⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢻⣷⡜⠣⠻⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠀⠀⠐⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠹⣿⣶⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⣴⠅⠀⠀⠀⣠⠀⠀⠀⠀⠀⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠡⡹⡌⣷⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⡟⠀⠀⠀⢸⠏⠀⠀⢀⣄⢎⣿⣿⡿⠀⠀⠀⠀⠀⢷⣶⡆⠀⠀⠀⠈⠀⠀⢡⠱⢹⣧⠸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡚⠋⠙⠁⠀⠀⠀⠄⠀⠘⡟⡇⠀⠀⠀⠀⠇⠀⠀⠇⠃⣿⠀⡇⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣇⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣇⠀⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⡿⢐⢘⣻⢟⠐⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⢸⠀⣿⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢈⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣾⣿⡄⠀⠁⢰⠇⢰⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣗⠁⠿⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠀⡇⠈⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣦⢰⡤⠁⠶⣿⣦⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠐⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⣭⡻⢿⡃⠼⣿⡏⣶⠟⠻⠛⢦⡁⢈⠀⢀⢸⠲⢏⡀⣤⡀⠴⣷⡶⠖⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠐⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢤⠀⢸⣿⣿⢿⣟⣹⣿⣾⣿⣿⣶⡾⢋⣵⠀⢀⣤⣌⠀⠙⢦⣢⡀⠹⣿⣿⣿⣿⣯⣴⣶⣿⣿⣷⣶⣶⣯⡅⠀⠀⠀⠀⠀⡇⠀⠀⠀⡁⣛⢎⢄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢼⠀⠸⣿⣿⠀⢻⣿⣿⣿⣿⡏⢙⡵⠿⣷⠀⠸⣿⣟⣿⡄⢦⡁⠈⠥⠣⢬⠭⢽⣥⣾⠟⠛⠛⠛⠻⠿⢿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⢷⠑⠋⠡⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⠀⠈⢷⣶⣤⣽⣿⣿⢿⠿⣘⣛⣭⣬⡀⠀⠙⠻⠿⠃⠚⡠⠐⠦⠾⠄⣴⣆⡏⣁⡀⠀⠀⣠⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢢⠭⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠙⣿⣿⣿⣿⡿⡈⡍⠉⠭⣍⠙⠂⡠⠐⡎⡁⢈⠋⠈⢻⣦⠻⣿⣿⣹⣬⣭⣭⣭⣤⡞⢻⠃⠀⠀⠀⠀⠀⢀⠈⢀⣤⡦⠂⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣄⠀⠀⠀⠘⢿⣿⣿⠓⢹⣆⡀⠀⣌⣷⡽⣎⢃⢈⣄⠆⠀⢤⣂⠘⣽⣦⣌⣛⣿⣪⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⣰⡿⠁⠸⠋⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⣷⣶⣦⣤⣤⣉⠋⢹⣠⠹⣿⣦⣍⠿⢇⣿⢦⢻⣿⡈⣿⣤⣷⣿⣤⣉⠻⠿⢿⣿⣿⣿⠿⢛⠕⠀⠀⠀⠀⣸⡏⣴⠀⠀⠀⠀⠀⡜⠆⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢻⣿⣿⣿⣟⡻⠿⣿⣿⡿⣰⡄⡲⣴⣦⡘⠻⠿⣦⣄⠐⣻⣟⣼⣿⡛⠿⠿⣿⣿⣿⣦⣄⣤⣶⣾⡿⠃⠀⠀⠀⠀⣼⡟⢰⡇⠀⠀⠀⠀⠀⢉⠞⠈⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠷⠾⢭⡁⣿⣇⢻⣮⠻⣿⣆⢠⡈⢍⡑⠈⢛⡿⠿⠿⠶⣾⣿⣿⣿⣿⠿⢛⡭⠈⠀⠀⠀⠀⠀⣼⣿⠇⢸⠁⠀⠀⠀⠀⠀⢸⡀⡣⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣤⣀⠀⠀⢿⣿⡘⣿⣧⠘⢿⣷⡙⢁⠀⢶⣶⣬⣭⣭⣿⣿⣟⣛⣩⣴⣿⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⠂⡿⠀⠀⠀⠀⠀⠀⠘⢁⠉⠀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⠸⣿⣷⡘⢿⡇⠈⠻⣿⣆⡙⢾⣿⣿⣯⣉⣉⣩⣽⣿⣿⡿⠃⠀⠀⢀⣠⣾⣿⣿⣿⣿⢋⠀⠃⠀⠀⠀⠀⠀⠀⠄⢲⢀⠀⠠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣝⢿⣿⡌⠻⠀⢠⢻⣿⣿⣶⣭⡛⠿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣥⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠌⠁⣀⢤⠀⠀⠀
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣹⡇⣧⠀⠀⣦⣹⠿⢿⣿⣿⣿⣦⣌⡛⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⢐⠠⡀⠀⠀⠀⠀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⣾⣿⣿⡿⠇⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠚⠟⠃⠤⠀⠐⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡆⠀⠀⣿⣿⣿⣷⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⣿⣿⣿⣿⣷⣦⡁⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠇⠐⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠠⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣫⣴⡇⠀⡇⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢘⠐
⠀⠀⠀⠀⠀⠐⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢰⣿⣿⣿⡇⠀⡇⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿