⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀恰武士绝活哥出没⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣦⣴⣦⡤⢤⡪⣄⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣞⣿⣫⡧⣖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢷⣿⣟⢿⣾⣿⣿⣿⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⠋⣦⣿⢿⣿⣧⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠸⠃⠁⢽⡿⠈⠻⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣯⢿⠇⠀⠀⠀⠊⠀⠀⠠⠌⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⢾ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡾⣯⠌⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⢔⡥⠴⡶⡤⡤⠠⠔⡀⠃⠈⠁⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠑⠠⠧⠈⢓⡠⠉⠑⠁⡠⠀⠀⣦⣀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠁⠠⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣿⡹⣬⣯⣿⣿⣿⣿⣿⣿⡛⢍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠔⢀⣠⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠀⠀⠀⠠⡈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠫⡙⣿⣿⣿⣿⣿⣿⣿⣿⡹⠼⠱⠀⠀⠀⠀⠀⠀⠰⠖⠒⠶⣶⢦⡤⢟⣿⣄⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⣿⣿⡿⠞⢔⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⠩⡿⣯⡿⣿⣿⣿⣿⣿⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢬⠽⠃⠸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢈⡐⠒⠂⣿⣿⣇⣌⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠻⡟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠤⣀⣀⡀⠀⠀⠀⠀⠀⣀⢦⣣⡙⡇⠀⠀⠀⠀⣀⠄⠊⠀⡴⠋⣠⠔⠒⠿⢿⡥⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠛⠫⡟⢿⣿⣿⣷⣿⣷⣌⢎⣙⣛⣟⣻⣿⠟⠇⢻⣽⣷⣵⠀⢠⠄⠒⠀⠀⠀⠒⠃⠪⢇⡫⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡿⢟⣿⣿⣿⣿⡯⠝⠚⠻⠿⠃⠚⠋⢀⣤⣿⢟⠊⠐⠁⣀⣠⠤⠒⡀⠀⠀⢠⡀⠀⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠙⠿⣿⣅⠀⠙⠿⣿⣿⣾⣦⣤⠀⢀⣀⣴⡿⡟⠓⠁⡰⣴⠴⣛⡡⢒⠢⠈⠂⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠘⣿⣧⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣫⣼⣿⠀⠀⠀⠂⡈⠩⠒⠊⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⡀⢠⠤⠀⢘⠿⣿⣶⣾⣿⣻⣿⠕⣊⣹⣿⣿⣿⡿⠇⠀⣶⡆⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣆⠑⠀⠌⠣⣿⣿⠿⠿⣿⣹⣿⣿⣿⣿⣿⣿⡇⠀⢰⣿⠁⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣿⣿⣮⡠⠚⠓⢤⠙⠆⠀⢹⢿⣿⣿⣿⣿⣿⠓⢐⣾⣿⣾⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⠀⠀⠀⣹⣿⠋⡑⢀⠀⠀⠀⢸⣷⣍⣿⣿⣿⣿⣻⡿⠀⢸⠿⢃⣴⡿⠚⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣾⣴⠭⣼⡉⢯⣳⣦⡀⣤⢆⢖⣴⣶⣿⣗⣿⣿⣿⣿⣶⣇⣲⣴⣿⣿⣍⠣⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠑⠐⣿⣷⣿⣿⣿⣷⢶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⠿⢿⣛⠛⠤⢤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⢿⣿⣴⣶⣿⣿⣿⣿⡿⣷⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣤⣶⣶⣶⣎⣹⡅⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣿⢿⣿⣿⣷⣶⣟⠝⡨⣿⣿⣽⣿⣭⣤⣽⣿⣿⣿⣶⣿⣿⣿⡿⣯⠏⠀⣠⣶⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⡝⢷⣿⣿⣻⣿⡍⢀⣾⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢣⣤⣾⣿⢿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠓⠒⠛⠛⠛⠋⠀⢾⣿⣿⣿⣿⣷⢿⣿⡿⠿⣿⣛⣻⣟⣵⣴⣞⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀