⠀⠒⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠛⣧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣞⢆⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀
⠀⡀⠀⠀⠀⠄⠙⠓⠒⠒⠒⠒⡒⠁⠀⠑⢆⡄⡀⢽⠃⠀⠀⠀⠀⠀⠀
⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⣆⣾⠂⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⣀⣀⣄⣠⢄⡀⢀⣂⢠⡖⢛⣶⣤⡌⢦⡇⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⣶⣯⣿⣿⣿⡇⠁⠈⢻⣿⢰⣿⣿⣿⣧⢠⣧⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠈⢻⡛⠛⠛⠉⠁⠘⣆⠀⠀⠀⠀⠀
⡇⠀⠀⠀⡀⡀⠀⠀⢀⣀⠤⢦⣤⡤⢽⠿⠒⢀⡀⠀⢀⣹⠀⠀⠀⠀⠀
⣇⠀⠤⢼⠊⠐⣲⡿⢋⢽⣛⣓⠊⣳⣃⣨⠶⡂⠈⠀⢈⢼⡆⠀⠀⠀⠀
⣿⡀⢄⡈⠀⠈⠾⢀⡏⢘⠉⠙⠛⢻⠛⠁⠀⣃⠀⢀⣼⡏⠀⠀⠀⠀⠀
⣿⣷⡈⢳⡐⠂⠀⠈⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡒⡿⠉⠂⠀⢀⠀⠀⠀
⣿⢹⣷⠀⠉⠦⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠻⠲⠄
⠁⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⠀⠀⠀⠀⠀⠀⠀
⡇⡤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⠀⠀⠀⣰⢿⡾⢧⣾⣷⠖⠀⠀⠀⠀⠀⢀⣤⢔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⠀⠀⠀⣼⢧⣟⡴⣫⠟⠁⠀⠀⠀⠀⣠⢞⣫⠞⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⣼⢣⣿⣟⡿⠋⠀⠀⠀⠀⣴⢟⣵⡿⢛⣯⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣧⣰⡏⣿⣟⡾⠁⠀⠀⠀⣠⢞⡵⣻⣵⣾⠭⢔⣒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠛⣿⡟⠛⠛⢛⠷⠶⠚⠓⠛⠾⣅⠄⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⣤⡤⡤⣤⡄⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⣄⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⡟⠿⣽⣢⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⠧⢍⣻⣥⠀⢸⠋⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣘⠋⣿⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢈⠥⠈⣟⣿⠀⠀⢸⡵⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⣧⡤⠴⠒⠀⠘⣿⠀⠀⠀⠸⠛⠉⢩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡾⠒⢋⣀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠛⣻⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣀⣠⣴⣿⣿⣷⣄⠀⢀⣻⣦⣤⡤⢴⣦⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠻⢾⡿⣿⣿⣼⡝⢷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡴⠛⠁⠒⠊⠉⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⣀⣀⣠⣾⣧⣿⣥⡾⠃⠀⠙⠷⣄⠀⠀⠀⠀
⢀⣤⠞⠋⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣛⠒⠧⠇⡛⣛⣯⡭⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⢀⣈⣻⣦⡀⠀
⠛⠁⠀⠀⠀⠀⠀⠀⢠⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠀⠀
⡀⠀⠀⠀⠀⠀⣀⣀⣼⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠛⠛⠛⠛⠛⠛⠉⠁⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⣟⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢀⣼⠟⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠈⠪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻