⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢱⢈⢉⢶⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠘⡏⢸⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢰⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢷⢦⠉⠲⢄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⡆⢠⡈⠙⠲⢄⠀⠀⠀⠀⠀⠀⢏⡸⣤⡑⢄⠀⠑⢤⣽⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣇⠀⡿⢿⣶⣄⡑⢄⡀⠀⠀⠀⠀⠙⢮⢻⡀⠑⢄⠀⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣤⣼⣿⠀⣰⣾⡏⠛⢿⣦⣕⢤⡀⠀⠀⠀⠀⢻⣷⣄⠀⢣⡀⠀⢿⢷⡄⠀⠀⠀⠀⢰⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣴⡜⣿⢿⡆⢹⡏⠀⠀⠀⠉⠈⢳⡈⠲⣄⠀⠀⠈⣿⠻⣦⡀⣇⠀⠈⢏⠻⡀⠀⠀⢀⡟⢸⠀⠀⠀⠀⠀⠀⣰⢾⠏⠀⠀⠀⢀⣴⡟⠀⠀⠀
⠀⠈⠁⢹⡎⢷⣀⢧⡀⠀⠀⠀⠀⠀⠙⢆⠈⢧⠀⠀⠸⡄⠹⡷⡜⢦⡀⠈⢢⠙⡄⠀⡞⡄⣎⡀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⡙⢧⡙⠢⣀⠀⠀⠀⠀⠈⢣⡀⢧⠀⠀⢣⢣⠙⡜⢆⢷⠀⢸⠇⡇⡸⢱⢱⢻⣳⠀⠀⠀⠀⠀⠀⠀⡠⢞⡵⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠻⣶⣬⣳⣌⠓⣄⠀⠀⠀⠘⡆⠘⣆⠀⠸⡜⣧⠘⣼⠘⣓⣩⠤⠟⠃⠛⠺⢤⣧⣳⠀⠘⣷⡤⢖⢉⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠈⠻⢿⣟⣿⣾⣧⠀⠀⠀⠈⠢⣈⣳⢤⡇⠿⠇⢈⡉⠁⣀⣤⠤⠶⠤⠤⢀⡈⡇⣴⢶⣭⠞⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⠇⠀⢀⣽⣟⣿⠊⠑⠢⢄⡀⠀⢈⡷⠋⣁⣴⠊⠁⠈⠛⢟⠯⣗⣦⣄⣀⠀⠙⢿⠇⣤⠈⢻⡤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠻⡿⣿⣷⣄⠸⣦⣄⠟⠉⢀⠜⠫⠈⠙⠦⣄⣀⠈⠳⡀⠉⠙⠢⢍⣒⠪⠷⣿⣇⠀⢻⣄⣲⣾⣆⣰⠽⠦⠼⠛⠓⠉
⠀⠀⠀⠈⠓⢿⣶⡤⣀⠀⠀⢹⡹⡀⠙⢿⠾⠁⢀⣾⡇⠀⢀⣄⢀⡰⠃⠀⠉⠙⠚⠀⠀⠀⠀⠀⠉⠒⢬⣿⣷⡼⢃⡤⠤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠛⢦⡉⢓⠮⢵⣹⣤⠏⢀⣴⠋⡿⣄⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣄⠉⠓⢮⡛⢩⣿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡮⡳⣤⡸⠃⢀⣿⠁⠀⠉⠰⡻⣦⡀⠘⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠙⢦⡀⢨⠛⢧⢠⣤⠤⠤⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣼⠚⠀⣼⡏⠘⡄⠀⠀⠀⠙⣎⠙⢫⡅⠒⠛⠇⠀⣀⡤⣤⡀⢀⡠⢾⡏⡰⠉⠙⣲⠻⣇⢧⣸⠀⢻⠫⣈⠉⠉⠀
⠀⠀⠀⢀⣀⣀⠤⠤⠖⢒⣉⣼⠀⢠⠃⠹⣦⣣⠀⠀⠀⠀⠸⣆⠀⠙⠦⣴⡖⠉⠁⠰⠃⠛⠋⠀⠀⣘⠀⠀⢸⣿⠀⢹⡓⣽⢄⣿⡖⠒⠻⠀⠀
⠶⠚⠛⠛⠛⠛⠒⢢⣄⠺⡋⡞⢀⣾⣶⠀⠹⡏⡆⠀⠀⠀⠀⢹⣿⣦⡀⠈⢻⣶⣦⡄⣰⣦⡀⢀⡼⠁⠀⠀⠘⢻⣄⠀⢳⠈⣷⣾⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣂⠽⣇⣸⣸⣿⣧⡀⢳⡸⣬⣧⡀⠀⠀⢳⡻⡇⠀⢀⠙⣦⡀⣽⠉⣻⢹⣗⣤⣤⣤⣤⣼⢠⢣⠉⣿⣿⢿⢣⣶⣦⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣫⣟⠋⢹⡯⠸⡟⠻⣦⠀⠹⡍⢻⡄⠀⠻⣿⣂⠒⠢⠷⣮⣷⣙⣤⣯⠉⠻⣤⠯⢿⣽⣇⠀⠁⠱⣼⣿⡟⠀⠉⠋⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⡅⠀⠈⠻⢀⠀⠀⠀⢷⡤⠁⠈⡏⠻⣦⣀⠉⢳⣄⡀⠀⠾⠉⠙⡷⠟⠆⠉⠀⠈⣸⣿⣼⣦⡀⠈⢯⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⢣⡀⣷⣀⠐⡖⠤⡀⠀⠉⠀⠀⠈⢠⠈⠙⢿⣄⢻⣿⠶⣤⣶⣖⣻⣦⠀⠀⠀⠀⣿⣿⡟⢿⣿⣦⡘⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠸⣼⠁⢀⣇⣼⠀⣄⢀⠀⠘⣇⠀⢸⠈⢎⣆⠀⠀⠀⠀⠈⠿⢿⣶⠒⠶⠞⠉⠀⠈⠉⠈⡷⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠸⠋⠈⣦⣿⣏⠀⡠⣹⡆⢻⢀⣬⣯⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠷⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡿⠛⣿⡇⣇⠻⡘⡌⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⣼⣿⣿⣦⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀