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|_ __ | |_ _| |_ _| / \ .' '. / |
| |_ \_| \ \ / / / _ \ ______ | .--. | `| |
| _| _ \ \ / / / ___ \ |______| | | | | | |
_| |__/ | \ ' / _/ / \ \_ | `--' | _| |_
|________| \_/ |____| |____| '.____.' |_____|
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠖⠒⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⢯⡝⣺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣧⣛⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⡀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⣧⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢁⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⡹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠹⣿⣿⣿⣿⣣⠔⡂⠍⣩⣷⣿⣦⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠝⢻⡿⠋⠉⡍⣿⣾⣿⣿⣿⠟⠋⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣖⣹⢣⣌⣩⣾⣿⣿⣿⣯⢹⣷⠶⢚⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡶⡯⢽⡯⡔⢠⣌⣭⣽⠆⢢⢡⣾⣿⣷⣶⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣷⣷⡶⢷⣶⣿⣾⣿⣿⣯⣁⣎⣰⣿⣿⣿⣿⣿⣿⣷⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣿⣿⠟⢩⡿⠀⢚⣿⣿⣿⡫⣽⣷⣿⢿⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡠⠄⢒⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⠂⣾⣿⢣⢡⢠⡿⡃⣰⡟⠻⣏⣰⢒⡉⠅⠀⢻⣿⣿⣿⣿⢏⡀⠈⣲⣬⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡎⡆⣾⡹⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣋⣬⣸⣆⣾⣠⢼⣛⡶⠷⢾⡇⣧⠀⠀⠀⠈⢻⣿⣿⢃⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣆⠇⣷⢭⢳⡜⣻⣿⣿⣿⣿⣿⠿⡉⣿⣿⣿⡟⢓⣠⣼⡵⢒⣂⡖⢋⢷⢸⡀⣀⣠⢤⡴⣻⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⡘⡜⣮⢓⡞⣵⣿⣿⣿⢿⣏⣤⡴⠻⣿⠁⣦⣵⣃⣟⠁⢻⠣⡘⣴⣿⣷⡑⡜⡧⢯⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⢱⢸⡭⢞⣼⣿⣿⣿⢻⣏⢵⡟⠂⢹⡝⠉⠀⢸⠟⠚⣧⣱⣾⣿⣿⣿⣇⣧⢛⠶⣹⣿⣿⣿⣿⣿⢈⠻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠸⣸⡻⣜⣿⣿⣿⣿⡄⣿⠘⢀⣤⣸⣧⣀⠀⢸⣸⣿⣿⣿⣿⣿⣿⡿⣿⣸⢸⢻⣿⣿⣿⣿⣿⣿⢀⠇⡸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠛⠷⢿⣿⣿⣿⣿⣷⣿⡄⣞⣿⢽⣿⣿⣷⣤⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⢈⠆⡱⢘⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣯⠿⣿⢾⣿⣿⣿⡿⠲⢯⢶⣩⣽⣿⣿⣿⢿⣿⣟⠃⠀⠀⠹⣿⣿⣿⢂⠜⡴⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣧⠛⢿⣿⡿⢉⠄⡃⢆⣢⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣩⡬⠋⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢟⠧⣝⢾⡅⠀⡏⢄⢣⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢽⣪⣿⣷⣄⣯⣴⣿⣿⣿⡿⢋⠍⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡕⢠⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣴⣿⣿⣿⢿⣿⣿⣿⣿⠋⣔⣵⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣼⣿⣿⣿⡆⠻⡿⢋⢤⣷⣿⣿⠿⢋⠽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿⣿⢫⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⡟⣧⡇⢠⢃⣼⣿⣿⠿⡉⢆⣵⣾⣿⣿⣿⣥⣤⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⡎⢷⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣏⣳⢻⣿⣶⣿⣿⡿⢋⢔⣵⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⢞⣣⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⡼⣿⣸⠉⢿⠟⡋⢄⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⣜⣲⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢧⣿⢿⢸⣶⣊⠔⡡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣟⠶⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣾⡏⢼⣺⢃⡙⣦⣿⣿⣿⣿⣿⠟⣋⢉⡉⡙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣯⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣹⢾⡗⢊⢿⡤⢸⣿⣿⣿⣿⡟⢡⠘⡄⠒⡌⠔⡌⣿⣿⣿⡿⠀⠀⠀⠀⠀⣼⣿⣿⣯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣳⠏⢸⣽⠀⢎⣱⡆⢿⣿⣿⣿⠘⡄⠣⢌⠱⣈⠒⡰⢸⣿⣿⣷⠀⠀⠀⠀⢠⣟⣿⣿⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠻⣿⣿⣿⠃⠀⠸⡿⡌⢢⣾⣿⣎⣿⣿⣷⡎⠰⡁⠎⡔⢢⠑⡰⢹⣿⣿⣿⠀⠀⠀⣠⣿⠙⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣗⢻⣿⣿⠃⠀⠀⠀⡇⡇⢂⢿⣿⣿⣿⣿⣿⣧⠃⡜⠰⡈⢆⠱⣀⢻⣿⣿⣿⠀⠀⡴⣷⢸⡍⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡜⣿⣉⣾⣿⣿⣿⡇⠀⠀⠀⣃⢷⠈⠼⣿⣿⣟⣿⣿⣿⡰⢈⠱⡈⢆⠱⡀⠎⣿⣿⣿⡇⠀⡷⣻⣿⢾⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣴⡿⣼⣿⣿⣿⡿⠁⠀⠀⠀⢻⠸⡘⢄⢻⣿⣿⡿⣿⣻⣇⠌⢢⠑⡾⠛⡲⣅⠚⣿⣿⣧⢸⡟⣿⣿⣻⢹⠃⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⢫⣾⣇⣿⣿⣿⡟⠁⠀⠀⠀⠀⠺⢸⡕⡨⠌⣿⣿⣿⣿⣿⣿⢈⠆⣹⣷⠁⢆⡹⣌⢻⣿⣿⣼⣧⡿⢿⢳⣿⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢺⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⢸⢳⠄⢣⢹⣿⣿⣽⣿⣿⡆⠎⢼⡟⡈⢆⠰⠹⣾⣿⣿⡏⠛⠁⢾⣸⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⢿⠿⣏⣿⣿⣿⣷⡀⠀⠀⠀⠀⢻⢸⠸⣏⡐⢂⢿⣿⣿⣿⡟⢿⡈⢆⡧⠑⡌⢢⠃⣽⣿⣿⣇⠀⠀⣸⣼⡏⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⣿⠀⢻⣹⡟⣿⣿⡷⠀⠀⠀⠀⢸⣸⠂⠽⣄⠣⣸⣿⣿⣿⠇⠈⢧⢂⣏⠱⡈⢆⠱⣿⣿⣿⣟⠀⠀⢩⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⢀⢀⣸⣏⠜⡰⢹⡰⢸⣿⣿⣿⠄⠀⠈⢷⣏⠰⣡⢪⠼⢿⣿⣿⡿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣴⣿⣿⠰⣀⢳⣧⣿⣿⣿⣿⠀⠀⠀⠈⣿⢠⢹⡜⡄⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⣿⣿⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣆⠺⣿⡔⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠹⡶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠻⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⢰⠟⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⡃⡼⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⢏⡇⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢘⣧⠇⢻⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⢸⠰⡁⠎⢿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⡀⢨⡌⢿⡯⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⡄⢸⢡⠘⡌⢌⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⡇⢸⠹⡀⢷⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⡸⡁⢎⠰⢌⢺⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⡇⠘⡤⢹⡸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇⠜⡠⢃⠌⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⣇⠢⢱⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈⠆⡱⢈⠜⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⡆⢱⠈⠆⡌⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⠁⡎⠐⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣷⠈⡏⢰⠈⢱⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⠄⠣⢌⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡘⣆⠉⢆⠡⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⡨⢑⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⡎⢄⠣⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠔⣱⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡼⢌⠢⢡⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢆⢩⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⢠⠃⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣗⠊⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⡘⠌⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡉⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⠂⡍⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⠰⡙⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⡐⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡏⢢⠑⠤⣹⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⢑⠢⠙⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣀⠀⣰⠿⣄⢩⡶⢑⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠢⣵⠿⡾⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡜⠛⢰⡿⣿⣹⣷⣤⣇⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⢹⢽⠹⠃⢸⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢰⠀⡞⣵⢣⢾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⡜⠀⠀⠀⣸⢞⣹⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⠉⠀⣰⢻⣬⣷⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⢺⡀⠀⠀⣟⢮⡹⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⢏⡀⠀⢀⡴⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⣿⡆⠀⠘⢧⡳⡝⣧⠀⠀⠀⠀⠀⠀
⠀⣀⣀⠤⡔⢚⠩⡐⢢⠘⡓⢛⠻⠿⢟⡛⠻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠐⣻⡿⠿⢄⣀⣀⣿⣷⣿⣷⣄⠀⠀⠀⠀
⡼⢉⠍⡱⢈⢆⣱⣬⣦⣑⣌⢢⡑⢌⣦⡷⢟⣫⡭⣯⢩⣭⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣠⠗⠫⢌⡙⢛⠻⣿⣿⣿⣿⣦⡀⠀
⢏⣓⠚⠒⡻⢛⡛⣛⠛⣛⣛⣛⣻⡭⠿⠚⠋⠉⠙⠓⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣏⣚⣮⡑⢢⠘⡄⢣⠐⡄⢂⣿⣿⣿⡀
⠀⠀⠉⠛⠙⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠬⣉⣓⣚⣒⣋⣉⣩⣍⣭⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀