⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠤⠶⠖⠉⠁⠴⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢽⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⣶⠀⢀⡏⢻⣆⠀⠀⠀⠀⢸⠀⠀⠀⠘⡆⠀⠀⠀⣀⣉⡲⣄⠀⠀⠀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠃⡇⠀⠀⠀⠀⠀⠀⢸⡆⢸⠇⠀⠻⣆⠀⠀⠀⢸⠀⠀⠀⠀⢿⠀⠀⠀⡿⠉⠉⠉⠛⠀⠀
⠀⠀⣠⠞⠁⠀⢀⡀⠀⠀⠀⠀⠀⠘⣿⣀⣠⣤⣟⣀⣀⢹⠀⠀⠀⠀⠀⠀⣼⣇⡏⠀⣀⣀⣽⡦⠤⣀⣏⠀⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀
⠐⠚⠓⠒⠚⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠏⠀⠀⠉⠙⣷⣤⡀⠀⢀⡾⢻⡿⠗⠋⠉⠁⠀⢱⡀⢸⡏⠀⠀⠀⠀⠀⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⣿⣠⣿⣤⣤⣤⣔⡒⢺⡀⠈⣠⠎⠀⡾⠁⠀⢐⣪⣯⣥⣼⣿⡟⡇⠀⠀⠀⠀⣦⣸⡀⢸⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⡸⢹⡀⠀⠀⢸⣷⠿⠉⢸⣿⣿⣿⡟⠃⣧⡴⠃⠀⠀⠀⠀⠀⢋⣿⣿⣿⣿⠊⢹⣇⠀⠀⢀⡆⣿⠙⢧⡘⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⠏⠀⢠⠇⢀⣧⠀⠀⠸⣿⣄⠀⢸⣿⠿⢹⡏⠀⠛⠁⠀⠀⠀⠀⠀⠀⢸⣿⢿⣽⡇⠀⢸⡟⠗⢀⣾⠀⢿⢸⣦⠀⢹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡼⢀⣰⠟⣠⡟⢽⣧⠀⠀⢿⠈⠃⠈⠻⢥⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⠟⠁⠀⡏⠀⣠⣮⠞⣇⢸⣸⠁⠻⢼⡆⠀⠀⠀⠀⠀
⠀⠀⣠⡼⠗⠿⠛⠋⠉⣇⣼⣿⣷⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⣾⣿⣿⣦⣹⣿⡇⠀⠀⠀⠣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣷⣷⢆⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⣸⣿⣿⡿⠻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢽⣯⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠟⣿⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⣧⣀⠙⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣼⠿⣟⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⣞⡿⠋⢹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠙⡆⢹⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⢿⡝⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢳⣽⡇⠉⡓⠦⣄⡀⣀⣤⠖⠉⢹⣸⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡿⡇⣧⡑⣶⣶⡾⠟⠁⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⠇⠘⣗⠚⠋⠀⠀⠀⠀⠀⢸⢿⣷⢦⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢲⡞⠹⣿⠁⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠃⢉⠷⣌⠉⠛⠶⣖⣒⠒⠲⠤⢤⣤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⠤⠔⠒⠊⠉⢡⡞⠀⢸⠳⡄⠈⠳⣄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⣎⣀⠈⢷⡀⣠⣤⣬⣴⡂⠀⠀⠀⠀⠙⣆⠀⠀⠀
⠀⠀⣠⠞⣏⠀⠀⠀⠀⠀⢀⣰⠏⠐⠒⠺⠰⠞⠲⣀⠈⠳⣄⠀⠈⣧⠀⠀⠀⠀⢀⡼⠁⢠⠏⠀⠀⠉⠉⠓⡄⠀⠀⠀⠀⠀⠠⢄⡀⠀⠈⢧⠀⠀
⠀⢰⡇⠀⠈⢧⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠓⢄⡈⠀⠀⢀⡰⠋⢀⣴⠃⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠰⠁⢀⠀⠈⢧⠀