⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠒⠒⠒⠒⠶⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠈⠉⠉⠽⠿⣲⣶⢬⣉⣛⣓⣶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣞⡋⠉⠁⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⠿⠁⠀⢀⡶⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡉⠛⠶⢄⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⢞⡿⠃⠀⠀⠠⠴⠋⠁⠀⠀⠀⢠⣤⣴⣾⣿⣧⣤⣖⣒⠀⠈⣿⣻⢷⣤⣼⡆⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣞⣧⠞⠁⠀⠀⠀⠀⠀⣀⡀⢀⣴⣾⣽⣿⣾⣿⣿⣿⣿⣿⣭⣄⡀⠙⣿⡳⣯⣷⡇⠀⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⠏⡾⠃⠀⠀⣠⣴⣶⡿⢋⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣦⣤⣈⣽⣶⣎⣠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡟⡼⠁⠀⣠⣾⣿⠿⣯⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡍⠛⠛⠻⣷⣯⡭⣿⣛⡻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠇⠇⠀⣴⣿⡿⣣⣾⡁⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣿⣿⡇⢈⣿⣿⣷⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⣟⠀⢀⣨⠿⢋⣼⣿⣿⣧⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠹⣦⣀⣤⡴⠋⣿⢸⣿⡇⣸⣿⡿⠓⠂⠀⢶⣦⣀⠀⠀⠀⠀⠀⣠⣴⠶⠀⠐⠻⣿⣿⣇⢻⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣼⡿⢀⣙⣀⡦⣤⣤⣀⠀⠈⠻⣿⣶⣶⣶⣿⠟⠁⠀⣀⣤⣶⢶⣄⣉⠀⢿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⠁⣹⣰⣿⣿⣿⣷⣿⣿⣦⣤⢼⡿⠿⣿⣧⣤⣴⣿⣿⣾⣿⣿⣿⡤⣍⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢹⣄⠁⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⢷⣿⣿⣿⣿⣿⣿⠟⢹⣀⣀⣐⣟⣻⣿⣿⣿⣿⣿⣧⡾⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⡿⡿⣃⠀⣉⡛⠛⠻⢿⡿⣞⣵⡞⣻⣿⣜⣿⣮⡻⢿⡭⡟⢛⣛⣁⠀⣉⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣷⢭⣭⣈⣥⡶⠖⠀⠈⠛⣽⢻⣿⣿⣿⡘⣏⠋⠃⠀⠺⢶⣄⣩⣭⡵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡛⠲⣔⡆⢸⡃⣾⣿⢹⣿⣧⢘⡂⢰⣠⠖⢿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠙⠽⢾⣧⣹⡟⠈⠛⣋⣿⡷⠶⠃⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⡿⣿⣤⣀⣬⣀⡈⢁⠀⡀⠀⣀⣀⢠⣴⣿⣿⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣏⣀⣿⣿⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⡿⡟⣿⣾⣀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡾⠋⠓⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣽⣸⡈⡽⠉⣿⠙⡏⢩⣇⣧⡗⠉⠉⠉⠉⠈⠉⠓⠒⠒⠒⠒⠒⢒⣲⠖⠊⢹⠟⠋
⠀⠀⠀⣧⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣶⣿⠿⠿⢉⣙⣛⣛⣛⠻⠷⠶⠶⠶⠶⠾⠟⠋⣉⣠⠴⠋⠁⠀⠀
⠀⠀⠀⢹⣿⣿⠟⠛⠛⠛⠛⠛⢻⣿⠛⡿⢻⣟⣟⢻⣿⣟⠉⡍⣽⣽⡟⢿⠉⣹⡟⠓⠒⠒⠒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠘⡈⠋⠛⢿⡟⠚⠛⠉⠈⠃⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠙⠰⠆⣴⠀⡴⢰⠀⠃⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣄⣠⣽⢤⣧⣄⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡀⢀⣀⣀⣀⣀⡀⠀⠀⣤⢠⣤⣤⣀⡄⣠⠠⣄⣀⣠⣤⣠⣠⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠛⠛⠛⠋⠋⠀⠀⠚⠒⠋⠚⠋⠋⠙⠓⠛⠛⠛⠋⠛⠛⠋⠀⠀⠀⠀⠀⠀