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