⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣋⣿⣷⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠫⠉⠉⠈⠙⢻⡟⢿⣿⣯⣭⣭⣴⡶⠶⠶⢶⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⡶⠴⠖⢁⣀⣤⣀⡤⠀⠉⠛⢿⡆⠀⠀⠀⠀⠀⠉⠙⢷⣝⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣴⣶⠟⡿⡉⠙⠿⣦⣀⡀⢹⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⣼⠏⢀⣤⣾⡿⠋⣼⠋⠁⠀⠀⠬⢿⡿⢿⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣠⣾⡿⠁⣼⠏⠀⠀⣀⠠⠤⠴⢖⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡝⣧⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢠⣻⡿⠁⣼⠏⠀⠀⢱⡟⠋⠉⠉⠉⢀⡄⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠘⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢠⣏⡿⠁⣰⠃⠀⠀⢂⣾⠁⠀⠀⠀⣰⠟⠝⣠⡞⠁⠀⠀⠀⠀⠀⢠⠄⢠⡾⠁⢀⣾⠃⢼⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣾⠀⣾⠾⠁⢠⡟⠀⠀⠀⢸⠇⠀⠀⢀⠜⣡⠎⣴⠏⣠⠆⠀⡀⠀⠀⡐⠋⡰⠋⠀⣰⠟⠃⠀⢸⣿⣿⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣹⣾⢣⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⢫⡞⠁⠌⠁⠀⠋⠉⣼⡟⠛⠛⠛⠒⢚⡿⣶⣷⣶⣿⣿⣛⣧⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣿⠏⣠⣿⠁⢸⠁⠀⢸⠁⠀⠀⠀⡇⣀⠀⠀⠟⠁⠉⡀⠀⠀⠀⢀⣰⠾⣿⠁⠀⠀⢀⣠⣿⣾⣿⣾⣿⣟⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣶⠟⣣⣾⣿⣾⣿⣿⠀⢼⠀⣠⣾⠀⠀⠀⢀⣟⢿⣷⣦⣄⡀⠊⠀⠀⢀⣼⠏⠀⠀⠘⢷⣤⣠⣿⣿⡿⣵⡿⣿⢣⣿⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⣿⢉⣿⡟⠀⡈⠀⣷⠉⠀⢢⢸⢸⠟⢿⣿⣿⣿⣿⣶⣤⣴⠟⠀⠀⠀⠀⠀⣠⡿⢿⣿⣏⣴⣿⣾⣷⡿⣧⣿⣿⠋⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢸⣿⠇⢸⡇⢠⣽⠀⢰⢸⡈⣼⠀⠘⠿⠿⠿⣿⣿⣿⣧⠀⠀⢀⣴⣶⣾⣯⣶⡾⣿⣿⣿⣿⣧⣿⣵⣿⣿⠃⠀⠀⠀⠀
⡀⡀⠀⠀⠀⠀⢰⠀⣠⣾⣿⣾⣸⢿⠀⣼⡇⢸⣿⠀⣸⢸⡇⣿⠀⠀⠀⠀⠀⠈⠉⠓⢿⣦⣴⡿⢿⡿⠹⠿⠛⢇⣼⣿⣿⣿⣿⣰⣿⣿⡏⠀⠀⠀⠀⠀
⡇⠇⠀⠀⠀⠀⢸⣾⣿⠛⣻⣗⣧⣿⠀⣿⡗⠈⣿⠀⣿⢰⣇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣴⣴⣏⣴⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀
⡇⠁⠀⢸⠀⢠⣾⣿⣏⣰⠟⠻⣿⣿⣿⠿⢿⣦⣿⣤⣿⣼⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠻⢿⣿⣿⣿⣟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⢸⣴⣿⣿⣿⣿⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣤⡿⠿⠿⠦⢶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⣀⡙⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀
⠀⢰⠀⣼⣿⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢷⡄⠀⠀⠀⠀⠀⠀⠙⢿⣶⣌⢻⣿⣧⡀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⡐⠀⠸⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣭⢻⣿⣦⡀⠀⠀
⠀⢠⣿⣿⣿⣿⠏⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣁⣤⡻⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣿⣷⡄⠀
⠀⢸⣿⣿⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⣿⣹⣇⠁⢈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⡀
⠀⠈⠉⢿⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣍⣡⣻⡏⢸⣉⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⢀⣶⣆⢀⠔⠁⠀⣷
⠀⠀⠀⠀⠀⠚⣿⣿⣷⡄⠀⠀⢸
⠀⠀⠀⠀⠀⣠⣺⣿⣿⡇⠀⠀⠸
⠀⠀⠀⠀⡸⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⡔⠁⢸⣿⣿⣿⣿⠀⠀⠀
⠀⠀⠌⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀
⠀⡌⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀
⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠉