Peppa Pig Text Art

Copy & Paste Peppa Pig Text Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠃⠀⠀⠈⢻⡆⠀⠀⠀⣠⣾⡶⠿⠿⣶⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⢸⣇⠀⠀⣼⣿⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⣼⠏⠀⢸⠏⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣠⣤⠶⠖⠶⠿⠛⠛⠒⠒⠒⠀⠈⠙⠲⠾⣯⣤⣤⣨⣸⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡶⣿⡟⠉⠉⢥⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠻⢶⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⡽⠊⠁⠀⠀⠀⠈⣷⠀⠀⠀⢶⡾⢿⣿⣿⠛⠶⣦⡀⣀⣠⣤⣴⡶⣴⣤⣀⠀⠀⠀⠀⠀⠛⠉⠳⣦⡀⠀⠀⠀⠀⠀ ⠀⣰⣿⠏⠀⠀⠀⠀⣠⠄⠀⢸⡇⠀⠀⠈⠻⢿⣿⣇⣤⢶⠿⠁⢿⣅⣸⣿⣿⠀⠈⢻⡗⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀ ⢀⣿⡇⠀⣶⣿⡆⠸⣿⣿⠀⢸⣧⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠉⠻⠿⠷⠶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀ ⠀⣿⣛⠀⠈⠉⠁⠀⠈⢁⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡄⠀⠀⠀⠀⢹⡆⠀ ⠀⢹⣿⡄⠀⠀⠀⠀⠔⢃⣼⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠙⢻⡧⠤⠤⢤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠉⠻⢷⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣶⣤⠒⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣽⡀⠀ ⠀⣜⠁⠀⠀⠀⠀⠀⠈⠈⠙⣦⠀⠀⠀⠀⠀⢹⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣾⣿⣷⡄ ⠀⠉⠓⠦⠤⠤⠤⠤⠤⠴⠚⡁⠀⠀⠀⠀⣴⣾⣿⣷⣍⡓⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠶⢾⣫⣴⣿⣿⡾⢿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣉⣙⣋⣓⣒⣚⣉⣉⣥⣤⣶⣿⣿⡛⣿⡇⠨⠇⠘⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⡄⠀⠐⣿⠿⠿⠿⠛⠛⠛⣿⣿⣩⢹⠩⣿⡏⠉⠉⠉⢉⡉⣹⣿⠛⠉⠛⠀⣷⣶⣤⣦⠀⢸⣿ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢀⣀⣀⣠⣤⣤⣶⠶⣟⣿⣶⣿⣾⣶⣿⣿⣄⢀⠰⣾⡿⡿⠿⠶⠶⣶⣶⣿⣿⣿⣿⠄⣾⣿ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⣿⣿⣿⣿⠁⣨⣷⣿⣭⣭⣿⣿⣿⣿⣿⣗⣝⣀⣀⣀⣠⣤⣀⣴⣿⣿⣿⣿⣿⣿⡇⢹⣿ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⣾⣿⣿⡟⠛⠛⠛⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⣾⣿
⠀⢠⡟⣁⠀⠀⠀⢹⡆⠀⠀⢀⣬⢭⡙⠳⣿⣤⣟⠀⣴⠏⠉⣿⠀⠀⠀⠀⠀ ⠀⣿⠀⠛⠀⠿⠀⣼⠁⠀⠀⡟⢷⢆⡿⠀⢁⠘⠙⢻⣧⣀⡼⠃⠀⠀⠀⠀⠀ ⠀⢿⡀⠀⠀⢀⣼⠃⠀⠀⠀⠙⠓⠛⠁⡼⢫⡿⣦⠀⠸⠻⣧⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⡶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⣬⣵⠏⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠷⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣿⠓⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠉⠳⡀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠀⣧⠀⠀⠀⣀⠀⠀⢸⡀⠀⠀⠀⢠⠇⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠳⠶⠞⠋⠀⠀⠈⠣⣀⣀⡴⠋⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣄⠀⠀⠀⠀⠀ ⢀⣸⣷⣤⣶⠶⣿⠃⠈⠙⠷⢶⣤⣤⣄⣠⣤⣤⡶⠞⠋⠀⢤⣿⣆⡀⠀⢀⣀ ⠈⠉⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⣿⣥ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡟⠁⣠⣶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣀⣀⣀⣿⣤⡶⠟⠉⠻⣦⣿⣾⣃⣤ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⡏⠉⠉⠉⠉⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁
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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉ ⣤⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣿⣿⣿⠟⠋⠁⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⠻⣿⡿⠋⠁⠀⠀⠀ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⡤⠄⠀⠀⠈⠙⠲⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡋⠀⠀⠀⠘⠛⢶⡄⠀⠀⠀⠀ ⠛⠿⠿⢿⣿⣷⣀⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡇⠀⢠⠏⠀⠀⠀⠀⣀⡠⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⣿⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠭⣭⣽⢿⣿⠟⠛⠛⢻⡟⠉⠁⠀⠀⢧⠀⡏⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⢹⡇⠀⣾⠏⠀⠀⡆⠀⠀⠘⣧⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢸⡇⢰⡿⠀⡄⠀⢿⡄⠀⢀⣽⠶⠋⣀⡀⠀⠀⠀⠀⣀⣰⠶⠗⠋⠉⢓⡾⠟⠉⢉⡶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠘⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠁⠘⠇⠀⠃⠀⠸⣷⣸⠋⠀⠀⠀⠀⠉⠀⢀⡶⠚⠉⠀⠀⠀⠀⣰⠟⠀⠀⣰⠋⠀⠀⠀⣠⣴⢶⣗⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢷⡄⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣠⡾⠚⣿⣦⣤⡀⠀⠀⠀⡼⠃⠀⢀⡴⠃⠀⣤⢠⡾⠋⠀⠀⠉⠁⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣄⠀⠀⠀⢀⢰⣿⠁⠀⠀⣴⠟⠋⠀⣼⣿⢻⣿⣿⡄⠀⠀⠁⠀⢠⣞⣅⣠⠞⠉⣩⣴⣶⣶⣦⣤⡀⠀⠙⢺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢲⣿⣦⠀⢠⣼⠏⠀⢀⣤⡾⠁⠀⠀⣿⣿⣷⣾⣿⣿⠁⢀⣀⣄⡠⠾⠿⠋⢀⣴⣿⣿⣿⢛⣽⣿⣿⣿⣷⣄⣉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⣞⣷⡀⢹⡷⠠⢀⠞⠀⠀⠀⠀⠙⠿⠿⠿⠟⠁⡠⠀⠀⣀⠀⠀⠀⠀⠘⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⠷⠌⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡦⣤⣿⣟⣷⠆⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠈⣳⣽⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣾⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡇⠛⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⠀⠀⠀⠀⠀⣠⡦⣤⡀⠀⠀⠀⠀⡀⠀⠠⣤⡀⠀⣴⠀⠀⢸⣷⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣞⠉⣩⠵⠒⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣷⣀⠀⠀⡀⣀⣛⠓⠲⣄⡙⠳⢦⣤⣀⣘⠶⣄⡀⠙⠚⠃⢀⣀⠈⢿⡀⢚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠋⠁⠀⠁⢀⣀⡤⢿⣟⣯⡀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣻⠛⠙⢠⣄⢠⠍⣻⠻⣶⢤⣉⠛⢾⣿⣍⢿⣛⠻⣮⣿⣷⡶⣤⣀⠀⠘⣿⣯⠀⣀⣤⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⢛⣫⣴⣶⡿⢟⣯⡆⠀⠀⠀⠀⠀⠈⣻⠁⠀⠃⠀⠀⣼⣿⣧⡀⡉⢷⣼⣧⣙⢿⣳⣿⣯⠛⢯⣝⠲⢬⣝⡻⢷⣿⣛⠓⢻⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⡽⢟⣭⣶⠟⠍⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⡻⣿⣝⣦⡀⢉⣳⡄⠙⢿⣶⣽⣿⣷⣬⡛⢿⣿⣿⣗⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣯⢆⣠⣾⠟⣿⠇⠀⠀⠶⠦⣤⣀⠀⠀⣾⢳⠇⠀⠀⣸⣿⣿⣿⣿⣿⣿⠙⠙⠉⣿⢸⣿⣨⣻⣿⣻⣾⡟⠛⠷⢦⡻⣿⣿⠙⣹⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣠⡾⠁⠀⠀⠀⠀⠀⠀⠈⠉⠑⣿⣿⣄⡞⢀⣿⢻⠟⠻⠉⠙⠈⠀⠀⢰⢿⡆⠻⣇⢳⣻⡟⠙⢷⡀⠀⠀⡿⣎⠙⢷⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣧⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠇⠀⢸⣼⣷⣽⣄⢨⢿⣄⠀⢸⣮⣿⣾⣿⣿⣿⣿⣿⡜⠁⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠉⠉⠉⠁⠉⠛⠒⠾⣿⣶⣶⣿⣶⣤⣼⣯⣿⣿⣻⣿⣷⣿⣷⣾⡿⣻⣿⣿⣿⣿⣿⣿⠧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣽⣿⣿⣿⣿⣿⢿⣿⣷⣿⣿⡿⢿⡿⠟⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣿⣋⠉⠏⢫⣭⠉⢻⣿⣟⣟⢿⠸⡇⠛⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣤⡄⢈⣁⣉⡉⠀⠃⠸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⢰⣄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡍⠛⠻⢦⣄⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠳⣿⣧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡆⠄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠛⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣷⣾⡇⠀⠀⣸⣦⡀⠀⢿⣧⠀⠀⠀⠘⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣸⣿⢸⠇⠀⠀⠘⣷⣷⡄⠀⢽⡏⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡸⣰⣿⠟⠀⠀⠀⠀⠰⣿⠿⣧⡀⣸⡇⠀⠀⠀⠘⠿⣿⠟⠁⠀⠀⠀⠀
⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⢻⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡄⠹⢈⣵⢖⣒⣲⣖⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀ ⠀⠸⡔⠋⠐⡈⠳⡌⢿⠎⠀⢀⣬⢅⠈⠀⠈⠙⠻⢽⣿⠇ ⠀⢰⠁⣠⣶⣶⢢⢮⢁⢀⣠⣤⣄⠙⢶⡀⢄⡲⠖⠋⠁⠀ ⠀⠸⠀⠛⠿⣿⡟⠀⢸⠘⠶⢿⣿⣇⢖⠉⡏⠀⠀⠀⠀⠀ ⠀⢸⡀⢆⠀⢺⡤⣾⡸⠓⠄⠀⠐⠨⢼⡂⡇⠀⠀⠀⠀⠀ ⡉⠀⠻⣝⣑⣠⣓⠛⠁⠀⠬⣤⣤⠀⠀⡱⠁⠀⠀⠀⠀⠀ ⠀⢀⠔⠉⠢⡘⣾⣿⣔⡔⢪⡍⡪⡲⡋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⡇⢈⡮⣃⠂⠿⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠶⠶⠶⠶⠶⠶⠶⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠻⣦⠀⠀⠀⠀⠀ ⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⢷⡀⠀⠀⠀ ⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢷⡀⠀⠀ ⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣇⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡄⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀ ⢸⡇⠀⠀⠀⠀⠀⢠⣿⡷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⢶⣄⠀⠀⠀⠀⣾⠀⠀⢸⡇⠀ ⠀⢷⠀⠀⠀⠀⠀⣿⣿⣧⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣇⠀⢻⡇⠀⠀⢰⡏⠀⠀⢸⡇⠀ ⠀⠘⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣼⠁⠀⢀⡟⠀⠀ ⠀⠀⠸⣆⠀⠀⠀⣿⣿⣿⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⢠⡿⠀⠀⠸⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠻⡀⠀⠀⠘⢿⣇⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⣠⡾⠃⠀⠀⠀⡀⢀⡿⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⡴⠶⠦⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⢼⣋⣉⡿⢤⣷⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠐⣷⣄⡴⣄⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⡟⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣶⠟⣛⣿⡏⠉⠓⠲⠶⠶⠶⠶⠶⠶⠶⠖⢲⡞⠉⠹⣯⡻⠙⠁⠙⣿⣷⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⣱⡾⠟⠁⣧⠀⠀⡠⠆⠀⠀⠀⠀⣀⣠⠶⠞⠓⠶⢦⡈⠻⣦⠀⠀⢿⣿⣿⡿⣷⡀⠀⠀ ⠀⠀⠀⣰⢏⡾⠋⠀⠀⠀⣿⠒⠒⠲⠶⠶⠶⣤⠶⠋⠁⠀⠀⠀⠀⠀⢿⣆⠈⢷⣄⣬⣿⣿⣗⢿⣷⡀⠀ ⠀⠀⢠⡿⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⣿⡿⠛⢻⣿⡻⢿⣧⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡷⠦⠤⠤⢤⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡇⢠⣿⠇⠀⠈⣿⣿⣡⣿⡆ ⠀⠀⢸⡇⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⣰⡟⢀⡾⠋⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠈⠻⠤⣤⠖⠻⡟⠲⠤⠤⣤⣤⣼⡀⠀⠀⠀⠀⠀⣠⡾⢋⣤⡾⠋⢠⣾⡿⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⠀⠀⠀⠀⠙⢧⣀⣀⣀⣠⣿⡿⠟⢻⠏⠀⢠⣿⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⢻⡄⣠⡿⠛⠛⠛⠳⢦⣄⠀⠀⠈⠁⠀⠀⢀⣀⣸⡆⠀⠀⢿⣯⡀⢤⡄⣠⣿⡻⣣⣾⡏⠀ ⠀⠀⠀⠀⣠⠞⠛⢿⣄⠀⠀⠀⠀⢸⡝⣿⡈⢉⣭⠟⠛⠉⠀⠉⠛⢧⡄⠀⠙⣿⡿⣮⣿⣦⣿⢻⡿⠁⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠈⣷⠀⣠⣼⢟⣁⣼⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⣻⡆⠀⠘⣷⣧⣿⣻⣿⡿⠀⠀⠀ ⠀⠀⢰⡟⠀⠀⠀⠀⣠⣼⠟⠃⠀⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣅⢻⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠈⣿⡆⠖⠚⠋⠉⠀⢀⣤⠾⠻⣇⠀⠀⠀⠀⠀⠀⢀⣤⡼⠟⠉⣻⡾⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠶⠤⣤⣤⠾⠛⠁⠀⠀⠘⢧⣄⡠⠐⠖⣛⣉⣥⣤⠴⠞⠻⠷⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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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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