⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠀⢀⢐⠌⠀⠠⢀⢔⠔⠙⠑⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⢨⢁⠑⠢⣂⡀⡀⠠⢀⠀⠄⠨⠊⡘⡀⠆⡁⢂⢈⢔⠡⠂⠀⠀⠊⢎⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢕⠅⡁⡀⢀⠀⢊⠪⡢⡀⡂⠈⠄⢑⠰⠀⠡⡀⠅⡈⠄⡁⠢⢄⠢⡑⢔⠕⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢕⠱⡑⡐⡁⡢⠂⠕⠁⢂⠠⠁⡐⠠⠈⠠⠑⠘⢑⠱⠢⡄⢂⠠⠑⢌⠪⡪⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡢⡣⡢⡊⡐⠄⠁⠂⡁⠄⢐⠠⠐⡀⢁⠂⢁⠈⠄⡐⠠⠈⠒⡢⡐⡀⠣⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢨⠢⣒⢜⢐⢡⠡⢀⠂⠄⢐⠬⠀⠄⠂⡐⡀⠂⢒⢄⢁⠢⡨⢪⢩⢍⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⡑⡕⡼⡸⡨⡢⡱⡐⢌⠔⡌⠜⡄⠅⡂⠄⡆⡑⢌⢳⢐⠕⡜⡌⡎⡎⡢⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢕⠕⢜⢔⢇⢎⢼⢘⢔⢱⢡⣝⣠⡑⡕⡱⡘⡜⢕⣜⠼⠐⣧⠧⠫⣣⢣⡣⢣⠣⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢅⢇⢣⢣⢣⡣⡣⡣⠕⠁⠁⠀⡾⣵⠉⠊⢎⢊⠎⠀⠀⠀⣿⢽⡄⠀⠑⡕⡱⡹⡨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⢌⠆⡇⡇⡣⡪⠢⡇⠀⠀⠀⠀⢟⣗⡇⠀⠈⡺⠀⠀⠀⠀⢺⣻⠆⠀⠀⡇⡕⢼⢸⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠌⢆⢇⢣⢣⢱⢨⢃⢇⠀⠀⠀⠀⠩⡷⡁⠀⡰⠁⠑⣀⠀⠀⠀⠫⠀⣠⢊⢎⢜⢸⠜⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢎⢾⡱⡘⡔⡅⡗⡑⠑⠤⠤⠤⠤⠒⠈⠀⢀⠄⠀⠉⡌⠊⠈⢁⢮⡊⡆⡕⡱⡑⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠍⡳⣣⠕⡜⢔⡯⢦⠡⠀⢀⠀⠀⠣⠤⠜⠈⠈⠒⠁⡀⠄⣢⡳⡳⡕⢜⢌⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠎⢣⢪⠳⡹⣝⠝⢵⣢⢤⣈⣀⢀⡀⡠⣐⡠⡴⣪⢞⠂⢝⢮⠃⠈⠢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠀⠙⠜⠀⠀⢈⠣⢃⢑⠡⢊⠔⠡⠉⠺⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢄⠀⠀⠀⠀⠀⠀⠀⠠⢂⢊⠆⡂⠅⠀⠄⠀⠀⠡⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢎⢪⠀⠀⠀⠀⠀⠀⡐⡡⠁⢎⠔⠀⠀⠀⠀⠀⠠⠀⢃⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠢⡃⡀⠀⢀⢠⠈⠀⠀⢀⡃⡂⠀⠀⢀⠀⠁⡀⠀⢘⢐⠔⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⢱⠰⠐⠈⠀⡉⠒⣄⠪⠐⠄⠀⠈⠀⠀⠠⠂⠀⠀⢕⠌⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡡⠀⡀⠄⠀⠠⠀⢪⣌⢌⠀⠀⡀⠀⠄⠕⠀⢀⣠⢕⠈⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡔⠠⠀⠀⠐⠀⡀⣺⣽⣗⣟⣶⣲⣞⣮⢮⡫⣗⡯⡺⡌⡀⠂⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠄⠅⢢⢮⢷⣗⣷⣻⣺⢞⢮⣞⢗⣝⢮⡫⣝⢮⠂⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣾⣗⣯⢾⡹⣕⢗⢗⣕⣧⡿⠼⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⢽⡻⠁⠈⠀⢀⣿⣻⣳⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⢾⣻⣏⠀⠀⠀⣸⢾⣽⣽⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣟⣿⣳⡇⠀⠀⠀⢺⣻⣗⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣞⡷⣯⠇⠀⠀⠀⣿⣗⣿⣺⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢷⢽⢝⣯⠀⠀⠀⠀⠿⣞⡷⡯⣗⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣽⡯⠟⠀⠀⠀⠀⠀⠈⠙⠛⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀