⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⣀⣤⠿⠿⠟⣉⣛⣟⣛⣷⡒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣠⠞⣱⠋⢀⣤⡺⠿⣿⢟⣿⡧⣯⣻⣽⣿⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⣰⡊⣡⠞⢁⣴⣿⢛⣓⡾⣿⡟⣧⡀⢸⣿⡟⣾⣧⣺⡛⣿⣖⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⠐⢚⡧⠞⠁⣰⣿⡿⢫⣿⢏⣾⣿⣧⣎⣟⣼⠿⠿⠟⢋⣄⣳⢰⢿⡀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢛⣿⣿⠉⠀⠀⣼⡿⣼⣧⣿⣧⡟⣿⡁⠀⠹⠋⠙⣆⣴⣾⡿⠟⠉⢿⡇⡇⠀⠀⠛⢻⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢵⡂⢀⣿⡿⣽⣿⣿⢿⠏⢰⡟⣧⡄⢀⡆⣰⣿⡄⣠⣴⣾⡟⢛⡇⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡏⠀⢸⡟⣼⣿⠋⣾⣯⣄⣸⢧⣿⡟⣾⢽⣿⡇⢹⣿⣿⣄⣇⠀⢷⢸⠆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣾⠁⡎⢸⣹⣿⠃⢐⣿⠀⠀⣿⣸⠀⠃⠃⡾⣿⣀⠸⣿⣿⡏⡿⢠⠸⡌⣇⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⣸⣿⢸⠀⣷⢸⣿⠃⠀⠸⣿⡀⠀⣿⣿⠀⠀⣸⣷⠃⠉⢹⡏⣿⢇⡇⠀⠀⢹⣼⣷⡄⢰⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣧⣰⣿⣿⢸⡄⢸⣼⣷⡶⠶⢶⣤⡈⠂⣿⣿⣤⢠⣿⠃⠀⠀⢸⠁⢸⣼⡿⠁⡀⣸⣾⡿⢯⣼⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡤⠴⠶⠿⣻⣿⣿⣿⣿⠁⡿⢸⢸⣇⠀⢿⣷⡀⠀⠀⠈⠙⠀⠘⠻⣿⡿⢉⣉⣉⣠⠇⠀⢸⣿⠁⢠⢇⡏⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣹⣿⡇⣰⣿⠸⣿⡿⣆⢈⢯⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢷⣄⡼⡋⠀⡼⣸⢻⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣫⣯⡿⣟⣷⡸⣿⣿⢻⣷⣿⣿⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢁⣼⣱⠏⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡞⠁⢸⡾⠀⣿⣿⡄⣿⣿⢸⣿⣿⣌⠻⠯⠛⠂⠘⠒⠒⠤⣀⣀⠀⠀⠀⣠⣾⠟⠁⣠⢞⣼⢿⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢺⡇⠀⢹⣿⣳⢷⢸⣿⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠼⠋⣠⡼⣿⡾⣿⣾⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢿⣿⣼⣾⣿⡿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠐⢿⣧⣶⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣬⣿⣿⣿⣟⢱⡿⠛⠉⡸⠀⠈⠓⠦⠤⠤⣶⢶⣿⡏⢹⣿⣿⢏⣿⢿⣿⣿⣿⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣤⣇⠀⠀⠀⠀⠀⠀⣏⡀⠻⣿⣼⡿⣿⣾⣣⣿⣿⣿⣿⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠚⣿⣿⣿⣿⣅⡤⠿⠿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣈⣷⣷⣿⣻⣿⣿⣿⠿⠁⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠖⠛⠉⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣬⠿⢧⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⠿⣯⣤⣤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⣿⡇⠠⠍⠀⠀⠰⣿⣶⣾⡧⠀⠀⢀⣠⣿⣿⣿⣿⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣿⣇⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⠀⢸⢿⣿⣿⠟⠃⠀⢀⣿⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣾⣿⠁⠀⠀⣀⣾⡟⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⣿⡿⡄⠀⡿⡷⠋⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡸⠃⠸⡄⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣧⢿⠋⢧⣄⡀⠀⠀⠀⠀⠀⠀⡼⠁⣿⣿⣿⡇⠀⡇⣿⡀⠀⠀⠀⠀⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡿⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢸⠘⣿⣽⣾⣇⠈⠻⣿⣷⣦⣴⣶⣿⠟⠁⠀⣿⡟⣿⣇⣼⡝⠀⢣⠀⠀⠀⠀⠸⡆⣝⠷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢸⠀⠈⠻⢿⣿⣦⣤⣿⣿⣿⣿⣿⣁⡀⠀⠀⣿⣿⣿⠿⠋⠀⠀⠈⡆⠀⠀⠀⠀⢧⡞⠀⢺⣆⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡟⠀⠀⠀⠀⢸⢧⡀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠁⠀⢨⣶⣾⡍⠛⠿⠟⢻⣿⣿⣿⢄⠀⣀⠖⢆⢱⠀⠀⠀⠀⣼⠁⠀⠀⠻⣧⡀⠀⠀⠀⠀
⠀⠀⣸⠃⠀⠀⠀⠀⢸⠀⢻⣆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠸⠟⠉⣁⣨⢟⣫⣵⡋⠉⢸⠀⠀⠀⢀⣏⠂⠀⠀⠀⠈⢷⡄⠀⠀⠀
⢀⣀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢻⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⢷⡔⠉⠈⠳⣯⡗⢸⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀
⢸⣿⣾⣷⠀⠀⠀⠀⢸⠀⠀⠀⠻⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢾⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⡀
⢸⣿⢥⡏⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣧⣀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇