⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⢢⡝⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠴⢷⢿⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣍⣵⣶⣮⣥⠄⠀⠀⠀⠀⠀⠀⢺⣷⣤⣄⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣤⡀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢸⡟⣿⣿⣃⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠸⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣿⢾⣻⢹⢻⡣⣤⣤⣤⡄⠀⠀⠀⠀⡀⠂⠀⠀⢀⠆⠙⠊⢿⠑⠂⠀⠀⠀⠀⡀⠀⢠⣾⡿⣋⣶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣡⣶⣦⢑⣛⣿⣽⣿⣿⠀⠀⠠⠂⠀⠀⠀⠀⠘⢀⢨⣤⣅⡀⠀⠀⠀⢀⠈⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣢⢷⣁⢮⣲⡙⠋⠉⠁⠀⣰⡖⠀⠀⠀⠠⠀⠈⠈⡎⣉⣉⣠⣤⡤⣤⣥⡀⠠⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣾⣿⢾⣽⣮⢿⣿⡆⠀⠀⢀⡝⠀⠀⡀⠂⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠊⠉⢻⢆⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠈⠹⠿⠟⠁⠀⠹⣿⣿⠿⠃⠀⠀⠘⠀⠀⠐⠀⢀⠞⠁⠰⠀⠀⠀⠀⠀⡀⠒⠠⠀⢂⠀⠈⠢⡀⢰⣶⣶⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⡄⢡⠀⢠⠃⢠⠋⠀⠀⠀⠄⠔⠀⠀⠀⠀⠃⣴⠌⠀⠀⣠⣴⣬⣼⣿⢹⡟⢀⣀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⣳⡀⠀⠀⠀⠀⣠⠘⠀⠸⠀⡆⠀⣴⠁⡠⠂⣠⠤⠰⠒⠢⠤⢄⢀⠀⠐⢿⣿⣽⣻⡿⣬⢟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠆⠀⠠⠡⠀⠀⠀⢀⠀⢱⡌⢺⣦⡀⠀⠀⢘⢧⢧⢸⠀⡇⣼⣿⠘⡱⠋⠀⠠⠀⠀⠀⠀⠄⠙⢄⠀⢀⣤⣿⣫⣽⡿⣼⡛⠛⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢂⠂⠀⠀⠌⠀⠈⠁⠈⢻⣷⡄⠀⠘⣮⡈⣌⡆⠇⢿⡿⣰⠃⠀⠀⢆⠠⠀⠂⠀⠀⠀⠈⠄⢾⣿⣿⡿⢹⣷⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠂⢀⡀⠀⠀⠀⠀⠀⠠⠀⠉⠻⣤⡀⠘⢷⣌⢲⣼⡜⠇⡇⠀⢈⣀⡀⠐⠴⡇⠃⠀⠀⣠⣨⡄⠉⠉⠀⠀⠻⠿⠛⠄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠶⣄⣙⠂⠙⣿⣄⢳⣔⠁⠀⠈⡆⠹⡏⠈⠀⠰⣿⢿⡆⠰⠀⠀⠀⠀⠀⠔⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⡀⢀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⣍⢙⠲⠦⣝⣷⣿⣆⠀⠡⡃⠐⣅⠄⠣⠀⠀⠇⠁⢠⠀⣠⠔⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⣷⣾⢿⡿⠋⠢⠀⣠⠈⡀⠀⠀⢠⡌⢑⣬⡁⠈⠡⠋⠐⠀⠉⠟⡛⠷⣦⣤⣀⠑⢗⣄⠐⠐⢦⡄⢼⠀⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠿⣾⡷⣻⢽⣿⣷⠆⠀⣀⠀⠀⠀⠀⠀⢹⡟⠫⠁⡤⡾⠀⠈⠒⠞⣛⣡⣭⢵⣫⠛⢿⣶⣬⣵⣪⠝⣊⠃⠄⣠⢶⠞⢉⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡫⣳⣼⣾⠿⠿⠿⠀⢝⢈⠁⠀⠀⠀⠀⠀⠠⠄⢂⠳⡹⠄⠀⢀⠉⣉⣩⣭⣯⣭⣥⣤⣤⣁⣛⡻⢿⣶⣭⡚⢌⡂⠀⠀⣉⣄⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⣿⣿⡆⠀⢄⡀⠀⠡⡱⣠⣀⡐⠁⠀⣀⡀⠤⢈⣹⡶⠭⣒⠛⣛⢭⢉⣩⠭⣝⣛⣛⣛⣿⠿⢷⣮⣿⡻⣷⣮⣓⢤⠉⠙⣸
⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁⠀⠀⡜⠁⠒⣦⣤⣤⣤⣴⡖⠒⠋⠉⠉⠀⣴⡟⢱⣿⡏⡑⢉⠊⠋⠀⠘⠉⠁⠁⠛⠉⠙⣩⣿⣿⣽⣿⣷⡝⣠⠁
⠀⠀⣴⠻⢏⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠠⠀⠀⠉⠕⡠⢢⡎⠀⠀⡀⠨⠘⢁⢰⠟⡅⡸⡁⡔⠀⣆⠀⢰⣅⠀⠒⢒⠠⣄⡀⠉⠫⣿⣯⡺⣿⣮⣧
⠈⠉⠛⢑⣟⢇⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡚⠀⠀⠅⠀⠀⠀⠀⠃⢺⡀⠀⠈⠀⠀⠄⠆⠊⠸⣧⠃⠃⢇⠀⠈⠁⠈⢷⠃⠀⠀⠀⠈⢿⣶⡀⠈⢻⣿⣎⢿⣿
⠀⠀⠀⡛⠆⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡐⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⣁⠘⠀⠀⠈⠐⠀⡀⠀⠘⡀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠦⠀⠱⡻⣮⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠙⣿⣿