Cool Glasses Aesrmthetic Emojis & Text

Copy & Paste Cool Glasses Aesrmthetic Emojis & Symbols ⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⣀⣤⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠉⠻⣾⠋⠀⡎⢱⠹

⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⣀⣤⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠀⠀⠀⠉⠻⣾⠋⠀⡎⢱⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠊⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⢛⠓⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣦⠀⢰⡆⠀⣰⠄⠀⠀⠀⢸⠁⢾⣉⣻⡿⠀⣹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢧⣤⣩⣉⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⣀⡀⢀⣀⣤⡞⠉⠉⠻⣦⠶⢶⣤⠴⠶⠚⠛⠒⠒⠶⠦⣤⡀⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⣩⡿⠋⠁⠀⠀⠀⠀⠀⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠉⠙⢦⡀⠀⠀⠀⠀ ⠀⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡆⠀⢘⡇⠀⠀⠀⠀ ⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⡼⠃⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣆⣀⠀⣶⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢏⢿⠧⢶⠉⡇⠲⠂⢱⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠛⢦⣬⣷⡞⠀⠑⠤⢤⣊⡀⠀⠀⠀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⣓⠶⣤⣤⣤⠀⠀⠀⠈⠉⠙⠋⠉⠉⠉⠉⠉⠷⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡟⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⠀⡇⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢻⠉⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⠀⢁⡾⠛⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣤⣤⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⠀⠀⠀⢱⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡖⡇⠀⠀⠀⠈⣿⠓⢲⡄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠲⠶⠾⣿⣾⣷⣧⣤⣤⣶⣾⣿⣶⣾⣷⣾⣶⣶⡿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣾⡟⣿⣿⡇⡟⣾⣿⣿⣿⡟⢿⣾⣾⣿⣿⣿⣿⣷⣾⣾⣿⡟🆒😎🆒🤏👓🕶😎⛸️😎
⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⣀⣤⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠀⠀⠀⠉⠻⣾⠋⠀⡎⢱⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠊⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⢛⠓⢦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣦⠀⢰⡆⠀⣰⠄⠀⠀⠀⢸⠁⢾⣉⣻⡿⠀⣹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢧⣤⣩⣉⣠⡴⠋⠀⠀⠀ ⠀⠀⠀⣀⡀⢀⣀⣤⡞⠉⠉⠻⣦⠶⢶⣤⠴⠶⠚⠛⠒⠒⠶⠦⣤⡀⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⣩⡿⠋⠁⠀⠀⠀⠀⠀⣿⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠉⠙⢦⡀⠀⠀⠀⠀ ⠀⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡆⠀⢘⡇⠀⠀⠀⠀ ⠀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⡼⠃⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣆⣀⠀⣶⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡿⢏⢿⠧⢶⠉⡇⠲⠂⢱⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠛⢦⣬⣷⡞⠀⠑⠤⢤⣊⡀⠀⠀⠀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⣓⠶⣤⣤⣤⠀⠀⠀⠈⠉⠙⠋⠉⠉⠉⠉⠉⠷⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⡟⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⠀⡇⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢻⠉⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠃⠀⢁⡾⠛⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⣤⣤⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⠀⠀⠀⢱⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⡖⡇⠀⠀⠀⠈⣿⠓⢲⡄⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠲⠶⠾⣿⣾⣷⣧⣤⣤⣶⣾⣿⣶⣾⣷⣾⣶⣶⡿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣾⡟⣿⣿⡇⡟⣾⣿⣿⣿⡟⢿⣾⣾⣿⣿⣿⣿⣷⣾⣾⣿⡟🆒😎🆒🤏👓🕶😎⛸️😎🕶

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