⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳⠀⢠⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠪⢻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠈⣆⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢋⡐⢠⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⢧⠀⠸⡄⠀⠀⢻⡄⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⢀⠞⢠⠏⠀⣼⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⢮⠀⠀⢳⣤⠤⠼⡗⠉⠉⠉⠉⢷⡆⢀⠴⠋⠀⠀⠀⢀⡴⠃⡰⠃⠀⣸⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢤⠗⢄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢧⣠⠀⠀⠀⣠⠎⣠⠞⠁⠀⣲⠏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣈⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡇⡤⠚⠀⣀⡴⠃⢠⣴⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠃⣀⡔⢊⣙⡢⡄⠀⠀⠀⠀⢀⣀⣀⠀⠸⡇⠀⢻⠅⠀⣤⠞⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠉⠁⢠⣿⣿⡏⢣⣀⣤⣀⡀⣫⣯⡈⠳⡀⠸⡾⢋⣰⠞⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⠈⠛⠋⠀⠀⢈⡟⠉⠁⢿⣿⣿⠀⠑⠀⢹⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡕⣄⡀⠀⠀⠀⠀⠸⢿⡿⠂⠀⠀⣉⠁⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠹⢦⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡷⠀⠀⠀⠀⠀⣶⣦⣶⠾⠟⠉⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢿⠁⠀⠀⠀⠀⠀⠀⠈⢟⢿⣇⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⣾⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⠈⠸⣿⡀⠀⠀⠀⢀⣼⠃⢀⡾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣶⠟⣀⣸⣦⠀⠀⢈⡳⣄⢀⣰⠛⠁⢀⣼⣃⣀⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣤⠶⠖⠛⠋⠉⢀⡼⠋⠉⠁⠈⢿⣮⠀⠀⠀⢸⡏⠁⠀⠀⢸⠏⠀⠀⠉⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠸⡇⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠢⠬⣧⠠⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀
⣾⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⠻⣦⠀⠀⠀⠀⠀⢠⣄⣨⣇⠀⠀⡿⠀⠀⡇⣠⠆⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠉⢲⣶⢿⡉⢯⣩⣽⡿⡀⢀⣧⡀⢘⣏⡜⢩⠍⢉⣥⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠉⠛⢾⡓⠛⠙⠛⠋⠈⠛⠛⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠻⣆⠀⠀⠀⠀⠀⣀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠓⢤⣀⠀⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠒⠚⠷⠒⠒⠚⠛⠒⠒⠒⠤⣄⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀