⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠐⣀⠂⠄⠒⡄⢂⠄⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢁⠠⠈⢄⠱⡈⢆⡘⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠉⢄⢢⡙⢤⠚⡴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠄⡀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠈⢄⠣⢜⢢⡙⡔⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⢃⡟⡡⠔⠚⡑⠒⠤⠀⣪⠇⡬⠔⡂⠢⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠈⠤⢉⠌⠢⡐⡱⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⣿⣚⠌⠀⣴⢮⢿⣿⣿⣿⣿⣦⡀⠑⢠⣲⢭⣗⣧⣦⡀⠀⠀⠁⠠⠀⠀⠀⡀⠀⠈⡐⠌⠠⢁⠐⣑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡺⢧⣅⠀⢞⡹⣷⡽⠿⠿⠿⠿⠿⠷⠀⠀⠫⢎⡻⡽⠽⠝⢢⠈⠐⠠⠀⠀⠀⢀⠀⡁⠐⡈⠐⡀⠂⢌⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⢀⡙⠇⢐⡘⣋⠃⠁⠔⠂⠙⣉⡩⣩⣍⠂⠀⠈⡀⠒⠒⢛⠒⣂⠀⠠⠀⠐⠀⠁⠀⡀⠄⠡⠀⠁⠠⠁⢢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢦⠭⣄⡘⠠⠀⠀⠀⠐⠚⠸⠄⢀⡈⢠⣿⠟⠀⢀⠀⠁⢆⢀⡠⢠⣿⠁⡀⠀⠡⠀⠈⢀⠀⠄⠡⠈⢀⠁⠀⢢⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢣⢟⡾⣵⣧⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣴⠀⠀⠀⠀⠉⠁⢠⠘⡠⠀⡁⢂⠀⠠⠈⠄⠁⡀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢎⠺⣹⡝⠯⠛⠛⢳⠒⠀⣀⠀⡀⢀⣀⢤⣃⢀⣻⡿⣧⡀⢢⣀⠀⠐⢢⠑⠠⢀⠀⠂⠈⠀⠐⠈⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠰⡈⠂⠅⠈⠀⡁⠼⠔⣛⢻⢾⡿⣽⣿⣿⣿⣿⣷⣻⣽⣹⣟⡷⣾⠽⡆⠁⠊⠁⠠⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠡⠐⠀⠀⠀⠄⠁⠀⠀⠀⠌⠁⠙⡙⢋⠯⠻⠝⡛⣾⣷⢾⣗⡟⣋⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠄⠂⡐⢀⠈⠄⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠈⢀⠂⡐⠠⠊⠤⡁⠌⡀⠁⠀⠀⠀⠀⠀⠒⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⠀⠂⢀⠀⢁⠢⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠤⡀⠄⣐⡀⠀⠀⠀⠀⠄⠐⠀⠁⢈⠞⡴⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠨⣎⡛⢺⠿⣳⠴⣖⢤⠒⣤⣴⣷⣿⣧⣤⡀⢂⠈⠤⢄⠀⠂⠀⠄⠂⠀⠄⢀⠀⠀⠀⠠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣒⢲⣬⡉⠀⣿⠻⣾⡅⣾⣿⣿⣶⡽⣫⣿⡇⠀⢂⠈⢡⠉⡐⢈⠠⠀⠡⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠛⠐⠁⣈⣮⣿⣷⠖⢹⢾⡿⠿⡗⣿⣿⡇⠀⠀⠄⠀⠒⢈⠐⢄⠈⡐⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⣀⡄⠀⢀⣿⣿⡿⠛⠈⠀⠁⢀⢠⣆⢀⠀⠀⠀⢈⠀⠈⡀⠈⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣧⠳⢠⣲⣴⣵⣯⡿⣴⣿⡆⠈⠳⣾⣿⣷⣄⠀⠀⢆⠀⢈⠰⠀⠐⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⢀⣿⣿⣿⣿⣿⣷⡿⡿⣧⠃⠈⡌⣻⣿⣿⡇⠀⠐⢂⠠⠘⡀⠀⠀⠁⠈⠦⠄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣾⣿⣿⣿⣿⡟⣼⢿⣥⣽⣾⣤⠘⣤⢻⣿⣿⡀⠀⠡⡙⠴⡀⠀⠀⠀⠈⢀⡙⠀⢀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠻⣿⡻⠏⡄⣿⣾⣿⣿⣿⡟⣇⠘⣧⡘⣿⣇⠀⠀⡘⠰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢾⣇⣿⣇⡿⠻⣿⣷⣿⠀⠻⠓⠈⠛⠀⠀⢀⠃⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⣿⣿⣮⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁