⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡐⡈⢦⠙⡆⠹⣡⠙⢴⢈⢺⣈⠸⣡⠘⢡⠘⠁⡁⠆⠡⠄⢁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⢱⠹⡌⢆⡌⢷⣈⠻⣠⠛⡤⠉⠴⠈⢔⠀⢰⠀⢠⠌⢡⠐⠈⠄⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠂⢦⠸⣆⠚⡤⠩⡆⡑⢇⡀⢇⡄⠋⡄⠈⡀⠘⠡⠘⢈⠐⠈⡄⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢧⠙⣆⠑⠣⠘⠲⣀⠠⠀⠐⠁⠀⠀⠀⠒⢀⠐⠈⠤⠁⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠹⠈⢣⣨⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣲⣲⢡⢠⢊⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣾⣺⣽⢽⢕⣗⣵⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠓⠿⠾⠿⣯⣽⣞⡽⠟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⣴⣶⠀⢀⠀⠀⠂⣺⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠀⠈⠀⠐⠂⠀⠀⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢀⣀⣀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⢀⣤⣶⣶⣾⣿⣿⣿⣿⠟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⣿⣿⣿⣿⣿⣿⣤⣄⣄⡀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⠇⢙⣿⣿⠀⠘⠿⣿⣹⣿⣿⠋⣿⣿⢿⡟⠁⠀⠈⠙⢿⣟⠙⣿⡿⠁⠉⠛⠀⠀⣟⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⡇⢿⣿⠏⠀⠀⠀⠙⠛⠛⠛⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠘⣅⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⡄⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⣿⠟⠂⠀⠀⠀⢶⣶⣶⣦⡤⠐⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣑⡁⠀⠀⣀⣠⣴⣿⣿⡧⢼⣿⣷⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡅⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠠⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠉⣹⠟⠿⠏⠂⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⡿⠿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⣶⣾⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣷⣦⣤⣤⣤⣤⣤⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠩⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⠀⠀⢀⠀⡀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠨⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⡴⠁⠀⠀⠀⢹⢀⡤⢀⢀⣿⣻⣷⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡠⡄⠒⣹⠄⡇⠀⠀⠠⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⠀⡐⠀⠀⠠⣯⢸⠀⠀⠠⠚⡛⠿⢿⣿⣿⣿⣿⣿⣿