⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢥⡀⠐⠒⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⢿⡆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⣦⠀⠀⠀⠉⣢⠀⠀⠀⠀⢸⠃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⢀⠇⠀⠀⠀⢴⣁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⢆⠀⠀⠀⠀⠙⣿⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣤⣀⠀⠈⠢⢤⣤⠶⡒⠋⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡏⠀⠀⠀⠉⠀⠙⠲⢤⡀⠀⠀⠉⡲⣤⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⠖⠂⠀⠀⣤⣀⣄⣀⠀⠈⣷⢤⢰⠿⢿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠀⠀⠀⠀⢠⣹⣷⠣⡼⢃⠀⠸⣯⠎⢉⣹⠷⣄⠀⠀⠀
⠛⠻⢭⣍⡑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡒⠁⠀⠀⠀⠀⠸⡕⢝⣦⡥⠛⣃⠀⠈⠉⠘⠫⠽⠙⢆⠀
⠀⠀⠀⠙⢿⣢⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠷⠂⠀⠀⠀⠀⠉⠀⠈⠳⠾⠇⠀⠀⠀⠀⠰⠦⠀⠐⡟⠀
⠀⠀⠀⠀⠀⢧⢣⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠐⠓⢲⠶⣖⣦⣄⠀⠚⠛⢴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢀⠤⠶⣿⣦⣀⠁⠙⢿⣶⣦⣤⣉⣙⡟⠲⠦⢤⠤⠴⢶⣻
⠀⠀⠀⠀⠀⠸⡇⢇⠀⠀⠀⠱⡀⠀⠀⠀⢰⡇⠒⢄⠈⢿⣿⠆⠠⠤⠬⠝⠻⡟⢻⠉⠉⠓⠒⠒⠚⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⠘⡄⠀⠀⠀⠱⡀⠀⠀⣸⡑⠊⠁⢀⣼⡷⠁⠀⠀⠀⠀⠀⡇⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡆⠈⠢⣀⡀⠀⣨⣴⣶⣿⠁⡔⠚⣿⢹⠓⢄⣤⠒⠀⢻⣾⡃⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢀⣿⣿⢻⢻⡃⠘⠓⠴⣿⠃⢠⣋⣘⣴⡶⣞⣷⠁⢠⠔⣩⠟⠦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡀⢸⣿⡟⣿⢸⡇⠀⣀⠠⠬⣆⠀⠀⠀⡟⣤⡏⡿⠷⣁⠞⠁⠀⠀⠈⢆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣾⡣⠊⣡⠔⠒⠓⡳⡀⠀⢉⠿⠀⡧⠊⠉⢢⢀⠖⠲⢠⣤⣣⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣧⠞⠁⢀⠠⣄⠈⠙⢤⠟⠒⡰⠀⠀⠀⠀⢾⣢⣴⢌⡛⣧⡄⠑⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢏⢆⢴⣁⢸⣍⠲⠀⠀⢱⣔⠉⠲⢄⡀⠀⢸⣿⣟⣲⣏⡬⣿⢦⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠱⡜⣶⣿⠟⠉⠀⠀⠀⠀⡜⠙⢗⠒⠀⢈⡭⠟⢧⢈⠹⡽⡀⠈⡆⠹⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⡈⠾⣳⡀⣀⠀⢠⠒⢾⡷⡀⠈⣶⣾⣅⣀⡀⠀⠻⣆⠰⡘⢷⢰⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠿⣶⣷⣽⠁⠙⣿⡀⠈⢟⢶⡄⢸⠋⡹⢷⡋⠐⢄⠈⠓⠷⠀⠻⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠟⠳⣦⣤⣤⣾⠁⠙⡆⠀⠸⢷⡄⠘⡦⣿⣄⣀⡧⡀⠘⢤⠤⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⡀⢀⠴⠿⠗⠊⠋⢉⣶⣜⢆⠀⢇⠙⢦⡇⠀⠉⠉⠁⠐⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢸⠀⠀⣠⡖⣤⡟⡆⠈⢊⠓⣼⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣵⣾⠇⡅⠈⡗⠮⢂⡬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠵⣦⣸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀