⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠠⡀⠄⡀⡀⠠⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⢌⠢⠡⡑⠄⠅⡂⠄⡁⢂⠐⠐⡈⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠢⡁⡪⡪⠨⠊⠄⠅⠅⡂⠅⡂⠔⡈⠄⠐⡈⠠⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⢐⠠⠡⠊⠂⠠⠨⠨⠑⡅⡑⡌⡐⠄⠅⡂⠌⡐⡀⡂⠌⠈⠄⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⡁⢂⠨⠀⠄⢁⠨⠐⠁⠌⡂⡳⣜⠐⠅⢕⠨⢐⢐⢐⠨⠠⠁⠌⠠⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⠄⢂⠐⠀⡀⠄⠐⠀⢂⠠⠁⢌⠐⢌⠢⠡⡃⢕⠌⡂⡂⡢⠡⡡⠡⠡⠨⠈⠔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⠡⠀⠄⠠⡰⠀⠨⠐⡀⡂⠁⠔⢈⠐⠌⠌⢌⠪⡸⡐⡐⢌⠌⡢⠡⡁⡊⠌⠢⡈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⢈⠐⣠⡂⡜⢀⠄⣱⠅⡜⠀⡁⠌⠠⠨⠨⠨⢐⢑⢈⢂⢪⢸⠐⢌⢂⢂⠢⠡⢑⢐⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠁⠐⡈⢀⠖⠷⠹⠇⠂⣐⡯⢰⡇⠀⠄⠂⡁⠌⠨⢈⠄⢂⠂⠅⢢⠃⢅⠕⡐⠄⠅⡊⢐⠐⠌⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠐⢀⣿⢠⣦⠇⠀⠀⠙⠇⡼⡇⡌⠀⢂⠠⠈⠨⠐⢀⠢⠨⠈⠄⢅⢑⠨⠠⠡⢁⠂⡂⠡⠁⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠈⠠⣹⡾⣾⠙⠀⠀⠀⡀⢀⣼⣇⠇⢨⠀⡐⢈⠀⠁⢀⠂⠅⡁⡑⡐⡐⠨⠠⠁⡂⢂⠂⡈⢈⡂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠐⢠⢡⣗⣿⣻⣦⣌⠠⢶⣴⣿⣿⣾⣦⡢⡂⠄⠂⡈⢀⠐⢈⠐⢀⠐⡀⠂⠡⡈⠠⠐⡀⡐⠀⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⢽⢾⡾⣽⣯⣿⣿⣿⡿⣿⣷⢿⣻⡇⠐⡀⠅⠌⠀⠄⠂⠌⢀⠂⠄⠁⠅⡀⠂⡁⢀⠠⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠸⢸⣿⣻⣟⣾⣷⡿⣷⣿⣿⣻⣿⣿⡇⠐⢀⢂⠐⠠⠈⠄⠂⠐⡈⠠⠈⠀⠂⠐⠀⠄⠠⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⢸⣿⣽⣿⣽⣾⣿⣿⣻⣾⡿⣿⣾⢿⠀⢄⡇⠨⠀⠅⠂⠀⠠⠐⢀⠁⠌⠠⠈⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⡀⠀⠐⣈⡀⠂⠀⠠⠀⠀⢻⣽⣷⣿⣟⣷⣿⣯⣷⣿⣿⣻⣿⡂⣴⢅⢑⠈⢀⠁⠠⠀⠈⠀⠀⡀⠂⠁⠂⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠄⠀⠀⠱⠵⡃⢱⡄⠐⠀⢡⢘⢿⣿⣽⣿⣽⣷⣻⢿⣽⣯⣿⢷⡷⣯⢃⢪⠀⠀⠀⠀⠌⠀⠀⠄⠀⢈⠠⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⢁⠈⠠⠐⠀⠸⠈⠀⡥⡵⣕⢰⡻⣽⣾⣿⣯⣿⡿⣿⣽⣾⣟⣯⡷⡅⡳⠀⠁⡀⠁⠀⠠⠐⠀⡈⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠠⠈⡐⠠⢂⠡⠈⠀⠠⢀⣗⣿⣽⣿⡪⡯⡯⣛⢿⠾⣟⡿⣯⢿⢾⠽⠚⢁⠁⠢⠀⠂⠠⠀⠅⡈⠠⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢢⠊⢌⢐⠈⡐⠀⠂⣸⣾⣿⣿⣿⣺⣿⣽⣽⣳⢯⢷⢝⡮⡣⠃⠄⠠⠀⠀⡀⠂⡁⢂⠁⠄⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠢⣓⡥⡕⡀⡢⡸⠀⢡⣿⣿⣿⣿⣻⣗⣿⣿⣽⣿⣯⢿⡹⡮⡏⡡⠈⠀⠀⢁⢀⠂⠄⠀⠄⠀⠄⡀⡀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⢐⠨⢈⠢⢑⢐⢑⠪⡠⠈⢸⣿⣿⢿⠛⢻⢛⣻⣫⣯⣾⣿⣯⠿⢝⣪⢅⠄⠠⠁⠀⠀⢀⠀⡐⠀⠅⢂⠠⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠠⢐⠈⠄⢁⢐⠐⡈⠄⢂⢂⢂⢂⠁⡀⠂⠈⡯⠷⣉⢁⠀⠉⠻⠟⢿⣿⣿⠶⠿⣋⢉⠠⠔⣖⣯⢶⣌⠀⠂⠄⠅⠨?