>>4296245baba
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐⢐⠌⢌⠪⢈⠪⠨⢂⠅⢕⠨⠨⢂⠅⢕⠨⡂⢅⠢⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⡀⡢⠨⢂⢊⢐⢐⠨⢐⢈⠂⢅⢑⠐⠌⠔⡨⠨⢂⠅⠕⡈⠢⠡⡑⢔⠡⡊⡊⢆⠢⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡨⢂⠢⡡⢂⠢⠡⠡⡂⠅⡂⡊⠔⡠⢑⢐⠔⢅⢣⢱⢰⡡⣂⢪⢐⢌⠌⠌⠔⡐⡡⢊⠜⡨⠪⡘⡌⢎⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠄⡕⡔⡕⡕⢕⢅⢊⠌⡂⡢⢑⢐⠌⢂⠂⡂⡢⢑⠅⡊⡘⢌⠪⡊⢇⠗⡕⡭⡣⡧⡱⡰⡡⣂⠪⡈⡢⠪⡘⢌⢆⢳⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⡲⡱⡱⢑⢑⠌⡒⢌⠢⠨⡂⡪⢐⠡⠨⡐⠨⢐⠨⢂⢂⠂⠌⠄⠅⠌⡂⢕⠡⡃⠏⡎⢯⣺⡪⡮⣪⣒⢔⠡⡊⡂⢇⠕⡍⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⡎⡗⡝⢌⠂⠅⠢⠨⡈⠢⠡⡑⡨⡐⠅⠕⡑⡨⠨⠂⠅⠅⢂⠨⠐⠈⠄⢅⢂⠢⣁⢢⢑⢌⢌⠢⠹⡸⡱⡣⡏⡎⡂⠪⢨⠪⡸⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢧⣫⢪⠪⡨⠂⢅⠡⢁⢂⠂⠅⡑⡐⢔⠨⢨⠨⠐⠄⠅⠅⡡⣨⢰⠰⠜⢜⠪⡚⡘⢍⢊⢊⠪⡊⡪⠩⡓⡢⡣⡱⡹⡸⡸⡨⡢⡑⡕⢅⢇⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡝⡮⢦⠵⠥⠮⢬⡢⣌⡢⡐⠨⢐⠨⢐⠡⡈⠢⠡⠡⢡⠕⠣⠩⡐⡄⡣⡑⢅⢌⠢⡊⡢⢑⠌⡢⢂⠪⠨⡂⢆⠪⡘⢦⢧⢧⣗⣕⡕⢜⢔⢅⢇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢐⠒⠍⠱⢐⢥⠣⡑⢅⠪⡘⢌⠢⢪⢐⠌⢕⣕⢅⣦⠵⠴⠮⠮⠮⣪⠪⡨⡘⡜⡌⠆⢕⠨⢂⠢⡑⢔⠨⡐⠌⢔⢐⠡⢑⠄⡑⠔⠌⡌⡺⡫⠫⡙⣾⣕⢕⢕⢜⠕⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠕⠁⠀⠀⠀⡌⢰⢑⠅⠪⡐⡑⢌⠢⡣⡑⢔⠡⡑⣼⢑⢆⢣⢑⢕⠱⡱⣸⡌⡢⡱⡸⢐⠅⠕⡈⡂⢅⠪⡐⡱⡨⡪⡐⢄⠕⡐⢌⢐⠡⢑⢐⢸⠨⡨⡘⠼⣿⣵⡱⡸⡸⡨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠪⣃⠁⠀⠀⠀⠀⢐⠠⡑⠄⢕⠡⠢⡱⡱⣕⣵⡸⡐⢅⢂⡷⡣⠢⣑⢢⢱⠱⡱⡺⣹⢬⢪⠨⠂⢌⠌⡂⡊⢔⣥⡷⠿⣾⣧⣯⡲⡐⢔⠰⢐⠡⡂⠆⡮⡑⠔⢌⠪⡢⡫⣿⢮⡪⡪⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⢔⢐⠅⢅⠪⢸⣸⣽⠫⣷⣿⣷⠢⡊⠔⢌⢊⢢⠡⡃⡇⡇⡏⡯⡫⡪⢪⠨⡂⢌⢂⠪⡚⢿⢷⣷⣿⣿⣿⣿⣞⠢⡡⢑⠌⡢⡱⣃⠪⠨⡂⡕⢜⢔⢎⠿⣷⡱⣑⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⢌⢂⠆⠪⡐⢌⢪⢾⣿⡿⢟⢏⠣⡑⡐⡡⠡⠢⠡⡑⢌⠆⡇⡇⣇⢧⢪⣐⠡⢊⠔⡐⠡⡈⡂⡂⡊⠜⡘⢍⢚⠔⡑⢌⢢⡨⡖⢕⢢⠣⡑⢌⠜⢌⠎⡆⡇⡧⡻⣮⢪⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢡⠑⢄⠣⡑⢌⢐⢐⠐⠄⡢⢑⠠⠡⢂⢂⠂⠅⠅⠕⡨⠢⠱⡸⡸⡸⣪⢲⢸⢸⢰⢪⠦⠧⠶⢜⠴⡸⠸⠸⡘⡒⢕⢙⢍⠣⡃⡣⡣⢣⢣⠪⡂⡣⢡⠣⡑⢕⢱⢹⢺⢵⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢐⠠⢁⢢⣡⣡⡱⡬⢴⠴⠦⡓⠕⢌⢂⠅⡑⡐⠄⠌⠄⠅⢕⢐⡑⡑⡌⢌⢌⠢⡃⢇⢇⢎⢆⠕⡩⢊⠪⡘⢌⠪⡑⢜⢘⠜⡰⢑⡑⢅⠣⡊⡢⡑⢕⢱⢘⢔⢑⠜⢌⠆⢇⠭⡫⣿⢜⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⠠⠀⢄⠢⠢⡪⠸⡐⢅⠕⡨⡊⢎⢔⠡⡊⢔⠡⡑⢅⠣⡡⣱⣨⣒⣜⣔⡢⡑⡌⡂⡪⠨⢪⢪⢢⢡⠑⢌⠔⡐⢌⢐⠐⠅⢌⠢⠨⡂⠕⡐⡌⢌⢪⢘⢌⢆⠕⡅⡣⢊⠪⡊⡎⡎⡟⣎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢂⠅⢅⠕⠡⢂⠕⡨⢂⠕⡬⣺⣺⣺⢮⡮⡢⢣⢑⢅⢕⢜⢞⠾⡽⣾⢷⣟⣟⣮⣖⢌⠪⡐⢅⢣⢣⡣⡁⡂⡊⠔⡠⢑⠡⠡⡊⠌⢔⠡⠢⡊⡢⡑⢌⢆⢣⠣⡣⡪⢪⢘⠌⡆⢇⢇⢇⢏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠔⡡⠑⠌⢌⢂⢂⡊⡢⢣⢻⢳⡫⡾⡝⠽⡙⡌⡆⢇⢎⢆⢇⢫⢊⢎⢛⢞⢯⡾⣺⢳⢑⢌⠢⡑⢕⢵⡱⡐⠌⢌⠐⠄⠅⠅⡂⠅⢅⠪⠨⡂⢆⠪⡢⡑⡅⢇⢇⢇⢇⠕⡕⢜⢜⢜⢜⢮⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠎⢌⠔⠡⡑⠰⢐⢐⠜⡌⡆⡅⢆⢣⢑⢅⢣⢑⠌⢌⠢⢑⢌⢪⢐⠕⡔⡱⡨⣂⠪⡂⠥⡑⡔⡱⡘⡜⣜⢼⢊⠨⢐⠨⠨⠨⠨⡐⠡⡡⢊⠌⡢⡑⡑⡌⡢⡱⡡⡣⡣⡣⡣⡃⡇⡎⡎⡎⣗⡝⣖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡊⡂⡪⠨⠠⠡⡁⡢⢈⠪⢪⢊⢌⢪⢪⠪⡢⡱⡘⢌⢌⠆⠕⢔⢅⢕⠸⡨⢪⢪⢪⢪⢕⢕⢜⢌⠪⠡⡑⢅⠢⠨⢐⠨⠨⢈⠔⠨⠨⢐⢐⠅⡢⢊⠆⡕⢌⢆⠪⡪⢪⢪⢪⢪⢪⢪⢪⢪⡺⣺⢪⢎⢏⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢌⢂⠢⠡⠡⡑⡐⡐⢅⢎⢎⢢⢣⢓⠕⠕⢅⠢⢊⠢⠡⡊⢜⢐⠌⡢⢑⢌⠢⡑⢅⠇⡇⡇⡇⣇⢇⢕⢐⠡⡑⠅⠅⠌⠄⠅⠌⠌⠌⡂⡢⢑⠌⡢⡑⡌⢆⢕⠱⡸⢸⢸⢸⢸⢸⢸⢸⢸⡪⡮⡣⡳⣝⡎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡊⡢⠡⠊⢌⢂⠢⢂⢕⢱⢸⢰⢱⠱⠡⡡⡑⢔⠡⡑⢌⠪⢐⠡⢂⢑⠌⢔⢐⢑⢌⠢⡑⢅⢇⢣⢣⢣⡣⣑⢅⠱⡡⠡⠡⠡⠡⠡⡡⢑⠨⡂⠕⢌⠢⡊⢔⠱⡐⢕⠸⡘⡌⡎⡆⡇⡇⡇⡗⡵⡝⣜⢵⢱⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⢌⠢⡑⡑⡐⢄⢑⢔⠸⡨⡢⣃⠣⡡⠃⢆⠪⡐⡡⠨⢂⠌⡢⢑⠨⡐⢌⢂⠢⡡⠢⡑⢜⢐⠱⡘⢜⢸⢘⢖⢔⡑⢌⠪⡨⢊⠌⡊⢄⠕⡨⢌⠪⠢⡑⡌⡢⡑⠜⢌⠪⡪⢸⢘⢌⢎⢎⢎⠮⣪⢳⢕⡇⡇⣇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡨⠢⡑⡰⢐⢌⠰⢐⠔⢕⠕⢔⠢⡑⡐⢅⠕⡰⢐⠌⢌⢂⠪⢐⢐⠅⢌⢂⠢⡑⠔⡑⢌⠪⡨⠪⡘⡨⢂⢕⢐⠢⡪⡐⡑⢔⢁⠪⡐⡡⠊⢔⠡⡑⡅⢕⠌⡢⢊⠪⡘⢜⢌⢪⢊⢎⢪⢪⠪⡕⡕⣝⢎⢎⢎⢖⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡑⠄⢕⠰⡈⡂⡢⢑⢐⠕⡡⡑⢅⠢⡊⢌⠢⡑⢌⠢⡑⢅⢢⢡⠡⡂⡅⢕⢐⠡⡂⢕⠨⡂⢕⡐⢕⠔⢜⠰⡡⡑⢕⢔⠱⡘⢔⠔⡡⢂⠪⡨⡂⡣⢊⢌⠢⡑⡌⡪⡘⢌⢆⢕⢜⢌⢎⢪⢪⢱⢱⢹⢸⢕⡇⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠔⠡⡑⡨⢂⢊⠄⠕⡐⢌⠢⡨⠢⡑⢌⠢⡑⢌⠢⡑⢌⢢⢑⠔⢅⠕⡌⢆⢕⠱⡘⡔⡱⢡⢃⠪⡂⢇⠕⡅⡣⡊⢆⢆⢣⠱⡡⢣⢊⢢⠑⠔⢌⠢⡑⠔⢅⠕⢔⠢⡑⡑⡌⡆⡕⡜⡜⡜⡜⡜⢜⢜⢜⡵⣝⢜⢌⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⡡⢂⠢⡑⡐⠅⠕⢌⠢⡑⢌⠪⡐⢅⠕⢌⠢⡃⡪⠨⡢⢑⠌⢆⢃⢊⠢⠡⠡⡑⠌⢜⢐⢅⢣⢑⢅⢣⢊⢆⢕⢱⢨⠢⡣⡱⡑⡕⢅⢇⠕⠡⡊⢌⢊⠆⠕⡅⢕⢌⠪⡘⡔⡕⢜⢜⢜⢜⢜⢜⢜⢵⢕⢗⣝⢜⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠌⢔⢐⠅⡂⡪⠨⡊⡢⡑⢜⢐⡑⢌⠢⡑⢅⠕⢌⢌⠪⡐⡡⢊⠔⢔⢡⢊⠪⡊⡢⡃⢕⠰⡐⢅⢊⠆⡕⡌⡆⡕⢜⢰⢑⠕⡌⡎⡜⢜⠔⡕⢅⠪⡐⠔⡡⡑⡌⡢⡡⡑⡕⢜⢌⠎⡆⡇⡇⡇⡇⢧⢳⡹⣕⢵⡱⣣⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⢕⢐⠌⠢⡨⠨⡂⡒⢌⡢⡱⠨⠢⡑⢜⢐⠕⡡⠢⡑⠬⡨⢢⢃⢣⢑⢌⠎⡌⢆⢎⢪⢘⢌⠪⡢⢱⢐⠕⡸⡸⡘⡌⡆⢇⡣⡪⡪⢪⠪⡪⡢⡑⠌⡢⢂⢆⠪⡐⡱⡨⢪⠪⡢⡃⡇⡇⣣⢣⢣⢳⢕⢧⡳⣱⢹⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠢⡂⠅⢕⠨⡊⢔⠡⡣⡊⡎⢜⠨⠨⡢⢑⢌⠢⡣⢱⢑⠕⢅⢣⢑⠕⡌⡪⡸⡐⢕⠌⡆⡣⡱⢸⢐⢅⢇⠪⡂⡇⡕⢜⢌⢪⢊⢎⢎⢎⢎⢜⢔⠡⡊⠔⠔⢅⠕⡌⡪⡂⢇⢣⢱⢱⢱⢱⡱⡱⡳⡹⣜⢞⡜⡜⢜⢜⢔⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠨⢊⠢⡑⢌⠢⡱⢨⢪⢨⢢⢑⢑⠌⡢⡊⡪⡸⢰⠡⡣⢣⢑⢅⢣⠪⡢⡱⡘⡌⡎⡜⢌⢪⠪⡸⢰⢡⢣⢱⠨⡊⡆⡕⡌⢆⠕⡕⢜⢔⢕⢅⢇⢘⠌⢅⢅⠕⡔⡢⢱⢑⢕⢕⢕⢕⡕⡵⡹⡸⡕⡧⡳⡱⡱⡑⡜⡌⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠢⡑⢌⠢⡑⢜⢨⢢⢱⠱⠨⡐⢌⢢⠱⡑⡜⡌⡎⡜⡌⢎⢜⠔⡕⡱⡘⡌⢎⢢⠣⡣⡃⡇⡣⡣⡱⡸⡰⡑⡕⢌⢆⢕⢅⢇⢣⠣⡣⡱⡸⣐⠢⡑⡑⢔⢑⢌⠜⡌⡪⡢⡣⡣⡣⣣⢳⢹⢸⡪⣺⢱⠱⡘⡌⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠡⡊⢔⠡⡊⡢⡑⢌⠢⡡⡱⡨⢂⢇⢕⠕⡜⢔⠕⡜⢌⠎⡆⢇⢣⢱⢑⢕⢕⢕⠕⡕⡅⡇⡕⡜⡌⡆⡇⢇⢎⢆⠊⢆⢣⢣⢱⠱⡑⡕⣑⢆⠣⡑⢌⠪⡐⢅⢣⠱⡱⡸⡸⡸⡪⡎⡮⡪⣣⡫⣎⠊⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠪⡐⢅⠪⡐⠅⡪⡰⡱⡘⡜⡔⢱⢘⢔⢕⢱⢡⢣⢱⠱⡱⢱⠱⡱⡑⡕⡕⡜⡔⡕⡕⡜⡜⢜⢜⢸⢘⢜⢜⢜⢜⢭⢢⢕⢘⠜⡜⢜⠜⡔⡅⡣⢊⠢⡑⡅⡣⡡⡣⡱⡸⡸⡸⡜⣎⢮⢣⡣⣇⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠨⡂⠕⡨⡸⢰⠱⡸⣸⢸⢘⢔⠱⡑⡜⢔⢕⢅⢇⢣⢣⠣⡣⡣⡣⡣⡱⡱⡑⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡕⡧⡣⡣⡣⡣⡑⢜⢸⢘⢌⢎⠌⢆⢣⢑⢌⢆⠕⡜⡌⡎⡮⡺⣸⢪⢎⢮⢪⢎⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢌⠢⡑⡌⢎⢢⢣⢏⢎⢆⢯⢆⢣⠣⡣⢣⢣⢪⠪⡪⡢⡣⡣⢕⢜⢜⢜⢜⢜⢜⢜⢌⢎⢎⢎⢎⢎⢎⢮⡣⡩⡪⡇⡇⡇⡣⡱⠨⡊⡎⢆⠣⡱⢨⠢⡱⡐⢕⠕⡜⡜⣜⢼⢸⢪⡪⡎⡮⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡐⢅⢪⠨⡢⢣⢣⢣⢣⡣⣏⢯⣎⢎⢪⢪⢢⢣⢣⢣⢣⢱⢱⢱⢱⢱⢑⢕⢕⢕⢕⢕⢕⢕⢕⢕⢕⡽⣵⡳⣌⠆⡏⡎⢜⠌⡜⢌⢪⠸⡘⠬⡘⢔⢑⢔⢑⢅⢇⢇⢇⢇⢧⢳⢱⢱⡱⡣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠌⡢⡡⢱⢨⢣⢳⢕⢗⣝⢮⣳⡳⡽⣜⢔⢕⢕⢱⢡⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⢣⡣⣳⡹⣝⡾⣕⡯⣞⣝⢮⡺⡐⢕⠸⡐⢅⢣⢑⢅⢣⢑⠕⢌⢪⠸⡰⡱⡹⡜⡎⡎⡎⡮⡪⣎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⢌⢌⢢⢱⢕⢇⢗⢧⢳⢳⢕⡯⣫⢮⡳⣕⢵⢱⢱⢱⢱⢱⢱⢱⢱⢱⢱⡱⡱⣕⣕⢧⢯⡺⡽⡵⣻⡺⣪⢗⡵⡳⣝⢌⠢⢣⢑⢅⢕⢑⢌⢆⠕⢅⢇⢕⢱⢱⢱⢣⢳⡹⡸⡸⡜⣜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢌⠢⡑⢔⢱⡱⡕⡇⡗⡝⡮⣳⢝⣗⡽⡮⡳⣝⢵⢝⢮⡺⣪⡺⣜⢮⢳⢕⣗⢽⣪⢮⢗⢯⣫⢯⡻⣺⡪⣗⡝⡮⣫⡺⡢⡑⠕⡌⡢⢱⢑⢌⢢⢑⠕⡌⢆⢣⢪⢪⢣⡣⡣⣣⢣⢫⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠢⡑⢅⠅⢕⢎⢎⢎⢎⢧⢫⢮⡳⣳⢝⡮⡯⡮⣳⡹⣕⢽⡸⣪⢺⢪⡳⡝⣎⢗⡵⣫⣫⣳⡳⡽⡺⡵⣝⢜⡎⡗⡵⣹⠰⡘⢌⢆⠪⡊⡆⢕⢢⠡⡣⡊⡎⡜⢜⢜⢕⢕⢕⡕⣕⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⢊⠢⡡⠡⢣⢣⢣⢣⢳⢱⡣⡯⡺⣕⢯⡺⣕⢧⡳⣕⢧⡫⡮⡳⡝⣎⢗⢵⡫⡮⡳⡵⡵⣝⢞⣝⢮⢎⢧⢳⢹⢜⠎⢌⠌⡆⢆⢣⠱⡸⡨⡂⢇⢪⠢⡱⡸⡸⡱⡱⡕⡇⣇⢧⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡡⡑⠌⢜⢐⠱⡱⡱⡱⡱⡱⡝⡮⡳⣝⢮⡳⡳⣝⢮⢺⡪⡳⡝⡞⣎⢏⢧⣫⡺⡝⡮⣺⢪⡳⡱⡕⣇⢗⢕⢕⢕⠡⡑⡑⢌⢢⢱⢑⠕⡔⢜⠰⡡⢱⠱⡸⡸⡸⡸⡜⣜⢜⡜⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠪⡨⢂⠢⡑⠌⡪⡘⡜⡜⡎⡮⡳⡕⡗⢝⠕⡃⡣⢃⠍⡊⢅⠍⡌⢕⠱⠱⡱⢝⡺⡪⡳⡹⡪⡣⡣⡣⡣⢃⠢⡑⡑⢌⢪⢸⢰⢱⠱⡘⢔⠱⡘⡌⢎⢪⡪⡪⡎⡮⡪⡪⡪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣊⠢⡡⠊⢄⠕⠄⢕⠸⢰⠱⡱⡱⡑⢌⠢⡑⢔⠨⡐⢌⢂⠕⡈⡢⠡⡊⢌⠢⠡⠢⡩⡊⢇⢏⠪⡊⡢⢊⠔⡑⢌⠌⡆⡇⡕⡜⡎⢎⠪⡨⡊⢔⠕⡕⡕⡕⡕⣕⢵⢹⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢑⢌⢪⢐⠌⡊⠔⢌⢂⠅⢕⠸⡘⢌⢪⠨⡂⢕⠨⢂⠢⢊⠔⡨⢂⠪⡐⢅⢍⠪⡰⢘⠌⡂⢕⠰⠨⡂⢕⠨⡂⡇⡇⢕⢱⣹⢪⠪⡘⢔⢘⢔⢕⢕⢇⢇⢏⢎⢎⢮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠆⡕⡨⠨⢂⠢⢡⠑⢔⠨⡂⠅⡅⠕⡑⡘⠔⡑⡑⢌⠢⠡⢃⢊⠢⠨⡂⡪⡐⢌⢌⠢⡑⡑⢌⢢⢣⢣⢣⢪⢊⢮⢎⢆⠣⡃⡅⡣⢪⢪⢪⢪⡪⡺⡸⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠸⡘⢜⢔⢡⠡⢊⠔⠡⢊⠌⡢⢑⠔⢌⠪⡐⢌⠢⡡⢃⠕⡠⢑⢑⠌⢔⠨⢂⠢⡑⡔⡜⡜⡜⡌⡎⡞⡪⣪⡳⡱⢡⢑⠌⡆⡣⡣⡣⡣⣣⢳⢹⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢔⠱⡑⡕⡌⡪⡐⢌⢐⢁⢊⠄⠕⡈⡢⠑⠌⠢⢑⢈⢂⢆⠪⡰⡘⡔⡕⡕⡕⢕⢕⢵⢱⠱⡱⣱⡳⡝⢌⠢⢅⢣⠱⡪⡺⡸⡱⡱⡕⣕⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢑⢱⠸⡘⡜⡜⡜⢜⢔⢕⢕⢌⢆⢇⢇⢝⢌⢎⢎⢆⢇⢇⢇⢇⢇⠧⡱⡱⣱⢣⢣⢣⢣⢳⢝⢌⠢⡃⡇⡕⡕⡕⣇⢯⢪⡣⡣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⡑⣕⢕⢎⢮⢪⢪⢢⢣⠣⡣⢃⠇⢇⠣⡃⡇⡣⡣⡣⡣⡕⡜⡼⡸⡪⡪⡣⡣⣪⢪⡚⢌⠢⡣⢱⢸⢸⢪⡳⣱⢱⡱⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠪⡪⣃⠧⡣⡣⡣⡣⡣⡪⡸⡸⡸⡸⡘⡜⡜⡜⣜⢜⢎⢎⢗⢽⢸⠸⡜⡮⣫⢪⢘⠔⡕⢜⢬⢪⢎⢧⡣⡣⡣⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⢸⢸⢸⢸⡪⡣⡣⡱⡱⡱⡱⡱⣱⢱⢱⡱⣣⢇⢗⢝⢜⢜⢜⢕⢭⢪⢳⢑⠌⡆⡣⣣⣣⡳⡹⡪⡣⡪⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠌⡎⣗⢵⡹⡜⡎⡎⡮⡪⡚⣜⢎⠮⣚⢼⢸⢪⡪⡣⡣⡧⣇⢇⢏⢊⢆⢕⢕⡕⣗⢼⢸⢕⢕⢕⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠬⡘⡜⢎⡳⡵⡕⣝⢎⢧⢳⢝⢜⣎⢞⡜⡵⡳⡭⡳⡹⡐⢅⡪⡢⣣⢳⢕⢽⢸⢜⢜⢜⢜⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡨⠨⡊⢆⢕⢱⠩⡪⡫⡺⡝⡼⢝⢎⢗⢍⠗⡍⢎⡊⡆⡣⡣⣎⢞⢜⢎⢇⢇⢇⠇⡕⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠌⡢⢑⠅⢇⠎⡆⡕⡌⡎⡌⡆⡇⡎⣎⢜⢆⢧⢳⢹⢜⢜⢜⢕⢕⢕⠱⡐⠕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢡⠑⡅⠕⡅⡣⡱⢱⢱⢱⢱⢱⢱⢱⢹⢸⢸⢸⠸⡘⡌⢆⠕⠔⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢑⢌⠪⡰⢨⢊⢢⠱⡡⡃⢇⠣⡃⡣⡱⢡⠣⡑⢕⠌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢕⠸⡐⠥⡑⢕⢌⢪⢘⢌⢪⠨⡊⡢⡑⢅⠣⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠔⢅⠕⠡⠡⡑⢔⢑⠌⡂⠅⡊⡐⠄⢣⠂⠅⡂⠍⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⣜⢔⢨⠌⡒⠂⠆⠢⠁⠪⠰⠰⡠⠑⢔⢑⢁⢪⠨⢐⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡂⢣⠊⠂⠂⠀⠀⠀⠀⢠⠆⠂⠀⠁⠉⠑⠁⠆⢎⠱⡐⢐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢼⠀⠁⠂⠂⠀⠈⠐⠈⢉⠬⠁⠐⠐⠐⠐⠈⠒⠨⠄⢑⢐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡟⡠⢐⠀⠀⠀⠁⠀⣶⠕⠀⣠⠊⡈⠄⠄⢄⠀⠀⢈⠰⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⡢⡑⡅⠀⠀⠈⠀⠀⠀⠀⠀⢀⠊⠄⢅⠑⢄⢑⠄⠜⡔⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠢⣂⠎⠄⠬⠀⠀⠂⠀⠈⠀⠀⠄⠢⠡⢑⠠⢑⠐⢄⠱⠀⡇⠡⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣧⢉⢇⠅⢊⠢⠀⠀⠐⠀⠈⠀⠨⠨⠨⢐⠨⢐⠨⢐⠨⡴⢐⢅⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡨⢐⠈⠥⡀⠐⠀⠀⠄⠨⠨⠨⢐⠨⢐⠨⢐⠠⡃⠠⡃⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠅⡂⠢⠢⣀⣀⣀⣨⡨⠨⢐⠨⠠⠨⢐⠐⡄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢈⠢⠨⠨⢐⠂⠀⠀⠀⠈⢢⠂⠌⠌⠌⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡊⠨⠨⢐⠀⠀⠀⠀⠀⠰⡈⠌⠌⡂⠌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠅⡂⢅⢑⠐⡄⠀⠀⠀⠀⡐⠄⠅⠅⡂⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡘⠄⡂⡂⡂⡂⠅⢒⡀⠀⠀⠀⡂⠅⠅⠅⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡐⠌⡂⠅⡂⡁⡂⡂⡂⡂⠅⡂⠢⠀⢀⠌⢄⢑⠨⠨⡈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠨⠠⡁⡂⠅⡂⢂⢂⢂⠂⡂⠅⡂⢅⠇⠔⠨⢐⢐⠨⢐⠨⡐⠄⡕⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠘⠈⠀⠁⠁⠈⠈⠀⠀⠈⠀⠑⠀⠁⠀⠈⠈⠒⠰⠌⣐⠨⠂⠔⡊⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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