⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡽⡿⠻⣯⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠿⠛⢝⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠩⡨⠨⡚⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠌⢌⠰⣽⣗⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣗⡢⠡⢘⣼⣿⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡐⢼⡏⠇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠌⣾⠯⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⢸⡇⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣿⡇⠅⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡯⡃⠅⣿⣮⣶⣤⣤⢤⢄⠄⠄⡀⠄⠀⠀⢰⣸⡫⡂⢽⡎⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣺⣿⡏⠌⡐⣿⣟⢟⢟⠻⡛⢟⢟⢟⠻⡻⡻⣿⣻⣿⣾⣶⣷⣧⣦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣻⣷⢿⣯⠇⠂⠄⢽⣷⢐⠐⠅⡊⠔⢀⠂⠡⠐⡀⠂⠄⢐⠠⠁⠍⠽⠽⡿⣿⣾⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⢟⠳⡘⠜⢗⠡⠁⠌⠸⠻⠐⡁⠡⠐⡈⠄⠨⠀⠅⠠⠁⠌⡀⢂⠁⡂⢁⠂⡐⢘⠸⠻⣿⣵⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣶⡟⡏⢍⠢⢑⠠⠁⡂⠄⠡⠈⠄⡁⢂⠐⡈⠄⢂⠨⠀⠅⠨⠀⠅⢂⠐⡀⢂⠐⡀⢂⠐⠠⠈⠄⡉⡛⣿⣶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣶⡾⣞⣾⣿⣷⣿⣾⣷⡇⠅⢂⠡⠐⡈⠄⡁⢂⠐⡀⢂⠐⡈⠄⢂⠡⠈⠄⠡⠈⠄⢂⠐⡀⢂⠐⠠⠈⠄⡁⢂⠐⡀⢊⠹⣿⣶⣤⣤⢤⢤⢤⢄⠄⠀⠀
⢰⣾⣿⡑⡐⡐⡐⠨⠈⠌⠡⠡⠈⠄⢂⠡⠐⡀⢂⠐⡀⢂⠐⡀⢂⠨⠀⢂⠡⠈⠄⠡⠈⠄⢂⠐⠠⠈⠄⡁⢂⠐⡀⢂⠐⡀⢂⢁⢻⣿⢿⠿⠿⠿⡻⣿⡇⡀
⠸⣾⣿⡐⡑⡑⠤⡡⠁⠅⠡⠈⠄⠡⠐⡀⠅⢐⠀⡂⢐⠀⡂⢐⠀⡂⠡⠐⡀⠅⠨⠀⠅⠨⠀⠌⠠⠁⡂⢐⠀⡂⢐⠀⡂⢐⠀⡂⡐⢼⣿⡜⢌⠌⢬⣿⢇⠂
⢈⢺⣿⣂⠢⢐⠡⢘⠨⠠⠡⠈⠄⡁⢂⠐⡈⠄⢂⠐⡀⢂⠐⡀⢂⠐⡈⠄⢐⠈⠄⠡⠈⠄⠡⠈⠄⠡⠐⡀⢂⠐⡀⢂⠐⡀⢂⠐⠠⠨⡿⣧⢑⢸⣼⠻⡁⠌
⠀⠙⣿⣧⠪⢐⠨⢐⠨⠈⠄⡁⢂⠐⡀⢂⠐⡈⡤⣦⣶⣶⣦⣦⡔⡀⢂⠨⠀⢂⠡⠈⠄⠡⠈⠄⠡⠈⠄⢂⢐⢠⣦⣶⣴⡔⡄⠌⠨⠀⡏⣿⢔⣽⡟⠨⠀⠀
⠀⠀⢟⣿⣯⢐⠨⢀⠂⠅⠡⠐⡀⢂⠐⡀⢂⢨⣿⠅⢀⣞⣿⣿⣿⣷⣒⡀⠅⢐⠀⠅⠨⠀⠅⠨⠀⠅⠨⣐⡾⠍⠿⣿⣿⣿⣗⠨⠠⢁⠪⣿⣿⠅⠅⠡⠀⠀
⠀⠀⠀⢿⣻⣦⢊⢐⠈⠌⠠⢁⠐⡀⢂⠐⠠⠐⡛⢿⣿⣿⣿⣿⡟⢟⣿⡕⡈⠄⢂⠡⠈⠄⠡⠈⠄⠡⠨⣿⣧⣥⣿⣿⣴⡽⠏⠄⠅⢂⢂⠿⣚⠀⠂⢀⠀⠀
⠀⠀⠀⢙⢾⣻⠆⢔⠈⠌⡐⢐⠠⠐⡀⠌⠠⠁⠄⡉⠙⡛⠻⢟⠷⠶⠛⠅⡐⠈⠄⢂⠡⠈⠄⠡⢈⠐⡈⠛⢿⢿⢻⢛⢙⠡⠡⠈⠌⡀⡂⢷⣷⡨⠐⠀⠀⠀
⠀⠀⠀⢰⣿⡻⡡⡑⠌⡐⢐⢀⢂⠡⠐⠠⠈⢀⠡⠀⠅⢐⢈⠂⠍⠨⠀⠅⠠⠁⠌⡀⠂⠅⢌⠔⢄⠂⠄⡁⠅⠡⠑⡐⢐⠀⠅⠨⢀⠂⡢⢹⣿⡆⠆⠀⠀⠀
⠀⠀⠀⢼⣿⡘⠔⢌⢂⢂⢂⢐⢀⠂⠅⠨⠐⡀⢂⠈⡀⠂⠄⢂⠡⠈⠄⠡⠈⢄⢑⢮⢟⠯⡫⢹⠹⡹⣕⠆⠌⠠⢁⢐⠀⡂⠅⠌⡐⠨⠠⢉⣍⣕⡡⠀⡀⠀
⠀⠀⠀⣿⡯⡨⢘⠐⢅⠂⠄⠄⠄⡂⡁⠌⠐⡀⢂⠐⠠⢈⠐⡀⢂⠡⠈⠄⠡⠐⠘⢝⢦⣇⣪⢢⢑⡽⡗⠈⠄⡁⡂⡐⢐⠐⠠⢁⠄⠅⡊⢄⠷⣿⣷⠁⠀⠀
⠀⠀⡕⣿⣯⢌⠢⡑⠄⠅⢅⠡⢂⢂⢐⠨⢐⢀⠂⠌⡀⡂⢐⢀⠂⠄⠡⠈⠄⡁⠅⢂⠐⡐⠋⣟⣟⢂⠂⠡⢁⢐⢀⠂⡂⠌⡨⢐⢈⠢⡈⢦⣿⡟⢇⠊⠀⠀
⠀⠀⢭⣿⣿⣶⡕⢔⠅⢕⢐⠨⢐⢀⠂⠌⡀⢂⠈⡐⢀⢂⠐⡀⠂⠅⠨⠠⢁⠐⡈⠄⠂⠄⡥⣿⢷⠠⠨⢈⢐⢀⠂⡂⡂⢅⢂⠢⡐⡰⠨⡪⣯⡣⢂⠈⠀⠀
⠀⠀⠁⢹⢿⣿⣯⡣⡑⢕⢐⢕⠰⡐⡨⢐⢐⠐⡐⢐⠐⡀⠢⠈⠌⠨⠠⢁⠂⡂⢄⢅⣵⡻⠽⠁⠍⢗⢕⢐⢀⠢⠨⡐⢌⠢⡂⡣⢪⣸⣷⣿⡩⢂⠡⠀⠄⠀
⠀⠀⠀⠀⠀⠓⣿⣿⣼⣵⣕⢔⠱⡨⡨⠢⠢⡑⢌⠢⡡⠨⡂⢅⠅⢅⠌⢔⣐⢐⢐⠑⡂⠌⡐⠡⢁⠂⢔⣐⡔⡕⢅⢊⢢⠱⡨⣊⣾⣿⢿⡻⣽⣄⡄⠀⠀⠀
⠀⠀⠀⠀⢀⣵⣿⣿⢻⢿⣿⣦⣣⢪⠨⡪⡑⡌⡢⡑⢌⠪⡨⠢⡑⢅⠅⢕⢐⢙⢪⠣⠧⠵⡬⠮⠮⠯⡻⠪⠢⡊⢆⠕⡅⣣⣪⣿⡿⣟⢕⢝⢮⢿⣯⣄⠀⠀
⠀⠀⠀⠠⣴⣿⡿⣎⢗⢭⢫⢻⣻⣾⣮⢢⠱⡨⠢⡊⢆⠕⡌⡪⢨⠢⡑⡑⡌⡢⡡⡑⢍⢊⢪⠩⡩⢪⠨⡪⡑⡅⡣⡱⣮⣾⣿⡻⣝⢜⢎⢧⡳⡽⣻⣿⡄⠄
⠀⠀⠀⣾⣿⣿⣝⢮⢺⢜⢕⢇⢗⢝⡽⡿⣷⣗⣕⡑⡅⡣⢪⠨⡢⢱⢘⢔⠱⡰⢨⠪⡨⡊⡢⡱⡘⢔⢱⢨⣲⣱⣷⣿⡿⡏⡧⡳⡱⡝⣎⢗⡵⡽⡽⣿⣗⡆