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⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀ ⠸⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣶⣄⠀ ⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⠀ ⠀⠀⢸⣿⣿⡇⠀⠀⢀⣠⣿⣿⠟⠀ ⠀⠀⢸⣿⣿⡿⠿⠿⠿⣿⣿⣥⣄⠀ ⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣧ ⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿ ⢰⣶⣿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠛⠁ ⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⣹⣉⣀⣀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠾⠚⠉⠉⢳⠞⠉⠀⠀⠀⠉⠓⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣷⣶⣆⠀⢰⣗⣶⣶⠶⠶⠶⣶⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠿⣿⣿⣿⣭⣿⡟⠛⣷⣶⣶⣶⣶⠿⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⢦⡀⠀⠀⠀⠀⠀ ⠀⠙⣷⡟⢛⣿⡿⠿⣷⣶⣿⠿⠿⠟⠋⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢻⠀⠀⠀⠀⠀ ⢠⣞⠉⠁⠞⠉⠀⠀⠈⠳⢤⣀⠀⠀⠀⣠⣿⡆⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠈⢻⣦⣄⣀⣀⣀⣀⣠⣤⣤⣔⣲⣶⣿⡿⠟⠁⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣧⣸⠁⡀⠀⠀⠀ ⠀⠸⣌⡉⠉⠉⠉⠉⢉⣉⣉⣡⠴⠋⠁⠀⠀⢀⡀⢀⠀⠀⢻⡄⠀⠀⠀⢀⣀⣤⣤⣴⠇⠀⠀⣸⣯⣴⣟⣷⠀⠀ ⠀⠀⢻⡌⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣇⠀⠀⢻⣄⣠⢶⣋⠉⠀⣠⣿⣠⣤⣄⣉⠉⠾⠿⠿⢶⡄ ⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡆⠀⠈⢿⠃⢠⣉⣿⠟⠉⠀⠀⠀⠀⠉⠻⣆⣀⠠⣤⡟ ⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⣷⠀⠀⠈⠓⠀⠾⠁⠀⢀⡤⠀⠀⠀⠀⠀⠸⡟⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⢿⣭⣽⠇⠀⠀⠀⠀⢴⣇⡀⠀⠀⠀⢀⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⣇⡿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⠀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⠈⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣶⢶⡶⠶⠶⠖⢛⣉⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇⠀⠀⠀⠸⣯⣉⠛⠛⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠙⠳⠶⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡉⠛⠇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠛⠋⠉⠉⠉⠉⠛⠛⠿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠟⠛⠉⠁⠀⠀⠀⠈⢙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢀⣀⣤⣶⠶⠶⠶⠿⠿⠿⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠾⠛⠉⢀⣀⣠⣤⣶⣶⣶⣶⣦⣄⡀⠉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⣀⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠉⠙⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣶⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠒⣿⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀ ⠀⠀⣰⡿⠛⠉⠀⠀⣠⣤⣤⣴⣶⣶⣶⣶⣦⣤⣬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⠶⠿⣛⣻⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀ ⠀⢰⣿⠁⢀⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⣿⣧⡆⠀⠀⢀⣤⣶⡶⣿⣿⣿⣿⣿⣿⠋⠉⢹⣿⠂⠀⢠⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀ ⠀⠈⢻⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣀⣤⡾⠟⠋⠁⠀⠘⣿⣿⣿⣿⣿⣦⣴⣿⠋⢀⣴⡟⢁⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⢠⣿⣠⡤⠄⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⡾⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⢋⣡⣶⠿⠋⣴⡿⠁⠀⢀⣠⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠀ ⠰⣤⡾⠛⣡⣤⡶⠟⠛⣿⣿⣿⣿⡏⠁⣹⣿⡇⠀⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠾⠟⠋⣁⣴⠿⠋⢀⣠⣾⠟⠋⠁⠀⠀⠈⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠘⣷⡿⠋⠁⠀⠀⠀⢿⣿⣿⣿⣿⣶⣿⠟⢠⣾⠟⠙⣿⡿⠷⠶⠶⠶⠶⠿⠛⠛⣉⣁⣤⣶⠿⠋⢁⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⢰⣿⣄⠀ ⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⣠⣿⠃⠀⠀⠙⠻⠶⣤⣤⣤⣶⠶⠿⠟⠛⠋⠁⢀⣠⡶⠟⠋⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⢀⣿⠋⣿⡄ ⠀⠀⠀⢿⡿⢶⣤⣀⣀⣀⣀⣀⣠⣤⣤⢾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢠⣾⠃⢀⣿⠛ ⠀⠀⠀⠈⣿⣦⣌⣉⠛⠛⠛⣉⣉⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠉⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠁⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⣠⣿⠃⢀⣾⠇⠀ ⠀⠀⠀⠀⢹⣧⢉⣿⡿⠛⠛⠛⠋⠁⠉⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⢀⣴⡟⠁⢠⡿⠋⠀⠀ ⠀⠀⠀⠀⠈⣿⡿⠿⣶⣦⣤⣤⣤⣤⣤⣶⠶⠶⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⣠⣿⠋⠀⣴⡿⠁⠀⣠⣼ ⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠏⠀⣠⣾⠏⠁ ⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⣀⣾⠟⠁⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣿⠿⠾⠿⠟⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⢀⣼⠟⠁⠀⠀⣾⡇⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⣠⣴⠟⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⣤⣤⣤⣤⣤⣶⣶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⢀⣤⣾⠟⠁⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⠶⠟⠛⠛⠛⠻⠿⣶⣦⣾⠟⠋⠀⠀⣀⣤⣴⣶⣶⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣽⣷⡶⠾⠛⠛⠉⠁⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡿⠛⠋⠉⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠈⠙⠲⡴⠚⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⢠⠴⠚⠋⠉⠉⠓⠲⣿⣤⠤⠤⠤⠤⢤⣷⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⣀⡤⣶⣺⠿⠭⠭⢿⣦⣀⣛⣯⡭⠽⠯⣽⣲⡀ ⠀⠀⠀⣠⠞⠉⠀⠀⠀⣴⣿⡗⢋⣁⣤⣴⣶⣖⡛⠛⡿⠴⠒⣻⢿⣿⡟⠛⢷ ⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⢿⣻⡥⣼⣷⣿⣼⣷⣾⠷⠤⠤⠿⡽⠶⢿⡶⠏ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣭⠟⠋⠀⠰⢤⣤⣤⠤⣴⠛⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⢧⡀⠀ ⢸⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠲⠶⠤⣤⣀⣀⣀⣀⣀⣀⣤⡤⠴⠚⢷⠀ ⠀⢷⡀⠀⠀⠀⠀⠀⡜⢧⣈⣩⣭⣝⣛⣒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠶⣾⠋⠀ ⠀⠀⠻⣦⣀⡀⠀⠀⠛⠲⠂⠀⠀⠀⠀⠉⠉⠙⠛⠛⠓⠒⢒⡶⠒⠚⠁⠀⠀ ⠀⠀⠀⠈⠙⠻⠿⣶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⣤⡴⠖⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀ ⠀⠀⣸⣿⡿⠀⠀⠀⠸⠿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢹⣿⣷⠀⠀ ⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣧⠀ ⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⠀ ⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⣿⣿⠀ ⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⢀⣿⣿⠀ ⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⣸⣿⡟⠀ ⠀⠀⢹⣿⣷⡀⠀⠀⢰⣶⣿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⣸⣿⡿⠀⠀ ⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠘⢻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠶⠶⣤⣄⠀⠀⣀⣤⡤⠤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠁⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⢶⣦⣌⣷⣀⣤⣤⣀⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⣀⣀⣈⣻⠿⣆⠈⠉⠙⠶⡶⠤⣤⡙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣴⣞⣛⣻⣯⣭⣟⡻⢿⣆⣀⣀⣀⣀⣄⣀⣙⠿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣼⠁⠀⠀⠀⠀⠀⢀⣶⡶⠿⠿⠛⠉⠉⠁⣀⣀⣉⣙⠻⢿⣍⣻⣯⣭⣭⣭⣛⡻⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣤⡴⠖⠛⣻⣿⣿⣯⣭⣟⠛⠿⣶⠶⠶⠶⠶⢾⣯⣿⣶⣽⡇ ⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣾⣿⣿⣿⣿⣿⣿⡇⢰⡿⠀⠀⢀⣴⣿⣿⣮⡙⢻⣧ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣷⣿⡟⠿⠶⣿⣿⣿⣿⣿⡷⢸⡟ ⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣿⡿⠙⠉⠉⠈⢿⣦⡀⠈⠙⠿⠿⠿⣿⡿⠁ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⡙⠷⠶⠶⢶⡟⠋⠀⠀ ⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠙⠛⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠘⣿⡐⠿⠿⠿⠷⠶⣤⣤⣈⠉⠛⠻⠶⣶⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⢿⣄⣠⠀⠈⠻⢶⣤⣤⣤⣄⡀⠈⠙⠻⢶⣤⣄⣀⡀⠀⠈⠁⠀⠀⠀⠉⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⢚⣷⣄⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⣦⣄⣀⠀⠉⠙⠛⠻⠿⠶⠶⠦⣤⡴⠟⠁⠀ ⠀⠀⠀⣠⣴⡶⠛⢷⣝⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⠦⣤⣤⣤⣤⣼⠇⠀⠀⠀ ⠀⣠⡾⠋⠀⠀⠀⠀⠙⠷⠾⣽⡻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣭⣙⡛⠷⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⠶⠶⢶⣦⣄⣀⣠⣄⣤⠶⠋⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣈⣿⣆⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠿⣦⣴⡾⠛⠛⠉⠉⠀⠀⠈⠉⠙⠛⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠏⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣈⣿⡀⠀⠀⠀⠠⠖⠒⠒⠶⠶⠶⠦⣤⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠊⠉⠁⣀⣀⣀⣀⣀⣀⣀⠈⠉⠛⢷⡆⣀⣀⣤⣤⡤⠤⠴⠶⢦⣤⣤⣈⣉⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠻⣶⣾⡟⠉⠉⠀⢀⣀⣤⡤⠴⠶⠶⠶⠿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠋⠁⠀⠀⠀⣀⣀⣠⡤⠴⠖⠚⠉⠉⠉⠉⠉⠛⠛⠶⣤⡀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣦⣬⣽⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣷⣶⣶⣶⣿⣿⣿⣯⣁⣩⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⡴⠚⠉⣀⣤⣤⣶⣾⣿⣿⣿⠋⢉⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢹⡿⠿⠿⠿⠟⠛⠛⠋⠉⠀⠀⢀⣠⣤⣾⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⣀⣀⣤⣴⠶⠟⠋⠁⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿⠟⠋⠁⢀⣠⡴⢿⣿⣦⡤⠤⠤⠤⠴⠶⠶⠚⢛⣋⣩⣴⠿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠁⠀⣠⡾⠛⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣤⣤⣤⠶⠶⠶⠶⠛⢋⣡⣴⡿⠃⠈⠻⣶⣿⠛⠛⠛⠛⠛⠛⣩⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠀⢿⡶⠟⠉⠁⣨⣭⣭⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠾⠛⠛⣹⠏⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⣠⣾⣯⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣤⣤⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠙⠻⢶⣤⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠈⠻⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠁⠀⠀⠀⢀⣼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠶⠟⠋⠁⠀⠀⠀⠀⠀⣀⣠⣾⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡤⠴⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠈⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⠒⠒⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡴⠶⠶⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡶⢾⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠶⠟⠛⠋⠉⠉⠀⣠⣿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⢤⣀⠤⠄⠠⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⠁⠠⠔⠒⠒⠒⢵⡤⠤⠤⠤⠧⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⡞⠀⠀⣀⡠⠔⣂⣉⡭⠽⣒⣊⡭⣭⡭⢕⡄⠀⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠉⢛⠭⣰⣿⣿⣦⠯⠤⠼⠿⠿⡴⠃⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠉⠽⠛⠋⠁⠐⠢⠔⠒⢮⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⢀⡤⠤⡤⣄⣀⣀⡀⠀⣠⢦⢀⡠⢧⠀⠀⠀ ⠀⠀⢣⡀⠀⠀⠀⢼⣶⡍⡏⢹⣐⣒⣒⣳⢯⢹⣒⣲⠋⠀⠀⠀ ⠀⠀⠀⢈⡲⠤⠤⣀⡇⡧⡇⣸⠚⡇⢀⡇⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⣠⠚⠉⠀⠀⠀⢠⠇⠁⠥⢸⠀⡇⠀⡇⢰⢸⠀⠀⠀⠀⠀⠀ ⠴⠁⠀⠀⠀⠀⠀⢸⢀⡀⢀⠀⠀⢰⢠⠃⠈⡎⡗⢤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠸⠜⠀⠀⠠⠇⠀⠀⠉⠑⠢
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡾⠿⠟⠛⠛⠛⠛⠛⠻⢿⣶⣤⡀⠀⠀⠀⢀⣠⣤⣴⣶⣾⡿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣶⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⣀⣴⣾⠿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⣷⣦⣼⣿⡀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣻⣿⣿⡟⠛⠛⠛⠉⠉⠉⢉⣉⣉⣛⣛⣻⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠿⠿⣛⣿⣛⣛⣛⣛⣻⠿⣶⣄⠀⠀⠸⠿⠿⠛⠛⢻⣻⣟⣿⣿⣟⡛⠻⢿⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠟⣫⣭⣶⣾⠿⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣷⣤⣴⣶⣶⣾⠿⠿⠟⠛⠛⠛⠛⠿⢿⣶⣽⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣛⣩⣵⣾⠿⠛⠉⠁⠀⠀⢀⣀⣀⣤⣤⣶⣶⣶⣶⣾⣿⣿⠉⣁⣀⣤⣴⣶⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣷⡆ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣻⣿⡛⠉⠀⣀⣀⣠⣴⣶⣿⣿⠿⣿⣿⣿⣥⡀⠀⠀⠈⣿⣿⠿⠟⠛⠋⠁⣠⣾⠛⢻⣿⣿⣷⣄⠀⠈⠉⢻⣷ ⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣿⣿⣟⠛⠋⠉⢰⣿⣿⣤⣿⡟⠉⢻⣿⡆⢀⣴⣿⣃⠀⠀⠀⠀⢰⣿⣿⠿⣿⡅⠈⣿⣿⣆⣀⣤⣾⠟ ⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣝⡻⢿⣶⣤⣼⣿⣿⣤⣽⣿⣶⣿⣿⡿⢿⣻⣿⠻⠿⣷⣶⣶⣾⣿⣿⣶⣿⣿⣾⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣼⣿⠉⠀⠀⠀ ⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣡⣴⣾⠿⠋⠁⠀⠀⠀⣿⣶⣦⣄⣀⣀⣠⣤⣤⣴⣶⣾⠿⠋⠁⠀⠀⠀⠀ ⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡛⠛⠉⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀ ⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀ ⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣷⡀⠀⠀ ⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠉⣀⣀⣀⣀⣀⠀⠈⠉⠉⠙⠛⠿⠿⢿⣶⣶⣶⣶⣤⣤⣤⣶⣶⣶⣶⣶⣶⡾⠿⠿⠿⠛⠉⠉⠀⠀⣿⡇⠀⠀ ⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠀⠘⠻⠛⠛⠛⠿⠿⠿⢿⣶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣴⣾⠿⠃⠀⠀ ⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠻⣷⣤⣤⣤⣤⣶⣶⣶⣶⣤⣤⣤⣉⣉⡙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠾⠶⠶⠶⠾⠿⠿⠿⠿⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣈⣉⡋⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⢷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣴⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⢛⣿⣿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢶⣶⣿⣭⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⣭⣽⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠒⠒⠲⠶⢤⣄⡀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⡶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣄⣈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠖⠊⠉⠉⠉⠉⠉⠙⠓⠾⢧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⡴⠶⠒⠛⠛⣛⠛⠛⠳⢦⡀⠀⣀⣤⠤⠶⠶⠶⠶⢼⣷⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣉⡤⠖⢒⣉⣩⣯⣭⣭⣓⡲⢤⣹⠊⢁⣠⡴⣶⣶⣿⣍⣙⣛⣛⠿⣷⡄⠀ ⠀⠀⠀⠀⠀⠀⣴⢿⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⡤⢞⡡⠖⠊⣽⠛⢛⣿⣿⣷⡀⠉⠓⢿⣾⠿⠒⢩⣿⠋⢹⣿⣷⣦⠈⠉⠛⠿⡆ ⠀⠀⠀⠀⠀⡼⠁⢸⠀⠀⠀⠀⠀⠀⣴⡋⠁⠀⣴⠋⠀⠀⢸⣿⣶⣾⣿⣿⣿⡇⠀⠀⢀⠏⠀⠀⢾⣿⣶⣿⣿⣿⣿⠀⠀⠀⠀⣹ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⣗⠚⠛⠲⢤⣈⣻⣿⣿⣿⣿⣟⣁⣠⠴⠋⡗⠲⠦⠬⠿⠿⠿⠿⠿⠷⠖⠒⠋⢉⡟ ⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠉⠉⠉⠉⠁⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠒⠒⠛⣛⠽⠋⠀⠀⠀⠀⠐⠢⣤⠀⠀⠤⠤⠶⣿⠁⠀⠀⠀ ⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣈⣧⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠂⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠚⠉⠉⠁⠀⣿⠀⠀ ⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⡏⠀⠸⡇⠐⠒⠉⠉⠉⠉⠉⠛⠒⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠋⠀⠀ ⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣧⠀⠀⠙⠶⢤⣀⣀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠭⠭⢭⣙⣛⠛⠛⠛⠛⠛⠛⠉⢉⡽⠃⠀⠀⠀ ⠀⠀⣀⡤⠞⢿⢷⣄⠀⠀⠀⠀⠈⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⢒⣶⠶⠚⠉⠀⠀⠀⠀⠀ ⠠⠚⠁⠀⠀⠀⠳⢍⡳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢭⣙⠳⠶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠶⣞⡿⢯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⠤⠬⠭⣭⣉⣉⣉⣉⣭⡭⠭⠥⠴⠒⠚⠉⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠈⠀⡤⠂⠉⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠀⠀⡀⠄⠂⠀⠉⠉⠐⠠⡈⣄⣀⡀⠠⠤⠄⣀⣡⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⡜⠀⠀⠀⢀⠄⠂⠉⡰⠒⠚⠩⠐⠷⣄⣀⠔⠀⠀⠐⣒⠨⠇⣄⠀⠀ ⠀⢀⠄⠊⠇⠀⢐⡂⠁⠀⠀⠀⢃⡀⠀⠀⡁⠀⠈⢧⠀⠀⢠⡎⠀⠈⢣⠈⠠⠀ ⠀⠎⠀⠘⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⢸⠄⠀⠀⠑⠤⠤⠊⠀⢠⠀ ⡜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢠⡤⠀⠠⠀⠀⠠⠔⢋⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠩⡍⠙⠛⠦⡁⠀⠀⠀ ⠀⠀⡀⠀⡀⠀⡇⠠⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀ ⠀⠰⢃⡠⢻⢠⢷⠄⡈⠂⠄⡀⠈⠐⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢗⡄⠀ ⠀⡆⠈⠁⢸⠃⢸⠀⠈⠒⠤⢀⠁⠒⠠⠤⠤⠤⠄⠀⠀⠀⠀⠁⠤⠤⠴⠹⢤⠄ ⢢⣃⠀⠀⠀⠀⠈⠣⣀⡀⠀⠀⠈⠁⠒⠒⠀⠠⠤⠤⠤⠤⠤⢤⠄⠀⣊⠔⠊⠀ ⠈⠒⠵⢄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣂⣁⠠⢺⠀⠀⠀⠀ ⠀⠀⠀⠀⠗⢄⡀⠀⠀⢀⡮⠬⠍⠉⠉⡉⠉⠩⠝⢙⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠎⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⠚⠐⠚⠂⠀⡌⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠞⠛⠋⠉⠙⠛⢶⣤⡀⠀⢀⣠⣤⡶⠶⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣀⣤⡶⠶⠾⠛⠛⠷⠶⣤⣹⣇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠡⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣻⣟⠉⠉⠁⠀⠀⢀⣈⣉⣉⣛⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠛⠋⠉⢉⠙⠛⢷⡤⠶⠖⠚⠛⠉⠉⢉⣉⠉⠙⠻⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢹⣿⠀⠀⠀⠀⢠⣶⡶⠶⠞⠋⠉⣀⣠⣤⣴⣶⡿⠛⠛⠛⣷⣤⣤⡶⠶⠚⣻⣿⣿⡟⠛⠲⢾⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠉⠀⠀⠀⠀⠘⠛⠻⢿⣟⠛⠋⠉⠁⣴⣿⣿⠿⣷⡄⠀⣸⡇⠀⠀⠀⣼⣯⣿⡿⢿⣷⠀⣠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⡛⠷⢦⣼⣿⣯⣿⣷⡿⢿⣿⡿⠟⠷⠶⠶⠿⠿⠾⠿⠿⢛⣻⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠤⣷⣾⣿⣿⠿⠛⠁⠀⢤⡀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠟⠛⠉⠀⠀⠀⠀⠀⠈⠛⠷⣶⡞⠛⠋⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⢷⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣦⠀⠀⠀⣀⣸⣷⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢸⣧⣬⣿⣤⣨⣿⡛⠛⠶⠶⠶⠶⠦⡤⠤⢴⣿⣀⣿⠦⠶⠛⠋⠁⣨⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣴⢿⡇⠀⢿⡏⠉⢹⡟⠛⠛⠛⠛⠷⠶⠶⢶⣾⣯⠀⣿⠦⠶⠶⠶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⡇⠀⢸⡇⠀⢸⣿⠾⣶⠶⣶⣦⣤⣤⡟⠁⡟⠀⣿⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣤⣀⠀⠀⠀⠀⢸⡇⠀⣷⣀⣸⡇⠀⢸⡷⠶⢻⡆⠀⠀⠀⢸⡇⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠉⠉⠙⠛⠶⠶⢾⡇⠀⡏⠉⢹⡇⠶⢾⡇⠀⠀⣷⣀⣀⣠⣿⠀⠀⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡇⠀⠈⣷⠀⠀⣏⠉⠁⠀⣿⠀⠀⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠸⠷⠀⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⣿⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢻⡇⠀⠀⣿⠀⠀⠘⣿⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣠⡀⠀⠀⣠⡀⠀⠀⠀⠀⢹⣇⠀⢸⡇⠀⠀⠈⣿⡄⢹⡙⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠃⠀⠈⠛⠃⠀⠀⠀⠀⠀⣿⢀⣾⠀⠀⠀⠀⠈⠁⢸⡇⠀⠀⠈⠙⠳⠶⣦⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⠀⠀⠀⠀⠀⢠⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣦⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⢤⠖⠛⠉⣿⠇⠻⣠⣿⣿⣿⣿⣇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠴⠚⠉⢯⣼⣾⡁⠀⣠⣴⣧⢻⣿⣿⡟⠛⠛⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠏⠀⠀⣧⣸⡶⠈⠉⣳⡀⢿⣿⣿⠓⠉⠈⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠒⢄⠀⠀⠀⠀⠀ ⠸⡄⠀⣦⣘⣻⠄⠀⠀⣿⣿⣾⠟⠈⠀⠀⠀⢀⠤⠒⠒⠒⠒⠤⣀⡀⠤⠤⢈⣣⡀⠀⠀⠀ ⠀⢹⣄⠻⣶⠃⠀⠀⠰⡦⣽⣷⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠈⠙⢦⠀⠀ ⠀⠀⡇⠀⢌⠑⠀⠀⠀⠘⣟⠿⡀⠀⠀⠀⢀⣴⠿⠛⠛⠛⠻⣿⣯⣙⢧⢀⣴⣿⣿⣿⣷⡦ ⠀⠀⢱⠘⢦⡙⠂⠀⠀⠀⢸⣷⢬⣦⡀⠀⠈⠙⢻⢭⣿⣿⣟⡿⠉⢹⣿⣤⣿⣿⣿⡟⢺⡇ ⠀⠀⠀⢣⠲⣌⠒⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠑⠬⠭⠿⠷⣶⣺⠟⠹⣟⣛⠛⢷⣽⠁ ⠀⠀⠀⠈⢷⠪⣁⠀⠀⠀⠀⠀⣀⠘⠾⢓⣚⡄⠀⠀⠀⢀⣀⠠⠞⠁⠀⠀⠈⠳⠀⠉⠈⣧ ⠀⠀⠀⠀⠀⠳⣄⠹⣶⠄⠀⠀⢹⡆⠀⠉⢿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⣀⣴⡿ ⠀⠀⠀⠀⠀⠀⠈⡗⢤⡀⠒⠀⠀⠱⡄⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⡤⠧⣄⣉⣀⣀⣀⣀⡈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠛⠋⡇⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠉⠉⠛⠒⠬⢍⡉⠁⠐⠒⠒⠢⠤⠤⠄⢀⣀⠀⠀⢠⠊⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⡀⠀⠀⠀⠘⢀⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⢿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀
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