⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⢜⢔⢔⢤⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢄⢄⢔⢔⢔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⡆⡆⡄⠀⠀⢕⠁⠑⠑⠑⢕⢕⢕⢲⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢆⢎⢎⠎⠎⠊⠊⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⢱⢱⢍⢇⠀⢱⠀⠀⡆⡦⡸⡂⠨⡪⡪⡢⡃⠀⠀⠀⠀⠀⢀⢔⢕⠕⠁⡗⡄⡔⡜⡍⡏⡇⡇⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⢸⢸⢸⢱⡘⡆⡌⡎⡎⡆⡄⡄⡇⡇⡇⣇⠀⠀⠀⠀⢠⢣⢣⢃⢀⢀⢇⢇⠧⠁⠁⡇⠃⡇⡇⡯⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⢸⢸⢸⢸⢸⢸⡘⠸⡸⡸⡸⠸⡸⡸⡸⡸⡒⡄⡀⠀⢰⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⢸⢌⠐⢱⠑⡕⡕⡕⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠸⡸⡸⡈⢎⢎⢎⢜⢜⢜⢤⢠⢀⢧⠱⡱⡱⠑⠁⢀⢇⢇⢃⢀⢕⢐⢕⢕⢕⢕⢕⢕⢕⢄⢇⢆⢇⢇⢇⢇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡪⡪⡂⢱⠱⡱⡱⡱⡱⡑⠕⡕⣗⢜⢜⢜⠀⢠⢣⢣⢣⠣⡣⢣⢣⢣⠃⣕⠁⠑⢱⢱⢱⢱⢱⢱⠱⡱⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢜⠆⡱⡱⡱⡱⣕⢲⢄⢮⢠⡣⣣⢲⢸⢜⢌⢮⡱⡀⡔⡕⡕⠀⡎⣀⡀⡕⣕⢕⢕⠨⡢⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢝⢆⢱⡁⡎⡮⡪⡪⣪⡪⣪⢪⢪⢎⢎⢎⡎⡎⢎⢎⡇⡇⡇⡗⣕⢕⢕⢁⠢⡣⡊⡇⡇⡎⠎⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢕⣕⡕⠰⣱⠙⡜⣜⢕⢱⢡⠊⢣⡫⡺⣸⢸⢸⡕⠸⡜⢪⢸⡸⣸⠸⢨⡢⠀⣀⢇⠆⢇⢇⢏⠆⡠⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡻⡮⡪⡎⡆⡰⢕⢵⡱⠱⣅⠨⠐⡇⡇⣟⢎⢮⢰⡙⣶⠑⣔⢕⣗⠄⠅⡂⠐⡕⡅⢣⢸⢱⢱⡳⡒⣎⡎⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠀⡝⡜⡼⠀⡗⢀⠑⣕⣝⠀⠔⡈⢰⢱⢕⢕⢕⢕⢂⢘⢆⠀⣺⢸⠺⣐⠈⠢⡂⠁⡣⠈⢮⠂⢱⢹⢪⢪⡃⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢝⡑⡉⢀⢗⠁⠀⣞⢪⡰⡁⡂⡨⡪⡃⢱⡃⠙⡆⢸⢲⠀⡘⡮⠅⡪⡀⠅⢂⠀⠀⡇⢧⠅⡣⡃⡃⠃⢑⠄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠀⡈⠐⢀⠁⡄⠇⡐⠌⢮⢪⠊⠢⠀⢧⢣⢳⢘⡆⢸⠀⠸⡸⠀⡀⢱⡁⡂⢐⠨⠐⡀⠄⢉⢜⠰⢘⠸⡠⠘⠈⡠⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡐⠀⢎⠀⠁⠀⠄⢰⠡⡣⠃⠈⠎⢜⠀⠌⠀⡝⠈⠥⠣⡫⠐⡌⠈⡯⠀⠂⢰⠁⢢⠐⠨⠀⡂⠱⡀⢧⠘⠀⠊⠂⠱⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡐⠀⡘⠂⠀⠄⡐⠁⡄⠰⡱⠀⠠⠁⢐⠠⠁⡰⠁⠀⡅⢘⠂⠀⠀⡠⡳⠀⢁⠨⡃⠀⠀⠨⠀⡂⢈⠆⢕⠆⡂⠀⠀⠀⢇⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡐⢀⠔⡉⠀⡘⠠⢀⠪⠤⢘⢜⠀⠊⢀⠂⠌⡐⠈⢲⠀⠅⠠⢱⠀⠈⠇⡳⢁⢐⠈⡜⠄⢠⠈⠄⢂⢐⠘⢎⢠⢁⠨⠡⢃⠐⡂⢱⠀⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡘⠠⠂⠀⠅⡐⢀⢁⠂⠀⢈⠐⠅⠨⢀⠅⢀⠡⠂⠀⠨⠠⠀⠈⢸⠀⡃⠁⢸⠨⠠⠀⠠⡃⢐⠅⠅⢐⢐⠀⢕⠨⠐⢨⠀⠀⠂⢉⠄⢇⠐⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡐⠠⠁⠀⠌⡠⠀⡌⠄⠀⢀⠁⡨⠀⠅⡐⠀⢐⠨⠀⠀⡂⠌⠀⠀⢉⠀⠇⡀⢸⠐⠄⠀⠀⢐⠐⡅⡁⠀⢆⠀⠑⡐⠀⢃⠄⠀⠘⠈⡈⠜⣂⠰⠀⠀⠀⠀⠀⠀
⠀⠀⠠⠡⠁⠀⡐⡐⠀⢠⠐⠀⠀⡌⠠⠀⢀⢁⠂⠀⡂⠅⠀⠠⢠⠁⠀⠀⠀⡀⡁⢀⠰⠀⠀⠀⠀⠀⢂⠕⠀⠀⠡⠂⠀⢇⠀⠈⠆⠀⠀⢁⠆⠈⠂⢂⠡⠀⠀⠀⠀⠀
⠀⠀⡇⠁⠀⡐⡐⠀⠀⠈⠁⠀⠠⠠⠁⠀⢐⠨⠀⠀⠈⠀⠀⠌⠄⠀⠀⠀⠀⡂⠄⠰⢘⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⢕⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠡⠡⠀⠀⠀⠀
⠀⠀⠀⠀⢌⠆⠀⠀⠀⠀⠀⠀⢢⠁⠀⠀⢐⡈⠀⠀⠀⠀⠠⡑⠀⠀⠀⠀⠀⢁⡃⠀⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠅⠀⠀⠀
⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠔⠄⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡵⣄⢤⢦⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣻⢸⢱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢯⣇⣇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢷⢯⣳⣿⣽⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄⢤⢠⠀⠀⠀⠀⠠⣯⣯⣻⣳⣳⣗⢷⡳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣽⢳⣓⣵⣽⣷⡅⠀⠀⠀⣰⣷⡻⣾⡻⢝⢞⢖⣕⣵⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣲⡺⡞⣝⠇⠀⠤⣾⣻⣟⢾⣷⣯⣣⣳⣷⢿⢟⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡎⡜⣕⢠⣸⣻⢹⣸⣜⣞⡾⣝⢿⢱⠹⡳⡣⡫⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⣜⢌⢪⣹⠜⡎⡢⡏⣟⢝⢿⣺⡱⣕⢕⢱⠸⡸⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢜⡎⣖⣟⡎⡪⣎⣗⣝⣕⡕⡽⣽⣗⢅⢇⢕⢌⣯⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠙⠹⢻⢪⢊⢿⣷⣫⡯⣿⢾⣽⡪⡢⣑⢧⣹⣷⢽⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢣⡫⠈⣻⣿⠏⠛⠛⢯⡪⡸⡸⠺⣯⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇⠀⢼⣯⠁⠀⠀⠐⡕⡕⡇⠀⢹⡺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⣯⠀⢺⡳⠀⠀⠀⠀⡣⣫⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢮⠀⢹⡹⠀⠀⠀⠀⢘⢮⠇⠀⠀⢘⢟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠀⠈⡮⠀⠀⠀⠀⠀⣝⡕⠀⠀⠀⢿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢮⡂⠀⠀⠀⢐⡕⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⠀⠀⡪⡢⠀⠀⠀⡞⠄⢀⣄⣄⣄⣬⣇⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢎⢎⣄⢔⢇⠧⡦⡴⣸⣵⣾⣾⣿⣿⡿⡿⡸⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠔⠜⠜⠘⠫⠋⡋⠑⢁⠈⡈⠊⡂⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⠾⢶⡤⠀⠀⠀⣰⣿⣧⠀⠀⠀⢽⡷⠀⠀⠀⠀⢸⣿⢟⠟⢟⠟⠆⠨⣿⣿⡆⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣨⠉⠀⠀⢠⣿⠙⣿⣇⠀⠀⢽⣟⠀⠀⠀⠀⢘⣿⣦⣴⣤⣴⠀⢘⣿⢿⣷⠠⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠉⠋⢻⣿⠄⢀⣿⣿⣴⣾⣿⣆⠀⢽⣯⠀⠀⠀⠀⢨⣿⠍⠈⠊⠈⠀⠨⣿⠅⣿⣿⡟⢜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⡾⠟⠁⡾⡟⠀⠂⠀⢻⣿⡄⢺⢿⢶⢶⢾⠦⠰⡿⡷⡷⡷⡷⡇⠨⡿⠅⠺⡿⡣⠸⡿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀