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⠐⣄⠀⠀⠀⠀⠈⠳⣽⣄⠀⠀⠀⠈⢢⠀⣫⣷⠂⠀⢳⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣰⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀ ⠀⠈⠳⣄⠀⠀⠀⠀⠈⢮⣦⠀⢀⡠⠞⠋⣁⡼⢧⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠱⣆⠈⢧⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠐⠁⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠹⣿⢋⣠⠴⠛⠁⠀⠈⢧⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⡘⠀⢠⠏⠀⠀⠈⢳⡀⠙⣆⣰⠃⠀⠀⠀⠀⠠⠃⠀⠀⠀ ⣄⠀⠀⢀⠀⠈⠳⣄⠀⠀⠀⠚⢻⡀⠀⠀⠀⠀⠀⢈⣷⣶⣿⣶⣿⣷⣶⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣅⣀⡞⠀⠀⠀⠀⠀⠙⢦⡜⢧⡀⠀⠀⠀⠊⠀⠀⠀⡠⠾ ⠈⠓⢆⡀⠙⢦⡀⠈⠳⣄⠀⠀⠀⠙⢦⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⣦⡄⠀⣠⠞⠛⠀⠓⢀⠞⠀⠀⠀⢀⠘⠁⠀ ⡄⠀⠀⠙⠦⣄⠙⠢⠀⠈⠳⣄⠀⠀⠈⠳⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣟⣽⣷⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⡴⠃⠀⠀⢀⡔⠃⠀⠀⢀⠀⠀⠀⠀⢀ ⠉⠳⢦⡀⠀⠈⠳⢤⡈⠀⠀⠈⠳⣄⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⡴⠉⠀⢀⣠⠄⠁⠀⠀⠠⡀⠀ ⠀⠀⠀⠙⠳⢄⡀⠀⠙⠢⣀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡴⠋⠀⢀⡠⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢤⣀⠀⠀⠀⠉⢲⣤⣤⣼⣶⣿⣿⣿⢟⣭⣾⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣼⣿⣿⣿⣿⣄⢀⡴⠊⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠ ⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠃⠀⠸⣿⣿⣿⣏⣿⣿⣿⣿⣿⡆⠀⠀⠀⠁⠀⠀⠀⢀⡠⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⣿⡿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⠄⠊⠁⠀⠀⠀⠀ ⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠋⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣤⣤⣀⣀⡄⠀⠀⠀ ⠀⠀⠀⠈⠀⠂⢀⣀⣴⣾⣿⣿⣿⣿⣿⢧⣿⣿⢟⣫⣿⣿⣿⣿⣿⡿⠋⢸⣿⣿⣟⣁⣀⠀⢟⣰⠀⠀⠀⣄⣄⣀⣤⠤⠴⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀ ⠀⠀⠠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣻⣵⣿⣿⣿⣿⣿⣿⠋⠀⠀⣾⡿⠁⠤⣬⡍⠛⢯⠟⠀⠀⠀⠈⠁⠠⠤⠄⠀⢸⣟⠀⢻⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⢿⣿⣥⣾⣿⣿⣟⣾⡿⣿⣿⣯⢠⡴⠶⠿⠿⢿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⣴⡶⣿⣛⠛⠛⠻⠶⢸⣿⡟⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣼⣯⣷⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀ ⠤⠄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⣿⣇⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⡿⠟⠀⠀⠀⣿⣿⣧⡟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣾⣿⣿⣿⠿⣒⣶⡶⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠯⠭⠏⢠⡇⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠟⣿⠘⢾⣿⣿⡟⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠋⠉⠀⠀⢈⣧⡀⠻⣿⡷⣄⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⣤⣠⠴⠆⠀⠀⠀⢀⣴⣿⡿⣿⣶⣽⣃⣀⠁⠘⠇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠙⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⡠⠤⠀⠒⠉⠁⠈⠻⣿⣿⣿⣿⣶⣶⣿⣿⣿⣳⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢰⡿⠒⠆⠀⢹⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⣤⣄⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣳⣿⡿⣟⡏⣼⣿⢧⡉⠳⢦⣀⠀⠀⠀⠀⠘⠗⠒⠒⠲⠾⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁ ⠀⣀⠠⠌⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣫⣵⣾⣿⢹⣷⣿⠀⠙⠲⢤⣈⠙⠲⠤⣄⣀⣀⠀⠀⠀⣀⣠⠴⣾⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠈⣧⣄⡀⠀⠈⠉⠓⠒⠒⠭⠭⢽⠓⠛⠋⠁⢠⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣹⠀⠀⠀⣿⣿⣿⣷⣶⣦⣤⣀⣀⠀⠀⢻⠀⠀⣴⣶⣿⠈⠻⢿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⡠⠾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠁⠀⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠀⢸⣿⣿⣿⠀⠀⠱⣌⠻⢄⡠⡀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠠⠒⠀⠄⠂⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⢠⠃⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⢸⠀⣸⡿⣻⣽⣧⠀⠀⠈⢆⠀⠛⣞⢦⡀⠀⢄⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀ ⠐⠈⠀⠀⠀⠀⣰⣿⣿⣿⣿⢷⣿⣿⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⢣⠀⠈⢳⡳⡄⠀⠳⢤⡀⢹⡀⡀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣾⣿⠃⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⢻⣿⣿⣿⣿⣿⡆⠀⠀⠀⢷⠀⠀⢹⡈⢧⡀⠈⢳⡄⢳⡀⠀⠀⠀⠀⠀⠄ ⠀⠀⣰⣾⣿⣿⣿⣿⠟⠋⣽⣿⠃⠀⠀⠀⠐⠀⠀⣇⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢹⣿⣧⣄⢀⣼⣿⣿⡿⠿⠿⠿⡀⠀⠀⠈⣧⠀⠀⢻⡀⠳⣄⠀⢳⡀⢳⡀⠀⠀⠀⠀⠀ ⠐⠛⠛⠉⠉⣠⠞⠁⠀⠀⣿⡻⠃⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⡆⠐⠒⠒⣷⠀⠀⠠⠘⡆⠀⠀⢷⠀⠈⢦⡀⢳⠐⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠁⠀⠀⠀⣰⢿⠟⣆⡠⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡄⠀⠀⢳⣽⡄⠀⢈⢧⠀⠀⠱⣔⣄⠈⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⢀⡜⢳⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢆⠀⠀⢳⣷⠀⠘⢿⣆⠀⠀⠘⢮⣢⡀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⣠⣺⠟⠁⣴⠋⠀⠀⠙⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⡜⡆⠀⠈⢫⠀⠀⠘⣿⡄⠀⠀⠈⠻⣕⠄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠊⠉⠁⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠋⠁⠁⠉⠉⠓⠌⡉⠂⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣀⣖⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠈⠓⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣿⣯⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠿⣟⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡉⠁⠀⡀⠀⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
/\___/\ (=✪o✪=)
(∩˃o˂∩)
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⢀⡴⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⣆⠀⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠉⠳⠦⠤⠤⠶⠶⠶⠶⠴⠟⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⢀⡏⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢸⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀ ⠀⠀⠈⠓⢦⣄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢀⣀⣀⣀⣠⡤⠴⠚⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣦⡀⢀⡀⠀⣀⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠿⠽⣿⣿⣿⣾⣿⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠭⣿⣿⢻⣟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣿⣧⠖⠴⡀⠀⡢⡤⢏⣿⣿⣝⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡷⣿⡷⠀⠀⣴⣬⡆⢻⡟⣣⠱⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡇⠀⠀⠀⠀⠀⠉⠀⣾⣯⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⠀⢀⢼⣿⢿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢿⢿⣅⡒⢒⣈⣵⣿⠻⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢜⣿⣇⣿⣿⣿⠟⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣸⣽⠛⣿⣿⡟⠀⠀⠳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣴⣿⣿⣿⣿⠉⡇⠀⢸⠀⢡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣿⣿⣷⠛⣿⣷⣶⠁⠀⠈⣠⠁⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢲⠀⢿⣿⣻⣿⣿⣿⣿⠀⠀⡜⠸⠀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠘⢀⣿⣿⣿⡏⣻⣿⣿⠂⡐⠀⡀⠀⢰⡀
⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬜⬛⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛⬜⬜ ⬜⬛⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬛⬜ ⬛⬜⬜⬜⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬛ ⬛⬜⬜⬛⬜⬜⬛🟨⬛⬜⬜⬛⬜⬜⬛ ⬛⬜⬜⬜⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬛ ⬛⬛⬜⬜⬜⬛🟨🟨🟨⬛⬜⬜⬜⬛⬛ ⬛🟨⬛⬛⬛🟨🟨🟨🟨🟨⬛⬛⬛🟨⬛ ⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬛🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨⬛⬜ ⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬛⬛🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜
⣿⡀⢻⣿⡄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠒⣄⠲⣄⠀⠀⡀⠸⣿⣼⡟⠛⣉⠙⠿⣦⣔⠠⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⣿⡇⠈⢿⣷⡀⠀⠀⢈⠀⠁⠘⢦⡀⠀⠀⢺⠩⣍⠱⣌⠚⡄⢣⠘⢢⠀⣌⣷⡿⣿⡮⠀⠀⠈⠄⡙⢻⣧⡀⠎⣀⠀⠘⣧⠂⠄⠀⠘⣿ ⣿⡇⢡⠈⢿⣷⡀⠀⠀⠂⢀⣠⠜⣿⣄⠀⢃⠳⡌⡱⢠⠩⡐⢡⠉⠴⠿⢻⣯⠄⣻⣷⠀⠀⠀⠀⢠⣷⠙⣿⣔⠀⠆⡀⢸⡇⠘⡄⠀⢹ ⢹⣿⠀⡌⠌⢿⣷⠀⠀⠁⡸⠄⢎⡘⣿⣧⡀⠓⡌⡑⢂⠱⢈⢂⠩⠐⠠⢘⣿⡆⠸⣯⠀⠀⠀⣠⣿⡏⢀⠈⢿⣶⡈⠐⠠⣿⠐⠌⡄⠘ ⠘⣿⡆⠀⠈⠌⢻⣷⡀⠀⢰⣉⠆⡒⠸⣿⣷⡀⠐⡡⠂⠔⡀⠂⠤⠉⠄⣈⡿⡇⢐⣯⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠂⣽⠂⡱⢠⠀ ⠀⢿⣿⣶⣶⣶⣶⣿⣿⣿⠟⢋⠱⡈⢁⢻⣟⣷⡄⠡⠌⡐⠠⢁⠂⡁⢂⠐⣇⢏⣾⣿⡿⠛⠉⠉⠈⠁⠉⠙⠛⠿⣿⣿⣧⣼⡇⠰⢡⠀ ⠀⠸⣷⡀⠄⠀⠀⠀⢬⡿⣦⡀⠁⠆⠡⠈⣿⡼⣷⠀⡐⢈⠐⡀⢂⠐⢠⡘⣤⣿⣿⠋⠀⣠⣶⣶⣿⣾⣶⣦⣄⠀⠘⠻⣿⣿⣆⣡⠂⠆ ⢀⠀⢻⣷⠈⣤⠀⠀⠀⠀⡹⣷⣌⠠⠁⠂⢹⣧⢿⡇⠀⠌⡀⣠⡤⢞⡡⠐⣾⣿⠏⠀⣾⠿⢿⣿⢿⣮⡉⢹⣿⣷⡄⠀⢙⣿⣿⡟⢁⠂ ⢀⠂⠈⢿⣆⣿⡇⠀⠀⠀⢀⣈⠻⣦⣐⣌⢈⠡⠌⣛⣤⠷⠛⠙⠋⠉⠀⢀⣿⠿⠀⢐⣿⠀⠀⢻⣇⠘⢿⣯⣵⣿⣿⡄⠀⠸⣿⣿⡀⠌ ⠠⠈⡔⡈⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣭⡀⠌⡐⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣠⣤⣿⠀⠀⢉⣥⣿⣿⣧⠀⠐⣿⣿⣅⠠ ⠠⢡⣹⣿⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣯⣭⣴⣶⠾⠟⡀⢸⣿⠀⠀⡔⢿⣷⣦ ⣀⣷⣿⣿⡿⠋⠀⢀⣠⣶⣾⣷⣶⣤⡀⠉⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠩⢍⠁⠀⠀⠈⣼⣿⠀⣴⡇⢺⣽⣿ ⣼⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⢋⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⢿⣔⡢⢀⠌⣀⣲⣿⢃⣼⣟⣿⠛⡩⠄ ⣾⣿⣿⠀⠀⠀⣿⠃⠀⢻⣏⠻⣿⣾⣓⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠋⠁⢻⣽⡟⢄⠣⣔⣽ ⣻⣿⡧⠀⠀⠀⣿⡅⠀⣀⣻⡅⠈⠉⢉⣹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠡⠈⠻⣾⠶⠿⠛⠉ ⣿⣿⡗⠀⠀⠀⢹⣿⣶⣿⠟⢀⣀⣠⡿⢏⠀⣹⣿⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢂⠁⠠⠐⠠⢁⠌ ⣿⣿⣿⡀⠀⠀⠀⢻⣿⣿⢾⡟⠛⠋⠀⠀⠡⢌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄⢁⠂⠌⡠ ⠈⢿⣿⢿⣤⠀⠀⠀⠙⢿⣿⣄⠉⠆⢀⠐⣠⣿⡿⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠈⡀⠄⠂⣅ ⠀⠈⢿⣷⡜⢃⠀⡀⠀⠀⠙⠻⠿⣶⣾⠾⠟⠋⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠣⣸ ⡀⠌⢢⠹⣿⣦⠠⡑⠂⢶⣶⣴⣦⢦⡄⠠⢀⠐⡀⠂⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⡤⢓⣌⢻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⣴⣿ ⠟⢦⣴⠒⡈⠛⣷⣾⣁⣾⣥⣶⠿⢾⣶⣄⠂⠐⡀⠡⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢩⢆⢣⣻⡇⠀⠀⠀⡀⠠⠀⡁⠈⢀⣼⣿⢟ ⡘⠤⠹⣿⣌⠓⣠⣿⠿⢋⠍⡐⢎⣰⣻⣏⠀⠂⠄⡁⠄⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣋⢮ ⠨⠜⣱⠘⣿⣿⣿⣇⠘⡌⣌⣱⣦⡿⠛⠀⠠⠁⢂⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⢀⠀⣀⣴⣿⣿⣿⣷⣿⣶ ⢈⠒⡡⢉⠜⣿⣯⡻⠿⠿⠛⠛⢁⠠⠐⠈⠄⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⣤⣴⣾⣿⡿⢟⡛⡭⠰⡌⢿ ⠀⢈⠐⠡⢈⣹⣿⣿⣷⣾⣥⣬⣤⡂⡈⠐⠠⠁⠂⠐⠈⡐⢀⠂⠄⠠⡀⠄⡀⢀⠠⡀⣄⣠⣤⣤⣬⣶⣿⣿⣟⣫⡕⣎⢧⡹⣜⣳⡜⣸
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⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⣀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢦⣤⣤⣀⣀⡀⠈⢻⣿⣿⣦⣤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠴⠶⣶⣿⣿⣿⣿⣿⠃⣰⣿⠿⢿⣿⣿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⠀⣿⡇⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠿⠿⠿⠀⣿⣧⡀⣠⣿⣧⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠘⠛⠛⠃⠀⠀⠀⠀
⠐⣄⠀⠀⠀⠘⢿⣄⠀⠀⠈⣆⡨⢷⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠈⠑⢄⠀⠀⠀⠹⣦⡤⠚⣉⠤⠚⢣⠀⢱⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣶⣦⣄⠀⠀⠀⠀⠀⢰⠁⠘⢦⠘⢆⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠳⣄⠀⠀⠨⢶⡉⠀⠀⠀⠀⣣⣤⣧⣤⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⢀⠃⠀⠀⠀⠱⣌⢿⡀⠀⠀⠀⠀⠀⠀⠠ ⠈⠢⣄⠐⢄⠈⠳⣄⠀⠀⠱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠀⢠⠞⠃⠙⡠⠂⠀⠀⠀⠀⠀ ⢦⡀⠀⠑⢄⡁⠀⠈⠳⣄⠀⠈⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠁⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⢤⡀⠉⠢⢀⠀⠈⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⠔⠁⢀⠔⠃⠀⠀⠀⠀⠀ ⠀⢀⡀⠀⠉⣲⣄⣬⣵⣾⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣆⢀⠔⠁⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⠀⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡠⠔⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢰⣿⠟⠁⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠋⣿⣿⣟⡁⠀⢾⣁⠀⠀⣀⣀⣀⣀⣽⣿⠽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀ ⠀⠀⠶⣶⣾⣿⣿⣿⣿⣿⣿⠿⣻⣵⣿⣿⣿⣿⠟⠁⢀⣿⣋⣠⠬⠙⠻⠃⠀⠀⠀⠠⢤⣀⣀⣿⠀⢻⣿⣿⣿⡛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠚⠋⣩⣿⣯⠙⠀⠀⠀⠀⠀⠀⢻⣿⣭⡉⠉⠃⣸⣿⣽⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⣿⣿⡿⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠏⢠⠏⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⢻⠘⢿⣿⡙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⢀⠉⠀⠀⠀⣀⣴⣷⣤⣿⠉⠊⠻⠆⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠈⠻⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣦⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⡾⠂⠀⢸⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⡿⣌⠓⠦⣀⠀⠀⠀⠛⠉⠑⠚⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣽⣿⣿⣿⣾⡿⢧⠀⠉⠒⠤⠭⢓⢶⣤⣤⣤⠴⠖⢹⣿⣿⣶⣤⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⢿⠁⠀⢸⣿⣶⣦⣤⣀⣀⠀⠀⠁⠀⣠⣴⡟⠻⢿⣿⣿⣿⠿⠛⠉⠁⠤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠒⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠘⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⠀⢀⠀⣿⣿⣇⠀⠹⡝⠣⡠⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠁⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣼⣴⣿⣿⣿⣆⠀⠘⢄⠈⢻⣦⡀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⡄⠀⠈⢆⠀⠹⡕⣄⠈⢣⠘⣆⠀⠀⠀⠀⠀ ⠀⣀⣴⣿⣿⣿⠟⠋⣿⠏⠀⠀⠐⠀⢠⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⣿⠿⠿⠷⡀⠀⠈⣆⠀⠱⡈⢦⠀⢳⠘⣆⠀⠀⠀⠀ ⠈⠉⠁⠀⠔⠁⠀⢠⣿⡁⠀⠀⠀⠀⡼⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣄⣀⣙⡇⠀⠰⡘⡄⠀⢳⠀⠱⣄⠃⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠋⢹⣆⠀⠀⡜⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠹⣷⠀⢸⣧⠀⠈⢿⡄⠈⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡟⠁⡔⠁⠈⢦⡞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⡟⡄⠀⢹⡅⠀⢻⡄⠀⠀⠹⣇⠀⠀⠀
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