Hug for you text Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣤⣄⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⣿⣿⡿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣠⣤⣤⣿⣿⣿⣿⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⢠⣿⣿⡿⢁⣤⣶⣶⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⠛⣿⣿⣿⣿⡇⢸⣿⣿⣧⣠⣿⣿⣿⡇⠀⢸⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢿⣿⣿⣦⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠙⠻⠿⠿⠟⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⢠⣴⣶⣶⣶⡀⠀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣧⢸⣿⣿⣿⣛⡛⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠙⠟⠋⠀⢿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⡙⠛⠋⠁⠀⠀⠀⠀⣀⡘⠿⠿⠿⠃⠻⠿⠿⠿⠿⠿⠛⣛⣃⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⡆⢠⣴⣶⣶⣶⣶⣶⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿⣿⣀⠀⠀⢀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⢶⠆⠰⣶⠾⠿⠿⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣾⣿⣿⠃⢸⣿⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠉⠉⣹⣿⣿⣿⡿⣾⣿⣿⠿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⣿⠃⠀⢻⣿⣿⡆⢸⣿⣿⢀⣸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠛⠋⠁⠀⣼⣿⡿⠀⠀⠘⣿⣿⡇⢸⣿⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠛⠛⠉⠀⠀⠀⠙⠛⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠀⠀⣿⣿⡟⠛⠈⠿⣿⣿⡿⠟⠀⠀⠀⣾⣿⣦⣿⣿⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⣿⣿⡿⠛⠀⠀⣿⣿⠇⠀⠀⠀⣸⣿⠿⠿⢿⣿⢦⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣦⢹⣿⣿⡿⠀⠀⠻⠿⠀⠀⠀⠀⠻⠋⠀⠀⠸⠿⠸⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⡋⠁⠀⠀⢀⣀⣀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⢠⣿⣿⣿⡇⢠⣿⣿⣿⡆⢠⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⠃⢸⣿⣿⣿⠀⣿⣿⡏⠙⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣀⣾⣿⣿⡿⢠⣿⣿⡇⣤⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⣿⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⣧⣹⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⠃⠈⢿⣿⣿⣿⣿⡿⠋⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠙⠋⠁⢀⣀⡉⠉⢁⣀⡀⠀⣉⣛⠉⠉⢀⡀⠀⢀⠀⠈⠙⠛⠉⠉⠋⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠘⢿⣿⣶⣿⡿⢡⣾⣿⣿⣷⠐⣿⣇⠀⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠸⣿⡇⣸⣿⠇⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠙⠿⠿⠟⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣀⣀⡀⣴⣿⠇⠀⠀⠀⠀⣀⣿⣷⠀⠀⠀⣀⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⡆⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠋⠀⠹⠿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⢻⣿⡇⠀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠰⠁⣼⣿⡄⠀⠀⢠⣦⡀⠀⠀⣾⣿⡇⠀⠀⢀⣾⡟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⣿⡇⠃⠀⣿⣿⠀⠀⠀⣸⣿⡇⠀⢰⣿⣿⠁⠀⠀⣼⣿⠃⠀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⡟⠀⢸⣿⡏⠀⠀⡐⢹⣿⡃⢀⠂⣿⣿⠀⠀⢀⢿⣿⡀⠀⠘⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⢸⣿⡇⠀⡔⠀⠀⠛⠧⠂⠀⢿⣿⠀⢀⠊⠈⠻⠧⠊⠀⣿⣷⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠃⠀⠀⠀⢀⠄⠊⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⢸⣿⣿⠀⠀⠀⣼⣿⠃⠀⠲⡄⠀⠀⣶⣦⠀⠀⢸⣿⣿⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣿⣿⠀⠀⡜⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠇⠀⠀⣿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⢃⠀⠀⢀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⡰⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠖⠁⠀⣿⣿⡀⠄⠐⠚⠛⠷⠂⠀⠀⠀⠀⠀⠙⠂⠀⠘⣿⣇⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣷⣶⣦⣤⣤⣤⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⣄⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣶⣶⣤⣭⣍⣻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⡇⣾⣆⢸⢱⣾⣿⡇⠀⣴⠀⣶⣠⡶⢦⣰⡆⢰⡆⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⠇⢻⣿⢸⣿⣿⡇⠀⢻⣴⢿⠻⣄⣼⢻⣧⢿⡇⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣈⠀⠀⢡⣤⡄⠁⢡⣦⡀⠀⢸⣀⣬⣤⣤⡅⠀⠀⢰⣶⣤⣦⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⠿⣿⣆⢸⣿⡇⠀⣸⣿⠇⣰⣾⠟⠋⢙⣿⡇⠀⠀⢸⣿⡿⠛⣿⣿⡟⠉⣿⡏⣹⣿⣙⣛⣿⡿⠿⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣸⣿⢸⣿⠇⢰⣿⣿⡄⣿⣏⢀⣠⣾⣿⡇⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⣿⡇⣿⣟⠛⠛⠛⡁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⣿⡿⠘⣿⣷⣿⠻⣿⡇⣙⠻⠿⠛⠁⣿⡇⠀⠀⢸⣿⡇⠀⢹⣿⠀⠀⣿⡇⠸⣿⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠈⠉⠁⢀⣽⣿⡟⢀⡀⠀⣰⣿⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠈⠻⣿⣿⣿⣤⣴⡦⢀⣠⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⣶⣶⣶⣿⠿⠿⠛⠋⢁⠀⠈⠉⠉⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣵⣶⣶⣿⣿⣿⠿⠟⠃⢀⣤⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣉⣉⣀⣀⣀⣀⠀⢸⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠁⠈⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣷⣶⣶⡶⠄⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⣾⣆⡀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣀⢀⠄⠀⠀⠀⠀⠀⠀⠸⣜⣀⣀⠀⠀⣀⡀
⠀⠀⠁⠉⠉⠏⡏⠉⠉⢉⠉⡡⠀⠀⡀⠀⠀⣀⠀⠁⠉⠉⠈⠀⠠⠀⠀⠀⠀⡄⠀⠈⠉⢉⣀⡉⢉⠅⡀
⠀⠀⠀⠀⢀⠀⠀⠛⠛⠛⠀⠛⠛⠛⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣶⣠⣄⡄⠀⠀⠀⠉⣉⠇⠈⠉⠉⠁
⠀⠀⣰⣀⣈⣀⡀⣀⢀⡀⠀⠀⣠⡀⣤⠀⠀⢠⣧⣇⡀⣀⣀⣀⡀⠀⠀⠀⠁⠁⠀⠀⣀⠀⠀⠀⠀⠂
⠀⠀⠉⠉⠋⠋⠉⠉⠈⠁⠀⠀⠈⠛⠁⠀⢀⠈⡈⠉⠹⠋⠏⠙⡇⠀⠀⢾⣅⡱⠀⠸⠳⠤⠤⠀⣤⣤
⠀⠀⠀⠀⠀⢠⠄⣄⢀⠀⠉⠀⠀⠀⠀⠀⣼⢀⣀⡆⡀⡀⡴⡞⡀⠀⢀
⠀⠀⣠⠤⢄⠉⠛⠉⠋⠂⠀⠀⢐⠀⠄⠀⠈⠈⠉⣉⠙⠛⠓⠛⠛⠃⠘⠀⠀⡀⠀⠀⠀⠀⠀⠸⣽⣹⠆
⠀⠀⠙⠓⠊⢠⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣏⣧⣤⣤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣾⡆⡀⡀
⠀⠀⠠⠄⠀⠠⠜⠶⠶⠀⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠀⡟⠀⠀⠀⢞⠀⡲⠀⠀⠀⣠⠉⠉⠹⢿⣟⠻
⠀⠀⣀⠀⠀⠀⠀⠀⠖⠳⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⢴⣄⡗⠀⠀⠉⠀⠀⠀⢸⣤⣾⣀⣤⣶⣈⣠⣀
⠀⠀⢀⡀⠀⠓⠶⡆⠧⠶⠴⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⣽⡉⠈⠉⠁⠉
⠀⠀⠈⠁⢀⣆⣂⡁⣀⡀⡀⠀⠀⠉⠀⡀⠀⠀⠛⠛⠛⠀⢺⠛⠛⠀⠀⠀⠀⠂⠀⠀⠀⠐⠋⡛⡻
⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠙⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠻⠿⣿⣿⣿⣆⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠶⠤⣤⣀⡈⠉⠉⠀⠀⠀⠹⣿⣿⣷⡀
⠀⠀⠀⣼⣿⣿⣿⣿⣿⠸⡟⢻⡇⡿⠄⠀⣿⡿⣿⢻⠟⠻⡿⢿⠟⣿⣶⣤⣤⣀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧
⠀⠀⢠⣿⣿⣿⡇⠈⣿⡆⢰⡌⢡⡇⠄⠀⣿⡇⢋⢀⠸⠗⡀⠘⠀⣟⣉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⣿⣿⣿⡇⠀⣿⡷⢿⣿⡞⠛⣿⡿⠛⢿⣿⠨⠗⠚⠛⢺⣷⣿⠋⠛⠛⠲⠒⠒
⠀⠀⢸⣿⣿⣿⡇⠀⠁⣠⡀⠹⡇⠀⣿⡇⠀⣿⠋⢠⣴⡶⠀⢸⣿⣿⠀⢀⣶⠀⠀⣴⡆⢸⠇⠐⠒⠀⢀⣤⣤⣄⣀
⠀⠀⢸⣿⣿⣿⡇⠀⢰⣿⡇⠀⡇⠀⡟⠀⠀⢿⡀⠙⠛⢁⠀⢸⣿⣿⠀⢸⣿⡀⢸⣿⡇⢸⡄⠸⣷⣾⠟⣿⣿⣿⣿⠇
⠀⠀⠀⣿⣿⣿⣇⣀⣿⣿⣇⣸⣷⣄⣠⣾⣄⠘⢹⣶⣾⣿⠀⢸⣿⣿⣄⣸⣿⣧⣼⣿⣧⣼⣷⣤⣀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣿⣍⠙⠃⠀⠿⠿⢿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠘⠛⠛⠋⢁⣀⣠⣤⣶⣿⣦⣴⣶⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠐⠛⠉⠉⠀⣀⣠⣤⣿⠛⠋⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠙⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠛⠛⠛⠛⠿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣶⣶⣿⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣠⣤⣤⢠⣤⠀⣶⡆⣶⡶⣦⡀⣾⡆⣶⡄⢰⡆⣰⣾⣿⣆⠀⣶⠀⢀⣶⠀⣠⣤⡄⢀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠃⣿⣏⡁⢸⣿⣧⣿⡇⢿⡇⢹⡇⣿⡇⣿⣷⣼⣧⣿⠁⣼⡋⠀⢻⣶⣿⡿⣼⠏⢉⣿⣼⡏⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⢹⣏⣁⠘⣿⢻⣿⡧⢸⣷⠿⠁⣿⠄⣿⠹⣿⠏⢿⣦⡿⠃⠐⣷⣤⡿⠁⣿⣦⣾⠃⢿⣧⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣾⠿⠙⠛⠉⠁⠉⣠⣀⠀⠀⣀⡀⠀⠀⠀⢀⣀⠀⣀⣀⣀⠀⢀⡀⠀⢁⡀⠀⠈⠉⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠿⠂⢼⣫⡽⣦⣴⣰⡟⣿⠂⢩⡿⠁⣰⡟⣿⠀⣼⠇⠀⣿⠁⢴⢿⡇⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⢠⡮⠙⢶⡄⣼⠛⠛⣿⠁⣿⠀⣨⠀⢸⡇⢠⣿⣤⣾⠂⣿⢀⣰⡟⢀⠀⠸⠷⢻⡟⠰⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣥⢿⣄⡆⠀⠸⣧⣠⡾⠃⠻⣦⡾⠃⠀⢿⡾⠏⢠⣿⡦⢸⠏⠀⠿⠂⢷⠟⠹⠷⠋⠸⣤⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⠀⢀⣠⣤⡁⣠⣄⡀⣠⣤⣤⣤⣄⢀⣤⡀⠀⣀⡀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⢷⡀⢸⡏⢰⣟⠙⠷⠈⠉⣿⠉⠁⣾⠛⣷⢀⣿⣇⢸⡿⢠⡟⢻⡇⢠⡾⢻⣧⠘⣿⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢸⡇⠀⡙⠳⣆⠀⢠⣿⠀⢸⣿⣶⣿⢸⡟⢻⣾⣷⡿⠀⢈⣡⡿⠷⠞⢃⢠⡟⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣾⠃⣸⣇⡸⣧⣠⡿⠀⢸⡿⠀⢼⠇⠀⣿⢸⡇⠘⢿⠛⣷⣴⠿⠹⣧⣀⣴⠟⢸⣇⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠉⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡀⠀⠀⢸⣿⣧⠀⣸⣿⡇⠀⠀⠀⣸⣿⡇⠀⣠⣾⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⢰⣿⣿⠋⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⣾⣿⡏⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⢹⣿⣧⠀⢿⣿⣷⠀⠀⢠⣿⣿⠁⣿⣿⡇⠀⠀⠾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⣿⠀⠘⢿⣿⣷⣶⣾⣿⡏⠀⠹⣿⣿⣦⣤⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠘⠛⠋⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠉⠛⠻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡆⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣧⠞⣡⣾⠴⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠈⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠈⠁⠼⠋⣠⣴⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠤⣄⡘⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠘⣩⣖⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠬⢷⣤⡈⠉⠁⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⠶⢤⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠤⠤⠤⠤⠶⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣒⡦⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠉⠉⠉⠉⠉⠉⠒⠒⠢⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⣿⣿⡿⠿⠿⠿⢿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⠃⠀⢠⠞⠙⣿⣆⠀⢈⣿⡗⠋⢦⠀⠀⠋⢀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⡆⢠⡞⢉⣿⣿⣀⣸⣿⡁⠀⡟⠀⠀⠀⢠⣿⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠴⠊⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢾⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⣀⠀⠀⢀⣀⡀⣀⣀⣀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣼⣷⢀⡿⠀⣸⠿⣧⠀⠀⣿⠁⠛⢹⣿⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠇⢹⣿⠃⣠⣟⠛⣻⣆⢀⣿⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠈⠉⠀⠉⠉⠈⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢲⣶⠒⡄⠀⠀⠀⠀⠀⠀⠀⢲⣶⠂⠀⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⠏⠙⢆⠀⠀⠀⢸⣿⢄⣤⡇⠀⣹⠀⠀⣿⠃⢰⠋⠉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠈⢿⣄⣀⠞⠀⠀⠀⣸⣿⡀⢀⣇⠀⢻⣀⣼⣿⡀⠸⣀⡠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⠀⢀⣀⣀⠀⢀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡀⠈⢻⣅⣼⠋⢰⡟⠉⠙⣷⠈⣿⠁⠈⣿⠀⣠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠏⠀⠀⣿⡃⠀⠸⣧⣀⣠⡿⠀⢿⣀⣠⡿⠈⠷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢀⡞⠑⢀⣀⣀⠀⠀⣀⡀⢀⠀⠀⠀⡇⢠⡄⢠⣏⠀⣀⣀⣠⠀⣴⠄⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⢸⠀⠀⢸⢛⠟⡷⠶⠉⡇⣿⣡⠀⠀⡇⠘⠴⠃⢿⠀⠋⠘⠐⣷⠷⠂⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠘⣆⢠⠏⠉⠀⠁⠀⠀⠛⠀⠀⠀⣀⣙⣉⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⠈⠉⠉⠉⠉⠉⠛⠒⠒⠒⠶⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠤⠤⠴⠖⠒⠒⠚⠋⠉⠉⢿⡄⠀⠛⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠗⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣀⣀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⠀⠀⡀⠀⢀⠀⢀⣀⠀⠀⠀⠀⣀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⠀⠀⡇⢸⡇⠀⢸⢀⡞⠀⠀⠀⡇⢀⣿⢀⡏⠈⡆⣿⠀⠀⣿⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⢸⠀⠀⡇⢸⠁⠀⡼⢸⠀⠀⠀⠀⠳⠞⢸⢸⠁⠀⡇⣿⠀⠀⡏⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⠒⠉⡇⢸⡄⢀⡇⢸⠀⢹⠀⠀⡀⠀⣾⢸⠀⢠⡇⣿⠀⢀⡇⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⢸⡆⠀⡇⠈⢧⠜⠀⠈⠳⠏⠀⠀⡇⢠⠇⠸⣄⡼⠀⢹⡀⡼⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠓⠚⠚⡛⢛⣛⠛⠛⠛⢛⡛⠛⠋⠉⠉⢉⠉⠉⠉⠉⣉⡉⡉⠉⠉⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡅⢸⣠⠇⡶⢆⣾⣀⠀⢀⣿⡠⢾⢀⣤⣶⢸⠠⡀⠑⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠸⠈⠦⠈⠉⠸⡅⠀⠀⠸⠀⠘⠞⠀⠈⠈⠚⠁⠿⠋⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠷⠖⠖⢴⠀⢘⠸⠶⠶⣶⣆⡆⠰⠀⠶⠆⡶⠶⢚⠀⢘⢰⠀⢰⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠻⣿⣺⡇⠀⢦⡷⡿⢿⠿⡁
⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⠀⠀⠀⢠⠀⡄⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠉
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⣨⣇⡈⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣠⣶⠆⢀⣀⢠⣀⡀
⠀⠀⠀⠀⠈⠻⠿⠇⠀⠤⠤⠴⠚⠁⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠉⠀⠨⠏⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⡴⠀⣖⢤⣴⣴⢰⠆⡇⠀⣤⣤⣠⣦⠀⢀⣦⡖⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⠛⠛⠛⠛⠛⠛⠻⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣖⣲⡁⠰⡶⢶⢶⠆⠀⢼⣐⣞⢼⠷⠺⠧
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣾⣿⣷⣶⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣾⣷⣶⣤⣾⣿⣦
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⣠⣾⣟⣿⣻⣛⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠟⠛⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠰⠂⠀⠒⠒⠀⠤⠆⠀⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣇⢸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠸⠴⠇⠸⠇⠿⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠿⠿⠿⠿⠿⣷⣆⠀⢀⣄⠀⠀⠀⠀⣰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣛⢉⣿⣿⠁⣠⣄⠀⠀⠀⠘⠁⠀⠺⠏⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⣿⣿⠿⠿⣿⠃⣾⡟⣴⣿⢇⣾⡗⠀⣴⡿⢻⣿⠏⣠⣾⡟⣷⣄⠀⣰⣿⠂⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⣿⠇⠀⠀⠁⢸⣿⡿⠹⡏⣼⡟⢀⣾⣿⠁⣾⡟⢰⣿⡏⢐⣿⡟⣰⣿⠇⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢻⡿⠁⠀⠀⣿⣧⠟⢿⣧⡾⢻⣧⣼⣿⣴⠿⣿⣴⠻⣿⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢰⣖⠐⡞⠀⠀⣶⣰⡆⣶⡂⠀⠀⠀⠸⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠘⠓⠘⠓⠀⠃⠀⠀⠛⠛⠃⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣤⡀⣄⠀⣤⢀⣤⡄⠀⠀⢀⡄⢠⡄⣠⠶⡄⢠⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢫⡟⣸⣏⣼⢇⣾⢃⡟⠀⠀⣾⢁⣿⢰⣧⣰⣧⣾⢡⣾⣡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠛⠙⠋⠙⠋⢛⣿⠃⠀⠀⢙⣿⠃⠈⠛⠋⠀⠙⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠙⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠛⠛⠿⢿⣿⣿⣿⣷⡄⠀⠈⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠉⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣿⡆
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡍⣿⠿⣿⡇⣙⣛⠹⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡀
⠀⠀⠀⢠⣿⣿⣿⣿⠟⢻⣿⡇⠹⢀⢹⡇⡏⠉⠰⠀⣿⡏⢸⡏⠸⢁⣤⠙⠇⣿⠃⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠧
⠀⠀⠀⣸⣿⣿⣿⣿⠀⠈⣿⣧⠀⣾⣄⢠⣇⢀⢀⠀⣿⣧⠈⣀⢰⡘⠛⣠⡆⠛⡀⣻⣤⣀⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⢿⣿⣿⡟⠛⢻⣿⡟⠉⢻⣿⣿⠘⠿⠛⠛⠛⢻⣿⣿⡏⠉⠛⠙⠛⠛⠛⠃⠂
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠋⠀⣀⠀⢻⡇⠀⢸⣿⡇⠀⢸⡿⠉⢀⣤⣶⡆⠀⢸⣿⣿⡇⠀⠀⣶⠀⠀⠀⣴⡆⠀⣿⠀⠰⠶⠄⠀⢀⣄⣀⡀
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⣾⣿⠀⠈⡇⠀⢸⡿⠁⠀⢸⡇⠀⣾⣿⠟⠀⠀⢸⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⣇⠀⢠⣤⣤⣤⣾⣿⣿⣿⣿⣶⠆
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣼⣿⣿⠀⢠⣇⠀⠘⠁⣠⠀⢸⣷⣄⣀⣀⣤⡆⠀⢸⣿⣿⡇⠀⢸⣿⡇⠀⢸⣿⡇⠀⣿⡄⠈⠻⠟⠋⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣦⣤⣿⣿⣿⣦⣾⣿⣶⣤⣶⣿⡦⠀⠀⣼⣿⣿⣿⠇⠀⣾⣿⣿⣷⣤⣾⣿⣷⣶⣿⣿⣷⣴⣿⣿⣶⣤⣤⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣌⠉⠉⠀⠰⠿⠿⠿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠐⠿⠿⠟⠛⠃⠀⠀⢀⣠⣴⣾⣯⣄⣤⣴⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠴⠶⠞⠛⠛⠋⠉⠉⣻⣿⣿⠿⠋⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣿⣿⡏⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠉⠉⠉⠉⠛⣻⣷⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣶⣶⣶⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢻⠿⠿⢿⠿⡹⠿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣟⣿⣟⣛⣛⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⣿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⢿⣆⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣴⡿⠋⠀⠀⠈⢧⡻⡄⠀⠀⣤⡆⠀⠀⢀⣴⠟⠁⠀⠀⣠⣴⠿⡟⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡾⠋⠀⠀⠀⠀⠀⠈⢧⢱⡀⠀⠛⠃⠀⣠⡾⠋⠀⢀⣴⡾⠋⠁⠀⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠞⣡⣤⣤⣤⣄⡀⠀⠀⠈⣧⢧⠀⢀⣠⣾⣿⣤⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⡾⠛⠋⠉⠉⠛⠻⣷⣄⠀⠈⢿⣷⢟⣛⣩⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠇
⠀⠀⠀⢀⣀⣤⣤⣶⣶⠿⠟⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢸⠁⠿⠛⢛⣻⡷⠀⠀⣰⣶⣶⣤⣤⣴⣶⣶⣶⣶⣾⠿⣦⣄⣀
⠀⠀⠀⣿⠛⠻⠿⠿⠷⣶⣶⣾⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣾⣿⣾⣿⣿⠟⣿⠛⠁⠀⠿⠿⠿⠛⠻⢿⣿⣍⣩⣭⣭⣥⣤⣶⣿⣿⣿⣿⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢉⣽⠿⠋⣡⡿⢫⡿⠋⠁⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⠛⠛⠋⠉⠉⠉⠉⡏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣼⠋⢠⡟⠀⠀⠀⠀⠀⣶⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡼⠃⢀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠘⠻⠿⣿⠿⣿⣿⣿⣶⣶⣶⠟⠁⠀⠀⢸⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣾⣿⣿⣿⣿⠇
⠀⠀⠀⣶⠀⢰⡇⠀⠀⠀⠀⠈⣹⠏⢀⣠⡆⠀⠀⠀⣸⢷⣶⣶⣦⣤⣄⣀⡀⢸⡇⢀⣠⣤⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⢸⡇⠀⠀⠀⠀⢠⣇⣴⠿⠋⠁⠀⠀⢀⡏⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⠿⠟⠛⠉⢹⠀⠀⢠⣿⣦⠀⠀⡸⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⢀⡟⠀⠘⣇⣰⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⡾⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣶⣦⣤⣄⣀⣀⠀⠀⠀⣸⡇⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣶⣾⣧⣶⣶⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⢀⣐⡍⠑⣠⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢤⠛⠶⢤⠷⢸⡷⠞⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⣀⣾⢦⣷⠠⠂⢉⡳
⠀⠀⠀⠀⠀⠀⠓⡐⢲⡎⠋⣍⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢸⡧⠓⢁⠋⢉⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠠⠀⢨⣇⢠⠈⡑⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⡂⡒⢄⢀⡠⠐⠂⣻⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢰⣁⡀⢸⢀⡀⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⡌⠈⠁⠀⠈⠃⠀⡁⠀⠀⠀⠀⠐⠀⠀⠊⢉⡹⢢⣍⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⠈⠀⠈⣡⣬⠈⠁⠉⠈⢃⣀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢁⡈⢈⠉⡇⠀⡦⠉⢀⡲⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠐⠀⠈⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠈⠀⠀⢡⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣀⠅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠂⠚⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⡁⠀⠀⣀⡸⠀⢸⣀⣀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⣄⠀⠦⡀⠀⢀⠀⠟⡀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣀⠀⢀⣀⣀
⠀⠐⢄⠂⠈⠒⠁⠀⠀⣻⡆⠀⠞⠤⠊⠠⠖⠡⠂⠴⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠦⠶⣛⢉⡩⢒⡛⠛⠻⣟⡓⠁⡀⠀⠑
⠴⠂⠀⠒⠒⠰⠷⠾⠲⠿⠿⠿⠒⠒⠢⠔⢲⠄⠈⠰⠐⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⡇⠀⠈⡀⠀⠀⠀⢆⠀⠀⡄⢠⠊⠉⠀⠁⠈⢛⠂⠀⠀⢀⡀
⠐⠀⠂⠉⠀⡀⠀⠀⠀⠰⠀⡎⠐⠂⠀⠀⠀⠂⠲⠘⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⠈⠉⣷⡋⠀⠻⠈⠁⠉⠈⠾⡅⠈⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠀⣠⣄⡀⠀⠀⡀⠄⠀⠘⡆⠀⠀⠣⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡧⠸⣷⠟⠃⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠉⡻⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠩⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣠⡆⠐⠃⠇⠤⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⡇⠀⢰⡶⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⢤⠤⠤⢄
⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣑⣦⡋⣐⡠⠂
⠀⠀⠀⠀⡈⠉⠘⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀⢀⠀⡀⠐⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠛⡿⠞⡋⠀⠀⠀⢀
⠀⠀⠀⠠⠇⠀⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠒⠒⠲⠶⠶⢧⡀⣅⡞⢁⠴⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠠⠖⠠⠄⣀⠀⢰⠂⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠴⠂⢤⠀⠀⠉⠁⠀⠀⢠⠄⠙⣀⠄⠀⠀⠈⠉⠈⠁⠓⠀⠤⠆⣀⠀⠇⠀⡨⠦⠛⠉⠁
⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⣀⠀⠈⠀⠐⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰
⠀⠀⢠⠹⣧⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢲⠖⠊⠀⡇⠀⣀⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠈⠐⠁⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠸⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⢠⢀⠀⠴
⠀⠈⠀⠂⠀⠄⢻⣷⡀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠘⠻⣶⣦⣄⡀⠀⢻⣷⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⢻⣷⡶⠿⠿⠿⠿⠿⢿⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⡙⣿⣧⣿⣷⣶⣶⣤⣤⡀⠀⢀⣨⣼⡿⠟⠻⠿⣶⣦⣤⣀⡀
⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⡿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠛⠉⠉⠙⠛⢿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⣿⣷⣦⣤⣀
⣶⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣦⣬⣿⣿⡀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣶⣶⣶⣶⣶⣶⣶⣾⣿⣯⣁⡈⠉⠛⠿⣷⣦⣄⡀
⣿⣯⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠿⠛⠛⠉⠉⠉⢛⣿⣷⣄⠀⠀⠀⠀⠀⢀⣿⣯⣀⣤⣤⣄⣀⠀⠀⠈⠉⠛⠿⣿⣦⡀⠀⠀⣉⣹⣿
⣿⣿⠀⠀⠈⠙⢿⣿⣶⣶⣶⠿⠻⣿⣉⡁⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⣹⣿⢿⣷⣶⣶⣾⣿⣿⡿⠛⠋⠉⠛⠻⣿⣦⡀⠀⠀⠀⠈⣿⣿⣾⠿⠛⠋⢹
⢿⣿⠀⠀⠀⠀⠀⢽⡿⣿⣶⣄⢸⣿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⢁⣴⠟⠁⠀⣠⣿⣏⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡷⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⢰⣿⠃⠈⠳⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠏⠀⠀⠀⣿⣿⣴⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣦⣤⣶⣶⣿⠟⢋⣁⣼⣿⠀⠀⠀⢸⣿⡟⠛⠉⠀⢸⣿⠻⣿⣦⣄⡀⠀⠀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡿⠟⠛⠋⠙⢿⣿⡿⠿⣿⣿⠀⠀⠀⠘⣿⣇⠀⠀⠀⢸⣿⠀⠉⠻⠿⣿⣿⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⡀⠀⠀⠀⠹⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⣧⡀⢀⣀⣀⣬⣿⣦⡄⠐⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⢿⣿⡿⠿⠛⠛⠉⠉⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣧⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢻⣿⡀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢿⣧⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢻⣷⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿
⠀⠀⠀⠀⠻⣿⣄⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⢀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⣠⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⢸⡇⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⢸⣿⡏⠀⠀⣀⣠⣴⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⣿⣷⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠋⠁
⣿⣿⣿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠤⠤⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠛⢄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⡆⠈⢳⡀⠀⢹⡤⠴⠖⠒⠒⠒⠂⠂⢄⡜⠁⠀⠀⣀⣠⣦⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡀⠱⡚⠉⠙⣄⠀⢇⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⣴⠋⠁⠀⠘⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠹⣦⡱⣄⠀⠘⣆⠘⡄⠀⠀⠀⠀⡴⠁⣠⠔⠃⣀⡽⢦⣀⠀⢸⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡳⣄⠘⡆⢹⣦⡀⢀⠞⣡⣞⡥⠖⠋⠁⠀⢀⣩⣷⣄⡇⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣿⡞⠉⢩⡿⠛⠉⢁⣀⡤⠴⠚⣋⣉⣀⣀⣼⠇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣿⡀⠀⢸⠉⠒⠚⠛⠛⠛⠛⣉⣉⣩⡭⠥⠖⠋⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠉⠢⣄⣀⡤⠴⠖⠋⠉⠀⠀⢀⣨⠽⠻⡏⠁⠉⠉⠙⠯⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⢨⡇⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠈⢢⡀⠀⠀⠀⠈⠳⢦⡀⠀⢀⣀⠤⠒⠋⠉⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠢⣀⠀⢸⡇⠀⠀⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⣀⡤⠖⢻⡟⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠼⣇⠀⠀⣿⠈⠑⢦⡀⠀⠀⠀⠀⠀⢀⠠⠄⠊⣯⠁⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠻⣤⡇⠀⠀⠀⠈⠢⢀⠠⠐⠈⠀⠀⠀⠀⢸⠄⠀⢀⣸⡧⠤⠶⠚⠉⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢈⡗⢄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⣀⡼⠓⠛⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣸⠀⠀⣼⠁⠀⠈⠒⢦⡀⣿⠀⣀⣠⠴⠚⠉⠀⢻⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⡟⠀⢰⠇⠀⠀⠀⠀⠀⠉⡟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣸⠇⠀⣾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⣇⠀⢀⣀⣠⣤⠼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⡤⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢸⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠁
⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⢶⡄⠀⠀⠱⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⣀⣀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠤⣤⣙⣦⣄⠀⠙⣆⢣⠀⠀⠀⠀⠀⠀⡠⠃⢀⠔⠉⠀⠀⡘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡈⠙⠻⠷⣤⣈⢙⣠⣤⣤⡀⡠⠜⡡⠔⢁⣀⣀⣀⣔⣁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠠⠀⡀⠀⠉⠛⠒⠒⠒⠊⢹⣀⠀⢡⡏⣐⠛⣉⣉⣁⣀⣀⣀⠀⠉⠳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣄⣀⠠⢤⣤⡄⠁⠒⠒⠒⢒⠶⠾⣿⣆⣸⡇⠀⠙⣦⠨⢭⣉⣀⠉⠀⠁⣰⣧⠴⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠒⢶⡎⣧⢀⣈⣉⣉⣁⠰⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⠤⢄⣀⣀⡤⠖⠇⢸⣦⡀⠀⠀⠉⢻⡇
⠀⠀⠀⠀⠀⢀⠁⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡀⡸⠀⠸⡇⠉⠛⠲⠒⠋
⠀⠀⠀⠀⠈⠓⠒⠛⡇⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠃⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⢸⡃⠀⢠⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡾⠉⠢⣸⠀⠀⢨⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠷⠒⠛⢆⢠⠇⠀⠀⢹⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠈⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠀⡆⠀⠀⢸⠀⠀⠀⠘⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⡇⠀⠀⢸⠀⠀⢀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣠⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⡀⠀⡇⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⣿⣏⢹⣟⠻⣿⣟⠟⡻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠢⡀⠀⠈⠪⡉⠐⠂⠔⠁⠀⠀⡠⠊⡹
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⡲⠏⢉⡒⠈⢐⣄⣀⡈⣦⠎⣀⣀⡔⠪⠔⣊⠉⠲⢄⣀
⠀⠀⠀⡤⣒⠊⠉⠀⠀⠀⠀⠄⢀⣀⡀⠁⣂⣬⠭⡿⣤⠼⡯⣥⣄⠈⢁⣀⡀⠀⠜⠀⠉⠉⠒⡢⡄
⠀⠀⠀⡆⠀⠉⠑⠢⠤⣠⡄⣒⡩⠥⠒⠉⠁⠂⠉⡠⠋⠢⣀⠁⠀⠁⠐⠢⠍⡒⢤⡤⠔⠊⠁⠀⡆
⠀⠀⠀⡇⠀⠀⠀⠀⢀⠗⠋⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠈⠣⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠢⣄⣀⢀⡴⠁⠀⠀⠀⠀⢀⠔⠉⠉⠒⠢⢄⣀⣀⡤⠐⠊⠉⠢⡀⠀⠀⠀⠈⠂⠀⣀⡤⠂
⠀⠀⠀⠀⡇⠀⢋⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⡗⢄⠀⠀⢠⠛⠉⠀⡇
⠀⠀⠀⠀⡇⠀⠈⢆⠀⠀⢀⠜⠓⡧⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⡷⠊⠢⡴⡇⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠈⠣⡤⠃⠀⠀⡇⠀⠈⠉⠒⠤⢄⣀⣃⡠⠔⠊⠁⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠧⢄⡀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⠧⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⢄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⢸⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠓⢤⠀⠀⠀⠀⢀⠴⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⢲⣄⢳⠀⠀⣰⠃⢀⠴⠒⠦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠙⢎⢧⣠⠇⢰⣋⠴⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠛⠒⠚⠛⠒⢺⠆⠀⠀⢯⠤⠤⠶⠥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠛⠛⢦⠀⠀⠉⠀⠀⡴⠉⠉⠳⣆⠀⢸⠁⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀⠀⠀⠀⡼⢁⡔⡂⠀⡧⠀⠄⠀⠀⡇⠠⠙⣦⡘⣆⡼⠀⡴⠋⠀⣀⣀⠙⡆
⠀⠀⠀⠀⠀⡜⢁⣠⣄⡀⠉⢦⡀⠀⡇⣾⠃⠀⡰⠃⣀⣄⣀⣀⢱⢄⡀⠘⢧⢳⣇⡜⢀⡴⢋⡠⠊⢀⡇
⠀⠀⠀⠀⠀⢣⡈⠑⠤⣉⣳⡀⠱⠶⢣⣡⠴⠞⠓⠉⠁⠈⣇⠈⠉⠉⠙⠓⠲⠆⠍⠁⣜⣉⣁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⠤⢼⠂⠈⠈⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠉⠉⠙⠓⢢
⠀⠀⠀⠀⠀⢰⠒⠉⠁⠀⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢡⠀⠀⠀⠆⠂⠈⠀⠀⠀⢩⠀⠀⠀⠙⠀⠀⠀⠗⠀⠠⠄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠤⠀⠀⠈⠈⠄⠀⠀⠰⡀⠀⠀⠀⠈⠙⡆⠀⠀⡄⠀⠀⢀⣀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠠⠀⠚⠀⠀⠀⢃⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⡈⠀⠀⠁⠀⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⣆⣀⣀⠴⠴⠒⠉⠉⠒⠒⠲⠤⠤⠴⣄⣀⣀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠲⡄
⠀⠀⠀⠀⠐⠀⣁⠃⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠉⠡⡀⡄⠠⠐⢀⠀⣀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿
⠀⠀⠨⠀⠁⠀⠀⠄⠈⠃⠋⠀⠀⠀⠀⠐⠀⠀⢒⠀⢢⣦⣄⠱⣤⣠⠊⢁⣨⠴⠠⠀⠂⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠋⠁⠉⢉
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠙⡿⠛⠓⢾⣃⣒⣚⣃⣀⣀⣀⠀⠀⠌⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠀⠈⠉⠉⠀⠀⠀⠀⠸⠁⠀⠀⠄⠀⠀⠿⠠⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠈⠀⠀⠐⠢⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠐⡄⠀⠀⠀⠀⠀⠀⡀⠸
⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠰⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠠⠃⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⢹⠂⡀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠜⠐⡇⠂⠀⠀⢰⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠒⠓⠀⠘⠒⠂⠀⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠘⢾⢀⡠⠞⠀⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡶⠀⠀⠀⠀⠀⠀⠀⢀⡁⠂⠀⣳⡤⠨⡭⠖⠐⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠅⠀⠄
⠀⠀⠀⢀⡠⠄⢲⠁⠀⣀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠖⠁⣀⠀⢄⣀⠠⣀⠀⠀⢠⣠
⠀⠀⠀⠀⠤⠠⡰⡀⡠⢊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠲⡈⠳⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⡁⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠙⠀⠘
⠀⠀⠀⢀⣀⠀⢀⣿⢋⡀
⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡀⠈⠠⡀⣜⠄⢸⣀⣄⢬⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢨⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠽⡶⢃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸
⡄⠀⠤⠄⠀⠢⢼⠄⠸⠴⠤⠴⠶⠦⠤⠤⠄⠀⠀⠀⠀⡀⠐⠰⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠠⠤⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣄⢀⡄⠀⢀⡀⣠⢤⣄⠀⠀⠀⣤⠀⢀⡄⢀⣤⡴⢤⣄⠀⣤⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣿⢸⡇⠀⢸⡇⣿⠀⠙⠀⠀⠀⠘⣦⡾⠁⣾⠁⠀⠀⢹⡆⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣿⢸⡇⠀⢸⡇⣿⠒⢶⠀⠀⠀⠀⢸⡁⠀⣿⠀⠀⠀⢸⡇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠿⠀⠳⣤⡼⠃⠹⢤⠾⠀⠀⠀⠀⠸⠀⠀⠘⢧⣤⡤⠞⠁⠸⢦⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⣀⠀⠀⠀⢻⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣦⣀⠀⠉⠙⠛⠶⠦⣿⣆⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠚⠉
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠸⣆⡀⠈⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⣀⠀⣀⣀⣀⣀⣤⣤⠶⠖⠛⠋⠁
⠀⠀⠀⠉⠳⣄⡀⠀⠀⢰⠞⠻⠶⣦⣄⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠳⢦⣀⡀⠈⠉⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⣨⡿⠷⠶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣠⡞⢁⣀⣀⣠⣤⡤⠶⣄⣀⣤⠴⠞⠛⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣤⣄⣀⣠⡤⠶⠋⠁⠀⠀⠀⠘⠛⠉⠉⠉⠉⠀⠀⣀⣠⣾⣥⡀
⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠚⠛⠉⠁⠀⣠⡟
⠀⠀⠈⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠴⠶⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠖⠛⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠙⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠛⠛⠛⢻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⠀⠋⡍⠉⠉⠙⢿⣿⣿⣿⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣯⠠⠈⠀⠀⠀⠀⠙⠛⠻⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣟⣉⣿⣿⣧⢏⣀⡀⠀⠀⠀⠐⣷⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⢸⣿⡇⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠘⣿⡆⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣷⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠶⠶⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠿⠄⠀⠀⠉⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⡂⠀⣦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠻⠾⣿⣷⣾⣯⣪⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠤⠸⡿⠉⠉⠛⢶⣄⢀⡀⠉⠉⠉⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠀⢷⡃⣀⡀⣴⡆⠈⢱⡈⠁⠀⠘⣁⣤⣶⣿⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣃⣡⣰⣿⣿⣇⣽⣷⣾⣿⣶⣶⣤⡿⠛⠋⠰⠟⠛⠛⠿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠛⠋⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣏⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣟⡫⠝⣻⣿⣶⣶⡶⣶⣶⣤⣦⣤⣀⣐⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⠒⠈⠉⠻⣿⣿⡿⢟⠿⠾⠛⠋⠀⠙⣿⣿⣿⢁⢠⠃⡹⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣧⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⣆⡆⠀⠂⠊⠹⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠈⣿⣿⣷⡀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠴⠚⠛⢿⣿⣿⡷⣴⠀⠀⠈⢿⣿⣿⣿⣯⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠙⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠁⠀⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀
⠀⠀⠀⡐⠒⣲⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣧⣧⢜⡆
⠀⠀⠀⣘⣬⡼⢦⠾⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⣀⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠉⡝⢉⠟⡇⠀⠀⠀⣀⣴⢶⠚⢒⣊⣳
⠀⠀⢀⠀⠀⡄⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠚⡀⡎⠀⡇⠀⠀⠈⡷⢧⡬⢶⣶⣮⣅⣄
⠀⠀⢸⡄⣠⠇⠸⠤⠤⠤⠤⠤⢼⠀⠀⠀⢸⠉⠉⠉⠋⠉⠉⣉⠉⠉⠍⡇⠀⠀⠀⡄⠀⣠⠃⡇⡴⡇⠀⠀⠀⣠⠊⢠⡎⢇⡱⣘⣾
⠀⠀⢸⠤⠤⡀⠀⡤⠤⠤⠤⠤⢼⠀⠀⠀⢸⠀⠁⠀⠈⢀⠀⠀⠀⠄⠀⢁⠀⠀⠀⡗⠊⠁⡠⢻⠀⡇⠀⠀⢸⣁⠜⠁⡳⠚⢀⡴⢻
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠐⠂⠀⡄⠀⠐⠀⠀⠆⣸⠀⠀⠀⡗⠒⠉⠀⡼⢀⡇⠀⠀⠀⡁⡠⠊⠀⡴⠋⡐⡻
⠀⠀⠈⠉⠀⠓⠚⠓⠒⠒⠒⠈⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⢀⣀
⠀⠀⣀⣫⣄⣦⣠⣯⣖⡀⠀⠀⠀⠀⠠⡀⠐⡆⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠤⢤⣤⣿⣧⣤⣤⠜⠀⠀⠀⠰⣒⢞⣛⣛⣯⡭⢀⣁⣱⠀⠀⠀⠀⠀⠀⠠⣈⣇⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⢄
⠀⠀⠀⠘⡀⢸⡇⢀⠇⠀⠀⠀⠀⢠⣡⠁⠀⠀⡀⠀⠗⠾⠂⠀⠀⠸⡁⠩⠍⠤⠤⠭⠯⠯⠭⠭⠭⠭⢽⠀⠀⠀⡏⠉⠉⠉⠉⠉⠷⡀⠀⠡⡀
⠀⠀⠀⠀⣇⢸⡇⣸⠀⠀⠀⢠⣔⠟⢹⢠⠀⠀⠇⠀⡄⠀⡅⠀⠀⠀⡄⢒⢐⡒⡂⢒⢖⠒⡒⣒⣒⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⣤⠊
⠀⠀⠀⠀⠘⠾⠷⠃⠀⠀⠀⠀⠈⠀⠸⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠃⠠⠥⠬⠬⠤⠥⠤⠤⠤⠥⠤⠞⠀⠀⠀⠣⠠⠤⠤⠤⠤⠤⠦⠼

⠀⠀⠀⠀⢀⢆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡠⠉⢢⡀
⠀⠀⠀⢠⢸⠴⣟⢰⣦⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣋⣄⣊⣁⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠄⠰⠛⠛⠂⠀⠤⠂⠀⠀⠀⡆⠀⠙⠛⠛⠛⠛⠋⠀⡂⠀⠀⠀⠀⠈⠀⠠⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⡇⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠄⠀⡃
⠀⠀⠀⠸⣀⢀⢘⠀⡸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣃⠀⠀⠀⣀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡀⡀⣈⣈⣀⣀⡀⢀⡁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠐⢠⠂⢀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠒⠬⢘⢭⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉
⠀⠄⠐⠂⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠄⠀⠀⠀⠀⠁⢀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘
⠠⠀⠌⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡤⠓⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠰⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠄⣖⡶⢔⡠⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠌⢘⣦⡀⠄⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠔⠚⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠀⠈⠀⠈⠄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⢀⣴⣶⣾⣦
⠀⠀⠀⠀⣤⡀⠀⢸⣧⠀⢿⣿⠀⠀⣠⣤⣄⠀⠀⣶⣿⣿⣆⠸⣿⡿⢻⣿⡀⣼⣿⣧⣿⣿⣤⣤⡀
⠀⠀⠀⠀⣿⣧⠀⢸⣿⡆⢸⣿⡇⣼⣿⠋⣿⣧⢀⣿⣿⢸⣿⣤⣿⣇⠸⣿⣿⡿⢿⣿⠟⠿⠿⠟⠁
⠀⠀⠀⠀⢹⣿⡆⢸⣿⣿⣾⣿⠇⢻⣿⣿⣿⣿⣿⡿⠿⠈⠛⠛⠛⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢿⣿⣿⡟⢻⣿⡿⠀⠀⠙⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣦⣀⣼⣷⢠⣿⣇
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣿⡇⢸⣟⢸⣿⠻⣿⣾⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⡿⢻⣷⡀⠀⠀⠀⠀⢿⣷⣰⣿⣷⣿⣿⣾⠏⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣠⣤⡀⠀⣶⡀⢸⣷⠀⣿⣧⣸⣿⣇⣠⣦⠀⠀⠈⠻⠟⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢹⣷⢀⣿⣧⣾⣿⣷⣿⠿⠿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠘⣿⣿⡟⠛⠋⠀⠈⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⢸⣿⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⡟⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠓⠛⠶⠦⣤⣁⡀
⠀⠀⠀⠀⠀⠀⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⢿⠸⢟⡿⠀⠀⠀⠀⠀⠀⣰⠟⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⢸⡇⢻⡁⠀⠀⠀⠀⠀⣼⠃⠀⠘⠿⠇⠀⠀⠀⠀⣤⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠰⣿⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠘⣇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣆⢹⣄⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠳⢤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢤⣤⡟⠧⠴⠶⠚⣛⣉⣭⠴⠖⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠛⠛⠋⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠴⠒⠛⠙⠛⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠒⠒⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠤⢤⣤⣐⡀⠈⠁
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⠈⠀⠀⠀⠀⠁⠈⠢⣀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡢⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠦⠤⢤⠤⠤⢤⣄⡀⠀⢨
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠁⠸⠀⠀⠀⠀⠀⡀⠀⠐⠲⢀⡄⠑⠀⠀⠀⢠⠀⠀⠆⠀⠀⠀⠀⠙⣦⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⣇⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⣇⠁⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠤⠁⢀⠉⠰⠀⠀⠘⠁⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⡀⠸⡆⠀⠀⠠⡀⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⣇⠀⢷⠀⠀⢀⣀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠃⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠹⡄⠸⡀⠒⠉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠿⡿⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⣠⠞⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣨⠞⠁⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⡴⠋⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠠⢀⡴⣫⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠀⢀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢳⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⢿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠢⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠉⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡠⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠔⠊⠁⠐⠓⢒⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠷⠾⣟⣋⠁⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⢆⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠂⠉⠉⠉⠉⠒⠒⠲⠤⠤⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣀⣶⣖⣒⣒⡒⠚⠂⠈⠉⠒⠒⠤⠐⠒⠒⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⣽⣶⠶⠶⠆⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠻⠿⠿⠟⠒⠒⠒⠊⠉⠁⠀⠈⠉⠉⠉⠉⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠔⠋



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⡟⠋⠉⢿⣴⠶⢤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢣⠀⠀⡼⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⡦⣤⡷⢶⣷⠲⢿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣊⡴⠚⢉⣴⠞⢹⡇⢸⠈⠳⣄⠈⠻⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣁⠀⣰⠟⠁⠀⢸⡇⢸⠀⠀⠘⢧⡀⣽⡇⠃
⠀⠀⠀⠀⠀⢀⣀⣐⠒⣠⠤⠤⠶⠶⣮⡭⠿⣞⣹⣄⠀⠀⢸⡇⢸⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⣠⠟⠡⡍⢻⡇⠀⠀⠀⠀⡿⣸⠃⠈⠛⣷⡖⠒⢾⠀⢸⠲⠶⠶⢶⡟⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠐⣇⠀⠀⠙⣾⣇⠀⠀⠂⢸⣿⠏⠀⠀⣰⣿⠀⠀⢸⠀⢸⠀⢀⠀⢸⠇⠀⣤⠶⠶⠛⠛⠛⢷
⠀⠀⠀⠀⠈⢧⣤⠖⠚⠿⢤⣴⠤⠟⠛⢶⣡⣾⣋⣿⠀⠂⢸⡇⣿⠠⠀⠀⣿⣤⣼⡇⠀⠀⠀⠀⠀⢸⣷⠞⡛⠳⣦⡀
⠀⠀⣠⡤⠶⣾⠃⠀⠀⠀⣴⠛⣆⠀⠀⠈⢿⡉⠛⠛⢻⡆⢸⠃⢻⣠⡴⠾⠋⢰⡂⣇⠀⠀⠀⠛⠀⢸⡇⢠⠇⠀⠈⠙⣷
⠀⠀⡇⠀⢰⣏⣴⣦⠀⣼⠃⠀⢸⡆⠀⠂⠈⣧⠀⠀⢸⡗⢺⠀⢺⣹⡇⠀⠀⠀⢳⡸⡄⠀⠀⠀⠀⢸⣧⠏⠀⠀⠀⢀⡿⢰
⠀⡆⢿⣠⣼⣯⣤⣽⣴⡇⠀⠀⠀⢿⠀⠀⠀⢸⡶⢶⡾⠛⣽⠀⢸⠀⢳⡀⠀⠀⠀⠹⣷⠀⠀⠀⠀⣼⡋⠀⠀⠀⣠⡾⠁⠁
⠀⠘⡄⣿⠀⠀⠁⠀⠉⣧⠀⠀⠀⢸⡇⢰⠷⣬⡇⢸⣇⡀⢸⠀⣸⣀⣀⣿⣦⠔⠒⠒⠚⣳⡤⡖⠋⠉⠉⠳⣶⠾⠿⠶⠶⠶⠶⣦⡈
⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣷⡏⠀⠘⠁⢸⡇⠁⢸⣼⡏⠉⠁⢠⠏⠀⠀⠀⡼⠁⠀⠈⢦⡀⠀⠀⠘⢷⣀⣀⣀⣀⣀⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠀⠀⠁⢸⡏⠀⠀⠀⠀⣸⠄⠀⢸⡝⣷⡤⢤⣿⡴⢶⡄⢸⠗⠖⠛⠛⠻⢷⡀⢠⣄⡈⢿⠉⠉⢉⡏⠁
⠀⠀⠀⢸⡇⠀⠈⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠠⠀⣾⠠⠀⢸⡇⣿⢹⡄⠁⠀⠀⠙⠟⠀⠀⠃⠀⠀⠈⣧⠟⠈⠙⠻⠆⠀⣾⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⡋⠀⢀⣀⣿⣤⣤⣼⣇⣿⣄⣱⣤⣤⣤⣤⣤⡤⣤⣤⣤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠶⠶⠶⠾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠀⠀⡄⠀⠈⠃⠀⠀⠀⠙⠁⠀⠀⠀⠹⠁⠀⠀⠀⣀⡀
⠀⠐⠀⠀⠀⢰⡄⢦⠀⣰⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⣦⡀⢸⠃⠈⢳⣿⡖⠃⠐⡆⢠⣆⢀⡆⠐⡆⢠⣆⠀⠀⢰⡀⢠⡆⢸⠃⠀⣦⡀⢀⡄⢀⡀⢀⣤⠀⡴
⠀⠀⡴⣿⡖⠃⠀⠀⢸⡿⣇⠀⠀⠈⢺⣷⠋⠀⠀⠈⣾⣷⠒⠢⠀⠙⢺⣷⠁⠀⡠⣿⣶⠋⠀⠀⠙⣲⣿⠞⠁
⠀⠀⠓⣿⡇⠀⠀⣰⠏⠀⠘⢦⠀⠀⢸⣿⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠓⢸⡿⡄⠀⠀⢠⣿⣿⡇⠈
⠀⠀⠀⣿⡇⠀⠀⠁⠀⠀⠀⠈⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⢃⡗⠀⠀⠀⣿⣿
⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⢀
⠀⠀⠀⠸⢿⡿⣿⠶⠄⠀⠀⠀⠀⢰⣾⣿⣦⠶⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⡄
⠀⠀⠀⠀⢸⡗⣧⠀⠀⠀⠀⠀⠀⠸⣿⣟⠿⣄⠀⠅⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⢀⣠⡀⠀⢀⡗
⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠀⠀⠀⢠⡀⠀⠀⢰⡄⠀⠙⣇⡘⠿⣿⣿⡾⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⣿⢷⡀⠸⣿⡷⢀⢰⡌⢻⣷⣿⣿⣶⣦⠈⠁⠀⣠⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣿⣶⣿⡟⣶⣾⣾⣿⣿⣧⣹⣯⣤⡶⠟⠁
⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⣿⡷⣶⣷⣾⡟⣿⢸⣿⣿⣷
⠀⠀⢠⣧⣀⣀⡀⠀⢀⣀⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⡇⣿⢸⣿⣿⣿⣇
⠀⠀⢸⣿⠈⠁⠀⠀⠀⠀⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⣻⡿⢿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠿⠛⢿⡟⣿⠛
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⢿⠟⠃⠀⠀⠀⠀⣠⡾⠋⠀⣾⠇⠁⢿⠿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣓⣤⣀⢳⣀⡤⠚⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⡤⠠⡄⠀⠀⣿⠀⠀⠈⠉⠙⡟⠺⡷⢮⣭⣉⣀
⠀⠀⠀⠀⠀⠀⠀⣼⡀⣈⠳⣄⣠⣼⣖⣙⣤⣯⣤⠀⠀⠀⢰⠀⠀⠇⠀⠀⠀⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣭⡿⡥⢞⠻⢍⡀⠀⠘⣧⣤⣄⡜⠀⢸⠀⠀⠀⠀⢀⡿⣀
⠀⠀⠀⠀⠀⠀⠀⣏⠉⠰⢯⡴⠇⠀⢳⡄⣾⠷⠶⣏⠀⠀⡇⠀⡼⢍⠙⢯⠁⣹⡇⠀⡱⠂
⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣸⡥⠾⡀⠀⢏⠃⠀⠀⠹⣆⠠⠇⣸⣀⣀⣙⠦⣧⣼⣴⣋⣠⣤⡀
⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠙⠓⠦⣧⣀⠈⡆⠀⠀⠀⠹⣼⠀⢸⣁⣨⡭⠿⠿⣿⢿⠍⠀⠈⣷⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣄⠀⢠⡶⠛⠛⠉⠁⠀⠀⣀⣀⣽⡎⣶⠚⠋⢻⡀
⠀⠀⠀⢰⣧⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢧⣠⣤⠴⠖⢛⡏⠉⠀⠼⠛⢇⠐⣂⣈⣷⣠⣄
⠀⠀⠀⣰⠃⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⢹⡄
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⡾⠀⠀⠀⡐⡗⣀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢸⠃⠀⠀⠿⡪⡻⣗⠓⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠚⠋⣧
⠀⣾⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠛⠛⡛⠛⢻⠛⠛⠉⠉⠁⠀⢠⡄⠀⠀⢹
⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⣀⠀⠀⠀⠤⣶⣶⠄⠀⠀⠀⢀⣇⠀⠈⠀⠀⠀⠀⠠⡮⣶⢕⠵⠆⢸
⠀⣇⠀⠀⠀⠀⠀⢀⢄⣹⣳⣿⣼⣏⡠⡀⠀⠀⠘⠀⠀⠀⠀⢰⠁⠀⣱⠔⠢⢄⠀⠀⠀⠈⠡⡇⠁⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠈⠉⣽⠟⣿⡻⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠴⡃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣸⠤⠤⠤⢀⣀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠑⠤⠤⠚⠁⠀⠀⢀⡀⠤⠒⠉⢧
⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠉⠙⠛⠓⠒⠒⠶⠶⠦⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⠀⢀⠀⠀⠀⠰⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢄⠍⡂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠖⠀⠀⠀⠘⠴⠂⠁⠀⢰⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠈
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔
⠀⠀⠀⠄⢁⠄⡀⠠⠀⠂⠀⢀⠈⠁⠀⠸⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⠔⠀⠄⠐⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢰⠂⢀⠀⠀⠀⠤⠀⢀⠡⠐
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠕⢂⠀⠠⠀⠢⠄⣀⠀⠀⠀⠀⠀⠀⡠⠌⠁⠁⠀⠀⠀⣀⡀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⢀⡔⠀⡀⠐⠂⠈⠁⠀⠌⠀⠐⠁⠙⢄⠀⠀⠠⠠⡀⠀⠀⠐⠠⠂
⠎⠋⡀⠀⠀⠀⠀⠐⠒⠀⠀⠠⠁⠈⠂⠀⠀⠀⠀⣔⠀⠀⠆⠀⠀⠀⠀⠡⡈⠠⠃⠀⠐⠄⠀⠀⠀⠀⠀⠤
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠈⠀⠢⡀⠈⠀⠀⢀⠓⠀⠨⡄⠀⠀⠁⠀⠀⠁
⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡁⠀⠀⣐⠚⡁⠀⠀⣤⠀⠘⠀⢁⠀⠀⠀⡀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⢐⢂⡀⠀⠘⠀⠀⡤⡄⠈⢀⡤⠀⡠⡀⠀⠀⡄⢀⠀⢀⢠⠀⠈⠀⠈
⢀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠁⠌⠢⠀⠀⠀⠀⠈⠁⢀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠰
⠀⠀⠁⠀⠀⠀⠀⠒⡀⠤⠀⠘⢄⠸⡀⠀⠀⡋⡀⠉⣇⠂⠀⠀⠀⠠⠨⠤⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢌⢈⠁⠂⠀⡀⠈⢀⠐⡀⠀⢠⠀⠀⠀⢀⠀⠀⠄⠲⠖⠁⠀⠀⠀⠀⠀⠀⢔⡸⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢔⢄⠀⠄⠀⢀⡀⠚⡀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠡⠂⠀⠀⠀⠈⣰⠀⠠⠀⠸⠐⠈⠀⠈
⣿⣿⠛⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠊⣉⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠸⠀⠈⢪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠐⢄⠀⢣⠀⠀⢿⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀⠀⠐⢤⡑⠄⠱⣄⠈⣧⡠⠤⡒⠁⠀⠀⣀⡀⠤⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣌⣉⣁⡀⣉⣉⣐⡊⣑⣦⣬⡗⢻⢡⠀⠘⣍⠉⠁⠀⠀⠀⠀⣀⣨
⠀⠀⠀⠀⠀⢸⠉⠉⠁⠐⠒⢲⠐⠂⢉⠭⠽⠟⠉⣉⢁⡉⣲⠰⠀⡴⠮⢍⠉⠉⠛⠛⠂⠈⠉⠉⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⢸⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣤⠄⢀⡀⢀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⢸⠀⠀⢇⡀⢀⡀⠠⡤⠆
⠀⠀⠀⠀⢀⠜⢸⠀⠀⠀⠀⢸⠀⠀⢸⠉⠉⠉⠁⠐⠚⠒⡇⠀⠀⢸⠉⢹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠓⠂⢹⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢣⠔⠂⠤⠄⠘⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠂⠐⠧⣀⡠⠄⢀⡀⢀⣀⣀⣀⣀⡀⢀⡀⠠⠴⠀⠠⠔⠐⠒⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢲⣤⣚⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠉⣭⣽⣿⣿⣿⡿⠟⢛⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣯⠤⣤⡴⠾⠿⣿⠿⣿⣦⣼⣿⢿⠛⠛⠻⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣒⣉⣽⣿⣿⣿⣿⣿⣿⣯⣀⠀⣀⣿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠃⢠⣿⣤⣶⣶⠖⠀⠀⠀⠀⠸⣿⡗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣤⣤⡀⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⣿⠇⢸⡿⢿⣿⣿⣿⣿⣿⠇⠀⠉⠉⠉⠛⢚⣛⣻⣿⣿⣿⠿⣆⠀⠀⠀⣨⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡯⠻⠇⢸⣧⣴⣿⡟⣿⣿⠋⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⢠⠃⠀⣿⠀⠀⠐⠛⢿⡟⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣯⣷⣿⣿⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠎⠀⣸⣿⡀⠀⠀⠀⠀⢻⡄⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠷⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣶⣤⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣠⣴⠶⠛⠛⠛⠂⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠈⠙⢿⣧⡀⠀⠀⠹⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡾⠁⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⣀⣴⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠘⢷⡀⠀⠀⣸⠁⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠘⣇⠀⠁⠇⠀⢠⠞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡀⠀⠸⡀⠀⠀⠀⠊⠀⢀⣴⡾⠿⠿⠿⢷⣦⣀⠀⠀⠀⠀⠀⠀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠿⠷⠶⣤⡀⠀⠘⠄⠀⠃⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠐⠂⠀⠀⠉⠲⠄⠀⠀⠀⣼⣾⣀⠞⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⣰⣶⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠴⠚⠉⠙⠛⢿⣦⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠃⠀⠀⠀⡼⠁⠀⠀⠀⠀⣠⣿⠟⠉⠀⠀⠉⠀⠀⠀⠸⠧⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠸⠁⢠⣤⠀⠀⢰⡿⠁⠀⠀⠀⢠⣶⠶⠆⠀⠀⠀⠀⠈⠁⠈⠙⣷⡀⠀⠀⠀⠀⢹⡆⠀⢠⣿⣿⡄⠀⠀⠆
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⢠⡟⠁⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠼⡿⠆⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠲⡖⠲⢄⠀⣀⣀⠀⠀⠀⢰⠁⠀⠀⠊⡥⠮⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⢶⣤⡀⠀⠀⠈⠫⡔⠢⡉⠑⢤⠇⠀⠀⠀⡼⢽⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⢍⠢⢝⢦⠀⠀⠀⡘⢦⡀⠁⡜⡄⠀⠀⣰⣫⢍⡜⡌
⠀⠀⠀⠀⠀⢀⡠⠤⠚⠛⢞⡻⣷⣧⣭⣳⣄⡒⢭⡖⠋⠉⠺⣦⢀⣴⣯⢕⣫⢞⣉⢶⣄
⠀⠀⠀⢀⣴⠏⠀⠀⣀⣠⣤⠤⠥⡭⢩⢧⣟⣶⣺⣴⣀⠠⣾⢴⡿⠿⢿⣿⡛⠉⠀⠀⠀⠉⢐⠢⢄⡀
⠀⠀⠀⢸⠸⣡⢶⣟⡕⠑⠁⠊⠈⣀⠥⠛⠋⠙⠑⠝⢿⣿⡶⡥⣀⠀⠀⠀⢨⡓⢄⠀⠀⠀⠀⠈⠖⣀⣽⠂
⠀⠀⠀⠀⡆⠘⠚⠊⠉⠒⡤⠒⠝⠀⠀⠀⠀⣀⠤⠒⠋⠁⠉⠲⢅⡋⠔⡢⡀⠕⣈⣆⠀⣀⡤⣖⢏⢜⢾
⠀⠀⠀⠀⠘⢦⡀⠀⠀⢸⠀⠀⠀⡀⢀⣴⠎⠉⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠩⠛⠥⠁⠙⣮⡮⠫⡪⣡⡏
⠀⠀⠀⠀⠀⡇⠉⠳⠦⣸⠀⠀⠀⠀⣼⠉⠑⠤⣄⠀⢀⠀⡀⠄⠀⢀⣠⢴⢻⡆⠀⢸⡃⣿⡕⣕⡴⡿⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⡀⣗⠀⠀⠀⠀⠉⠒⢍⣁⡴⡚⡕⡱⣱⢿⡇⠀⢔⠂⣾⢏⢼⣫⡇
⠀⠀⠀⠀⠀⢩⠀⠀⠀⢸⠀⠀⠀⡀⡟⠓⣤⡀⠀⠀⢀⠀⣏⢮⢊⢎⢚⣯⣷⡇⠀⢕⡂⣭⠳⡟⣱
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄⠀⠀⠂⣽⠀⠀⠈⠑⠦⣜⣂⣷⣡⢷⢗⢟⢝⢼⡇⠸⣓⠄⣿⢏⢜⣼
⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⡇⠀⢨⠀⢾⠀⠀⠀⠀⠀⠀⢹⡯⡡⡣⣫⢪⡮⣻⠀⠮⣐⠠⢋⢎⡾⡏
⠀⠀⠀⠀⠀⠀⠑⢤⡑⠀⡇⠀⠀⠂⣿⠀⠀⠀⠀⠀⠀⢸⢕⠝⡰⡕⣕⢝⣽⠀⡩⢔⢸⡣⣟⢵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢇⠀⠀⠅⢸⠀⠀⠀⠀⠀⠀⣸⢫⢎⢎⢎⢮⣮⣿⠐⡪⠕⢸⣯⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢔⠅⢸⠀⠀⠀⠀⠀⠂⢸⡱⡡⡣⣣⡳⣕⡏⠠⣲⣥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠓⠤⡀⢀⣴⡂⢸⡔⡕⣕⣝⡼⠾⡣⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⡀⠀⡈⠑⠪⢔⣸⣎⠾⠊⠁
⠀⠀⠀⠀⠠⠲⢔⠩⣂⠕⡪⠔⡨⠔⡈⠔⢉⠔⡨⠔⡠⠆⡠⢚⠔⡢⠀⡠⢂⡠⢂⡠⡠⢀⠔⣀⢀⠄⡠⢀⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠁⠊⠐⠊⠐⠈⠴⠊⡠⠊⠠⢊⡄⢊⠔⡨⢊⡤⢊⠔⢈⠔⡡⠔⡡⣪⢖⡡⢊⠔⠡⠊⠐⠑⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠐⠁⠀⠁⠘⠁⠊⠀⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠰⢄⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⠂⠀⠀⠀⠀⠀⣠⠏⡐⠶⠃⠀⠀⠀⢀⡐⠂⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⢀⣞⠉⠳⠞⠀⠀⠀⠀⠀⠀⠀⠡⡌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢦⡵⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠸⠃⠀⠀⠀⠀⠀⠀⠀⣾⠤⣌⠆⠀⠀⠀⢰⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢥⠊⠀⠀⢔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣤⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢢⣀⡀⠀⠀⠀⢤⡐⠀⠁⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⡀⠀⠈⠢⡤⠀⢄⠀⠀⠀⠀⠀⠀⠠⣎⢂⢈⡰⠂⠁⠀⠀⠀⠀⢈⡤⠂⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡐⠉⢆⠀⠀⢄⡀⣠⠀⠀⠀⠀⡖⢢⠀⣩⠜⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡐⠀⠀⠀⠑⡄⠀⠀⠀⠑⢤⡈⢆⢙⡸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠒⠣⣰⣁⠁⠑⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⡠⠊⠈⠢⡀⠀⠀⡠⣅⡜⠉⠀⠀⠀⢀⠊⠈⠲⠀⠀⠀⠀⢀⣠⢉⠀⠐⠗⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⢀⠔⠁⠀⠀⢀⠜⠓⢄⠑⠉⠈⢢⠀⠀⠀⠀⠢⠄⠘⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠃⡜⠀⠀⡰⠃⠀⠀⡠⠖⠁⠀⠀⠀⣁⠦⢀⡀⠡
⠀⠀⠀⠀⠀⠀⡌⠌⠀⡠⠊⠀⢀⠤⠊⠀⠀⢀⠠⠒⠉⠀⣀⠠⠘⠋
⠀⠀⠀⠀⠀⡐⠌⢀⠔⠁⡠⠐⠁⢀⡠⠐⠈⣀⠠⠐⠊⠉
⠀⠀⠀⠀⢰⠏⡠⢃⠴⠊⡀⠄⢂⠡⠔⠒⠉
⠀⠀⠀⢠⣏⣨⢔⣡⠔⠍⠒⠉
⠀⠀⢠⡿⠟⠛⠉


⣿⢿⠿⡿⡿⠛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣟⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠈⠙⠢⣤⠶⠶⠶⣴⠊⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡤⣀⣀
⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⡟⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⣉⡹⢶
⠀⠀⠀⠀⡏⠉⠓⠲⠤⣼⡁⠀⠀⠀⠀⢀⣠⠴⠓⡶⠒⢶⡛⠦⢤⣀⠀⠀⠀⠀⢸⠛⠉⠁⠀⢸
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢳⠤⠴⠒⡿⡽⠁⠀⡼⠀⠀⠀⢱⡄⠀⠙⣟⠙⠒⢲⡏⠀⠀⢀⣀⡼
⠀⠀⠀⠀⢸⠓⠲⠤⢤⣀⣸⠀⠀⢀⠟⠀⠀⣰⠋⠑⡖⠋⠁⢱⡀⠀⠈⢦⣀⣸⡧⠖⠊⠉⠈⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⠉⢳⢋⣀⠀⢠⡃⠀⠀⡇⠀⠀⣀⣧⠀⢀⣀⢣⠰⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠉⠉⣿⡰⠋⠉⠙⠒⡗⠚⠉⠀⠀⢣⣼⠈⠙⢡⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⢤⣀⡀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠸⣇⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠾⣄⣀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⣀⡀⡇⣀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠂⢄⠀⠀⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡌⠀⠀⠀⠠⢂⢈⠀⢠⠀⢀⣔⡁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠀⠈⠀⠀⠀⠑⠀⠀⠘⠒⠈⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠀⢀⠄⠊⠈⠀⠄⠐⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠄⠀⠠⠊⠀⡁⠀⠂⢈⠀⠘⢹⠀⠋⡇⢘⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡀⢀⠔⡀⢡⠠⠖⠁⠀⠀⠈⡛⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡵⠀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢺⡬⠳⡄⠀⡀⢠⠀⠀⠀⠀⠄⠀⣀⡄⠀⠈⠀⠀⠀⠃⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠘⠀⡀⢈⡔⠦⠤⠤⢤⡤⠖⠊⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠌⡠⢊⢔⡇⠀⠀⢀⡴⢙⡧⠁⠀⠀⠒⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠂⠤⠤⠰⠊⢄⠔⠡⡇⠔⣠⢎⡽⠶⠀⠀⠀⠠⠊⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡰⠁⡵⠎⠀⣃⠈⠁⠀⠻⢟⠥⠶⠐⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⢗⡵⣿⠸⠾⢿⠀⣾⢗⣕⣿⡷⢳⣿⠿⠅⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢐⢿⡂⢀⠀⣀⢰⠀⢀⡄⡀⣀⠀⢸⣖⢐⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡊⢙⠃⠉⠈⡃⠈⡛⠋⠑⠃⠘⠑⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠿⠻⠛⠃⠀⡟⡇⠀⢚⠕⡫⠟⢻⠟⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠠⠀⠁⠀⢙⡃⠀⢐⠨⡠⠀⡔⡊⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠀⠀⠀⢰⡅⠀⠐⡨⠐⠁⣏⠀⠁⠠⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⢰⠠⡀⠠⠅⠀⠥⢒⠁⢀⠔⠀⠊⠊⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⠀⠀⠘⢦⢙⡲⠀⠐⠉⠔⡁⢘⠤⠠⠤⠒⠋⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠻⠘⠫⣏⠁⠀⠀⠀⣀⠀⠛⠀⠀⠠⠐⠨⣀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠋⠁⠁⠐⠀⠐⠈⠐⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠛⠤⡀⠀⠀⠈⠲⣖⠛⠒⠦⠤⣠⠞⠁⠀⠀⠀⢀⠼⠛⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡼⠦⣄⠈⠢⢄⠀⠀⠈⠳⡀⢀⡴⠁⠀⠀⠀⡠⠔⢁⡠⠴⢥⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠒⠉⠁⡔⠛⠒⠢⠤⣉⡒⠢⠭⣶⣤⣤⡬⠿⣤⣤⣤⢶⠭⠐⣊⣡⠤⠐⠒⠛⠳⠦⢤⣄⣀
⠀⠀⠀⠀⡴⣖⡋⠉⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣀⣀⣀⠈⣑⣢⣤⠴⣿⢤⡤⢞⡳⠤⣴⣒⠉⣁⣀⣀⡀⢀⣀⠔⠁⠀⠀⠈⠉⢑⣲⣦
⠀⠀⠀⠀⡇⠀⠉⠙⠒⠤⣄⣀⠀⢀⣀⠤⠒⢋⣉⠤⠔⠚⠉⠱⠒⠋⠁⡼⠳⣀⠉⠉⠀⠈⠑⠒⠤⢍⣙⠒⠤⣀⡀⣀⡠⠴⠚⠉⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢹⢛⡶⠒⠋⠉⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠈⠙⠢⡖⢹⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣤⡚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⡀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠳⢤⣀⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠙⠒⠦⣄⣀⠀⢀⣠⠴⠒⠉⠁⠈⢦⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⢸⠀⠉⢱⠋⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢠⡷⠒⠋⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠈⢇⠀⠀⠀⠀⠀⢀⣼⡁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⢈⣦⠀⠀⣠⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢦⠀⠀⠀⣠⠋⠀⠉⡗⠲⢤⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⡠⠔⡟⠉⠀⠱⠔⢹⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠳⣄⡜⠁⠀⠀⠀⡇⠀⠀⠀⠉⠓⠲⢤⣀⡀⢸⠀⣀⡤⠖⠋⠁⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠲⠤⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣀⡤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢼⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡼⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣯⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢄⡀⣿⢀⡠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡟⠉⠙⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠁⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠷⠀⠀⠉⠓⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠴⠶⠾⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠳⣄⠀⠀⠀⠀⢠⡞⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⠟⠶⠶⠦⠤⣀⠈⠙⢷⣤⠙⣦⠀⢀⢀⡞⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⣀⠐⠲⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣶⣤⡙⢷⣈⣏⣉⣸⢁⣾⠙⣀⣤⣴⣶⣾⣿⠿⠛⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣶⣤⣤⣤⣀⣀⣀⣀⣤⣿⣿⣿⣿⣏⣉⠉⠉⣿⣷⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣈⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣾⣉⡉⣩⠟⠉⠉⠉⠉⠉⠉⣉⣽⠿⣿⣿⢿⣿⣿⣿⣿⣿⣷⡶⠶⠶⣶⠶⠶⠒⠚⠛⠋⠭⣙⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢈⡟⠁⠀⠀⠀⢀⣤⠖⠋⠁⢀⡤⠚⠁⠀⠀⠀⠙⠻⣄⡉⠉⠛⠒⠦⢤⣀⠀⠀⠀⠀⢀⢀⣹⡏⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠏⠀⠀⠀⠀⣰⣿⣿⣿⣷⣲⢯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⣀⣀⣼⣦⣴⠀⠾⡘⠃⢳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⡁⠀⠀⠀⢀⣴⡯⣿⣿⣿⣿⡏⠀⠀⠉⠛⢲⢤⣄⡀⢀⣀⣠⡴⠚⢿⠻⠿⠻⠿⣿⣿⡆⠀⠁⠀⠈⡆⡇
⠀⠀⠀⠀⠀⢀⣴⣚⣉⣀⣊⡀⠀⠀⢠⣾⣿⡇⣿⣷⣿⣿⡇⠀⠀⠀⠐⢀⡄⢉⣿⠉⠁⠀⠀⠀⢸⠀⠀⢬⠀⢽⢹⡇⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⢠⣿⠇⢀⣴⡿⠿⢾⡇⡟⢹⣿⣿⡇⠀⠀⠀⠀⠢⣠⣷⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢃⣴⣿⠿⠀⠀⠀⡿⡇⢸⣿⣿⣧⣤⣀⠀⠀⠀⠩⣙⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⣤⣀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠞⠉⢹⠀⠀⠀⠀⠀⢻⡀⢰⡱⣿⡇⠉⠙⠻⢶⣦⣴⣾⣿⠀⢀⣠⣴⠶⢿⡇⠀⠀⠀⠀⢸⠛⣿⣆⠀⠟⣿⠑⠲⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣺⠀⢠⡿⢸⡇⠀⠀⠀⣠⠋⠙⢿⡟⠟⠋⠉⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠈⠻⣷⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠈⠘⢹⡇⠀⠀⡰⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⡇⠀⠈⠀⠀⠠⠈⠸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣤⣀⠀⢻⡀⣀⠀⢸⡇⠀⠀⠀⠀⠁⠂⠠⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣿⣮⡀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢀⣠⣶⣾⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢴⣧⣀⠀⠀⠀⠀⢀⢋⣷⠀⠀⠀⠀⠀⠀⡇⢀⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣀⠀⠘⡟⠀⢀⣠⡤⠶⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠿⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢶⣶⣄⣿⣿⣤⣄⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣶⣾⣿⣿⣿⣿⠛⠉⢩⣽⣿⣿⣿⣿⡟⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⣿⣿⣿⣿⠧⠤⢤⡶⠾⠿⢿⣿⠻⣿⣷⣴⣿⡿⢟⡋⠉⠛⠛⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡚⣋⣽⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⢨⣿⠀⠸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡇⠀⣿⣇⣠⣤⣤⡤⠄⠀⠀⠀⠀⠸⣿⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣡⣾⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⣿⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣽⣿⣿⢿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠻⠿⠭⢭⣍⣛⣻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠙⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⣿⣇⠀⣾⡟⠛⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⠿⣿⠋⢹⡇⠀⠀⠀⢰⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠙⠛⠀⣿⣴⢶⣿⣿⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢠⠃⠀⢸⡇⠀⠀⠀⠉⠙⢿⡝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣮⣷⣿⣾⣿⣟⠀⠀⠀⠀⠀⠤⣤⣀⡀⠀⠀⠀⢀⠎⠀⢀⣿⣯⡀⠀⠀⠀⠀⠀⢳⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⣀⣎⣀⣴⣿⣿⣿⣷⣆⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⢻⣿⣿⣾⣿⡿⠉⠙⠛⠿⢿⣷⣆⣤⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⡿⠛⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠈⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⡀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠸⢷⣄
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢞⠛⢶⠹⡊⡴⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⠶⣶⢏⢹⣿⡐⠢⣜⠐⠀⣣⠔⢒⣿⡏⡹⣖⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⠁
⠀⠀⠀⠀⠘⣿⣏⣾⣺⠁⠙⢽⠻⡟⠑⡼⠂⣰⢿⡟⣧⠙⢿⣦⡑⠂⠘⢊⣴⡾⠋⣾⢛⡿⣆⠐⢤⠊⢹⠿⡯⠋⠉⣗⣷⣻⣿⠃
⠀⠀⠀⠀⠀⠙⣿⣡⣿⣭⣒⡬⢄⡁⠠⣕⣻⠃⢾⠧⠟⣤⣦⡍⠛⢦⡴⠛⢩⣴⣤⠷⢾⣷⠘⢟⡫⠄⢈⡠⣥⣖⣽⣿⣬⣿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣉⡽⣿⡿⣷⣌⠄⠩⢙⡲⠛⠉⢰⣿⣿⡏⠀⠘⠋⠀⢹⣿⣿⡆⠹⠛⠖⢏⠌⠐⣡⣾⢿⣿⢧⣘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣞⢟⡄⢙⣿⡌⢠⡆⢀⡀⠰⠄⢸⣿⡇⣤⣠⣆⣤⢸⣿⡃⠰⠄⢀⡀⢰⠄⢁⣿⡋⢠⡻⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢰⣷⡇⠀⠁⡿⡏⢠⢒⡟⢢⢹⣾⠳⢞⣷⡏⡔⢳⡒⡆⢹⣿⠈⠀⢸⢿⡄⣸⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣗⡇⠀⠀⡇⢠⠌⠉⢸⡟⣸⠛⠃⠘⠛⣇⢿⡇⠉⠡⡄⠺⠀⠀⢸⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⢿⣳⣶⣾⣧⣿⡀⠀⠀⢀⣿⣼⣷⣦⣞⡿⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⣷⣽⣆⣸⢿⢧⡀⢀⡼⡿⣅⢰⣯⣾⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢀⣤⣤⣤⡀⠉⠉⢿⠿⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢀⠀⠀⣀⠀⣄⠀⢀⣀⢀⣀⠈⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠈⠛⠛⠋⠀⢹⠀⠀⠉⠋⠁⠀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠛⠒⠒⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠦⣤⣄⣠⡤⠴⠚⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣏⠻⢅⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢦⡈⠳⡄⠻⡌⢳⡀⠀⠀⠀⠀⠀⢀⡴⢲⡶⠋⣡⠿⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⢦⣈⠃⠀⠀⠀⠀⢳⡀⠀⠀⠀⣠⠏⠀⠁⠰⢋⡠⠖⢛⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠙⠦⣌⠀⠀⠀⠀⠀⠀⢳⡀⠀⣴⠃⠀⠀⠀⠀⠈⠤⠞⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠈⠻⣆⠀⠀⠀⠀⠀⠹⣾⠁⠀⠀⠀⠀⠀⣠⠴⠋⠁⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣴⠋⠁⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠻⣤⡞⠁⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣻⣦⡀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣠⡴⠞⠉⠈⠙⠶⠦⠴⠞⠋

⠀⠀⠀⠀⠀⢰⠀⠀⡆⢰⢠⠰⠀⠀⡂⠀⢰⡆⡜⡀⠂⢰⠀⠀⠀⠀⢀⣀⣠⣤⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⢸⠀⠀⡂⠸⠸⠀⡷⠰⡁⠀⠈⠀⢇⡀⢀⠈⠀⠀⠀⠀⠈⠿⣿⠏⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢨⠀⡏⡄⠀⢰⠀⣖⠀⢸⢠⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠆⢃⠇⠀⠆⠞⢸⠀⡘⠘⡀⠊⠇⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⡀⠀⠁⠀⠀⠀⠉⠉⠉⠉⢹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠣⠀⠀⠀⠀⠀⠀⠀⣀⠈⠿⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⡔⢹⠖⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠳⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⠄⠀⠀⢀⠀⢀⠠⠀⠀⢀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢸⠀⠁⠀⢀⠔⠁⡠⠁⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⣸⠀⠀⠀⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⡘⢀⠀⡠⠊⢀⠔⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⠇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠠⠄⠒⠁⠀⣉⣀⠐⠁⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠚⠿⣿⣿⣿⣿⡀⠀⠀⠈⠀⠀⢆⠀⠀⠉⠑⠢⣄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⢀⠀⠈⡆⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⡘⠒⠢⠥⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⣴⣾⠿⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⡠⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡆⠈⠳⠄⢠⣾⣿⣿⣿⣾⣿⠇⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⣠⠃⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠤⠀⠃⠀⠀⠀⠈⠻⣿⣿⠟⠋⠀⠀⠁⠒⢤⡀⠀⣸⠁⠀⢀⠞⠁⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠐⠢⣀⠀⠀⠀⠈⠀⠀⠢⢄⠀⠀⠐⡉⠓⠀⠃⢀⣴⣿⣦⡀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡠⠈⢙⠀⠠⠀⡀⠀⠁⡀⠌⠂⠀⠈⠂⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⡐⠀⠰⠁⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⠉⠀⠀⠀⠀⠀⠹⣿⡿⣷⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠙⠲⠤⣤⣀⠰⠀⠀⠤⠤⠄⠀⠐⠊⠀⠓⠤⠤⠀⠀⠀⢀⠊⠀⠀⢹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠶⠴⠶⠶⠖⠒⠊⠐⠒⠒⠶⠶⠶⠶⠖⠒⠒⠒⠂⠁