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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⢋⣉⠠⠀⠀⠀⠉⣉⡴⠖⢢⠈⠳⣄⠙⠲⠦⣀⡀⠈⠉⠛⠶⣦⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡾⠛⢁⡤⠞⠉⠀⠀⠀⣠⠴⠛⠀⢀⡴⠃⠀⠀⠘⢆⠀⠀⠀⠉⠳⢤⣀⠀⠀⠉⠳⣦⡀⠀⠀⠀
⠀⠀⠀⢠⡾⠋⢠⡜⠋⠀⠀⠀⠀⡠⠞⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠈⠻⣆⠀⠀
⠀⠀⣰⡏⠀⡴⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠹⣧⠀
⠀⣰⠏⢀⡼⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢹⡆
⠀⡟⠀⡾⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣿
⣼⠇⢰⠇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⣿⠀⣿⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣄⣤⣤⣾⣤⡿
⣿⠀⣿⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣀⣼⠋⠈⠀
⣿⠀⢿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀
⠛⠓⠚⠛⠒⠒⠒⠶⢶⣖⠲⠶⠶⠶⠶⠶⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⢤⡈⠛⠶⠤⣤⣀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣄⠉⢹⡀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠙⠻⣿⡿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⣤⡟⠀⠀⠀⠀⠀⠸⡿⢦⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣀⢀⣠⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣷⠈⣷⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠋⠁⠀⠀⢀⣠⣤⠴⢶⡶⠒⠒⠒⡿⠀⠀⠀⠀⠀⠀⠀⢻⡀⣾⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣈⣤⣧⠶⠟⢻⠁⠀⠀⣼⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠀⠀⠀⣸⡇⠀⢀⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇⠀⢸⠃⡄⠀⠀⡈⢿⡀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⣿⢰⡇⠀⠀⠀⠈⠛⠲⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⣀⣿⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢹⡿⣿⣟⡟⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢿⠟⣾⠟⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⠀⠁⠀⢸⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣼⠀⠀⠀⢸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢰⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⡄⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠁⠀⠀⢀⠀⢀⣉⡉⠉⠉⠙⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⠀⣿⣿
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠆⢸⣠⢿⣏⣙⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣉⣁⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣴⠐⠒⡀⠀⠀⠀⠀⠀⠀⢈⣼⠀⣸⡄⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢹⡇⠀⠀
⡀⠀⠀⡆⠀⠆⠘⣿⣧⣴⣿⣿⡟⠀⠀⠆⠀⠀⠀⠀⣠⣾⣿⣿⢂⣹⣥⣶⣿⣤⣶⣀⣀⣠⠀⠀⢀⣤⣄⠀⠀⢠⡾⠋⢠⣤⣶⣇⡀⠀
⣿⡿⠿⢷⣦⣤⣀⣤⣼⣋⡉⠁⠀⠀⠀⢀⡀⠀⢀⣀⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣿⡿⣿⣷⣶⢟⠁⠀⠀⣀⣀⡉⢳⡀
⣿⣇⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣭⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠛⠉⠉⠀⣼⠀⠀⠸⢿⣿⠟⢉⣿
⣿⣿⠟⠛⠂⠀⠀⠙⡿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣴⠆⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⣤⠾⠋
⣿⣁⣤⣶⣶⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠑⠀⣤⣤⣴⣾⣿⣾⣿⣷⣤⣶⣋⡁⠀⠀
⣯⡉⠙⠿⠋⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠈⠻⢶⣤⣀⣀⣠⣶⣿⠾⠋⠉⢒⣶⡖⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣤⠀⠀⠀⣴⠟⠛⡏⠉⠉⠹⠙⠻⣧⡛⢹⡿⡋⢉⡙⠻
⠀⠀⠀⠀⠈⣿⡿⠛⠁⠀⡤⠂⠉⠄⢻⡄⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠅⠠⠀⢹⠀⣀⡀
⠀⠀⠀⠀⢸⡋⣀⠀⣠⠼⠁⠀⠸⠀⢸⣷⡀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀
⠀⠀⠀⠀⠀⠙⠉⠉⠁⢠⣀⢀⠀⠀⢈⣿⡇⠳⢷⢳⡀⣦⡀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠆⢀⣸⣿⣇⠀⠀⠀⠀⢻⡻⣦⠀⠀⠀⠀⠀⠘⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠟⠋⠉⠈⠙⢷⣤⠀⠀⠃⢹⠷⣄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠁⠀⢀⣀⠀⠀⠈⣿⣇⣀⠀⣾⠛⠈⢷⣄⡀⠀⠀⠀⠹⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⢸⡆⠘⣿⣿⠆⢠⣿⣿⣿⣿⣿⣿⣦⣄⣈⣻⣦⠀⠀⠀⣠⠝⠛⠷⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢀⠈⣿⣦⣈⣻⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠁⠀⠀⣀⣀⠈⠻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠟⠛⠻⠿⠟⢻⣿⣟⠛⠉⠒⠛⠛⠛⠛⠛⠛⠻⣿⣿⠀⠀⠀⢰⣿⣿⠷⠒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣀⣠⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢳⣄⠀⠈⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⣶⣤⣀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠄⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣗⣿⡿⠿⠿⠿⣟⡿⢟⠿⡻⠽⣿⣻⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⣏⣭⣷⡼⠟⠚⠋⠒⠉⠚⠑⠛⠷⢶⣯⣟⡻⢿⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣫⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣽⡛⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣳⣽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣬⡛⣿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣼⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⡟⠁⠄⡁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠀⠂⡁⠌⢻⣷⣽⡺⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣼⡛⢄⢃⠂⠄⡁⠂⢀⢠⣰⣾⡟⠀⠀⠀⠀⠀⠀⢹⣷⣄⡀⠂⢀⠁⡂⠜⣀⠣⡝⣷⢿⣽⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⡘⢢⠌⣂⣖⣤⣵⣾⣿⠟⠋⠀⠀⠀⡀⠀⠀⠂⠀⠙⢿⣿⣶⣤⣂⣤⠑⡠⢃⠼⣹⣯⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣻⠦⡝⢢⡑⢄⠻⣙⠩⠁⠄⡐⣀⣂⠌⠀⠄⠡⠈⡐⢠⠈⡀⢈⠉⠛⡛⢛⠣⢰⡉⠖⣭⣿⢿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢣⡛⡴⣉⢦⢩⣿⣿⣿⣿⣿⣿⣿⠆⠡⠌⡄⠡⠸⣿⣿⣷⣾⣾⣷⡿⣌⠣⣇⡜⣭⢲⣿⢺⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⡧⣝⢲⡍⣖⢣⢦⡹⢍⡛⣉⠉⡄⢠⠁⣂⠘⡠⢁⠌⡙⢛⢛⡛⣫⠵⣌⠳⡜⡜⣦⢻⣿⣿⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⡽⣿⣷⢭⡲⡹⢬⡓⢮⡱⣎⣴⣥⡷⠾⠷⠟⠾⠛⠷⠻⠶⢷⣮⣦⡳⣡⢛⡬⣛⠼⣱⢎⣿⣯⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⣿⣷⢇⡹⢇⣹⣷⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣷⣸⢁⡏⣱⣾⣿⡿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠓⢿⣎⢷⣩⢛⡻⢟⣿⡶⢷⢾⡶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣴⣴⣶⣿⣿⡗⣺⢵⡿⣽⣱⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡘⢻⣷⣎⢧⡓⣎⠾⣙⢎⡞⡱⢎⡖⢬⢩⡛⢿⣯⣿⣽⣻⣿⣽⡿⢫⡼⣽⠿⣷⣾⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣿⣿⡷⠿⢾⣵⡩⢖⡼⣑⠫⣜⢢⡓⣬⠣⡝⣛⢻⡛⣏⢷⣹⣷⡿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣟⡿⢏⣷⣆⢢⠉⠿⣷⡼⣌⡗⢌⠳⢾⣔⣫⡜⣧⢳⣝⣾⣷⣿⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣟⠫⢍⡘⢡⢊⡙⢿⣮⠓⠛⠟⢛⠛⠿⠶⠣⢌⡙⣿⠾⢿⣿⣟⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢡⠃⢂⠉⡁⢢⠘⢠⢙⡟⠛⡛⢒⠛⡄⢂⠅⡂⠔⠠⠓⡈⢿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⡟⡌⢢⣼⣤⣖⣠⣂⣜⣤⣿⢿⣷⣿⢬⣷⡐⢌⠰⡁⢎⡑⢢⡁⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⢣⠘⣾⠋⡍⠋⡟⢫⢹⣿⣶⡟⠉⠛⢻⣤⢹⡎⣧⣽⣶⣿⣷⣯⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣯⣿⣬⠿⢣⡙⣌⡕⡂⢮⣼⣯⡿⠃⠀⠀⠀⠙⢯⣟⣛⣻⣭⡽⣭⠭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣿⢿⡗⢬⠧⣱⡾⡱⢁⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⢻⣔⣫⢲⠟⣡⢃⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⢷⣮⣼⡵⢿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠙⢿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠉⠑⢢⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀
⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡜⠁⠀⣠⣤⣤⡀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⢀⣤⣶⣤⡀⠀⠱⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⠀⠀⡿⠛⠀⠀⠀⠀⠀⠀⠛⢹⠀⠀⢸⣿⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀
⠀⢠⠃⠀⠀⠀⠀⠀⠀⣠⢧⡀⠀⠙⠛⠛⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠙⠛⠋⠀⠀⡰⢧⡀⠀⠀⠀⠀⠀⠀⡇⠀
⠀⢸⠀⠀⠀⠀⠀⢀⡞⠁⠀⠑⠤⣀⣀⣀⣠⣴⣧⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣵⣤⣄⣀⣀⠤⠚⠁⠀⠙⣄⠀⠀⠀⠀⠀⢰⠀
⠀⡎⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⠀
⠀⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡇
⢠⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇
⢸⠃⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡇
⠈⢇⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⢀⡴⠋⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠈⢳⣄⠀⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⢀⠇
⠀⠈⠣⡀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠋⠁⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
✵✶✷❃✾✽✼❈❇❀✲❅✤❋✸✹✺≛✻❉❊✢✣✿❄✳❆✴⁂⁎⁑✩✫★☆✭✮✪✡✰✬⋆✯✦✧✥✱❁❂