⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠛⢻⡑⣓⡋⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣼⣿⡆⡝⢿⣿⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣷⡤⢿⣠⡿⠤⠞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢟⡤⠴⠋⠀⠀⠀⠈⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀⡀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡜⢦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢾⡇⠀⠀⠉⠙⠢⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⡠⠔⠂⠀⠀⢤⢖⡾⠃⠀⡆⠀⠀⠀⠹⣆⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡘⣇⠀⠀⠀⠀⠀⠙⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⢀⡠⣖⠵⠊⠀⠀⢠⠇⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⡆⠑⢾⣽⠆⠀⠀⠠⡀⣳⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣂⣭⠔⠚⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⡄⠀⠙⠢⣄⠀⠀⢸⣏⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠀⠀⣀⣠⠔⠂⢀⡴⠃⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⣼⣿⣿⣆⠀⡄⠀⠀⠹⡄⠀⠀⠀⠙⠒⠡⢼⡀⠀⠀
⠀⠀⠀⢀⣼⣿⣭⣴⣶⣶⣾⡟⠉⠁⠀⣀⠴⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⢁⠏⠉⠻⣾⣿⣄⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⣾⣿⣿⠻⠩⠍⣻⢿⣷⣶⣶⣾⣿⣦⣄⣀⣀⣠⣴⣾⣿⣿⠿⢋⡠⠤⣦⡷⠂⢐⠲⠬⢉⡻⣷⡄⠀⠀⠀⣀⢤⣤⢴⡶⡤⣀⢳

⠀⠀⠠⢋⠞⠘⢆⠀⠀⢹⠒⠒⢌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡭⠤⢏⠤⠭⣏⣠⣴⣨⡶⠂⠈⠁⠀⢹⣷⢦⠞⠁⠈⢯⠟⣰⡇⠈⢾
⠀⠀⠀⡜⠀⠀⠀⠑⢤⡀⠀⠀⠀⢩⠟⠛⠛⠛⠛⢟⡻⠏⠈⠈⠙⠒⠦⣀⠀⣇⠀⠀⢀⣧⣀⣀⠀⠀⢸⣿⣆⠀⠀⠀⠀⡰⠃⣧⠀⠘
⠀⠀⢀⠃⠀⠀⠀⠀⢀⣨⠝⠒⠚⠉⠉⠉⠉⠙⡲⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡶⠚⠁⠀⠀⠀⠈⠙⠢⣿⢧⣕⣢⣤⣾⣴⡿⠃⠀⠀
⠀⢀⠎⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⠛⢿⠋⠀⠀⠀⠀

⢠⠏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠳⡀⠀⠀⠀
⢸⣷⡶⠞⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣼⢳⠀⠀⠀
⠘⣿⠀⠀⠀⠻⠦⢤⣤⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣿⠟⠈⡇⠀⠀
⠀⠈⣆⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⠻⣿⣿⣿⣷⣄⠀⠻⡆⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠝⠛⣇⠀⡴⠃⠀⠀
⠀⠀⠙⣦⣿⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⠪⣛⢿⣷⣤⣀⠀⠀⢀⣀⣠⣶⣿⣿⣿⣧⣀⡀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⡸⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠻⣦⣿⣀⡀⠀⠀⠀⠀⠀⠀⢀⢈⡑⠬⣛⠿⣿⣿⣿⣿⠿⠟⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⠴⠊⠀

⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠤⠀⠀⠀⠀⠸⢾⡇⠀⠀⠉⢢⡠⠤⠙⡀⠀⠀⢠⠋⠀⠉⠻⡭⠽⠓⢸⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡰⠋⠀⠀⢠⠁⠀⠀⠸⡀⠀⠀⠀⠸⡄⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢰⠃⠀⠀⡴⠁⠀⠀⠀⠀⠱⡀⠀⠀⠀⢡⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠜⠁⢠⠇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠣⡀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⡠⠊⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⢢⣄⠀⣈⣣⠀⠀⠀⠀⠀⠀⠀