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⠀⠀⠀⠀⡴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⠁⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠒⠒⠂⠀⢿⡆⢀⣀⣴⠏⠀⠀⢾⡀⠀⣧⠀⠀⡇⠀⠈⣷⣄⠀⢀⣰⠃⠀⠈⠉⠉⠁ ⡤⠖⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠈⠷⠿⠙⠳⠞⠃⠀⠀⠈⠻⠷⠛⠁⠀⠀⡈⠑⠢⡄ ⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠛⠛⠛⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀ ⠀⠀⢸⡩⠋⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀ ⠀⠀⠀⢹⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀ ⠀⠀⠀⣼⡇⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⢠⣿⠋⣿⠿⠙⢿⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣍⡀⣼⣿⣿⡆⠀⠀⠀⢰⣦⠖⢾⡧⠤⡄ ⠀⠀⠀⢻⣇⣶⠀⢸⣿⠀⢿⣶⣄⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⢸⣷⢠⣄⢿⣆⠙⠙⣆⣈⣻⠇ ⠀⠀⠀⠘⣿⡿⣶⣾⣿⡀⠈⢿⣿⣿⣿⠿⢿⡇⠀⠀⠈⣿⣿⠿⣿⣿⣿⡟⢸⣿⠀⢿⣆⢻⣧⣼⡟⠀⠀⠀ ⣶⣤⣿⠀⠹⣷⡻⢿⡟⣿⡄⠀⠙⢿⣿⣦⣨⣿⠐⠉⠁⠸⣿⣄⣼⣿⠟⠁⣸⡟⠀⠘⠿⠀⣰⡿⠀⠀⠀⠀ ⠀⠉⠛⠀⠀⠹⣧⡚⠃⠈⢿⣦⡀⠀⠈⢛⣿⠇⠈⠉⠉⠁⠙⢿⣍⣁⣀⣰⡿⠁⠀⠀⢀⣼⠟⠀⣶⣴⠟⠀ ⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⠀⠉⠻⠷⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠋⠀⢀⣠⣴⠟⠁⠀⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣥⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⠶⠶⠶⠶⠶⠶⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡤⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⣿⣿⣿⣿⣶⣄⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⡿⠛⠉⠛⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣀⣀⡈⣿⣿⣿⡿⠟⠉⠁⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣻⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣀⠀⢘⣿⣿⣿⡃⠀⠀⠀⢘⣿⣿⣧⡀⠉⠹⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⣠⣾⣿⣿⣿⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣿⣦⣀⣠⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠿⢻⣿⣿⡇⠀⠀⠀⠀⠀ ⣀⣤⣤⣤⣾⣿⣿⣤⣄⡀⠀⠀⢠⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠈⠉⠁⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀ ⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣶⣾⣟⠋⠈⠛⠛⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠛⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠻⣿⡿⠟⠀⠀⠀⠀⠈⠉⢉⣿⣿⡏⠉⠙⠛⠋⠀ ⠀⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣤⣤⠀⠀ ⠀⢸⣿⣿⡏⠁⠙⢿⣿⣧⠀⠀⢹⣿⣿⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡿⠿⠿⠿⠿⠀⠀ ⠀⠸⣿⣿⣧⣀⠀⠀⠙⠟⠀⠀⠈⠿⠿⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀ ⠀⠀⢘⣿⣿⣿⣷⣄⡀⠀⠀⠀⣠⣴⣶⣿⣷⣿⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠈⠉⢙⣿⣿⣿⡟⠀⠀⢰⣿⣿⠿⠛⠿⠟⠀⢻⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣿⠟⠁⠀⠈⠙⠛⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠹⣿⣿⡄⠀⠀⠸⣿⣿⣦⣤⣾⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠀⠙⠻⠿⠿⠟⢛⣽⣿⣿⡏⠻⣿⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣤⣀⠀⣀⣠⣴⣿⣿⣿⣟⠁⠀⠀⠉⢙⣛⣋⠉⠀⠀⣠⣾⣿⣿⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣶⣤⣀⣈⣻⣿⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠐⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⢛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠂⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡆⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⢣⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠠⠀⡖⣗⣄⠀⠁⠀⠀⠑⠀⡂⡀⠀⠀ ⠀⠀⠀⠀⠠⠐⠀⠐⢠⠃⡧⠀⠑⡄⠀⠀⠀⠀⠀⠈⠀⡀ ⠀⠀⠀⠀⠈⠐⠄⢰⠥⠤⠯⠤⠎⢏⠀⠕⠀⢄⠀⠀⢂⠀ ⠀⠀⠀⠐⡖⡓⠒⢺⠤⣀⠅⠆⠀⢺⡀⠄⠀⠅⢀⡁⢄⠀ ⠀⠀⠀⠊⡑⢀⠀⢺⣈⠁⠬⠂⠲⡲⠂⡀⠀⠀⠈⠐⠁⡀ ⠀⠀⠀⠁⡁⠁⠒⢝⠍⠊⠀⡁⠀⢘⠈⠊⠂⠀⢄⠤⠀⠁ ⠀⠀⠀⠐⠨⠀⠨⠎⠊⠀⠁⠐⡜⢐⠂⢀⠂⠁⠀⠀⠀⠂ ⠀⠀⠀⠀⢒⠂⠁⡓⡡⠀⠀⠀⢀⠨⠅⠈⠐⠀⡂⠐⠁⠀ ⠀⠀⠀⠀⠈⡰⡈⠧⠢⠔⠀⠀⠀⢘⠂⠂⢃⠀⣂⠀⠁⠐ ⠀⠀⠀⠀⠀⠀⠀⡇⠕⡒⡦⠀⠀⢘⢀⠊⡤⡐⠐⠀⠐⠀ ⠀⠀⠀⢠⠋⠉⠙⣇⠳⣉⠝⠶⡖⡿⣖⣉⡄⠀⠁⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠅⣀⢀⠏⡀⠂⠉⡆⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠉⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠁⠃⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⡆ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⢳⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⡆⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⠁⠀ ⠀⠑⢦⣀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠁⠈⠒⠢⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠁⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⢀⣠⣾⡿⠃⠀⢀⠀⣀⠀⡀⠀⠀ ⠀⣠⣐⢣⢎⡕⡣⢖⣠⠈⠛⠿⣿⣿⡿⠟⠋⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⢀⠰⡸⣌⠳⣌⠳⣔⢢⡀ ⡴⢱⡘⠮⡜⣌⣓⢣⡌⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣠⣄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡱⢓⡬⠳⣌⠳⡜⢦⡱ ⡇⣇⢹⢱⠾⣀⢇⠷⣸⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⡿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠹⡎⣰⠏⣈⢷⡸⢇⣱ ⢗⠬⣓⠎⣎⠵⣊⠳⢥⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠳⣩⠖⡹⣌⠶⣉⠶⡑ ⠈⠳⢬⡙⢦⢛⢬⣹⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢡⢞⡱⢎⡲⣭⠚⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⠙⠻⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠿⠛⠛⠻⠿⣟⡛⠛⠛⠿⠿⠿⠿⣿ ⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⣭⣷⣄⡀⠀⠀⠀⠀ ⠟⠋⠉⠀⣴⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠀⡄⠹⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⢹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⡶⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀ ⠀⡀⠀⠀⠒⠚⠛⠻⣍⠀⠀⠀⠀⢀⡴⢋⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠙⢦⠀⠀ ⡜⠀⠀⢠⡇⠐⠒⡟⠉⠙⠓⠖⣾⣽⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣿⣷⣤⣄⣠⣤⣤⣤⣤⠴⠆⠀⠀⢦⣄⠀⠤⠤ ⠁⠀⠀⣼⣁⣠⠀⡇⠀⠘⢩⠉⠉⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣟⢆⠀⠴⢒⡚⠀⠙⢦⡀⠀ ⠀⠀⢹⡏⠁⠀⢰⣃⡀⠀⢸⡆⠐⠚⢹⠉⠻⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⡋⠀⠈⢧⠀⠀⠙⢦⡀⠠⠖⠚ ⠀⠀⢸⠇⠐⠚⣿⠉⠁⠀⡼⠀⠀⠀⢸⡄⠀⠚⣋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠹⣿⡄⠀⠀⠻⣄⠠⠴⠖⠛⠉⠃⡹⡄⠀⠀ ⠀⠀⠏⠀⠀⠀⣿⠀⠤⠖⠛⠋⠉⠀⢸⠇⠀⠀⠘⡆⠀⠤⠴⠒⠛⠃⢈⣿⠀⠀⢈⣷⡀⠀⣤⠴⠒⠒⠂⢹⣆⠀⠀⠙⣦⠀⢀⣠⠤⠶ ⠠⠀⠒⠂⠀⠀⡟⠀⠀⠀⢰⠀⢀⣠⡽⠶⠶⠀⠀⣧⠀⠀⠀⢲⡀⠀⢀⣠⡤⠤⠄⢻⢻⡀⠀⠀⠀⡄⠀⠈⢉⣠⣤⠄⠻⠳⡄⠀⠀⠀

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⣿⣿⡿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⢿⣻⢿⡿⣿⣿⣿⣿⣿⣿⣟⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢘⣶⣶⡉⡤ ⣿⣷⡿⣟⣿⠃⢹⣿⣿⣿⢿⣾⣿⣿⣯⣿⣷⡿⣿⣿⡞⣸⣿⣟⣯⣿⡝⡿⢛⣿⡿⣯⣿⣟⣿⣿⣶⣯⣽⣿⣿⣟⣿⣟⣿⣿⡿⣿⢢⠀ ⣿⣷⣿⣿⡿⠈⡨⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⡷⡇⡿⣷⣻⣞⡽⢱⡛⢸⣽⣻⣟⣾⣽⣳⡿⣾⣻⣽⡷⣿⣻⣯⣭⣽⣷⣏⣉⣎⡑ ⣿⣿⣾⣿⣇⠀⢀⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⣾⢿⣟⡁⢹⣷⣳⢯⣖⢸⡇⢸⣽⢺⣟⣾⣳⣯⣟⣿⣟⡾⣽⣿⡿⣽⣯⡷⣿⣿⣿⣿⣧ ⣿⣿⣷⣿⠘⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢾⣿⣷⣶⣯⣋⠷⣋⠸⡃⠘⣾⠘⣿⣞⡷⣯⣿⢣⣿⣟⡿⢻⣿⣳⣯⢿⣿⣿⣿⣿⣿ ⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⢧⠘⠀⠀⠀⠉⠂⠹⠯⠟⣷⣿⢰⣿⣞⣿⢸⣿⢯⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣏⡃⢸⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⢻⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢛⠺⠁⡜⣿⣟⣿⣿⣿⣿⣿⣿⣿ ⣿⡟⡤⠁⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠶⢡⣨⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣾⣿⣿⢶⣤⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣷⡱⣓⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⣿⢅⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡷⣯⢵⣻⠀⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⢛⡀⠁⠀⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡷⣯⡿⠀⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣳⣿⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣽⣟⠀⠘⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⠀⠀⢠⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⠈⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠤⡀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡂⣁⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣷⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⢄⠆⠤⢐⠠⠑⡂⢅⠣⡐⢄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣶⠈⠄⢣⠘⡠⢁⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢇⡿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡬⣤⡀⢁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣼⠃ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣻⢿⣿⣟⢿⣱⢚⡴⢣⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣰⠃⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣳⣎⣽⢿⣾⣩⠳⣜⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡐⠁⠀⠀ ⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣏⣻⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠄⠀⠀⠀⠀ ⠀⠀⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣍⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣤⣤⣤⣤⣤ ⠀⠀⠀⣂⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠻⡀⠀⠀⠀⠀⠀⠀

Venus planet of love was destroied by global warming ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⢿⠿⠿⠿⠿⠿⡿⠿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠉⠉⢀⣠⣾⡆⠀⠀⠀⠀⣿⣦⠀⠈⠉⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠟⠉⠀⠀⠀⠀⣶⠿⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣦⣤⣄⡀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⠟⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⠛⣿⣿⣷⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡏⠀⠀⠀⣠⣾⣿⣿⣿⣿⣂⣤⡼⠿⢿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣷⣄⠀⠈⢿⣿⡄⠀⠀⠀ ⠀⠀⠀⣿⡿⠀⠀⠀⣰⣿⣿⠟⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠁⠀⠈⠹⣿⣤⣦⣸⣿⣿⡟⣿⣦⠀⠘⣿⣷⠀⠀⠀ ⠀⠀⢸⣿⠇⠀⠀⢰⣿⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠉⠉⠁⠈⢹⣿⡇⠈⢿⣇⠀⢹⣿⡄⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⣼⡇⠀⣿⣦⣀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠘⣿⠀⠘⣿⡇⠀⠀ ⠀⠀⢸⣿⠀⠀⠸⣿⡇⠀⠘⢿⣿⣟⠛⢳⣶⣾⣿⣿⣿⡏⠀⠀⢻⣿⣿⠿⠻⣷⡄⠀⠀⣀⣠⣴⣿⠟⠀⠀⢀⣿⠀⠀⣿⡇⠀⠀ ⠀⠀⢸⣿⡀⠀⠀⢹⣿⡀⠀⠀⠉⠛⠿⠿⠿⠿⢟⣿⣿⠁⠀⠀⠘⣿⣿⣷⣦⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣠⣾⡿⠀⢀⣿⡇⠀⠀ ⠀⠀⠈⣿⣇⠀⠀⠈⢿⣿⣤⣄⣀⣀⣀⣀⣠⣶⣿⠟⠁⠀⠀⠀⠀⠈⠻⣿⣦⣍⣉⠉⠉⠀⢀⣀⣠⣴⣾⣿⠟⠁⠀⣸⣿⠃⠀⠀ ⠀⠀⠀⢻⣿⡄⠀⠀⣰⣾⣿⣿⣿⡛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠛⢻⣿⣿⣯⣭⡀⠀⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣄⣰⣿⡟⠉⠻⣿⣷⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠙⢿⣿⣧⣤⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠸⠿⠛⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠙⢿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀ ⢀⣾⣿⠟⠁⠀⠀⠀⣶⣴⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣼⣿⡿⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀ ⣼⣿⠃⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣦⣶⣶⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀ ⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⣤⣀⣀⣀⣼⣿⣿⣦⣤⣠⣤⣤⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠉⢻⣿⡏⠉⠙⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣶⣦⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠘⣿⣿⣆⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏ ⠀⠈⠻⣿⣷⣄⡀⠀⠀⢿⣶⣤⣄⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣤⣶⣆⠀⠀⠀⠀⢀⣠⣶⣿⡿⠋⠀ ⠀⠀⠀⠈⠙⠿⢿⣷⣶⣤⣽⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣯⣤⣤⣤⣶⣿⡿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠘⠒⠶⢁⡀⣤⡶⡞⣯⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⢟⣿⣿⣿⠟⢁⢴⡽⣽⣿⠿⣻⣿⣷⣿⣿⣿⣦⣦⡄⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⢿⢧⠻⣿⡿⣿⢿⡿⣿⣯⢿⡘⡌⣷⣸⣾ ⠪⠀⢈⠖⠕⢙⣪⣾⣿⣿⣿⣿⣿⢫⣾⢯⢏⡾⢋⣾⣿⠟⢎⡼⣫⣳⣿⣯⣾⣿⣻⣿⣶⡶⡿⢿⢿⣿⣿⣧⣄⠀⣿⣿⣿⣯⣿⢹⠼⡎⠟⣧⢻⠝⠘⠋⢟⡙⣯⠈⢣⠈⣼⡟⣿ ⠀⠀⢂⠂⣰⣾⣿⣿⣿⣿⡏⡿⢡⣿⠏⢁⠚⢡⣿⣿⠏⣠⡯⣱⣾⣾⣿⢻⣿⣿⠯⣟⣷⣶⠿⠿⣿⠿⣿⣿⣿⡄⣿⣿⣿⡓⣿⣟⠀⡇⠀⣿⡆⡄⢀⣀⠈⣷⢺⣧⠀⣄⣴⢻⣿ ⡆⡤⣌⣜⢍⣿⣿⣿⣿⠝⠰⠁⣾⣿⢠⡞⢀⣿⡿⡏⢠⡏⣿⢋⣿⠿⣿⣿⣯⣾⣿⢿⣯⣵⡾⣷⣟⣟⣟⣾⢿⣿⣸⣿⣿⣗⣿⣿⡇⣇⠂⣿⢿⢰⢼⣿⡆⢸⣾⣿⣷⣿⣼⣿⣿ ⠀⠉⡏⠁⣹⣿⣿⣿⣿⡷⠁⢸⣿⣇⣆⡇⣾⣿⣿⠀⣾⣹⡁⣾⠏⣸⡏⠉⣾⠏⢀⣾⡏⣿⡿⠏⣉⣷⣇⣉⣿⣿⠇⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣾⣀⣿⣷⣿⣿⣏⣿⣿⣿⣿⣿ ⣀⢸⠠⢢⢿⣿⣿⣿⣿⡖⢘⣾⣿⣿⣿⡇⣿⣿⡟⢰⡻⡞⢸⡏⢠⡟⠀⣼⠇⢠⠟⢁⡾⠃⡴⢋⣩⡤⠤⢻⣝⣾⡍⣿⣿⣿⣿⡿⣿⣿⡇⣿⣿⡇⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠙⠛⠷⢥⣿⣿⣿⣿⣿⡇⣿⣿⡿⣿⣿⣿⣿⣿⡇⢸⡇⡇⣾⡀⢼⡇⢠⡗⠀⡿⢠⡟⢀⡞⢡⡞⢡⠜⣩⠭⢍⣺⠅⡛⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡄⠀⣠⣮⣿⣿⣿⣿⣿⣷⣿⣿⣿⢻⣿⣿⣿⣿⣃⠸⣇⡇⢸⠂⢸⠇⢘⡇⠀⡇⢸⡇⢸⡇⣼⢀⡏⢸⢣⢞⣯⡽⣁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠉⠛⣾⡏⣿⣿⣿⣿⣿⣿⣿⣾⣿⡜⣿⣿⣿⢿⣿⠄⠹⣼⠸⣦⢘⡇⠐⣧⠘⡇⢸⡇⢸⡆⢻⠠⡇⢻⢸⡺⢭⠇⠸⠰⢹⣿⣿⣏⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢨⠃⡇⣿⣿⣿⣿⣧⢿⣿⣟⣿⣿⡴⢻⣿⣯⠻⣯⠈⣫⡇⢻⡎⢿⡀⢿⠄⢳⡈⣧⠘⢷⠈⢇⡙⠬⣲⡭⡿⠀⠀⠆⠞⣿⣿⣿⣻⣿⡇⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠐⠁⡀⠇⣿⣿⣿⣿⣿⣯⣿⣿⡿⣻⣿⣇⡑⠹⡇⠘⠓⠈⠛⣤⡳⣌⠧⣌⢷⡈⠧⡙⢧⣈⠓⠶⠭⢭⠝⠃⠀⠀⠀⠐⡈⠘⣿⣿⡧⢿⣷⢿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠛⠪⠥⣀⣀⣀⣀⠀⠀⠈⠻⠞⣷⣯⣷⢾⡢⢍⡒⢬⡭⠭⠛⠃⠀⠀⠀⣀⣀⡤⠤⠤⠼⣌⠩⢏⣛⡻⠛⢡⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⡞⢟⣿⣿⣿⣿⣿⣿⣿⣿⡇⡠⡐⢖⡒⠉⠵⡶⣄⠀⠀⠀⠀⠀⠉⠉⠀⠃⠙⢛⡗⠶⡶⡶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢂⠉⠀⠊⡁⡐⠋⠉⠁⣿⣿⣿⣿⣿ ⠀⢀⠉⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢿⣿⣷⣈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⢏⠈⠀⢀⠶⢹⣸⡰⣉⡉⡉⠰⠶⣀⣀⠀⠀⢁⠀⠀⠀⢁⠆⠀⣸⣿⣿⣿⣿⣿ ⠀⠀⠀⡈⢼⣼⣿⣿⣿⣿⣿⣿⣿⣿⠘⠃⢻⣾⣿⣿⣿⢷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠨⡼⠒⠁⠀⢐⣿⣞⢻⣿⣿⣿⣿⡷⢷⣶⣤⣈⡙⠶⠢⠀⡀⠀⠀⠀⢢⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡗⠻⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠻⢿⡿⠟⠀⠿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢳⡃⠘⢿⣿⢿⣿⡿⠃⠀⢨⢿⣿⡛⠂⠀⠀⠈⠂⠀⢠⢡⣿⣿⣿⣿⣿⣿ ⠐⠠⠄⣛⠊⣟⢽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠫⠦⣤⢤⠤⢴⣿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⡀⠉⠉⣉⠀⣄⣰⡵⡚⠃⠂⠀⠀⠀⠀⠀⠀⣝⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⠛⠉⢷⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠞⠉⠟⠫⠱⠥⠒⠠⠀⠀⠀⠀⠀⠀⠀⠑⡘⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣴⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣠⡄⠀ ⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠻⠇⠀ ⠀⠀⠀⠀⢠⠇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⢸⠀⣰⣦⣄⣹⣆⠀⢀⣀⡀⠀⢀⣤⣶⣟⣁⣠⡀⠀⠀⡇⠀⠀ ⠀⢰⡆⠀⢸⡰⣈⢉⠹⠿⡿⠰⠷⠶⠸⢰⣿⣿⡿⠿⠿⡉⢇⠀⢀⡇⠀⠀ ⠘⠿⠇⠀⠀⢧⠑⠪⠴⠡⣞⣤⣀⡀⣀⡠⣷⠠⢂⡑⢢⢱⡨⠃⡼⠀⢀⠀ ⠀⠀⣠⣄⠀⠈⠳⡀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠉⠀⠈⠉⠀⣠⠞⠁⢻⡿⠀ ⠀⢸⡵⠚⠉⢉⡽⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠥⢤⣀⣠⣄⠀ ⠀⠈⣇⠀⠀⠁⠠⠞⠁⢳⡉⠙⠒⠒⠶⠶⠒⢚⠟⠯⣄⠈⠦⠀⠈⢳⢸⠇ ⠀⠀⠸⣆⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠀⠀⠀⠀⣸⡾⠀ ⠀⠀⠀⠈⠓⠦⠤⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣠⠼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⢄⡐⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡇⢸⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⣇⢸⣿⣿⣿⡇⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣿⡏⡇⢸⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡕⣯⠳⠱⣸⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣺⣏⣿⣿⠼⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⡯⠟⠉⠀⠈⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣝⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣙⣿⣫⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢗⣯⣿⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣳⡷⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⣾⣯⣟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣶⡧⣟⢽⡗⠺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣩⡇⢫⡆⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⢛⣉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠾⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣄⣀⠔⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⣠⠞⠉⠁⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⡀⠀⠀⠙⢦⣀⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠴⣒ ⣶⣤⣄⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⠦⡀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡀⠘⣇⠀⠀⠀⠴ ⣿⣿⣿⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠢⢀⡇⠀⠀⠀⢀⡄⠀⠀⠀⣿⠀⠸⡀⠀⠀⠀ ⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⠳⣄⠀⠀⢸⡇⠀⠀⠀⣼⢳⠀⡇⢀⡏⠀⠀⣧⠀⠀⠀ ⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⣧⠀⠀⢸⠿⢼⡇⠟⢫⠇⠀⠀⢿⠀⠀⠀ ⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢻⡙⠦⡀⠀⠀⠀⠀⠙⢦⠲⣄⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠰⣄⠀⠙⣆⢸⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠳⡜⣇⠀⠈⠳⣄⠠⡀⠀⠈⠳⡘⢿⡦⣄⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠘⢆⠀⠀⠀⢷⠀⠀⠀⠰⣦⣤⡀⠀⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠹⣾⠀⠀⠀⠈⠳⣴⡄⠀⠀⠙⢌⢣⠈⠳⣄⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⢳⠀⠀⠈⢧⠀⠀⠀⠹⡿⠁⠀⠀⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⡏⢧⠀⠸⣇⠀⠀⠀⠀⢈⣿⣄⣀⣀⠬⢿⣷⠶⠚⠳⡀⠀⠀⠘⣆⠙⢄⠀⠀⠀⣧⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⡇⠈⣇⠐⢻⡛⠛⠉⠉⠉⠉⠙⣆⠀⠀⠀⠹⡄⠀⠀⠙⢦⡀⠀⠈⣆⠘⣆⠀⠀⠸⡆⠀⠀⠀⡝⠢⣤⣀⣠⡾⠙⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣆⠀⠸⡄⢸⠀⠘⡆⠈⡇⠀⠀⠀⠀⢀⡠⠜⢧⠀⠀⠀⢻⡀⠀⠀⠀⢻⣄⣀⠘⡆⠘⡆⠀⠀⢹⡀⠀⠀⣷⠀⠰⣹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⠸⡄⠀⠀⠀⠘⡄⠀⠹⡄⣧⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⢀⣈⣷⡤⣤⣾⣷⣶⣾⣟⣿⠿⣇⠀⢹⠀⢱⠀⠀⠀⢷⠀⠀⢸⠀⠀⣿⡇⣇⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⡟⣆⢱⡄⠀⠀⠀⠘⣆⠀⠙⣜⡆⠀⢻⡘⡄⠀⠀⠀⠀⣴⢉⣥⣾⣿⣿⣿⣿⠟⠛⠋⠀⠀⠘⡆⠘⠀⠘⡇⠀⠀⠈⣇⠀⠸⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⢀⡀⣿⠀⡇⠘⣆⢻⣆⡀⠀⠀⠈⢧⡀⠘⣾⡄⠀⢧⣇⠀⠀⠀⠰⣷⣿⠟⣿⡾⣿⣿⢸⡄⠀⠀⠀⠀⠀⢹⣤⠀⠀⢳⠀⠀⠀⠸⡆⠀⠀⢰⢡⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⡇⠘⡆⢹⠀⠙⣦⢫⡳⣄⠀⠀⠀⠙⢤⡈⢿⡄⠘⣿⠀⠀⠀⠰⢿⠏⠀⠀⠀⣹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⠀⠀⣸⡄⠀⠀⠀⢹⣀⠀⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢳⠀⢧⠸⡀⠀⠈⣯⣳⠈⠳⢤⡀⠀⠀⠙⢦⡹⣄⢻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⢻⣿⡇⠀⠀⠀⠀⠀⢀⡏⠀⢰⠏⢿⠀⠀⠀⠀⣿⡼⠁⡾⡟⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡾⡄⠘⣇⣷⠀⠀⢿⠻⣷⡄⠀⠉⠓⠦⣄⣀⠉⠻⣿⡀⠀⠀⡤⢹⠀⠀⠀⠀⠀⠀⢿⠁⠀⡀⠈⠀⠀⡼⢁⡴⠋⠀⠸⡇⠀⠀⢀⣿⠃⣸⠃⠹⡹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢧⢷⠀⠸⣼⡆⠀⡆⠀⠈⢻⣇⠀⠀⠀⡈⢩⣿⠒⠶⠭⣷⡦⣤⣤⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⠒⠒⠚⠓⠉⠀⠀⠀⠀⢹⠀⠀⣸⣁⡾⠃⠀⠀⠻⡽⣄⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠸⣎⣇⠀⢹⣷⠀⡇⠀⠀⠀⠀⢹⣿⡋⣵⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⡆⢼⠛⠁⡆⠀⠀⠰⣀⠻⣜⣆⠀⠀⠀ ⣇⢀⠀⠀⠀⠀⠻⡜⣆⠀⠹⣧⡇⠀⠀⠀⠀⡼⠁⣽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠐⢠⣤⣀⠀⠀⠀⠀⠈⣇⠀⠀⣸⡇⢸⡇⢿⡇⠀⠀⠀⢈⣳⣾⣿⡄⠀⠀ ⢿⠀⣧⠀⠀⠀⠀⡿⣌⢦⠀⢻⣇⠀⠀⠀⠀⡇⣸⣿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣿⣿⣿⣿⣿⢿⣦⡀⠀⠀⢸⡀⢠⣿⣧⠈⡇⢸⣷⡄⠀⢸⠉⠀⠈⠙⢷⡀⣀ ⢸⡀⠸⡆⠀⢠⠀⢣⡘⢯⡳⣄⠻⣆⠀⠀⠀⢷⡿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⡄⠀⠘⣗⣾⣿⣿⠀⡇⣿⠸⡿⣄⠈⠳⣄⠀⠀⠀⠑⠈ ⠘⣧⠀⠻⡄⠀⢷⡀⢳⡀⠙⣿⣦⡻⣶⡀⠀⣼⡷⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⢿⣽⡇⠀⠀⠈⡇⠀⢀⣾⣿⣿⣿⢰⡇⣿⡀⢻⡈⢳⣄⠻⣷⣄⠀⠀⠰ ⠀⣿⡄⠀⠹⣆⠀⢷⡄⠹⣄⠹⣿⣷⣽⣿⣷⣯⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣟⢿⠿⠀⠀⠀⠀⠀⠀⡄⠀⡾⠟⠁⠀⣿⢸⢿⠃⠳⣄⢻⡅⠛⠳⣝⡛⢷⡀⠀ ⠀⢿⡸⣆⠀⠈⢣⡈⢿⣦⠈⢦⣹⣿⣿⣿⠿⣿⡟⡀⠣⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠠⣧⡾⠁⠀⠀⢀⡟⢨⡏⠀⠀⠉⠢⣽⣄⠀⠈⠉⣻⣿⡄ ⠀⠸⣇⠻⣧⡀⠀⠙⢮⡻⡵⣄⠙⢿⣿⣇⣾⣿⢻⣻⣆⠀⠈⢳⣄⣀⠀⠈⠲⣄⢄⣀⣀⣀⣀⡀⠀⠀⠈⠉⢳⣖⣒⣶⡏⠀⠀⠀⠀⣸⣃⡟⠀⠀⠀⢀⣠⡴⠾⠛⠛⠉⠀⠀⠻ ⠀⠀⣏⢧⢳⡈⠳⣄⡀⠙⠾⣮⣷⣦⡙⠏⢀⠀⠀⠈⣿⡟⠋⠋⠇⡄⢹⠻⠱⠿⠟⠛⣤⢸⠀⣀⡄⡄⡄⢠⢹⢡⡜⡏⡆⣿⢠⢹⢹⡟⡟⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠀⣧⣳⡀⠈⠉⠲⢤⣈⠙⢿⣿⡇⣼⡤⢤⣤⢿⣧⣴⣴⣧⣧⣼⣀⣴⣾⣴⣧⣿⣬⣥⣿⣧⣥⣷⣬⣼⠮⡤⠣⠭⠿⠌⠘⣬⠽⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣼⣥⣧⣥⣽⠤⢤⢤⣤⣿⣿⣿⣯⣥⣭⣥⣼⣭⣬⣭⣭⣭⣭⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣭⣤⣧⣤⣤⣤⣤⣾⣥⣤⣤⣤⠤⣤⠤⠬⠤⠤⠤⠤⠤⠤⠤⠤⠤

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⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢎⡈⠀⠁⠈⠀⠉⠁⠁⠀⠀⠀⠀⠀⠠⠀⠀⡠⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⡈⠀⠀⠀⠀⠀⡂⠀⠀⠀⠄⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⡒⠉⠉⢩⠀⠠⠁⠀⠀⠠⠡⠉⠈⠁⠉⠀⠁⠁⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢌⢃⠄⠄⠠⠀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠨⠀⢸⠁⠀⠀⢸⠀⠎⠄⠄⠄⢒⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠇⢀⠑⡣⠠⠐⠀⠒⠄⠈⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣀⠆⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡐⠂⢀⢌⡀⠀⠀⠀⠀⡁⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⡐⠀⠂⠠⡉⠀⠀⠀⠀⠀⠂⢀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⡁⣴⠯⠀⠀⠀⠀⠠⡁⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⡉⡗⠐⠐⣂⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠁⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠌⠄⡈⠀⠀⠁⠂⠂⢃⠃⠃⠊⠉⠁⠀⠀⠀⠀⢀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⠀⠂⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠐⠐⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡂⠀⠁⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢘⠐⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⠀⠀⡁⠄⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠉⠈⠐⡄⠀⢈⠀⠀⠀⠤⢤⡀⡀⢴⠠⢁⠄⢄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠰⡅⢀⡀⣀⢀⠀⡀⣰⢀⢀⢀⢀⡰⠨⡀⠀⠀⠀⠀⠀⢀⠅⠀⠨⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠂⠂⠂⠒⠀⠀⠀⠈⠂⠂⠂⠒⠚⠀⠀⠂⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⡆⠀⠀⠀⠀⠀⢰⣆⣀⡀ ⠸⣿⡿⠃⠀⠀⠀⠀⠀⠸⣿⣿⠃ ⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀ ⠀⣿⣄⣼⣦⣠⣞⣦⣰⣷⣰⣿⠀ ⠀⣿⡿⡯⢿⣿⡟⣿⣟⢿⣷⣿⠀ ⠀⣟⣁⣘⣋⣀⣙⣁⣈⣋⣈⣯⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⡁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡑⠘⠍⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⠉⢜⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠐⡘⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠃⠀⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠈⠑⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡿⠃⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⠀⠀⠀⠉⠛⢆⠀⠀⠀⠀⠀⠀⠀⠠⡳⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⡄⠀⠀⠀⠀⠀⠀⠀⡘⢃⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠓⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢫⠀⠀⠀⠀⠀⠀⠈⢸⡫⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠀⠀⠀⢂⡟⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠄⠀⠀⠀⠀⠀⠀⣀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠭⣆⠀⠀⠀⣰⣞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡂⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⢞⠟⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⡠⣤⣰⣘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⡀⠀⢀⢄⠊⠉⡂⠀ ⠀⠀⡔⡫⠲⠢⢄⡀⠀⡰⠋⠀⠀⠀⢻⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠄⠀⠠⡀⠂⠀⠀⠀⠉⠀ ⠀⠀⡚⣥⡀⠀⠀⠈⢟⡅⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠕⠀⠀⠛⠀⠀⠠⠈⡃⠀ ⠀⠀⠀⢙⡰⢠⡀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣟⣃⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠠⠲⠁⠀⠀ ⠀⠀⠀⠀⠀⠓⣠⢆⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠈⡆⡄⢀⣜⠲⣃⠂⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠱⡄⡴⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠠⠚⢇⡀⠀⢬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⠗⠀⠀⠧⠡⢀⠤⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⡠⠫⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢼⣋⡿⣿⣿⠰⣃⠞⣢⡄⠊⢢⠃⢅⠐⠁⡇⢁⠔⡱⣍⠞⣥⢛⡼⣙⢮⣙⢮⡹⣱⢋⠷⣩⠳⣍⡳⣍⡳⣍⢳⡹⣜⢣⡝⢮⡱⣍⠞⣥⢫⢜⡣⢝⡢⣿⡛⡟⡻⢻⢻⡟⣍⢹⡷ ⣢⠑⢦⡑⣆⠳⢌⠣⡕⠺⡡⡀⠀⠀⠀⠀⠁⠀⢡⠘⠣⢛⡌⣳⠼⡱⢎⡞⢦⡓⢧⡫⣝⢲⡛⣬⠳⣜⡱⢎⢧⠳⣬⠳⣜⢣⠳⣌⢻⡰⡍⠶⣉⠶⡱⢿⣭⣶⣵⣮⣾⢧⣣⣾⠷ ⡥⢛⠤⡓⣌⡓⡚⢂⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⢲⡙⡮⣝⢣⢞⣣⡝⣣⠗⣭⢞⣱⢣⠟⣬⢓⡏⣎⠷⣘⡳⢬⢣⡛⣬⢣⢧⡙⢧⣙⠲⡍⡖⠲⡔⣢⢒⣌⠲⡐⢆⢣ ⡱⢋⠖⡱⢢⡱⢍⠎⡵⡩⢦⠐⠈⠀⢀⠀⠀⠀⠀⠀⠉⠖⢩⢳⡱⢮⣙⠮⣖⠭⣇⠿⣘⢮⣱⢫⢞⡥⢯⡜⣎⡳⣍⠞⣥⢳⡙⢦⣋⠶⣙⠦⣃⢏⢖⣩⢓⡱⢆⢣⡌⢣⡙⣌⠲ ⡇⢟⡸⢃⠧⡸⣘⢻⠠⢇⠃⢄⠠⡀⡤⢀⠘⠀⡀⢣⣟⢤⣃⡿⢇⣧⢛⡧⡜⢿⣘⡟⡻⡤⢇⡟⡼⣸⢇⡼⣃⢧⡜⡻⣄⢧⠻⣄⠻⣜⢣⢻⡘⡼⣘⡄⡻⢠⡛⢤⡘⢇⡸⣀⠧ ⢎⡣⢜⡡⢞⡱⡘⣬⢙⡲⢎⡱⢲⣙⢷⢸⡘⢮⡽⣄⡙⣮⠖⣭⠳⣬⠳⣎⠽⣣⠞⣜⡳⢭⣫⢜⣳⡱⣎⢳⢭⡲⣍⡳⡜⣎⠳⣍⠳⣌⢧⠳⣸⢑⠦⡓⣍⢣⡜⡡⠞⣌⠲⣡⠚ ⣣⠓⣌⠲⡡⢖⡩⢆⡣⢝⡢⣍⢇⡞⢼⣸⢯⣚⠴⣫⠞⣧⢛⣬⢓⢧⣛⡼⣙⡖⣻⢬⡓⣏⡖⣫⠖⣵⡩⡗⢮⡱⢎⡵⡹⣌⠗⣮⠹⣜⢪⡕⢣⢎⡣⢝⡰⢣⠜⣡⢋⡔⢣⢆⡙ ⡆⢏⡔⢣⢱⢊⡴⢣⡙⢆⡳⢌⠶⣘⢇⡞⢦⣍⠳⣥⢛⡴⣋⢖⡫⢞⢦⢳⣍⡞⣱⢮⣙⠶⣩⢧⡛⣦⢝⡺⢥⣛⠼⣒⢧⡙⡞⡴⢫⡜⣥⠚⡵⣊⠵⣊⡕⢣⢎⡱⢊⡜⡡⢎⠴ ⢎⡣⢜⡡⢎⠲⣌⠣⡜⢣⡜⣩⠎⡵⢪⡜⣣⢜⡹⢆⡏⢶⡩⢎⡳⢭⡚⢧⣚⠼⣣⠞⣟⡞⣱⢎⡳⢵⢪⠳⣍⣎⠳⣍⠶⡹⣜⡱⢣⠞⣔⠫⢖⣡⠳⢬⢸⠡⡎⡔⢣⠜⡑⢎⡒ ⡣⠞⡤⢓⡌⠳⣌⠳⡘⣥⠚⡴⣙⢬⠓⡼⣑⢮⡱⢫⡜⣣⢝⡣⣝⢣⡝⣣⢞⡹⢖⡻⡜⡼⢣⢏⡝⣎⡳⣋⠶⣜⡹⣌⡳⡱⢎⡵⢋⡞⢬⡙⣎⠴⣋⠖⣣⠓⡜⣌⠣⢎⡙⢢⠱ ⣴⣉⡖⢥⢊⠵⣈⠧⡱⢂⡛⡴⣉⠶⣙⢲⢩⠖⣭⠳⣜⡱⢎⡵⣊⠷⣸⡱⢎⡝⢮⡱⣝⠺⣍⡞⡜⢶⡱⣙⠞⡴⢳⣌⢳⡙⢮⢜⢣⠞⣡⠳⡌⠶⡑⢮⠰⣍⠲⣌⠳⡌⡜⣡⠣ ⣿⣟⣛⢿⡿⢗⡡⢎⡱⣉⠖⡱⢜⠲⣉⢮⢱⡚⡴⢋⠶⣙⢎⠶⣩⠞⣥⢛⡜⣎⢧⡓⢮⡝⢦⣙⢎⢧⠳⣍⢞⡱⢣⢎⢧⡙⣎⢎⡣⢞⡡⢧⡙⡜⡱⢊⠵⣈⠇⣆⠳⡘⠴⡡⢃ ⣧⣽⡏⢻⡟⠛⡟⣦⢱⡌⠚⢱⠊⣧⡍⢲⢣⡜⢱⠋⡞⢱⡎⢳⣥⠛⣴⢫⡜⡜⣦⢹⢣⡞⢱⡎⡝⡎⢳⡜⣮⢱⠋⡞⢢⡝⣴⠊⣵⠊⣵⢢⠙⣴⠉⡇⠚⣤⠋⡔⢣⠙⣦⠑⢣ ⠰⡐⢌⡒⠬⣑⠲⡌⢦⠙⣌⠣⠞⡤⣙⡒⢎⡱⣃⠯⡜⣱⢊⡗⡬⢳⡱⢎⡵⠳⣌⠳⣎⡜⣣⢞⡱⣙⢦⠳⣌⠧⣛⢬⠣⡕⢎⡱⣃⠞⣡⢎⡱⢆⡹⢌⠳⢌⢎⡱⢊⡕⢢⡙⢢ ⢣⡙⢢⠜⡱⢌⠣⡜⢢⡙⢤⢋⠼⡰⢡⢎⠣⡕⢎⡲⡙⣔⠫⡴⢩⡓⣜⠣⢞⡱⣍⠳⡜⡼⣑⠮⡱⡍⠶⣙⢬⡚⠴⢣⡹⢌⠧⣑⠎⣜⡡⢎⡔⢣⠜⣌⠳⡌⠦⣑⠣⣌⢣⡘⡡ ⢣⠜⣡⠚⢤⢋⠴⡉⢦⢙⠢⣍⠲⣡⠓⣌⠳⣌⠳⡰⣙⢤⠛⡴⢣⢹⠰⣋⠮⡱⣌⢳⢩⠖⡥⣋⠵⣊⠗⣩⠦⡍⡝⢆⡣⣍⢚⠤⣋⠴⡑⢎⡜⣡⠚⡤⢓⡌⢣⠜⡒⢤⢃⡒⢡ ⡃⡞⢠⠙⡂⢎⠒⣩⠂⣎⠱⢌⡓⢤⢋⡔⢣⢌⠣⡕⣊⢆⡛⠴⣩⠲⣙⠴⡩⡕⡜⢪⡱⢪⡱⢌⡳⢬⡙⢆⠳⣘⠬⣃⠶⡘⣌⠳⢌⠲⣉⠖⡸⢄⠫⠔⠣⡌⢃⠎⡱⢊⠔⡨⢁

⠀⠀⢀⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤ ⠀⠀⣼⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⡇ ⠀⠰⠃⠀⠈⣧⣤⡴⣤⣠⣀⡀⡒⠁⠀⠄⡇ ⠀⣈⠀⣀⣀⡈⠘⠀⠉⠀⠋⠀⣀⣀⡈⠀⡅ ⠻⢟⢒⡿⠂⠀⢳⡤⢆⡠⠆⠀⠀⣴⡂⢁⡇ ⠀⠄⠈⠙⠭⠆⠄⠤⠠⠠⣐⣒⠄⣄⡙⠚⠀

⠅⠉⠉⠀⠉⠉⠥⠠⠠⠀⠀⠀⠘⠈⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⢸⠀⠉⠉⠉⠉⠉⠉⠉⢉⢉⣉⡉⠉⠉⠉⠉⠉⣉⣉⣹⠈⠉⠉⠉⠉⣡⢤⣉⠀⠀⠀⠉⠉⠁⠈⠀⠁ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⢼⣟⠙⠇⣹⣠⡴⣦⣄⠘⣇⣡⣿⠀⢀⣤⢶⣄⣧⢈⣩⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣤⣤⣤⣤⣴⠶⣶⣄⢀⡀⠤⠤⠄⢒⣲⣼⣉⣸⡀⠀⠀⠀⠀⠀⢹⠉⠻⢿⡾⢫⡟⢠⣄⡙⣿⡉⠉⢛⣴⢟⣥⡀⢻⡟⠛⠛⠓⡖⠂⠐⠀⠐⠀⠀⠀ ⠀⡀⠀⠀⠀⢀⣀⣀⢠⣿⠁⠀⣠⠏⡤⢀⡾⠛⠛⠛⠻⡟⠛⠻⣧⡈⠙⣟⣷⠀⠀⠀⣀⣠⡾⢤⡀⠀⠀⣸⢧⡿⠛⠛⠚⠛⢻⠟⢱⣿⣿⣧⠈⣷⠀⠀⣴⠟⢳⣄⡀⠀⠀⠀⠀ ⠒⠒⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⠞⢠⠟⣴⣿⣿⣿⣦⢹⣴⣿⣿⣷⡀⠀⢻⣇⢠⡿⡏⠉⠂⢀⣷⠀⢀⣿⣾⣤⣤⡄⠀⠀⣀⣤⣤⣬⡻⠿⠀⣿⠀⢸⣧⠀⠋⢉⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⣾⠃⠀⢠⠏⢠⡏⠸⣿⣿⣿⣿⣻⡆⣿⣿⣿⣻⣷⡀⠀⢻⣮⠷⣍⣓⠲⣾⠋⠉⢹⣿⡟⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⡄⠀⢿⡖⠒⣿⣛⣛⣫⠼⠧⢤⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢠⢏⡶⠛⠩⢍⣻⣶⣮⡭⠿⢅⣿⣿⡿⠿⠿⣷⣄⡀⠹⣧⠀⠈⠉⠋⣀⣠⣿⠹⣷⠿⣿⣿⠹⣾⣿⠿⠿⠿⠿⠇⠴⢾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠠⠄⠐⠚⣼⠟⠀⢀⡟⣾⣖⠀⢠⠋⢰⠃⠀⢨⠛⠒⡟⠛⢻⢦⡀⢀⣿⠃⠀⠘⢷⣤⢤⣼⣿⣗⠘⣏⠀⠀⢺⣿⡿⠃⠀⠀⠀⢰⣿⠓⠂⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠀ ⠀⠀⠀⠠⠀⣼⠏⠀⢀⡞⠀⠈⠻⣇⣎⣀⣘⣀⠤⠼⠶⠶⠷⠤⠼⣀⡇⣸⠛⠀⠀⠀⠀⠹⡆⠈⠿⣿⠀⠸⣷⣶⣾⣿⣷⣶⣤⣴⣶⣿⣿⡄⠀⢰⢿⡟⠋⠐⡖⠂⠀⠂⠀⠠⠄ ⠀⠀⠀⢸⠰⣿⠀⢠⠏⠀⠀⠀⢀⣼⣿⣤⣒⠦⣄⣀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⣸⣇⣀⣤⡹⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⢠⣿⡿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⣀⠀⠇⠻⣶⣃⠀⣀⣤⣶⠿⣻⠏⠀⠈⠙⡖⠬⠭⠥⠖⠊⠉⠉⢷⣄⣀⡀⣂⣠⣾⣿⣿⣿⣿⣿⡿⣧⡀⠈⠛⠿⣿⣿⣿⣉⣡⠴⢃⣴⣿⣟⡁⠀⠀⠀⣐⣠⣴⠶⠞⠛⠛ ⠁⠀⠀⠀⠀⢀⣈⠙⠛⠋⠁⠀⠀⣿⢀⣠⣤⠖⠒⢲⡒⠒⣖⠲⠤⣤⣘⣿⣙⣛⣋⣿⣿⣿⡿⣿⣿⣿⡇⠈⢙⣷⣤⣄⣀⣈⣩⣡⡴⠾⣛⣫⠍⠉⠛⠻⣯⡿⠋⠁⢀⣠⠀⠐⠀ ⠀⠀⠀⠀⢀⡿⠙⣧⠠⠤⠖⠚⢹⡟⠙⢦⢈⣳⡤⣤⠵⢤⠬⠦⢤⣱⣌⠙⡏⡹⢉⣟⣤⣾⣶⣿⣿⠟⢻⡟⢫⠁⣦⠞⠁⡤⠟⠑⠒⣉⣵⣾⣷⣤⠀⠀⠈⠳⡄⠀⢿⣰⣶⣟⡛ ⣠⠠⠤⠐⣾⠃⠀⢻⡄⠀⠀⠀⠘⣷⢲⠋⣹⣤⡤⠧⢤⠾⢤⡤⣏⣀⣸⣙⣿⣿⣯⣉⣙⣿⣩⡉⠀⠀⠀⣠⢋⣴⣿⠀⠸⣅⠀⣰⣾⣿⣿⣿⣿⣿⣷⡀⠀⣼⠿⢶⣤⡈⠙⢯⠻ ⠀⠀⠀⠀⣿⠀⠀⠘⣷⠀⠀⠀⢠⡿⠚⠙⣆⣠⠽⠒⡞⠓⡞⠓⢢⠽⠤⣬⣿⠀⠀⠀⠀⠘⢿⣕⠦⢖⣫⣶⠟⣿⠏⠳⠤⠬⠟⢻⣿⣿⣿⣿⣿⣿⣿⣧⣾⠋⠀⢀⣨⣿⠀⠀⠃ ⠀⠀⠀⠀⢻⡄⠀⠀⢻⣦⠤⠖⠚⣿⠒⣉⡥⢞⣚⣍⣉⣻⣌⣹⣯⣽⣟⣓⣿⠀⠀⠀⠀⠀⠀⠉⠻⣿⡉⠀⢠⣿⢸⠀⠀⠀⠀⠸⣝⢿⣿⣿⣿⣿⣿⡿⠿⠟⣛⣫⠭⣓⣠⣤⠾ ⣀⣠⠤⠴⠒⣻⣆⠀⠀⠻⢦⣤⣀⣽⣯⡵⠚⠉⣧⠔⠚⠉⠁⠉⠳⣤⠷⠚⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⠀⠀⠀⠀⠀⠈⠧⣝⣛⢻⣯⡵⠾⠷⠶⠞⠛⠛⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⢿⣟⡀⠀⠀⠀⠀⠉⠁⣸⡖⠦⣶⠏⢀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⡀⣀⣉⣛⣛⣲⣶⣶⣞⣛⣙⣷⣀⣀⣀⣘⣆⣀⣀⣀⣀⣀⣟⣇⣀⣀⣀⣀⣀⠹⣦⢀⣀⣀⣀⣀⢀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⣿⣻⠿⠻⢛⠛⢋⠛⠛⠛⠛⠿⠿⣿⣿⢿⡿⣷⣷⣦⣑⢂⡒⢄⠢⢄⠰⣀⢒⡐⣢⢵⣶⢿⣿⣿⣿⣿⡿⠿⠛⠻⠙⢋⠛⠛⠻⠿⢿⣿ ⢁⠂⠌⡐⠠⠈⠄⢂⠐⠠⠀⠄⡀⠀⠉⠛⠻⣿⡿⣵⢿⣷⣼⣄⠣⡌⢒⢤⣮⣼⣿⣿⣿⡿⡽⠚⠉⠀⡀⠀⠄⡐⢀⠂⠌⡠⢁⠂⠄⠠ ⠠⢈⠐⠠⢁⠘⠠⠈⠄⢃⠁⡂⠄⡁⠢⠀⠄⠀⠉⠛⠿⣟⣻⣾⣷⡾⣽⣾⢿⣻⠷⠏⠃⠁⠀⠠⢀⠡⢀⠃⡐⢀⠊⡐⠐⡀⠂⠌⡠⢁ ⠐⡀⢊⠐⡈⢄⠣⣉⠒⡌⠒⡄⢣⠐⡠⠁⠈⠐⠠⢀⠀⠈⠙⢫⣽⡿⣯⡟⠎⠁⢀⠠⢀⠂⠁⢂⡁⢆⠢⡘⢄⢃⠒⣌⠰⢠⢁⠒⡀⢂ ⠐⢠⢂⠱⡈⢆⡱⢈⡱⠌⡓⡘⠤⢋⠔⡉⢆⠡⢂⠄⠈⠂⠄⡀⠀⠉⠁⠀⠠⠐⠀⠂⢠⠐⡌⢢⠜⢢⡑⠬⣈⠌⡱⢠⢉⡒⢌⠒⡰⢀ ⡈⢆⠌⢢⠑⡢⢔⡣⣔⣧⣳⣽⣾⣵⢮⣕⣎⡱⢊⡔⢡⠂⡄⠀⠁⠂⠄⠁⡀⠄⠦⡉⢆⡱⣌⣶⣬⣷⣾⣷⡶⣾⣴⡡⢆⡜⢠⠣⠔⡃ ⡘⠤⢊⠥⣪⣵⣯⣿⣿⣿⣿⣿⡿⠾⡿⣿⡿⣿⢷⣞⣦⠣⡜⣄⢃⡀⡀⢆⡘⠌⢂⣽⡾⣿⢿⡿⡾⠾⣟⡿⣿⢿⣻⣿⣿⣼⣦⢡⠓⡌ ⢄⢣⣉⣶⣿⣷⣾⣻⠟⠃⠉⠀⠀⢀⠀⠀⠀⠉⠙⠫⢽⣟⣳⣴⣊⠔⡱⣂⣴⣾⠿⡗⠋⠉⠀⡀⢀⠀⠀⠀⠉⠙⠛⢾⡿⣷⣿⣷⡎⡔ ⢌⣲⣿⣿⣿⡷⠋⠀⠀⠠⠐⡈⠐⠀⠈⠠⠑⠀⠂⡀⠀⠈⠙⠾⣽⢿⣽⡟⠎⠉⠀⡀⠄⠂⠡⠀⠀⠈⠠⢁⠀⢂⠀⠀⠙⠿⣿⣾⣿⣮ ⣬⣿⣻⣟⡞⠁⠀⡐⢈⠁⠂⢀⠠⡐⢄⠒⡄⠣⢄⡀⢁⠈⠠⠀⠀⠉⠂⠀⠀⠂⠁⡀⢄⢢⡐⢡⠊⡔⢠⠀⠈⠠⢈⠐⡀⠀⠙⣯⡿⣿ ⣾⣷⣿⡏⠀⢀⠐⠠⠁⢀⠰⡈⢆⠱⣈⠒⡌⣑⠢⠜⡐⠢⢄⡀⠀⠐⠀⠀⣀⠢⡑⠬⣈⠆⣌⠡⢊⠔⡁⢎⡐⡀⠀⠂⢀⠂⠀⠹⣿⣿ ⣿⣟⣿⠀⠀⠂⠌⠁⠠⢌⢢⠱⡈⠖⠤⢋⣔⣦⣳⣬⣅⣣⠒⡌⡑⠢⢌⡱⠀⠧⢘⣴⣡⣎⣤⣃⠘⠤⢃⢆⠰⣁⠆⠀⠠⠈⠄⠀⢻⣿ ⣿⣿⣏⠀⠌⡐⠈⠀⡒⢌⠢⢅⢣⠉⣴⡾⣯⣷⡿⣯⢿⡷⣟⣦⣉⠑⠂⣤⣶⣾⢿⣯⣿⣿⣛⣿⣷⣆⠡⢊⡒⠔⡨⢂⠀⠡⠈⠄⢩⣿ ⣿⣿⣎⠀⢂⠐⠀⢠⡑⢊⡜⠠⣃⣾⡿⣽⠛⠃⠁⠀⠀⠀⠉⠙⠻⢿⡟⠏⠁⠀⠀⠀⠀⠉⠹⢿⣹⣿⢦⡁⠜⣨⠐⡡⠀⠄⡉⠄⢪⣿ ⣿⣿⡖⡀⢂⠡⠀⢢⠘⢢⠌⡡⣾⣿⣻⠃⠀⢀⠂⠡⠌⠠⠁⠂⠀⠀⠀⠀⠠⠁⠌⠠⢁⠂⠀⠈⢿⣽⣻⡥⢘⠄⢣⠐⡁⠐⠠⢈⢲⣿ ⣿⡿⣽⠀⢂⠐⡀⠤⣉⠒⡌⠡⣿⣿⡯⠀⠀⠂⠌⠀⢠⠐⡄⢂⠄⠀⡀⢄⠰⡀⢆⠀⠀⠌⠐⠀⢘⣯⣿⡝⢢⠉⢆⠱⠀⠡⠈⠄⣻⣿ ⠼⣿⣽⡇⠀⠐⠠⠐⡠⢉⢆⡁⢻⣿⣳⠀⠈⡐⠀⢈⠆⡱⣈⢖⡬⡑⣌⢢⠱⣈⠆⡌⠀⢈⠐⠀⢘⣼⣟⡎⢆⡉⢆⠡⠀⢂⠡⢘⣯⣿ ⡘⢷⣻⢷⡀⠈⡐⠀⠐⡩⠐⡄⠘⣿⣷⠀⠀⡐⠀⠈⡔⡁⢾⡿⣷⣿⣾⣿⣳⠆⢎⠰⠀⠠⢈⠀⣰⢿⣞⡘⢤⠘⡄⠂⠀⠂⢄⣻⣾⣿ ⢌⠚⣿⣟⣦⠀⠐⡀⠀⢡⠣⠜⡀⢹⡿⣇⠀⠠⠁⠐⢠⠁⠘⣿⣿⣿⢿⣳⠏⢈⠆⠂⢀⠂⠀⢀⣿⡻⠁⡘⡄⢃⠄⠀⡈⠐⣤⣿⣿⡋ ⢢⢉⡜⣿⢾⣇⠀⠠⠁⠀⠘⡌⠱⢂⢻⣟⣆⠀⠁⢂⠀⠱⡀⠘⠿⣿⡻⠉⡀⠎⠀⠀⢂⠈⢀⡿⣿⠃⠰⡁⢐⠀⠀⠐⠀⢠⣿⡾⢧⡑ ⠐⢢⠐⡌⢿⣿⣦⠀⠐⠀⠈⢐⠂⢡⠂⠹⣟⣧⡀⠀⢂⠀⠈⠄⡓⢄⠣⡑⠌⠀⠀⠌⠀⣰⣿⡻⠁⣠⠃⡄⠃⠀⡐⠀⣠⡿⣟⠟⡰⢈ ⠈⢂⠱⡐⡈⠻⣿⣣⡄⠐⠀⡀⠘⠠⣉⠆⡈⢿⢷⣂⡀⠈⠐⡀⠈⠄⠃⠀⠀⠀⠀⣠⢾⡿⠋⢀⠒⡄⠃⠀⢀⠐⠀⣰⢯⣟⠯⢌⡑⠂ ⠈⠄⠑⡰⢁⠆⠙⣿⣿⡄⠀⠠⢀⠐⠠⢎⠡⠄⠹⣿⡷⣄⡀⠀⠄⠀⠠⠀⠁⣠⣾⣿⠛⠀⡄⢣⠘⠀⢀⠐⠀⢀⣼⢿⡟⡌⢒⠢⠌⡁ ⢈⠐⠠⠀⠡⢊⠔⡈⢿⣿⣶⠀⠀⢂⠀⠈⠜⡈⠆⡄⠙⢿⣷⣦⣄⠀⣀⣴⣾⣿⠃⣀⠢⣉⠔⠁⠀⢀⠂⠀⣤⣿⣿⠛⡤⢉⠆⡁⢂⠐ ⠠⢈⠁⠂⠄⠈⠜⡰⢀⠹⢾⣿⣆⡀⠈⠄⠀⠑⠌⡰⢉⡄⠌⠻⣿⢿⣿⠿⢁⠢⠜⣠⠃⠌⠀⠠⠈⠀⣠⣞⡷⡟⢀⠋⡔⡁⠂⠔⡈⠐ ⠐⠠⢁⠊⡐⠀⠀⠑⢂⠰⡈⠛⣯⣷⣄⡀⠁⠠⠀⠁⠊⡔⡉⢆⠠⡛⢌⠰⣀⢃⠚⠀⠈⡀⠂⠁⣠⣾⣽⠟⢉⢠⠘⡰⠀⢀⠉⡐⠠⢁ ⢈⠐⢂⡐⠠⢁⠂⡀⠀⠐⡡⢒⡀⠻⣾⣷⣆⡀⠁⠌⡀⠀⠘⠄⡓⠌⡜⠒⡄⠊⠀⠠⠁⠀⣠⣾⣿⡽⠊⡀⢆⠢⠁⠀⡀⠂⠌⠠⢁⠂ ⠠⠈⡄⠠⢁⠂⡐⠡⠐⡀⠀⠅⡊⠥⢈⠛⣾⣿⣦⣀⠀⠡⢀⠀⠘⠈⠔⠁⠀⠄⠈⢀⣤⣾⣿⠾⠃⡀⢆⠱⠈⠀⢀⠂⡐⠉⠄⡡⠂⠌ ⣦⡁⠄⡁⠂⠌⠠⢁⠂⡐⠠⠀⠈⠰⡁⢆⠄⠻⢿⣿⣶⣀⠀⠈⠐⡈⠠⠈⠀⢠⣴⢯⣿⡝⠊⣀⠖⢡⠊⠀⠀⡐⠠⠒⠠⢁⠂⠤⠑⠠ ⣿⣷⣆⠄⠉⠄⣁⠂⠰⢀⠑⡈⠄⡀⠈⠂⡍⢢⢈⡘⠿⣿⣿⣦⣀⠀⢀⡴⢾⣟⡾⠏⡁⡐⢢⠡⠌⠀⠀⠄⢂⢁⠂⣁⠒⠠⠈⢄⣡⣿ ⣿⣷⡿⣿⣄⠀⠠⠘⠠⢈⠐⡀⠒⡀⠂⠄⠀⠁⢆⠰⢂⠌⠛⢿⣿⣿⣻⡽⡛⠊⠠⢄⠱⠈⠂⠀⡀⢂⠡⠈⠄⠂⠌⠠⠈⠀⣁⣾⣿⣾ ⠰⡙⣿⣷⣿⣷⡄⠀⠁⠂⠌⢠⠁⠤⠑⡈⢐⠠⠀⠁⠊⡔⢢⢀⠉⠛⠋⢄⠰⣈⠱⠈⠀⠠⠐⠀⠁⠂⠀⠉⠀⠉⠀⠁⠀⠚⠙⠛⠛⠋ ⢂⡱⢈⠽⣟⣯⣽⣷⣄⠁⠈⠄⠌⠠⢁⠐⠂⠄⡁⢂⠀⡀⠃⠌⢢⠑⡌⢢⠑⠀⠀⠠⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠄ ⠂⠔⣃⠒⢬⡙⠾⠿⣻⡷⣄⡀⢈⠐⡈⠤⠁⠌⡐⠠⢁⡐⠠⠈⠀⠑⠈⠀⠀⢄⠘⡀⠂⠌⠀⠀⠂⠠⠀⠁⠀⠊⠀⠘⠠⠁⠀⠜⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠉⠉⠉⠈⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠁⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⡤⠤⠤⠤⡀⠀⠡⡠⠄⠤⠤⠤⠤⠤⠤⠤⠔⠁⠁⠀⠀⠀⢀⣀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆⠀⠀⠈⠉⡽⠁⠀⠀⣀⠤⠤⠤⠤⡄⠀⠀⠀⠈⡏⠁⡋⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⢉⡤⠪⠑⡓⠖⠀⠀⡇⢸⠬⡷⡀⠀⠀⠓⡆⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠎⠧⢀⠎⡉⠐⠫⡰⠃⡛⡯⡝⣢⣀⣅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⠽⠊⠈⠁⡰⡤⠈⠀⣜⡥⡞⢰⠁⠉⠿⠗⣿⡃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠁⠀⠬⠀⠁⠒⠀⠀⡪⠁⠫⣴⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢯⡾⡙⢁⡀⡁⠔⠀⠆⠏⠀⡇⡕⠁⣀⡠⡤⠤⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⡁⡌⡍⠀⣈⠉⠀⢠⡧⡟⠘⢉⠍⠀⠀⢹⡟⠀⠀⠀⢀⠅⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢾⠁⣨⠅⡂⡠⠄⣠⠞⡯⣏⣁⡤⡋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡈⠄⢰⡣⡵⢋⠇⣍⡗⡫⢿⣭⣤⣤⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⣀⣭⣼⢹⢈⣜⠕⣇⡀⠀⠉⠉⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢰⡇⡇⢈⡮⠁⠀⠀⠀⡧⠤⠄⢂⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⣾⠀⣧⠏⠀⡠⠤⠤⠤⣇⣀⣀⣤⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠤⠤⠤⠤⠤⡀⠀⢇⣈⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⡀⠁⠀⢸⠀⠀⡀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠱⡄⠀⠀⠹⡄⠀⠀⠀⠀⠀⡇⠀⡤⠋⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⣆⠀⡄⠁⠀⠀⠀⣘⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⡰⠃⡏⠁⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⠈⠉⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⡄⠀⠙⠦⠤⠴⡔⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⢇⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⢢⡀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣙⡗⡄⠀⠈⠉⠒⠒⠶⠶⣄⣤⡀⣀⣠⣾⡬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠁⢀⣤⣴⣶⣷⣦⣤⣄⣀⣀⠘⠙⠯⢝⠉⠀⠘⢆⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⢀⣴⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⣯⡿⡦⣄⠀⠙⢦⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⣰⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠓⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⣾⣿⣿⣿⡅⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⣿⣿⣧⡀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡩⢿⣿⣿⣿⣿⣿⠏⢉⣽⠟⠉⠐⠉⠿⣽⣷⣿⣿⣿⣿⣿⣿⣷⡄⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⢇⣾⣿⣿⣿⣿⣿⡶⠛⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧⢼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢸⣿⣿⣿⣿⡿⢷⣤⣄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣎⣿⣿⣿⣿⣿⣵⣶⣦⣉⠁⠀⠀⠐⠾⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⣿⣿⣿⣿⣿⠋⠻⡮⠿⠛⠆⠀⠀⠆⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠛⠻⠛⠉⣿⣿⣿⣿⣿⣿⣿⠹⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⠀⠀⢨⢦⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣯⠀⠀⠀⠈⠻⢿⠿⠚⠀⠀⠀⠀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⣿⣿⣿⣆⠀⢶⣶⡢⠤⣀⠀⢀⡤⠀⡰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢪⣙⣹⣿⠟⡉⠐⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣠⠀⢀⣼⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠉⠁⡀⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⠏⢹⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡶⢟⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⣾⣿⠉⢹⡟⠻⣿⣿⣿⣿⡷⠋⠀⢸⣿⣿⣿⣿⣿⣿ ⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣷⣶⣾⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠉⠉⠉⠈⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠁⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡄⡤⠤⠤⠤⡀⠀⠡⡠⠄⠤⠤⠤⠤⠤⠤⠤⠔⠁⠁⠀⠀⠀⢀⣀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆⠀⠀⠈⠉⡽⠁⠀⠀⣀⠤⠤⠤⠤⡄⠀⠀⠀⠈⡏⠁⡋⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠉⠉⠉⢉⡤⠪⠑⡓⠖⠀⠀⡇⢸⠬⡷⡀⠀⠀⠓⡆⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠎⠧⢀⠎⡉⠐⠫⡰⠃⡛⡯⡝⣢⣀⣅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣠⠽⠊⠈⠁⡰⡤⠈⠀⣜⡥⡞⢰⠁⠉⠿⠗⣿⡃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠁⠀⠬⠀⠁⠒⠀⠀⡪⠁⠫⣴⠋⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢯⡾⡙⢁⡀⡁⠔⠀⠆⠏⠀⡇⡕⠁⣀⡠⡤⠤⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⡁⡌⡍⠀⣈⠉⠀⢠⡧⡟⠘⢉⠍⠀⠀⢹⡟⠀⠀⠀⢀⠅⠀⠀⡎⠁⠀⠀⡖⡟⠉⡇⠀⠀⢰⠀⠠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢾⠁⣨⠅⡂⡠⠄⣠⠞⡯⣏⣁⡤⡋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠀⠀⠀⡟⠁⠀⢀⠇⠀⡰⠉⢓⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡈⠄⢰⡣⡵⢋⠇⣍⡗⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⢠⠏⠀⡠⠂⠁⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⣀⣭⣼⢹⢈⣜⠕⣇⡀⠈⠉⠁⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⢰⡇⡇⢈⡮⠁⠀⠀⠀⡧⠤⠄⢂⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠈⣾⠀⣧⠏⠀⡠⠤⠤⠤⣇⣀⣀⣤⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⣈⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⠋⠀⠀⠀⠀⠀⠀⠸⡀⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡏⠁⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⢿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⢿⣟⡿⣿⣻⢿⣟⡿⣟⡿⣟⡿⣿⡿⠋⣩⣍⠙⠿⣿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣻⢟⣿⡿⠿⠛⠋⠉⠁⣀⣠⡤⠴⠒⠚⠉⠉⠁⠀⠀⠀⠀ ⣿⣳⢯⣟⡾⣯⢿⡽⣯⢿⡽⣯⢿⡽⣯⣟⣷⠿⢾⣽⣳⣯⣟⡾⣽⢯⡿⣽⣻⠏⢀⣼⢏⡽⣳⣄⢀⠉⠳⣿⡾⣵⣻⢮⣷⣻⡼⠾⠛⠉⠁⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢯⡿⣞⡿⣽⢯⡿⣽⢯⡿⣽⢯⣟⣳⣿⠁⣶⢦⣤⣭⣉⡙⠛⠿⢿⣾⠷⠟⢀⣾⢭⡚⣴⢣⡛⣿⡳⣄⠀⠛⢷⡿⠛⠉⢁⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀ ⣿⢯⡿⣽⣻⡽⣯⢿⡽⣯⢿⣽⣻⢾⣽⡇⠐⣿⣚⡴⢣⠯⣝⠷⣦⣄⡀⣠⣴⣾⣋⠶⣙⠦⢧⡹⣜⣷⠈⠳⣄⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⠀⠀⠀ ⣿⢯⣟⡷⣯⢿⡽⣯⢿⣽⣻⢾⣽⣻⢾⡇⠈⣿⢦⣹⡙⣞⢬⣳⣱⣮⣿⡿⠶⠿⠛⠛⠿⠾⢧⣷⣼⡾⣧⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣯⣟⣯⣿⠀⠀⠀ ⣿⣻⢾⡽⣯⢿⡽⣯⣟⡾⣽⣻⢶⣯⢿⡇⠀⣿⢲⢣⣽⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣟⣷⣻⢷⣻⣞⣿⠀⠀⠀ ⣿⡽⣯⢿⡽⣯⣟⡷⣯⣟⡷⣯⣟⣾⠿⠃⢀⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⢀⣠⣾⣿⣻⢷⣻⢾⡽⣯⢷⣻⡇⠀⠀⠀ ⣷⣻⡽⣯⣟⡷⣯⢿⣵⣯⠿⠛⠉⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠙⢢⡀⣀⣴⣿⣿⠿⢾⣯⡿⣽⢯⡿⣽⢯⣿⠃⠀⠀⠀ ⣯⢷⣻⢷⣫⣿⠾⠛⠉⢀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢈⠉⠀⠀⠄⡀⠀⠻⣏⠉⠀⠀⢀⣾⣿⣽⣯⢿⡽⣯⣟⣿⠀⠀⠀⢠ ⡿⣞⣿⣾⠛⠉⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⢠⠓⢚⠀⣮⠆⠀⠹⣄⠀⠀⠈⠉⠉⠛⢻⣾⣳⢯⣿⡏⠀⠀⠀⣸ ⡿⣽⢿⣧⡀⠴⣾⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢠⠀⢀⣳⠖⢂⡀⠀⠹⣆⠀⠀⠀⠀⠀⣼⣿⡽⣯⣿⠁⠀⠀⢀⠇ ⣿⡽⣯⣟⡿⣷⣦⣉⡉⠛⠛⣲⡶⠶⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡀⠈⠀⠄⠃⠀⢸⡇⠀⠀⢹⡄⠀⠀⠀⢾⣿⣳⢿⣽⡇⠀⠀⠀⡜⠀ ⣷⣻⠷⣯⣟⣷⠿⠋⢁⡴⠞⠁⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢀⣿⠀⢀⡀⢀⣻⡿⣯⣿⠀⠀⠀⢠⠇⢠ ⣯⣟⣿⠷⠋⢁⣠⠞⠋⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣄⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⠋⣿⣇⠈⣿⣿⣟⡿⣽⡏⠀⠀⠀⡼⠀⣾ ⣷⠟⠉⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡆⠀⠀⠀⠀⠀⠀⣾⠦⠟⠀⢸⠇⠸⣿⣿⣻⢾⡽⣿⠃⠀⠀⢰⠇⣸⣿ ⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⣤⠀⠀⠀⠀⠀⡾⠀⣷⠀⢀⡀⠀⠀⣰⠏⠀⠀⠀⠻⠖⠚⠛⠉⠙⠛⠛⠛⠒⠒⢶⣼⢠⡿⣞ ⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⣿⠀⠀⠀⠀⣸⣧⣶⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⣀⣠⣤⣶⡖⠀⠀⠀⠀⠀⢀⣤⠾⡇⣸⡿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣠⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⣾⣿⣟⢹⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⡴⠋⠀⢸⠁⣿⣽⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠠⣴⣞⠉⠀⠀⢀⡏⢸⣟⣾⣳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡟⣿⣿⣿⣿⣿⣿⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠓⠦⣄⡼⠀⣾⣟⡾⣵ ⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠟⢿⠿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣿⣿⣿⣿⣿⣿⣿⡏⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⣿⡿⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠳⡌⠿⣾⣽⣳ ⣿⣟⡿⣿⢿⣿⣻⣟⣿⣁⣀⣠⠼⡇⠀⢩⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢻⣻⣿⣿⣿⣿⣇⠀⠸⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠸⣿⣜⣧⣶⡿⠃⠀⢸⡓⠶⠤⣤⢤⡤⣤⠽⠆⠙⣾⣳ ⠛⠿⢿⣽⣻⣞⡷⣯⣟⣿⣻⣿⣾⣇⠀⠛⠛⢿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢷⡻⣿⣿⣿⠏⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⢸⡇⢲⣤⣤⣤⣠⣠⣤⡤⠴⠟⢛ ⠷⣤⣄⣈⠉⠛⠛⠿⠾⣷⣿⣞⣿⣿⠀⠀⢠⡟⢻⡟⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⣮⣷⢾⠋⠀⠀⠀⠀⣀⣀⣼⠃⠀⠀⠀⠀⣠⡴⠚⠛⠦⣄⣀⠀⠀⠀⢸⠅⢸⡿⠟⠛⠋⣉⣠⣤⣶⣾⣿ ⣷⣤⣌⣉⠛⠓⠶⠦⣤⣄⣀⣈⡉⢛⣧⠀⡾⢡⣿⣧⣤⡈⠉⠓⢲⣶⠶⠶⡶⣾⠋⠉⠀⠀⠀⠚⣡⣴⣿⢿⣽⡟⢀⣠⡴⠞⢋⣥⣴⠿⠗⠂⠀⠉⠙⢲⣤⣼⣦⣤⣾⣷⡿⣿⣟⡿⣯⣟⣾⣳ ⡿⣽⣻⣟⡿⣿⢶⣤⣄⣀⣀⠉⠉⠙⢻⣦⣿⣿⣻⣯⣹⣿⣶⣀⠈⠉⠛⠛⠻⣿⠶⡤⢤⣤⠤⡴⣤⡾⢿⢿⣿⣛⡯⣹⣧⠈⠋⠁⣀⣀⡤⠴⠖⠚⠋⢿⣿⣟⣯⣟⡷⣯⣟⡷⣯⣟⣷⣻⢾⡽ ⣿⣳⣟⡾⣽⢯⡿⣽⣻⣟⣿⣻⢿⣻⣿⢻⣿⣿⢿⣿⣿⣿⣽⣻⣷⣤⡀⠀⣰⠃⣰⣧⠀⡿⠶⣄⣸⣧⣿⠋⢉⡉⣻⣦⡿⠗⣻⡏⠉⠀⠀⠀⠀⠀⠀⣹⣿⣞⡷⣯⣟⡷⣯⣟⣷⣻⢾⡽⣯⣟ ⣿⢯⣟⣷⣻⣞⡷⣯⢿⡽⣯⣟⡾⣯⢿⣮⣿⣯⣼⣿⡿⣿⣯⡿⣽⣿⣷⣤⡏⣠⣿⣿⡀⢳⣤⣉⠛⠿⢿⡶⠾⣗⣿⢋⣡⠶⢛⡇⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡷⣯⣟⡷⣯⢿⣽⣻⣞⡷⣯⣟ ⣿⣻⣞⣷⣻⢾⡽⣯⢿⣽⣳⢯⡿⣽⣻⣞⣿⡿⠻⣷⡿⣽⣻⣿⣿⣻⣞⡿⣷⣌⠁⢸⡗⠞⣇⠉⠙⠓⠶⠙⠛⠉⠀⠀⠀⠀⣸⣃⣀⣀⠀⠀⠀⠀⠀⣿⢷⣯⣟⡷⣯⢿⣽⣻⣞⡷⣯⣟⡷⣯ ⣿⣳⣟⡾⣽⢯⡿⣽⣻⢾⡽⣯⣟⣷⣻⢾⣽⠁⢠⣿⣿⣿⣿⣿⣷⣿⣾⣿⡽⣿⣦⠀⣹⣀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢩⡿⠀⠀⠀⠀⠀⣿⣟⡾⣽⣻⣽⣻⣞⡷⣯⣟⡷⣯⣟⡷ ⣿⣳⢯⡿⣽⢯⣟⡷⣯⢿⣽⣳⣟⡾⣳⣿⡃⢠⣾⣿⣷⢯⣟⣿⡆⣹⣿⣳⣟⣷⣻⣷⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⢤⣀⠀⠀⠀⠐⣿⣯⣟⣷⣻⣞⡷⣯⣟⡷⣯⣟⡷⣯⣟ ⣿⡽⣯⢿⣽⣻⢾⡽⣯⣟⣾⣳⢯⣟⣷⣻⡅⠈⢿⣟⡿⣿⣾⣟⣠⣿⢷⣻⣞⡷⣯⣟⣿⡈⢩⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣈⣙⣷⠆⠀⡈⠙⠒⠦⣼⣿⣾⡽⣞⡷⣯⣟⡷⣯⣟⡷⣯⣟⡷⣯ ⣿⡽⣯⣟⡾⣽⢯⣟⣷⣻⢾⣽⣻⣞⡷⣯⢿⣄⠀⠻⢿⣷⣿⣿⣻⡽⣯⢷⣯⣟⡷⣯⣟⣷⡾⠲⢶⡖⠀⠀⠀⠀⠀⠀⠈⡿⢀⣀⣀⣤⣿⢿⣶⣤⣄⣀⠉⠙⠛⠿⢷⣯⣟⡷⣯⣟⡷⣯⣟⡷ ⣿⣻⢷⣯⢿⣽⣻⣞⡷⣯⣟⣾⣳⢯⡿⣽⢯⣟⡿⣶⣶⣶⣌⡙⢿⣽⣯⣟⡾⣽⣻⢷⣯⣿⠳⣄⠀⣷⠀⠀⠀⠀⠀⠀⠀⣷⠈⣿⢯⣟⣾⢻⣼⣳⢯⣟⡿⣶⣦⣄⡀⠀⠉⠙⠓⠿⢽⣷⣯⣟ ⣿⣯⣟⣾⣻⣞⡷⣯⣟⣷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣳⣟⡾⣽⢷⣆⠉⠻⣾⣽⣳⢯⣟⣾⠃⠀⠈⢧⡿⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⣿⢾⣭⣟⡾⣭⣟⡾⣽⣳⢟⣾⣻⢿⡶⣤⣀⡀⠀⠀⠉⠙ ⣿⡷⣿⣞⣷⣯⣟⣷⣻⢾⡽⣯⢿⣽⣻⢾⣽⣻⣞⡷⣯⢿⡽⣯⣟⣿⣤⡈⠻⣿⣿⣾⠃⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⠻⣾⣭⣟⣷⣫⣽⣳⣏⣿⣾⣽⣳⣿⣽⣻⣽⣷⣦⣄⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠉⠉⢠⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢠⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⡇⢠⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⡾⢉⠀⠀⠠⠠⠁⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⡄⠉⠘⣿⣶⣾⣶⣖⡀ ⠀⠀⠀⠀⢀⡤⣲⣿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢱⠀⢰⣿⣿⡿⠋⠉⠙ ⠀⠀⠀⣴⡯⣋⣽⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⢿⢻⠀⠀⠀⢁ ⣦⣤⣾⣿⣷⣿⣿⣿⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⣁⣿⡋⠀⠀⠀⣠⠞ ⠈⠿⣿⣿⣿⣽⣿⢨⠀⢰⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⠀⠁⠀⠀⡀⠈⠁⠉⠇⠀⠀⠀⠀⣩⡆⠀⠀⣠⠟⠁⠀ ⠀⢠⡙⣷⡾⡟⣧⡿⠀⢀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡂⠀⠐⠐⢈⢭⠈⡘⠀⠀⠀⢰⣟⣷⣶⠊⡅⠀⠀⠀ ⡀⠀⢀⠊⢳⣦⢸⣾⣆⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⡀⠀⠀⡀⠁⠀⠀⠅⠈⠠⠀⠀⠄⠀⠀⣾⣻⣿⠃⡼⠁⣰⠆⠀ ⠹⣄⠀⢧⠀⢻⣿⣿⣿⣦⠀⠎⠀⠁⣁⡅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⢀⡼⢱⢿⠃⡰⠁⢀⡏⠀⢀ ⠀⢻⡄⠘⣆⠀⢻⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢡⡰⠀⠀⠁⠀⠀⠀⠉⠀⠐⠁⠀⠔⠀⠁⠂⠂⠂⠂⠘⠛⢐⣿⣿⢠⠃⢀⣾⠁⠀⢈ ⡇⠀⢿⠀⢹⡆⠘⣿⣿⣿⣿⣗⡄⠀⠈⡠⠄⠒⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠐⠒⠠⠤⠠⠀⠀⠂⠐⠀⢀⣿⣿⣿⣞⡆⢻⣿⠀⠀⠏ ⣷⠀⢨⠇⢠⣧⠀⢸⣿⣿⣿⡾⠹⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠠⠀⣸⣿⣿⣿⣧⣿⠚⠻⠀⢸⠀ ⡏⠀⡸⠀⡾⠈⢧⣈⣿⣿⣿⡟⠹⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣷⣂⣀⡇⠀ ⢱⡀⢁⡰⠁⠀⠀⢛⡛⣿⣿⣿⠘⢠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡿⠉⠉⢉⠁⠀

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⢯⡻⣝⢯⡟⡽⣯⢟⡽⣯⣟⣯⣿⣽⣿⢿⣿⣟⣿⣻⣟⡗⠀⠀⠤⠀⠀⠀⠘⠀ ⡳⣝⢮⡳⣝⡳⣝⣮⣿⣟⣿⣿⣽⣿⡾⣿⣻⣾⣟⣿⣾⣯⡆⠀⠀⠀⠀⠀⠀⠀ ⣝⢮⡳⣝⢮⣳⣿⣿⣯⣿⣯⣷⣿⣻⣿⢿⣽⣷⡿⣯⣿⣿⣧⡀⠀⠀⠀⠈⣁⢠ ⣎⠷⣹⢎⣷⣿⣿⣾⢿⣽⡧⣿⣿⣻⣏⢻⣿⣯⣿⣟⣷⣿⣿⣵⡀⠀⠀⠀⢺⣹ ⣎⠿⣱⢞⣾⣿⣟⡛⠿⠋⡠⣿⣿⣿⣽⠀⠜⠿⣿⣽⣿⣯⣿⣟⣧⠀⠀⠀⣹⢼ ⡝⣦⢛⣼⣿⣿⣿⢷⡖⠀⠁⢹⠻⣿⣿⡀⠀⡀⠙⢿⣿⣿⣿⣿⢿⠀⠀⠀⣹⢼ ⣝⠲⣏⣾⣿⣿⣾⢿⡁⠀⣐⡀⠇⠙⢯⣇⢡⣞⡲⣄⢿⣿⣿⣿⣿⡀⠀⠀⢼⢸ ⣎⡿⢫⣿⣿⣿⣿⣷⢡⡞⣕⣾⡄⠀⠀⠉⢲⣾⣿⣼⠸⣿⣿⣿⣿⠀⠀⠀⣸⢹ ⡞⣼⢣⣿⣿⣿⣿⣿⡉⠧⢻⣿⠇⠀⢀⠀⠈⠛⠛⠁⢰⣿⣿⣿⣿⠀⠀⠀⢽⢸ ⣝⡲⢫⣽⣿⣿⣿⣿⣧⠀⠠⠠⠀⢀⡠⣤⡀⠈⠒⠀⣾⣿⣿⣿⡇⠀⠀⠀⣚⢸ ⢮⢵⢫⢾⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⡿⣽⡛⠀⠀⢠⣿⣿⣿⣿⡇⠈⠅⠀⡜⣺ ⣏⢾⣹⡀⣾⡿⣿⣟⣿⣿⣶⣤⣀⡀⠈⠉⢀⣤⣶⣿⣿⣷⣿⡟⡗⢳⠠⡐⣰⢹ ⣎⠦⡑⠓⠳⡯⢽⢿⣿⣿⠿⢟⢏⡳⢥⢉⡦⢏⡿⢏⣿⡿⠿⠄⡃⢉⢤⠌⢿⢸ ⣬⢻⠐⢤⠄⠉⡇⠀⠙⠧⠀⠢⢧⡘⣶⣿⣶⢡⡏⠊⠈⠁⡆⠀⠇⠈⠱⡠⢸⡭ ⢦⡛⡆⠉⠙⠀⡇⠀⢠⠍⠀⠀⠈⣕⣿⢻⢿⡄⠁⠀⠀⠀⡇⠀⠐⠄⠀⠀⡾⣱ ⢎⡳⡕⡆⠀⠀⠇⢠⠈⠀⠀⠀⠀⣹⢯⢸⣼⡇⠀⠀⠀⠀⠇⠔⢠⠀⠀⠀⢧⢏ ⣝⡲⣽⡜⠀⠀⢀⠈⡞⠀⠀⠀⠀⠈⣹⣠⡟⠀⠀⠀⠀⠀⢨⠆⢈⠀⠀⢠⣏⣚ ⡿⣝⣳⠇⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠙⠘⠃⠀⠀⠀⠀⠀⢰⠀⠂⠀⠀⢸⡷⣹ ⣿⣽⣹⠀⠀⠀⠀⠆⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠈⣿⢵ ⣿⣞⣽⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⣟⢮

⠀⠀⠀⠀⠀⠀⣀⠄⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠂⠉⠐⠢⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⢀⡀⠆⠂⠉⠁⠉⠁⠉⠉⠁⠁⠉⠑⠂⠢⠅⡓⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡇⠀⠀⠈⠑⢌⢆⡀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠈⢢⡀⠀⠀⠀⢱⠣⡀⠀⠀ ⠀⠀⠀⡁⠀⠀⠀⢀⠇⠀⠀⠀⠠⠐⠁⠀⠈⢧⠀⠀⠀⠀⠀⡌⠀⠀⡠⠄⡅⠤⣀⠀⢸⠀⡃⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⡴⢋⡕⠛⠓⢧⡀⠐⠀⠀⠀⠀⡐⠀⢀⠗⠋⢙⠛⢏⡆⠁⡅⠀⡅⠀⠀ ⠀⠀⡁⠀⠀⠀⢐⠀⠀⡎⡎⠃⠀⠀⠀⠀⢽⡄⢁⠀⠀⠀⠅⠘⡍⠀⠀⡜⠀⡇⠁⠔⠀⢀⠅⠀⠀ ⠀⠀⡀⠀⠀⠀⠨⠀⣨⡗⠀⠀⠀⠀⠀⠀⠀⠃⠀⡂⠀⠀⠅⢱⠃⠀⠀⡇⢀⡆⠊⠀⠀⡊⠀⠀⠀ ⠀⠠⠀⠀⠀⠀⠨⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠁⠈⠀⠀⠀⡑⠗⠤⢄⣀⡤⠃⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⢘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠨⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⢇⠀⠀⠀⠀ ⢀⠃⠀⠀⠀⠀⢨⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⢐⠀⠀⠀⠀⠀⠼⣀⠀⠀⠀⠀⣐⠅⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠐⠀⢧⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠌⠀⠘⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⡤⠔⠋⠁⠀⢀⣀⣀⣤⠏⠀⠀⠀⠀⠀ ⠄⢀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠔⠋⠀⢨⠀⠐⠀⠀⠀⠀⠀ ⡁⠀⠉⠆⢄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⡗⠋⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⠇ ⠠⠀⠀⠀⠀⠙⡕⠒⠂⠒⠂⠒⠂⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⡊⠀ ⠀⠄⠀⠀⠀⠀⠙⡄⠀⠀⠀⠠⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠑⠦⠤⠤⠔⠅⠀⠀ ⠀⠀⠄⠀⠀⠀⠀⠈⠑⠒⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⡀⡀⣀⣀⠄⠃⠀⠀⠀ ⠀⠀⠀⠈⠂⣄⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠘⣳⠀⠀ ⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠓⡄⠀⠀⠀⢸⠁⣃⠀⠀⠀⠀⢸⠁⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡏⠀⠘⡆⠀⠀⢀⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀ ⠀⠀⠀⠐⢧⡀⠀⠀⠀⢀⣀⠾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠁⠀⠀⠘⣇⠀⢰⠁⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⠀⠀⠀⠀⠛⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⢢⢄⣀⣀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⡖⠒⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⡏⠀⠀⠀⠸⡀⠀⠀⢀⡞⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠘⡟⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠘⠆⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠦⠦⠶⠶⠶⠒⠒⠒⠒⠋⠉⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠷⠶⢤⣄⣀⡀⠀⠘⠛⠐⣆⠟⢦⡴⠀⠛⠃⢀⣀⣠⡼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠈⠉⠛⠛⠧⠭⠭⠬⠭⠥⠟⠛⠛⠉⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣀⣀⣀⡀⡀⣀⣀⣀⣀⣀⣀⢀⡀⡀⡠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠟⠋⠉⠉⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣡⠃⠀⠀⠀⠀⠀⠈⢳⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠲⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠩⣆⠀⠀⠀⢀⡟⢇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀ ⠀⠀⢐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⠙⡆⠀⢀⡝⠀⠈⢇⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⡐⡞⠀⠀⠀⠙⢶⡷⠁⠀⠀⠀⢣⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⣃⢄⠀⠀⠀⠀⠀⣐⡟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⢯⣱⠀ ⡧⡞⠁⠻⢗⣦⡀⠀⠀⣐⣦⣬⡼⢟⠳⠶⣄⣀⠠⡞⡴⠋⠀⡗⠂ ⡗⣇⠀⢁⠀⢺⡕⢶⡚⡱⢌⡱⢚⡋⣌⢣⠹⣌⠳⢿⡀⠐⣰⠽⠀ ⠸⡞⣆⡀⠂⢠⠞⡡⢜⡡⠎⡔⢣⠜⢤⠃⠧⣌⢣⡙⣶⡼⡳⠃⠀ ⠀⠘⠦⣝⡣⢟⡌⠷⠃⢸⡱⣌⢣⠚⡤⢋⠖⡤⢃⡞⠈⡟⠁⠀⠀ ⠀⠀⠀⠈⠙⣷⢸⢦⣤⣶⣶⣡⠃⣝⡰⣉⠖⣡⢟⣾⣟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣋⢞⠘⣿⣿⣿⣿⣧⠘⡰⢡⠚⡤⣿⣿⡿⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠩⢞⣑⡹⢿⣿⣿⠟⠀⠷⢓⣻⣲⠿⢟⠱⡚⠀⠀⠀ ⠀⠀⣠⠄⠀⠀⠙⢿⣏⠀⠀⠈⠀⠀⠀⠠⠿⠧⠀⣀⠔⠀⠀⠀⠀ ⠀⣰⣅⣽⣀⣀⣀⣀⠈⢁⡖⢢⢠⡤⠤⢤⠐⠒⠉⠀⠀⠀⠀⠀⠀ ⠀⣿⣩⢛⠤⣃⠎⡥⢋⠵⣈⠇⣎⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢹⡌⢲⢡⠚⡴⢉⠲⣡⠚⡤⠇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⣎⡱⢌⠽⠢⢽⡦⡑⢎⡜⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣟⢡⠚⢞⠛⡦⢸⡇⡜⡾⡘⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡩⣬⢣⣝⣄⠈⡓⠬⣷⣡⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣉⣉⠠⣤⣇⠀⢋⠛⢃⣌⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⠃⠈⠁⠀⠈⢶⣿⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣾⠢⢴⡒⠈⠉⠉⠉⠀⡶⣖⠒⠴⣦⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠈⠿⣒⡒⠒⠒⠄⢸⠾⠁⠀⢸⣿⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⡞⠁⠀⢀⠤⠒⠀⠀⢀⣤⠖⢀⠃⡆⠀⡀⢸⣿⣿⣿⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡔⢥⡀⣸⡴⠁⢀⠄⠀⡠⢊⠏⠀⢸⠀⠳⣰⣿⣿⣿⣿⣿⣷⣷⡀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡎⠀⠘⣟⠻⢴⣚⡥⠔⠋⠀⣼⠀⠀⠈⢦⡀⠮⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡏⠁⢠⣄⣤⠟⠂⠀⠀⠀⣀⡼⢽⠀⠀⠀⠀⠈⣽⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣧⡇⠈⢑⣦⣤⣴⣶⣶⣚⠉⠀⠸⡄⡤⠀⢀⡴⠛⡇⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡟⠰⣄⡞⢋⠂⣾⣿⣿⣿⣷⡄⠶⢯⡴⢠⠟⠁⠀⢡⠀⡌⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡥⠸⢏⠁⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠙⢺⣿⣿⣷⣾⣼⣷⢧⠹⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠹⡍⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠿⣿⣿⠟⠺⣿⣞⣠⢿⡟⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠉⠛⠃⠚⡻⠛⣿⠁⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠰⡀⠀⠀⢻⠀⠉⠑⠒⠠⢤⣀⠀⠀⠀⠀⠀⢀⠜⡇⢾⡌⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⢄⡀⠀⠀⠀⣀⡿⠀⠀⢀⣴⣻⠿⠷⡉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⣬⣷⣄⠀⠀⠉⣉⠿⠫⢅⣀⡤⣒⠉⠀⠉⠀⠀⢨⢦⣄⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⠀⠀⠀⠘⣏⣽⢿⡬⢷⣄⠞⠁⣠⠄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠈⠀⠛⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠀⠀⢀⠼⠛⠉⣠⢴⠾⠀⢸⠀⣀⠜⠉⠒⠒⠛⠒⢂⣶⣟⡱⠃⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⡤⡖⣷⣶⣶⣿⠃⡎⠀⣶⠛⠯⠤⣤⠤⢀⡀⢀⣴⣾⡿⠋⠢⡀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⡽⠓⣿⣿⣿⣿⠀⠁⢀⣿⣿⠿⠛⠁⢀⣤⣷⣿⣿⠟⠁⠀⠀⠑⡄⠀⠀⠀⠀⠈⢧⡀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠊⠀⡰⢇⣙⣿⡇⢸⣀⣾⣿⣅⣠⣴⣾⣿⣿⣿⣟⣁⣀⠀⠀⢀⣀⣘⣆⠀⠀⠀⠀⠀⠹⣄

⠀⡆⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣦⡀⠀⠀⢀⡤⡟⠵⠃⠀⠀⠀⠀⠀⠀⣶⠦⡄⠀⠀⠀⠀⡰⡶⡆ ⠀⠀⠻⡿⠿⠽⠿⡺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣯⡓⢆⣀⣷⣿⡗⡇ ⢀⣀⡀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠒⠒⠋⠁⠀ ⡏⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠳⣄⠴⠃⠀⠀⠀⠀⠀⠀⠳⠾⢷⡤⣾⠃⠀⠀⠀⠀⡞⠉⠀⠙⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣤⡟

ALL DEEZ TAGS VERY SUS TURN BACKKK

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⢶⣾⣻⣯⣽⣾⡿⠾⢶⣦⡝⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢶⣾⣿⣿⣿⣿⣶⠿⠟⠛⠋⢉⢉⣀⣤⣄⡀⠻⣷⡝⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣷⣿⠟⠛⠛⠋⢁⠀⣠⣤⣤⣴⣾⣿⣿⠿⠿⠛⠻⣿⣧⡛⣿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⣿⠋⠁⣀⣤⣶⣾⣿⠿⠿⠿⠛⠛⠉⠉⡀⠀⠄⠠⠐⠀⠘⣿⣷⢛⣿⡽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣰⣾⣿⡿⠛⠁⢠⣿⠀⡀⣿⣿⠉⠁⡀⠠⠀⠄⠐⡀⠡⠐⠀⢁⠀⠂⠠⠈⣀⠘⣿⣷⢹⣿⡜⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⣿⣿⠟⠉⠀⠀⠀⠀⣿⡀⢀⣿⣿⡀⠐⠀⡁⠐⠈⡀⠄⠐⢀⢈⣀⣠⣼⣤⡼⣿⣦⠘⣿⣷⢻⣿⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣾⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣄⢻⣿⣇⠀⢁⡠⠈⣴⣶⡀⣶⣤⣾⣿⠋⢿⣿⣶⣿⣿⠀⢹⣿⡎⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢿⣿⡄⢸⣿⣆⣘⣿⡧⠈⠛⠉⠁⠀⡀⠉⠉⠁⠀⠀⣨⣿⡧⠈⢿⣏⢻⣆⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡌⢿⣷⡌⠻⢿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⡿⠟⠁⠄⠘⣿⣷⢻⡇⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡘⢻⣿⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠟⠛⠀⣠⣾⣿⣿⣿⣿⣿⣧⢿⡄⠀⠀⠀⠀ ⠀⠀⣿⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠈⢿⣿⣆⣀⣀⣰⣶⣿⣿⣿⡿⠏⠁⢀⠰⠀⢱⣿⣿⣿⣹⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠈⠛⠿⢿⠿⡿⠟⠛⠋⢀⠀⣂⠐⠓⢈⠐⠈⣿⣿⣷⣯⣿⣿⠃⠹⣷⣹⣷⡀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠂⠄⠠⢀⡐⢠⣦⣄⣦⣅⠠⢈⠀⠂⡁⢀⠙⠛⠛⠛⠁⡀⠂⢿⣿⣹⣧⠀⠀ ⠀⠀⠀⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⢁⠈⡐⠀⣠⣶⣾⣿⣿⣿⣧⣤⣌⡐⠀⢂⣨⣶⣶⣶⣧⣄⠂⠈⢿⣧⢻⣶⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠠⢀⠘⣿⣿⣄⠐⠀⡁⣿⣿⣏⠡⠘⣿⣿⣿⣿⣧⠐⣼⣿⡟⣩⠙⣿⣿⡆⠁⡘⣿⣮⣿⠆ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⣝⣆⠀⢀⠠⠐⡈⢐⠠⢊⠼⣿⣿⠀⠂⣤⣾⣿⣿⠶⢁⠋⣅⣢⣿⣿⡄⠹⣿⣷⣦⣿⣿⡿⠁⡐⠀⣹⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣎⣇⠀⣂⠐⡄⢃⠜⡠⢎⡹⣿⣷⠀⢿⣿⡍⣁⣲⡈⡜⢻⣿⣿⠛⠀⠄⠉⠛⠛⠛⠉⡀⠐⡀⢁⣼⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣜⡣⢠⠑⡌⢒⠬⡑⠦⣑⢻⣿⣧⠘⣿⣿⣿⣿⣷⣬⣹⣿⣿⠄⢈⠐⠈⠠⢈⠐⠠⢀⣡⣴⣿⣿⡿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡕⢣⡘⣌⠣⢎⠱⡘⢤⢋⢿⣿⣆⠀⠡⠀⢻⣿⣿⠟⠋⠡⢀⠂⠈⠄⠡⠀⣂⣵⣿⢟⣿⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡤⣑⢢⡉⢆⣣⡙⢦⣋⠞⣿⣿⡆⠁⡐⠠⢀⠀⠄⡈⠐⠠⢀⠡⣈⣴⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣻⣷⣣⢆⡹⣜⡰⡹⣆⢯⡞⡽⣿⣿⡀⠐⡀⠂⡈⠄⠠⢁⣢⣴⣾⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣋⠶⣡⢯⢵⣫⢶⣹⢳⡽⣿⣷⣤⠀⡁⢄⣴⣶⡿⣿⣿⡾⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣯⣗⣯⣞⣵⣫⢾⣝⣾⣵⣯⣿⣷⣿⣿⣿⣷⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⣟⣻⣟⣟⣻⣿⣿⣛⣯⣯⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ε(´｡•᎑•`)っ 💕⠀⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⢺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡉⠉⠉⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡿⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⡏⢹⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⢺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⠁⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠃⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢠⡇⠀⠀⠀⠀⠀⣠⠀⣰⣴⡿⠂⠀⠀⠐⣾⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⣾⠀⠀⠀⠀⠀⡐⠁⢀⣼⠛⠁⠀⠀⠀⢠⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢠⠃⠀⠀⠀⠀⡰⠃⢄⣾⡛⠀⠀⠀⠀⠀⣼⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⡘⠀⠀⠀⠀⡔⠁⢰⣿⠇⠀⠀⠀⠀⠀⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⣠⣶⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⡀⠀⠀⠀⠀⢸⠀⠸ ⢠⠇⠀⠀⠀⡄⠁⣴⢟⠀⠀⠀⠀⠀⠀⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣇⠀⠀⠀⠀⢸⠀⢸ ⠐⠀⠀⢀⡼⣤⣵⠟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⣠⠄⢀⣴⢟⠀⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⡀⠀⠀⣸⠀⢸ ⠀⠀⠀⠊⣠⡿⠃⠀⠈⠀⠀⠀⠀⠀⢠⢻⡏⠁⠀⠀⠀⣠⠒⠁⣴⠞⢉⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⢻⡵⠀⠀⡿⠀⢸ ⠀⠀⠀⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠀⢠⠶⠁⣠⣾⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣤⣶⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠀⢸⡇⠀⢸ ⠀⢀⡼⡋⠙⠳⢶⣤⣤⣄⣤⠤⣴⠟⡾⠇⠀⠠⠀⢡⣤⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⡯⠝⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣼⠀⠀⢸ ⡶⠋⣷⠁⠀⠀⠀⠀⠉⡝⠛⠛⠥⡾⢅⣀⡠⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣟⣋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⢸ ⠀⠀⢿⠀⣀⣀⣀⣤⣤⣥⣤⣤⣤⣷⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣤⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸ ⠀⠀⣼⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢸ ⠀⠀⣿⣿⣿⠟⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡟⠉⠈⢻⣿⣿⣿⣿⣿⡟⡻⢿⣿⣿⣶⣄⣀⠀⠀⢀⣸⠀⠀⢸ ⠀⠀⠹⣿⡇⠀⣿⣿⣿⣿⡀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸⣿⣿⣿⣿⣿⣷⣀⣀⣾⣿⣿⣿⣿⣿⣿⣆⡀⠉⠻⣿⡿⠿⠛⠉⠀⣺⡇⠀⢸ ⠀⠀⠀⣹⠷⠀⣿⣿⣟⣟⣿⣿⣿⣯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠿⣟⣥⡶⠦⠽⢿⣿⣟⣿⣟⢻⣿⡿⠀⠀⠀⣩⡞⠋⠀⠀⠀⠀⠀⢹⣇⠀⢸ ⠀⠀⠀⣼⠀⡀⠸⠗⠋⠁⠀⠀⠀⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠁⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⠤⣄⡐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸ ⠀⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⠀⢸ ⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸ ⠀⠀⠀⣾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢈ ⠀⠀⠀⢯⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈ ⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢘ ⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣼⠀⢸ ⠀⠀⠀⠀⠲⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣠⡀⣀⣀⠀⣄⣀⣀⣄⡤⣤⣤⣀⣀⢠⣠⣄⣤⣤⣤⣀⣤⣄⣴⣿⣿⣽⣝⠛⣃⣾⠀⢸ ⠀⠀⠀⠀⠀⠉⠨⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠷⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣟⣿⠿⠿⠿⠻⠿⠿⠿⢿⡟⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⢼⢃⡴⣻

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⠀⠀⢀⠏⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⡆⡅ ⠀⠀⠀⠀⠀⠀⡔⢦⡀⠀⠀⣀⡠⠤⢲⠓⢳⠒⠒⠒⠀⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⡳⡀⠀⠀⠀⠀⢘⠀⣿⠀⣟ ⠀⠀⠀⠀⠀⡎⢀⡬⢳⠉⠀⠀⠀⡜⠁⠀⠀⠱⠀⠀⠀⡅⠀⠀⠈⠉⠹⡉⠉⠉⡋⠑⠳⠤⣄⠀⠨⠀⢯⢸⡇⡇ ⠀⠀⢀⡤⠻⠁⠀⠀⡇⠀⠀⡠⠃⠀⠀⠀⠀⠀⠑⡀⠀⠇⠀⠀⠀⠀⠀⠈⡂⠀⡜⠀⠀⠀⠈⡌⠑⢦⠅⢘⣏⡅ ⠱⣞⠁⠀⢪⠀⠀⢠⢃⣠⡾⠛⠙⢯⠁⠀⠀⠀⠈⢂⠀⠍⠁⡇⠈⠉⠙⣿⣕⣆⠀⠀⠀⠈⢂⠀⡗⠀⡟⠀⣿⢐ ⠀⠀⠈⠒⢄⣃⣠⡽⠋⠀⡠⣦⠀⠀⡇⠀⠀⠀⠀⠀⠑⠄⡆⠀⡇⠀⠀⣾⣇⠇⠘⣷⡀⠀⠀⠀⠂⣸⠀⠉⠀⢸ ⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⣺⡿⡇⠀⢳⠀⠀⠀⠀⠀⠀⠡⠇⢸⠀⠀⠘⣿⡟⡇⠀⢹⣷⡀⠀⠀⠀⠹⡀⠀⠀⡗ ⠀⠀⠀⠚⠋⣏⠀⠀⠀⢀⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⣹⠀⠀⠸⢟⡟⠀⠀⢸⠛⣷⠀⠀⠀⠀⠉⠀⠀⣻ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡿⠟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨ ⠀⠀⠀⠀⠀⠸⡅⠀⢀⣀⠀⠀⠀⡀⢸⡀⣀⠀⡰⢶⣷⣏⣢⣝⣶⡉⡻⣷⠚⢟⣺⡥⡴⣢⡜⣳⠀⠀⠀⡇⣜⠸ ⣸⠱⠤⣧⣫⣤⢸⠯⠶⢟⠳⠓⢛⢏⡇⠥⠝⠚⠃⠉⣿⠀⠈⠋⠉⠓⠉⢣⠎⠈⠒⠋⠙⠓⠶⠋⠀⡸⢸⣇⢧⠀ ⠀⠀⠀⠈⠀⠑⠷⠤⠗⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇ ⠀⣤⠖⠒⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⡅⠀⠀⠀⠀⠀⢰⡍ ⢸⢿⡳⡏⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣩⣣⡤⡇⠀⠀⠀⠀⡎⠡⣃ ⠀⠳⣅⣠⠇⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣜⠟⠀⠀⠀⠀⡞⠀⡝⣉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠮ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠰⠅ ⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠠⡇⢌ ⡀⢹⠑⠒⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⡋ ⠅⡜⠀⠀⢐⠃⠀⠀⠉⠉⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠼⠀ ⠅⡃⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠴⠋⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀ ⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀ ⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢐⡁⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀ ⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠘⠒⠂⠂⠂⠠⠀⠤⠤⠖⠃⠀⠀ ⠀⠀⠀⠀⠘⠀⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠈⠂⠄⠄⠀⣀⣀⠴⠃⠀⠀ ⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠄⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠁⠀⠀⠀⡀⠀⠀⠀⠢⠭⣒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠉⠀⠀⠀⠀⢀⠀⠁⠐⠈⠀⠀⠀⠀⠈⠑⠲⣻⠴⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡗⠋⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣭⡓⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⠋⠀⠀⠀⠀⠀⠀⢠⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⢝⢆⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡾⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⡺⢦⡀⠀ ⠀⠀⣾⣿⡟⡇⠀⠀⠀⠀⠀⢀⣠⣾⡇⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⡈⢳⡀ ⢀⣼⡿⣫⡞⠀⠀⠀⢀⡠⠞⠁⡀⠀⡇⢸⡀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡝⢮⡗ ⢸⣿⣾⡗⡇⠀⠀⢠⣮⠵⠶⠶⡀⠈⢹⡀⢷⠀⠀⠀⠀⢹⠶⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣏⠰⣀ ⡞⠿⡹⣳⠃⠠⢰⠏⠁⠀⠀⠀⢣⠀⠀⢧⠈⢇⡀⠀⠀⡜⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⢀⣿⠋⡇⠰⠠ ⢉⠆⠡⡟⡄⢠⣿⣠⣤⣤⣽⣙⠚⠀⠀⠈⠳⡈⢣⡀⠀⣷⣲⣚⣏⣀⣤⣀⣑⣆⠀⠀⠀⠀⣾⢣⠇⢿⠀⠁ ⠸⠀⣤⣿⡅⠘⣿⣏⣿⣿⡿⠛⡿⣆⡀⠀⠀⠹⣄⠙⣴⣿⣿⠛⠋⣭⠛⢻⡙⢻⣷⡂⠀⢠⡟⢸⠀⣰⠀⠀ ⢇⣰⠟⠚⢱⡄⢸⣿⣯⠙⠏⠒⡧⠁⠀⠀⣸⣆⠀⠓⠚⣿⡏⠀⠸⠟⠀⢺⡇⣾⠙⠀⢀⡞⢁⡞⢀⠏⠀⠀ ⣰⠏⠑⠢⣤⣿⢠⣿⢿⣄⣀⣨⠃⠀⠀⠀⠀⠙⠣⡄⠀⢸⡻⣄⣀⣀⣀⣾⡽⠃⠀⢀⡾⠁⡞⠀⡼⠀⠀⠀ ⠛⢀⡴⣮⣽⣿⣿⣯⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠈⢠⡏⠀⢠⠟⠀⣼⢣⣾⣧⣶⡀⠀ ⠀⢸⡎⠉⠀⠈⠙⠛⢄⠀⠀⠀⠀⠀⢠⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡿⢀⡖⠋⠀⣸⣇⣾⣿⣯⠝⠆⠀ ⠀⠀⠣⣄⠀⠀⠀⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⡶⠋⠀⠀⣼⡯⠛⠋⠋⠙⠂⠸⡀ ⠀⠀⠀⠈⠉⠑⠒⠒⠒⠛⠒⠊⠉⠉⠐⠒⠤⠤⠀⠀⣀⡀⠀⠀⠤⢴⠏⢀⣀⠤⣞⠋⠀⠀⠀⠀⠀⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠈⠓⠠⢤⣀⣀⣀⠤⠃⠀

⣿⣿⡆⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣾⣿⡆⠀ ⣿⣿⡇⠀⠀⢸⣿⢰⣿⡆⠀⣾⣿⡆⠀⣾⣷ ⣿⣿⡇⠀⠀⣿⣿⡇⠀ ⣿⣿⡇⠀⠀⢸⣿⠘⣿⣿⣤⣿⣿⣿⣤⣿⡇⢻⣿⡇⠀⠀⣿⣿⡇⠀ ⣿⣿⡇⠀⠀⢸⡿⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣇⠀⢀⣿⣿⠇⠀ ⠙⢿⣷⣶⣶⡿⠁⠀⠈⣿⣿⠟⠀⣿⣿⠇⠀⠈⠻⣿⣶⣾⡿⠋⠀⠀

⡘⡌⡒⠥⡒⡔⢆⢆⢒⠔⡔⡔⡔⡔⡔⡔⡕⡌⡜⡜⡽⡸⠀⠀⠀⠀⠀⠀⠀⠀⢯⣹⡜⡌⢎⢇⢆⢆⢆⢆⢒⠔⡔⡔⢆⢒⠔⠥⡒⠥⣊⢒⠥⢣ ⢒⠥⡘⡔⢆⢒⠔⡔⡔⡔⠔⡔⠔⡔⠔⡔⡇⡒⠥⢣⣻⠢⠀⠀⠀⠀⠀⠀⠀⠀⠭⣫⢎⠜⡌⢎⠆⢆⢆⢆⢆⢆⢆⢆⢆⢆⢒⠔⡔⢆⢒⠔⢆⠥ ⢢⢒⠔⢆⢆⢆⢆⢆⢆⠆⢆⠆⠆⠆⠆⡜⡜⡔⡔⡱⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⢯⢊⢆⠜⡔⡐⠔⡔⠔⡔⠔⡔⠔⡔⡔⡔⡔⡔⡔⡔⢆⢆⢆ ⢢⢒⠔⡔⡔⠔⡔⠔⠔⠔⠔⠰⡐⠔⡐⢐⠥⢢⢢⢒⠱⣣⠀⠀⠀⠀⠀⠀⠀⢰⡽⡘⡔⡔⠔⠔⠄⢂⠆⠆⠆⠆⠆⠆⢆⠆⢆⠆⢆⢆⢆⢆⢆⢆ ⢢⢢⢢⠢⢢⠢⠢⠢⡂⠆⠢⢂⢂⢂⠀⡐⠥⢂⠆⢆⢣⢣⠡⠀⠀⠀⠀⠀⠀⡏⢎⢆⠆⠆⠢⢂⢂⠀⢂⠢⢂⠆⠢⡂⠆⠆⠆⠆⠆⢆⢆⢆⢆⠆ ⢢⠢⢢⠢⠢⠢⡂⠆⡂⡂⢂⢂⢂⠄⠀⡐⡐⡐⡐⠰⠰⡡⡣⠀⠀⠀⠀⠀⠀⢎⢆⠆⡂⢂⢂⢂⢂⢂⠀⡐⡐⡐⡐⡐⠰⡐⠰⡐⠔⠔⠔⠔⠔⡔ ⠢⠢⠢⡂⠆⡂⡂⢂⢂⢂⢂⢂⠄⠀⢀⠄⢢⢂⠐⡐⡐⠔⡱⡁⠀⠀⠀⠀⠰⡱⡐⡐⠄⢂⠐⠰⠠⢂⠀⠀⠄⢂⠐⡐⡐⡐⡐⡐⡐⠔⡐⠔⠰⡐ ⠰⡐⠔⡐⡐⡐⡐⡐⠄⢂⠄⠄⠀⠀⠠⠠⢂⠄⠄⠄⠄⠄⢂⠆⠀⠀⠀⠀⢢⢂⠄⠄⠠⠠⠠⠠⢂⠀⠄⠀⠀⠄⠄⠄⡐⡐⡐⡐⡐⡐⡐⡐⡐⡐ ⡐⡐⡐⡐⡐⡐⠄⠄⠄⠄⠄⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠠⠠⠠⠠⢂⠐⡐⡐⡐⡰⣰ ⣶⣔⡐⡐⠄⠄⠄⠄⡀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠀⠀⠀⠀⠀⠀⡀⠄⠄⣦⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣶⠠⠀⠀⠀⠀⠀⠀⠀⠢⢢⢡⢢⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡔⠔⠔⡐⠄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠠⡀⡐⠰⠰⡰⡡⣊⢒⠥⡡⡂⠀⠀⠐⡌⢆⢒⠔⡔⠔⠔⡐⡐⠄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣆⠀⠀⠀⠄⠢⡀⢂⠢⠢⠢⢢⢢⠢⠂⠀⠀⠠⢢⠢⢢⠢⡂⠆⡂⡂⠂⡐⠀⠀⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣻⡽⡌⠀⠀⠀⠄⡐⡐⠔⠔⡔⢆⢆⢆⠆⡂⠀⠀⠠⢢⠢⠢⠢⢢⢢⠢⠢⢂⠄⠄⠀⠀⠀⠀⡹⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣟⢯⢳⠀⠀⠀⠀⠄⡐⡐⡐⡐⠔⡰⠰⡰⡰⡐⠀⠀⠠⢢⢢⢢⠢⠢⡂⡂⢂⢂⠐⠄⡀⠀⠀⠀⢘⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⣝⠆⠀⠀⠀⠀⠄⡐⡐⡐⡐⡐⠔⠰⠰⠰⠠⠀⠀⠠⢢⠢⠢⡂⠆⣂⢂⢂⢂⢂⠄⠄⠀⠀⠀⠀⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣟⢯⢳⠀⠀⠀⠀⠀⠄⡐⡐⡐⡐⡐⡐⠔⠔⠔⡄⠀⠀⢀⠆⢆⠆⠆⠆⢆⠆⢂⢂⢂⠄⠄⡀⠀⠀⠀⢹⡽⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣻⡝⠆⠀⠀⠀⠀⢀⠄⡐⡐⡐⠔⡌⢆⠢⠢⠢⡀⠀⠀⠰⡰⠰⡰⣘⢌⢆⠆⢂⢂⢂⠄⠄⠄⠀⠀⠀⠐⡽⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣟⢯⢣⠀⠀⠀⠀⠀⠀⠄⠄⡐⡐⠰⠰⡡⢣⢣⢣⢂⠀⠀⢢⢢⢊⢎⢎⢆⠆⠢⢂⢂⢂⠄⠄⡀⠀⠀⠀⠀⢹⣻⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⡹⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⢂⢂⢆⢌⢎⢎⢒⠀⠠⢢⡘⡜⡌⢆⠆⠆⠢⢂⢂⠄⠄⠄⡀⠀⠀⠀⠀⠀⢯⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣟⡽⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⢂⢂⠆⢆⢌⠆⠀⠰⡰⡘⡔⡔⠔⡔⠔⡐⡐⠄⠄⠄⡀⠀⠀⠀⠀⠀⠀⢈⢯⣻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢯⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⢂⢂⢂⠆⢂⠀⡂⠆⢢⠢⠢⡂⠢⢂⢂⢂⠄⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡽⣿⣿⣿⣿⣿ ⣿⣿⣿⣟⣝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⡐⡐⡐⠄⠀⡰⡰⣙⢦⢣⢂⢂⠐⠄⠄⠄⡀⢀⠀⠀⠀⡐⡐⠀⠀⠀⠀⡹⡽⣿⣿⣿⣿ ⣿⣿⣿⢯⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠄⠄⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀⠄⠀⠀⡀⡐⡐⢄⠰⡱⡐⠄⠀⠀⠀⠐⡽⣿⣿⣿⣿ ⣿⣿⣟⡽⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⢀⠴⣲⣄⠄⠄⠄⠄⡐⠔⠸⡰⡡⡌⢆⠆⢣⠠⠀⠀⠀⠀⢹⡽⣿⣿⣿ ⣿⣿⣻⢭⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢡⠐⡰⡐⢀⢀⢠⢌⣼⠀⠀⠀⣜⣷⣿⣿⣿⡏⠄⠄⢂⡼⡍⣎⢖⢆⢆⠆⠆⢂⠄⠀⠀⠀⠀⢘⣟⣿⣿⣿ ⣿⣿⡽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠰⠰⡰⡰⡰⡌⢆⢿⡏⠀⠀⠀⣏⣿⣿⠟⠔⠄⡐⡐⡜⡜⡜⡜⡾⣇⠆⠆⢂⢂⠄⠀⠀⠀⠀⠀⡿⣻⣿⣿ ⣿⣟⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⢂⠆⢆⠆⣼⡿⣿⡇⠀⠀⠀⠀⠄⠄⠄⡐⠄⢂⢆⢣⢣⣿⣿⣿⡏⡃⡐⠄⠄⠄⠀⠀⠀⠀⠀⢹⡿⣿⣿ ⡿⣝⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⡐⡐⠔⢰⣿⣿⣿⣿⢸⠀⠀⠀⣂⢆⢆⢆⠆⢆⢇⠥⢣⢷⣿⢌⠜⡴⡂⠄⠄⡀⠀⠀⠀⠀⠀⠀⣿⢿⣿ ⢯⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⢂⢂⠀⣿⣿⣿⣿⣿⢸⠀⠀⠀⢎⢎⢎⢎⡖⡔⡥⡒⢿⡶⡘⡥⡏⡜⡆⡆⠠⡀⡀⠀⠀⠀⠀⠀⠸⣻⢿ ⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⢂⠄⢠⣿⣿⣿⣿⣿⡆⠀⠀⠀⡏⣉⣾⣿⣿⢣⢻⡟⣶⣻⣿⣎⣧⢊⣿⣿⣇⠠⠠⠠⡀⡀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⢂⠄⠀⣟⣿⣿⣿⣿⣿⡟⠀⠀⠀⣧⢃⢆⢒⢯⢢⢒⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣧⠐⡐⡐⠄⠄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡐⡐⡐⠄⢀⠉⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣞⢍⢆⢻⣆⠥⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⢢⠢⡂⢂⠄⡀⠀

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