⠀⠀⠀ ⡤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢤⡤⢤⢤⠤⢤⢤⢤⢤⢤⡤⣤⢤⡤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡐⢌⢊⡫⡕⡝⣉⠣⡢⡑⡐⡢⠒⢌⠨⡑⡋⢆⠸⢟⣛⣟⣻⣻⣻⣟⣿⣯⣿⣽⣧⡿⡿⣵⣤⢃⠢⡑⠜⡈⢎⠐⢕⠌⣊⢒⢐⠀⢘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⢜⢤⡣⡳⣜⠵⣬⣧⣮⣬⣬⣬⣧⣮⣦⣬⣬⣴⣥⣼⣿⣭⣥⣭⠬⣵⣼⢢⣷⣮⣮⣾⣵⣽⣿⢽⣷⣎⢢⢑⠌⡂⠕⠰⡠⡑⢄⠁⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣷⢾⠾⡿⠞⠙⠺⡿⣬⣧⢉⢫⣮⣮⣮⡮⡵⣭⣿⣟⣷⡅⢻⢜⣝⣽⡟⢽⣿⣿⠟⣿⣿⢿⡿⣧⢿⡻⣗⠷⠷⠾⣾⡆⠢⡊⡢⠁⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡷⡲⢦⡺⡁⢊⠀⠌⠺⣽⡔⢢⠢⡣⠌⢼⢳⣸⢻⣇⣿⡍⢹⢗⡬⡙⡿⢼⠟⠡⡌⢿⣎⡥⠓⢴⡳⡴⣲⡓⡟⢗⢻⣟⣟⠿⣾⢷⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡿⣽⣣⢧⡇⠠⡑⠠⠂⠈⢳⡑⡑⢮⢊⡐⢗⢆⢽⣿⢻⡇⣊⠺⡗⢍⡔⡡⢪⠐⢄⢿⣿⡽⣰⡂⣙⢙⢜⣝⡨⣪⡟⣯⠟⢋⠁⠂⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣾⢀⢄⠡⡊⡐⠠⢁⠌⢂⠀⡑⡩⠢⠢⡡⢫⠪⡳⣿⢸⡿⡄⢑⠻⡖⡡⠢⡂⢕⠂⢾⣻⣞⢧⡡⠪⣖⠵⡐⢗⠝⠊⡀⠂⠄⡨⠀⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣁⠲⡠⢑⢜⠀⠕⠠⠂⠢⠐⡠⢊⠜⡌⠲⡁⢏⠸⡁⡫⢚⢔⠕⡌⡻⣑⠣⡣⣌⠪⡢⠸⡏⢟⢄⠣⡠⢋⠆⢑⠀⠅⠠⠑⠠⠀⠌⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⢦⠱⡑⡢⣣⢈⠪⡈⢅⠱⡈⢆⠱⠨⡈⡊⡐⠡⡈⠔⡈⠢⡡⠪⡈⢎⠴⡉⠖⡨⢑⠡⢃⠜⡠⢡⠂⠕⠐⠄⠂⠄⠡⠈⠄⡑⠀⠂⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡢⢣⢊⠮⣟⠀⢕⠌⡢⡁⡊⠠⠀⡁⠄⠨⠐⡡⠐⡌⢐⠅⡊⡢⡑⢕⠊⢌⠂⠐⠄⠑⡠⢑⠌⢆⠱⢁⠅⢊⠨⠀⢅⢈⠂⢄⠈⡂⢘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣳⢱⡑⡦⣣⠘⠔⠡⠂⠌⠀⡠⠠⣀⠄⠠⠀⢌⢸⢀⢇⢘⠔⢌⠪⡈⡂⡁⢈⠄⠡⡈⠄⠂⠌⡠⠑⢄⢊⠐⡄⠑⡠⠂⡡⠂⠌⡀⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠟⠻⠛⢟⢥⠩⡪⡨⡢⠑⢰⠈⠐⠏⠀⢀⠀⢢⢣⢑⠤⠃⠌⠊⠢⡨⠠⡂⢆⠄⠡⠀⡀⠐⠀⠀⠂⠀⠅⡨⠐⡁⡐⠄⠄⠑⠄⡀⢘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣵⢕⡝⡱⡑⢕⠘⡔⢱⠁⡎⠠⠀⠀⢐⠀⣄⠣⡡⡪⢢⡉⡪⡈⢆⠘⡰⢁⢇⠂⡐⠀⣤⠌⠀⡁⠢⢀⠀⠄⠡⡈⠄⡂⡈⠂⠌⠠⠨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣴⢌⢎⢎⠪⢂⠕⡨⢢⠑⡜⡰⡡⡣⣑⢕⢔⢕⠱⡡⢃⠜⡰⢡⠑⢅⠪⡠⡑⠠⡀⠀⠉⠀⠀⡀⠀⠢⢂⠀⠠⠀⢌⠠⡈⠌⠠⠁⢘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡿⡨⡣⢕⡑⢅⠪⡐⢅⠱⡈⢖⢕⢮⢪⠎⠦⠁⢂⠐⠁⠌⠐⠠⠑⠨⡂⢅⠜⡰⢢⡐⡀⡀⠐⠀⠀⡨⡣⠀⡕⡀⢂⠐⠠⢊⠐⡀⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡹⡘⢜⠄⡣⢊⠔⡱⢈⠆⢕⢘⢢⢣⢣⡓⡐⠀⠀⡀⠁⡀⠁⠐⠀⠁⠈⡢⢑⠕⡱⢨⢊⢜⠐⢆⠢⢊⠔⡨⢂⠎⡐⢅⠑⢄⠑⢄⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡧⡙⢄⠣⡨⢠⠑⡔⠠⡊⢠⢁⢑⠕⡧⢪⢊⠢⠀⠀⠀⠀⠀⠀⢀⠠⢂⠆⡕⡨⢊⠆⡕⢌⠥⡡⢊⠀⡂⠐⠠⠂⡨⠀⠕⠠⡑⡐⠨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡗⢨⠂⠕⠠⢃⠌⡊⠜⠠⢃⠢⡣⡙⢔⠡⢃⠌⡀⠂⠀⠂⡀⢊⢄⢑⠌⡪⠰⡊⢆⢕⢘⠔⡡⢂⠡⠂⠌⠠⠁⠄⡀⢊⢈⠂⠢⡈⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡕⠢⡡⢁⠑⡐⠔⢨⢈⠢⡂⢡⠂⢌⠠⠊⡀⠢⠀⠀⠠⡈⠔⢁⠢⢐⠡⡊⠔⡁⠢⠀⠅⠊⠠⠃⢄⠑⡈⢀⠡⠐⠀⠢⠠⠁⢌⠐⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣏⠜⠐⠄⠡⠀⠌⠀⠂⠐⡈⠀⢂⠐⢀⠂⢀⠂⠀⠀⠐⠠⠈⠄⠂⠄⠁⠌⡐⢡⢉⠪⡐⢁⠔⢁⠄⠑⠄⠂⢀⠂⢁⠐⠁⠌⢂⠐⢐⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⡹⢌⠊⡠⢁⠌⠀⠌⠐⠀⡀⠁⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠂⡈⠠⠈⠠⠀⠄⢂⠠⢀⢁⠐⢁⠈⠂⠅⢈⠀⠀⠂⠈⡀⠑⠠⡁⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣔⢅⢊⠄⠂⢄⠡⠐⠀⠄⢀⠀⠀⠀⠂⠀⠀⠀⠂⠈⠀⠀⠄⠀⠀⠐⡀⠁⡀⠑⠀⠂⠢⠀⠅⢄⠨⠈⠂⠠⠀⠁⠐⢀⠀⡈⢐⠀⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⠗⢕⠔⡡⠑⡠⠂⡁⢂⠐⠀⠠⠀⠀⢁⠑⠀⡈⢀⠁⡈⠀⠄⢈⠀⠂⠀⠀⠀⠁⠈⠐⠀⢁⠐⠀⠂⠂⠄⢀⠈⠀⠂⢀⠀⠄⠠⠈⢨⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡇⣬⢪⡨⠂⢅⠐⡈⠔⠠⡈⠄⡁⠀⠄⠠⡁⢀⠐⠀⠂⠠⠈⡠⠀⠄⠀⠀⡐⠀⠁⠀⠀⠂⠀⠠⠁⠈⠐⠀⢂⠀⡈⠀⡀⢀⠐⠀⡁⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢇⠓⢕⠘⡌⠢⡡⠌⠔⢅⠔⠤⢌⠤⠤⠤⠰⠄⠥⢌⠔⠤⠡⠄⠦⠰⠄⠬⠠⠅⠤⠤⠤⠤⠄⠦⠠⢅⠬⡠⠢⠤⠤⠤⠤⠄⠔⠤⠄⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠒⣶⠒⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣿⠀⠀⠀ ⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀ ⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢀⣿⣀⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀