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⡇⢹⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⢠⡟⠉⠛⢦⣀⠀⠀⠀⢠⠇⠀⠀⠚⠙⠻⣹⣗⣠⢴⢧⡀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠋⠁⠀⠀
⠎⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠀⡀⠀⠘⡆⠀⢠⡦⡀⣗⣿⡘⣿⡴⢧⣇⠀⢸⠆⠀⢄⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢀⡠
⣼⡏⠀⣡⣶⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠉⠲⣄⠈⡦⠘⢧⣹⡾⣷⡻⣯⢷⠼⠋⠻⣞⠀⠀⢈⣞⣄⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣠⢴⡴⢊⡝⠀⠀⠀⢀⣀⠤⠒⠊⠁⠀
⠟⢀⣾⣿⡿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⢣⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠓⠲⠤⣄⡀⠀⠀⠀⣛⡆⡅⠀⠀⣹⠣⡘⢷⢍⣾⠀⠀⡠⠋⠋⠛⠛⠻⠟⠻⠗⠒⠒⠦⢤⠏⠀⠀⣠⢾⡿⠋⢀⠞⣀⢤⠖⠚⠉⠀⠀⠀⠀⠀⠀
⣰⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⢣⣇⢆⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⣷⣿⡷⡀⠈⠁⠀⠀⠈⢳⡼⢴⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⡞⠁⢹⡇⢠⠟⠉⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢻⢿⣿⣿⣿⡌⣾⡾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣌⠉⠑⠂⢤⠒⠁⠈⠒⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⡴⠋⠀⠀⢸⡇⠀⠀⠀⢸⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀
⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢃⡞⡿⣿⣿⣿⡿⡏⣼⠹⡿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⢫⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠞⠀⠀⠀⠀⢸⡅⠀⠀⠀⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣎⡟⡱⣻⣿⣿⣷⡷⢋⢱⣷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡩⠤⠔⠒⠚⠋⠉⠉⠉⠓⠒⠒⠦⠤⣟⡁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠱⣣⢷⣿⣿⣿⣿⡣⢏⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⠤⠤⠚⠀⠀⠀⠀⠀⠀⠀⠑⠒⢤⡀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⢻⠎⣽⣿⣿⡏⣻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠤⠶⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠹⣿⡜⣼⢻⢹⣻⡟⢁⢘⢦⠌⠙⢷⡀⢰⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⡡⠂⡡⠒⠁⠀⠀⠀⢻⣿⣫⢢⠿⣿⡟⠕⠁⠀⠀⠀⢀⡩⠟⠁⢀⡱⠖⠂⠀⠀⢀⣀⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⢊⠔⢉⠔⠈⠀⠀⠀⠀⠀⣠⠞⣿⣧⣽⣼⡟⡿⠀⠀⠀⠲⠎⣁⠀⢀⠔⠉⠒⢦⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠔⣡⠒⣁⠔⠁⠀⠀⠈⠐⢀⡴⠋⠀⠀⠘⢿⣦⡈⣠⣷⠀⠀⠀⠀⠀⠀⠩⠇⢠⢺⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡡⠊⡠⠊⠀⠀⢢⠀⠀⣠⡴⠉⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡠⠊⣠⣊⣀⣀⣀⡀⢀⡠⠚⠁⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡠⠊⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢀⣤⡐⠈⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⡀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀
⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠜⠀⡟⠘⣿⡇⡴⣦⡀⠀⠀⢰⣇⣠⠖⠞⡉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣇⢸⠀⠀⠀⠀⠀⡜⠀⠀
⠞⠁⠀⠀⠀⣀⡤⠔⠒⠒⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠁⢀⣀⡭⠥⠶⢖⣿⠟⠁⠈⠀⠀⠀⠀⢻⡕⢤⡀⠀⠀⠀⢀⡶⠀⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢻⡈⣇⠀⠀⠀⡸⠁⠀⢀
⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠀⠀⢀⡜⣫⣏⠀⠈⠀⢀⠀⡀⠀⠀⣿⡄⠈⠒⢄⡐⢉⣀⣴⢋⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⢿⣸⠀⠀⢠⠃⠀⠀⡜
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠈⢀⠂⡁⠂⠀⠀⢸⣧⠀⠀⠀⠈⠻⣄⡈⠈⠛⢋⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡎⠀⠀⡸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡆⠀⢀⡞⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠈⠛⢦⡀⠈⠛⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣀⣤⣷⠀⡼⠀⠀⢠⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣾⣿⣦⣌⣤⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⢷⠃⠀⢀⡇⠘⠌
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠏⠀⠀⡞⠀⠀⠀
⠑⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡏⠀⡇⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡜⠀⠀⢰⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣸⢱⠀⢹⠀⢃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢀⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠁⠀⢠⠇⠀⠀⠀⠀
⠀⠲⠀⣀⣀⠤⠴⢾⣷⣤⢀⣴⠏⠀⠀⠀⡆⠘⡀⢰⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠈⣧⢸⠄⠀⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣼⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⡇⠀⠀⡜⡆⠀⠀⠀⠀
⡠⠒⠉⠁⣀⣀⣀⣀⣀⡛⡷⣽⣞⠓⠂⠐⣴⣀⢣⠀⠆⠀⠀⠀⠀⠀⣶⠀⠀⠀⠰⠀⠐⡀⠀⡀⠘⠄⠀⠐⡀⠈⢄⠈⢆⠀⠀⠀⠀⠀⠐⡀⠈⣇⠃⠀⠘⣇⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠛⠉⠀⠀⠀⣸⠀⠀⣰⠃⣧⠀⠀⠀⠀
⢀⣤⣊⣉⣥⠠⡖⠙⡀⣿⣿⠁⠻⣷⣤⣾⣿⣿⣿⡖⢮⣤⣠⣀⠈⠄⠘⡄⠀⠄⠀⢣⠀⠱⡀⠱⡀⠈⢄⠀⠘⡀⠈⢆⠈⢂⠀⢢⠀⠣⠀⠘⡄⠈⢄⠀⠀⢸⡉⠒⠂⢄⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇⠀⢸⡄⠀⠀⠀
⠉⢀⣤⡄⡸⠏⠛⢄⣿⣹⡏⠀⠀⠡⠉⢻⠻⢿⣷⣿⣽⣿⣿⢧⠀⠀⡀⠱⡀⠘⡄⠀⢃⠀⠱⡀⠑⡄⠈⢆⠀⠘⡄⠈⢆⠀⠣⠀⠡⡀⠱⡀⠈⠄⠈⢂⠀⡄⢆⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⣠⠇⠀⠀⠈⣇⠀⠀⠀
⠴⢻⣏⣠⠟⢦⡄⠘⡷⡝⢡⡀⠀⠀⠀⠀⢎⠐⠢⠭⢏⣙⢻⠋⢇⠀⠰⡀⠱⠀⠰⡀⠀⢆⠀⠱⣀⡘⢄⠀⢢⠀⠘⠄⠀⢢⠀⠡⡀⠱⡀⠐⡄⠈⢂⠀⠣⠈⢂⠈⢳⠠⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⠁⠀⠀⠀⠀⢹⡀⠀⠀
⢆⡈⠉⢁⠀⠀⠹⡆⢸⡷⠀⠁⠳⢄⠀⠀⠈⢆⠀⢃⠘⡄⠈⢆⠀⢂⠀⠱⡀⢡⠀⠐⡀⠀⠀⢀⣑⣼⣿⣶⣦⣧⣤⣈⣆⣀⣱⣀⠑⡄⠐⠄⠈⢂⠀⠡⡀⠡⣰⠳⡋⠀⢡⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡤⠤⠤⠼⠧⠤⠐
⣀⠌⡶⠋⠀⠀⠀⢻⣰⠇⠀⠀⠀⠀⠱⡀⠀⠀⠂⠀⢢⡸⡄⠈⢆⠀⢢⠀⠑⡀⠣⡀⠐⡄⠈⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠌⢿⣆⠈⢆⠀⠑⡄⠑⠄⣹⢄⠈⢢⠈⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀
⠉⠘⠳⣒⠦⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⢲⡀⠀⠀⠐⠃⠘⢄⠀⠁⠀⠁⠀⠘⢄⠑⡀⠘⢄⠈⠱⠂⠤⢀⣉⠙⠛⠻⠿⠿⠿⢿⠿⢻⠓⠣⡀⠡⡀⠈⠢⠀⢽⠢⠡⡎⠀⠃⠀⣷⠀⠀⠀⠀⠀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣵⠒⠒
⠀⠀⠀⠈⣻⣵⠀⣸⠃⡀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⢤⠈⠢⠀⠑⡀⠀⠐⠍⠉⠩⠀⠠⡀⠈⠢⡀⠑⡀⠑⢄⠘⠄⣠⠀⠈⢧⡀⣀⢎⡀⠼⠿⠤⠤⢄⡀⠰⣾⣿⠅⠛⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣴⣦⣴⣶⠶⠛⠛⢿⠀⠀
⠀⠀⣦⡀⣠⡉⠻⣇⣽⡃⠀⠀⠀⠀⠀⠀⠀⡀⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠑⢄⠈⠢⡀⠈⠢⠀⠑⠄⠈⠢⠀⠈⠀⠈⡆⣠⠢⡀⣷⣧⣣⡤⣻⡭⠀⠈⠓⠒⠦⣤⡀⠐⢯⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠈⠉⠑⢺⠀⠀
⠀⣀⠙⢿⡿⠃⠀⠀⠛⡇⠀⠀⠀⠀⣀⠔⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⣿⣏⡼⠷⡈⠢⠀⠀⣰⣶⣤⠢⢈⡻⣷⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡛⠝⠁⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀
⠁⠀⠀⠀⠁⠈⠑⠢⡀⢸⣆⠀⢀⠔⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⣒⠊⠉⠉⠉⠁⠀⠀⠀⢠⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⢿⠈⠑⠀⠉⠢⢤⡈⣻⡿⠗⠙⠺⠁⠘⢦⡟⢿⣷⣶⣦⣤⣤⡤⠴⢖⠋⢁⠔⣉⡓⡄⠀⠀⠀⠀⠀⠀⣤⣾⣿⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣹⢀⠏⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠀⠀⠀⣠⠒⠁⠘⣷⣀⠀⠀⠀⢤⠀⠸⡛⠀⠈⠙⠛⠶⣾⣋⠉⠀⢠⠃⠜⠀⢻⢸⠀⠀⠀⢀⡀⡾⠟⠛⣻⠕⠁
⣀⠀⠠⠤⠄⣀⡀⠀⠀⠀⢸⣬⠀⠀⢸⠁⠀⠀⢠⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠘⠂⠉⠉⠉⢉⣩⠥⢦⠀⠉⠢⡀⢸⣷⣤⣷⠢⡀⠀⠀⠀⠀⠀⠉⠀⠇⡜⠒⢒⠏⢸⠐⠊⠉⠁⣀⡀⣠⠖⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⡘⣇⠀⠀⠸⡄⠀⠀⠀⢣⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠘⠓⢦⠈⢦⠀⠀⠈⢢⠋⠉⠀⢦⠋⢢⠀⠀⠀⠀⠀⣼⢀⠇⢀⠊⢀⠦⠒⠊⠉⢁⡤⠚⠁⠀⠀⠀⢀
⠀⠀⣀⡤⠄⠒⠒⠒⠂⠤⢄⣿⡀⠀⠀⣇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣀⡰⠾⠋⠀⢀⣀⣀⠠⠤⠄⠠⢤⣼⠗⠀⢣⠀⠀⠀⠱⡄⢀⠇⢀⠎⠳⣄⡀⠀⣾⠉⢼⣀⠞⡠⢻⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣠⠊
⠔⠈⠁⠀⠀⠀⢀⣀⠠⠤⠀⠘⣧⠀⠀⠘⣄⣀⣀⠀⠀⠀⢀⣀⠤⡤⡖⠒⠉⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡸⠀⠀⠀⣴⢻⠗⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣘⣫⠑⠢⡀⢷⠀⠀⠀⠇⡌⠀⡜⠀⠀⠈⠳⠤⡇⢀⣌⠤⠊⠀⣼⠀⠀⠀⠀⣸⡄⠀⠀⢀⡴⠁⠀
⠀⠀⢀⡠⡼⠂⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠉⠀⠀⠈⡡⠊⠉⠀⣼⠊⠀⠀⠀⠀⠀⠀⢧⣀⣠⢀⣄⠀⠀⢠⠃⠀⠀⢀⠃⣀⠤⠼⠧⢎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠀⠀⠈⠘⣇⠀⡼⡼⠀⡰⠀⠀⠀⠀⠀⠀⡗⠀⡇⠐⠦⠤⡯⠀⠀⢀⡞⡻⠳⢦⠴⡻⠃⠀⠀
⡤⠂⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠒⠒⠒⡺⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡄⠀⣿⠟⠃⠿⣶⡒⠉⢀⡠⠔⠋⠉⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠘⣿⣷⠄⠀⠀⠀⠀⠀⢸⡸⢰⠁⢠⠁⠀⠀⠀⠀⠀⠀⡧⠀⢧⠀⠀⠀⡇⣀⡶⠁⡜⠀⠀⠀⢸⠁⠀⠀⢰
⠀⠀⠎⠀⠀⠀⠀⠀⠀⡠⢄⠤⠊⠉⠀⠀⢀⠄⢰⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠈⣉⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠣⣤⠤⠤⠤⣀⠙⢕⢄⠀⠀⠀⠀⠀⠀⠇⠆⢀⢧⣀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡀⠀⢀⡷⠋⠀⡜⠀⠀⠀⠀⡏⠀⠀⠀⠀
⠀⡈⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⢠⠋⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢸⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠰⡄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠹⡛⠒⠒⠒⠧⡌⢢⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠉⠚⠶⠤⣄⣀⣀⣧⠀⢘⣑⣶⡏⠀⠀⡜⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠀⠀⠀⠀⣷⣀⠀⢸⠙⠢⣄⡀⠈⢆⢤⡀⠀⠀⠀⢱⠀⠀⠀⠀⠹⣦⠁⠀⠀⠀⠀⣰⠁⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣐⠏⠀⡋⠀⠰⣇⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀