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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⡾⠿⠿⠟⠛⣛⣛⣻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⠿⠟⠛⠋⠉⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠿⠿⠛⠛⠉⠁⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠿⠛⠋⠉⠁⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣟⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⠿⢿⡟⠉⠉⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣉⡀⠀⠀⠈⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⠛⠋⠉⠁⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⣀⣀⣤⣤⣶⠟⠋⠁⢿⣦⡀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠿⠛⠛⠉⣀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠀⣀⣤⣶⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠛⠋⢉⣀⣠⣤⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⢀⣀⣀⣴⣾⠿⠛⠉⠀⠀⠀⢠⣆⣤⣴⣶⠄⠀⠀⠀⠀⢹⣧⡀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠿⠟⠛⠉⢁⣀⣭⣵⣶⣿⡿⠟⠛⠉⢩⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠿⠿⠋⠉⠁⠀⢀⣠⣤⣶⣶⠿⠛⠛⠉⠉⠀⠀⠀⢀⣀⣀⣀⠸⣿⡟⠋⣉⡀⠀⠀⠀⠀⠀⢹⣧⡀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⡿⠿⠛⠉⠁⢀⣀⣤⣴⣾⢿⣿⣿⠉⢻⣿⢇⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⣀⣠⣴⣶⡿⠟⠋⠙⠁⠀⣀⠀⠀⠺⠀⣼⣧⢰⣿⡿⢿⠿⠀⣿⣷⣾⠿⠟⠀⠀⠀⠀⠀⠀⢹⣷⠀⢸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠿⠟⠋⠉⠁⢀⣀⣤⣤⣶⣿⣿⡟⣿⣯⢻⣮⣿⣿⡞⢿⣿⣿⣧⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠿⠛⠋⠁⠀⠀⢀⠀⢀⣠⣤⡍⣾⣿⣤⡄⢻⣿⡼⣿⣦⣤⣀⣀⡘⣿⣧⣠⣾⣿⠀⠀⠀⠀⠀⠀⢿⣦⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣶⣿⠿⠛⠉⠀⢀⣠⣤⣶⣿⢿⣿⢻⣯⣈⣻⣿⣅⣿⡿⣷⠿⣏⣿⣥⣶⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡴⠿⠛⠛⠉⠁⠀⠀⢀⣀⣀⣀⡀⣿⣿⡿⠛⣋⡁⠘⣿⣿⣿⣶⣿⣷⢈⣉⣙⣻⣿⣿⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣿⡿⠋⠀⣀⣤⣴⣾⣿⣿⣏⢹⣇⣨⣿⡇⠉⢻⡇⠛⣛⣩⣥⣶⣿⠿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠋⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣼⣿⢿⣿⡷⢹⣿⣶⣿⠿⠃⠀⠸⣿⣎⠛⠿⠿⠘⠛⠛⠛⠋⠁⠀⠀⠀⠀⢀⡀⠀⢀⣤⣀⠀⠀⠘⣿⡄⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣰⣿⣿⠃⣿⣿⢿⣿⣿⣦⣸⣏⣹⣿⣿⡾⢇⣛⣠⣴⣿⡿⠿⢛⣉⣥⣶⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢿⣧⣀⣸⣿⡛⠀⠀⠀⠀⢻⣿⡀⣀⣶⣶⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣄⣿⣿⣿⡆⠀⠀⠘⣿⡄⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣿⡿⡀⠸⣿⣾⣿⣄⣿⡏⠛⣛⣯⣶⣿⠿⠟⣛⣭⣵⣶⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠸⣿⡆⠀⠀⠀⠀⠸⣿⣇⠈⣿⣷⣆⠀⣠⣶⡌⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣾⣷⠀⠀⣿⣿⣋⣫⡿⣿⣇⠀⠀⠀⠸⣷⡀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣧⠁⠀⠹⣿⣯⣽⣿⣿⡿⢟⣛⣭⣴⣶⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣿⣂⠀⠀⠀⠀⢻⣿⣤⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣦⣹⣿⡟⣋⣦⡄⠀⠈⠙⠿⣿⣿⣿⠟⠀⠀⠀⠀⢻⣇⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀
⠀⢹⣿⣿⣄⠀⠀⠹⣿⣛⣭⣴⣾⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠈⢿⣿⠀⢀⣠⣦⡈⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⣿⣿⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⡆⠛⢿⣷⡀⠀⠀⠀⠀⠀
⠀⠸⣿⢿⣿⣀⡀⠉⢻⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣄⡀⠀⠀⠀⠀⠘⣿⡄⠀⠘⣿⣷⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⣍⣀⣀⡀⠀⠀⠀⠀⠈⢿⣷⣾⣿⢿⣿⣿⣿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⣿⣇⠀⠀⠀⠀⠀
⠀⠀⣿⣷⣿⣏⣁⣀⡈⠻⢷⣆⢰⣦⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠙⣷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠳⣾⡿⠛⢻⣿⣆⠀⠀⠀⠀⠀⢻⣿⣤⣼⣿⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣽⣿⡄⠀⠀⠀⠀
⠀⠀⠸⣿⣿⣿⣉⣝⡛⣷⡄⢻⣧⢹⣧⠀⣾⠟⠉⣥⣭⣛⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠄⠀⣠⣿⣧⠀⠀⠀⠀⠀⠀⣿⠀⠘⢷⡿⢿⣿⡅⠀⠰⣿⡇⠀⠀⣹⣿⠀⠀⠀⠀⠀⠈⢻⣿⠋⠁⠀⠀⠀⢀⣤⠀⠀⠀⠚⠃⢰⣆⠀⠀⠀⠀⠀⠀⠈⢻⣥⣬⣿⣇⠀⠀⠀⠀
⠀⠀⠀⠹⣿⣿⣧⡝⢿⣎⢿⡄⢻⡇⣿⠸⣿⣸⣇⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⢰⡿⠁⢿⣇⠀⠀⠀⣠⠀⣹⣶⣦⡀⠀⠈⣿⣧⠀⠀⠻⣿⣦⣶⡿⠃⠀⠀⠀⠀⠀⠀⣀⠀⢴⡀⠀⠀⠀⣾⠇⠸⣇⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢹⣿⡆⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⠈⠁⢸⡇⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠛⠿⠿⣿⣿⣿⣿⣿⣿⡶⠀⢸⣇⢸⣎⢿⡆⠀⣿⣿⣷⣿⠙⣿⡇⠀⠀⠈⣿⣷⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠈⣿⡄⠀⠈⢻⣿⡀⠙⠻⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡈⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⡿⣁⢀⣤⣾⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠸⣿⣶⣤⣾⣎⡙⢿⣿⣿⣿⣷⡄⠀⢻⣮⡻⣮⣿⡆⠻⢿⣾⣿⣦⣿⣷⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢋⣻⠀⠀⢿⣿⣤⣀⠀⢿⣿⡄⠀⠀⠈⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢟⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣬⣍⣭⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⠏⢈⣿⡇⠰⣦⠰⣿⣭⣭⣾⡷⠀⢻⣿⣿⣿⣿⡄⠀⠙⠿⣶⣽⣷⠀⠀⠉⠛⠻⠛⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢿⣷⠀⠈⢿⣿⣿⣷⣮⣿⣷⡆⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⢀⣴⢶⣦⣀⣾⢿⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣤⠉⠉⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣠⣾⡟⣿⡟⢡⢶⣿⣯⡉⠁⠀⠀⠈⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⣦⢠⡄⣶⣾⣿⣿⣶⣬⢽⣿⣿⣧⣤⣄⡈⢿⣷⣌⠙⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡎⣿⣷⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠉⣡⣾⡿⠃⣸⣾⠿⣻⣿⣷⣦⡀⢰⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢠⣼⣿⠀⠀⠻⣿⣇⠀⢹⣿⠃⠈⠙⣿⡟⢹⣿⣿⠛⠻⠏⠈⠻⠟⠁⠀⠀⠀⣀⣀⣠⣴⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠟⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠉⠉⠀⢰⣿⣷⣿⣿⡿⠿⠿⢣⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠈⠙⣿⣷⣴⣿⣿⣿⣆⠛⢿⣦⣜⣠⣿⡇⠈⠛⠛⠀⠀⠀⠀⠀⠂⣀⣠⣴⣶⣿⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠙⣿⣿⡋⠀⢻⣿⣧⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⣀⣤⣶⢾⣿⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣴⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⢀⣤⣴⣿⣿⣿⣿⣶⣀⣀⣀⣰⣶⡈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠿⠛⠋⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠿⠛⠉⢀⣀⣀⣀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣫⣿⣿⣿⣿⣿⠇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⣀⢀⣰⣦⣾⣿⣿⣿⡇⠘⣿⣿⣟⣭⢹⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣿⣿⣿⣿⡟⠿⣿⣏⣩⣦⣿⡍⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣿⣩⡉⢸⣿⣿⣿⣿⣿⣿⠛⢻⣧⣶⣾⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⡞⠻⠿⣿⣯⡁⠀⣾⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⣿⣧⣴⣾⣿⣿⣧⠀⠙⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⠀⠀⠀⠀⠀⠻⡿⠉⠁⠀⠀⢸⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⣤⣤⣤⣴⣶⣶⣾⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠀⠀⢠⣤⣤⠀⣀⡀⢀⣤⣤⠀⣀⣤⣤⣄⠀⠀⣀⣤⡄⠀⢠⡄⠀⠀⣴⡄⣀⣤⣤⡄⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⢠⣿⠿⣿⠀⣿⣿⣼⣿⣿⢀⣿⠏⠙⣿⡆⢰⡿⠋⠁⠀⢸⣧⠀⠀⣿⡇⣿⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣶⣿⡄⣿⡿⠿⢹⣿⢸⣿⣀⣀⣿⠃⢸⣧⢘⣿⡇⠘⣿⣄⣠⣿⠁⢠⣬⣽⣿⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠿⠀⠀⠿⠇⠿⠇⠀⠈⠛⠀⠙⠛⠛⠛⠀⠈⠻⠿⠛⠀⠀⠈⠛⠛⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣀⣀⣤⣤⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⡆⠀⠀⠀⢀⣾⠟⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠉⠙⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠐⠟⠋⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣉⠉⠉⢹⣿⣿⣿⠇⣾⠛⠷⢶⣶⣶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠈⠙⠛⠷⠿⠛⠋⠁⢀⣻⢶⣤⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⣿⡛⠛⠻⢶⣦⣤⣼⠿⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⡙⠛⠛⠛⠛⢋⣩⡶⢀⣠⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠛⢻⡿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⡟⠉⠀⠈⠉⠉⠉⠛⠻⢷⣤⣄⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠿⠁⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣤⣤⣤⣤⣤⣤⣤⣀⢨⠿⣿⡀⠀
⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⣾⡋⢤⣠⣀⣀⣀⢈⣿⡌⠀⢹⣧⠀
⠀⠀⠀⢸⡟⠀⠀⢀⣤⡶⣦⣄⡀⠀⠀⠀⠀⣤⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠻⣿⣷⣶⣿⡿⠟⠉⠀⠀⠀⢻⡆
⠀⠀⠀⣾⠃⠀⢠⡿⠋⠀⠀⠙⢷⣦⣴⡶⣶⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⢰⡟⠀⠀⢸⣷⡟⣶⢀⣴⡾⠋⠁⠀⣿⠁⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⠃⠀⣤⣈⠙⣷⣿⣾⠋⠀⠀⢀⣠⡟⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠈⠻⣷⣄⡀⠀⢀⣠⣴⣟⠋⠁⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡟⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠉⠙⠿⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⢸⡏
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠒⠺⠿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⢸⡏⠀⠀⠀⠀⠀⠀⣴⡟⠛⢿⡄⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇⠀⠀⣀⣀⣠⣿⠀⠀⠀⠀⠀⢸⠇
⢸⡇⠀⠀⠀⠀⠀⣼⡟⠀⠀⢸⡇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠦⠶⠴⠶⠞⠛⠁⠀⢠⡿⠋⠉⠉⠁⠀⠀⠀⠀⢀⣼⠀
⢸⡇⠀⠀⢀⣀⣀⣿⡀⠀⠀⢸⡇⠀⠀⠀⠿⠛⠛⠲⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣴⠾⠟⠛⠋⠀
⢸⣧⠀⠀⠈⠉⠉⠉⠛⢷⡄⢸⣇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢿⣦⣀⠀⠀⠀⠀⠀⣸⠃⠈⠛⠛⠓⠶⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣤⣠⡈⠙⠛⠛⠶⠶⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⣰⣿⣿⣿⡿⠿⠻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠀⣴⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⢻⣿⣿⣇⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣼⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀
⠀⠀⢰⣿⣿⡿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠁⠀⠀
⠀⠀⣿⣿⣿⠁⣿⣿⣿⡇⠀⠀⠻⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⠃⠀⠀⠀
⠀⢰⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⢸⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢉⣿⣿⠀⠀⠀⠀⠀⠀
⠀⢸⣿⣿⣇⠀⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢸⣿⣿⣿⣷⣦⠀⠀⠀
⠀⠀⢻⣿⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠉⠉⠻⣿⣿⡇⠀⠀
⠀⠀⠀⠛⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠈⠹⣿⣿⣇⣀⠀⣠⣾⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠛⠋⠉⠉⠁⠀⠀⠀⠀😎🦢🦢🦢👁️🗨️💰
✝️✖
₊˚ʚ ᗢ₊˚✧ ゚.