⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣢⣉⠀⠀⠀⠠⠤⢀⠀⢠⡟⣱⡿⠋⠀⠀⠀⣠⠾⠍⠉⠻⢦⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠤⠤⠤⣠⣀⣀⡀⠀⢀⡤⠞⠡⠘⠁⠀⠀⠀⠈⠀⠀⢤⣩⠏⣴⠁⠁⡠⠀⣠⣾⠃⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⡀⡾⠲⢶⣴⣤⠄⡙⢙⣿⠞⠉⠈⢁⠀⠀⠀⡀⠀⠀⠀⠄⠄⠈⠑⢝⢾⢈⢀⣴⣿⡅⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⢦⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠛⠀⠀⠀⢠⣃⠀⠀⠀⠀⠉⢳⢾⠁⡆⠀⠀⠋⠄⠀⠀⠐⠂⠀⡀⠑⢕⢀⡀⠈⠛⣖⠚⢡⡣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡾⠛⠛⠿⠷⢾⣤⣸⠃⡜⢐⡁⠀⠂⠀⠀⠀⠀⠠⠀⠀⡀⠀⠱⡈⠀⠀⠉⣧⠨⣷⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⡍⢠⠃⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠀⣌⠀⠠⠀⠀⠀⢎⢃⢉⠰⠐⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣠⠇
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢰⠁⠸⢀⠇⡇⢰⠀⠀⡀⠀⢆⠀⠀⠀⡓⠱⠑⡀⢱⠀⠘⠌⢷⡠⢱⠰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁⠀
⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠈⠁⣧⠸⣧⠀⢱⡄⠈⣦⡀⠀⠙⠀⢹⡙⡠⠂⠐⢆⠛⡅⠚⡾⡌⡠⠖⠓⠉⠁⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡌⠀⠀⠀⠀⠀⠐⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢸⡁⢏⢃⠘⡟⠂⠊⢔⠀⠀⣀⢂⠖⣎⠀⡐⠘⠂⢷⢀⢸⠺⡢⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⢸⡏⣷⠸⣆⢡⠘⡄⠀⠀⡀⢀⡠⠋⠷⡌⠁⠀⠃⠘⠛⠈⣾⣧⡀⠐⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⢀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⡔⢂⠜⠻⡎⢡⠀⠁⠀⠢⠞⠈⠀⠀⠀⠀⢱⠀⠠⠀⢰⣘⠀⣷⢛⣶⣫⢤⢤⣀⠀⠀⠗⠒⠀⡖⠀⠀⠀⠀
⠈⠉⠂⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣸⡐⣼⢦⡀⠀⣠⡧⠅⠁⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⢸⣿⣔⣷⣾⢈⠻⣿⣣⣠⣵⣮⣀⠤⢤⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⡇⣜⣟⢻⢻⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣇⣼⣈⠀⢸⢮⡾⡶⣧⣌⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣧⠸⣨⠆⣮⢧⡀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣾⠇⡦⣱⣿⣿⠴⣶⣞⣛⡇⢧⡀⠉⢫⢦⢀⠔⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⢧⣻⡆⠸⡄⢾⣐⣦⣄⣈⡈⢀⡤⠊⣡⣯⡧⡄⠏⣩⣍⣔⠙⠙⣾⣍⣚⢤⣠⣾⠀⠯⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡷⣥⣶⢪⢭⡳⢿⡼⠷⣼⣻⠒⠀⣡⠞⢳⣟⠈⠵⢕⡿⠒⡥⠓⣸⢟⣷⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡎⣀⣠⠢⠨⢧⡸⠷⣆⡋⠙⠠⠊⠀⡴⢫⠒⢀⢐⡡⠐⣨⣤⣶⣯⢞⡆⣷⢂⠹⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⣉⣿⣵⣟⠂⠽⢳⡄⢍⢈⣂⠢⡫⣺⠅⠊⣁⡼⣪⣷⢿⠋⠀⠈⠙⣻⢩⣤⢀⢺⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠛⠉⠀⠈⠓⣙⣚⡿⡧⣄⣊⠄⢀⡀⠢⠏⠹⣾⣯⣇⠖⠂⠀⠀⠀⣈⡜⣱⠇⡿⠁⠀⠀⠀⠀⠀⠀