Steam Dot Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠉⠙⠲⠦⣄⡀⠀⠀⠀⠀⣀⣠⠴⠶⠒⠒⠛⠛⠒⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠂⠀⠀⠀⠈⠙⠓⠶⣤⡀⣿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠶⠒⠒⠂⠀⠸⠶⢤⣄⡀⠀⠀⢀⣀⠠⠤⠄⠒⠒⠀⠐⠒⠲⠦⠿⣷⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣞⣯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣧⠀⣀⣠⡤⠤⠀⠀⠐⠛⠛⠛⠛⠓⠲⠤⢤⣙⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⣚⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡘⣿⠉⠀⠀⠀⠀⣀⣀⣠⣄⣠⣠⣤⣤⣄⣀⣙⡛⢻⣦⡀ ⠀⠀⠀⠀⠀⠀⣠⠞⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠓⠛⠉⠀⠀⠀⠀⣀⣤⣤⣶⣾⣿⣯⣍⠉⠉⠉⠉⠉⢻⣠⡤⠖⠚⠉⠉⠉⣽⣿⣿⣿⣿⣿⣦⠀⠉⠉⠛⣿⠇ ⠀⠀⠀⠀⠀⣸⠋⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢶⣶⠶⠶⠒⠚⠋⢉⣼⣿⠉⣿⡿⠿⣿⣷⡀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⣾⣿⣠⣿⡏⠉⢻⣿⣷⠀⠀⢀⣸⠃ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣌⠙⠶⢤⣀⡀⣿⣿⣿⢻⣿⡀⠀⣼⣿⣧⣀⣴⣿⡷⢤⣀⣀⣀⡀⢸⣿⣿⣭⣿⣷⣶⣿⣿⠿⢶⣾⡿⠁⠀ ⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣌⣉⣛⣛⣛⣛⣛⡛⣛⣛⡛⣭⣴⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠉⠁⠀⠀⣠⠟⠁⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢀⣤⠞⠁⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠀⢀⣤⡤⠖⠛⠁⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠉⠉⠁⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀ ⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠉⠉⠉⠉⠉⠉⠉⠛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⢧⠀⠀⠀ ⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⣤⣤⠴⠶⠶⠶⠶⣤⣄⣀⠀⠈⠉⠉⠉⠙⠛⠓⠒⠒⠶⠶⠶⠶⠶⠶⠒⠚⠛⠛⠉⠉⠉⠁⢀⣿⡿⠀⠀⠀ ⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⢷⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠙⠳⠶⢦⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⢶⢿⠋⠁⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⠤⢤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠒⠒⠒⢛⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠟⠛⢷⣄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⢐⡆⠀⠉⠻⢦⣄⣉⠉⠓⠒⠶⠦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠈⠉⠛⠷⠶⣦⣤⣀⣀⠀⠈⠉⠉⠉⠂⠐⠒⠂⠠⠤⠤⠄⠀⠠⠄⠤⠤⠤⠀⠒⠂⣀⣼⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠾⠛⠋⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠷⠿⠿⠿⠾⠶⠾⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⡠⠬⡡⠬⡋⠀⡄⠀⠀⠀⠀⠀⠀⠀ ⡀⠁⠢⡀⠀⠀⢰⠠⢷⠰⠆⡅⠀⡇⠀⠀⠀⣀⠔⠂⡂ ⠱⡀⠀⠈⠒⢄⡸⡑⠊⢒⣂⣦⠄⢃⢀⠔⠈⠀⠀⡰⠁ ⠀⠱⡀⠀⠀⡰⣁⣼⡿⡿⢿⠃⠠⠚⠁⠀⠀⢀⠜⠀⠀ ⠀⠀⠐⢄⠜⠀⠈⠓⠒⠈⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀ ⠀⠀⢀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡀⠀⠀⠀⠀ ⠀⠀⢸⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀ ⠀⠀⠸⢸⣳⠦⣍⣁⣀⣀⣀⣀⣠⠴⠚⠁⠇⠀⠀⠀⠀ ⠀⠀⠀⢳⣿⠄⠸⠢⠍⠉⠉⠀⠀⡠⢒⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠣⣀⠁⠒⡤⠤⢤⠀⠀⠐⠙⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⡀⡼⠀⠀⠈⠱⡒⠂⡸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠀⠀⣾⣷⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣠⣤⣤⡄⠀⢠⡆⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⡇⠀⠀⣾⠃⣿⠀⠀⠀⠀⠀⠸⠁⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠶⠟⠛⠛⠃⠀⣼⠇⠀⣾⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⡿⠷⠶⣤⣟⠀⣿⠀⠀⢠⣴⠀⢠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣴⠿⢛⣿⣿⠁⠀⠀⠀⠀⠀⢰⡟⠀⣸⡏⢸⣿⡇⠀⠀⠀⠀⢠⣿⠀⠀⠀⣰⣿⠃⠀⢀⡾⠛⢷⣿⠀⢀⡿⠃⠀⢸⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⠋⠀⣀⣼⣟⠇⠀⠀⠀⠀⠀⣰⡿⠁⣰⡿⠁⢸⣿⡇⠀⠀⠀⠀⣿⠛⠀⠀⣼⡟⡝⠀⣰⠿⠁⣀⣤⡿⢳⣿⠁⢠⡄⢸⡆⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣴⣿⡿⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⣰⣿⣿⡇⢰⣿⠁⠀⢸⣿⡇⠀⠀⠀⢸⡿⠀⠀⢰⡿⠀⠇⣸⣿⢴⣾⣿⠋⠀⠞⠁⠀⢸⡇⢸⡇⠰⣿⡇⠀⠀ ⡆⠀⠀⠀⠀⠀⢸⡇⠀⣴⡿⠋⣼⡇⠀⢀⣾⣿⡏⠀⠀⠀⢀⣴⠟⠛⡏⣠⠟⠁⠀⠀⠘⣿⡇⠀⠀⢠⣿⠃⠀⢠⡿⠁⣸⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣷⡾⠁⠀⢻⡇⠀⠀ ⢿⡀⠀⠀⠀⠀⢸⣿⠾⠉⠀⢰⣿⠀⠀⣼⡿⠾⠂⢀⣩⣿⣿⣹⣿⣿⣿⠿⣦⡄⠀⠀⢸⣿⡇⠀⢠⣿⡏⠀⣴⡿⠁⢀⣿⣿⡿⠛⠉⠉⠉⠛⣿⣿⣿⣿⣿⠋⢰⠀⠀⠀⣿⣦⠀ ⠈⣷⣄⠀⠀⠀⢸⡿⡆⠀⠀⣾⠃⠀⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣦⡄⠀⠀⢸⣿⠃⢀⣾⡟⢀⡼⠛⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡶⠒⠀⠀⠀⢸⢿⣇ ⠀⠸⣿⣄⠀⠀⢸⡇⠇⠀⣾⡿⠀⣰⣿⣿⣿⡿⠿⠛⠒⠒⠚⠛⠛⠿⣿⣧⠐⠛⠀⠀⢸⣿⠀⣼⡿⣀⡼⠁⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿ ⠀⠀⠉⢿⣆⠀⢸⡇⠀⢰⣿⣁⣾⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⣿⣿⣶⡿⠛⠋⠀⠀⠀⣾⣯⡟⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⡟⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⢻⣆⢸⣇⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠰⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠃⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⣿⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠘⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣤⣄⠸⣧⡀⠀⠀⠀⠀⠀⢀⣤⡿⠻⣆⠘⢻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠒⠶⣤⣤⣄⡒⠲⣤⣀⠈⠙⠳⠿⣷⣦⣤⣶⣶⣶⠛⢫⣄⠲⣭⢂⡨⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠓⠲⢤⣄⡉⠙⠒⠶⠭⠉⠛⠲⠀⠀⠈⠹⣿⣿⠙⠲⠦⠌⠓⠮⠉⠁⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠹⣷⣍⡻⠿⠿⠷⠶⣶⣶⣶⣶⣶⠶⠖⠂⠀⠉⠁⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡙⣷⣮⣉⠛⠛⠷⠶⢤⣤⣌⣁⡀⠠⠤⠄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⠛⠛⠉⠁⠀⠀⣀⠀⢤⣀⡉⠛⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠀⠀⠀⠀⠀⠐⠂⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠉⠓⠲⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⡻⣿⡟⠶⠶⠶⠶⠶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣏⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠿⠛⠛⠛⠛⠻⠷⣦⣤⣄⣀⣀⣀⣀⣴⡾⣿⡿⠋⠁⠀⠀⠀⣼⣿⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣶⠀⠀⠙⢻⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢰⣾⠇⠀⠀⠀⠀⣼⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⡄⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⣿⠀⠀⠀⠀⣴⠟⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠋⠉⠁⠈⠉⠉⠉⠉⠉⠉⡉⣁⠀⠀⢠⣾⣿⠀⠀⢀⣼⠏⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⣿⣆⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⠀⢠⣖⣃⣀⣴⣾⠷⠶⠶⠤⢴⣾⡿⠏⠁⠀⣰⡿⠃⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⢻⣧⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⢀⣠⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠀⢻⣷⡀⠀⠸⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠀⠀⠀⠀⢀⣰⣿⠁⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣿⡇⠀⠀⢿⡆⠙⠛⢿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠃⠀⠀⢠⣿⠃⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⣿⠀⠀⠘⣿⡀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣄⣠⣤⡤⠤⠤⠤⠶⠶⠾⠛⠋⠁⠀⠀⠀⣰⡿⠃⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣇⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⣷⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⢀⣼⡿⠃⢀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⣿⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⡟⠻⠿⠶⠴⠴⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣶⡾⠛⢀⣠⣴⡿⣋⣀⠴⠛⠁⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⣩⡽⠞⠋⠉⠉⣉⣽⡿⢻⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣏⢩⡉⠉⠉⠉⠉⠁⠀⢉⡙⢻⣿⣿⣯⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢁⣤⣾⣉⣤⣤⡶⠶⠿⠋⠁⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡳⣄⠀⠀⡀⠠⠏⠀⠈⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣰⡿⠋⢀⣀⣀⣤⣤⣤⣤⣤⣤⣿⣥⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡈⠳⣦⡀⠀⠀⠀⠀⣿⠿⠿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢀⣼⣿⠶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠻⣄⠀⠀⠀⣿⠀⠀⣿⠋⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⠙⣷⣾⣷⡄⠀⡛⠀⢨⠃⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⡌⣷⣶⣾⠆⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣟⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⢤⣤⣤⠤⠤⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣄⠀⠀⠀⠀⢻⣷⡖⠻⣷⣿⣿⣿⡇⠀⡇ ⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠈⠷⣄⣠⡴⢚⠋⠉⠀⠀⠀⠀⣠⡏⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠛⣶⢦⢤⣀⡀⠀⠀⠀⠈⠻⣧⡀⠀⠀⢸⡇⠛⠛⢻⣿⣿⣾⣷⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠉⢸⠃⠒⠒⠒⡗⠚⢻⣿⡧⣄⡄⠀⠠⠤⠤⠤⠄⣽⡇⢀⣿⣼⡦⠉⠙⣒⢦⣄⡀⠀⠘⢷⡄⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⡆⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡏⡄⠀⠀⢰⡇⠀⣿⢸⡇⠀⣿⠀⠀⠀⠀⣇⠀⢸⡇⠀⢹⠻⡄⠀⠀⠀⠀⠈⢹⠶⢦⡈⣷⡄⢸⣧⠀⠀⢀⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⢸⡇⡇⠀⠀⢸⡇⠀⡏⢸⡇⠀⡇⠀⠀⠀⠀⣿⠀⢸⡇⠀⢸⠀⣧⠀⠀⠀⠀⠀⢸⡀⠀⠉⢻⣿⣹⠟⠀⠀⣸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣛⢸⡇⡇⠀⠀⣸⣇⢸⣷⣾⡷⢤⣿⠀⠀⠀⠀⣿⠀⢸⢸⡤⢼⣦⣿⡀⠀⢰⡆⠀⢸⠁⠀⠀⠀⣿⠻⣦⡀⢰⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⠸⡇⣧⣀⣶⣿⣿⣿⣿⣿⣿⣿⣟⠧⠤⠤⠤⠿⠷⠾⢸⣿⣿⣿⣿⣿⣷⣾⣧⣀⣸⠀⠀⠀⠀⣿⠀⠈⠻⢿⣿⣿⣿⣿⣿⣼⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡇⣿⠀⠛⣿⡟⣿⢿⣧⣴⣿⣿⣿⡆⠁⠀⠀⠀⠀⠀⠀⠀⢀⣯⣀⣿⣿⣿⣿⡟⢻⣿⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⡇⣿⠀⠀⣿⡇⠙⢺⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⡇⢠⠇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⢧⣿⠀⠀⣷⡇⠀⠈⠻⣖⣀⣶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠉⣹⣿⠇⠀⠀⡇⠀⠀⠀⢸⣧⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⢸⡇⠀⠀⠀⣼⠈⢳⡀⠃⠀⠘⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡀⠀⡏⠀⣸⠃⢆⠀⠀⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠠⣌⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡇⠀⡇⣠⠏⠀⢸⡀⠀⠹⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡄⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢠⡟⠁⣇⠀⢸⣧⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⡧⠘⣷⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣿⠀⣸⠃⣼⠀⠀⣿⠀⣾⡟⠀⣰⣿⣿⣿⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⡇⠀⣏⣿⡄⠈⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡞⠻⣄⠀⡇⠀⣿⠀⡿⠀⠀⣿⣠⢏⣠⣾⣿⣿⣿⣿⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢠⣿⡀⣿⢮⣳⡀⠀⠀⢀⡴⠛⠉⢩⣽⣿⠉⠉⠉⠉⠀⣹⠟⠛⣦⣬⣿⡇⢴⠿⣼⣧⣀⣴⣿⣟⠋⠁⣿⣿⣿⣿⣿⢿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⢿⣿⣶⣿⣿⣷⣶⣿⡗⣲⠞⢿⠉⢿⣄⣀⣠⣴⠞⠉⢀⡴⠋⠈⢹⡇⣸⣼⣿⣿⣿⣿⣿⠛⣧⡀⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠸⣿⡿⣼⡟⣿⣿⣿⣿⣿⡿⠛⠁⠀⠘⢷⣄⡈⠉⣀⣀⡤⠞⠋⠀⠀⠀⣼⢳⣿⣹⣿⣿⣿⣿⣿⠻⢿⡇⣿⣿⣿⡿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⡟⠃⠿⠇⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⣼⣿⢏⣿⠏⠹⣿⣿⣿⡟⠀⣸⡇⣿⣿⣿⣾⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡤⢤⣦⣼⣦⠀⢰⣻⣆⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠘⣿⣿⣷⠰⣯⣀⣿⣿⣿⣿⣿⣿⡇ ⣠⡀⠀⠀⠀⢀⡀⠀⠀⢠⡀⠈⠀⠙⢿⣆⢀⣿⣽⣷⡄⠀⣿⡿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇ ⠟⠁⠀⠀⠀⢀⠼⠂⠀⠀⠻⣷⣦⠀⠀⠹⣿⡁⠀⣾⣿⣄⣿⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⣛⡛⣿⣫⣽⣿⡇ ⠀⠀⠀⠀⣴⠿⢶⠤⣶⣶⣄⣼⣏⠀⠀⠀⢸⣧⣼⡿⠷⠶⢿⡄⠈⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢰⣆⣨⣇⣿⣽⣿⣿⡇ ⠀⠀⡀⣠⣾⣷⣦⣾⣿⣿⣿⣿⣿⣇⣀⣀⠀⣿⠏⠀⠀⠒⠲⢿⣆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠙⠛⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠀⠀⠀⠀⣠⣴⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣤⡴⠟⠋⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠛⣷⣤⣴⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⣻⡿⠀⠀⠀⠀⠀⢀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣠⣾⡿⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡾⢫⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⠟⢡⡟⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣰⠟⠁⢠⡿⠀⢿⡄⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢠⣾⠋⠀⢀⡿⠁⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣴⢿⡟⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣾⠋⠘⣧⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠀⢀⣤⡴⠶⠶⠶⠺⠷⡷⠶⠶⠤⣤⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠯⡉⠉⠀⠀⠀⠀ ⠀⢀⡼⠋⠀⠀⢀⣔⠤⠤⠄⣀⢀⠀⠀⠀⣀⠤⠄⠀⣀⠀⠀⠀⠈⠲⢄⠀⠀⠀ ⠀⣾⠁⠀⠀⠀⣾⠁⠀⢠⣤⡀⠙⢧⡶⠛⠉⣉⣉⠉⠻⡆⠀⠀⠀⠀⠈⠣⡀⠀ ⢰⣿⡀⠀⢀⠾⣿⢠⠀⠘⠻⠛⠀⢀⡅⠀⠘⠿⠿⠂⠀⡿⠀⠀⠀⠀⠀⠀⢣⠀ ⢺⠀⠀⢢⣆⡀⢘⢷⡥⣀⣀⣠⠖⠚⠓⢄⠀⠀⢀⣠⢜⠄⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡆⠀⠈⣿⣿⣦⡀⠈⠁⡾⣿⠀⠀⠀⠀⢹⣛⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠘⡀⠀⢸⣿⣿⣿⣀⣀⢳⣹⢦⣄⢀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀ ⠀⠀⠑⣄⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣯⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣴⣶⣿⣿⠟⠀⠑⢄ ⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⠀⠀⠀⢠⠊⠀⠀⣠⣜⣠⣦⡴⣦⣴⣿⣶⣿⣿⠾⠿⣿⣿⣗⣓⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⢠⣿⡴⣗⣶⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⢿⣯⡍⣿⡿⢿⡿⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⢹⣟⣿⣿⣿⣾⡿⢻⣿⣿⠛⠁⠛⠁⠈⠁⠀⠁⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⠀⠀⣼⡿⠛⠟⢁⡜⡰⠋⠀⣿⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡼⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⣻⡇⠀⢀⣾⡼⠥⠔⠒⣿⣿⠀⢠⠀⠀⢰⠀⣿⡀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠁⠸⢀⡟⠀⠀⠀⠀⢸⠸⡄⠸⡄⠀⢸⣸⠋⢻⠒⣿⣾⣄⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡏⠀⠀⢸⢷⡾⢿⣷⣶⣾⡆⢣⠀⣷⡀⢸⡟⠀⠀⢣⡇⠹⣿⡍⠚⠦⡀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⢰⣿⡇⠀⡄⢼⠀⠃⢸⣿⣿⣿⡇⠀⢣⣿⣧⠈⡇⠀⣰⣮⣿⣶⣾⣿⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀ ⠀⣾⣿⡇⠀⠃⠀⡇⠀⠈⠧⣤⡿⠁⠀⠀⠻⡏⢣⡇⠀⠉⣿⣿⣿⣿⠉⢹⡿⠂⢸⠀⠀⠀⠀⠀⠀⠇ ⠀⣾⣿⡇⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⠤⡶⠏⠀⠉⠀⠀⡆⢸⠀⠀⢀⠀⢸⠀ ⢰⣿⣿⣿⠀⠐⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⡌⠀⠀⠀⡜⠀ ⢸⣿⢿⡿⡆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠇⠀⡄⠀⡇⠀ ⢸⣿⣿⡄⢃⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⣸⢠⠀⠀⡇⠀⠁⠀ ⢸⣧⣿⡁⢸⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣿⡿⠀⠀⣸⡇⢸⠀⠀⡇⢰⠀⠀ ⠀⠉⢻⡇⢘⢧⠀⠀⣿⢻⣿⣟⣦⣀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⢸⣿⣇⠀⢰⢿⡇⢸⠀⠀⡇⢸⠀⠀ ⠀⠀⡤⠀⢸⠘⣇⠀⣿⣨⣿⣿⣿⣿⣷⠤⠔⠚⠉⠀⠀⠀⠀⢀⣾⣿⡟⠀⣎⣿⣇⣿⡆⠀⣧⡌⠀⠀ ⠀⣰⠇⠀⣿⠀⣿⡄⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⡤⠚⠁⢸⣿⠇⠈⣾⣿⣿⣿⣇⠀⣿⣇⠀⠀ ⣠⡏⢠⠼⠓⠚⠛⠿⢆⠋⠉⠙⠛⠉⠙⡇⣠⠤⠖⠊⠁⠀⠀⠀⢸⠙⠐⢿⢿⣿⣿⣿⣿⠀⢸⣹⠀⠀

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⣿⣿⡿⠿⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⣀⣀⠀⣀⣀⣤ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣤⠶⠶⠚⠛⠛⠛⠛⠻⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣀⣠⣤⣶⣶⣶⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿ ⣿⣿⣿⡿⠃⣀⣳⢯⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿ ⣿⣿⡟⠁⠀⠟⢳⣾⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢹⣿ ⣿⣿⠃⠀⠀⠀⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⢀⡆⣀⣿ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⡿⠀⠀⠠⣄⠀⠀⠀⣸⠂⠀⠀⠉⠀⠟⡼⠃⢹ ⣿⣧⠀⠀⠀⠀⠀⠀⣴⢣⡞⠉⠁⠀⠀⠀⠈⠳⢦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸ ⣿⣿⡀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿ ⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀ ⣿⣿⡿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⢦⡘⢷⡀⠀⠀⠀⠀⢠⣄⠀⠀⠉⠱⣄⣀⠀⠈⠉⠙⣥⣀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣝⢦⡀⠀⠀⠀⠘⢦⡀⠀⠀⢷⠈⠓⢦⡀⠀⠀⢮⠑⠲⣄⡀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣤⡄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣦⡀⠀⠀⠀⠙⢄⠀⠀⢧⠀⠀⠈⠓⠦⣌⣣⡀⠀⠉⠓⣶⢤⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠞⠁⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⣀⡤⠷⣏⠈⣧⣀⣀⣀⣀⠀⠈⠛⠦⡀⠀⠈⠙⠲⢭⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠈⢦⡀⠀⠈⣧⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢯⣀⡴⠾⠻⣍⣿⡿⠿⢿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠉⠓⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡟⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠷⠾⣿⣉⣘⣧⣀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣼⡿⠁⠀⣤⣾⣿⣿⣮⣿⣿⢦⣄⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣸⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣼⣿⣿⣴⣧⣄⠘⢧⣀⣿⣧⡐⠢⢀⠀⠈⠻⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⡄⠀⠙⢦⠀⠙⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣯⣒⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣿⣿⣿⣿⣿⢿⣿⠟⠻⣿⣿⣿⣿⡄⠀⠀⠱⠀⠈⣿⣿⠗⠂ ⠀⠀⠀⠀⠀⣠⣾⣿⠛⠉⠀⣀⣀⣀⡀⠀⠀⠉⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⣿⡏⡟⢿⣇⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⡏⠀⠀ ⠀⠀⠀⣠⣾⡿⠋⠀⢀⣴⣿⣿⠟⡻⠛⠷⣦⠀⠈⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠷⠾⣟⢷⣄⠀⣰⠟⠻⢿⣿⡿⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠀⢀⣼⣿⠟⠀⠀⣴⣿⣿⣿⣶⠀⠷⠤⠤⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡾⠀⠙⣳⣟⣀⡀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⣶⣤⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⠰⠛⠉⠀⠹⣯⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠏⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⡟⠛⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠀⠐⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡏⠀⠀⢰⠁⣿⣿⠿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠁⠀⠀⠇⠀⢻⣿⣠⡾⢿⡷⣄⡀⠀⣿⠛⣉⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⢸⡈⠛⣾⣷⠶⢯⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡄⠀⠀⠀⠀⠀⠀⢲⣶⣶⡚⢠⡼⠉⠀⠀⣰⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣧⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢄⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠛⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⠀⠀⠀⠓⢄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⠀⠀⠉⡝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠋⠻⣤⣀⡀⡀⣀⣠⡴⠟⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠉⠙⠛⠋⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣏⠉⠉⠛⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣿⣷⣆⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀ ⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢤⣶⣾⠿⢿⣿⣿⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀ ⢸⣿⣿⣿⣏⣿⣿⣿⣿⣿⣷⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⢿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠸⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢻⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⣿⣿⣿⣿⠘⠻⠿⢛⣛⣭⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⣿⣿⠏⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋ ⠀⠀⠀⠈⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣥⣿⢀⡜⠁⣾⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⣽⣏⡞⣠⠾⣿⣯⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⣿⡟⡴⠃⠀⣿⡞⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⠀⠀⠀⠀⡄⠀ ⣿⡽⠁⠀⠀⣿⣿⢸⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣸⣀⣀⣙⣷⣀⣀⣀⣀⣤⣤⣼⣿⣿⠯⠛⢷⠀⠀⠀⠀⢳⣠ ⣿⠁⠀⠀⠀⡟⢿⢸⣧⡄⠙⡟⠿⣶⣦⣤⣀⣀⣰⣃⣹⡄⠀⠀⠀⠀⠀⠘⣇⢹⡇⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⢿⣟⣿⣻⡿⠿⣿⡿⠛⠋⠉⢨⡇⢹⣦⠀⠘⣆⠀⠀⠀⢸⡿ ⠟⠀⠀⡄⠀⠀⢸⢸⢏⣇⠀⡇⢠⢸⡏⠛⠿⣿⣿⣦⣬⣿⡿⣿⣿⣾⡖⠀⢻⡸⣧⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠉⣁⡀⡆⠘⢿⡄⠀⠀⢸⡇⢀⣻⣧⠀⣿⣀⣀⠀⠈⣿ ⠂⠀⢸⠁⠀⠀⢸⢸⢸⠈⠀⡇⢸⢸⠀⠀⢠⢿⠁⠘⠉⠉⢿⡉⠉⠙⠂⠀⠈⣇⢻⡇⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠚⠉⠉⠓⠃⠀⠈⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣟⡀⢰⠀⢻ ⠀⠀⡼⠀⠀⣼⣿⢸⠘⠀⠀⡇⠈⣸⠀⠀⡾⡏⢀⣀⣀⠀⠈⣧⠀⢦⠀⠀⠀⠸⡌⢿⡄⠃⠀⠀⠀⣿⡀⠀⠀⠀⢸⢀⣠⠀⢀⣤⣶⢾⣿⣿⣻⡿⠉⠙⢿⣿⣿⢿⡟⠛⠃⡇⢸ ⠀⠀⡇⠀⠀⠸⡟⠲⢦⠀⠀⣧⣿⣿⣿⣽⣿⣷⣶⣄⣉⠳⢦⣈⣷⣨⢧⡀⠀⠀⢱⡘⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⢸⢋⣤⣾⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⣼⣿⡿⡇⠀⠘⢣⠀ ⠀⢰⡇⠀⠀⠰⣿⣄⡈⢙⣶⣿⣿⠻⠉⢻⣿⣿⣿⣿⣿⣿⣶⣄⡀⠹⣷⣆⠀⠀⠀⢷⡙⠀⠀⠀⢰⡏⣷⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡇⠀⠀⣿⣿⣿⣿⡇⠀⠰⣼⠀ ⠀⢸⠇⠀⠀⢠⡇⠙⢿⣍⣿⣿⠃⠀⡇⣿⣿⢿⣿⣿⣿⣻⡻⣟⣿⣶⣬⡻⣧⡀⠀⢼⣷⣄⠀⠀⣾⠇⢹⣠⣴⣿⠟⣿⣿⡏⠛⠻⠃⠀⣼⣿⣿⡇⠀⢠⣿⣿⠟⢠⡇⠀⢀⡏⣆ ⠀⣾⠀⠀⠀⡞⡇⠀⠓⠿⣿⣿⡆⠀⡇⡏⣿⣿⣻⡉⠙⣿⠟⠁⣿⣿⣟⡟⠿⠻⢦⡌⠻⣿⡄⢀⣿⠀⢹⡇⢀⡿⠀⣿⣿⣿⣦⣀⣀⣸⣿⣿⣿⡏⠀⠜⠛⠋⣀⢸⡇⠀⢸⢱⡏ ⢰⡟⠀⣠⡾⠁⡇⠀⠀⢀⣿⠹⣿⡄⣿⡇⢿⣿⣿⣷⡄⠀⠀⣸⣿⣿⣾⡇⠀⠀⠀⢹⣦⡹⣷⣼⠏⠀⢀⣇⡞⠁⠀⢻⣿⣿⣿⣿⣿⣿⣯⢛⡿⠁⠀⠀⠀⣤⡇⢸⡇⠀⡏⣼⢇ ⣿⣡⣾⣿⠃⢸⡇⠀⠀⣼⠻⡄⠘⣿⣽⡇⠈⣿⣾⣿⣿⣦⣾⣿⣿⣿⣏⡇⠀⠀⠀⢸⠏⢻⣾⣿⣶⣤⣾⡞⢀⡞⠀⢈⣿⣿⣿⣿⢿⣿⡿⠏⠀⠀⠠⣴⠸⣧⡇⢸⠁⠈⠁⢸⢸ ⣿⣿⢿⡏⠀⣼⡇⢀⣼⠇⠀⣷⡀⠈⢿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⣾⣰⣿⡏⣿⣿⣿⠿⣤⠏⠀⣰⠋⣴⢋⡛⣛⣋⣝⣁⣤⣴⡞⠙⠓⠀⠀⡄⢸⠀⠀⠀⠸⣼ ⣾⡿⣾⠁⢠⣿⠀⣼⣿⡀⠀⢸⣧⠀⠈⣠⢆⠀⠈⠙⠻⢿⣷⡾⠏⠀⢀⡠⣾⣿⣿⡿⣻⢟⣾⣿⣿⠃⣰⠃⢀⡾⢁⡾⢩⠿⠛⣳⢿⢟⡿⠋⡽⢃⡀⠀⢀⡼⡇⣿⠀⠀⠀⠀⣿ ⣽⣽⠇⠀⣼⣟⣞⣋⣼⣇⠀⠀⢿⡀⠈⠱⠟⠒⣦⣄⡀⠀⢀⣀⣠⣴⡏⣰⢋⣾⡏⣴⢻⣿⣟⠛⠃⣰⠃⢠⠟⢠⠞⣰⠋⡼⡿⣱⣯⠞⢠⡟⣡⣾⢦⠞⡾⣹⠀⡿⠀⠀⠀⠠⢻ ⣿⡏⠀⢸⣿⣿⢟⣽⣿⣿⠀⠀⢸⣇⡸⠀⣠⡴⠋⣿⡿⣛⠛⣽⡿⠋⣰⢣⠏⡞⣼⣱⠿⠃⠙⠧⠘⠁⠀⠏⣰⠏⡰⠃⢼⡟⠱⣻⠃⢠⠟⡴⣿⢣⢋⠞⢀⣵⣾⡇⠀⠀⠀⠀⢺ ⡿⠀⠀⠏⢹⣃⣿⣿⣿⣿⡆⠀⠀⣿⣇⣾⠟⢁⡞⣟⡵⢃⣼⡟⠁⡼⣱⢃⡞⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⡴⠁⠐⠃⢀⣾⣤⡼⠁⢠⣏⡜⣽⠁⢠⠏⣠⠾⢃⣿⠃⠀⠀⢠⠃⠘ ⢁⣤⡶⢾⣿⣏⢻⣟⣿⣿⡇⠀⠀⣿⣿⠏⣠⢏⣾⠟⢠⣞⡞⢀⡞⢱⢃⡞⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣈⣠⠤⠖⠊⠉⢻⣿⠃⠀⠉⠉⠈⠹⠞⣡⣾⡷⣁⣼⣿⠀⠀⣠⠆⠀⠀ ⣋⣥⣾⣿⣿⣻⠈⢿⣿⢿⡇⠀⢠⣾⡏⡰⢃⣾⠏⢠⢿⠞⠀⠎⣀⠐⢦⣤⣤⠤⠖⢲⡖⢲⠒⠋⠉⠁⠀⡀⠀⠀⠒⢋⡿⠃⠀⠀⠀⠀⣀⢸⣾⣿⣿⣷⣿⣿⡜⠀⢀⣾⣏⠀⠀ ⣯⣼⡟⢻⣻⣿⣦⠈⠛⢛⣿⠀⣹⡟⡿⣥⣿⠏⣠⢿⠏⢀⡀⣄⣸⠀⠀⠻⣿⣗⣒⣒⣧⣶⠒⠚⠉⢉⣀⣀⣠⣄⡀⢻⠀⠀⠀⠀⢀⣠⣿⣼⣿⠋⢹⢹⣿⣿⡇⠀⣼⣿⣝⣆⠀ ⣿⠉⠀⠈⢿⣏⣿⣾⣿⠿⣿⢰⡿⠄⠀⠻⠛⣶⣧⣀⢰⡄⢻⡄⠀⠀⠀⠀⠈⣀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢷⢸⠀⠀⣠⣴⣿⣿⣿⡟⠁⠀⠸⣾⣿⢸⡀⢠⣿⡏⠀⢈⣷ ⢿⣆⠀⠀⠈⣿⣽⣷⡀⠀⣿⡿⠁⠀⠀⠀⠀⠁⠈⠛⢿⣿⣴⣧⣤⣤⣀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣿⡌⡇⣾⡏⠀⠀⣼⠟ ⠈⢻⣧⠀⠀⠸⣿⡿⣷⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢿⣿⣿⣿⣿⣶⣤⣄⡏⣾⠁⠀⠐⠄⢢⠀⠀⢀⣠⣾⣇⣽⣿⣿⣽⠋⠀⠀⠀⠀⠀⣼⣿⢹⣇⢹⣸⠃⠀⣸⠏⣼ ⠀⠀⠻⣷⡄⠀⠻⣿⡞⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⣿⣿⣶⡦⣼⣼⣤⣾⣿⣿⣿⣿⣿⣿⢟⣿⣦⡀⠀⠀⠀⢰⡿⢸⠈⣿⠀⢿⡆⢰⡟⣰⠏ ⠀⠀⠀⠘⢿⢀⠀⠈⢷⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣯⣿⡿⣿⣿⣧⢻⣿⣿⣿⣿⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⣦⡀⢰⡿⡇⢸⡆⢸⡇⠀⢡⡟⢰⡏⠀ ⠀⠀⠀⠀⠘⣆⠀⠀⠈⣳⣷⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠸⣷⠙⢷⣌⢹⠻⢼⣿⣿⣿⣿⣿⡿⢛⣿⣿⢟⣽⡿⡟⠁⠀⠀⠀⠙⢷⣄⣀⡀⢸⣧⠘⡇⢀⡿⢡⡟⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣯⣽⣟⠿⠟⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⡹⢁⣴⣷⣿⣿⣷⣆⣤⡀⠠⢬⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⠿⠩⢠⣿⣿⣿⣿⣿⣏⣿⢸⣿⡖⣄⠹⣷⡌⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣼⠂⢸⣿⣿⣾⠯⢟⠋⠿⣿⡿⣳⡿⣳⣿⣷⡈⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⢡⣿⡀⢻⣿⣿⣷⣭⣯⡆⢰⣤⣥⣶⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣤⡈⠛⠛⠙⠛⠁⣸⣿⣿⣿⣿⣿⡿⠉⣤⣤⡉⢻⣿⣿ ⣿⣿⣿⣿⣿⠿⠛⢋⣉⣁⣈⣉⣀⣈⣉⣉⣉⣁⡐⠚⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡀⢿⣿ ⣿⣿⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿ ⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿ ⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⠇⣸⣿ ⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣧⡈⠛⠿⠋⢠⣿⣿ ⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣾⣿⣿⣿ ⣿⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿ ⣿⣿⣿⣆⠘⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿ ⣿⣿⣿⠋⣠⣶⣶⣶⣶⣶⣶⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿ ⣿⣿⠃⣰⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿ ⣿⡏⠀⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿ ⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿ ⣿⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿ ⣿⣿⣷⣄⠙⠿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿ ⣿⣿⣿⣿⣷⡄⢀⣉⣩⣿⣿⣿⠋⢠⣄⣀⣀⣀⣀⡀⢶⣿⣿⣿⣿⣿⣿⣿⣿⡏⢁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⡿⢁⣼⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⡿⠃⣰⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠉⠛⠻⠿⠏⣠⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⣈⠉⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⣤⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⣿ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⠿⠿⠿⠻⠿⠿⠟⠿⠛⠉⠀⠀⠀⠀⠀⣸⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣹⡆⠀⠀⠀⠀⠀⠀⣭⣷⠀⠀⠀⠸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠉⠀⠀⠤⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣷⠀⠀⠀⠀⡠⠤⢄⠀⠀⠀⠠⣿⣿⣷⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠷⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣠⣀⣤⣴⣶⣶⣾⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠻⣧⡀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⢀⣠⣴⣾⠿⠟⠛⠛⠋⠉⠉⠙⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢳⢒⣛⡶⣤⣄⡈⠷⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢀⡾⠛⠉⠀⢤⢶⣶⣲⣖⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⣹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣾⢣⣴⣶⣶⣿⣿⣿⣿⣿⠛⣿⣿⠳⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢩⡿⠙⢿⣿⣿⣿⣿⣿⣟⢻⣿⡆⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢺⣟⣿⣿⣿⣿⣿⣿⣁⣿⡿⠀⠈⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⠻⢿⣿⣿⣿⣿⡿⢠⡇⠈⡇⠰⣚⣿⣿⣷ ⠀⣀⣀⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿⠟⢁⣤⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠾⠾⠭⠭⠴⠿⠁⠀⠙⠞⠁⠀⣼⠁ ⢸⡗⠮⣍⣻⡏⢿⣬⣛⣛⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀ ⠈⣧⠀⠀⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀ ⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣻⡀⠀⠀ ⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⡀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣨⡵⠛⣷⠀⠀ ⠀⠀⠀⢀⡼⡃⡂⠀⠀⠀⠀⠀⢰⣴⣶⡈⠀⠀⣀⡀⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣵⡶⠟⠋⠀⠀⠀⠀⠀⠀⢀⡟⠉⠀⠠⣿⠀⠀ ⠀⠀⠀⣾⡏⡉⠋⠳⡆⠀⠀⠀⠈⠁⠉⠛⠿⢿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⡾⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣀⠀⠀⣿⠀⠀ ⠀⠀⠀⢿⡇⣇⠀⠀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠰⢦⣤⡿⠋⠀⠀ ⠀⠀⠀⠘⢷⣉⠃⢀⣿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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