⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⢁⣠⣤⠶⠞⠛⠋⠉⣀⠀⠀⢠⠞⠉⢀⣴⣾⣷⠀⠀⠂⢠⣿⠁⠀⠀⡠⠔⢁⣴⠟⠁⠀⠀⠠⠀⠀⢠⠏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠉⣠⣴⡿⠋⠀⠀⠐⠁⣠⡾⠛⢉⣠⣴⠶⠚⢉⣠⠄⣁⠀⠀⠀⠶⢿⣿⡏⢹⠀⠀⠀⢈⣁⣠⡶⠋⣠⡴⠛⢁⣠⠶⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⡠⠃⣠⣾⠟⠉⠀⠀⠀⠀⢠⠞⠁⠀⣰⠟⠋⠀⠀⠈⢉⡀⠀⠀⠁⠀⠤⠦⠈⣿⠀⢸⠀⠀⠃⠈⠉⠛⠧⣌⣉⣠⣴⡿⠉⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⡐⢀⣼⠟⠁⠀⠀⠀⠀⠀⠐⢁⡔⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠰⣄⠀⠀⠈⠙⠿⠋⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⠟
⠀⠀⠀⠜⢀⠞⠁⠀⠀⠀⠀⠀⡄⠀⣰⡟⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⠀⠀⠇⠸⠀⠀⠈⠳⣄⠐⢤⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⢠⡴
⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠁⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡆⠀⠀⠀⠀⠹⣆⢘⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⣀⣤⠖⠋⠀⠀
⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠘⣿⡇⠀⡴⠋⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠋⠀⡀⠀⢀
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⠀⠀⢀⣾⣿⡿⠋⠁⢀⣤⠊⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⣠⣶⠟⠁⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⡴⠟⠉⠀⢀⣴⣾⡿⠃⠀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣠⣤⣤⠞⠛⠟⠋⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⡰⠛⢁⣠⣶⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣸⠟⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣰⣶⣿⠁⠀⠀⠀⠀⠀⢀⠤⠊⢁⣤⣶⠃⠀⠀⢀⡴⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡆⠀⠀⠀⠀⠀⠹⣿⠻⡆⠸⠀⠀⠀⠀⠀⠀⠁⠀⢀⣿⡿⠏⠀⣠⣴⣿⠃⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠉⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⠇⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡟⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠖⠀⠀⠀⠀⠀⢺⣦⣀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡟⠀⢀⡀⠀⠬⠋⠙⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠁⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠟⠛⢿⣿⣿⣿⣿⠋⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠦⣤⣤⣼⣿⣿⠛⠁⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⢍⣧⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⡾⣿⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⢻⣿⡇⠀⠈⠙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠀⠏⠹⠟⠋⠉⠁⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢸⣿⡇⠀⠀⠀⠀⠈⠙⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢠⣿⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣸⡟⠀⠀⠀⣾⠇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⠀⠀⠀⢰⣤⣄⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⡿⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠁⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿