀⣠⠟⣠⣾⣿⣿⣿⢀⣤⣔⣿⠟⠋⣙⢛⡺⠛⠛⢛⡻⠟⠛⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣭⣅⢻⣿⣿⣿⣿⣿⣧⡻⣧⠀⠀⣇⣇⠈⠂⠀ ⠀⢠⣇⣞⣼⣿⣿⣿⠀⣰⢃⣾⣿⣿⣿⣿⣿⡗⠿⣍⡠⣒⠽⠊⢉⡨⠖⣯⣥⠄⢠⣄⣀⡀⠀⢀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡙⢃⣸⣿⣿⣿⣿⣯⣿⣿⣾⣷⡀⣿⣿⠀⠀⠀ ⠀⢸⡿⢹⣿⣿⣿⣿⣰⣷⣿⣿⣿⣿⣿⣿⣿⣗⠾⠗⢉⣠⠴⠊⠁⠀⠀⣿⢺⠀⠀⡏⠀⡇⠀⢸⠊⡇⠀⢸⠟⡇⠀⠀⠀⠔⠋⢿⡿⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⣸⠁⢨⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠖⠋⠀⠀⠐⠒⠦⠤⡏⢸⠶⠶⡇⠀⡵⠶⢮⠀⡵⠶⢦⡇⣷⡶⠖⠚⠛⣠⠟⣠⣿⠿⣿⣿⣿⣿⣿⣿⢟⣥⣼⡿⣿⣷⠀⠀ ⡆⠇⣰⣿⣿⣽⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠁⠀⠀⠀⠀⠀⠀⠀⠷⠾⠁⠀⡿⠾⠅⠀⢸⣤⠁⠠⠼⣧⠇⠀⠀⢠⡾⠃⣻⣿⣿⠀⣾⣿⡿⣟⣿⣿⣿⣿⣻⢁⣽⣿⣶⢠ ⡇⠀⣨⣿⣿⣿⣿⠀⠀⠹⡿⢿⡙⠻⠿⢿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠂⠀⠀⢀⡴⣋⣠⣾⣿⣿⣯⣾⣿⡽⠾⠋⢠⣧⠸⢟⣽⣿⠛⢿⣿⣾ ⠀⢠⣿⡿⣿⣿⣿⡆⠀⠀⣷⡟⠁⢼⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣋⣁⣀⡀⠀⠀⣿⠀⢸⣿⣿⣆⣸⣿⣼ ⠁⠈⣹⡇⢿⣯⣿⡇⠀⠀⢻⡇⠀⠈⢷⡀⠀⢠⠉⣽⠉⢩⡛⠛⡿⢿⣿⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⡉⠹⡀⠘⡇⠹⣽⡿⠁⠀⠀⢸⡄⣿⣿⡿⡇⢿⣿⢿ ⠀⢰⣿⣇⢸⡍⢿⣿⠀⠀⣾⠂⠀⠀⠈⢻⣆⠸⠀⠸⣄⠈⠯⡤⣤⢤⠛⣿⣿⣿⣿⣿⠖⠋⠁⠈⢾⣿⣿⡿⢛⠁⢸⡀⠉⠥⣶⡦⠖⡇⣰⠟⠀⠀⠀⠀⣾⣿⣿⣿⢗⡇⣬⣿⢸ ⡄⠀⣿⣿⡀⢳⡄⡿⣇⢀⣿⠀⠀⠀⠀⠀⠈⠻⠷⣤⣈⣛⣊⣁⣠⣞⣠⡻⠿⠟⢿⠀⠀⠀⢀⣤⣿⡿⣯⣳⣌⣆⣀⣉⣛⣛⣉⣠⡾⠟⠁⠀⠀⠀⠀⠀⢹⣿⣿⣿⠙⢹⣿⣿⢛ ⠁⢀⡘⢿⡇⡀⣿⣶⣿⣼⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣄⠠⠞⠉⠀⣿⣥⡁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣇⢠⣾⡏⠀⠀ ⣶⣿⡇⢠⣿⣞⣿⣿⡿⣿⣧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠓⠇⠀⠀⠀⠀⢷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⡝⢀⣿⣿⠇⠀⠀ ⣾⣿⡿⠋⠻⣿⣿⡟⠁⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⣼⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠞⢠⣷⣿⡇⠀⠐⣶ ⣿⡏⠀⠀⢐⣼⡿⣿⣦⣌⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠀⠀⠀⠀⠀⣘⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⢀⣾⣿⣽⢿⣦⣀⠈ ⠃⠀⠀⢘⡿⣝⢀⣿⠋⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣾⣿⣿⡟⠈⠛⣿⣷ ⠀⢀⣴⣿⡯⠃⣸⠃⠀⣤⢿⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⠁⣹⠘⠃⢈⣢⡘⢯ ⡾⢛⢥⣬⡂⢠⡏⢀⡞⢏⣎⢞⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠤⠀⠀⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⢀⣾⡄⢻⡄⠀⠲⡙⢟⡆ ⣿⢕⢿⡫⠀⣾⣶⣯⢯⠈⠎⡜⠃⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢱⣷⠙⢾⡇⠀⠐⢜⢎⠳ ⣟⠕⢋⣴⣾⡿⣿⠋⢸⡌⠰⣿⡄⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⢀⣿⣿⣷⣦⣿⠀⠀⠐⠳⡁ ⣷⣄⡉⠸⠋⠘⣡⣦⡜⢧⡼⣡⣿⡀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠒⠒⠒⠒⠒⠒⠒⠒⠲⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣿⡇⢻⣿⣿⣿⣟⠛⣷⣀⣤⣴⣿ ⡟⠿⣿⣷⣦⡀⠹⡿⣡⣾⣿⣿⣷⣷⡀⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡉⠉⠉⠉⢉⣉⢉⣉⢉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢿⡟⣹⣯⣽⣿⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣦⡻⣿⣿⣿⣷⣤⣫⠿⢻⣿⣿⣿⣧⡿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢿⡋⠉⠉⠉⠉⠉⠉⠉⠉⢸⡟⠀⠀⠀⠀⠀⠀⣀⣴⣿⣥⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠙⣯⣿⣿⣿⣿⣿⣷⣯⣿⣻⣿⣿⣧⣿⣿⣿⣧⣿⣿⣦⣠⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⣠⣴⣶⣾⣿⡿⠿⢛⣻⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⡿⠿⣛⣿⣿⡢⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⠿⢿⣛⣫⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣦⣭⣴⣽⣿⣾⡷⢶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠐

⢠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⣀⠙⠛⢿⡿⠛⠋⣀⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⣀⣠⣀⠀⠀⣀⣤⣴⣶⢾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣾⠏⠉⠀⠀⠀⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢀⣀⡀⠀⢀⣀⢸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⣰⣿⣿⣿⣿⡀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠀⡦⣴⣖⣛⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⠧⠊⠤⡭⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠅⠂⠀⡱⠀⠀⢐⠀⠈⠟⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠒⣷⢇⢡⠀⣷⡆⢀⢸⡄⠀⠸⠀⠟⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⣕⣺⣧⣼⣾⣶⡵⠛⣦⣰⣞⣶⠼⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⣻⡏⠉⠻⠉⠁⠀⠉⠻⠛⢱⡤⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢅⡀⠀⠀⠀⠀⠀⠀⡠⢵⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠂⠀⠀⣠⡞⠀⠀⠙⡟⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢠⣾⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠇⠧⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⡤⠒⢉⣢⣉⠂⢀⡃⠀⢰⡀⠔⢁⠌⠣⡂⠤⢀⡀⠀⠀⠀ ⠀⠀⣠⡒⠈⠐⠊⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠂⠈⠉⠀⠀⠀⠈⠁⠈⠉⢒⡄ ⠀⡎⢀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱ ⢸⠇⠈⠧⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣠⠄⠀⠀⣫⡇⠀⠈⠉⠉⠉⠛⠒⠶⢤⣌⡲⣄⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠉⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⢠⣄⠀⠁⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠑⠲⣦⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠋⠀⠀⠀⣴⢿⣽⣆⢀⡼⣷⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⠽⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⠀⠀⠀⢠⡾⡿⠛⣿⡿⠿⠿⠟⠻⣯⣙⣆⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣖⣋⣁⣤⣴⠃⠀⠀⣰⠏⣼⢣⡞⠁⠀⠀⠀⠀⠀⠈⢻⣜⣆⠈⢳⡄⠀⠀⠀⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣴⠃⢰⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⣿⣆⠀⠀⣿⣄⠀⢻⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⡼⠃⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⣿⣦⢠⣿⣿⡆⢸⣿⣌⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⠀⣼⠁⠀⢸⠃⠒⢦⣀⠀⠀⠀⠀⠀⢀⣀⡠⠆⠀⠙⣿⡄⠘⣿⣿⡇⠘⣿⡸⣿⡿⣿⣷⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⢴⢫⡏⣼⠃⠀⠀⣾⠀⠀⠀⠙⢧⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠘⣟⡄⠸⣿⡇⠀⢹⣿⣿⡇⠹⣇⠻⡄⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠈⠓⢤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⣾⡞⠐⠃⠀⠀⣠⣿⡌⠙⠒⢦⡞⠀⠀⠀⠀⢔⣲⠴⠒⠒⠒⠢⠼⣵⡀⢿⡇⣠⠀⢿⣿⠀⠀⣿⠀⢹⣄⠀⡀⠀⢹⡙⠢⣄⠀⠀⢶⡒⠒⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢀⡾⠋⣹⢣⠀⢠⣾⡷⠀⠀⠀⣰⠞⠁⠀⠀⠀⢠⣶⣦⢻⡇⠘⢣⡿⠄⠀⢿⠀⢸⣿⡄⠀⡟⢣⠹⣄⠀⢧⡀⠈⠓⢤⣄⠙⠢⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡇⠀⣠⠟⠀⠀⡇⠈⠓⣾⠟⠁⠀⠀⠀⠙⠶⠤⣀⣀⣀⣺⣿⡿⠻⡇⠀⣸⠀⠸⡀⠈⠀⢸⣉⢿⡄⣷⠀⠀⠈⠳⡘⠃⣻⡖⠲⠿⠓⠛⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⢫⡇⣰⠟⠲⣄⢀⡇⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢴⣿⡄⠀⢷⠀⠀⣿⡿⢸⢧⣿⠀⠀⠀⠀⠀⠀⢹⣷⠃⠀⠀⣻⠄⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠚⣸⡾⢹⡀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣀⣿⡀⠸⡆⢰⣿⣇⡾⠟⢿⠀⠀⠀⠀⠀⢦⡀⠸⡀⢀⣴⣿⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠿⠁⠈⣇⣠⠞⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⠹⣧⠀⡇⡼⢺⡟⠁⠀⠀⠀⠀⠀⠀⠀⢈⣷⣤⣷⣿⣿⣿⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣱⡀⠀⠀⢠⣤⣤⣀⣒⣒⣒⣒⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡽⠁⢣⠀⠀⠈⠻⠿⠭⠍⠉⠩⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⡿⢻⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⡶⠶⠤⡬⠿⠛⢿⢻⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢀⡟⠛⢻⣾⣦⡀⣀⠀⢀⡏⠙⠶⣤⣻⣅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⣍⡛⠙⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠋⠁⠀⣠⠏⠀⠀⠸⣿⣛⠛⠿⠿⠾⣵⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡏⠀⠉⠙⠿⣶⣄⠛⠙⠒⣶⠒⠶⣶⣶⣾⣿⡿⣻⣿⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢻⠿⣷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡇⠀⠀⠀⠀⢈⣿⣦⠀⠀⢷⠖⠋⠹⡎⠙⡷⠖⠋⠁⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠈⡆⢨⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠖⣿⠲⢦⣄⣰⠏⠀⢹⣧⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⠞⣹⠃⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡄⠀⡿⠀⣠⡿⡇⠀⢀⣀⣿⣦⣶⣶⣶⣤⣼⡀⠢⣄⡤⠞⠁⢠⠇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣴⣶⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⣽⣦⣧⣴⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢀⡴⠁⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠏⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠀⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠤⠒⣲⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠐⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⢏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠒⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠈⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣿⡷⠟⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⠤⠤⠤⠤⠤⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡀⠤⠤⠤⠤⠤⠤⢀⣀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢫⠀⠀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠈⠻⣍⠉⣩⣉⣩⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁⣠⠎⠐⠉⠀⡀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠈⡓⠈⠩⣟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠖⠉⢀⡶⠋⣸⠀⠀⠀⢠⠈⠓⢄⠈⠉⠒⢄⠈⠑⠢⣄⠀⠀⠀⠀⠀⢄⠈⠛⢗⠢⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⣠⣿⢁⡤⠃⢰⠀⠀⠀⢣⠘⢦⠱⣄⠐⢆⠑⣄⠀⠀⠑⢤⡀⠀⠀⠀⠑⢄⠀⠑⠮⣽⣮⣍⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠰⢁⣿⡁⠀⠀⠀⢣⠀⢂⠀⠳⣴⡳⡈⠳⡌⠣⡡⡑⢄⠀⢠⡉⠢⡀⠑⡄⠀⡙⢿⣦⡈⠛⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡇⠈⢰⠳⡄⠠⠘⢄⠣⡀⣧⠱⣽⡖⠺⢵⡌⠢⣽⣿⡌⠣⡀⠙⢦⡘⢄⠈⢦⠘⢤⣽⡿⣦⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠀⣿⡇⢸⠆⢸⣆⠱⡌⢢⠱⡙⢷⡈⠻⣦⣄⠉⠳⢮⣿⣷⡶⢿⣀⣤⡙⢮⣯⠣⡳⣈⢻⣿⡛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⣟⠰⡃⠙⣼⠈⢆⠺⣆⠱⡘⠢⣙⠄⢬⣓⣝⣢⣄⡈⠙⢦⡾⠛⣶⣽⣷⣝⣆⡑⢈⠳⡝⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣼⣿⡀⠹⣤⡌⢣⡈⠳⢽⣦⠼⠦⡈⠳⣦⣝⣻⣛⣿⣽⢷⡚⢷⡒⠉⠙⡟⠏⣿⣿⣾⣖⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠟⢿⢟⣿⣄⠹⡙⢿⢟⢦⡀⠈⠑⠢⣬⣦⡙⢾⣙⢙⣦⣀⠀⣸⣾⢶⠯⠄⣸⡘⣾⣿⢿⣟⢿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡟⠀⠘⣿⣏⢻⡆⢱⣤⣿⣕⢿⣲⣖⡈⡿⠃⣈⠓⠛⠃⠀⡸⣿⡿⣿⣿⣿⣿⠋⠑⣿⢻⣦⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⢰⣯⣿⡧⣴⡀⡟⣿⣦⠹⣦⢣⢈⣿⣑⣬⣿⣿⢤⣀⠀⠣⠀⠀⠀⠀⠟⠀⢻⠿⣿⣿⠃⠀⡿⠃⡼⢧⡼⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⢿⣏⡇⡇⠉⡿⣷⣽⣆⢿⣽⣿⡿⢿⣿⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠐⠚⢋⡁⠀⠀⣧⠼⢿⠾⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢉⣧⡆⡇⢿⣿⡛⣿⠚⠋⠀⢚⢻⣿⡇⣠⠶⠀⢀⣀⠀⠀⢀⡤⠚⠉⣹⠂⢀⡇⠀⣀⠀⠀⠹⡍⠑⠒⠤⢄⣀⠀ ⠀⠀⠀⠀⢀⣞⢸⣇⠳⢾⣷⠿⣿⣷⡀⠲⠾⠾⠛⡻⠁⢰⠀⠀⣀⠤⠚⠁⢀⠤⠊⣠⠔⢻⣻⠆⡍⢳⣄⠀⠈⢦⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠉⠉⠛⠒⠞⢸⢳⣮⣽⣷⡀⠀⠀⡰⠁⢀⡼⠖⠉⠀⢀⡤⣚⡡⠒⠉⢀⣠⣾⣯⠈⠉⠀⠀⠀⢀⠦⣱⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛⠛⣿⣻⠶⠊⠥⠒⠉⠀⡀⠀⠴⠟⠋⠁⢀⣠⣴⠿⠛⢩⣽⡄⢀⠟⢦⡀⠺⠐⠛⠙⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⢈⣹⠀⠀⠀⠀⠤⠚⠀⠀⠀⠀⢠⡶⠟⠋⠀⣠⣶⣿⣿⣷⠐⠒⠊⠉⢀⡀⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⠁⡉⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⢿⣿⣿⣇⠀⠀⠀⣜⢉⣷⠄⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠈⡘⢙⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⢀⣠⣾⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡇⠛⠉⢸⠉⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠞⠡⠳⣄⠀⠃⢠⣦⣧⡀⠀⠀⠀⠈⠑⠢⣄⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⣌⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀ ⠀⣀⣴⣿⡿⠿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⣿⣿⠿⢿⣿⣦⣀⠀ ⣰⣿⠟⠁⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠈⠻⣿⣆ ⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿ ⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⠉⠉⣿⣿ ⣿⣿⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣿⣿ ⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⣄⣾⣿⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⣿⣿⣿⣿⡿ ⠈⠙⠛⢿⣿⣄⣀⣠⣿⡿⠛⠛⠛⠛⠛⠛⢿⣿⣄⣀⣠⣿⡿⠛⠋⠁ ⠀⠀⠀⠈⠛⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠙⢦⡀⠐⠀⠀⣽⢸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈⠲⡀⢳⡀⠀⠀⠿⠾⣀⣙⢦⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⠉⢁⠀⠈⠉⠑⠲⠄⠘⣆⠻⣆⢠⠾⠽⠶⠾⠟⢋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠔⠋⠀⠀⠀⢀⣀⣀⡀⠈⢧⠘⡯⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣀⡴⠋⠀⠀⠀⠀⣠⠖⠋⣁⣈⣓⣄⠘⠄⡇⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣠⣀⣀⣀⣀⣀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡴⠃⠀⠀⠀⠀⢀⡼⢃⡴⠋⠁⢀⣀⣉⣷⣄⠃⢀⣀⡀⠀⣄⠀⠈⣿⣗⠒⠛⠓⠒⠶⠾⣧⣤⣤⣀⣿⠋⠀⠀⠀⠀⠀⠀⣠⠁⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠋⠀⠀⠀⠀⠀⢠⡞⢠⣎⡤⣖⠽⠗⠋⠉⠉⠉⠉⠷⣭⣅⣀⡈⠙⢦⣘⣮⠳⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠶⠶⠶⠾⠧⣤⣴⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⡴⠀⠀⢀⡇⢀⠟⢰⣯⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⠉⠉⢙⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⣴⠃⢀⠀⢸⢀⡞⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣼⠟⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⡆⠀⠀⠀⠀⢀⡞⠀⡴⢁⡄⢸⠀⠃⣸⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⣤⠟⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡇⠀⠀⠀⡇⠀⠀⠀⠀⡞⢀⡞⢡⠞⠀⢸⠀⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⣾⣿⡄⠈⢧⠙⢦⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⠁⣸⠀⡇⠁⡀⠀⠀⠰⡳⢋⡶⠃⠀⠀⣸⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠥⠀⠀⠀⠙⣿⡟⡀⠸⡀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡼⠁⠀⡇⠀⡇⢀⣴⡿⠞⠁⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣿⣿⠟⢁⣀⣴⡶⠖⢛⣀⡗⣿⢇⠀⢧⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⢴⣤⠤⢣⠀⡟⢉⠀⠀⠀⠀⠀⠀⣇⣰⠟⡼⠀⠀⠀⠀⣀⡀⢀⡀⢳⡄⠀⠀⠀⣸⣟⡟⣰⣿⣻⢶⡀⠀⢸⡿⡇⣿⡸⡆⢸⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢷⣼⡀⣇⡟⠀⠀⢠⠀⠀⡀⢿⡇⠀⡷⣶⣶⣾⣿⣿⣿⣿⣿⡄⠯⢦⠀⠀⢫⠈⣰⠟⢸⠷⠾⠃⣠⠟⠁⢳⣇⠇⢱⠀⢳⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⣿⣽⠃⠀⠀⠸⡇⠀⡡⢸⢷⣸⠁⠀⠀⠈⠉⢩⣝⡋⠛⠇⠀⠀⠀⠀⠸⠀⠛⠀⠘⢻⣯⠟⠁⠀⠀⢸⡙⣶⡌⡆⠘⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⣇⣿⡇⠀⣸⢤⠀⢹⡀⡇⣼⣾⡟⠀⣀⣤⡶⠿⣿⣛⠛⠻⡶⠀⠀⠀⠀⠀⢰⡌⠉⠉⠉⠀⠀⠀⠀⠀⢸⣇⢳⣇⢱⡀⢷⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡾⠁⢻⠹⡟⠓⣧⢠⡳⣾⣿⣷⣿⣿⠁⢸⡅⠀⠀⣴⢿⣿⡇⢠⡆⠀⠀⠀⠀⢀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡘⡿⡈⣇⠸⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡃⣇⠸⡄⡇⠀⣿⡀⢹⣿⣿⣿⣿⣧⠀⠸⠿⠶⢤⣉⣻⡾⠗⠋⠀⠀⠀⠀⠀⠀⠙⠦⣼⠃⠀⠀⠀⠀⠀⠀⡼⠀⡇⢹⢧⠸⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡿⡇⢻⠀⣧⢸⡀⢿⢳⣌⢻⣎⠉⠻⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡏⠀⠀⠀⠀⠀⠀⠀⡇⣇⢹⡈⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⣇⢱⠈⡇⢹⡈⢇⢸⡆⠘⣷⣬⡉⠳⠈⢧⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣼⡇⢹⡈⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤ ⡈⣿⡸⡄⢻⠀⡇⢸⡀⢳⠀⢸⠙⢿⣶⣾⣿⣷⡀⠀⠈⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⣠⣿⡆⠀⠀⢠⡟⢸⠀⣷⣌⣀⣀⣀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⡖⠉⠀⠀ ⠁⢹⣧⣧⠘⡄⢹⠀⡇⠘⡄⠀⣇⢸⢿⣿⣟⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠤⢾⡫⣾⠀⠀⠀⡼⠀⡌⡇⠸⡆⠸⡇⠉⠉⠉⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢ ⡀⠀⠹⣜⡄⢿⠘⡇⢸⡀⢧⠀⢻⠀⣇⠻⢿⣿⣯⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣺⠽⠛⠁⠀⢀⣼⡃⠀⡇⢹⠀⢧⠀⢳⣰⣶⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠇⣄⠀⠙⣧⠈⡆⢳⠘⣇⢸⡆⢈⡇⢻⡀⠀⠉⠉⢛⣿⠿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠻⡅⢱⠀⢧⠀⡇⢸⣀⣼⣿⠯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠘⡆⣀⢈⢷⣳⣨⣤⡴⠾⢗⠚⡏⠉⡏⣗⠶⡶⢣⠀⡀⢸⠙⡏⢻⠿⣿⣿⣿⣿⡿⣷⣞⢻⢹⡄⢧⠀⣷⠈⣆⠘⡄⣸⡶⣿⣍⣉⣉⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣹⣄⣸⠹⣼⡶⢲⡞⡇⢹⡀⢸⣄⣹⣄⣳⣽⡆⢸⠘⡇⢳⡈⡆⢧⠈⡇⢸⠉⣇⠀⡄⠘⣿⣾⣿⣷⣸⡧⠼⣶⣹⡶⠟⠁⢰⣃⣀⡠⠤⠤⠝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠛⠛⠚⠧⢼⣶⠛⠋⠉⠀⠀⠀⠉⠙⠻⠷⣽⣤⣷⣗⣿⣷⣿⠾⠶⠿⠖⠓⠒⠛⠛⠋⠉⠀⢢⡀⠘⠿⣄⠀⠀⠀⠻⣤⡤⠤⠖⠒⠚⠳⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠤⠄⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⠖⢛⣻⣦⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢳⣤⠂⠈⠳⣆⠀⠀⠙⠳⢶⣶⣶⠶⠖⠒⠛⠳⣦⣄⠀⠀⠀⠀⣀⣀ ⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣭⡤⠌⢻⡆⠀⠀⠀⢳⠀⠀⠀⠀⠀⣼⣿⣀⣀⣴⠿⠓⠶⠖⠚⠉⠙⢢⡀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠖⢋⡇⠀⠀⣠⠎⠀⠀⠀⣀⡤⠶⡟⠋⠁⠉⠑⠶⢤⣀⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠉⢸⠁⠀⠜⠁⣠⠴⠞⡋⠉⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⡤⠞⠛⢉⠉⠉⢡⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⣉⡿⡷⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠰⠥⠛⣮⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠠⣄⣒⣒⣒⣂⣠⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣿⣿⣿⠿⣿⣿⣿⣿⣮⣒⢼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⢛⣒⠀⠈⠻⠿⢿⣿⣿⣦⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠈⠉⠀⠀⠀⠛⠂⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⢿⣿⡇⠀⠀⠀⠂⠀⠀⠂⠀⠐⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠓⠋⠭⠝⠀⠁⣸⣿⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⡀⠀⢀⠄⢼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠐⠀⠀⠀⢸⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠐⡩⠚⡜⢄⠀⠀⠀⠀⠀⢀⠃⣰⠤⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⢎⢋⠁⠐⠀⢧⣀⠑⠂⠠⠤⠐⢁⠴⢸⠀⠀⠁⠈⢳⠠⡀⠀⠀ ⠀⢠⠃⠀⠈⠎⠀⢰⠀⠈⣇⠁⠐⠒⠒⠀⠁⢸⡄⠀⣀⡀⣀⡘⠀⠐⡀⠀ ⠀⡄⠀⠀⠀⠈⡇⠂⠀⠀⠸⠀⠀⠀⠀⠀⠀⣸⢻⣀⢴⣄⣸⠕⠀⠀⢰⠀ ⢠⠁⠀⠀⠐⠄⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈⠈⠉⠁⢸⡤⡄⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⡄⠀⡀⠙⢣⣿⡿⠿⣿⣟⢿⡝⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠖⠋⠉⠳⣄⠀⠀⣺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣄⣸⣶⣿⣶⣶⣿⡏⢀⣿⣿⠂⠙⢤⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠀⢸⣶⣾⠁⢮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠳⠤⠤⣴⣿⣿⣟⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣿⣿⠋⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢺⡿⢿⣠⣿⣿⣿⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⡏⠀⢹⣿⣿⠀⢻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣄⣸⣿⣿⣿⣿⣿⡏⢿⣿⠀⠀⢿⣿⣿⠁⠀⠈⣿⠇⠀⠘⢿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⣿⡇⠬⢿⢤⣀⣈⣚⣿⠀⠀⠀⣏⣀⣠⠤⢼⠗⠒⠉⢿⢻⣿⣿⣿⣿⣿⣿⣶⠤⣀⡀⢀⣀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠿⣦⣈⣧⣤⣤⣤⣤⣌⠉⠛⠀⠀⠀⠉⠁⣀⣠⣤⣤⣤⣄⣸⡶⠻⣿⣻⣿⣿⡟⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢩⣧⡀⡇⠙⢦⡈⢿⣽⠿⠛⠃⢋⢷⣤⢾⠋⠙⠙⠿⣿⠟⣠⠞⠀⣼⣶⡯⡼⣿⢹⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⡇⢹⡏⣿⣿⠻⣆⠀⠈⠉⠉⠁⠀⠀⣼⣿⠉⢿⣆⠀⠀⠉⠉⠉⠀⢀⡴⠛⣿⣷⢣⠏⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠳⣿⣿⡄⠀⠉⠳⠗⠛⠒⠒⢈⠁⡼⠀⠀⠈⠁⠒⠒⠿⠟⠟⠁⠀⠀⡟⢫⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢮⣧⠀⠀⠀⠀⠀⠀⠀⠈⠷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠀⠀⣠⠴⠒⠒⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠘⢷⣠⣾⠇⠀⠀⠀⠀⢀⣴⢿⠇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢹⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⢦⡀⠀⠀⠀⣀⡴⠊⠁⠀⠀⣿⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠓⠒⠚⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⠀⠀⠀⡋⠓⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡿⣿⠋⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢭⡿⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠹⣽⣦⡈⠙⢳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣧⣠⠞⢰⠀⢻⠈⠑⠢⢤⣀⡀⠀⠀⠀ ⠀⠀⣀⡠⠔⠒⠉⠀⠉⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠉⠑⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⡈⠀⠀⠹⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⠄⠀⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⡈⢩⡿⣿⡷⣜⠃⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣤⠊⠁⠀⠀⠘⣹⣿⡳⠷⠽⣽⣇⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀ ⠀⠀⠀⡠⠋⣿⣆⠀⠀⠀⠀⢽⢿⡧⣔⠻⠸⣣⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀ ⠀⢀⠜⢀⠄⣿⡼⡄⠀⠀⠠⠄⢹⣷⣼⡀⠚⢻⣇⡀⠀⠀⠀⠀⠀⠈⢆⠀ ⠀⡌⠀⠎⠀⠸⣷⡷⠑⠆⠀⢼⣿⣿⣧⠈⡹⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠆ ⠸⠀⠀⠀⣀⠀⠘⣷⢤⠀⠀⠹⣿⣿⣦⣷⣷⣿⣫⣿⣿⠷⡂⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠈⠛⢗⣦⣴⣧⡀⢾⣿⣿⣿⣯⣵⡿⢽⣿⣷⣦⣱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⡀⢸⣿⣿⢿⣳⣾⢿⣿⣿⣿⣿⣾⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⡿⠿⣿⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣽⣹⡇⢻⣿⣿⣿⣿⣿⣷⣽⣾⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⢿⣿⠿⡿⡇⣸⣿⣿⣿⣿⣿⡕⠻⢻⠘⡄⠀⠀ ⠀⠀⠘⢏⣉⣩⠴⡶⢶⡧⡿⡛⠲⠤⢼⣿⣿⣿⣿⣿⣿⠇⢀⣾⢀⠕⠀⠀ ⠀⠀⠀⠀⠙⢾⣥⣴⣢⣦⣴⣴⣶⡖⢾⣿⣿⣿⣿⣿⣿⣦⣴⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡴⠖⠋⣡⢶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣠⠞⠁⠀⠛⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⡤⠶⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠉⠳⣄⡴⠞⠋⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠴⠟⠃⣀⣘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣠⠆⢀⣀⣠⠤⠚⠁⠀⢀⡴⠒⠦⣀⠀⠀⡠⢄⡀⠀⣌⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⣴⣿⠏⠀⠀⠀⢀⡴⣋⠀⠀⠀⠘⢦⡀⠂⠀⠁⠒⢨⡑⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⡀⢀⡤⠞⠉⣠⠴⠋⠉⠁⠀⠀⢀⡴⣫⣾⠟⢦⡀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠹⣌⠳⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡴⢺⠷⠋⠀⢰⠞⠁⠀⠀⣀⡤⢤⡴⣪⣾⣿⡇⠘⢷⡱⣄⠀⠀⠀⠸⣄⠀⠀⠀⠀⠈⠁⠹⣆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢰⠋⠀⠀⠀⠀⣠⠏⢀⣠⠶⣛⣁⣤⣤⠀⣽⣿⣿⡄⠀⡄⠻⣮⢆⠀⠀⠀⠹⣇⠀⠀⠀⢧⡀⠀⠘⢦⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠈⢀⡴⠀⢀⡼⠁⣰⣿⠗⠺⠉⣥⡀⢈⣻⣿⣿⢿⣿⣷⣷⡄⠘⣿⢧⠀⠀⠀⢿⣧⠀⠀⠀⠳⡀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡰⡿⠀⢀⡞⠀⣰⠃⡿⠀⠀⠀⣨⡶⣿⡿⠋⠀⠀⠀⠈⠻⣿⣦⢹⣟⣧⠀⠀⢸⣿⢧⡀⠀⠀⠁⠀⠀⠈⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠞⢱⠁⢀⡞⠀⢰⠇⢸⠃⠀⣠⣾⣫⣾⣿⠀⠀⠀⠀⠀⠀⠑⢮⣿⣿⣿⡌⢧⠀⢸⣿⣯⣷⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡏⠀⢸⠀⢸⠁⢠⡏⠀⣸⣦⣾⠟⢟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡈⣧⢸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⡿⢀⡟⠀⣴⣿⣿⣿⣤⢾⣧⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠸⣼⣿⣏⢿⣿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠖⢛⡳⣿⣠⡾⣿⡿⣿⠁⣄⢀⣠⣬⣉⡙⠛⠿⣿⡷⠄⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡞⣿⣷⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣴⣿⣿⣿⣿⠇⣿⣧⣿⣶⣾⣿⣿⣶⣶⣝⡻⣯⣍⣂⠀⠀⠀⠀⠀⠀⣠⣾⣿⢛⣟⣿⣷⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢹⡟⠉⠀⣿⡿⠀⠻⣿⠋⠙⢿⣿⣿⣿⣶⡿⠃⠀⠀⠀⠀⢠⡾⠛⠟⢁⣀⣀⣻⣿⡆⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⠁⠀⢰⣿⠇⣠⠄⠙⠷⣤⣘⣻⢟⣁⡿⠀⠀⠀⠀⠀⢰⡿⠃⣤⣾⣿⣿⣿⣿⣿⣷⡈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⡇⠀⢸⡇⠘⠁⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⢿⠦⢾⣁⠸⠿⠿⠛⣳⡿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⡖⠚⠉⢨⣾⡇⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣍⣉⣓⣛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠆⡀⠀⠀⠀⠐⡀⠀⠀⠀⠘⢿⣶⣤⣤⣶⣦⠀⠀⠀⠀⠀⢸⣯⣿⡏⠉⠉⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢨⣷⠀⢻⠀⠀⠀⣼⣧⣀⣀⣀⣀⣀⠙⠻⠿⠋⠀⣤⡀⠀⠀⠀⢸⣹⣿⣷⢠⣼⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢸⣿⡀⠀⡄⠀⠀⠀⠘⢻⣟⠛⠛⠿⠿⠾⣿⣶⡶⠚⠙⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣽⣧⠀⢷⡀⠀⠀⠀⠀⠻⣷⣶⣤⣄⣴⡿⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⣟⢷⣄⠻⣆⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⣠⡾⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⣿⣿⡀⠻⢦⣈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣿⣿⣿⣿⡇⠸⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢷⣾⣿⠇⠀⠉⠙⠳⣌⡛⢦⡀⠀⠀⠀⠀⠀⣿⣟⡁⠀⠀⠀⠀⣿⣿⣿⣿⠿⢿⡶⠿⠿⠿⣿⣿⣾⣻⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠿⣟⣿⠀⠀⠀⠀⠀⠀⠙⠒⠒⠶⠭⠗⠒⠚⣿⣇⠙⢦⡀⠀⠀⣿⣿⢿⣷⡀⠈⠁⠀⠀⠀⠀⠉⠉⠛⢿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣴⠋⠀⢻⣾⠆⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⢦⡀⠙⠦⣤⣿⣧⣮⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⡞⣿⠀⠀⠸⣿⡄⢀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⣦⡀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⡾⠀⠙⢦⣀⠀⢹⣇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣶⣯⡉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣟⠀⡀⠀⠛⣆ ⢀⠀⠀⢀⣀⠀⣠⡞⠁⠀⢀⡞⠀⠀⠀⠀⠈⠙⠓⠙⠷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⢙⣷⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⢀⠀⠈⠙⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠛⠋⠉⠙⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠞⠛⠋⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⢠⣤⠶⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⣀⣀⣤⣤⠶⠶⠛⠀ ⢸⡇⢰⣶⣦⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠶⠛⠛⠙⠟⠛⢉⡉⣿⠀⠀⠀⠀⠀ ⠸⣇⠈⢛⣁⣠⣤⡴⠶⠞⠛⠋⢹⡷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠿⠀⠀⠀⠀⠀ ⠀⠙⠛⢻⡏⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀ ⣴⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠿⠶⠶⠶⣦⠀ ⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⣀⣤⣾⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⣈⢶⡄⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⠉⠉⠛⠛⠉⣿⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀ ⠸⣿⡿⠟⠋⡟⢛⣿⣿⣿⣿⣧⡐⠒⠒⢀⣾⣿⠀⠀⣠⣀⠀⢸⣿⡿⠀⠀ ⠀⠀⠀⢀⣀⣲⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣧⡀⠀⠙⢷⣿⣿⡇⠀⠀ ⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣹⣿⣿⠀⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⢀⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠀⠀⠈⢐⠀⠀ ⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠀⢬⣿⣿⣿⣿⡿⠘⠋⠛⠋⠋⠛⠙⠋⠙⠉⠋⠉⠙⠑⠿⠫⠻⣄⠀⠀⠘⢦⠀ ⠰⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡀⢀⡠⣀⠀⣀⡆⢀⠄⠀⠀⠀⢻⠀⠀⠀⡎⠀ ⠀⠹⣿⣿⣿⡏⠀⠀⠀⢀⡝⠆⢧⢹⣇⣠⡏⣿⢣⣿⣦⠀⠀⠀⠹⣇⠀⢀⡏⠀ ⠐⢾⣿⣿⣿⠀⠀⠀⠀⢾⡇⣼⣸⣾⣿⣿⣿⡹⢸⣻⡭⢄⠀⠀⣌⣿⣦⣾⡇⠀ ⠀⠒⣿⣿⡏⠀⠀⠒⣉⠳⠌⠣⣷⣿⣹⣿⡿⣓⡡⢈⡠⠞⠓⠄⠸⣿⣿⡿⠁⠀ ⢄⢰⣧⡹⡇⠀⣴⣯⣿⣷⣤⡀⠈⠉⣸⢹⡈⠁⠀⣠⣴⣿⣷⣦⠀⣸⠟⡝⡄⠀ ⠀⢹⠈⢵⣿⢢⠘⠻⣢⣭⣯⢭⢿⠟⢇⢠⢻⣾⣭⣭⣿⣵⠾⠋⣠⣏⡮⡢⡀⠀ ⠁⠢⣇⠎⠛⣇⠁⠀⠀⠙⠫⠐⢩⠃⢨⡼⠀⠑⠌⠉⠀⠀⠠⠚⡽⠟⣦⡱⠀⠀ ⠀⠀⠀⠙⠪⢼⡧⡀⠀⠀⠀⠀⢇⠀⢺⡃⠀⠀⠀⠀⠀⠀⣠⢊⠖⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠈⠐⠠⢀⠀⠢⡼⢽⢄⣀⡤⢄⠶⡊⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠠ ⣿⣿⣶⣶⣄⣀⡀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣤⣤⣤⣤⣀⠙⠛

⠀⠀⠀⠀⠀⠐⣲⠒⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⢂⢔⠏⡠⠠⠀⡏⡀⠂⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⢦⣇⣿⣲⣯⣄⡋⢃⣇⣸⡁⠃⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⠏⠉⠉⣇⠈⢻⠉⣀⡇⡄⠀⠀⠀⠀⠀⠀ ⠹⣅⠝⠋⠀⠀⠀⠉⢤⡏⠍⠀⠝⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡶⠂⠀⠀⠀⢀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠡⠀⡤⠐⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⠔⠐⠤⣀⡦⣤⣀⠀⠀ ⠀⠀⠀⠀⠤⠐⠃⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠑⢧⡀ ⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⠃

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣝⣎⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⣸⣿⣿⣍⢿⣹⡇⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⡇⠀⠛⠿⠿⠛⢷⡆⠙⢿⠛⠉⢺⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣇⠀⠀⠀⠀⠤⣸⡃⢠⡀⠀⠀⢠⣿⡎⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠈⠛⠏⠋⠀⢀⠀⢾⣿⣯⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣻⠻⢿⣿⣧⠀⠀⠲⢿⣿⣩⡍⠒⠀⣠⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠈⠉⠙⡦⢅⣀⣀⣀⣀⠤⠊⢛⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⢇⠀⣿⠟⢡⠋⠀⠀⠀⠑⢂⣥⢦⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡀⠀⣼⠀⢺⠀⠁⠀⠀⣁⣤⣶⣿⣶⣿⣿⣾⣅⠢⡀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⡄⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠘⢄ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣇⠀⠈ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣿⣿⡄⢠ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣄⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡤⢤⣄⣀⡀⠀⠀⠀⠀⠘⢷⣄⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣉⠉⠛⠲⢤⣀⡀⠀⠙⢦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠈⠙⠦⣄⠀⠹⣦⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠉⠙⠒⠒⠶⠶⠶⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠀⠈⠑⢤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⢤⣾⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⠳⣄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢿⠈⠉⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠘⣆⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢹⡆⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⢤⣀⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⢻⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣭⣑⠦⣄⡀⠀⢀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠙⢤⡀⠀⠘⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣳⣄⡉⠓⠢⠖⠢⠤⠤⣄⠀⠀⠈⠓⠊⣙⣷⣾⠃⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⣄⠀⠙⢦⡀⢹⣆⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡾⠿⠀⠀⣀⣠⠤⠴⣾⡷⠦⣤⠴⠞⢋⡵⠋⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣟⣄⠀⠀⠉⠃⠹⣦⠀⠀⠀⠀⠀⠈⠛⠒⠦⠤⣤⣤⣤⣤⣤⣤⣤⢴⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣮⢦⡀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠁⠀⣰⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠄⠈⠳⢦⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢧⣳⡀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⢀⣠⠞⠛⠲⢤⡀⠀⠀⠹⣆⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣝⣆⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⡀⠀⠀⠀⠀⠀⠀⣇⠀⣒⣒⠚⢉⡩⠭⠴⠶⠀⠀⠀⠈⠙⠲⣶⣶⣞⠉⠀⠀⠀⠀⠀⠈⠳⢦⡀⠘⢦⡀⠀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣮⡣⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠦⠤⡟⠀⠀⠉⢫⠉⠀⠀⠀⢠⡔⠋⠙⠢⠀⠀⠉⠘⡍⠙⢦⣄⠀⠀⠀⠀⠀⠀⠙⠢⣄⠻⡄⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⢭⣇⡀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠘⣷⡒⠺⢷⣒⣦⣄⣘⣧⣀⣀⣴⣻⠿⡟⠛⠓⠀⣠⠀⣰⠷⣄⡀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠈⢷⡝⣦⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢝⢦⡀⢈⡗⢻⡟⠉⢱⠀⠙⢯⠉⠁⠀⠀⣰⠁⢰⡇⠀⠉⢿⡷⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠙⢮⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢾⡄⠀⣇⠀⠀⣷⡦⣀⠙⠦⠀⢰⠃⠀⠸⢣⠀⠀⠀⠙⢦⡳⢄⠘⢦⡀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⣀⠀⠀⠀⠀⢱⡀⠟⣦⣖⣿⣥⣾⣷⣄⡀⠸⠀⠀⠀⣸⠀⡀⠀⠀⠈⠻⡄⠀⠈⠳⣄⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣤⣿⣟⢛⣻⣽⣯⣽⣿⣿⣿⠀⠀⣤⠞⠁⢸⠇⠀⠀⠀⠀⠻⣷⣄⠀⠈⢳⡀⠀⠀⠀⣼⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠉⢹⣿⣿⣶⡿⠿⠛⠋⠁⣠⠞⠁⠀⠀⣼⠀⢰⡀⠀⠀⠀⠸⣌⠳⣄⠈⢳⡀⠀⢀⡏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠰⣽⡄⠚⠛⠛⠀⢀⡴⠻⠀⠀⠀⢠⠇⠀⠀⢣⠀⠀⠀⠀⣻⣤⣬⣢⡀⠳⣄⣸⠁⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣏⣀⣀⣂⣀⣤⠟⠁⠀⠀⠀⠀⡼⠀⠀⠀⠈⠷⣠⢴⡋⠁⠀⠀⠈⠙⠲⢾⣿⠀⢸⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⣻⡁⡏⠀⠀⠀⠀⡀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠁⠀⠙⢦⡀⠀⠀⠀⠀⢠⡇⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠛⠁⢻⠇⠀⠀⠀⣸⠃⠀⣰⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢱⡄⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣁⣤⣤⠤⠴⣦⣤⣤⠞⠁⠀⣴⣥⡤⠤⠖⠓⠒⠲⠤⠤⣤⣄⣀⠀⢣⡴⠋⠁⢸⠀⠀⠀⠀⠀⠂⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠉⢳⠖⠩⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠃⠀⠀⠀⣸⠀⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠘⢓⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢳⡀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡔⣫⠎⢦⡀⠈⣆⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⠒⠋⠁⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠽⠽⢛⠑⡋⠀⠀⠀⠙⣦⡈⡆⠀⠀⠀⠁

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⡄⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀ ⡒⠒⠒⠒⠒⠒⠒⡏⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠈⡗⠒⠒⠒⠒⠒⠒ ⣷⣄⡀⠀⠀⠀⠀⣇⠀⢸⡏⣰⣷⢾⡀⠀⣧⠀⣶⣶⣼⠀⣾⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⠟⠛⠒⠒⠀⡿⠀⢸⣿⢼⣿⣘⣷⣄⢿⣷⣾⣿⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠉⠁⠀⠀⠀⠀⠀⣷⠀⢸⡧⣼⣷⣦⠈⠙⢻⢿⣿⢯⢻⠀⣿⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⠑⠚⠛⠀⠀⠀⠀⠚⠛⠂⢸⠀⣿⠀⠀⠀⠀⠀⠀⢻ ⣀⡀⠀⠀⠀⠀⠀⢸⢸⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡟⠀⠀⠀⠀⠀⠀⢩ ⠙⢿⣿⣷⣾⣿⣿⣿⢸⡆⣧⡀⠀⠀⠠⠤⠀⠀⢀⣴⡇⡀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⡀⡇⣿⣿⠢⢄⠀⠀⢀⠴⢻⡋⡇⡟⡀⠠⠤⠤⣀⢀⠤⠐ ⠀⠸⣿⣿⣿⣿⣿⣿⣇⢷⣟⠛⡄⠀⠉⠉⠁⠀⡌⡻⣇⣿⣾⡏⢠⣴⠈⢟⣦⣤ ⡀⡇⣸⣿⣿⣿⣿⣿⢻⣸⡇⠑⢇⣀⠀⢀⠠⠐⠉⢁⣿⡿⠛⢧⣼⣷⣶⣾⣿⣿ ⡽⠔⠚⣻⣿⣿⠿⠃⠸⢃⣧⠀⠀⣜⣹⣉⣣⠀⠀⢸⣿⠇⠀⠈⠻⣿⡻⠿⣿⣿ ⣰⣴⣿⠿⠋⠁⠀⠀⠀⢿⡼⣄⠼⣿⣿⣿⣿⣷⣀⣿⣿⠀⠀⠀⠀⠈⢻⣦⡀⠈ ⢔⣿⣷⣷⣶⡂⢤⡀⢀⣨⣿⣿⡢⢿⣿⣿⡿⢞⣽⣿⢼⢷⣄⠠⢖⣿⣿⣿⣵⣄ ⠀⠉⢹⣿⠛⣿⣿⡻⠝⠉⡗⠌⠺⣸⣿⣿⡏⠘⠋⠀⢸⢠⣶⣿⣿⣿⣿⠟⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠄ ⠀⠙⢿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠟⠋⠉⠀⣠⣦⠖⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠴⠃ ⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠟⠋⠁⠀⠀⣰⢏⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⡾⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⢀⣠ ⣀⣴⣾⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠢⡀⣧⠀⠀⠀⠀⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠀⠀⠀⠘⠛⣻ ⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡼⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠃⠀⡇⢸⠀⠀⠀⠀⣿⣿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⢷ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡇⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⣼⠀⡇⣿⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠙⣿⣦⣤⡤⠶⠶⠿⠛ ⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⣴⣿⣿⡋⠀⠀⠀⣿⠀⣿⠃⠀⠀⠀⢠⣿⣿⡇⠙⢿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠈⣿⣿⣆⠀⠀⠀⠀⠀ ⠛⢿⣿⣭⣭⣿⠄⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⢀⡾⣫⣿⣿⡇⠀⠀⠀⣿⢠⡇⠀⠀⠀⠀⣸⡟⣾⠁⠀⠀⠈⠻⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⢿⣿⡇⠀⠙⢿⣿⣷⣶⣶⣶⣿ ⡿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⣠⠏⣴⠏⢹⣿⡇⠀⠀⢰⣿⣼⠇⠀⠀⠀⢠⡿⣵⡏⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣸⣿⡇⠀⠀⢠⣌⠉⠉⣹⣿⣿ ⡀⠀⣠⣶⠖⠀⠀⣤⠀⠀⠀⠀⠀⢸⡀⠹⣏⣶⠃⠀⢸⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⣡⡿⢡⡟⠀⠀⠀⠀⠀⠀⢀⣠⠤⠋⣙⣛⡿⠿⢿⣿⣿⡿⣿⣿⡇⠀⢠⣿⣿⢀⣾⣿⣿⠃ ⢻⣿⣿⠁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠘⢧⣠⠾⠁⠀⠀⣾⣿⡇⠀⠀⢸⣿⣿⠀⢀⣴⡿⣥⡏⠀⠀⠀⠀⠀⢀⡴⠋⢠⡴⠋⠉⠀⠀⠀⠀⠈⠉⣱⣿⣿⠁⢠⣿⣿⣣⣾⣿⡿⠃⠀ ⣾⡿⠁⠀⠀⢠⣿⡇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣤⣾⢟⡵⠋⠀⠀⠀⠀⢀⣴⠏⢀⡴⣫⠴⠞⠋⠉⠉⠳⣆⠀⣰⢏⣾⠇⣠⣿⣿⣿⣿⣿⡿⠁⠀⣠ ⡿⠁⠀⠀⠀⣾⣿⡇⠀⣠⠞⡥⣿⢹⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣼⠏⣰⠏⣴⢃⣀⣀⠀⠀⣀⡴⠛⣰⣿⣿⣏⣼⣿⣏⣼⣿⣿⠟⠁⠀⣰⣿ ⠃⠀⠀⠀⠀⣿⢿⡇⣰⢏⡞⠁⡇⢸⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠈⠻⣿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣸⠏⠀⣿⠀⠀⣘⡴⠛⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⠃ ⠀⠀⠀⠀⢠⣿⣸⣧⡏⣸⠃⠀⡇⢸⠀⠀⢀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠙⠷⠞⠉⠀⠀⠀⣼⣿⣿⡟⠀⣭⣿⣿⣿⠟⠁⠀⢰⣿⣿⡿⠀ ⠀⠀⠀⠀⢸⡟⣿⡟⢠⡟⠀⠀⡇⢸⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⣷⣿⣿⣿⠟⠁⠀⢀⣤⣿⣿⣿⢃⣴ ⠀⠀⠀⠀⢸⣿⢹⡇⣼⠃⠀⠀⣿⣾⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣥⣴⣶⣾⣿⣿⣿⠟⢡⣾⣿ ⠀⠀⠀⢩⣿⣿⣘⣿⠇⠀⢺⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠿⠛⠛⠉⣿⣿⣀⣿⣿⡿ ⠀⠀⠀⣼⣿⡏⠛⠋⠀⠀⣼⣿⠟⣹⣿⣇⣀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠁ ⠀⣠⣾⣿⡿⠀⠀⠀⠀⢰⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶ ⣿⣿⣿⠟⠁⠀⠀⠀⢠⣿⡟⠀⣾⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⣛⠷⣦⠄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠻⢿⣿ ⡿⠋⠁⠀⠀⠀⠀⣠⣿⣿⠁⢀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⠇⠉⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⢠⣾⣿ ⣿⣷⣦⣤⣤⣴⣾⣿⡿⠁⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⠻ ⠛⠿⠿⠿⢿⣿⣿⡿⠁⠀⣼⣿⣿⠈⢿⣿⣿⣧⠀⠀⣀⣶⣿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏⠻⣿⣿⣷ ⠀⠀⠀⣠⣿⣿⡟⠀⣠⣾⣿⡟⠁⢀⣨⣿⣿⣿⣆⣴⣿⡿⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⢹⣿⣿ ⠀⢀⣼⣿⣿⠏⠀⣨⣿⡟⠿⣽⣟⣯⠞⠹⣿⣿⣿⣿⠏⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⠀⠀⣠⡟⣿⣿ ⣰⣿⣿⣿⠃⢀⣾⣿⡟⠁⠀⠀⠀⠀⣀⣴⣿⣿⡿⠁⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣣⡟⠀⣠⡾⢃⡿⠛⣿ ⣿⣿⠟⠁⢀⣾⣿⡿⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⣿⣿⣯⣀⣼⠋⣵⠟⠁⠀⣿ ⡿⠉⠀⠀⣾⣿⣿⡇⠀⢀⣴⣿⣿⡿⠟⠉⠀⣠⣶⣿⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⢋⣼⡿⣡⡾⠃⠀⠀⠀⣿ ⠀⠀⠀⠀⠙⠹⣿⣷⣾⣿⣿⠟⠉⢀⣤⣶⣿⣿⡿⠋⠙⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⢀⣽⣿⣿⣿⠟⣡⣾⣻⡿⠋⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⣀⣤⣤⣝⠛⠋⠉⠀⢀⣴⣿⡿⠟⣿⣿⠃⠀⠀⠀⠙⢿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣟⣱⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣿ ⠀⢠⣾⣿⡿⢋⣿⣇⠀⠀⣴⣿⠟⠁⠀⣼⣿⡇⠀⠀⠀⠀⢀⣼⡟⠉⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿ ⣦⣿⣿⣿⣿⣿⣿⣿⣠⣾⡟⠃⠀⠀⢠⣿⡿⠀⢈⡏⠘⢒⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡛⠛⠛⠛⠛⠋⠉⠙⠛⡟⢻⠉⠉⠉⢀⣼⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿

⠀⡰⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⢣⠠⣄⣌⠑⣄⢷⡈⡁ ⢈⣠⣒⣁⡴⠀⠀⡜⠀⠀⠦⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢳⡈⢻⣿⣮⣿⣿⣶ ⠝⠸⠀⡠⠁⠀⡼⠀⠀⣸⠀⠘⡒⠤⣁⠂⢦⣘⡀⠀⠀⠀⠆⢷⣆⠹⣿⣿⣿⣿ ⢣⠃⡐⠁⣠⣾⠃⡔⣰⠃⠀⠐⠰⠀⠀⠁⠢⣌⢣⠀⠀⠀⣸⢸⣿⣷⣿⣿⣿⣿ ⣾⣼⠴⠚⢩⣂⢼⣶⢋⠀⠀⠀⢃⡆⢀⡴⠊⣁⣹⣤⠀⠀⣿⣾⣿⡿⠛⡻⢿⣿ ⣿⠘⡀⠐⡏⠀⢠⠹⠈⡀⠀⢠⠸⡷⣫⣾⡟⢋⣰⡿⢸⠀⣿⣿⠻⣷⠩⠘⡈⣿ ⣿⢀⠀⠀⣧⠀⡌⠀⠡⠇⠀⠘⣾⠁⠏⠓⠊⠉⠀⡇⢾⣼⣿⣿⠀⢹⡝⡠⣷⣿ ⢿⣿⡆⠀⢇⡦⣗⣶⡶⣿⢀⠇⠸⠀⠀⠀⠀⠀⠀⠏⢸⣿⡏⡏⠀⠀⡋⣰⣿⡇ ⡆⠹⣿⡀⢼⣾⣍⣳⠓⠁⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⢼⡽⣿⣿⣿ ⠉⠀⠹⣷⡀⢻⣍⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢬⣏⠛ ⠀⠀⢰⡟⢿⢪⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠉⠑⢴⠁⠀ ⠀⠠⠋⠀⠘⣏⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡇⠀⠀⠀⠰⠱⣦ ⠀⠀⠀⠀⠀⠘⠐⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠃⠀⢀⠠⠒⠃⢻ ⡀⠀⠀⢀⠀⠀⠇⠹⣹⣿⣿⠈⠒⠄⡀⠀⠀⣠⠔⠁⠀⠀⠀⡠⠐⠁⠀⠀⠘⠀ ⠇⠞⠳⠛⠛⠂⠈⠂⢩⣿⣿⡆⠀⠀⠈⠁⢁⠨⣷⠄⢀⠄⠊⠀⠀⠀⠀⠀⠀⠂

⣿⣿⣿⣿⣿⣿⡏⢛⣿⣿⡟⠉⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⢛⡳⠤⠴⡺⠿⡛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⢠⠁⠀⢀⠠⢁⡠⠃⡀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣶⡟⡃⢖⠋⠁⠉⣀⣀⡠⠈⠑⠂⢇⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣷⣶⡎⠀⠁⠀⣀⠠⠐⠒⡢⠀⠘⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡙⠒⠩⠿⠘⢄⠀⢐⣁⠜⠀⢠⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢄⠀⠀⠀⠀⠉⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⠑⢄⠀⠀⠀⢶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡿ ⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠐⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⣽⡟⠄ ⣿⣿⣿⣿⣿⠋⠰⡀⠀⠤⠀⠀⠀⠀⠸⢀⠔⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⠃⠀ ⣿⣿⣿⣿⣧⠇⡄⠈⣢⣀⣀⠀⣀⣀⢴⡎⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⡆⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠿⠿⠿⢿⣛⡉⠉⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠟⠻⣟⠶⢤⣀⡀⠀⠀⠀⠈⠱⢦⡀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠈⠳⢦⣍⡳⣄⠈⢉⣳⣦⣄⡀⢀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠛⠛⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⣩⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⠓⢲⣶⠦⠤⣤⣀⣀⠀⠀⠈⠙⠲⣤⣼⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠛⣇⣏⣽⣠⣎⣽⢀⡴⢻⠋⢉⣿⡶⠤⣤⠀⠈⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⢀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⣈⣉⣁⣘⠉⠻⠿⠶⢿⣴⢋⣼⣇⡤⣿⢀⣠⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⣠⠴⠚⠉⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⣀⠴⠶⠒⠒⠶⢬⡙⠢⠀⠀⠀⢹⠃⠼⣯⣴⡿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⠖⠋⠀⠀⢀⣾⠏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣠⢞⠕⠋⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠘⢀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢰⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣵⣃⣤⣤⣄⣀⠀⠀⠀⠀⢀⡾⢁⠀⢀⢀⣴⡿⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢠⠀⢸⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠉⠉⠉⠒⢦⣾⣶⣞⣠⣶⡿⠋⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀ ⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠸⡄⢸⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯⢽⣦⠀⠀⠀⠀⠀⠀⠀⠈⡏⣾⠭⣿⡏⠀⠀⠀⠀⠀⠀⢸⡿⣧⠀⠀⠀⠀ ⢰⡟⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢀⣧⠀⢧⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⢽⡴⡆⠀⠀⠀⠀⠀⠀⢿⢳⣾⣿⠁⠀⠀⠀⠀⠀⠀⢸⡇⢿⡄⠀⠀⠀ ⠘⠿⠟⠛⠋⠉⠉⠛⠿⣶⣄⢀⣸⡟⠀⠀⠀⠀⠀⣞⢧⠈⠣⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⠦⢷⣴⣶⠀⠀⠀⠀⣷⣯⣼⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⠃⠀⠀⠀⠀⠀⠈⠳⣕⢦⣈⠓⢿⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣞⣤⠿⢻⡴⣦⣠⣇⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢠⣤⡶⠞⠛⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣾⣖⣋⣽⣩⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣬⣿⠿⠿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⡾⠟⠋⢀⡀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⣠⣿⡇⢀⢾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⡷⣦⣄⡀⢠⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⡟⠀⢠⠏⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣰⠋⢧⡄⠈⠉⠻⢿⣇⠀⠀⠀⠀⠀⠀⠙⢷⣤⢸⣇⡴⠁⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠳⢦⣄⡀⠉⠛⠶⣦⣄⡀⠀⠀⠀⠙⢿⣅⠀⠀⣼⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⠭⠿⠷⢦⣄⡀⠈⠻⣦⣰⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣝⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠻⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⣠⡾⢿⣦⡀⠀⠀⠀⠀⠀⠙⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣀⣴⡶⠟⠋⠉⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢖⣺⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣥⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡛⠛⠻⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠞⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡇⢻⣿⡻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⣿⣿⣿⢿⠣⢼⣿⣶⣾⣿⣏⠂⠤⠀⠀⠀⠀⠀ ⢸⡸⢿⣿⣿⣿⣿⣿⣯⣫⣇⣤⠛⠋⠈⢢⣶⣾⣿⣿⣿⣿⡿⣀⠀⠀⠀⠀⠀⠀ ⠉⠃⠉⠉⠙⠻⣿⣿⣗⠝⠿⠖⠀⠀⠀⠘⠛⠋⢻⣿⣿⣿⠃⠠⠥⢤⠀⡒⠂⠠ ⠀⠀⠤⠤⠄⠤⠬⣻⣧⣑⠂⠀⠀⢀⠄⠀⠀⡀⣜⠿⠋⢁⡡⠖⡠⠛⣾⠹⠥⠄ ⠂⠂⠀⠂⠉⠉⠁⠀⠊⠙⢿⣿⣷⡾⠿⠿⢿⣿⡳⣤⣧⣫⠀⣈⣠⠞⣿⠀⠀⣄ ⠀⠀⠀⠀⢀⣤⠒⠔⣒⠘⠍⢘⡩⠋⠉⢛⠍⠀⠀⠀⠒⠙⠒⠼⣸⡠⠟⠀⠀⠉ ⠳⠶⣦⣂⠁⠀⠐⠁⠀⡠⠺⠉⠀⡐⠈⢁⣉⠀⠒⠀⠀⡤⠔⠚⠉⠉⠍⡑⡀⠀ ⠀⠀⠀⠉⠙⠲⢤⣦⡁⠸⡠⢴⠞⠛⣻⠯⣍⡙⠓⠶⢬⣀⡀⠀⢀⡀⠢⡈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠃⠀⠈⠁⠋⠾⡤⣙⡛⠳⣶⠎⢿⣧⣤⣹⡷⢜⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣷⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣀⠉⣹⡗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏⠀⢀⡤⠒⠒⠒⠦⣄⠀⣠⡾⠋⠉⠛⠻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⣿⣿⣆⢠⡟⠀⠀⢠⢠⠞⠽⣿⡁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣾⣿⣦⣄⣇⣇⣤⣾⣿⡇⠀⠀⠀⠐⣤⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠜⡟⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣠⠖⠁⡀⢀⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠀⣠⣾⣿⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠘⣿⣿⣿⣿⣿⣿⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⢾⠏⢀⣾⣿⡿⠿⣿⣿⣿⣿⣿⠋⣿⣧⣤⣾⣥⣤⣝⣿⣿⣹⠓⣏⠀⠀⠙⢆⠀⠀⠀⠀ ⠀⢀⡞⢁⡟⣰⣿⣿⣥⠤⢔⣛⣻⠿⣏⣱⣿⠟⠉⠉⠁⠀⠈⣿⣾⣿⣿⣀⠈⡟⠦⢀⡼⠀⠀⠀⠀ ⢀⡎⠀⢸⣿⣿⣟⡭⠶⠛⠛⠛⢻⣿⠋⠉⣿⠀⢰⡾⠛⠛⠂⣿⣿⣿⢅⠉⠙⠿⢴⣿⠀⠀⠀⠀⠀ ⣼⡆⠀⢸⣿⣿⣟⡇⣴⠶⠶⠶⠆⣿⠀⠀⠹⣧⣈⣁⣀⣤⡾⠟⣻⠃⠀⠙⠒⢢⠞⠙⡇⠀⠀⠀⠀ ⡿⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠀⣰⡟⠀⠀⠀⠈⠉⣩⠟⠉⢀⡔⠁⠀⠀⠀⢀⡎⠀⠀⣿⡀⠀⠀⠀ ⡇⠀⠀⢸⣿⣿⣿⣿⡻⠶⠶⠟⠉⣀⡤⠤⠴⢦⡾⠁⠀⠀⢮⠀⠀⠀⠀⠀⣸⠀⢠⠀⡇⠈⠢⡀⠀ ⣇⠀⡄⠘⣿⢿⣿⣽⣻⡆⠐⠀⠘⣧⡴⠒⠋⡟⠁⠀⢀⣤⠚⠳⢤⣤⣤⣾⡇⠀⣿⣼⣷⣶⣤⡹⡄ ⢹⡆⣧⠀⠀⠈⢻⣿⣿⣷⣄⠀⠀⠈⠉⠉⡿⠀⢀⡴⠋⡼⠀⠀⠀⠻⡿⠻⠁⢠⣿⣿⡟⢉⣿⣿⡇ ⠀⠳⣿⡄⠀⠀⠀⠻⣿⣿⠏⠳⣦⣤⣤⣴⣧⣾⣿⡇⠀⡇⠀⠀⠀⢠⡇⢀⡴⠛⢮⣻⣷⣿⡟⣹⠁ ⠀⠀⠈⠻⣆⢧⠀⠀⢨⡏⢀⡞⢁⣠⠔⠋⠁⣀⣀⡏⠉⡇⠀⠀⢠⡿⠛⠁⠙⢄⠀⠙⠯⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠙⠓⠦⢤⣧⣾⠴⠋⣁⠄⠚⠉⠀⠀⠹⡀⢹⣦⣀⣸⠁⠀⠀⠀⠀⠑⠦⣤⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡇⡠⢊⣷⠒⠋⠉⠉⠹⡖⠻⣶⡟⠛⠻⡆⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⣸⠋⢙⡏⠁⡿⡄⠀⠀⠀⢀⡇⠀⣿⠑⠒⠒⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠴⠊⠉⠳⡀⡗⠒⠊⡇⢀⣧⠓⠶⠶⠎⢉⣷⣄⣸⡀⢀⣀⣿⣤⣖⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡁⠀⣀⠀⣀⠽⢷⣤⡤⠯⣍⣋⠟⠒⠛⠛⣟⣩⠿⠋⠉⠹⣯⡻⣻⠏⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠀⣼⣸⠀⣴⡆⢹⢿⠀⠀⢰⢿⡇⠀⣴⣶⣄⠈⢿⡟⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠻⡏⠀⣿⡇⢸⢸⠀⠀⢸⠸⡇⠀⣿⣿⣿⣦⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⢸⣿⠀⢾⢰⡀⠀⣸⣶⡇⠀⢹⣿⣿⣿⣷⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠸⣼⣷⣜⣿⡿⠃⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⢿⣧⣤⣀⣀⣀⣀⣠⠤⣤⣴⠿⠟⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣀⣀⠀⠈⠉⠉⢻⠀⠀⠘⣇⠀⣀⣀⣠⠤⡶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣢⠌⠉⣛⣒⡖⠋⠀⠀⠀⠈⠹⡑⢒⣛⡀⢳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠁⠀⢱⠖⠃⠀⠀⠀⠀⠀⠀⠱⣤⡤⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡿⢿⣿⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⣿⣿⣿⣿⣿⣿ ⡿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⡤⢄⣙⢶⣄⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡿⠛⣿⣷⢀⣸⣿⣿⣿⣿⣿⠿⣦⣤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⡀⢀⣿⣿⣾⡏⣴⣿⣿⣷⣿⡷⣿⣌⡇⠀⣀⣀⣿⣦⣤⣀⣀⡀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣕⣿⣿⣿⣿⡿⣶⠟⠉⠉⠁⠀⠀⠀⠻⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠠⡙⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣒⣤⣀⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠒⠂⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⣭⣿⣙⣻⡿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣟⣿⣿⣏⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⢀⣞⠳⣄⡀⠀ ⠀⠀⠀⢀⣀⣧⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⢧⡀⠀⢠⣿⡿⢿⣒⠿⡓ ⠀⠀⠠⣯⣿⣿⣿⣿⣿⣿⡟⡿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣧⡀⣸⣿⣿⣷⡾⣧⣿ ⠀⠀⣸⣿⣿⣿⡿⠿⠛⠉⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⠉⠙⣆⠀⠈ ⠀⠀⠈⠉⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠉⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⠿⠟⠋⠀⠀⠀⠀⠙⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣴⣶⣶⣶⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣠⣶⣿⡀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⡎⢻⣿⣿⡿⣿⡇⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠇⠺⠿⠿⠖⠚⣿⡄⠀⠀⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⣲⣾⣿⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⣿⣿⣿⡷⢞⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠏⠛⠛⠋⠉⠉⠁⠙⠃⠉⠛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣨⢊⣵⡿⣽⢯⣿⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢡⡾⢋⣾⢏⠎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠠⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡁⠄⣀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠡⢐⠠⢐⣨⣔⡮⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣾⣦⣀⠐⠈⠔⠊⠉⠙⠣⣚⠂⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠀⠀⠈⠙⠻⣿⡆⡐⢢⠀⠀⠀⠀⣀⠩⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⡿⣾⠥⠤⠐⠂⢁⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⣿⠀⠀⠲⠂⠀⠀⠀⠴⠄⢸⣧⠐⠒⣂⣨⣤⡆⢸⣿ ⠀⠀⠀⠀⠀⢀⠤⣺⣿⣿⣇⣀⣀⣀⣀⡀⢀⣀⢀⡀⢘⣿⡿⣿⣿⣿⣿⡇⢸⣿ ⠀⠀⠀⠐⠈⠀⣰⣿⣿⣟⠓⣦⢁⠀⠑⡃⠀⠀⠀⠙⠈⣿⣿⣟⡟⠻⠽⡇⢸⠛ ⠀⠀⠀⠀⠀⣠⣿⣿⣟⣷⣠⣾⣖⠒⠒⠒⠒⠒⢒⣷⣶⣾⣟⡇⠁⠈⠁⡇⢨⠀ ⡀⠀⠀⢀⣴⣿⢿⣿⣿⣯⣿⣿⣧⠈⠣⡐⠠⢉⣿⣿⣇⣿⣿⡇⠀⠀⠀⡃⠀⠀ ⠀⠀⠀⣾⡿⠃⣸⣿⢽⣿⣿⣿⣇⢣⢀⠜⠁⡼⣿⣿⣿⢿⣿⡇⢀⠤⡰⠃⠐⠀ ⠀⠀⠀⣿⠁⢠⣿⣿⣿⣿⣿⣿⡒⠘⣙⣄⣎⡘⣿⣿⣾⣏⣿⡧⢸⠀⡏⢦⠀⠀ ⠀⠀⠀⣿⣠⣿⣿⣿⣿⣿⣿⣿⠶⡟⣨⡋⡠⣗⢸⣿⣿⣇⠸⣷⣿⠀⠇⢸⠀⠀ ⠀⠀⢀⣽⣿⡿⣿⣿⣿⣿⣿⡏⣥⣀⣢⠀⠩⠀⣾⣿⣿⣿⡄⠈⢷⣄⡐⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠤⠒⠒⠠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣤⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠊⣩⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⠀⢰⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠈⢳⣤⡈⠢⡀⠀⠀⠀⢄⢣⡀⠀⠈⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢳⡀⠈⢆⠀⠀⠀⢹⡢⣄⠀⠀⠈⣢⡀⠀⠳⡈⠓⠬⡲⢄⠀⠀⠋⢻⢆⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠳⡀⠈⢦⡀⠀⠀⢣⠈⠑⠮⣅⡀⠉⠳⣄⠱⡄⠀⠀⠀⠁⠀⠀⠈⡆⠱⡀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣀⠤⠒⠚⠛⣄⠀⠹⣆⠀⠀⠳⡀⠀⠀⠉⠓⠦⣤⣑⣦⣀⠀⠀⠀⠰⡄⠀⠸⡀⠘⢄⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠳⣄⠘⢷⣄⠀⠱⣄⣀⣶⡾⠿⠛⠻⠛⡄⠉⠢⠀⠀⢳⠀⠀⢃⠀⠈⠂⠀ ⠀⠀⠀⠀⢸⠀⠀⠃⠀⢰⠁⠀⢠⣤⣤⣤⠤⣀⠀⠑⢤⡑⠙⠢⣘⣟⠛⠀⠀⠀⠀⠀⠃⠀⠀⢳⠀⠈⡇⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠀⠀⣠⠀⢸⢤⣾⠿⠛⠛⠛⠿⠯⠀⠀⠀⠈⠚⠤⠈⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⡇⠀⢻⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⢠⢻⠀⡄⢸⡀⢸⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢿⡀⢸⡇⠀⡇⠀⠀⠀ ⠀⠀⣇⠏⢘⢠⡇⠘⣧⣸⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠘⠇⠘⢡⠀⢹⠀⠀⠀ ⠀⣸⠟⠀⡎⡸⡇⠀⢹⣿⣗⣤⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣇⠀⠀⠀⠸⠸⢸⠀⢸⠀⠀⠀ ⠠⠋⠀⢠⢧⠃⢸⠀⠀⢣⡀⠙⣌⠉⠚⠋⠒⠂⠀⠀⢀⣀⡀⠤⠤⢒⡷⠀⠀⢀⡠⠋⡰⢿⠀⠀⡀⠀⡄⠸⠀⡸⠀⠀⠀ ⠀⠀⠀⣼⠏⠀⠀⢇⠀⠸⡷⡀⠈⢣⡀⠀⠀⠀⠀⠀⠘⠓⠄⠒⠚⠉⠀⠀⠀⠀⣠⠞⢀⣸⠀⠀⡇⠀⢡⢀⠀⡇⠀⠀⠀ ⠀⠀⠰⠋⠀⠀⠀⠘⡄⠀⢡⠙⢄⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡇⠀⡎⢸⠀⢰⠁⠀⢸⢸⣼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇⠈⢢⡀⠰⠀⠸⣏⡷⢦⣄⣀⠀⠀⣀⣴⣾⠋⢻⡇⠰⠃⣀⠀⡜⠀⠀⡗⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⢆⠀⠑⡄⣇⠀⡯⣷⠀⠀⠉⠙⠛⠉⠉⠀⠀⠘⡇⡀⠀⡈⢰⠁⠀⢰⡷⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⢿⣠⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢧⣄⣷⣇⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡩⠿⣏⡀⠀⠈⠳⢤⠤⢤⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣥⣄⠀⠈⠑⠢⢤⣀⡙⣺⡁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣆⠀⠙⢿⣿⣿⣿⣦⣴⣿⣿⣿⡿⠋⠀⣰⣦⣄⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣧⡀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠁⢀⣼⣿⣿⣿⣿⣦⠀ ⠸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠻⠟⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠙⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⡀⢀⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠙⣿⡿⠿⠛⠁⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠉⠛⠿⢿⣿⠋⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⣦⣤⣀⡀⠀⠉⠛⠛⠉⠀⢀⣀⣤⣴⣾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣤⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⣿⣶⣿⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⡟⠛⢿⣿⠿⠛⣿⣤⣤⣖⠋⠉⠙⠓⠶⠶⠒⠲⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⣿⣿⠁⠴⣾⠯⠀⠚⢻⣶⠃⡾⠀⣠⡖⠛⠻⡗⠢⡀⢈⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣰⡇⠀⠀⠀⢠⣿⣿⠢⠀⠀⠀⠤⠆⣸⡇⣸⢁⡜⠁⠉⠓⢦⣧⠀⢻⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⢯⣄⣀⡀⠉⠓⠢⣄⣠⠞⠈⣿⢦⡀⠀⠘⠓⠊⢸⠃⣇⡾⠀⠀⠀⠀⠘⣿⡣⣈⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣄⡙⠢⡀⠸⡄⠈⠓⠶⢴⠖⣯⢸⡿⠁⠀⠀⠀⠀⠀⡏⠳⣎⠙⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠂⠈⢢⡇⠀⠳⡀⠀⢀⣼⣽⠖⣳⢄⠀⠀⠀⡴⠀⠀⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣤⠶⠚⣻⠛⢉⠝⠋⠉⠈⠉⡹⠏⠉⠙⠛⠒⢒⣒⣻⣒⣶⣿⣿⣟⣥⠼⣷⡼⠛⣿⣦⡞⠁⠀⠀⠀⠈⢣⡀⠀⠀⠀ ⠀⠀⠀⣠⣟⡟⠁⠀⢰⠃⠀⡟⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣿⡿⠂⡠⠒⠉⠉⠀⠀⣀⣠⡤⣤⣿⡿⠙⣄⠀⠀⡇⠀⠘⣿⣆⠀⠀ ⠀⣠⠎⣾⡞⠀⠀⢀⡟⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣎⡀⢀⣀⡤⠖⣉⣠⠤⣄⡼⣿⠃⠀⠈⣿⠓⣧⡀⠀⠸⣿⠀⠀ ⢰⠇⢰⣿⠀⠀⡠⠏⠀⠀⢰⡟⣆⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣻⡀⠈⠉⣉⣥⣖⠋⢁⣠⢶⠟⢻⠏⠀⠀⠀⠈⠳⡀⠱⠀⠀⢸⠀⠀ ⣿⠀⠸⣿⡠⠊⠀⠀⠀⠀⣿⠀⠀⠀⠠⣤⣤⣤⠴⢺⡟⠦⣈⠙⠓⢶⣯⣷⣉⣨⣭⣷⣿⣥⡴⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⡇⠀ ⢻⠀⠀⢻⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣽⢧⡀⠸⢭⣍⠉⠁⢀⡠⣞⠿⠓⣒⣼⠃⠀⠀⠀⠀⠀⠀⢀⡰⠻⠛⠉⠉⢻⣀ ⠈⢣⠀⢸⡆⠀⠀⠀⠀⠀⡿⢳⠀⠀⠀⢤⠀⠀⢠⡇⠨⡿⢮⣙⣓⣡⣶⣉⣨⠥⣴⠞⢁⣾⠀⠀⠀⠀⠀⠀⠀⣯⣤⣤⡀⠀⢀⣸⣗ ⠀⠀⢳⢸⠃⠀⠀⠀⠀⠰⣇⡾⠀⠀⠀⢸⣆⣤⣟⠀⠀⢻⣄⣉⠉⠛⠛⠚⠛⠋⢁⠔⠁⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣷⣄⢸⡿⠀ ⠀⠀⠀⠿⠀⠀⠀⠀⠀⣰⡿⢷⡀⠀⠀⠀⣧⣾⠀⠀⠀⠘⡇⠉⠉⠛⠲⠶⢤⡖⠁⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⠀⠀⠀⢨⠏⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⡞⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡟⢧⠀⢀⡟⠀⠀⠀⠀⠀⢻⣀⡤⠀⢠⠞⠊⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠁⠀⠀⢸⠁⠀⠀⠀⠀⢸⣏⡁⠀⢀⡞⠀⢈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣿⠀⠀⠀⠀⠀⢀⡟⠻⢿⠟⠛⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⠉⠁⠈⣙⣆⠀⠀⠀⣾⠁⠀⡏⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣞⣦⡆⢠⠞⠿⠼⠁⠀⠀⢹⡀⠀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣅⣿⠗⠀⠀⠀⠀⠀⠘⢷⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣁⣀⣸⣿⣿⣶⠗⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⠴⠛⠉⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠃⢀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠁⠀⠀⠀⠀⡠⠋⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡗⠊⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⠤⠾⠧⠤⣴⣶⡯⠵⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀ ⠳⢄⡀⠀⠀⠉⢶⡶⠬⠭⢒⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢦⠤⠔⠒⠉⠉⠁⣀⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣄⠀⠀⠈⢿⣦⣤⣤⣠⣄⣈⠑⢦⣄⡀⠠⡀⠱⡀⢣⠀⣀⣠⡴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠈⢿⣿⣏⠉⠉⠛⠻⣶⣽⣿⣄⠘⣄⠹⣦⣿⠿⠝⣊⡽⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⡆⠀⡇⢀⠀⠀⠘⡜⣿⡄⠀⡴⢋⡟⠉⢻⣿⣆⠸⡄⢹⣿⡶⠞⠛⠉⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⢰⠁⠀⣿⠀⢇⠀⠀⠱⠘⣷⣼⡡⢣⠋⣽⣟⠙⠈⢣⣇⠀⣿⣇⠀⠀⠀⠀⢀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀ ⢀⡟⠀⡄⡟⢠⠘⣧⠀⠀⢇⣸⣿⠁⠈⣸⣿⣿⣧⡀⠀⣿⣠⢿⠹⠀⠀⠀⢠⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀ ⡞⠀⠀⡇⣹⠃⠀⣿⣧⠀⣸⡏⢻⡆⠀⣿⠛⢧⠟⠿⢷⣾⣿⢸⠀⠀⠀⠀⠀⠀⠀⠈⠒⢦⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠹⡀⠀ ⠇⠀⠀⡇⣿⠀⠀⡟⣿⣷⡃⠠⣸⣿⣀⣿⣤⣤⠬⠟⠛⢋⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠛⣄ ⠀⠀⢰⠃⣿⡇⠀⡇⢹⡇⢳⠀⢻⡛⣿⡉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢙⡆⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠐⡌ ⠀⠀⣼⢸⠹⣷⠀⢱⠸⣧⢸⣧⡀⣇⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⢎⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿ ⢦⣀⢻⡟⢆⠹⡆⢸⠀⢻⡄⢧⡳⣽⠷⣦⣭⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠛⠉⠀⠀⠈⠓⢔⠻⣶⣶⣿⣂⣘⣿⠦⢀ ⠀⠉⠛⢧⡈⢆⢻⡄⡇⠈⢿⡈⣿⣿⣧⠀⠨⢭⣬⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⠟⠻⣿⠹⠿⠊⠉ ⠀⠀⠀⠀⠈⠛⢧⣻⣷⡀⠘⣷⡘⡟⠿⣦⣀⠀⠈⠉⠛⠢⠤⢤⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⣘⣷⡘⢄⠀⠙⠻⢶⡤⣤⣤⡄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢀⣠⠴⣶⣶⣖⣒⣒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣖⣤⠄⣀⣀⣀⡈⠭⢖⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢫⡟⠁⠀⣠⠴⣛⣴⣾⣿⣿⣿⣾⣶ ⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣦⡤⠤⣤⣄⣀⣈⡙⠿⣦⣄⠀⠀⣀⠴⠊⠁⠀⠿⣤⣠⠞⣡⠾⠟⠛⡿⢛⣥⠍⢙⡛ ⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡈⠙⠢⣽⠿⠿⠿⢟⡋⠀⠀⠀⠀⠀⠀⠈⠙⢯⡀⣀⠴⣋⡴⠛⠁⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⢸⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠶⠮⣷⡄⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀ ⠀⣷⣄⠀⠀⠀⠈⡇⠈⣆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢷⡤⣄⣈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣎⠑⢄⠀⠀⢇⠀⠸⡀⠀⠀⠀⠀⡰⡇⠀⣀⣤⠆⠀⠀⠀⠀⠙⢶⣮⣍⡑⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠲⠋⣨⢷⠀⠑⣄⢸⡀⠀⡇⠀⡠⢀⣜⣠⠗⢈⡴⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠶⢮⣽⣒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣠⡤⠖⠋⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣤⣺⠥⡔⠁⠀⠀⠀⠀⠀⠠⢄⡉⠑⠦⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀ ⣤⡴⠞⠋⠁⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⢀⡤⣲⠿⠛⠡⠤⣤⣧⣀⡀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡈⠹⣍⠀⠉⠙⢿⣿⣿⣿⣿⣶⣄⠀⠀ ⠙⣆⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⣠⣴⡪⠕⠋⠀⠀⠀⠀⣀⣠⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⣄⠀⠠⢿⣿⣿⣿⣿⣿⣦⠀ ⠀⠘⣇⠀⠐⢀⡀⠀⣀⠤⣒⠽⠛⠁⠀⠀⠀⣠⣴⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠈⢢⠈⢣⡀⢸⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠸⡶⠚⡡⢔⡫⠖⣫⠄⠀⠀⠀⠀⢀⣼⣿⣿⢫⣾⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠳⡀⠱⣼⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣷⠤⢊⣡⠔⠊⠁⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⡿⢛⣿⣿⡿⠋⣠⣿⣿⡏⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢱⡄⠈⢿⣿⠿⠿⠿⠿⢿ ⠀⠀⠀⢸⠚⠉⠀⠀⠀⠀⠀⠀⠀⣠⢟⣿⣟⡿⣿⠋⣠⣾⣿⠏⠀⣴⣿⣿⡿⣹⣿⣿⣿⣿⠋⢻⣿⡷⣄⠀⠀⣹⠖⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠤⠊⠁⠀⠀⠀⠀⢣⡾⢻⣯⣾⠉⣷⣿⣿⡟⢀⣾⣿⣿⣿⢡⢟⣿⣿⣿⣿⣴⢸⣿⣿⡌⣳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⢀⠤⠒⠁⠀⠀⢀⣠⠼⣤⡏⣹⡟⡾⣽⣿⡿⢀⣾⢟⣵⡿⢛⣾⣾⡿⣿⢣⣿⡇⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠊⠁⠀⠀⠀⢠⣶⡿⣥⣀⣈⠻⡿⠟⣹⣿⣿⣷⡿⢋⡿⠻⢦⣾⡿⠃⢰⣿⣿⣿⣇⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⢠⣏⠞⠀⠀⠀⠀⠀⠀⠰⠛⢻⣿⠟⠠⣿⣑⣲⣟⠛⢦⡀⣾⡿⣹⣿⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠀⠄⠀⠀⢀⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⡒⠶⣤⣽⡖⢄⠱⡀⢹⣿⣡⠏⣼⣿⣷⡏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠁⠀⠀⠀⠀⠀⣸⢱⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⠛⣿⣷⣄⠸⣾⡸⢧⣼⠟⣹⣿⣿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠒⣤⠟⡜⡆⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⣠⠢⣄⠻⣶⣙⠛⣿⣆⠛⠁⣼⣣⣦⡟⣼⠃⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⡟⠀⠀⠈⠢⣀⠀⠀⠙⠶⣤⡄⢀⣾⣙⣶⣿⠳⡈⠻⣯⣽⣿⠀⢰⣿⢃⣏⡜⡛⢰⣿⡿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠃⠀⣰⡇⠀⠀⠀⠀⠀⠉⠒⠤⠤⣼⠿⣧⣿⡿⣿⣛⣤⣮⢢⠀⠉⠛⣠⣿⣧⡾⢋⢀⣷⣿⡿⠀⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠞⠁⠀⢰⠟⢷⣄⠀⠀⠀⠀⠀⠀⣀⠴⣧⣶⣟⣛⡧⢨⣿⣿⡥⠋⠀⠀⢘⣿⣿⠟⣠⠏⢸⡿⣹⢣⢠⡇⢠⠙⡶⠤⣀⣀⠀⣀⣠⣴ ⠀⠀⣠⡴⠋⠀⠀⠈⠓⢤⣀⠀⠀⠈⠣⡀⠉⠉⣠⣤⡶⢋⡡⠋⠀⠀⠀⢀⣸⣿⣇⣼⠏⢠⣾⣧⣏⡇⣼⠁⣾⢰⠃⣠⢿⣿⡇⢹⠟⠋ ⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⡦⠄⠀⠈⠢⣄⠛⣡⠔⠁⠀⠀⠀⠀⢀⣠⣿⡭⠚⣿⣔⣿⢻⣿⣼⣇⣟⣼⣿⣼⣼⡿⣦⢻⣿⣄⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠈⠉⠀⠶⢴⣶⣶⣖⠚⠻⣿⡟⠀⠀⠉⠉⣿⡏⣿⣿⣷⣿⣿⣿⡿⡿⡇⠸⠈⠿⠉⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⣀⠑⠄⠠⠤⠔⢋⣾⣿⣿⣿⣿⠃⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⢀⢴⣿⠟⠉⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣶⠖⠾⠛⠹⠋⠘⠟⠋⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠀⠰⠀⠀⠀⠀⢸⣯⠧⢤⣞⣡⠷⠤⢤⡖⣒⣒⣒⣒⣒⣚⣛⣛⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀⠀⣼⣧⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠒⢋⡴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⣠⠔⠋⠀⠀⠄⠉⠑⠢⣄⠀⣀⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⡤⠴⠋⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠉⠀⠀⡠⠔⠊⠁⠀⠀⠀⣠⠆⣠⡠⠔⠊⠀⣠⠔⠒⢦⡀⠀⠤⢄⠀⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠄⠀⠀⠀⠀⢀⠴⠊⣠⠾⠟⠀⠀⢀⣴⣥⡄⠀⠀⠙⢄⠀⠀⠈⠰⡑⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⢀⢴⡦⠊⢁⠔⠋⠀⢀⡀⣠⣴⣿⣿⠁⢾⣦⡀⠀⠈⢦⠀⠀⠀⠈⠊⢣⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡀⠰⠁⠀⠀⢀⠞⣀⡤⣚⡡⠤⣄⣸⣿⣿⡀⡄⠻⣷⡀⠀⠈⣧⡀⠀⠠⡄⠀⠑⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡇⢀⡔⠀⣠⠃⡰⣿⠉⠁⠲⣀⣼⡿⠟⠛⠻⣿⣄⠹⣿⡀⠀⢹⣷⡀⠀⠙⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⡠⢾⠀⣰⠃⣰⢡⡇⠀⣠⣞⣽⡟⠀⠀⠀⠀⠨⣿⣷⣿⡿⡄⠀⣿⣿⡀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⠁⢸⢀⡇⢠⠃⣸⣦⣾⠛⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⠱⠀⣿⣿⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⡀⣀⣼⣡⠏⣰⣿⣿⠗⠚⠓⠶⠶⣶⣦⣄⡀⠀⠀⠀⠈⠻⣷⣾⣿⣯⣿⡆⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⣡⣶⣽⣿⢻⣿⣿⣴⣶⣾⣷⣶⣶⣟⡻⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⡹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢋⡟⠉⢸⡿⠈⠻⡟⠛⢿⣿⣿⣾⠟⠀⠀⠀⢀⡴⠛⢋⣁⣐⣿⣗⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣾⡇⠀⢸⢃⡴⠀⠙⠲⠼⢿⡥⠉⠀⠀⠀⠀⣞⣡⠶⣿⣿⣿⣿⣿⡌⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠲⠬⡭⠴⠛⣹⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣟⣛⣺⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢃⠀⢸⠂⡄⠀⠀⢀⡀⠀⠀⠘⢿⣶⣶⡾⠀⠀⠀⠀⢀⣿⣿⠈⢉⣽⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⢻⡇⠀⠀⠀⠘⠳⣶⠶⢶⣦⣬⣭⣤⡸⠦⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⢸⣷⡀⢇⠀⠀⠀⠘⢷⣦⣄⣠⡿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⠳⣌⠳⣄⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⡴⠋⢸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣌⣿⡇⠈⠷⢬⡳⣄⡀⠀⠀⠀⠀⣤⠖⠋⠀⠀⢸⣿⣿⣧⣬⣹⣿⣿⣿⣯⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⣠⢿⣿⡀⠀⠀⠀⠉⠒⠵⠦⠶⠶⠲⣿⡑⢤⡀⠀⢸⡿⢿⣅⠘⠁⠀⠈⠉⠙⠻⢿⣿⠀⠀⠀ ⠀⠀⠀⢀⡔⠁⣦⠃⠈⣿⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡏⠙⢄⠉⠲⣿⣷⣿⣿⣿⣿⣷⣶⣦⣤⡀⠀⢻⡀⠀⠀ ⠀⠀⣠⠏⠀⡜⠸⡀⠀⢹⡇⢠⠀⠀⠀⠉⠀⠀⠀⠀⠀⣧⠀⠈⠳⣄⣿⠿⠛⠛⠛⠛⠛⠻⠿⣿⣿⡦⠀⠙⢦⡀ ⢀⠜⠁⢀⡞⠀⠀⠈⠑⠒⠙⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠈⣿⣤⣤⣀⣀⣀⣀⠀⠀⠀⠈⠉⠐⠀⠀⠀

⣿⣿⡏⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⢻⣿⡇⠀ ⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢼⣿⣿⠉⠀⣀⣀⣠⣍⠃⠀ ⠀⠀⠉⠀⠀⢰⣷⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⢄⣻⣿⣿⣿⣆⠀ ⢢⡀⠀⠀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣷ ⢸⣧⣤⣾⣿⠛⠲⣦⣤⣤⣦⣤⣴⣶⣤⣤⣤⣤⣤⣀⠀⢀⣀⡠⠚⢹⣴⣿⣿⣿ ⠈⣏⠁⠈⠉⠀⣰⣿⡟⡟⠿⢿⣯⣭⣹⣿⣿⠁⠁⢸⣿⣿⢹⠀⠀⠘⣿⣿⣿⣿ ⠀⠀⠀⠀⡀⣬⠟⣿⣧⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⡸⣿⣿⣧⣵⢄⠀⢸⣿⣿⣿ ⠀⠀⣠⢾⠞⠀⣸⣿⣿⠀⠀⠉⠓⠲⠌⠑⠀⠀⠀⣿⣿⣿⣿⣾⣿⣧⢸⣿⣿⣿ ⠀⠀⡟⣎⣤⣶⣿⣿⣿⣿⣤⣄⣤⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⡏⡿⠳⣸⣿⣿⣿ ⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣷⡿⠧⣿⣟⢻⣿ ⢸⣿⣿⣟⡻⣿⣿⣿⣿⣿⣿⠷⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣧⣞⣿⣾⣿ ⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⣛⣿⡟⣹⣿⣿⣿⣿⣿⣿⣧⡿⠿⣿⣿⣿ ⠀⠛⠉⡇⣿⣟⣛⣻⡙⠛⠻⡄⠀⠀⠀⠋⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⠟⠛⠿ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣄⡈⢶⠄⠀⠀⠀⢰⢋⣼⣿⣿⣿⣿⣿⣿⣧⡠⠀⠀ ⣾⣧⡀⢸⣿⣿⣿⡏⣙⣿⣿⣿⣶⣧⡀⠀⢰⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣷⣄⢀

⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀ ⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⢻⣿⡏⢸⣿⣿⣿⣿⡿⠉⢀ ⠀⠀⠈⠹⢻⣿⣿⣿⣿⣿⣿⡟⠁⣾⡿⢹⣿⣿⠏⢸⡿⠀⢀⣿⣿⣿⣿⡇⠀⠈ ⠀⢠⠊⠀⡄⢸⣿⣿⣿⡿⠹⣂⡤⣿⠁⢸⣿⠏⠀⣸⣧⢢⣅⣹⣿⣿⣿⣇⠀⠀ ⡐⠁⠀⢀⠀⣿⣿⣿⣿⠃⢧⠛⠻⢿⣫⣹⠃⢀⣼⢿⣿⣻⡻⠊⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⠸⠀⣿⣿⣿⣟⠀⠀⠀⠉⠉⠁⠀⠀⢸⡽⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⡋⢸⣿⣏⣆⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⢸⣿⣿⡟⡂⠀⠀⠀⠀⢤⣤⣤⠆⠀⠀⠀⢀⣼⣿⣿⠀⠀⠃⠀ ⠀⠀⠀⢀⠀⠀⢸⡇⠸⣾⡕⢤⡀⠀⢀⠀⠁⠡⠤⠀⠀⣠⣿⠏⢹⡏⠀⠀⠀⠀ ⠀⣦⢠⠘⡀⠀⠸⠇⠀⢧⣱⣮⣫⠂⠀⠀⠀⠁⠀⣠⡾⣻⣿⠁⢿⠁⠀⠀⠠⠀ ⠀⠈⠄⢢⣣⡀⠀⠀⠀⠘⡿⡨⠋⠔⠤⡱⡲⣰⠝⣡⠞⡱⠇⡀⠈⠀⣀⠄⠀⠀

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⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶ ⣿⡇⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⢠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿ ⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣾⣶⡄⢸⣿⣿⣿⡇⢀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿ ⣿⡇⠀⠀⠀⣾⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⡏⠈⠹⣿⣿⣿⡀⠀⠀⠸⣿⣿⣿⠈⠻⠿⠟⠁⣿⣿⣿⡄⠀⣿⣿⣿⡏⠉⠉⣿⣿⣿⣷⠉⠉⢹⣿⣿⣿⠉⠉⠁⢸⣿ ⣿⡇⠀⠀⢰⣿⣿⠀⣿⣿⣷⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⡇⢠⣶⣦⡙⠛⢃⣤⣶⣶⣤⡀⢿⣿⣿⠇⠀⣿⣿⣿⣧⣤⣴⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿ ⣿⡇⠀⠀⣾⣿⣧⣤⣿⣿⣿⡆⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⡇⠘⣿⣿⣷⢠⣾⣿⣿⣿⣿⣿⣄⠉⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣇⣀⣴⣿⣿⡿⠀⠀⠈⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠀⣿⣿⡏⠀⠀⠀⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⡇ ⣿⡇⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⣼⡇ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇

⠀⠀⠀⢀⣾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⠄⠀⠀⣰⠟⠉⠁⠀⠈⣿⡆⠀⠀ ⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⣰⡿⣁⣤⣤⡴⠶⡶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀ ⢀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣾⣯⠀⠀⠀ ⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⡿⢻⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠑⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣡⣴⣿⠋⠀⢸⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠱⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣄⣀⣀⢀⣀⣀⣀⣠⣤⣶⠿⢿⣅⣸⠀⢀⣸⣆⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠉⠙⠛⠛⠛⠉⣽⢿⡷⠦⣄⠈⠻⣄⢈⣿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠉⠙⠒⢦⣄⡀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢸⠃⠀⢻⣷⣦⡑⡄⠈⠻⡀⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡀⢸⡇⠀⠀⠀⠀⡏⠀⠀⢸⣿⣿⣷⡈⢆⠀⢱⡎⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣠⡴⢶⣶⣶⣶⣤⣄⡀⠙⢿⣿⠁⠀⠀⠀⠀⣧⠀⠀⣸⣿⢿⣿⣷⠸⠀⠀⣿⡸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠟⠉⢠⡿⠉⠀⠙⣿⣿⣿⣦⡈⠃⠀⠀⠀⠀⠀⠺⣄⣴⢿⣷⣤⣿⣿⠆⡇⠀⢸⣇⣇⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⣄⣠⡏⠀⢠⣿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⣿⣿⡿⢠⣀⣀⣸⣿⣿⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⠈⢹⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠛⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⡟⠃⠈⠀⠀⠀⢹⣾⠀ ⠀⠀⠀⠀⢳⠀⠀⢤⡤⠿⠀⠀⠘⡎⢧⡀⠀⣠⡿⣿⣷⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣈⠟⠁⠀⠀⠀⠀⠀⠀⡏⡇⠀ ⠀⠀⠀⠘⡄⢧⠀⠀⠀⠘⡄⠀⠀⠱⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀⠀⡤⠖⠋⠉⠀⡀⠀⠀⠀⠀⠀⣼⣳⡇⠀ ⠀⠈⠳⢄⠸⡌⢧⠀⠀⠀⠱⡀⠀⠀⠱⣄⠙⢿⣿⣿⣿⡟⠛⠛⠛⠉⠀⠀⠈⢀⠀⠀⠀⠀⠁⡄⠀⠀⠀⢰⣿⠿⡇⠀ ⠀⣠⣔⣺⣷⣦⡈⠳⡀⠀⠀⠑⣄⠀⠀⠈⠓⣤⡾⠃⠀⠀⢠⠖⠁⠀⠀⢸⡀⠀⠀⠀⠀⢠⣼⠁⠀⠀⢰⣿⣟⣧⠀⠀ ⠀⠈⠻⣿⣿⣍⡉⠃⡙⢦⡀⠀⠈⠳⢄⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣤⣶⣿⠋⠀⠀⣰⡿⠁⠈⠙⠀⡀ ⠀⠀⠀⠈⢻⣿⣿⣛⠿⢦⣙⢦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⣥⣼⠏⠀⢀⣾⣿⡅⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠘⠎⠙⠿⣷⣦⣌⡳⢍⡓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡠⠚⣠⣾⠟⠃⠈⠇⢸⡆⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠛⠿⠿⣷⣶⢈⠙⠿⠶⠤⡤⠄⠀⠀⠀⠀⢀⣀⣀⡤⡴⠞⠋⠛⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢹⣿⠁⠀⢀⣀⠀⠀⢠⠄⠀⠀⠀⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢷⣄⠀⠀⠀⠀⠀⠀ ⣿⢷⠿⣽⣿⣾⣷⣿⣿⣿⣿⣿⣿⣏⣟⣦⠀⠀⠀⠀⠀ ⣿⣿⣴⣿⣺⣿⣿⣿⡟⢻⣿⣿⣿⣿⣹⣿⣧⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡟⠃⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⢈⡙⠯⣿⣿⣿⣿⣿⠀⠀⠀ ⣿⣿⣿⣿⠸⡀⠒⠲⠿⣖⠀⠀⠀⠒⠛⢿⣿⣿⡇⠀⠀ ⣿⣿⣿⡇⢄⠑⠄⡠⡷⠀⠀⠀⠚⠷⢦⣼⣿⡏⡇⠀⠀ ⢻⣿⣿⡇⠈⠑⠀⠀⠀⠀⠀⠀⡻⡠⣾⣿⠉⠃⠀⠀⠀ ⡾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⡏⠀⠀⠀⠀⠀ ⣡⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠃⠀⠀⠀⠀⠀ ⠈⠠⠙⣿⠀⠈⠲⡤⠤⠤⠔⡻⡿⣿⡿⠀⠀⠀⠀⠀⠀ ⣶⠆⠀⠘⠀⠀⠀⣤⣤⣀⠐⡡⢇⠸⡇⠀⣀⠀⠀⠀⠀ ⣿⣿⣀⣀⠀⢀⠔⠉⠉⠉⠂⢤⣁⠒⡾⠧⡀⢼⠀⠀⠀ ⣥⣴⢶⠒⡨⠃⠀⡔⣛⡿⢉⣉⣯⣯⣋⢏⠽⣘⢄⡀⠀ ⣿⡿⢺⠔⠀⠀⠘⠁⠉⣉⡀⢤⣿⣤⡀⡱⠋⠀⡠⠐⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⢶⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⣀⡤⠴⠒⠊⣉⣽⠿⠟⠋⠉⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⠀⠀⣠⡴⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⢀⣠⡶⠛⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢀⣠⠶⠋⠁⠀⢀⣠⡴⠞⠋⠁⡠⠖⠉⠉⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡴⠋⠁⢀⣠⡴⠞⠋⠁⠀⣀⡴⠋⠀⠀⣀⡀⢠⠀⢇⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣋⣥⡴⠶⠛⠉⣁⣠⣤⣶⣾⣟⡁⠀⠀⣾⣿⣿⣃⣼⠀⡼⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣖⣯⠷⠟⠛⠉⠀⢀⡤⠖⠋⠩⡀⠀⠉⠛⠛⠉⠀⠀⠙⠛⠛⠋⢸⣠⠃⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣤⠶⠛⠋⠉⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⣠⢞⠄⠀⠀⠀⠀⠈⠃⠒⠀⠀⠀⠀⡸⠘⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⡜⢣⡀⠀⠀⠐⢶⣶⣶⠶⠀⠀⣰⠃⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⣠⠞⠀⠀⠙⠦⣀⠀⠀⠀⠁⠀⢀⡔⠁⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠘⢀⡠⠖⠉⠀⠀⣠⠤⠤⠤⠬⠽⠶⠤⠤⢶⡉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⠁⠀⠀⣀⠔⠉⠀⠀⡤⢭⣟⡒⠢⣄⠈⠉⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣀⠔⠊⠁⠀⠀⠀⢀⠭⠭⣉⢯⠳⣬⡓⣄⠀⠀⠈⠑⠢⠤⠤⠤⠴⠒⠒⠤⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⢿⠎⠙⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣦⢀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠤⠂⡨⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⠬⠍⠀⠀⠀⠀⣀⡠⡀⢀⠀⠀⠐⠀⠀⡀⢁⡀⠀⠀⠀⠀⠀⠀⠾ ⣿⣿⠟⠛⠉⠁⠀⠀⣀⢔⢈⠩⠠⢢⠟⠀⡚⠄⠁⢊⠖⠠⠤⠀⠒⠞⠒⡀⠈⠙ ⣿⣷⣶⣶⣶⠶⠚⡉⢉⡱⢁⡴⢡⡎⡀⢰⣹⡈⡕⢄⠩⡒⢶⣈⣁⠀⠀⠈⠙⢿ ⣿⣿⣿⣿⣶⡾⣡⣴⢿⢶⣿⢡⣿⠡⠇⠸⣿⣡⢱⡀⢩⠚⠢⠐⡢⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢿⠋⠇⢻⠿⣧⢻⣧⣧⣿⣧⣼⣷⣄⡗⠈⢆⠬⡯⢖⣶⣶⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⠆⠈⠙⢂⡜⠀⠘⠈⢇⠻⠿⢁⠟⢯⣦⢬⢳⡇⣀⣈⣙⣻ ⠟⠛⠛⠛⢿⠋⠉⠙⠳⣄⠀⠘⠀⠀⠀⠀⠀⠉⠈⠁⣰⣙⣑⠗⣚⢌⣿⣿⣿⣿ ⠀⠀⠀⠐⡀⢦⣉⣉⠢⠈⢵⡀⠈⠓⠀⠀⣀⣤⣶⢯⢻⣧⣆⢸⣿⣧⣿⣿⣿⣿ ⣦⢤⡔⠀⢹⢸⣿⣿⡇⢱⣾⣯⡖⠒⡨⠛⣡⠾⠥⠮⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿ ⠀⠀⠹⢶⣪⡈⠙⠉⣀⠞⡡⢂⢵⠪⠂⠁⠀⢀⡠⠤⠤⠤⠤⡈⢿⣿⣿⣿⣿⣿ ⣀⣀⣤⢀⠙⠛⠋⠁⠠⡎⡴⠕⠁⠀⢀⡠⡞⢻⡎⣚⠆⠀⠀⠀⠘⣿⣿⣿⣿⣿ ⣊⢴⣅⠉⠻⢦⡀⠠⠃⠈⠀⠀⠀⣶⣯⡿⡛⢪⣿⣿⢠⠀⢀⠊⠁⣉⣿⣿⣿⣿ ⣿⣿⣿⣷⣄⠀⠹⠁⠀⠀⠀⠀⣾⢿⠁⡇⡁⣿⣇⠁⡏⡢⡉⣱⠞⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⠀⠀⠫⠜⣤⣷⣹⣷⣿⣿⣿⣱⡿⠁⠀⠈⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠐⠈⠉⢳⣠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠐⠢⡀⠀⠀⠀⠀⠀⢐⠻⠛⠛⢻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⢁⠒⢢⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡆⢸⡌⠉⡄⢸⣿⠿⡛⠿⠀⠀⠀⠔⡀ ⠀⠀⠀⡜⠤⠤⢀⠀⠀⠀⣧⡘⣝⣍⡀⠨⠠⢂⡷⠷⠶⠟⠳⠲⠇ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⢼⣿⣷⡿⣈⣘⡵⣊⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢭⣽⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢓⣿⠃⠐⢄⠤⠒⠒⠂⢄⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠖⠒⠒⠒⠲⠶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⢀⣠⡶⠞⠋⠉⠉⠉⠉⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠰⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠐⣤⡀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣤⡶⠛⠀⠀⠀⠀⠘⢧⡈⢻⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠈⠙⠓⠶⢤⣤⣤⣤⡴⠿⠻⢿⣦⡾⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠶⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠞⠛⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠉⠁⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡴⠋⠀⠀⠀⠀⠹⣦⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⣠⡟⠐⠀⠀⣼⣿⣷⡟⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⡿⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀ ⠀⠀⣠⡶⠋⡟⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠙⠟⣿⡃⠀⠀⠀⠀⠀⠀⢻⡿⠗⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⢀⣼⠋⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠀⠘⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⠀⠛⢷⡀⡟⠀⢀⡆⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀ ⣸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠷⠤⣼⠃⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠉⠉⠻⣦⠀⠀⣼⠃⠀⠀⠀ ⠘⠿⢦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠛⢶⡄⠀⢸⠆⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⠶⠶⣤⠀⠁⠀⡞⢰⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣀⣀⠀⠀⠀⠀⠀⣷⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⣿⠁⠀⠈⠙⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠉⠛⠛⠒⠶⠤⠴⠶⠦⣤⣴⠋⠀⠀⣠⠏⠙⢳⣄⡤⠞⠛⠦⢤⡄⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣰⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠛⠿⠿⠿⠶⠾⠿⠿⢦⣼⡀⠀⠀⠀⠀⣼⠋⣀⣴⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠟⢳⡖⠒⢾⣟⣻⡽⠛⠁⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠈⢷⡀⠀⠀⣀⣴⠾⠋⠁⠀⠀⢸⣧⡴⢿⡏⠁⢀⣤⠶⠶⣦⠈⠙⢦⣀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣧⣀⡤⠖⠚⢷⣠⠾⢋⣦⠶⣤⡀⠀⢠⡞⠁⠀⠘⣇⣀⡞⠁⣀⡼⠋⠀⠀⡀⠙⠳⢦⣀⣰⣏⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⣀⢀⠀⢘⠛⠀⠀⢀⢀⣈⠛⠒⠋⡀⠀⠀⠀⠘⣿⠛⠛⠋⣀⡴⠞⠛⣿⠀⠀⢀⠈⣙⣿⠿⠛⢛⣛⠛

⠠⣄⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠳⢦⣀⣼⠇⠁⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠀⠀⠀⢐⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠟⠸⠣⠳⠎⠼⠃⠀⠘⠀⠡⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠶⠴⠴⢰⡄⠀⠐⠁⠀⠀⠀⠀⠀⠁⠀⠀⠈ ⠀⣆⢰⠖⡴⠰⢲⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔ ⠀⠀⠀⣠⢠⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⢠⠄⡤⢠⢥⢡⡄⣄⡄⠀⢲⠒⠠⢀⠀⠀⠌⠀⠀ ⠈⠀⠁⠈⠈⠈⠁⠈⣁⣤⣾⠀⠀⠀⢱⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⣀⣠⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⡟⠉⠻⣿⣯⡀⢀⣽⣿⠟⠙⢿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣷⡀⠀ ⢀⣾⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢻⣿⣿⣿⣷⡀ ⢸⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠛⠛⠟⠉⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣤⣶⣿⣿⡟⠉⠙⣿⣿⣿⡇ ⢸⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣷⣀⠀⠀⣀⣾⣿⣿⣿⣿⣷⣦⣶⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⠇ ⠀⠹⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⠏⠀ ⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⡀⠀⠀⠀⠀⡀⠁⠀⠀⢠⠀⢀⠒⢤⠀⠀⠈⡆⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠉⠠⠠⠤⡄⠈⠀⠀⢠⠀⠀⠀⢣⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠴⠻⠄⠀⠀⠫⠥⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣒⣒⠛⢛⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠞⠋⣀⡴⣞⡏⠁⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⢀⣼⠀⠀ ⠈⠑⠦⣤⣤⣤⣤⣤⣤⠀⠀⢈⡩⠚⠉⠡⣤⣴⡏⠀⢀⢀⣀⣀⣤⣠⣤⣀⠀⠀⠀⠀⠸⣦⣤⣤⣴⣿⡿⠀⠀ ⠀⠀⠀⠈⠉⠙⠋⠉⠁⣀⣴⡟⠀⢀⡀⠀⠈⠛⠁⠀⠈⠋⢉⣉⣀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠙⢿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⡿⠀⠀⠋⠈⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠨⡻⠂⠀⠀⠠⢻⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠀⢀⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠁⠴⠋⡄⠀⠀ ⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣰⡿⠀⠀⠰⠆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⣀⡼⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⡈⠦⣤⣴⡿⠋⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣫⣴⣾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣤⣼⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⠿⢋⢀⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁⠀⠠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⢛⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⣃⠔⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣼⣿⣿⠿⠟⠛⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⡶⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠾⠛⠉⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠅⠀⠠⠤⢤⣀⠀⣀⡤⠟⠁⡀⠀⠀⣀⣀⣤⡤⠴⠶⠶⠶⠶⠶⠶⠤⠌⠙⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠤⠒⠉⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣏⠀⠀⠉⠉⠉⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠁⠛⠤⣭⠙⠀⠀⣒⢺⣿⣄⠀⠀⠀⠀ ⢀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠉⣹⣿⣿⡀⠀⠀⠀ ⠞⢹⣿⣿⣿⣿⡦⠀⠘⠓⢀⣴⣿⣿⣿⣿⡆⠀⠀ ⠀⣼⣿⡿⠟⠛⠁⢀⣀⠀⠙⠛⠿⣿⣿⣿⣁⠀⠀ ⠸⠟⠉⠀⠀⠀⢀⡧⡭⢻⠀⠀⠀⠈⠻⣿⣯⡙⡆ ⠀⠀⠀⠀⠀⠀⠈⠛⠙⠃⠀⠀⠀⠀⠀⠈⠻⡇⠁

⠀⠙⢶⣿⣿⣿⣿⡷⠂⠄⣊⠤⠒⠊⠁⠀⠀⠈⠀⠀⠒⠤⣀⠀⢈⣙⣷⢀⠀⢀ ⢆⠀⠀⠚⠛⣻⣿⣋⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡉⠫⡒⢹⡿⠀⠀⠀ ⢧⡧⡀⠤⢒⣉⣉⢙⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠈⠢⣣⠀⠀⠀ ⢬⢇⠚⠀⠀⡰⠁⡞⠶⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣶⣯⣤⣴⠶⠊⠉⡗⠆⠀⠀ ⢮⢏⢇⣠⠔⣡⢾⣀⣀⣠⣄⡭⡉⢂⠀⠀⠀⠈⡉⣉⣽⠯⣤⣄⡀⠀⡶⢈⢆⠀ ⢨⡧⠈⠐⡟⡘⢸⠻⠀⢮⣍⠹⢞⠀⠀⠀⠀⠈⠜⢏⡝⠕⠄⣰⠃⠀⠰⠀⠞⡀ ⠻⠠⠴⠘⣲⡥⣸⠑⢕⠕⢓⣊⢸⡴⠀⠀⠀⠸⠄⠑⠃⠮⠂⠁⠀⠀⣘⠰⠀⠰ ⠀⠀⠀⠀⣍⣴⣽⠀⠀⠀⠀⠀⢸⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠘⡀⢀ ⠉⠒⢄⠀⢃⣡⢻⠀⠀⠀⠀⠀⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠠⢀⠋⠈ ⠀⠀⠀⠔⠌⢇⢻⡄⠀⠀⠀⢠⡒⠈⣉⣉⣉⣁⠊⠀⠀⠀⣰⠕⠆⠠⠁⡜⡁⠖ ⠀⠀⣌⡜⠈⣄⢺⠰⡀⠀⠀⠀⢿⠟⠟⠉⢉⢙⠀⠀⠀⠀⠀⡌⡀⡇⣀⢀⡠⠊ ⠀⠀⢃⣇⠰⢯⠘⢲⡺⠕⠀⠀⠈⠢⣉⣉⠅⠊⠀⠀⠀⠀⢠⡑⡇⡇⣧⡀⠀⠀ ⡬⠥⢒⡪⠅⢒⣈⢄⠀⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢠⣷⣹⣯⡉⡘⢸ ⠒⠋⣵⣶⣶⣿⣧⣢⠄⣄⣀⠏⠦⡀⠀⠀⣀⣠⡤⠶⠉⠀⢰⣿⣿⣿⡟⡐⠔⢀ ⠀⢸⡿⣿⣿⣿⣇⠊⢞⣣⣤⣶⣶⣮⠛⢡⣶⣿⣿⣿⣶⣿⣿⢿⣿⣿⢯⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢀⣢⣤⣶⣦⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡀⠉⠉⢋⣹⣏⣽⣿⣿⣻⣏⡉⣉⡁⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣷⣿⣿⣿⡿⢿⣿⣿⠹⡿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⡟⠀⢸⣿⡏⠀⡘⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⢃⣠⣼⣿⠓⠘⠲⠚⠹⣿⣿⣿⣿⣿⡏⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⣿⣿⣿⠀⠁⡽⠈⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣧⡀⠁⠐⠀⠀⠀⠀⠼⣿⣿⣿⡟⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣻⠻⡿⠟⠂⡀⠐⠀⣀⠀⢀⠽⠏⠟⠸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡀⣤⡀⠉⠉⠀⠀⠂⣠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣁⠀⠉⠐⠒⠓⠒⢊⡽⢿⡿⠝⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠂⠄⠁⠟⠁⢂⠀⠠⢴⡎⠁⠀⠈⠃⠈⠀⠀⠂⠉⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⣤⠄⡤⠖⢂⢄⠀⠈⡒⠄⠀⠀⠀⣀⠄⠀⠄⢸⠿⠀⠀⠀⠀⠀⠀ ⠀⠡⢀⠀⠈⠀⠀⠅⣀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠂⠂⠻⠷⠀⠀⠀⠀⠀ ⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄ ⠐⠀⠀⡄⢀⣀⠆⢀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠐⠀⠄⠀⠀⠄⢠⡁⣤⡀⠀⠀⠀ ⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⢸⣷⡀⠁⡀⠀⠊⠁⠀⠀⠀ ⠀⠀⠀⠀⠉⠐⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⠄⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⡀⠴⠀⠒⠬⠤⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡠⠂⠁⠀⠀⠀⠀⠀⠀⠐⢣⠤⠐⢀⠍⣁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⡐⠁⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢳⡄⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢨⢁⠔⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡬⣂⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠠⠂⠠⠎⠠⡌ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡟⠀⠠⡀⠀⠀⠀⣀⠈⠉⠉⠁⠀⠐⣆⠠⡀⠌⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠳⣄⠐⠁⠀⡠⠮⠙⣀⡄⠠⠀⣄⠘⠁⠑⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⠁⠁⠉⠭⠭⠱⠊⠀⠄⠔⢠⠉⡆⠀⢰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⣰⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠑⣇⣀⠌⠀⠀⠀ ⡐⡅⠐⠉⠐⠒⠀⠈⠉⠙⠣⡎⠈⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠨⠀⠀⠐⢨⠁ ⠁⢄⠒⠐⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠄⠠⠁⠀⢸⠀ ⠀⠀⢋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠢⡉⠀⠈⠇⠀⠁⠀⠀⣸⠀ ⠀⠀⠀⠑⠒⠀⠉⠉⠑⠠⡀⠀⠀⢀⣌⣀⡀⠀⠀⠀⢡⠀⡐⠉⠁⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡌⢤⠧⢀⠢⠀⠀⢸⡐⠀⠀⠀⠀⠀⡠⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡈⠀⠊⡁⡔⢀⣎⠀⠀⠀⢐⠖⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠠⠎⠐⠁⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠠⠄⢀⡤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠚⢅⠈⠡⡀⠄⠊⠀⠉⠉⢂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢓⡆⠀⡇⠀⡇⠎⠉⣥⠈⠂⠀⠣⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⢀⡠⠁⢠⠀⡄⠘⠣⠀⠀⡠⠊⡘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠄⢀⠔⠁⠀⠈⠉⠁⠀⠈⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢥⡀⠀⠀⠘⠤⠆⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⠀⡀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣄⣤⣤⣤⡀⠀⠀⠀⢀⣠⡜⠀⠣⢄⡀⠀⠀⠀⠀⠀⣠⣾⠀⣀⣤⡶ ⢶⣶⣼⣿⣿⣿⡗⢄⠀⠀⡎⠈⣼⣦⡀⢀⣽⢆⠀⠀⢀⣿⣛⣟⣿⠽⠛⠁ ⠈⠉⠉⠛⠉⠀⢻⣦⠱⢼⠁⣼⣿⣿⣿⣿⣿⡇⢆⣴⣿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣯⡷⠉⢻⣿⣿⠿⣿⣧⣣⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠋⢨⠀⡉⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⣀⣀⠠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⢿⣟⣋⣭⡶⠓⢈⠩⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⢀⣀⣤⣾⠥⣒⠍⠀⠀⣪⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣼⣶⣿⢯⣴⣿⣥⣶⣿⠿⢟⣿⣿⠏⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠬⠠⠴⢞⣷⢿⣿⣿⣟⠗⣿⡶⣻⢿⣷⣂⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢉⣴⣿⣿⣿⡇⠀⠀⣰⠁⢎⢎⣽⣿⣿⣿⡧⠒⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⠋⡴⢟⣿⣿⣧⠀⠀⣹⣀⡨⠝⣫⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⡾⢟⣳⣀⣋⣀⣤⣾⣿⣿⠛⠀⠀⠀⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠤⣶⡪⢵⡧⣤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠀ ⢠⣺⣿⣶⣴⡗⢈⣿⣱⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀ ⠀⢽⣿⣿⠟⢰⠒⢽⣟⣿⣿⣾⣭⣽⣿⣭⣤⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⢀⡟⠃⣠⢸⣇⣼⡾⣹⡿⠀⢠⡟⠉⢉⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶ ⠀⠹⠅⠀⣸⢸⢈⣇⣯⣿⡇⢀⣾⠁⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠋⣻⢻⣿⠻⣷⣿⣿⣿⣿⠳⠃⣿⠠⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⡉⢁

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⠿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢿⣿⣿⣿⠿⠿ ⠟⠹⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⠁⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⡿⠀⠀⢸⣿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⣿⣼⣿⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢿⣿⠇⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣾⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠂⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⡠⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣧⣤⣄⣤⣴⠶⠟⠛⠛⠛⠛⠛⠛⠶⢦⣤⣀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣻⣧⡀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⠀⠀⠀⠀⠉⠍⢉⣉⣉⣽⣿⣥⠀⠀⠀⠀⠉⣽⣿⠯⢻⣦⡀⣀⣴⠞⠃ ⠀⠀⠀⠀⠀⣀⣀⣀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠙⢿⣏⠁⠀⠀ ⠀⠀⠀⣰⡟⠋⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣼⠿⣷⡄⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠀⢸⡏⠈⠘⣿⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⠀⢰⡟⢠⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠸⣿⠀⠀⣿⠀ ⠀⠀⠈⠻⣶⣄⣀⣠⣴⠿⠁⠊⠀⠀⠀⠀⢸⣏⣬⡿⠁⠀⠀⠀⠀⠸⣧⣴⠇⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠹⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣆⠀⠀⠀⢹⡆ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣤⡾⠃ ⡆⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⣇⣠⡾⠟⠋⠀⠀ ⣷⣀⣀⣀⣠⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣆⣀⣀⣀⣼⣟⣁⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡶⢤⡀⢰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣶⠶⢤⣄⣀⣹⣿⣄⠈⠙⠛⠛⠛⠒⠤⣀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣴⣦⡟⠣⢌⡙⠳⢶⣶⡿⣶⣤⣄⡘⢿⣌⣿⣾⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⡻⣿⣾⣶⣿⠟⠋⢉⡏⠹⡻⣿⣿⠳⣝⢷⡝⣄⠀⣠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠋⢀⣼⡿⡟⢉⡿⠃⠀⣠⠾⡟⣸⣻⡾⣿⣷⡘⢆⠳⣬⣿⣿⣧⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠷⣾⣿⣿⣿⢿⡗⢺⠃⢀⠔⢡⣼⣷⣿⣻⣡⢼⣿⣇⠈⢷⡁⢸⣿⡾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⣿⣄⢸⠀⢀⣸⣿⣿⣿⠵⢛⣟⣻⣿⣯⠀⠈⠻⣿⡏⠟⠷⠙⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣼⣿⣿⠀⣤⣿⡿⠭⠀⢀⣨⣿⣯⣽⡇⠀⠀⠀⠹⢧⣀⣀⡠⠖⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣼⣿⠇⠀⢀⣴⡿⠋⣩⡏⠙⡇⠀⠀⠀⠀⠀⠈⢏⢳⣤⣾⣯⣉⠻⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⢻⣏⣿⠟⠾⠟⠋⢀⣀⣩⠴⢺⡁⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⠿⠿⣿⡟⠁⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣿⡿⢿⣿⡿⢄⡀⠀⠀⠀⠀⠀⠚⡿⠷⣦⣤⣤⣀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠻⣷⣤⣀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⣠⣾⡽⣻⣿⢻⣿⣿⣿⠈⠻⡀⠀⠈⠛⣶⡖⠒⠒⠈⠀⠀⠀⠙⣦⠙⣲⣄⣀⣀⡴⢾⣷⣄⠀⠀⢀⣿⠻⠷⣦⡀ ⠀⠀⢀⣀⣀⣒⣿⣽⣿⣿⣸⣿⠛⢿⡝⣧⠀⠈⠢⡀⠀⢸⣷⠀⣠⣴⣶⣖⢺⣷⣾⡿⠿⠿⠟⣿⢥⣼⠟⢻⣷⣄⠀⠉⠻⢉⣉⣿ ⢀⠖⠋⠀⠀⠀⠀⠙⣷⡌⠛⢻⣷⠾⣿⣿⠂⣠⣤⣼⣦⣾⣧⣴⣋⣿⣯⣿⣿⣿⡉⠀⠀⠀⣼⠁⠘⠁⠀⠐⣿⣿⢦⠀⠀⠀⢹⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠒⠉⢹⣿⣿⣿⣿⣿⣄⠀⠘⣿⠀⠙⣿⣿⡿⠿⣿⣿⣷⣄⠀⡜⠁⠀⠀⠀⠀⠀⣿⡟⠀⠁⠀⠀⠾⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣴⣶⠿⠛⠁⠰⠟⠿⣄⠑⣾⡏⠀⠀⠈⢳⣇⣀⣿⣿⣿⣿⣿⠀⠀⠀⠐⢂⣀⣸⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⡿⣧⠀⠀⠀⠀⠀⠀⢸⣿⡟⡰⠀⣀⣼⣷⣿⣇⠉⣯⠉⠉⢹⠀⢀⣤⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣶⠻⣧⠊⠀⠘⣧⠀⠀⠀⠀⠀⢸⣇⢻⣰⠿⠛⢙⣿⣿⣟⠀⢸⡆⠀⠼⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡰⠋⡟⠀⢻⡏⠙⠷⣄⠀⣿⣆⠀⠀⠀⣰⣿⠏⠉⠁⣠⡶⠟⢋⣹⣿⣆⢠⠇⠀⣠⣶⣆⣤⢄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢈⡿⠓⢄⠀⠘⢦⣼⡇⢀⣠⠔⢹⠇⠀⢀⣾⠏⠀⠀⣺⢴⣿⣿⡏⠀⠀⣯⣩⣽⣼⣭⣤⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠟⠁⠀⠀⠀⢡⠀⠈⠛⢷⣼⣇⠀⡏⠀⢀⣾⡏⠀⢀⡜⠁⣾⣿⡿⠀⠀⠚⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠉⠙⣿⡇⠀⢸⡟⠣⠤⠋⢀⣼⠟⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢹⣷⡀⠘⣅⢀⣵⣶⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠺⣿⡿⡒⠚⠛⡹⣿⢿⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣈⣸⣾⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣶⣦⣤⣀⣀⣀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡿⢿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣿⡿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢧⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠖⠁⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣗⡾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⢉⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣷⡀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⣹⣿⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⢩⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⠁⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣁⣀⣉⡻⣿⣿⣿⣿⡿⠿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣿⣿⣿⣿⠷⠖⠊⠉⠉⠀⠉⡙⠻⠟⠈⠀⠀⢽⡿⠀⠀⠀⠀⠀⠉⠛⣿⡟⣿⡷⢦⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣸⡀⠀⣀⡠⠤⢤⡤⠤⢤⡀⠀⠀⠀⠀⢰⠖⠛⢻⣟⠓⠢⢤⠀⠌⠀⣏⢀⠀⣼⡿⠿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠳⣧⠀⢷⡀⠀⠘⠃⠀⣸⠁⠐⣦⠀⠀⠘⢧⡀⠈⠋⠁⢀⡜⠀⠀⢀⣏⡜⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⠀⠀⠙⠒⠒⢲⠿⠃⠀⠀⢹⠀⠀⠀⠈⠻⠖⠒⠒⠋⠀⠀⠀⢸⠋⣠⣿⠁⣾⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢹⣿⠘⣿⣦⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⡸⢹⡇⠸⡿⠿⠿⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣴⠛⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠤⠼⠉⠳⣄⠀⠀⠀⠀⠀⠐⠚⠛⠃⠀⠀⠀⠀⠀⠀⣻⠟⠁⠀⠀⠙⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡷⠐⠄⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣥⠀⠀⠀⠀⠀⠈⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡆⠀⠀⠀⡀⠀⠀⠀⠀⣹⣷⣦⣄⣀⣀⣀⣀⠴⠖⠉⠀⣽⡟⠀⠀⠀⠀⣠⠎⣀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠹⡄⠀⠀⠸⣟⣯⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠊⠁⠀⢿⠀⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠉⢳⡆⠀⠀⠈⢦⠀⣰⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠋⠀⠀⠀⢀⡟⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠁⠀⠀⠀⡈⢀⣽⣧⠹⠷⣤⣀⠀⠀⠀⠀⣀⣤⣾⣿⠆⢀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢹⢄⠀⠀⠀⠛⢸⡇⠙⢷⣤⡈⠉⠛⠓⠒⠛⠉⣠⣿⡏⣠⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠈⢷⠀⠀⠈⠙⠻⠶⠶⠾⠷⠟⣋⣉⣿⠃⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⡿⠲⢦⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡿⡅⠀⠀⠀⠀⠢⠀⢸⡆⠀⠀⠈⠉⠐⠀⠀⠀⠀⣯⣥⠌⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⠈⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢽⣇⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡍⢷⣔⡄⠘⠻⡄

⠀⠀⠀⠀⠀⡠⠔⠉⠁⡀⠔⣂⣤⠤⣤⢀⠉⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠀⡰⢈⣠⠞⠋⠀⠀⠈⡄⢇⠀⠈⠣⡀⠀⠀ ⠀⠀⢠⡆⢠⠁⡜⢠⣷⣻⢲⣶⠀⠀⣠⠀⠸⡇⡀⢀⠱⡀⠀ ⠀⠀⠉⡇⡇⢀⢃⣾⠏⡹⣷⡖⣚⣻⡼⠀⢰⢡⢡⠸⠀⢱⠀ ⠀⠀⠀⢇⣧⣸⢾⠃⠀⠀⠀⠙⠓⠊⣥⢃⠈⣸⡈⡄⡇⢸⠀ ⠀⠀⠘⢻⢹⡇⢀⡋⣁⠀⠀⢀⡀⢀⡟⣸⠣⣵⣇⢇⡇⠸⠀ ⠀⠀⠀⠀⢻⠁⠏⣉⡐⠫⣶⠝⠋⠈⠀⣿⡼⣿⡏⣾⢀⡆⠀ ⠀⠀⠀⠀⠸⣀⢰⡇⠈⠂⠈⠀⠀⠀⠀⣹⣲⣅⡷⠨⠚⠋⠒ ⠀⠀⠀⠀⠀⠛⣻⣿⣶⢤⣶⣶⣶⢦⡟⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠴⡈⠉⠑⡹⡉⠛⠿⡟⠓⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄ ⢀⠮⠉⠀⡀⣤⣶⠕⢣⠀⣠⡏⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶ ⢰⠄⠀⠀⢽⣯⠀⣠⣸⠘⣿⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠈⠂⠠⠀⠪⣿⣶⣿⠟⢀⣟⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⣾⣷⣂⠀⢻⣿⢷⣀⣼⡋⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡁⠀⣹⠁⠀⠀⠀⠉⠉⠐⣦⣤⣤⣄⣠⣤⣄⠀⣠⣤⣤⣄⣤⢤⣤⣤⣤⣤⡄ ⠀⡟⠒⢿⢷⣾⣴⣦⣀⠀⠀⠟⣿⣽⡟⣿⣉⣿⣿⣯⣉⣿⣿⡇⢸⣷⡆⢸⣿⠀ ⠀⢳⣤⣀⡘⠋⠉⠿⠧⣙⡾⢰⣿⠙⢳⣭⣿⠉⣤⡍⢛⣿⣯⣻⣾⢻⣯⣼⣯⡄ ⠀⠀⠻⡈⠉⠁⠢⡀⠀⡼⠁⢸⣿⣀⣸⣷⣆⣸⣿⣷⢿⣏⣿⡾⣿⣸⣿⣿⣷⡀ ⠀⠀⠀⠙⢦⣀⢀⡸⠎⠀⠀⠀⠛⠛⠙⠛⠋⠙⠁⠙⠉⠙⠋⠀⠉⠛⠁⠙⠛⠁ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣘⣿⣟⣿⣿⣿⣿⣿⣿⡿⠯⠿⠿⠿⢿⡿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⣟⡛⠻⠿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⢦⢀⣠⣄⠀⠀⠒⠒ ⣿⠿⠿⠾⢿⣿⣿⡿⣿⣸⣿⣟⠿⢿⣿⣶⣾⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢨⣿⡟⠉⠀⠀⣀⠀ ⣿⣆⠐⠀⢸⣿⣿⡿⣿⣿⡏⠉⢛⠦⣌⡿⣟⣸⡟⢀⣻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣍⡥⢿⣿⣿⣿⣿⣿⠿⠉⣠⠐⢻⠟⠀⢠⡀⣻⣿⣇ ⣿⣿⣷⣶⣼⣿⣿⡇⢿⣿⡇⢠⣽⡆⠀⠙⠲⣧⡇⢸⠉⠉⠙⠋⢠⠖⡛⢯⠝⠋⢁⡀⢸⣿⣿⡿⣁⣘⣴⣤⣿⣷⡯⣼⣤⣿⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⣿⡇⢸⣿⣿⣾⣿⣇⣀⣠⡄⢿⣷⠈⣷⠄⢠⡞⣯⡀⢙⣦⡀⠉⣥⢇⣾⣏⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠂⠹⣷⣿⣿⣿⣿⣿⣯⣷⡀⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢰⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⣿⣿⢿⣿⣿⠿⣿⣿⣷⣾⣿⣿⡼⣾⣷⣴⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢹⣿⣾⣿⣿⣦⣄⠙⣿⣿⢿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣧⣾⢸⣿⡇⢸⣿⣿⣿⣿⣿⣾⣶⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣯⣽⣾⣿⠏⣸⣿⣿⡄⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⠟⡇⠀⢘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣏⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠅⠀⠀⠀⠀⠀⢀⣤⡶⠾⠛⠋⠉⠉⠉⠈⠉⠉⠉⠙⠛⠶⢦⣌⡀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡗⠂⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣧⣿⣷⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠿⠃⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣠⣾⢿⠇⠀⢀⣀⠀⠈⠙⣷⣄⠀⠀⠀ ⠀⠀⠀⣼⣿⠁⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠶⣤⣤⣾⣿⠇⠀⠀⠀⢸⣿⠀⠀⠀⠸⢿⣆⠀⠀ ⠀⠀⣼⡟⠁⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⣄⡀⢀⡿⠋⠻⣆⠀⠀⠀⠀⢿⡆⠀ ⠀⢰⡿⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣠⡤⠶⠖⠒⠲⠶⢦⣄⣐⣀⠀⠀⠀⠋⢿⣷⠟⠁⠀⠀⠹⣆⠀⠀⠀⠀⢿⡄ ⢀⣿⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⣿⠿⠀⠀⠀⢀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣇⢀⠀⠀⠘⢻⡄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘⣷ ⢸⡇⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡿⡿⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢽ ⣿⠁⠀⠀⠀⠾⠷⠶⠶⠶⣶⣾⡇⠂⠀⡀⣰⡟⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢸⣇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢿⣿⠃⠀⠀⠀⠀⢰⣿⣿⠀⢈⣿⡇⠀⠀⠀⠀⠘⡇⣿⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⢻⣮⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡇⠈⠀⠀⠘⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠙⠛⠛⠓⠒⠒⠒⠛⠛⠛⢻⣌⣣⠀⠀⠿⣷⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⣤⣾⠛⠀⠀⠀⣸⡏⠀⠀⠀⠀⣼⠇⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⡄⠀⠹⣷⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢈⣾⠷⠀⠀⠀⢢⣾⠁⠀⠀⠀⢠⡿⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡆⠀⠀⠀⠹⢦⣄⡉⠉⠀⠀⠀⠊⢉⣠⡴⠛⠇⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣼⠇⠀⠀⠀⢠⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⠀⠀⠈⠙⠛⠓⠖⠒⠛⠋⠍⠉⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⣾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⣼⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⣀⣀⠀⢀⣀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⢀⣼⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠃⠀⠀⠀⣰⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠛⠙⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⠶⠶⠛⠛⠋⠉⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣄⡀⠀⢀⣀⣀⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⣸⡿⠗⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠇⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡿⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⡇⠀⢀⣿⠃⢀⣀⣠⣤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀ ⣼⣿⡇⢀⣾⣿⣿⠟⠋⠉⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢺⡄ ⣿⣿⣷⣾⣿⠋⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢰⡆⠀⠀⠀⣿⡄⠀⠀⠀⣀⢸⣇ ⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⡇⠀⠀⠀⢹⣾⡿ ⠈⠻⣿⣿⣿⣦⣄⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⣧⡀⠀⢀⣼⣿⠇ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣾⣿⣶⣿⣿⣤⣤⣴⣿⣿⣿⣿⠿⠟⠁⠀ ⠀⠀⠀⠙⢿⣿⣧⡈⠙⠛⠿⠿⠿⢿⣿⡿⢿⣿⣿⣿⣿⠿⠛⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣷⣶⣶⣤⡀⠀⠈⠻⠶⠀⠉⠉⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠟⠛⣿⣿⣄⠀⠀⢀⣀⣀⣀⣀⣀⣴⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠛⠛⠻⠿⣷⣦⣄⣀⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀ ⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⠀⠀ ⣴⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣦ ⣿⣿⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣿⣿ ⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿ ⢹⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇ ⠀⣿⣿⣿⣿⣿⡁⠀⠀⣿⣿⠀⠀⢈⣿⣿⣿⣿⣿⠀ ⠀⠹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠏⠀ ⠀⠀⢈⠙⠛⠿⠿⣿⣶⣦⣴⣶⣿⠿⠿⠛⠋⡁⠀⠀ ⠀⠀⠈⣿⣷⣶⣤⣤⣄⣀⣀⣠⣤⣤⣶⣾⣿⠁⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⠀⠀⢀⠀⢀⣉⡉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⠀⣿⣿ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠆⢸⣠⢿⣏⣙⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣉⣁⠀⠙⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠐⠒⡀⠀⠀⠀⠀⠀⠀⢈⣼⠀⣸⡄⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢹⡇⠀⠀ ⡀⠀⠀⡆⠀⠆⠘⣿⣧⣴⣿⣿⡟⠀⠀⠆⠀⠀⠀⠀⣠⣾⣿⣿⢂⣹⣥⣶⣿⣤⣶⣀⣀⣠⠀⠀⢀⣤⣄⠀⠀⢠⡾⠋⢠⣤⣶⣇⡀⠀ ⣿⡿⠿⢷⣦⣤⣀⣤⣼⣋⡉⠁⠀⠀⠀⢀⡀⠀⢀⣀⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣿⡿⣿⣷⣶⢟⠁⠀⠀⣀⣀⡉⢳⡀ ⣿⣇⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣭⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⠉⠉⠀⣼⠀⠀⠸⢿⣿⠟⢉⣿ ⣿⣿⠟⠛⠂⠀⠀⠙⡿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣴⠆⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⣤⠾⠋ ⣿⣁⣤⣶⣶⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠑⠀⣤⣤⣴⣾⣿⣾⣿⣷⣤⣶⣋⡁⠀⠀ ⣯⡉⠙⠿⠋⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠈⠻⢶⣤⣀⣀⣠⣶⣿⠾⠋⠉⢒⣶⡖⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣤⠀⠀⠀⣴⠟⠛⡏⠉⠉⠹⠙⠻⣧⡛⢹⡿⡋⢉⡙⠻ ⠀⠀⠀⠀⠈⣿⡿⠛⠁⠀⡤⠂⠉⠄⢻⡄⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠅⠠⠀⢹⠀⣀⡀ ⠀⠀⠀⠀⢸⡋⣀⠀⣠⠼⠁⠀⠸⠀⢸⣷⡀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀ ⠀⠀⠀⠀⠀⠙⠉⠉⠁⢠⣀⢀⠀⠀⢈⣿⡇⠳⢷⢳⡀⣦⡀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠆⢀⣸⣿⣇⠀⠀⠀⠀⢻⡻⣦⠀⠀⠀⠀⠀⠘⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠟⠋⠉⠈⠙⢷⣤⠀⠀⠃⢹⠷⣄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠁⠀⢀⣀⠀⠀⠈⣿⣇⣀⠀⣾⠛⠈⢷⣄⡀⠀⠀⠀⠹⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⢸⡆⠘⣿⣿⠆⢠⣿⣿⣿⣿⣿⣿⣦⣄⣈⣻⣦⠀⠀⠀⣠⠝⠛⠷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢀⠈⣿⣦⣈⣻⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠁⠀⠀⣀⣀⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠟⠛⠻⠿⠟⢻⣿⣟⠛⠉⠒⠛⠛⠛⠛⠛⠛⠻⣿⣿⠀⠀⠀⢰⣿⣿⠷⠒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⣄⠀⠈⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⣶⣤⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⣲⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⣼⡳⠋⠉⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⡿⠛⠓⢿⠃⡠⣄⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣤⡄⣀⣠⠤⠴⠒⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣿⣧⡀⣠⣯⣼⣆⠈⠳⡀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⡟⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⠿⣽⣿⡟⠉⡿⣷⡄⢹⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣷⣤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢄⡹⠈⠁⠐⠃⣸⠇⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⢀⣶⡻⣍⠙⠻⣧⠀⠀⢤⣤⠀⢀⣿⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠈⢹⢹⠹⡜⡆⠀⠈⡷⣤⣀⣀⣤⣾⣿⢏⠉⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⣀⡴⠿⠛⠒⠒⣾⡿⠀⢳⠸⣄⢀⡇⠈⠙⠒⠚⠛⠁⠀⢻⣼⡇⠀⠀⣀⣴⣶⣷⠒⢤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠒⠲⡿⠿⢏⣀⠀⠀⠀⠀⠀⠀⢀⣸⡿⢻⠖⡿⢩⠿⠤⡀⠁⠀⢹⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⡄⠀⠀⠀⡔⠁⣸⣰⠃⢰⣵⠛⠦⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⠤⠒⠉⠒⠒⠚⠳⣤⠋⢿⠀⠈⣿⢦⡄⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡄⠀⠘⢾⣷⣤⣤⣤⣶⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠒⠠⣄⠀⠀⢠⠖⣇⠀⠀⠘⠦⣀⠀⠉⠛⢻⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣄⠀⠀⠈⠉⠉⠁⠀⣸⠦⣄⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠑⢬⣷⡄⠀⠀⠀⠀⣰⡿⠀⠀⠉⠒⠦⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢹⠟⠒⠒⠒⠚⠛⠦⢄⣀⡀⠀⠀⣰⡿⠋⠀⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠚⠳⡄⠀⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢷⣠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠼⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠔⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢿⡓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠤⠤⢄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠼ ⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠀⠀⠠⠤⠐⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣾⠟⠿⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⣄⠙⠻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠿⠟⠋⣉⣁⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡼⣿⣿⣧⡀⠈⢙⣿⡿⠿⠶⢿⣷⣶⣶⣶⣶⣦⣤⣄⡀⢀⣴⣿⠟⠋⠁⣠⣴⣿⣿⡏⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⡄⠉⠀⠀⠀⣰⣿⠟⠋⠁⠀⠀⠀⠉⠛⠿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⠇⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣜⣿⡿⠋⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⣿⣿⣿⣿⣿⡿⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⢁⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⣸⣿⣶⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⢀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠏⢀⣴⣿⣿⣿⣿⣦⠀⡾⠀⠀⠀⣀⣴⣿⣿⣿⣿⣟⢓⣢⡶⠀⠀⠀⠀⠀⠘⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠟⠁⣰⣿⣿⣿⠟⢀⠙⣿⣾⡇⠀⣠⣾⣿⣿⡿⠿⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⡿⠗⢰⣼⣿⣿⣿⣿⠀⣹⣿⣿⣿⣧⣾⣿⣿⣿⠃⠀⢠⣤⣹⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀ ⣾⣿⣯⣤⠀⠈⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠄⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀ ⠀⠙⢿⣿⣄⠀⢈⣙⣛⣋⣥⣿⣿⠿⠛⠉⠁⠀⢭⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⠆⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀ ⠀⠀⠀⠻⣿⣦⣿⣿⣶⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀ ⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣾⣿⣿⠆ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⡉⣭⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣦⣤⣄⣠⣤⣴⣶⠞⠛⠋⠙⠓⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⡛⠛⠛⠋⠁⠀⠀⢀⣀⣤⣶⣮⣥⣴⣶⣶⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣶⣶⣶⣶⠿⠟⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣄⠦⡦⣆⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⡀⠀⠀⠀⠀⠀ ⠀⣀⣀⣀⣀⡐⣿⣿⣿⣿⣇⣀⣀⣀⣀⡀ ⢸⣿⠀⠀⠀⠀⢉⣻⣿⠋⠁⠀⠀⠀⢸⣿ ⠀⠀⠙⠀⠀⣼⣿⣿⣶⣿⣿⠀⠀⠈⠁⠀ ⠀⠀⠀⠀⣰⡟⠙⣿⣿⠟⠹⣇⠀⠠⠀⠀ ⠀⣖⣲⠿⠋⠀⣴⣿⣿⣷⡄⠙⠻⢶⡒⡆ ⠀⣿⢇⠀⠀⢸⣽⣿⣿⣿⣿⠀⠀⠠⢿⠇ ⠀⡇⠀⠀⠤⢼⣿⣿⣿⣿⠧⠤⠄⠀⠀⡇ ⠀⡇⠀⠀⣆⣿⣿⣿⣿⣿⠀⠀⡇⠀⠀⡇ ⠀⡇⠀⠀⣿⡿⢻⣿⣿⣿⠀⠀⠃⠀⠀⡇ ⠀⡇⠀⢾⣿⣷⣿⣿⣿⣿⣷⣤⣀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⣷⡀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢹⡇⠀⠀⣠⣶⡿⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢸⡇⣠⣾⠟⠋⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⣸⣿⠟⣡⣴⣿⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢠⣾⠟⢁⣴⡟⢁⣿⠁⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⢀⣴⡿⠃⣠⣾⠏⠀⢸⡿⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⣀⣤⣤⠀⣠⡿⠋⢀⣴⣿⣥⣀⡀⣸⡇⠀⢰⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣿⡏⠀⢀⣴⡾⠛⢩⣿⣼⡟⠁⣠⡿⢋⣨⣽⡟⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⢠⣿⢀⣴⡿⠋⠀⢀⣾⡿⠋⢀⣼⠟⠁⢘⣿⣯⠀⠀⣿⡇⠀⣼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⢸⣿⡿⠋⢀⣤⡄⠈⠛⠀⢰⡟⠋⠀⠀⢿⣿⣏⠀⠀⣿⠃⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣀⠀⠘⠛⢁⣴⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⢀⣼⢻⣇⢀⣼⠟⠁⠀⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡀⠀⠘⠁⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠉⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠛⢿⣦⡀⠀⠀⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⢻⣇⠀⠀ ⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣷⣤⡀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀ ⠀⠀⢀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠋⠈⠙⢿⣦⣄⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⣀⡀⠀⠀⢰⣦⢹⣷⠀ ⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⢠⣼⣿⣿⣷⣶⣶⠾⠿⠛⠛⠉⠉⠉⠙⠛⠻⣿⣦⠈⣿⣿⣿⡆ ⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⠁⣀⣀⣈⠉⠻⣷⡄⠀⠀⠀⢀⣀⣤⡶⠖⠛⣿⡇⢻⡏⠙⠃ ⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⡿⠛⠛⢿⣧⡙⢿⣦⠴⠞⠛⠉⠀⠀⠀⣰⣿⠀⢸⡇⠀⠀ ⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⢹⣷⠈⣿⡆⠀⠀⠀⠀⢀⣾⡿⠁⠀⠘⣿⡀⠀ ⣿⡇⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠹⣿⣄⠀⠀⣸⡿⠀⣿⡇⠀⠀⢀⣴⡿⠋⠀⠀⣀⠀⢿⣇⠀ ⣿⡇⠀⠸⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⢻⣷⣼⡟⠁⢠⣿⠃⣠⣶⡿⠋⠀⠀⠀⠀⢿⣷⣼⣿⡄ ⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠶⠟⠀⠀⠀⠙⠿⣷⣬⣉⣁⣠⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠙⠛⠃ ⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣋⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢸⣿⠀⠀⠀ ⠀⠀⠀⠙⢿⣶⣄⡀⠀⠠⠖⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠛⠋⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠻⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀

⠀⠀⠀⢰⢠⣥⡀⠄⢀⠃⡐⡀⡤⠖⠂⡘⡠⠄⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀ ⠀⠀⢀⢾⡈⠀⠆⠃⡌⡐⢎⠀⢀⠔⢜⠔⠀⠉⠀⠀⢀⣠⠀⠀⠠⢤⣉⡢⡀⠀ ⠀⠀⢸⡎⢗⢄⡀⠔⢐⣊⢘⣐⠁⢊⠎⢄⠒⢀⠔⠈⠂⠀⠐⡖⠀⢢⡁⠪⡞⠀ ⠀⠀⠈⢔⣄⣵⡠⠐⠒⠒⠲⠊⠁⠁⠀⠀⠀⠐⢝⣦⠈⠓⠫⣐⠖⡸⢜⠑⣥⠀ ⠀⠀⠀⠀⠀⡸⠐⢋⢉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⢉⠫⣤⠀⠁⣪⠘⣍⠉⢅⡃ ⠀⡠⢢⠻⡆⡇⣰⢁⠆⠀⠀⠀⠉⠓⢦⠀⠀⠁⠀⠁⠀⠈⢲⡲⠖⡆⠷⠈⠉⠈ ⡀⢇⠠⠀⢡⢤⣵⡣⠲⡒⠗⠞⡻⢖⠀⠀⠀⠴⢐⣒⡒⠀⠿⣿⣶⠛⢔⢧⣀⠠ ⣰⠋⠂⠵⣦⠞⣟⠇⠀⠐⠀⠉⠀⠀⠀⠀⠀⢚⠝⠤⠉⣹⢿⠹⣩⠑⠂⠤⠟⠊ ⠏⠦⠌⢂⡿⡌⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣸⢆⡇⠡⢫⡂⠄⡀⠀ ⠚⢪⣫⣜⢵⠏⣶⣬⣆⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡰⢼⣌⢮⢄⢢⠣⡈⢉⠉ ⠀⠀⠪⠄⠅⡺⣻⡝⣿⣶⣿⡀⠀⠀⠀⠀⠀⠀⣀⣴⢃⢁⠐⠁⠤⢭⠱⠈⠀⠈ ⠀⠀⠀⠀⠀⠁⢃⠇⣿⣿⣿⣿⣶⣤⣀⣠⠔⣯⣻⣽⣦⣍⣾⣶⣞⣁⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠙⠓⠘⠽⣿⣿⣿⡟⡛⠉⠀⢠⣿⣿⣿⣿⣿⣯⣽⡴⣶⡨⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⣄⠀⠀⠸⠿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣤⣤⣴⣶⣿⡿⣿⣿⣿⣿⣿⣷⣦⣄⣲⣾⣿⣿⣷⣖⠢⠤⡀⠀⠀⠀⠀