⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠋⠉⠉⣠⠀⠊⠁⢄⡀⠀⠈⠉⠙⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠈⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢈⠉⠙⣦⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢈⠉⠀⠀⠈⠀⠘⣤⡃⠀⢀⠓⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣔⠈⠁⢈⠀⢸⠀⠀⢋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢀⠀⠀⣍⢀⠒⠀⣠⠀⣼⢣⣾⠀⠀⠀⠀⢀⠀⠀⢀⢇⠀⠀⠀⣀⠤⠆⠀⠀⠈⢀⠀⠈⠙⠃⣌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⠀⢠⠀⠀⣠⣤⣀⣴⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⢸⢸⢀⣠⠀⠀⢀⣀⠓⠀⠂⠀⢻⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⢠⣦⢤⣄⣀⣞⢀⡇⣦⢇⢊⢓⣆⢀⠀⠀⢠⠀⣖⠀⣿⢻⣀⠀⢸⢀⣀⣠⣠⡀⠀⢀⠀⠀⣖⢒⣾⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣸⠑⢓⢣⢋⣰⣇⢂⣎⢋⣇⢀⢀⢀⢸⢀⢸⢀⣯⠈⢻⣆⡇⢇⢦⢦⢂⢣⣀⣈⣀⣠⢃⣏⢀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢒⠖⢊⣫⠁⠀⠀⢀⢀⢃⠘⣄⣛⠀⣇⢀⢀⢀⢸⢀⢀⢧⢻⢀⢀⠈⡇⢀⣏⢸⢘⢫⢤⢦⠆⢻⢀⠈⣆⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣡⣄⢀⢇⡀⠀⠀⠀⣸⣶⢿⢟⣷⣬⢹⢰⣆⢀⢸⢀⡟⠀⣫⣤⣦⣦⣶⣁⢻⣾⢀⠀⠀⠀⠀⠀⣆⢂⠈⢦⠀⠀⠀⢢⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢸⢀⣇⢀⠀⢐⣿⠀⣼⣿⣯⣿⣄⢣⠈⢦⢀⡞⠀⠀⣠⣻⣿⣯⣷⡛⣿⣏⢀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠙⢤⣀⠀⠀⠓⢤⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⣯⣎⢘⡀⣧⢢⢸⠀⣇⣧⢻⢣⡇⠀⠀⠀⠑⢧⠀⠀⣯⣧⢿⢏⣏⡏⣰⠋⠀⢀⢀⢀⣸⣶⠀⢧⢀⢈⣅⢀⠀⣆⠒⠒⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣯⢦⣺⣫⣀⢎⠃⢛⣆⣄⠈⢣⢦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣤⣼⠊⢠⠃⢀⢠⢂⢀⣰⢁⢀⢈⠁⠀⠀⠋⡓⠢⢤⢭⠆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢇⣤⣯⠉⠀⢀⣇⠀⢀⢀⢀⢀⠀⢀⣤⣤⣤⣄⠀⠀⢀⢀⢀⢀⣤⣁⣤⢖⢋⣠⢞⢀⣠⢢⢀⢂⢀⢀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠫⢁⣴⠋⠀⠀⠐⣫⠻⣀⠀⠀⠀⠀⠀⣯⢇⢁⢀⢨⠀⠀⠀⠀⢀⡔⠉⠀⢀⢹⡈⢣⠆⠋⣶⣤⢦⢳⣄⢣⠒⠢⠄⠊⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠲⣮⣫⣠⠊⣀⢀⠊⠓⢦⣄⢀⠀⠈⠃⠂⠢⠈⠀⠀⢀⡔⠁⠀⠀⢀⣦⢋⣀⠀⠀⠀⢰⣏⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⢯⣤⢀⣪⣤⣤⣶⣎⣏⣏⣿⣫⣟⣫⢏⣫⠋⠀⠀⢀⣠⢏⢒⢣⢻⣧⣦⣤⣧⠉⠉⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⢌⢧⣦⡎⣏⢫⡎⡟⢋⢚⠇⠗⠋⡓⣠⠒⣯⠋⠀⢣⣌⢂⢈⢫⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣯⢃⣯⠫⣗⢦⢀⠀⠀⠀⠀⠀⡟⠉⠉⠉⢉⣯⣖⢒⣎⢉⢪⠇⠈⠀⡎⠉⠀⠈⠀⠀⠀⠀⢀⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣏⣦⠀⠀⣰⢉⠀⠈⢋⣇⣿⣍⢫⢲⣤⣮⡇⠀⠀⠘⢷⢮⣢⢆⢢⣄⠎⠂⠂⠈⠁⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠑⠊⠓⢢⣄⢀⢀⠏⣸⠊⢧⣪⣯⢏⢳⣄⠀⠀⠀⢸⠄⢊⢀⡔⣆⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢦⣍⢀⣤⢫⣻⢦⣌⠂⢋⣷⠀⠘⣀⢪⢀⢤⠃⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣔⣦⣖⢶⣈⠀⠀⢃⡈⣇⣎⢳⡈⣈⢧⠀⣀⣨⠁⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢣⣆⢣⠈⠁⡆⣀⣀⢤⢧⠯⢷⣿⣿⣀⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠏⢾⣤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀