⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣲⣞⣗⡦⡐⠀⠄⠄⠠⠀⠄⠠⠀⠠⠀⡀⠀⠄⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢯⡯⣷⣳⣳⢕⣟⢮⢦⡈⠐⡀⢁⠀⠂⢀⠁⢀⠠⠐⠀⡁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⢞⣯⢿⣽⣳⣳⢽⢽⡺⡵⡳⣍⢇⢄⠠⠐⠈⠀⢀⠠⠀⡀⠂⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⡷⣯⢿⢽⡽⣞⣞⢾⣝⣗⢯⢯⢯⢮⣣⢣⠢⡂⠈⠠⠀⠄⠠⠐⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣺⢽⣳⣻⢽⡽⣳⣝⣗⢗⣗⢯⢯⢯⣻⣺⢽⣣⣎⠢⡁⡀⠁⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⢽⡺⡯⣗⡯⣟⢾⢕⡧⣳⣝⢮⡳⡽⡵⣳⢯⢯⣗⣟⡿⣶⣬⣂⠄⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡮⡿⢽⡻⣺⢮⣭⣫⢱⡹⣱⡱⡝⡎⡧⡫⡺⡽⣽⣺⡽⣯⡷⣟⣾⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢷⢽⣳⢎⢞⠷⣕⣗⢝⣝⣜⣎⠗⡝⠎⠞⡝⣞⢵⣳⣟⣯⣿⣻⣽⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⢽⣻⡺⡯⠪⣛⡖⣗⢽⢼⢔⡴⣝⢮⣫⢳⢬⠪⣟⡾⣞⣷⢿⡽⣯⣯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠪⠣⠑⠱⢹⢢⢣⢝⢼⢹⠍⡜⡎⡗⡕⢕⢝⢜⢅⢯⣗⢝⣾⣟⣿⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡣⠁⠠⢐⠈⠊⢪⢹⡸⡸⡱⡱⠑⠑⠈⠈⠊⡎⡲⡹⣗⡷⡽⣷⣻⣇⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡪⣒⣄⡈⢀⡠⡠⣄⣗⡵⡨⢢⠀⠐⠈⠄⠈⠀⡀⠕⡍⣿⢽⡮⣟⣷⣫⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡺⣝⣗⡯⣗⢾⢽⣝⣗⣯⢳⢱⢱⢱⣑⠔⡄⡠⡡⡰⡱⡘⣞⣯⣗⣿⣓⡷⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡧⡳⣝⢵⢫⣳⣳⢷⢽⢸⢘⢜⠜⡎⡯⣲⠵⡵⡱⡵⡹⡸⣳⢿⢾⣹⢽⣳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡹⢨⢊⢊⢞⣗⣯⣳⡱⡱⡑⡅⡣⡫⡪⡪⡪⣪⡳⣝⢽⡽⣝⢷⢽⢝⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣊⠢⠁⢈⠐⣫⠚⡼⠪⡨⠢⠱⠰⠨⠪⡘⡔⡼⡺⣜⣯⢿⣸⡳⣝⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⡃⡀⠐⠀⠄⠁⠁⡀⠀⠄⠂⠀⡁⠈⠨⡪⣺⢘⢾⢝⡷⣕⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡎⡀⠀⠅⡠⢀⠁⠀⠀⡀⠐⠀⠀⠈⢐⢕⡏⡪⣺⢽⣏⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡗⡄⠐⡀⠂⠁⠀⠂⠀⡀⠀⠄⠀⠁⡐⢵⢑⢕⢽⣽⣣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⢞⡲⡀⠄⠐⠠⠐⠀⠁⠀⠀⠄⠈⠠⡪⢇⢣⢣⢓⣟⣞⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⢽⣲⣄⢁⠠⠀⠄⠂⠈⢀⢰⠰⡑⣝⢜⢜⢬⡻⣪⢾⢽⣯⣟⣷⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢯⣞⢾⢵⡳⣖⢖⡔⡎⡪⡢⡫⡪⡺⠪⡊⡎⡎⡮⣻⢵⣻⣺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⢀⡠⢧⢳⣫⡳⣝⢮⡳⡹⡜⣜⢜⠼⡊⠪⢑⡑⢬⢲⢹⡪⡫⡞⣞⡝⡖⠠⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⢇⠣⡵⣕⡝⠪⡎⡎⡞⡪⢣⠫⡣⠫⡪⠨⡂⡪⢊⠕⡘⢌⠪⢪⢪⠣⠣⠑⠀⢠⢐⢮⢚⣖⢷⣹⢝⢦⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⢝⡎⡇⢕⢕⢧⡣⡞⣄⠈⠣⢣⢊⢆⠑⠄⢅⢂⠁⡊⠌⠢⡑⠌⢄⠑⠀⠄⠀⡀⡄⢎⢝⢗⢗⢕⢗⢯⡻⣝⢷⢽⡻⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠄⠹⡸⣪⡳⡕⡕⣕⣝⢵⢕⢝⡬⣒⡢⣄⡀⡀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⢀⡀⢄⠔⡜⡌⢎⢪⢪⡪⡪⡪⡪⡣⡫⡪⠺⠘⠘⠜⠠⠀⠀⠀⠀⠀
⢠⢄⡖⡖⡆⡄⠀⠄⠈⠸⢪⢗⣕⢵⢵⢝⡮⣳⢝⢴⢝⡮⣪⢪⠪⡪⡘⢄⠲⡐⡢⡂⢎⠸⡘⠜⡌⡪⡸⡘⡌⡎⡎⡎⡎⡎⡎⡎⠊⠀⠠⠀⠂⠁⠀⡀⠀⠀⠀⠀
⣹⢱⢝⢎⢇⢗⢤⠀⠠⠀⢀⠙⡮⣺⡹⣕⢯⡪⣗⢽⢕⣯⡺⡕⡝⡐⢅⢪⠪⡪⢨⢐⢥⡣⡫⡘⡌⡆⡕⡜⡸⡸⠘⠊⠊⠊⠈⠀⠀⠠⠀⠠⠀⠄⠁⡀⠁⠁⠁⢐
⢪⡪⡎⡗⡕⡝⣜⢕⢆⢀⠀⠀⠈⢖⢽⡪⣣⢯⢪⢓⢝⠰⡑⡜⢌⡪⡜⡎⡪⠢⡑⡴⡳⡱⡘⡔⡕⡜⡬⠊⠀⡀⠀⠂⠀⠠⠐⠀⠐⠀⠠⠀⠠⠐⠀⡠⣔⢮⣫⣳
⢰⢱⢱⢹⡸⡸⡸⡜⡎⡖⣄⠐⠀⠀⠙⠪⢺⢸⢘⢌⢆⡣⡕⡼⡕⣝⢎⢎⢎⢪⣪⢳⠱⡘⡬⣪⠞⠉⠀⠀⡀⠀⠀⡀⠄⠀⠀⡀⠠⠀⠠⠀⢀⡴⡺⡩⡮⣺⡪⡞