⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠈⢻⣆⠀⠀⠀⠀⠀⣰⠿⠋⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⡔⠲⣄⡠⢿⡆⠀⠀⢀⣼⠋⢈⠄⠠⣠⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢆⠀⠀⠀⢸⣷⣀⣠⡾⢣⠞⠸⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡃⠀⠀⠀⠈⠢⣀⡴⠃⠘⠋⠉⠁⠀⠀⠀⠑⣄⢀⡴⠁⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠁⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢰⡦⠀⠀⠘⢿⠿⣓⣞⣹⡧⠤⠄⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣀⠀⢀⣀⣻⠿⠛⠀⠀⠀⠀⠰⠞⠛⠒⠀⠀⠀⠀⠉⠀⢸⣧⡴⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠹⣏⠫⠉⠉⣉⣹⣽⠙⠲⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⠃⠀⠀⠈⣿⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠶⠶⢶⣤⣴⢿⣧⡒⠄⣀⣼⠏⠉⠉⠉⣉⢹⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠋⠁⠀⠀⠀⢀⣿⡻⠁⠙⠛⠛⠛⠉⠀⠀⠀⠃⠈⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⠀⠀⠀⠀⠀⢀⣤⡿⠧⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠞⢻⣿⣷⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⡻⠛⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣃⢈⠻⣷⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠻⢟⡷⢾⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢃⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠇⠀⣀⣠⡴⠾⠛⢹⣇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣘⣒⣒⣒⣒⣂⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣷⠶⠟⠏⠉⠀⠀⠀⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡩⠹⡉⠁⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⢃⠷⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀
⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⢨⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠧⠤⠄⠀⠀⠀⠀⠠⠠⠤⠄⠀⠸⠼⠤⠤⠄⣿⠒⠊⠁⠀⠀⠀⠀⠀⠀⣿⠀
⢀⣰⠟⠁⠀⠀⠉⠛⠷⢦⣤⣤⠶⠋⢻⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡔⡀⠂⡐⢢⢠⡆⠀⠆⠀⠐⡆⣀⣤⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀
⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢹⣦⡘⠄⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⣷⢁⢱⠀⠘⢸⡇⠀⠀⠀⠐⣩⡠⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡠⠖⣿⠀
⠐⠘⣷⣄⠀⠀⠀⠀⠤⠔⠊⠀⠀⣠⣴⠟⠉⠻⣦⡀⠀⠀⠀⠀⠀⣾⣥⣸⡇⠀⠹⠁⠛⠀⠊⠸⠆⠐⠤⠆⠠⠃⠈⠪⠆⠀⣿⠀⢀⡠⠄⠒⠊⠁⠀⠀⣿⠀
⠀⠀⠀⠙⠳⢶⣤⣤⣤⣤⣴⠾⠛⠋⠀⠀⠇⠀⠘⣧⢀⠀⠀⠀⢰⡟⡌⢿⡇⡖⠛⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⣿⡌⠁⠀⠀⠀⠀⠀⣠⡾⠏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠸⣧⡑⠤⠄⢸⡇⠇⢸⡇⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣤⣶⠟⠋⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣤⡾⠃⠀⠈⠿⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣧⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀