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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢸⠟⣠⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⠴⠴⠶⠚⠿⠿⠾⠭⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠴⢋⡽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡔⠁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⣖⠀⠀⠀⠀ ⠀⢀⡏⠀⡼⢡⠚⡛⠒⣄⠀⠀⠀⠀⣠⠖⠛⠛⠲⡄⠐⢯⠁⠀⠀⠹⡧⠀⠀⠀ ⠀⣸⠀⠀⡇⠘⠦⣭⡤⢟⡤⠤⣀⠀⠣⣀⡉⢁⣀⠟⠀⠀⢷⠀⠀⠀⠙⣗⠀⠀ ⠁⢻⠀⠀⢷⢀⡔⠉⢻⡅⣀⣤⡈⠙⠒⠺⠯⡍⠁⠀⠀⠀⢸⡆⠀⠀⠀⠘⡶⠄ ⠀⣈⣧⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠸⣔ ⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⡤⠴⠖⠋⢹⠃⠀⠀⠀⠀⠀⣷ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼ ⠙⠑⣤⣀⠀⠀⠀⠀⠀⢀⠀⠀⢄⣐⠴⠋⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⣰⠟ ⠀⠀⠀⣑⡟⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⠋⠀ ⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠙⠛⠛⠛⠻⠿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⡿⠃⠀⠀⣠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀ ⠀⣰⣿⣿⠁⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀ ⢠⣿⣿⠇⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀ ⣼⣿⡟⠀⢸⣿⣿⠟⠀⢀⣴⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀ ⣿⣿⡇⠀⠀⠉⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀ ⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇ ⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀ ⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣷⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀ ⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀ ⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣕⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡳⡀⠀⠀⠀ ⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠀ ⣼⡟⠁⡟⢛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢦ ⢿⡇⠀⠀⠂⠐⠉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠉⠠⠢⢹⣣ ⣿⣧⠀⠀⠀⠀⠸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠏⣿⣿⣿⣟⢠⡄⠀⠀⠀⢀⣿ ⣿⣿⡆⠀⠀⠀⠀⢻⣿⣿⣯⣤⣬⡁⠀⠀⠀⠁⠀⠁⠀⢿⣿⣿⠁⠀⠀⠀⣼⠇ ⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣴⣶⣍⠛⠀⠀⠀⠀⢰⡿⠿⢿⣿⡇⠀⠀⠀⢰⠀⠀ ⣿⣿⣿⠄⣀⠀⣼⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢰⣿⣿⣇⢻⣿⡀⠀⠀⢸⡀⠀ ⣿⠏⠀⠑⠄⠙⣿⣿⣟⣹⠿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿⡃⣼⣿⣷⡀⠀⡸⢻⠷ ⡏⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠅⠋⢁⠔⠁⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⠀⠀⠠⠶⠦⠤⠦⠀⠀⠀⣠⣿⣿⣌⠓⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⢹⠉⠳⠶⢤⣀⣀⣀⣠⠴⠶⠿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠠⣿⠛⠛⢻⠼⠤⠤⠤⠾⠬⢮⠷⠤⠤⠤⠤⠬⠿⠛⠛⢻⠿⠢⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠛⠛⠛⠓⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡞⠛⣱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠳⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⢣⢊⣹⡇⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡾⠙⠶⣄⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠹⣎⣀⣉⣡⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣨⣤⣤⣀⣈⢷⣄⠀⠀ ⠀⣼⠃⢀⣴⠛⠛⠋⠀⠀⠀⠉⠛⢷⡄⢀⠀⣴⠞⠋⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀ ⢠⡇⢠⡟⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠻⣿⣿⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠻⡆ ⢸⢣⣿⠀⠀⠀⢠⣾⣿⣿⣿⣷⡄⠀⠀⢻⣿⡀⠀⠀⢠⣿⣿⣿⣷⡄⠀⠀⠀⢿ ⢸⡼⣷⠀⠀⠀⠘⢭⣭⣭⠿⠋⠁⠀⢀⣼⣿⣷⡀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⣸ ⠘⡇⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿ ⠀⢿⡀⠘⢻⣷⣶⣤⣤⣤⣤⣶⣿⡿⠟⠉⠉⠓⠻⢿⣿⣷⣶⣶⣶⣶⣾⠿⢣⡟ ⠀⠈⢿⡀⠀⡌⢻⣛⠿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣏⢙⡿⡏⢹⠁⣰⠏⠀ ⠀⠀⠀⠻⣤⣧⣸⠙⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡙⣻⡞⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣻⡶⣤⣄⣀⣀⣀⣀⣀⣤⣤⠴⠾⣻⣯⠞⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠛⠛⠛⠓⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣤⡞⠋⣱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠳⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⢣⢊⣩⡇⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡾⠙⠶⣄⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠹⣎⣀⣈⣡⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣈⣤⣤⣀⣈⢷⡀⠀⠀ ⠀⣼⠃⢀⣴⠛⠛⠋⠀⠀⠀⠉⠛⢷⡄⢀⠀⣴⠟⠋⠀⠀⠀⠀⠀⠙⠻⣿⣆⠀ ⢠⡇⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆ ⢸⢣⡿⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿ ⢸⡼⣷⢀⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣼⣿⣷⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸ ⠘⡇⠻⣿⣭⣩⣭⡿⠛⠁⠀⠀⠀⢠⣾⡿⣿⠿⣷⣶⡛⠛⠁⠀⠀⠀⠀⣀⣴⣿ ⠀⢿⡀⠘⢻⣷⣶⣤⣤⣤⣤⣶⣿⡿⠟⠉⠉⠓⠻⢿⣿⣷⣶⣶⣶⣶⣾⠿⢣⡟ ⠀⠈⢿⡀⠀⡌⢻⣛⠿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⡏⢙⡿⡏⢹⠁⣰⠏⠀ ⠀⠀⠀⠻⣤⣧⣸⠙⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⡙⣻⡞⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣻⡶⣤⣄⣀⣀⣀⣀⣠⣤⣤⠴⠾⣻⣯⠞⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⡞⠃⣰⠶⢶⠀⣀⠀⠀⠀⢠⡀⣴⠶⣆⠘⢷⣄⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠙⠶⠞⠀⣿⠛⣛⣛⣻⡇⠙⠛⠋⠀⠀⠹⣆⠀⠀ ⢀⣀⣤⡟⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⣿⣶⣦ ⢸⡁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿ ⢸⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣿ ⠘⠃⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠿⠿⠿⠿⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⠈⠻⣦⡀⠀⠀⠀ ⠀⢀⣾⠋⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠂⠀⠀⠙⣷⡄⠀⠀ ⠀⣾⠇⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠀⠀⠀⠀⠀⠸⣷⡀⠀ ⢸⡟⠘⠛⠁⣰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀ ⢸⡇⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⢠⣿⠃ ⠀⣿⡄⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⢀⣿⣦⣤⡿⠁⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠸⣧⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀ ⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⣿⠋⠀⠀⠀ ⠀⠀⠀⠈⠙⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⢁⣽⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⣸⠃⠳⣿⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣼⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⡿⠋⠀⡾⠃⣤⠾⢿⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣴⠟⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠁⠀⠈⢧⡾⠋⠀⠈⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣉⣀⣀⣀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣿⠏⠀⠀⠀⣀⣴⣷⣾⣿⡿⠿⠿⠿⠿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠛⠛⠛⠻⠿⠿⢶⣶⣤⣛⣿⣆⠀⠀⠀ ⠀⢀⣾⠏⠀⠀⣠⣾⡟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡄⢀⡀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣦⠀⠀ ⠀⣸⣿⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⣧⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣧⠀ ⠀⣿⡏⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⣆ ⢰⣿⠇⣾⡏⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢹⣿ ⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⢿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣿ ⢸⣿⡆⣿⣇⠀⠀⠀⠀⠀⠈⢻⣦⣤⣤⣴⡾⠿⠛⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⣿⣇⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿ ⠀⢹⣿⠀⠘⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣏⠹⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⢻⣿ ⠀⠈⣿⡆⠀⠀⠛⢿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠟⠉⠀⠀⠙⠃⠻⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣟⣿⠿⢁⣾⠏ ⠀⠀⠘⣿⡄⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣭⣿⣿⣿⣿⣿⡿⣿⠿⠟⠁⢀⣾⠏⠀ ⠀⠀⠀⠹⣿⣄⠀⠀⢠⠇⠉⣯⣭⠛⠛⢻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⣽⠟⣇⠀⣼⠀⠀⣠⡿⠃⠀⠀ ⠀⠀⠀⠀⠘⢿⣦⡀⢸⡆⢀⣿⠹⣷⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠃⠀⠻⡶⡿⣠⣾⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⡻⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣾⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠟⢋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣙⡻⠿⣷⣶⣦⣤⣤⣤⣤⣠⣤⣠⣤⣴⣶⣾⡿⠟⠛⣟⣠⣟⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣾⣴⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⢛⡋⢉⠩⢀⠄⠤⡀⢄⠠⡈⠄⡉⠙⠛⠻⠿⢿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣛⡏⢰⣿⢿⣦⠁⡘⢄⢊⡐⣁⠊⠔⡁⠎⡐⢩⡐⢡⠂⡐⢌⣟⠻⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣾⣿⡏⣾⠛⢻⣿⡇⢠⣿⠂⡌⠂⢢⠐⢠⠉⠂⠁⡎⠐⢡⠈⡆⢡⠐⢸⣿⡄⠀⣿⠛⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠟⣩⣿⠋⣠⣾⣿⣅⣾⠏⡐⠀⠎⢠⠃⢌⠂⣉⠒⡀⢃⠌⢒⠠⣁⠂⢂⠹⣷⣴⡿⢁⠘⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⡟⠣⠘⡸⣷⣾⠟⣀⡘⢻⢉⣰⣀⡉⠐⠂⢌⠢⠑⡄⢢⠑⡈⠔⡈⡐⠄⡘⢀⣦⣜⣻⣄⣂⣌⡐⢈⠻⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢠⣿⡟⠠⢁⢢⣱⣼⣿⣿⣿⡿⢿⠿⢿⠿⣿⣿⣷⣦⣀⠃⠌⡀⠆⡑⡈⡐⣄⣾⣾⡿⠟⢛⠻⠟⠻⠿⢿⣿⣶⣮⣿⣷⣄⠀⠀⠀ ⠀⢀⣿⡟⢠⣑⣾⣿⡿⢛⠛⡩⢁⡒⢌⠒⠤⠒⡄⢊⡙⠿⣿⣿⣆⣵⡄⡐⣴⣿⡿⢛⠡⣂⠍⢢⠃⣎⠱⢌⠢⢄⠩⡙⠻⣿⣿⣆⠀⠀ ⠀⣼⣿⢡⢶⣿⡿⢋⠔⡡⠎⡔⢣⠘⡄⢋⡌⠱⡘⢤⠘⡰⢈⢿⣿⣾⣷⣿⣿⢏⠰⡁⢖⡐⢊⠅⣊⠤⢃⠎⠢⢍⡒⢡⠃⡜⠻⣿⣧⠀ ⢀⣿⡟⣼⣿⡟⢠⠃⢎⠰⢡⠘⡄⢓⠌⡒⡌⡱⢌⢢⠩⢔⡡⢂⠽⣿⣿⣿⡿⢀⠣⠜⢢⠘⡄⢋⡔⢌⠲⢨⡑⠦⣘⢡⢊⠔⡡⠹⣿⣧ ⣼⣿⢯⣿⣟⠠⢃⠜⡈⢆⣅⣎⣰⠁⢎⠱⡐⠥⢊⡄⢓⠢⠆⡅⢊⢿⣿⣿⣿⡀⢃⠎⣄⣣⡘⠤⡘⢄⡋⠴⡀⠧⡐⠣⢌⢊⡅⢣⢹⣿ ⣸⣿⣾⣿⣇⠸⡀⢾⣸⣿⣿⣿⣿⣿⣆⠱⠸⠆⢇⠸⣀⠷⠸⣀⠏⣸⣿⣿⣿⡁⣾⣾⣿⣿⣿⣷⡎⠰⠈⠆⠱⠆⠉⠱⠈⠆⠈⠀⠈⣿ ⢹⣿⡞⣿⣧⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠄⠀⠀⠁⠀⢀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢢⣿ ⠘⣿⣯⣹⣿⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿ ⠀⢻⣿⡔⣻⣿⣿⣿⣾⡷⠿⠛⠏⠉⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⢻⣿ ⠀⠘⣿⣿⡔⣎⠿⣿⣿⣿⣶⣦⣤⣤⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⡿⠋⠌⡁⠛⢟⣻⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣾⣿⣿⣿⡿⣣⣿⠟ ⠀⠀⠸⣿⡷⣌⠳⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⡾⢁⡘⠰⢠⠉⠄⡘⢯⡙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⡱⣾⣿⠏⠀ ⠀⠀⠀⠹⣿⣮⠳⣌⣷⠃⠈⣿⣽⡛⠛⣻⡿⣩⢏⡝⢦⠫⠑⡀⢆⠰⢁⢂⠩⠐⡄⢂⠙⡘⢧⣿⡆⣨⣽⢿⣷⠀⣼⣋⢮⣷⣿⠋⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⣄⣿⣃⢠⣿⠹⢷⡾⠟⢣⠓⢊⠘⡠⠑⠌⡰⢈⠂⡌⠰⢈⠡⠒⡈⠆⡐⠠⠘⠟⠟⢋⠚⠻⣿⣿⣽⣿⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⡿⠟⠠⢀⠠⢘⢀⡘⢀⠇⠠⠃⠜⠠⡀⠇⢠⠃⠜⡀⠇⢠⠃⡄⠣⠘⢠⠘⢠⠘⣿⣤⣿⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣌⡐⢁⠂⠅⠢⠌⡂⢌⠂⡍⠰⠁⠆⡉⢄⠊⠤⠁⠎⠤⡈⠤⠑⡈⢤⣈⣦⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣬⣌⡄⠑⡈⠄⠊⠄⢃⠡⢊⠐⠌⣈⠂⣉⠰⢀⣢⣴⣱⣾⣿⠟⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣛⣿⢿⣿⣷⣾⣾⣴⣬⣴⣦⣥⣶⣶⣶⣾⣿⡿⠿⢻⣟⣩⣿⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⢸⣿⠉⠀⠙⣿⡇⠀⣶⣆⣀⣀⣀⣀⣀⣀⣈⣿⣧⠀⢸⣿⠀⢉⣿⡇⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠘⢿⣷⣤⣾⡿⠃⢰⣿⡿⠿⠛⠛⠛⠛⠛⠛⢿⣿⡄⠘⠿⠿⠿⠟⠁⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⣿⣇⣠⣤⣤⣤⣤⣤⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀ ⠀⠀⣀⣀⣀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠛⠛⠉⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⣶⣄ ⢰⣿⡿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠈⣿⣿ ⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿ ⠘⣿⣇⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⣿⣿ ⠀⣿⣿⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⣿⣿ ⠀⣿⣿⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠿⠏ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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