⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢄⢖⡲⡪⣳⢤⢤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡎⡮⡺⡸⡑⡕⡱⡑⡝⣝⢵⢳⣣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢕⡧⢗⢝⠜⡌⡎⡪⡸⡨⡒⡜⣎⢆⠳⣝⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣺⢮⡯⣟⣮⣞⢗⢝⠜⡜⡌⢎⢪⢸⡸⡜⢜⢌⢎⡞⡜⢌⢢⢫⣖⣆⣆⣆⡦⣠⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡢⡍⣊⠪⡩⣎⢗⣵⢳⢩⡢⡣⢑⢌⢮⢮⡣⡻⡘⢌⢆⢗⢯⡪⡸⣸⢕⢧⣳⢟⣮⣟⣗⡷⡯⣯⡗⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣕⢵⢌⠎⣞⢮⢳⠫⣪⡺⡨⡢⣕⢝⡕⠃⠀⢌⢢⢱⡹⠊⠀⠵⣝⢼⣱⣫⢺⡯⡖⡔⡡⣑⢭⡲⣕⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⣕⡑⢌⢢⡫⣗⡿⡽⡱⡱⡱⢕⣁⠄⠀⠀⡇⡎⡎⢂⠨⠐⠀⢳⢕⢎⣞⡷⣽⡺⡨⠢⡩⣇⢟⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⡽⠽⡽⢯⢟⣜⢕⣕⡇⡏⢵⠯⡯⠀⢨⠪⠊⠀⢒⡾⡶⣮⠐⣝⢮⡪⣫⢝⣮⣨⣩⢩⢪⡣⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡪⡕⡬⡪⣞⡷⣻⣝⣇⠣⠘⢘⠁⠀⠂⠀⠠⠐⠸⡪⡫⢺⢱⢸⢵⣻⢮⢖⡯⢚⢓⠽⣕⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡜⢞⢞⣗⠽⣳⡕⣟⠠⠐⡀⠄⠀⠐⠀⠄⠠⠠⠈⢄⢈⢆⢯⣫⣗⢗⡵⠣⡱⣑⢽⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣣⢺⡜⠃⠈⢻⢼⢆⠐⢀⠠⢀⢁⠐⡠⠂⠨⢈⠐⡺⣕⡯⣗⠗⣝⠻⠷⡾⣞⠇⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⠀⠀⠘⠌⡇⠑⠠⢂⠐⡀⢂⠐⡈⡈⠄⢊⠽⠀⠉⠀⠈⣪⣌⢎⢞⠜⠀⠀⠀⢐⠀⠅⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠈⠉⢀⢀⢇⠢⡢⡒⡌⠀⠀⠊⠀⠀⠀⠀⠀⠂⣯⠂⠀⠐⠄⠁⠐⢆⢀⠆⢈⠠⠉⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⡠⣄⢖⢽⠃⠀⠃⠊⠢⠙⣗⣄⣀⣀⠀⡀⠀⠠⠐⠊⠀⠀⠀⠀⠁⠂⠀⡈⠒⠕⠊⢜⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢀⠐⢰⢱⢕⡗⣝⢼⠀⠀⠂⠁⡀⣜⢮⣺⢵⠁⠐⢀⠁⡂⠄⠀⠀⠀⠀⠀⣸⣆⠁⡀⠐⠀⠂⣴⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⡪⡪⡣⣏⢮⡪⡳⣈⢀⡢⣪⡺⣪⢾⢽⠀⠀⠠⠀⠐⠈⠄⠀⠀⠀⠀⠐⡻⡖⡢⡃⡅⡎⡟⣕⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣌⢄⠈⠀⠈⢀⡇⡎⡧⡳⡵⣽⣟⢯⢳⡿⣜⢮⣓⡯⣯⠀⠀⠄⠀⠁⡌⠬⡂⠀⠀⠀⠀⢱⢱⢳⡸⡸⡸⡘⢬⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣗⢽⡺⣳⢕⡀⠡⢸⡪⣺⡸⣹⡹⡜⡆⣏⢧⡫⣝⡳⣵⣫⣞⠆⡀⠄⠂⠑⡍⠅⡁⢂⠀⠀⠀⠨⡮⡣⡳⣝⡼⡜⣎⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⢴⢕⡧⣗⢯⣫⢞⣝⡆⣡⢳⡱⡵⡵⣕⣽⢪⡪⢢⠣⡣⣇⡧⣳⣕⣗⣯⢪⢰⡀⠡⠀⢂⠐⣀⢯⣄⡀⢨⢯⡪⡳⣕⢗⢽⡣⠀⠀⠀⠀⠀⠀⠀