⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⣀⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠖⠊⠉⠉⠉⠚⠺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠤⠤⠶⠤⢂⠤⠤⠤⠤⠴⠄⡤⢤⠤⡤⣤⠄⢀⢀⣀⣀⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠴⢊⠥⢢⠌⡡⢆⠱⠌⡄⢣⠒⡌⢢⠑⡰⢂⠥⡙⠤⣭⡤⠌⠓⠊⠉⠁⠀⠀⠀⠀
⠀⠀⠀⣠⠞⡡⢘⡈⠜⡠⢊⠔⡨⢁⠎⣀⠣⡁⠜⡠⢉⠔⡡⣧⠘⣠⣁⠮⠒⠀⡀⠀⠀⠀⠀⠀⠀
⠀⢀⠞⣡⢈⠑⠢⢉⠆⡱⠈⢆⠡⠅⡊⠤⢑⡈⢱⠠⠭⠆⠑⠛⠈⠁⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀
⢀⡞⣡⢣⠥⣾⠷⠼⢆⡅⢈⣀⣈⣀⣀⣀⣀⣀⣸⣀⣀⣀⠀⣎⣀⣤⠤⠤⠤⠤⠄⣀⡈⢆⠀⠀⠀
⢰⢄⢧⠣⣼⠃⢆⢒⡾⢐⠢⣐⣴⣾⡟⡙⢢⡴⡏⡔⠤⢂⢜⣧⠡⣌⠳⡝⣎⠧⢻⡔⢂⠜⣧⠀⠀
⡎⣌⢉⢲⠏⣌⡐⡾⡄⢃⠆⣭⣟⣿⠁⢬⡜⠀⡧⡌⢢⠁⡞⠈⠳⣄⠥⢂⢹⡔⡈⢏⠑⠪⣌⢇⠀
⡏⠤⡈⣟⡈⠤⢸⠇⡌⢡⢺⡿⣯⠏⣨⠞⠀⠀⡏⠤⣁⣹⠁⠀⠀⠙⣎⠡⠌⣷⢁⠚⡄⠀⠈⠙⢆
⡏⠆⣩⡇⢌⠡⣿⠉⡌⢢⣿⢿⣻⢨⡝⠀⠀⠀⡏⠒⢤⠃⠀⠀⠀⠀⠈⢷⠨⢽⣎⠡⢇⠀⠀⠀⠈
⣏⠒⣼⠘⠤⣳⣯⠰⢡⣿⣻⠃⣇⠏⠀⠀⠀⠀⣏⢱⠏⠀⠀⢀⣀⣰⣆⣸⣧⢼⣿⡌⢺⠀⠀⠀⠀
⢹⡂⣹⠔⣰⣿⣯⡀⢮⣿⣿⠀⣿⣤⣄⣠⣶⡀⢯⡞⠀⠀⠀⢼⣿⣿⣿⣿⢿⣾⣿⣅⢺⠀⠀⠀⠀
⠸⡇⢸⣯⡟⠁⡷⡈⣾⣿⣻⣿⣿⣿⠿⠿⠿⠃⠘⠀⠀⠀⠀⠈⠁⠀⠀⢻⣿⡿⣳⣯⢹⠀⠀⠀⠀
⠈⣿⢘⠃⢧⠀⡷⢰⣿⢿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠹⣾⡏⠀⠀⠀⠀
⠀⠘⡆⡿⢸⣷⣾⣸⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠂⠀⠀⣀⣴⢻⡾⠀⠀⢻⡇⠀⠀⠀⠀
⠀⠀⢸⡗⣸⣷⣻⣾⣷⢯⣿⣹⣤⣤⣀⡀⠀⢀⡀⢀⡀⣀⣤⣴⣿⣻⣿⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⡧⣸⣷⣻⣿⣞⡟⡈⣿⣿⣾⣿⠀⠉⠈⢹⣿⣿⣽⢾⣽⡾⣽⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡗⣸⣷⢿⣾⣿⡠⢁⠺⣿⣟⣯⠀⢈⠀⢈⢻⣿⣽⣾⣽⡷⣟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⢾⣿⢹⣿⣾⣷⢈⠂⢿⡿⣿⢷⠚⠒⠒⢾⡿⣷⣻⢿⡽⢇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢡⣻⡏⢼⣿⣖⣭⣧⠚⠌⣿⢷⢯⣧⠀⠀⠠⣿⡟⣵⢟⡟⣼⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⢰⡏⡐⡞⠀⠈⠘⠫⢷⣌⠸⣶⣌⡛⢧⡀⠀⣷⣻⣻⣾⣱⡿⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡇⢢⡄⢹⠀⠀⠀⠀⠀⠀⠙⣶⣽⣮⠙⣷⣵⠀⠛⣽⣿⣽⡟⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢰⠌⢆⢉⡇⠀⠀⠀⠀⠀⠀⠀⠱⡙⠻⣿⣪⣙⠧⣸⢏⣽⠟⣽⠄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠯⡐⢎⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠳⡡⠔⡉⠿⣽⣿⡿⠋⣄⣿⠂⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀
⢨⠇⠌⠆⣞⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠉⠉⠉⠉⡸⢩⡝⣅⠀⠠⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀
⡼⢈⠌⡑⣾⠀⠀⠀⠀⠀⠀⠀⣃⠇⠀⠀⠀⢀⡜⠤⢹⡋⢤⠣⣀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀
⠓⠚⠒⠓⠋⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠋⠒⠚⠙⠓⠂⠓⠚⠃⠀⠀⠀⠃⠀