⢀⣿⠇⠀⠀⠀⠀⢠⠃⠀⠸⣀⠀⠈⢄⡔⠁⠀⠀⣼⣿⣻⣟⠔⢱⡴⠛⠁⠾⣻⠟⡿⠀⠀⣷⠀⠈⡇⠇⠀⠈⢇⠀⢃⠀⠙⢦⠀⠀⠀⠀⠈⢺⡷⡀⢳⡀
⢼⡏⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠑⠠⣠⠀⠀⠀⡐⣸⡟⠋⠀⠀⠉⠀⠀⠀⠈⠀⠀⡇⠀⢸⣿⠀⠀⡇⢰⠀⠀⠸⡀⠈⡀⠀⠈⢳⡄⠀⠀⠀⠀⠹⡼⣢⣷
⡞⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⡜⣿⠀⠀⣧⢸⠀⠀⠀⢇⠀⠃⠀⠀⠀⠹⣆⠀⠀⠀⠀⠹⡗⢝
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠄⠀⠀⠀⠀⡇⠀⠈⠚⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠃⣿⠀⠀⡏⠘⣄⣀⢀⣸⠀⢰⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⡘⠀⠀⢀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡌⢀⡎⠀⠸⠀⠀⡇⠘⡏⠁⠀⠘⡀⢸⠀⠀⣧⠀⠀⢀⠙⢦⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢰⠀⡇⠀⢤⣠⠀⢸⣐⣶⠀⠀⠀⠀⠀⠀⠀⢀⢃⡞⠀⠀⡇⠀⢰⠁⠀⡇⠀⠀⠀⡇⠀⠀⠀⡿⡆⠀⢸⣆⠀⠉⠢⣀⠀
⢀⠂⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⣿⣖⡇⠊⠁⠈⠀⠸⡅⠈⠉⠑⠀⠀⠀⠀⠀⢸⠜⠀⠀⢀⠇⠀⠀⠀⢀⠇⠀⣀⣠⡇⠀⠀⠀⡇⢱⠀⠀⡿⡆⠀⠀⠈⠙
⡘⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⡏⣇⢁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢸⠀⠀⠀⠀⢸⠒⠉⠀⣩⡇⠀⠀⣸⣉⣙⠀⠀⡇⢷⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡇⠸⡈⠀⠀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠇⠀⠀⠀⢠⠇⣠⣾⣿⣿⠀⠀⢠⣿⣿⣿⡇⠀⣏⣻⡆⠀⠀⠀
⣇⡀⢰⠀⢱⠀⠀⠀⡇⠀⠀⠀⡇⠀⠹⡀⠀⢀⣳⠀⢰⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡴⢀⢊⢞⣽⠿⣻⣿⡞⠓⠊⠉⠉⢹⡇⠀⣿⣿⣧⠀⠀⠀
⡇⠈⠙⠐⠃⠀⠀⠀⣇⡀⢰⢆⡇⠤⢐⣙⢵⣿⣯⣷⣼⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠞⢡⣾⣿⣿⣿⣿⣦⡀⠀⠸⠒⢴⢿⣿⣿⠀⠀⠀
⢣⠀⠀⠀⠀⠀⠀⠀⣿⣇⡾⣄⣿⡾⣿⡿⣿⡿⠿⠿⠿⣶⣿⣅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⢿⠟⢻⣿⣿⡀⠀⠀⠀⢸⣿⣿⡆⠀⠀
⠀⡉⠅⠀⠀⠀⠀⠀⣿⡝⢉⣿⣵⣿⠕⠉⠀⣠⣶⣿⣿⣷⣶⣌⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⢻⡇⠀⠀
⠀⡏⢑⡄⠀⠀⠀⠀⢏⣼⣷⢿⡿⠋⠀⠀⢰⣿⡿⢿⣿⠟⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣦⣠⢚⠛⣿⠁⠀⠀⠀⣼⡏⢸⠁⠀⠀
⠀⠀⠘⡇⠀⠀⠀⠀⢹⡿⡯⡟⠀⠀⠀⠀⣿⣿⡇⠀⠈⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣤⡶⠞⠁⠀⠀⠀⠀⠑⠀⡞⠀⢀⡇
⡆⢇⢸⡑⠀⠀⠀⠀⠈⢷⣟⣧⠀⠀⠀⠀⠛⣿⣿⣦⣄⡀⣼⣿⣿⠃⠀⠀⠀⠀⢀⠀⠀⠤⣤⠀⠠⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⣾⡇
⢇⠐⠊⢇⢤⠀⠀⠘⠀⠘⣿⢿⣦⡀⠀⠀⠀⠪⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠐⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠐⠊⠉⠐⠀⠀⠀⠀⢀⢔⣁⠔⣿⣿⡇
⠀⡸⡀⢅⠎⠀⠀⠀⣇⠀⠸⡣⡫⣷⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠄⡀⠀⠀⠀⠠⠀⠀⠄⡀⠀⠀⠁⠐⡈⠄⠀⢀⢠⠀⠀⠃⠀⠀⠈⠉⡁⠀⠀⣿⣿⡟
⢀⡇⠁⡅⠀⠀⠀⠀⣿⣆⠀⠐⣮⠈⠛⠆⠀⠀⠀⠀⡀⡔⡤⠃⠉⠈⠐⠀⠀⡁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠐⠘⠈⠀⠂⠀⠀⠀⠄⠀⠠⠐⠀⠀⣻⣿⠀
⡜⠀⢠⡇⠀⠀⠀⢰⣿⣿⣧⡀⠈⢆⠄⠁⢀⠀⠀⢀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⢀⡤⠒⠊⣉⣉⢈⣉⡈⠋⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀
⠤⠤⠊⡇⠀⠀⠀⢸⣻⣾⣧⢹⣶⡀⣀⠔⠀⢂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢹⡵⢖⣶⣿⣿⣿⢸⣿⣷⣼⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡿⠀⠀
⠀⠀⠀⡇⠀⠀⠀⣸⢻⡺⣿⢎⠹⡟⢥⡳⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⢹⢏⢃⠃⠛⠙⠛⠸⠛⠛⠋⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀
⠀⠀⢰⠁⠀⠀⠀⡿⡆⢻⡿⠀⠀⡹⡊⠙⠺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⢸⣋⣀⡀⠀⠀⢀⢀⣠⣀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢀⡾
⠀⢀⡏⠀⠀⠀⢰⠃⠙⢦⡱⡀⠀⠀⢿⣄⠀⠀⠉⠑⠀⠀⢀⢀⠀⠀⠀⠀⡇⣴⠈⠁⠈⠉⠉⠈⠉⠀⠉⢹⡆⠀⢸⠀⠀⢀⠀⠃⠀⠀⣠⢿⠏⠀⢀⣾⠁
⣠⠾⠊⡆⠀⠀⢸⠀⠀⠀⠈⢱⠸⠈⠹⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡇⢀⠚⠀⠀⠀⠉⠀⡠⠞⢁⡟⠀⠀⠊⡆⠀
⠀⠀⠀⡇⠀⠀⣸⠀⠀⠀⠀⠀⢣⠀⠀⡇⠈⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠓⠆⠀⠀⠀⢀⡴⠋⠀⠀⣸⠃⠀⡼⢠⡇⠀
⠀⠀⠀⢇⠀⠀⡇⠀⠀⠀⠀⠀⠈⡆⠀⡇⠀⠈⢗⡝⢿⣶⣤⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠀⢰⠇⢸⡇⢠
⠀⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⢹⢠⠃⠀⠀⠈⢎⢠⠙⠯⡛⠂⠀⢤⣤⡀⣸⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠆⢠⡖⠁⠀⠀⠀⠀⠀⠰⣿⠀⣾⠀⢸⡇⠈
⠀⠀⠀⠀⢧⠀⢻⠀⠀⠢⡀⠀⠀⢸⡸⠀⠀⠀⠀⠀⢣⠳⡀⠀⠘⠤⠶⠤⠆⠟⣇⠀⠀⠀⠀⢀⣴⣋⢀⠈⠀⡏⠀⠀⠀⠀⠀⠀⠀⡰⢻⠀⠻⠀⠀⠘⢄