Sweetness Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠀⠄⢀⣀⣀⢀⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⢀⡠⠄⠠⡀⠀⠀⠀⠈⠃⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⠉⠀⠀⠀⠈⢢⠀⠀⢠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣁⠈⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠣⡀⠀⠀⡠⠂⠐⠒⠀⠐⠁⠀⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣀⠤⠤⣀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠣⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠀⠀⠑⡀⠀⠈⢆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣎⢄⡀⠀⠀⠣⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⣰⠀⢀⡠⠜⠒⠒⠈⠁
⠀⠀⠀⠀⢀⠔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠀⠀⠀⡃⠈⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠂⠐⠒⠚⠢⠔⠊⠁⢱⠀⠀⡎⠀⠈⢆⠀⠀⠀⡠⠠⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢃⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠁
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠒⠀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠀⠒⠒⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠄⠠⠄⠀⠒⠒⠒⠀⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣤⣶⣶⣷⣿⣿⣶⣄
⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠛⠛⠋⠀⠀⣀⠀⠀⠀⠘⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠛⠛⠉⠀⠀⣀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⣄⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣹⠀⠀⠀⠀⣶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠃⠩⣆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠗⠣⠶⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠟⠣⠶⠂⠀⠀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠾⠤⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠋⡘⠒⠒⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠋⡐⠒⠖
⠀⠀⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢠⠖⠒⠒⠦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡅⣀⡄⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠠⠄⡀⠀⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠠⢌⡀⠀⡃
⠆⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣖⡶⠂⠀⠀⠀⠘⠂⠠⠠⠔⠁⣀⡀⠀⡂⠈⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠰⠋⠘⠃⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡍⠙⢠⠆⠀⠀⢸⠐⠋⠘⠃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡍⠉
⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⡁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⠤⡤⠞⠁⠀⢀⡀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⠀⠀⢶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠄⠀⢲⣶⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⠀⠀⡀⠀⠀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠈⠛⠛⠉⢀⠀⡀⠀⠀⠀⠘⠉⠛
⠀⡀⡄⢠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣻⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣠⠀⠀⠈⠀⠀⠀⠀⠀⠤⠤⠈⣛⠀⠀⠀⠀⢶
⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠉⣦⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠃⠩⣦⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⡄⠈⠛⠁⠀⠀⠈⠕⠃⠶⠂⠀⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠙⠁⠀⠀⠈⠟⠣⠶⠂⠀⢀⠀⠀⠤
⣤⠀⡀⠀⠀⠀⠙⠺⠤⠄⠀⠀⠀⠀⢀⠀⠀⠰⠀⠋⡐⠖⠐⠀⠀⠁⠀⠀⣤⠀⡀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢋⡐⠖⠚
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠁⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⢠
⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢠⠖⠒⠒⠦⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢠⠖⠒⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣆⠠⠌⠁⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡆⠠⠌⡉⠀⡃
⡆⠈⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠃⣀⡀⠀⠂⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⢠⣖⡶⠂⠀⠀⠀⠐⠂⠠⠠⠔⠁⣀⡀
⠃⠀⠀⢸⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠝⢰⠆⠀⠀⢘⠐⠋⠘⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⡝⠙
⠀⠀⠀⠈⠷⠤⠤⠞⠁⠀⢀⣀⠀⠀⠀⣾⣷⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⢦⡴⠞⠁⠀⢀⣀⠀⠀⠀⣸⣷⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠹⡿
⠀⠀⠀⠤⠀⠀⢀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⢲⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣼⠏⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⣠⣴⠾⠋⠀⠀⠀⢀⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣴⡿⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⢀⣴⠟⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡀⠀⣰⡿⠁⠀⠀⢀⣀⣀⡀⠀⣴⠟⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⣀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠈⢻⣶⣿⣤⣴⠶⠟⠛⢻⡏⠻⢿⣯⣀⣀⣤⣴⠾⠛⢻⣿⠛⠷⢶⣶⡟⠋⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡟⠉⠁⠀⠀⠀⢸⡏⠀⠀⠀⣿⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢿⡄⠀⠀⠀⠘⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠘⣷⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣧⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⣼⡇⠀⢸⡏⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⢿⡆⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣦⣾⣧⣤⣤⣿⣄⣀⣀⣀⣴⣿⣤⣴⣿⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⡶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⣶⣶⣶⣶⢶⣶⠶⣶

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣌⣡⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠿⣿⣿⠿⣛⣛⠿⣿⣿⠿⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣝⡛⢿⡿⣛⣫⣝⣛⢿⡿⢛⣫⣝⣛⢿⡿⢛⣋⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣝⠻⢟⣭⣭⣭⣍⡻⢟⣩⣭⣭⣍⡻⠟⣫⣭⣭⣭⡻⠟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄
⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠄⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠃⠀⠂⠐⠈⠠⠀⠈⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⢠⠀⠂⠀⠐⠀⠂⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⢥⡿⠳
⠀⠀⠀⠀⢣⠀⠁⠀⠀⠈⠀⡰⠐⢆⠀⢩⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠩⠀⢘⣄⢀⠀⡰⢅
⠀⠀⠀⠀⠈⡄⠁⢸⠉⠑⠒⠁⠀⠈⠂⠔⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡀⠀⠀⠉⠈⠁⠠⠱⡀
⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣤⡦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⢤⡞⡻⠁⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡡⠊⡜⠀⠀⢇⠁⠚⠤⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢰⠁⢐⠁⠀⠀⠀⠳⡄⠀⠀⠻⡝⢧⡇⣐⢲⣄⣀⡤⡀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⡀⡤⠒⢺⡅⠀⢠⠀⠐⡆⠀⠀⠀⠀⢸⠀⠀⠀⣟⠻⠀⢏⠁⠈⢢⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⡀⡜⠑⠤⠌⢦⡀⠘⣦⣀⢀⡀⠜⠀⠔⠊⠇⠓⢖⠈⠙⢍⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠕⠒⢘⡛⠊⠍⣢⡠⠊⠢⡠⠚⠳⣠⠞⠒⠤⠒⢆⡤⠲⢖⡚⡳⣆⣞⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡹⠁⢙⠒⠶⠀⢵⠀⠀⢆⠀⠀⡆⠀⠀⠇⠀⣘⡠⠚⡉⠁⠄⠀⠀⠀⠠⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠘⡀⠘⡀⠀⡆⠀⢸⠀⠀⡇⠀⢸⠀⡠⠋⠀⢂⠀⠀⡤⠤⠊⠢⢄⡀⠁⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢱⣀⡵⠤⣰⠀⠘⡂⠀⠀⠀⡌⢠⠁⡀⠀⠀⢪⠝⠉⠈⠉⠈⢰⠇⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⠹⠆⠀⠺⡁⠈⠛⠀⠀⠈⡇⠀⠇⠀⠀⠀⠇⢰⣀⡀⢀⡁⠀⡑⠲⠄⠒⠒⠅⠀⠀⡘⠑⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⡌⠁⠘⣄⡠⠤⡀⠀⡤⠤⠰⠋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠠⠊⠑⠠⠄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⠈⠉⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⢤⡤⣤⡷⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⠬⡇⠀⠀⠀⠀⠀⠀⣠⠼⠁⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⡟⠲⠊⠙⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⣇⢀⣀⠀⢀⣀⠀⣸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢛⡏⠀⠀⠀⠀⠀⠀⠈⢻⡀⡍⢩⠄⡏⠁⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣇⡖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣄⣠⢧⡀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠱⡖⠁⠀⠀⠀⠀⠀⠀⢀⡤⠧⠾⢤
⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⡞⠛⠒⠛⠛⠛⠋⣻⠀⠀⠀⠀⠀⠰⣧⣠⢄⣤⣤⡷⠀⠀⠀⠀⠀⠀⠀⣸⠖⠦⠔⠺⡇
⠀⠀⠀⠀⠀⠘⠲⣍⣙⣚⣉⣙⣒⣋⡹⠚⠁⠀⠀⠀⡿⠿⠿⠿⠿⠝⠛⢿⠀⠀⠀⠀⠀⠀⠘⢦⣶⣤⡞⠀⠀⠀⠀⠀⠀⠐⢾⣛⣒⠒⠒⣓⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡗⢯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡔⣩⠥⠬⣝⢦⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠎⣡⠤⣍⠓⣄⠀⢳⠀⠀⠀⠀⠀⢸⢸⠁⡏⠵⣸⢀⡇⠀⠀⠀⠀⠀⢸⡁⢀⡀⢀⡀⢀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡁⣄⠈⡇⢸⡆⣸⠀⠀⠀⠀⠀⠈⢮⡳⢬⣯⡵⠾⠃⠀⠀⠀⠀⠀⣿⠙⣯⢹⡏⢹⡇⣹⠂⠀⠀⠀⠀⠀⣿⣿⣯⣍⣉⣽⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡳⣌⣙⣁⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢿⢸⡇⣼⢠⡏⠀⠀⠀⠀⠀⠐⡏⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠛⠛⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠠⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⢮⡹⣆⠀⠀⠀⠀⠀⠀⠀⢧⢠⡤⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠸⠁⠀⢀⠁⠀⢳⠀⠀⠀⠀⠀⠀⣰⢻⡄⢳⠀⡟⠋⠀⠀⠀⠀⠀⢰⡋⠚⠁⠀⠙⢋⣷⠀⠀⠀⠀⢰⢏⠀⢧⠀⠀⡼⠁⡹⡆
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠃⢀⡏⠀⠀⠀⠀⠰⣎⠳⣀⢣⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠰⡏⠀⠀⠀⠀⠀⠸⣄⢹⡚⠓⠚⢑⡟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡖⠛⠋⠀⠀⠀⠀⠀⠀⠘⠲⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠲⣄⠙⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⣤⠖⢿⠉⡟⢑⠦⣄⠀⠀⠀⠀⠀⠀⠀⡖⠒⢏⠉⠓⢦⡀⠀⠀⡞⢳⠞⢳⠞⢛⠖⢛⡖⢛⡆
⠀⠀⠀⠀⢀⠾⣀⠳⣸⣼⣡⣋⠴⠚⢧⠀⠀⠀⠀⠀⢠⠟⢦⡀⠑⢄⠀⢳⠀⠀⣇⡏⢀⡎⠀⡞⠀⡞⠀⡼⡇
⠀⠀⠀⠀⢸⠦⠬⢵⣿⣿⣿⣷⣚⣉⣙⡆⠀⠀⠀⠀⠈⣇⠀⠙⢦⡀⠑⡏⠀⠀⣟⣀⣜⣀⣼⣀⣼⣁⣸⣁⡇
⠀⠀⠀⠀⠸⡖⠒⣩⢿⢿⢿⢯⠲⢤⣹⠁⠀⠀⠀⣠⢞⡽⠓⠲⠶⠛⠒⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡽⣏⣠⠏⡼⠸⡆⢳⡴⠃⠀⠀⣠⢞⡵⠋⢀⣀⠤⣀⣀⠀⠀⠀⠀⣠⠖⠒⠒⠒⠦⣄⠀⠀⠀⢠⠒⡿⠛⠛⠓⣦
⠀⠀⢀⡴⡫⠊⠀⠉⠓⠓⠒⠋⠁⠀⠀⠀⣞⡵⠋⠀⠀⡇⠀⠀⠈⢉⠇⠀⠀⣼⠁⢠⠖⠓⠂⠀⠘⡆⠀⠀⡞⠉⠛⠓⠒⠋⢹
⢀⡴⡫⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡜⠀⠀⠀⠹⣄⠀⠁⠀⠀⠀⡰⠃⠀⠀⣇⠀⠀⠀⠀⠀⣀
⠻⠚⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣼⡅⠀⠀⠀⠀⠈⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢶⠲⢤⠋⠉⠉⠉⠈⠈⠙⡤⠖⡆⠀⠀⠀⡼⠉⠉⠉⢧⠀⠀⠀⠀⢠⠤⣄⣀⠔⠚⠉⠓⢦⣀⣠⠤⣤
⠀⠀⠀⠀⠀⢯⢀⣸⣄⠀⠀⠀⠀⠀⢠⣇⠀⡝⠀⠀⢰⠁⠀⠀⠀⠈⣇⠀⠀⠀⢞⠀⠀⡏⠀⠀⠀⠀⠀⡯⠀⠀⣣
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠺⠤⠤⠤⠤⠤⠿⠀⠀⠀⠾⠴⠒⠛⢦⣀⣀⣀⠴⠋⠒⠮⠇
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⡅⡇⠀⠀⠀⣀⣠⣄⣀⡀⠀⠀⢸⢨⠆⠀⠀⠀⠀⡏⠀⢠⠃⠀⡼⠁⠀⡼⠁⠀⡼⠀⢈⡷⡄
⠀⠀⠀⠀⠀⠀⢘⡅⡇⠀⠀⡎⠁⠀⠀⠀⢹⠄⠀⢸⠠⡃⠀⠀⠀⠀⠈⠓⠛⠒⠚⠓⠒⠚⠓⠒⠚⠓⢲⠋⠀⢹
⠀⠀⠀⠀⠀⠀⢨⠆⡇⠀⠀⠈⠒⠶⠴⠒⠋⠀⠀⢸⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⠚⠒⠋⡽
⠀⠀⠀⠀⠀⠀⠰⠷⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣓⡦⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣺⠝⡎⣿⢟⡯⣑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢤⡀⡵⠚⠁⣸⢸⡇⢸⡆⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠞⣋⣁⡿⢭⣶⠛⠃⠛⡠⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠠⠂⠉⢀⣡⣤⣴⣶⡦⠥⣤⡤⣶⢿⣿⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⣠⠶⠛⢋⡉⠏⠤⢐⣒⠿⠩⢞⠟⣸⣿⡇⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡞⢁⡤⠊⢁⡠⠖⠋⢀⣀⠀⠤⠐⢒⣹⠟⣡⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⢿⡇⡎⠀⢠⠋⢀⡴⠊⠉⣠⠤⠐⢚⡩⠔⠉⢁⣰⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡷⢤⣀⠙⠻⢤⣽⣀⣾⢀⣴⣏⣁⣠⡴⣿⣗⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⠁⠒⠂⢬⠭⠽⡭⢿⢿⠾⡷⢿⡛⣻⣹⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢸⠀⡏⡾⡇⣇⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⢹⢸⢈⢠⢇⣃⣹⢻⢳⣿⣿⣥⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣄⡆⣰⡀⠀⡄⢸⣼⣴⣸⣸⣷⣾⣿⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠽⣿⣧⣠⡦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⣿⣿⣿⣿⡿⠿⠻⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠶⠶⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠳⢤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡶⠶⠟⠋⠉⠀⢀⡿⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠻⣦⡀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⢤⣀⠻⣤⣈⡙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠋⣁⡰⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠉⢳⡘⢷⢮⣯⡹⣦⣤⣀⣀⣩⡭⠿⠿⠿⠭⣤⣤⣤⡴⠶⠞⣉⡴⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡆⠹⣟⠳⢦⣍⣉⣁⣀⣀⢀⣀⣀⣀⣀⣤⠤⠖⠛⠉⢀⡴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⢰⡄⠈⡇⢹⡀⢸⡆⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢀⣀⣠⡤⠄⠀⠉⢠⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠃⠀⣧⠀⠀⠐⠒⠒⠒⠒⠛⠛⠋⠉⠉⠀⠀⠀⣠⡴⠋⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⣼⠀⠀⡿⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⠁⣠⠞⣽⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣸⠇⡿⠀⢰⡗⠦⣄⣀⣀⣀⣩⡥⠶⠛⠒⠚⠛⠓⠶⠶⢛⣩⣾⡃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡿⢰⡇⠀⣾⠷⢦⣬⣉⣉⣉⣀⣀⠀⢀⣀⣀⣀⣤⣴⠾⠛⠉⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⠃⣼⠀⢸⠏⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⢀⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠏⣰⠇⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠚⠉⣠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢠⡞⢁⡼⠃⣰⠋⢠⡞⢣⡉⠓⠶⢤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣞⣩⡴⢋⣠⠞⣁⡴⠋⠹⣦⡳⠶⣄⠀⢀⣈⣭⣙⣛⣛⣛⠛⠛⠛⠛⠋⣉⣤⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠠⠖⠛⠚⠋⠉⠀⠀⠀⠈⠛⠶⣬⣍⣉⡀⠀⠀⠀⠈⠙⠛⠛⠋⠉⢉⣉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⢀⣠⣶⣶⣤⡀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⣠⣶⣿⣿⡆
⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⠟⠁
⠀⠀⠉⠛⠿⠟⠉⠀⠀⠀⠀⠿⣿⣿⡿⠇⠀⠀⢠⡾⠋⠉⠁

⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⣶⣿⣿⣷⡆⠀⠀⠀⢀⣤⣶⣶⣤⡀
⠀⠀⢿⣿⣿⣿⣶⣦⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠿⣿⠿⠛⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠠⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⣾⣿⣿⣿⣷⣦⠀⠀⢰⣿⣿⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠻⠟⠹⠿⠋⠁⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠘⠿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⣠⣴⡄⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⢀⣤⣾⣿⣿⡿⠃⠀⢰⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⡿⠟⠋⠀⠀⠀⢾⣿⣿⡿⠟⠁⠀⠀⠘⠿⢿⣿⡿⠿⠃
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣠⣾⣿⣿⠇⠀⠀⣠⣾⣿⣿⣿⣷⡀⠀⠀⢀⣼⣿⣿⣶
⠀⠀⢼⣿⣿⡿⠋⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⣡⡤⠀⢀⡄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⡀⠁⠀⠀⠉⠀⠀⠀⣀⠀⠀⠠⠤⡦⠀⣶⠁⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠁⠀⢠⣴⠀⠀⠀⠈⣠⣤⡀⠀⠀⠀⠀⣿⠀⠁⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠁⠀⠐⠿⠋⠀⠀⠀⠠⠿⠛⠀⠀⠀⠀⢴⡏⠀⠀⠈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠀⣼⠇⠀⠀⠀⠈⠀⠈⠁⠀⢸⣷⠀⠀⢠⡄⠻
⠀⠀⠀⠀⠀⢀⠀⠀⠸⠋⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣼⠋⠀⠀⠀⠠⣶⣶⣄⠀⠀⠀⢀⠀⠀⡈⠀⢠⣷
⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⣠⠀⠀⠀⠸⣿⡇⠀⠀⠀⠊⠀⢀⠀⣠⣾⣥⣤⠆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠐⠀⣰⣿⠃
⠀⠀⠀⠀⣿⢠⡷⣤⠄⠘⠁⠀⠀⠀⠘⠉⠀⠀⠀⠀⠊⠀⣠⣿⣯⣇⠉⠡⠄⠀⠀⠐⠃⢀⡤⠀⠀⠀⠀⢈⣦⣾⡿⠃
⠀⠀⠀⠀⢀⣌⡛⠯⡀⠀⠀⠀⠀⡀⡤⠶⠄⢀⣠⣤⣾⣿⣿⡞⠉⠩⡍⠁⢉⠉⠉⠉⠀⠈⠄⢀⣀⣴⣾⡿⠟⠋
⠀⠀⠀⠀⠈⠛⢧⣤⣄⣀⠀⠀⠀⣤⣴⣶⣿⣿⣿⡿⢿⡿⢿⡷⣤⣴⣿⣿⣿⣦⣤⣤⣤⣾⠿⣿⠛⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠐


⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡿⠿⠿⠿⠿⠛⠋⠉⠙⠻⢿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣿⣦⣤⣴⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣉⠛⠻⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⠿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣧⠀⠈⠻⣿⣿⣷⡄
⠀⠀⢀⣾⣿⡟⠁⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢻⣿⣿⣿
⠀⠀⢸⣿⣿⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿
⠀⠀⠈⢿⣿⣆⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠟⠁⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠙⢿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣾⣿⣿⣿⡿⠋⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⢀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣀⣤⣴⣶⣶⡄⠀⣶⣦⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⠇⣰⣿⡿⠛⠉⠉⠁⠀⠀⣿⡏⠀⠀⠀⠀⣿⡇⠀⢀⣴⣶⣿⣿⣷⠀⠀⠀⠀⢀⡄⠀⠀⠀⣶⣶⣶⣄⡀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⠀⣿⣏⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⣿⡇⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⣿⣿⠙⢿⣷⡀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⠀⠹⢿⣷⣤⣀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⣿⡇⣸⣿⠇⠀⣀⣀⣀⠀⠀⠀⣼⣿⣿⡇⠀⠀⣿⡏⠀⢸⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠉⠛⢿⣿⣦⠀⠀⣿⣷⠀⠀⠀⣸⣿⠃⣿⣿⠀⠀⠛⠛⢿⣷⠀⣰⣿⣏⣿⣿⡀⢸⣿⣇⢀⣼⣿⠇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⢹⣿⣆⠀⣠⣿⡟⠀⢿⣿⡄⠀⠀⢀⣾⡿⢠⣿⡿⠿⠿⣿⣧⢸⣿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠇⠀⢿⣿⣿⣶⣿⡿⠟⠀⠀⠀⠙⠿⣿⡿⠟⠀⠀⠈⠿⣿⣷⣾⣿⠟⠁⠻⠟⠁⠀⠀⠹⣿⢾⣿⡏⠻⣿⣷⡀⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠻⠿⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣇⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠉⠉⠛⠿⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⣼⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠹⣿⣿⣷⣦⣤⣤⣤⣴⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄
⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣦⡀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣿⡿⠿⠿⣿⠉⠛⠋⠀⠰⠞⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⠛⠀⠀⠀⠀⠀⠤⠤⢆⣀⠀⠀⠀⠈⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡇⠀⠀⠀⠀⠀⠀⠲⡤⠀⠀⠣⠄⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡐⠄⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣴⣿⣶⣦⣦⣄⡀⠀⠀⠈⠻⣿⣿⣦⡀⠠⢼⣇⠀⢀⠀⠀⡄⠀⠀⢀⣀⣤⠖⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡿⠋⠀⠀⠈⠛⠀⠈⠻⠛⠛⠻⢷⣄⡀⠈⠻⢿⣿⣾⣷⡌⠉⠛⠁⠛⣭⡀⠛⠉⡿⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣧⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⡀⠀⠈⠙⢦⠀⠀⠈⠉⠀⠙⠛⠀⠤⠶⠿⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣇⣹⠾⠻⠛⠀⠀⠐⠆⠉⠈⠙⠖⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⢀⣤⡴⣺⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⣀⠀⠐⠒⠒⠞⠲⢌⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠿⠁⣾⣿⣿⣿⣿⣿⣿⣧⣻⣦⣀⡀⠚⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⢦⣼⡄
⠀⠀⠀⠀⢴⠆⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⣻⣷
⠀⠀⠀⠀⢸⣧⡈⠻⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣦⣄⣀⠀⠉⠁⠐⠀⠒⠚⣥⣶⣿⡿
⠀⠀⠀⠀⠘⣿⣟⠳⣄⣙⠻⢿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣽⡟⠿⠿⣿⠿⠿⠟⠋⠁⠈⠉
⠀⠀⠀⠀⠀⠈⢿⣿⣶⣬⡃⢤⣈⡙⠿⠿⠿⠿⠿⠛⠛⠋⢉⡋⠰⢲⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⣾⣿⣿⣏⣃⣀⠳⠴⠦⠶⠖⢀⣠⣶⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠛⠲⠶⠿⠿⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠒⢂⣤⣭⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⢛⣭⣶⣦⠀⠀⠀⠀⠘⠿⠿⢟⡶⠈⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠘⣘⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠘⠃⠀⠀⠀⣀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣄⣦⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠋⠟⠀⠀⣠⢰⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠰⣿⣿⠃⠀⠀⠀⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠛⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠮⠍⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡴⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣆⠀⠀⠀⠐⠇⢾⣿⣿⡿⠀⠰⢆⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⣤⣬⣭⠤⠶⠚⠋⠁

⣠⠚⠉⠓⢦⡀
⣇⠀⠀⠀⠀⠙⢄
⠈⢤⡀⠀⠀⠀⠀⠳⡀
⠀⠀⠙⢦⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠛⠛⠉⠑⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢦⡴⠒⠊⠙⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡼⠲⣄⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠈⣦⣀⣳⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢀⣀⣠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣤
⠀⡞⠉⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀
⠀⡞⠃⠀⠀⠑⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠒⠉⠀⠀⠈
⠀⠑⡶⠠⢄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠐⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚
⠀⢰⠇⠀⠀⠀⠀⠀⠐⠒⠀⠠
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠐⣇⠈⠁⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡟
⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣓⣒⣲⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣖⣒⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠛⠳⢦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠶⠟⠋⢀⣶⣟⣻⣦⠀⠀⠀⠀⠀⠉⠛⣷⣶⡦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡋⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢮⣙⢷⡄
⠀⠀⠀⠀⠀⣠⡶⣫⣵⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⢰⢏⣼⠋⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⡀
⠀⠀⠀⡰⢡⠞⠁⠀⠀⠀⠀⣿⣿⣷⣌⣳⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣧⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⣌⢷⡄
⠀⢀⡾⠕⠁⠀⠀⠀⠀⠀⠀⠸⣿⢿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠀⠀⢼⣿⣿⣟⣻⡄⠀⠀⢸⢸⡗
⠀⣿⠁⠀⠀⣀⣴⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⣾⢸⣇
⠀⡏⠀⠘⣿⣿⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⠀⠀⠀⠀⠀⠀⠈⠃⢿
⢰⠃⠀⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⢷⠀⠀⠀⢀⣶⣆⢆⠸
⣿⣮⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⢸⣿⣿⣿⣦⡇⠀⠀⠀⠀⠀⠀⠘⠦⠿⠿⠋⠉⠀⠀⣴⣻⣿⡿⣸⢸
⢿⣿⡀⠀⠀⠀⠀⣾⣿⣿⣮⣷⠀⠀⠀⠈⠛⠿⢿⣻⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢣⣿⡟
⠈⢧⣛⣦⣐⣶⣤⣜⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⣿
⠀⠈⠻⢻⡝⠿⠋⣙⠿⠛⣷⣶⣄⡀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⣠⣼⡇⣿⠋
⠀⠀⠀⠰⠍⠀⠀⠉⠀⠀⠉⠉⣿⣅⢸⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⡇⠀⠀⣨⣵⠟⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠀⢟⡿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡻⠁⢀⣾⢟⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⢙⡷⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣾⢧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⣧⣤⠀⠀⠄⣿⣿⣶⣿⡇⣠⣴⣶⠷⣟⣋⣉⣩⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣽⣿⣛⣛⣓⣚⡛⠛⣋⣈⣥⣾⣶⡿⠟⠛⠛⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣬⣽⣿⣿⣿⣯⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢖⣛⣛⣓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⣿⣿⣿⣿⣿⣿⣷⣭⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⣿⡟⠛⢻⣿⣿⠟⠛⢿⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⣷⣤⣼⣿⣿⣧⣤⣾⣿⣿⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⣿⣟⠻⣿⣿⣿⣿⣿⣿⡟⢻⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣦⣌⠛⠿⠿⠛⢋⣴⣿⣿⢣⡟⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⣭⣭⣭⡛⠳⠦⣤⣀⡀⠈⢷⣝⢿⣿⣿⣷⣶⣿⣿⣿⢟⣵⠟⢀⣀⣤⠴⠞⢛⣭⣭⣭⣝⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣿⣿⡿⣛⣼⣿⣶⣯⣽⣛⠶⠿⠇⠛⠻⣿⣿⠟⠛⠱⣿⠶⢞⣫⣭⣶⣿⣧⣘⢻⣿⣿⣿⣧⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⣿⣿⣿⠗⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠠⠉⠉⠄⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⡰⢿⣿⣿⡟⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣝⡻⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣾⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣛⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢮⣭⣛⣻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢟⣛⣭⡵⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣮⢻⣿⣿⣿⣿⣏⠀⠀⢈⣿⣿⣿⣿⣏⡴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⡏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣾⣿⣿⣿⣿⣧⣀⣀⣠⣿⣿⣿⣿⣿⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⢭⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⡙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣷⣬⣍⢻⣿⣿⣿⣿⡿⢋⡼⠋⠀⠀⠈⠻⣮⠻⣿⣿⣿⣿⣿⢫⣭⣴⣿⣮⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢿⣿⣿⣿⣷⣌⣛⢻⡿⢋⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⣌⢿⡿⢛⣋⣼⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⢿⣿⣿⣿⣿⡿⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⣿⣿⣿⣿⣿⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣭⣭⣥⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣭⣭⣭⠶⠋



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⡶⠶⠶⠶⣶⣶⠶⠶⡶⢶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠋⠉⠀⠀⠀⠉⠙⠒⠢⠤⣄⡀⠀⠹⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠁⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠉⠓⠒⠶⣤⡀
⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣄⣀
⠀⠀⠀⣠⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀
⠀⠀⠀⢧⡀⠉⠒⠀⠀⠤⠀⢀⣀⠀⠀⠀⠀⠀⠈⢀⣁⣀⣀⣀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠴⠒⠉⣹⠆
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢠⡇⠀⠀⠀⣀⡤⣄⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⠀⠀⢀⡠⠤⠤⡀⠀⠀⠀⠀⠘⡇
⠀⠀⢸⠃⠀⠀⡜⠁⡔⠊⠀⢸⢸⠀⢸⢡⢠⠊⡠⠔⠁⠀⠀⡏⠈⡇⠀⡇⢀⣄⡀⠘⡀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠱⢤⣓⡒⠢⣼⠸⠀⠀⢸⡏⢸⠁⠀⠀⠀⢸⢱⡇⢹⠀⢇⠀⠓⢁⡰⠁⠀⠀⠀⢠⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠀⢘⡆⢹⠀⠧⠃⡼⡇⠸⡀⡯⠉⣑⣼⠈⢣⠀⠇⢸⠀⣄⠘⡄⠀⠀⠀⠀⣸⠁
⠀⠀⠀⢷⡀⠀⢠⡖⠒⣉⡠⠛⣄⢀⡠⠃⠙⢄⣈⣴⣀⡇⡆⢠⠀⢣⠸⡘⠀⡏⡆⠘⡆⠀⠀⣰⠃
⠀⠀⠀⠀⠳⡄⠀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠒⠃⠓⠁⠈⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣠⣤⣴⠏



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⡀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠉⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⢀⣻⠴⠶⠶⠒⠒⣦⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⢀⣄⠀⠀⠀⢸⡧⡀⢀⡤⠖⠉⡟⠀⠀⠀⠀⠀⣘⣦⡴⠛⠓⢦⡴⠚⠁⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉
⠀⠀⠀⠈⢋⣀⣀⣀⣬⣧⣉⡷⠖⠒⠒⠓⢲⣤⡖⠉⠉⠁⠈⢦⢀⡴⠋⠀⠀⠀⢀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⣿⠉⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⡄⡟⣆⠀⠀⢀⡼⠃⠀⠀⣠⣴⠚⠉
⠀⠀⠀⠀⣿⠀⠀⠐⠀⠸⡄⠷⠀⠀⠀⠀⢸⡇⢱⠘⢆⡰⠋⠀⣠⠔⠋⠀⢸⠀⠀⠀⢀⡀
⠀⣀⣠⡤⠿⠒⢶⠒⢲⠚⠛⠋⠉⠉⠹⡗⢶⡻⠛⠒⠚⠳⢴⣏⣀⣀⣀⣠⠼⠤⢤⠀⠙⠃
⠀⢿⠀⠀⠀⠀⠘⡆⠀⢧⠀⠀⠀⠀⠀⣇⠘⡇⠀⠀⠀⠀⢸⠉⠀⠀⠀⢹⠀⠀⠘⡇
⣠⡼⠦⠤⠤⠤⠤⠿⠴⠼⠶⠶⠶⠦⠤⠾⠤⠷⠤⠤⠤⠤⠾⠤⠤⠤⠤⠼⠤⠤⠤⠷⠶⠶⢶⡄
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⢤⡤⠴⠂⠀⠀⠀⠀⠀⠐⠲⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠂⠲⠥⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⣶⢤⣀
⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠇⠀⠀⠀⠀⠀⠀⢀⡴⢃⣀⣠⡤⠶⣦⣤⡏⠀⠀⠀⠀⢸⠀⠈⡇
⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⢸⠁⠀⠀⠀⢸⠀⠉⢳⡀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢼⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⣻⠀⠀⠀⠀⢸⡄⠀⠄⠀⠸⡄⠀⢸⣇⣀⣀⣸⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠲⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠖⠚⠛⠁⠀⠀⠀⢠⣼⠓⠒⣶⣖⠚⠓⠒⣏⣹⠏⠉⠀⠉⣩⢤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣯⣤⣬⣷⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭
⣿⣿⣄⣭⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠽⠋⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣤⣠⣴⣶⣦⣄⠀⠀⠀⢻⡄⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠘⠃⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠱⠂⠀⠀⠀⣰⡿⠣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠻⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠟⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⠛⠋⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣤⣤⣤⣤⣤⣶⠶⠶⠶⠾⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡴⣶⡍⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣬⠀⠀⠀⣠⣠⡈⠁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠰⠋⠁⡀⠈⠁⠀⠀⠀⠉⠀⠀⣤⣠⠆⠀⠀⠀⠋⣀⡀⠀⠀⠀⠀⠀⢴⣄
⠀⠀⢠⠁⠀⠀⣴⡦⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⣤⠄⠀⠀⠐⠀⢀⡵⠁⠀⠀⣎⡀⠐⠛⠁⠀⠀⠀⠰⣦
⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠌⠁⠀⡀⣀⠠⠀⠀⢰⡿⠶⠒⠁⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢸⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠞⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⡴⢦⠀⠀⠀⣠⡄⠀⠐
⠀⠀⠸⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠘⠳⠀⠀⠀⠀⣴⠀⢰⡿⠁⠀⠀⢀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣴⠋⡇⠀⠀⠀⠀⣀⠀⠀⠀⠈⠠⢠⣤⠀⠀⠉⠓⠀⠀⡴⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣹⡗⠀⣾⠟⠛⠿⠿⠶⣾⡿⠞⠁⡶⢀⣀⣸⣍⠇⠀⠀⠀⠀⠈⠉⠒⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣾⡿⠁⣠⡴⡄⢰⡖⢳⢠⣿⢎⣽⢸⡏⣾⠵⢃⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠛⠗⣰⣿⡀⣿⣾⠧⣼⢿⡿⣿⡅⠸⢗⣙⡒⠱⣏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣴⠻⣯⡽⠃⠙⠒⢁⣈⣥⣼⠿⣿⣉⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠁⠀⠀⠀⠻⠿⠿⠟⠛⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠛⠁⣀⣉⠉⠀⢤
⠀⠀⠀⠀⠶⣀⠀⠠⠆⠀⠀⠀⠈⠁⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢀⡴⠂⠛⣉⠉⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⢠⣯⡴⠟⠋⠁⠀⡀⠉⠀⠀⠀⠐⠋
⠀⠀⠀⣦⠀⠙⠃⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠁⠀⡀⠀⠀⣠⠊⣉⠁⠀⠈⠋⢡⡀⠀⠰⠦⠀⢤⡄⠀⠀⠀⠈⠻⠀⠴⢦⣠⣤⣥⣤⣄⣶⠀⠀⠰⡄
⠀⠀⢀⣿⣦⣀⠀⠶⠀⠺⠷⠂⠀⠰⠟⠶⠀⢈⡞⠁⠀⠸⠇⠀⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡷⠞⠁⠀⢠⡄⠀⠀⠈⠑⠠⡦
⠀⠀⢸⣿⣿⠿⠿⠿⠿⣤⣾⣶⣤⣤⡤⢶⡖⠿⡀⠀⠀⢼⡃⠀⠀⢀⢀⠀⠀⠀⠄⡻⠆⠀⢀⡀⠁⠀⠀⠀⠐⡿⠉⢠⣦⠄⠀⠀⠀⠀⠶⠄⠀⠀⡀
⠀⠀⠈⢙⣷⣶⡴⠖⢀⠉⠁⠀⢀⣄⣰⣿⣿⣾⡧⠀⠀⠈⠁⠀⠉⠁⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢻⠛⠻⠟⠋⠛⠛⠛⠛⣻⡋⠉⠉⠀⡀⣠⡄⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠐⠆⠀⠈⠁⠀⠔⠲⠄⠀⠸⣧⠋⠀⡀⠀⠀⠀⠛⠀⠀⠀⢰⡀
⠀⠀⠀⠟⣿⠟⢲⡶⠶⠶⢶⡾⢧⡴⠶⠶⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⠂⢀⣀⠀⠀⠀⠃
⠀⠀⢠⣾⡶⢤⣬⣝⣀⣀⣈⣁⣈⣁⣤⡦⠶⠚⢋⢡⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⣠⣀⡀⠀⠀⠠⠗⠀⣀⠀⠀⠀⠱⣄⡀⠀⠀⠀⢠⣠⠀⣀⡀
⠀⠀⠈⢻⣥⣾⣆⠉⠩⣿⠉⠉⠈⠀⠀⠀⠾⣆⡤⠊⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠉⠉⠳⠦⠤⠅⠚⠁
⠀⠀⠀⠀⠁⠉⠉⠉⠓⠀⠒⠖⠚⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠛⠃⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠂⠉⠡⡖⠦⠀⠈⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⢀⣤⡄⢰⣦⠆⠀⣶⢢⠀⠀⢾⣌⡁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠈⠛⠉⠀⣠⡴⡆⢀⣤⢄⠫⠄⠀⠀⢠⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠒⠀⡐⠀⠈⠋⠀⠈⠑⠉⠀⠀⠀⠒⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠳⣤⣀⣤⣀⠀⠀⠀⠈⠀⣀⣀⣀⣠⠾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠀⠠⠈⠉⠛⠛⠒⠲⡶⠚⠛⠋⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣷⣦⣀⠁⠠⡀⠈⡸⠷⠋⠀⣀⣤⣴⠚⣅⠴⠒⠒⠲⡦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠈⠉⢙⣿⡟⡿⠛⠛⠛⠋⠉⠋⠀⠀⡴⠁⠰⠆⢀⣀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠘⠃⡭⠅⠀⠀⠀⠀⠀⠀⢤⣠⣼⠁⣄⢂⠀⠸⠿⠇⠀⠀⢰⣿⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠿⡲⣷⢿⣶⠶⠶⢲⢗⢾⠉⠽⣿⠀⠙⢉⠀⠀⠀⠺⠈⠰⠆⠀⠄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⢙⠒⠋⠀⠀⠈⠙⠁⠀⢀⣿⣠⠀⠹⡦⠃⠸⣭⠀⠀⢠⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⡊⣿⡿⣧⣤⣀⣀⣀⣀⣀⣴⣿⡿⣧⠁⠀⢀⡤⠄⠀⣆⡀⠀⠁⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢲⣿⣿⣧⡀⠉⠛⡙⠁⠈⢉⠉⠉⠠⣄⣂⣹⣧⣀⠀⠙⠇⠀⠀⠀⠀⣶⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠙⠻⠿⣷⣿⣧⣴⣦⣤⣄⣤⣴⣥⣿⣷⣟⢿⡄⠀⠸⠇⠀⠀⠀⠉⠁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⠀⠀⣀⡄⠀⠀⠀⠈⠉⠉⣩⣄⠀⠀⠀⠀⡒⢲⣶⣶⣤⣙⣳⣤⣀⣁⣀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠼⠿⠇⠀⠀⣀⣩⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠈⠁⠀⡀⠀⠀⠆⠀⢀⠀⠂⠀⠀⠌⠁⠀⠀⠀⠈⠀⠸⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠁⠀⠠⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣋⠁⠄⠀⠀⠀⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠀⠘⠄⢀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠶⢲⡷⠃⢴⠶⠀⠀⠀⠀⠀⠋⠁⢀⣴⠞⠹⠆⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⡰⠡⠀⠉⠀⠀⣾⣇⣴⡄⠀⠀⠀⢀⣄⠀⠀⣶⣿⣿⠀⠀⠀⠀⠛⠏⠀⣠⣴⠞
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠶⡶⠂⣿⡿⡌⢁⠀⠀⠈⠛⠛⠁⣼⡿⠘⢃⡄⠀⠀⠂⢀⣶⠻⡿
⠀⠀⠀⠀⢰⣇⠀⠀⠀⢀⣤⣀⢸⣿⣾⣤⣄⠀⠂⠀⢿⣿⣿⣿⠒⠂⠁⠀⢠⣍⣿⠷⠞⠀⠀⣈⠁⠀⣀
⠀⠀⠀⠀⠸⣯⠈⠂⠘⠧⠀⠀⢼⣿⣿⣿⡋⡀⠊⢘⣶⣿⣿⣿⣶⡆⠀⠀⠈⢹⣷⡌⡼⠳⠈⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠀⠼⢟⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣍⠀⠀⠀⠸⡧⠇⠃⠈⠀⠖⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠘⣷⡏⠀⠀⣀⠀⢻⣛⠁⠙⣿⡿⠋⠀⠀⠀⠀⠈⠻⠀⠰⣖⠰⣿⠀⠀⣵⣧⡄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠭⠿⠖⠄⠀⠚⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⣀⣹⡆⠀⠉⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣐⡋⢩⠁⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣯⣄⡉⠉⠀⠐⠀⠀⢀⡀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠊⠑⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠈⠀⠰⠀⠰⠛⢿⣷⡠⡶⠀⠲⡷⠀⠙⠂⣙⠀⠀⠀⠀⠀⣰⠆⣴⡄⠀⠀⠀⠚⠃⠀⠀⢁
⠀⠀⠀⠀⠠⣄⠀⠰⠗⠀⠻⣻⡶⣧⠀⠀⠆⢀⠀⢀⠀⠀⠀⠀⠀⣿⣶⠄⠀⢀⣠⡄⠀⠂⠤⠔⠻⡄
⠀⠀⠀⠀⢀⠈⢳⡠⠕⠦⠤⠈⠻⡻⣶⡆⡀⠈⡀⡾⠀⠀⠀⠀⠀⢻⣳⠐⠀⠄⢨⣥⠀⠀⠲⠄
⠀⠀⠀⠀⢹⣄⠊⣍⢷⣄⠀⣖⡀⠘⢾⣧⡙⣠⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠐⠢⠤⠂⣁⡀⢠⠃
⠀⠀⠀⠀⠀⠙⠿⣟⡙⡍⠓⢤⡀⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⠌⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠤⢰⠃⠴⠄⠀⠀⠀⠋⢀⣴⠺⠌⠁⡙⠋
⠀⠀⠀⠀⢠⠂⠡⠀⠉⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠃⠀⣀⡀⣿⡶⠆⠀⠠⣴⠄⣸⠿⡇⠀⠀⠈⢁⣤⡞⠃
⠀⠀⠀⠀⠁⠁⢠⣤⠄⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⡇⠀⠀⢉⡀⣿⣷⣀⡀⠂⢰⣶⣿⠆⠈⠀⣀⣲⣯⠎⢀⡐⠀⡀
⠀⠀⠀⣇⠀⠀⠀⢤⣀⠀⠀⠿⠀⠀⠘⢀⠁⠀⠀⢧⡀⠈⠃⠀⢾⣿⣿⣥⣈⣽⣿⣿⣿⠆⠀⠈⣿⡦⡏⠊⡀⠀⡃
⠀⠀⠀⢿⡈⠀⠙⠀⠀⠀⠀⠀⠁⠐⠀⠸⠀⠀⠀⠈⢳⡆⠀⢀⠑⡿⠻⣿⡿⠋⠉⠉⠙⠇⠠⡄⢽⠁⢠⣦⡁⠠
⠀⠀⠀⠈⢻⣤⠄⠀⠀⠂⣴⡄⠀⠀⠼⡇⠀⠀⠀⠀⠀⠉⠛⠛⠒⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠼⠆⠈⠉
⠀⠀⠀⠀⠈⠻⢦⡤⣶⣀⡀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠀⠘⠁⠀⢈⡀⠀⠀⢠⡄⢰⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠃⠀⣰⡆⠀⠀⢀⣤⡄⠀⠀⠀⣼⠄⠠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠋⠀⠀⠀⠘⠋⠀⠀⠀⠀⡏⠀⠀⠀⢄⠠⠀⢀⣄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⡼⠃⠀⠀⣠⣤⡀⠀⠀⠉⠁⠀⡈⠀⣦
⠀⠀⠀⢀⠘⠀⠀⠀⡀⠀⠀⠰⣿⠇⠀⠀⠊⠀⠀⣠⣾⣥⡄⠀⠀⠈⠙⠋⠀⠀⠀⠀⠈⢀⣼⠏
⠀⠀⠀⠸⢰⣶⡄⠈⠁⠀⠀⠈⠁⠀⠀⠀⢀⣠⡾⣿⣦⡉⠂⣀⠀⡈⠀⠔⠀⠀⢀⣠⣶⡷⠃
⠀⠀⠀⠰⣶⡈⠒⠀⠀⠀⠀⢚⣩⣤⣴⣾⣿⣿⣿⡀⣰⣤⣤⡀⠀⠀⣀⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠾⠟⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠁



⣿⣟⣛⣛⣛⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⢉⡿⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠁⠀⢀⡴⠋⣠⠎⠙⠳⣤⣈⣉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢫⡟⠁⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠈⠉⠛⣶⣤⡉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣴⠏⠀⠀⢠⠞⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⡜⠛⢦⣀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣰⠋⠁⠀⠀⣰⠋⣰⠋⠀⠀⠀⠀⠀⢀⡴⠚⣁⡴⠚⠉⠀⢠⠞⢉⠟⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢰⡇⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⠀⡴⠋⡴⠚⠁⠀⠀⠀⢠⠏⢰⠏⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡴⠋⠀⢀⡴⠋⣠⠞⠀⡤⠖⣲⡶⠶⠾⠷⠾⢧⣤⡀⠀⠀⢀⡟⢀⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢠⠏⣠⠞⠁⠀⣾⢀⡾⠋⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⠞⢀⡞⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⣰⠃⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡝⣷⠋⠀⠀⠀⠀⠀⠀⢀⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣠⠏⣠⠏⠀⢀⣠⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⣁⠴⣁⠴⠒⢋⣠⠴⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⠟⠀⠀⠀⠀⢀⡴⠋⣹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢳⠚⣡⠴⠛⠉⠀⠀⠀⣿⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢀⣠⠴⠋⡴⠛⠁⢹⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⣌⣙⠲⠶⠶⠶⢛⡇⠀⠀⢀⡴⠚⢉⣠⠶⠋⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣿⠦⠤⠶⠟⠁⠀⣠⠏⣠⠞⠉⠀⠀⠀⢀⣠⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡼⠁⠀⠀⠀⠀⢀⡴⠃⡴⠃⠀⠀⠀⠀⣰⠏⢡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⡤⣤⠀⠀⡠⠞⢉⡴⠋⠀⠀⠀⣀⡤⠖⢋⣠⠞⠁⠀⠀⠀⠀⠀⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⡇⡾⠁⡴⠋⠀⠀⢀⡴⠚⣁⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⣸⠁⣀⣤⠴⠟⠛⠛⠛⠶⠶⢤⣀⡀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠙⠛⠲⠶⠶⠤⠤⠤⠴⠶⠞⠛⠛⠒⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⠶⠶⢶⣶⡶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠲⠶⣯⣴⣿⣟⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⣀⡤⠖⠶⣖⠒⠒⠒⠶⠤⣤⡖⠚⠉⠙⠉⠀⠀⠀⠀⠀⠙⢿⣟⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⢏⠻⢋⣿⡻⠿⣾⡆⠀⠀⠈⠳⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⡻⡱⡱⣁⣴⢟⣍⠪⢍⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⣥⠶⡟⡷⡱⡱⣗⢮⡿⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⡟⡳⢿⢨⢸⠹⡑⡌⢢⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⣠⠞⠋⠉
⠀⠀⠀⠀⠀⠀⣠⠖⠙⠛⠛⠛⠛⠛⠚⠓⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡴⠚⠁
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⢰⠋⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⢀⡇⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣯⡑⣝⣄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡌⢜⠝⡒⠩⣷
⢸⠃⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢼⢋⢮⡪⣗⠭⣪⡵⠃
⡏⠀⠀⠀⠀⠀⠀⠐⢻⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⣣⣣⠱⡷⣕⢫⣢⡵⠋
⢧⣀⣀⣤⣤⣤⣀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠈⢳⠒⠀⠀⠀⠀⢀⣀⣤⣶⡺⡡⡳⡱⡑⢝⢟⢎⣮⠞⠁
⢀⡿⣹⣇⢐⡼⣯⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⡴⣏⢫⠣⣟⢎⢷⣕⢕⢌⢊⣢⠵⠋
⢸⣿⠼⠼⠼⢷⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⡝⣧⢡⢹⠪⡻⣮⣻⠶⠋⠁
⠈⠛⠳⠶⠶⠾⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣫⣢⣣⡵⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⢂⡐⠉⡉⡉⠉⠉⣘⡓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡋⠀⠐⠂⠰⠀⠀⠀⠀⠆⠲⠄⠈⠀⠀⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠛⠁⠀⠀⠀⠀⠀⣠⡀⠀⡴⡒⠆⠐⠛⠁⠀⠀⠋⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⢡⣒⣦⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠫⣇⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠺⠭⠿⢛⠰⠄⠈⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠴⠂⠀⠈⠉⠑⠤⢀⡀⠀⠀⠀⠀⠈⠁⣀⣤⣀⠠⠴⢲⡏
⠀⠀⠀⠀⣀⠀⠤⠐⠂⠈⠛⢉⣁⠀⠐⢒⠂⢤⠁⠀⡀⠀⠉⠀⠙⠀⠀⢀⡀⠙⠀⠛⢀⡬⣁⠀⠀⠚⠓⠃⡇
⠀⣠⠖⠁⠀⢊⠝⠀⢠⣤⠀⠘⠘⠀⠀⠉⠀⠈⢧⣀⠉⠠⢔⡒⠆⣤⠀⠈⠁⠄⠀⠀⠈⠈⠉⢀⡀⠄⠀⢀⡇
⡰⡁⠀⡓⠀⠀⠀⠀⡈⠀⠀⠤⠀⠀⢀⡀⠀⢠⡀⢉⠶⣄⣀⠀⠀⠀⠉⠀⠒⠀⠐⠐⠋⠉⠉⠁⠀⣀⡴⠍⠉⢂⠀⢀⣀⣠⣤⣄⣀⣀⣀⡀
⡃⠐⢜⠉⠀⠀⠀⠀⠉⠀⠀⠀⠲⠖⠃⠀⠀⣨⡅⠈⠂⠀⠙⠛⠉⢀⡄⠠⠤⠤⠄⢤⡤⡤⠔⠂⠉⣠⠀⠐⡤⠛⠉⠙⠉⠀⠰⠆⠘⠃⠀⠉⠓⠢⣄
⢇⠰⣛⠁⠦⣶⡄⠀⠀⠂⠀⠤⡄⠀⢠⣀⣤⠈⡐⢻⡀⠀⢀⡈⠁⢈⡀⠀⠀⠀⠄⠀⠉⠁⠘⠃⠀⢀⠖⠁⡠⡀⠒⠂⠀⠀⠀⠀⠀⡾⠆⠀⠰⠀⢈⠳⣄
⠈⠲⣌⠀⠀⣠⠀⠒⠃⠀⡈⠉⠀⠀⠀⠈⣀⡘⢲⠀⠑⣦⣘⠊⠀⠒⠀⠈⠉⢩⣏⠁⢀⡤⠀⠀⠴⠞⠀⠀⠁⠀⢀⠀⠰⠲⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⢳⡄
⠀⠀⠈⠉⠓⠄⠀⠀⠀⠀⠀⠉⠁⠀⢠⡾⠁⢙⠀⠑⢦⠀⠀⠽⠲⠤⢤⣀⣀⣀⣁⡀⢀⣁⣠⣴⣶⠀⠀⠁⠠⡄⠈⠀⠀⠀⠀⠈⠙⠀⠈⠁⠀⠀⣤⢀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠤⠀⠀⠀⠐⠒⢻⡀⢀⡀⠈⠒⠤⠀⠀⠀⢈⣅⠀⡈⢁⡀⡀⠀⠠⢾⠀⢃⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠙⠫⢼⡀⠀⠰⠦⠀⠀⠈⠉⠀⠁⠀⠶⠀⠀⠀⠘⢆⠘⠟⠁⠀⠀⠀⠀⣏⡈⠆⠐⠿⠃⠀⢀⣘⠃⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠴⠖⠂⠀⠀⣄⠀⠠⠀⠚⠋⠙⠒⠤⢍⡓⠦⠤⠤⠤⣤⠄⠐⠀⡀⠄⠆⠒⠚⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠧⣼⠃⠀⠠⣏⣹
⠀⠀⠀⣠⠖⠉⠙⠆⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠃⠀⠸⠽⠗⠈⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠉⠲⡛⣆⠤⠀⠀⠀⠀⠰⣯⠆⠰⠗⢀⣤⢞⡽
⠀⠀⢰⠃⠀⠁⠀⠀⠘⠃⠀⠤⠀⠀⠀⠲⠆⠈⠁⠀⠀⠀⡤⡄⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠉⠀⠠⠤⣠⣤⠠⠤⠄⠀⠈⢁⣠⠞
⠀⠀⡄⠀⠐⠠⠘⠃⢰⣑⣴⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠈⠏⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠐⠢⠦⣬⣭⡤⠤⠤⠴⠖⠋⠁
⠀⠀⠃⠀⠈⠂⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠠⠦⠀⠀⠘⠶⠁⢀⣼
⠀⠀⢸⡀⢤⡲⠀⠀⠀⠀⠈⢉⠁⠀⣀⣤⣀⣀⠀⠙⠀⠀⠦⢀⠀⠤⢚⣅⡜
⠀⠀⠀⠉⠳⢄⡀⠀⠿⠀⠀⠀⠁⠈⠓⢲⡤⠟⠀⠠⠤⠔⠂⠈⠴⠀⣈⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠤⢀⣀⡀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⣁⣠⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠶⣦⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡾⠏⠀⣠⣶⠶⣶⣄⠀⠉⠉⠉⠉⠉⠛⠻⢷⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠑⠛⠿⢯⣝⡛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⣫⠆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣹⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡟⢡⡾⠉⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀
⠀⠀⠀⠀⢠⠎⣠⡿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣍⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣬⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⡄
⠀⠀⠀⣴⢫⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠻⠿⠿⠃⠀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⢹⡘⣿⡆
⠀⢀⣾⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣼⡿⠀⠀⠀⢸⡇⣿⡇
⠀⣼⡏⠀⠀⠀⣀⡤⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁⠀⠀⠀⣾⡇⣿⡇
⠀⣿⠀⠀⠸⣿⣿⣇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣤⡀⠈⠀⠀⠀⠀⠀⠀⠈⠳⢹⣷
⠀⡏⠀⠀⠀⠙⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢀⠀⠀⠀⠀⠀⣠⣄⢀⠀⢻
⣸⢡⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⢸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣯⠹⣿⣿⣿⡟⡞⠀⠀⠀⣠⣾⣿⣿⢸⡆⢸
⣿⣼⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣶⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠰⢯⣼⣿⣿⢸⣇⣿
⢻⡿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣼⣷⠀⠀⠀⠀⠀⠙⠛⢛⣛⡥⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢃⡾⣿⠃
⠈⢿⡙⢷⣄⡰⠶⣄⣀⡙⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣼⡇
⠀⠈⠻⣿⠿⠻⣿⣿⠟⠿⣿⣿⣷⣤⣄⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣾⣿⠃
⠀⠀⠀⠀⠘⢧⠈⠁⠠⡶⠉⠀⠸⠿⢿⣷⠦⠀⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡻⣦⠀⠀⠀⢀⡴⣣⡿⢡⣿⠃
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⡄⢿⣿⣿⣿⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⠁⠀⢀⣴⣾⠟⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠸⣝⣻⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⣛⡯⠅⠀⢠⣿⢟⣵⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠘⣿⡄⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢇⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⣟⢀⠀⠀⠀⠀⢰⣿⣿⣤⣿⣧⠀⢀⣀⣠⣴⣤⡾⠷⠾⠿⠛⣋⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣭⣤⣬⡘⣿⣿⣿⣿⠟⣠⠞⣫⢍⣩⣥⣶⣶⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣿⣭⣴⣶⣮⣤⣭⣉⣥⣤⣶⡾⠿⠿⠿⠛⠉⠁⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⣤⣽⣿⣿⣯⣭⣭⣽⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⣁⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢶⣄⠀⠀⢀⠀⢹⢿⣿⢇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈⠀⠉⠙⠳⠶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⣀⣬⡷⠾⡋⠁⠟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣠⠀⠀⠀⢤⠀⠀⠀⠉⠛⠒⠶⠚⠲⠶⢶⢲⣾⣺⢗⡪⣽⡿⠚⡂⠀⢀⣴⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠉⠛⠛⠻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠹⠻⠻⠁⠐⡿⠙⠙⠁⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣀⡠⣄⡀⠈⠛⠻⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⣂⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢟⠛⠉⠛⠷⣷⡤⣤⣄⡀⠀⠀⠀⣀⣴⣖⣳⠤⠀⠀⠀⠀⠐⠷⣶⣢⣤⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠛⢿⠛⠛⣛⠷⠶⠿⠿⠟⠛⠛⠿⣟⣻⡿⠛⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡛⠁⠀⠀⠀⠀⢋⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠣⡈⠿⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡖⠄⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠸⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡐⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠙⠓⣦⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡭⣽⣯⡍⠁⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⡶⠞⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠩⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡍⠑⠿⡷⡀
⠀⠀⠀⠀⠀⠀⠸⣵⣀⣀⣤⣦⡄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣌⣻⣷⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠧⡀⢠⣄⣀⣀⣀⣀⣀⣀⣠⠈⠉⠬⣅⣀⣠⣤⣠⣤⣤⣠⣼⡿⠿⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠛⠛⠟⠶⠾⠿⠶⣤⣄⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠾⢯⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠊⠀⠀⢀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠟⠿⠿⠟⠋⠉⠙⣶⣄⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⡀⠀⠶⠖⠒⠒⠌⠻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠳⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣷⠀⠘⢿⡛⠖⠀⠀⠙⣿⣿⣶⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠌⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣆⡀⠀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡟⠀⠤⠄⠀⠀⠀⠀⢸⣿⣿⣏⢿⣿⣿⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⣿⣦⣤⣤⡤⠀⠀⠀⠀⢸⣿⣿⣦⡑⠙⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⠀⠀⠀⠀⠀⢀⣠⡴⣿⣿⣿⡝⢦⣄⣨⣝⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣦⣴⣶⣾⠟⠁⠀⠈⢻⣿⣿⣦⣝⢿⣿⣷⣽⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣷⣿⣿⡿⣻⣿⣿⣆⠀⠀⠀⣸⣿⣷⣭⣿⣷⣿⣇⣿⢿⡟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⡿⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣿⣿⣦⡁⠀⢾⣿⣿⢿⠻⣿⣆⠀⡇⠀⣄⣸⠿⠛⣿⣿⡿⠟⠁⠀⢀⣀⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢿⣿⢦⡀⠹⣿⡧⠂⠀⠙⠿⡷⠾⠋⠁⢠⣾⡿⠋⢀⣠⠴⣺⣿⡿⠟⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢙⣷⡟⣄⠘⣿⡀⠀⠀⣤⣄⠀⠀⢀⣾⠋⣠⠞⣩⡴⠟⠙⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠻⣎⢂⠈⢿⣦⡘⣿⣟⣠⣴⡿⠁⠞⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⠣⠈⢟⠛⠛⠛⠛⠟⠀⠀⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⣾⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣧⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣏⣩⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⢀⣴⣄
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠚⠉⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣷⢲⣶⣾⣿⣷⡄
⠀⢀⡴⠚⠁⠀⠀⠀⣼⣿⡄⠀⠀⢀⣄⠀⠙⢦⡀⠀⢸⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⡞⠀⢀⡀⠀⠀⠀⠈⠉⠀⠀⠀⠸⣿⡗⠀⠀⠳⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣏⣹⣿⣿
⣸⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿
⡇⠀⠀⠀⣴⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠰⣿⡷⠀⢸⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠁
⢳⡀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⠿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠳⣄⠀⠀⠀⠀⣠⣤⡀⠀⢸⣿⠇⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠈⠢⣄⠀⠀⠘⠛⠀⠀⠀⠀⠀⣀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠤⡤⢤⠤⡤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⠀⠃⠘⠀⠃⠘⠀⠃⠘⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠉⠉⠋⠙⠉⠉⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠤⠒⣤⣤⣒⣒⣦⣤⡒⣲⡇⠀⢀⣀⣀⡀⠤⠤⠐⢒⣒⣒⡒⠒⢊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢆⠀⠒⠊⠉⠉⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⡴⣂⠉⠉⠒⣤⠔⠒⠒⣲⢆⠀⠀⠀⠀⠣⡀⠀⠀⣀⡀⣀⢀⡄⢸⣾⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢰⠀⠀⠙⠎⣿⣁⣀⣠⠞⣁⠈⢇⠀⡀⠀⠙⠁⠓⢃⠛⡏⠛⠉⠀⢸⣿⠀⠀⢸⠀⠀⠧⣀⠀⡀⣤⣀⣶⢰⠀⢸
⠀⠀⠀⠀⠓⡤⠜⠋⠉⠒⡢⡄⢣⠀⢁⠜⠀⣇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣘⡏⠀⠀⢰⠀⠀⠊⠁⠓⠃⣉⡇⠉⠀⠀⢸
⠀⠀⠀⠀⢸⠁⠒⠲⡔⢉⠀⢸⠤⠷⠋⠀⠀⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠈⣄⠀⠀⢃⠀⢁⡜⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⠀⠠⠄⠀⡇
⠀⠀⠀⠀⠀⠈⠉⠒⠸⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇⡠⠤⠤⠤⠄⠒⠒⠒⠈⠉⠓⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡚⢦⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡰⠚⠙⠒⠐⢦⡀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⢀⠀⠑⡄⢣
⠀⠀⠀⠀⠀⠀⣰⣋⣀⣀⣀⣀⣀⣀⣹⣄⠀⠀⣠⠔⡋⠀⠀⢰⡜⠋⠀⣀⠜⠚
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡝⡅⠀⠀⠇⠁⢀⡪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠈⠀⠀⠀⠀⡇⠀⠳⡘⢆⡠⠴⠒⠁⠀⠀⡀⠴⠔⠒⠢⣀⠀⠀⠀⠀⢀⣀⣀⠀⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⠀⢀⡀⢀⡰⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡙⠒⠒⠒⠒⠚⠃⢐⣀⠭⠤⠤⠀⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠤⠔⠒⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⣄⠀⠠⡀⠄⠀⡄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁⠁
⠀⠀⠀⠀⢀⠀⠄⠂⠀⠂⠠⢄⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡦⢶⣦⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⣀⠀⠦⡀⠀⢀⢼⠦⣀⠀⡎⠯⢠⠀⠀⠀⢴⣿⣿⣜⣥⣷⣳⣽⣯⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠐
⠀⠀⠈⠙⠒⠂⢴⣡⢾⠷⣄⣱⠒⠊⠁⠀⠀⠀⠀⠈⠁⠘⠉⠁⠙⠈⠁
⠀⠀⠀⠀⠀⠀⠸⠁⠘⠳⡄⢹⠀⠀⢀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠠⡀⠀⠤⠤⠄⠠⠀⠄⠐⠆
⠀⠀⠀⠑⠢⠀⢰⠎⠀⠀⠀⠙⠤⠊⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⣀⠤⠞⠋⠀⠀⠀⠀⢀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠤⢤⡀⠁
⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣚⣿⣿⠟⠂⠀⠀⠀⠀⠀⠈⠁⠈⠈⠑⠒
⠀⠀⢄⡀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠍⠀⠀⠂⠀⠀⠀⠀⠐⠶⠤⠤⠠⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠁⠐⠀⠠⠐⢈⣀⡤⠊⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠠⠄⠤⠒⠀⠚⠀⠀⠀⡀⢀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠠⠄⠙⢋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣟⣻⡽⣿⣻⣛⡀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠄⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠠⢠⡄⠀⢐⠀⢀⡀⠀⢸
⠀⠀⠀⠠⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢨⡇⠀⠀⠀⠈⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠅⠐

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢲⠒⡶⢢⡤⡤⣤⢤⣤⡤⣤⢤⡴⡖⢶⠛⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣿⣰⣇⣸⢁⡇⣿⢸⡇⣇⢸⣈⣧⣷⣼⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⢁⠘⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠧⣬⣤⡄⠰⢀⡀⠠⠄⠀⠀⢠⠀⠀⠴⠀⠀⠓⠀⡈⢀⡶⠚⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠛⠦⣄⣀⠙⠓⠋⠙⠶⠴⠛⢦⣤⡴⠶⠤⠴⠓⠶⠞⠉⢉⣀⡤⠖⠋⠻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣤⡤⠀⠀⠉⠙⠓⠲⠶⠤⠤⢤⣤⣤⣤⡤⠤⠴⠶⠖⠒⠛⠉⠁⠀⣀⠀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⣹⢿⣿⣆
⠀⢀⡞⠉⢦⡀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡼⢃⠀⣿⣿⡆
⠀⡞⢧⣉⡀⠙⢦⣄⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⢶⠆⠀⠀⠠⡶⢰⡷⡄⠀⠀⠀⣠⠴⠫⡄⣨⠼⢻⣿⣷
⢀⢷⣄⠈⢧⣘⣀⠈⡳⢦⣀⣀⣾⠟⡇⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠲⡖⠋⣅⠀⡶⠒⢁⣴⡿⣝⣿
⣧⢞⡽⢳⣤⡉⠹⣤⣥⣤⣼⡿⠃⢠⠃⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⢻⣿⡀⠀⠙⠦⣤⢞⣡⣴⡿⣏⣹⠞⠁
⠈⠻⣵⢋⣾⣹⣷⣿⠿⠟⠋⠀⠀⡸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠈⠉⠉⠓⠛⠋
⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⡇⢠⡦⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠲⠤⣤⣀⣀⣀⣀⣙⣁⣀⣀⣀⣀⣀⣀⣥⣤⠴⠖⠚⠋⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢃⣀⠰⠀⡀⠬⠉⠉⡍⠉⢩⡍⠉⢡⠀⠀⠶⢀⡀⠘⢀⣄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢭⣍⣓⡚⠙⠒⠛⠳⠖⠳⠤⠴⠛⠶⠞⠛⠒⠛⠙⠛⢉⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠁⡏⢹⡟⣷⠲⡶⢶⡶⢶⢶⡶⣶⢶⡖⢲⢺⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢤⣇⣸⣁⣯⣸⣇⣸⣁⣽⣸⣇⣿⣸⣧⣼⣧⣷⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡞⠁⠽⠿⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⣀⣠⠴⠛⠛⠳⡄⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣵⣋⣉⡝⠁⠀⠀⠀⣸⣥⣤⡧⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⢀⣠⣾⠿⠛⢉⣤⣤⡤⡔⠛⠓⠒⠓⠶⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠀⣀⠴⠛⠁⢀⣠⠞⣿⣚⣯⡀⠧⡀⠀⠀⠀⢀⡧⣤⡼⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⢀⡤⠖⠋⠁⢀⣠⠖⡏⠀⠀⡇⡇⠀⠀⠀⢸⣄⣀⣀⣸⣇⠘⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⢀⣠⡴⠚⠉⠀⢀⡤⡞⠉⠉⠉⢱⣤⣴⣇⡟⠉⠉⠙⠛⣆⠀⠀⠀⢸⣉⡩⠭⠛⠛⡶⢤⡀
⠀⠀⠀⠀⠀⡠⠞⠉⣀⡤⠖⠋⠁⠀⣀⡴⢚⡇⣠⠦⣄⣠⠤⠾⣭⣤⣸⠀⠀⠀⠀⡏⠉⠉⠉⠉⢹⡿⠤⠤⣄⠀⡇⠀⠙⣦
⠀⠀⠀⠀⣮⣤⠴⠚⠉⠀⠀⣀⠴⠊⢷⡀⠈⢷⠃⠀⠀⠈⠉⢲⠀⠈⠉⠉⠙⠛⡻⣇⣀⣀⣀⣀⣸⠛⠛⠓⠚⢳⠟⠀⢀⡟
⠀⠀⠀⠀⠘⣆⠀⠀⣠⠴⠋⠁⠀⠀⠀⠙⠶⣇⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠋⠀⠉⠉⠉⠉⡏⠀⠀⠀⢀⣸⡤⠞⠋
⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣶⣧⣤⣤⣤⣄⣀⣸⣇⣤⣤⣤⣤⣤⣿⣶⠶⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠚⠚⠛⠛⠛⠚⠛⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⡿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠠⠄⣀⣠⡴⠶⢞⡛⠋⠉⠁⠐⠚⣛⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⣿⠁⠒⠺⠥⡴⢒⠛⠉⣉⣭⣭⣽⣿⣿⣫⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⢻⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢽⠛⣿⡿⢭⣄⣓⠀⠌⠳⣍⠉⠙⠒⠲⠤⢤⣀
⠀⠀⢀⣤⠶⠋⠉⠀⠀⢀⣠⢴⣿⡇⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠇⠀⠀⠉⠀⢸⡇⠀⠀⠈⠉⠛⠒⠾⠷⣦⠀⠀⠀⠀⠀⠉⠑⠢⢤⡀
⢀⣾⠟⠁⠀⠀⠀⣠⡖⠋⠁⢸⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣤⡀
⣿⡏⠀⠀⠀⠀⣼⣟⠀⠀⠠⠊⠉⠙⠛⠛⠿⠷⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⠢⡀⠀⠈⢦⠀⠀⠀⠈⢳
⢻⣷⡀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣷⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸
⠈⠻⣿⣦⡀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⣶⣶⣤⣤⣄⣸⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⣠⡿
⠀⠀⠈⠻⢿⣷⣦⣄⣀⠀⠈⠉⠛⠳⠶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣛⣻⣤⠴⠶⠛⠉⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠯⣿⣷⠦⢤⣤⣀⣀⡀⠈⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠉⠀⠀⣀⣀⣤⠴⣶⣿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠫⠭⠭⢝⣛⣓⣒⣲⡶⠶⠦⠤⠤⠤⢤⡤⠤⠤⡤⢶⡶⢒⣒⣾⣛⠯⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠛⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣆
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠘⠻⠛⠁⠀⠀⠀⠀⠀⠀⠘⡆
⠀⣠⠏⠀⠀⠀⠀⢀⣴⣶⣤⣀⠀⠀⠀⠘⠛⠓⠦⠤⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⢰⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠲⢦⡀⠀⠀⠀⠀⢻
⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⣀
⢿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷
⠘⣧⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⠀⢰
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠘⡇⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠸⣧⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠃⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠈⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣦⣤⣤⣤⣴⣶⣶⣾⣿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢠⣶⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⠀⠀⠀⠸⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠿⣄
⠀⠀⠀⠀⠀⠀⢀⡞⠿⠃⠀⢀⡴⠀⠀⠀⠀⠉⣠⡾⠁⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣤⣶⣿⣦⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠋⠀⠀⠀⠀⠀⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣄⡀⠀⠀⢻⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠉⠉⠉⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠘⠇⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠀⢸⡿⠿⣿⣿⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣈⠛⠛⠁⠀⠀⠀⠀⠀⠰⠛⠻⠟⠃⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⠴⠶⠶⠶⠶⠶⠚⠛⠋⠁

⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⢀⠔⠁⢀⡸⠉⠒⢄⠀⠐⠗
⠀⠀⠀⢎⠄⠚⠉⢀⡀⠤⠚⠆⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⢠⠚⠛⢢
⠀⠀⠀⣧⠔⠒⠋⠁⠀⠀⣀⡔⢾⡏⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⢈⠟⠚⠑⠒⣉⠦⡀
⠀⠀⠀⠈⠦⣤⠄⣒⠊⠩⢀⢱⣀⣹⣆⡀⠀⠀⡄⠀⠀⠄⠀⡠⠚⠀⠉⠉⠉⠀⠀⢹⡀⠘⠃
⠀⠀⠀⠀⡐⢩⣆⠀⢰⠶⠋⡥⠤⠤⠒⢌⣉⡒⢄⠀⠈⠀⠠⠋⠉⠉⠉⠐⠒⠒⠒⠋⢹⣌⣉⠲⣄
⠀⠀⠀⠀⡇⣿⡇⣷⢋⠔⢊⠀⠲⠀⠐⠂⠀⠡⣀⢱⠀⠀⢰⠒⠊⠙⠋⠑⠊⠑⠛⠖⣞⡛⢿⣷⠈⡆
⠀⠀⠀⠀⢃⠹⣷⡇⡜⠀⠀⠀⢈⣒⡊⠀⠀⠀⢨⡀⡇⠀⢸⠀⠀⠀⠃⠀⠐⠃⡤⠞⣣⠼⠼⢿⣃⠇
⠀⠀⠀⠀⣀⠑⢬⡇⡱⠀⠀⠀⢪⣀⡱⣀⣀⣀⠰⠥⠷⠤⠾⢄⣄⣀⡒⠤⠔⠀⠺⣴⠁⠘⠃⢀⠙⡄
⠀⠀⠀⠈⠛⠃⠀⢣⠘⡆⠀⠂⠀⡜⢩⣄⣦⣴⣿⣿⣿⣿⣿⣶⣶⣦⡌⠙⡤⢒⣐⡣⡧⣌⠒⠈⢀⠏⢹
⠀⠀⠀⠀⢰⢒⠉⣻⠉⠛⣧⠤⣀⡏⠒⠊⠭⠿⠻⠿⠿⠿⠿⠛⠯⠍⠒⠉⡟⣁⡎⢘⢸⠀⣉⡊⠉⠢⠋
⠀⠀⠀⠀⡧⠠⠊⠀⠰⠀⠘⡖⠂⠻⡀⠀⠀⢠⣦⠀⠀⠀⠀⣤⠀⠀⠀⢠⠁⠁⣀⠎⡜⠀⠙⠋
⠀⠀⠀⠀⢣⡀⠀⠂⠀⡠⠀⢸⠀⠀⠳⡀⠀⠀⠠⣄⠀⢀⡠⠀⠀⠀⢠⠏⠭⠭⠔⠊
⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠴⠃⠀⠀⠀⠈⠲⢤⣀⡀⠀⠀⢀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢧⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⣧⠉⣹⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠉⠛⠛⠷⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠟⠛⠋⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⠉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⡆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣶⠤⣤⣤⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⣁⣀⡀⠀⢻⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⣀⣄⡀⣀⠀⣀⢀⣤⣤⡀⢀⣶⡄⠸⣯⣼⡇⠀⠘⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⢀⡻⢦⡅⣿⠀⣿⢸⡅⠰⣦⢸⡷⠻⡆⠿⠀⠙⠂⠀⣿⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡀⠈⠓⠚⠃⠙⠶⠛⠀⠙⠛⠉⠈⠀⣀⣀⣠⡤⠶⠒⠛⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠀⠀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠖⠒⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠷⠶⠶⢦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⡶⠶⠶⠞⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠛⠛⠋⠁⠀⠈⠉⠉⠉⠉⠉⠳⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⢀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠠⠄⠀⠂⠀⠀⠀⢄⠀⠀⠀⠀⢀⡠⠠⢄⠀⠀⠘⠒⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠓⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠤⠀⣇⠀⠀⠀⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⣹⠀⠀⠘⠠⢤⠃⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡀⢀⠀⠀⠀⡀⠀⠁⠁⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠈⠑⠂⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠈⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⣯⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡃⠀⠀⠈⠑⢤⠄⠀⠀⠀⠀⢘⡇
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠒⠀⠀⢀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢺⠃
⠀⠀⠀⠘⢧⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀⣾
⠀⠀⠀⠀⠀⢹⡌⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⡏
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⡀⠈⠐⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠐⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣄⣀⣀⡀⠀⠀⠈⠑⠀⠀⠂⠁⠀⠀⠈⠁⠀⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠴⢦⣀⠀⠀⣀⡤⢤⣤⠤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠉⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⢤⣄⣀⣠⠤⠖⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠄⠀⠀⠀⠀⠀⠀⠸⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠶⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⠉⠓⠒⢒⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣄⠀⠘⠗⠤⢈⡁⠄⠚⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠘⢓⢬⠀⢀⡀⠀⢤⡘⠋⠈⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠋⠙⠂⢀⠠⠻⠟⠄⣀⠄⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣤⠜⠎⠰⢀⠴⠦⡀⠁⠛⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⠀⠀⠀⠀⠟⠀⠰⠦⠈⠹⠄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡼⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠇⡿⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠖⣏⠀⢳⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢻⠀⡷⠦⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⣿⠀⠈⢧⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣾⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠈⠓⠲⢤⣄⣀⣀⠀⠀⢀⣀⣀⣀⣤⠤⠖⠋⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⠧⢤⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢘⡷⠊⠁⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠀⠈⠙⠲⡇
⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡰⠃

⡠⠊⠉⠓⢄
⣇⠀⠀⠀⠀⠳⣄
⠘⢦⡀⠀⠀⠀⠈⢢⡀
⠀⠀⠉⠢⡀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠳⡀⠀⠀⣀⣀⣀⣀⣠⡴⠾⠁⠀⠀⠀⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠹⡞⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⢄⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠚⠉⠳⡄⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄
⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠘⠒⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄
⠀⠀⠀⠀⢀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⡴⠒⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⡷⠄⠀⠐⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠛
⠈⠧⡤⣀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠠⠄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠄⠒⠒⠂⠉⠉⠉⠀⠀⠀⠀⠄⢾
⠀⢰⠃⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠸⣄⠈⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠀⠤⠤⠴⢲⣦⣦⣶⠆⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣊⣍⠁⢠⣶⣿⠏⠐⠀⠀⠩⠍⣁⣀⣀⢠⡑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠿⣿⡟⠈⢉⠀⣀⠀⠀⠀⠄⠀⠀⠸⠛⠿⠟⢤⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⢻⠖⢲⣤⠾⡙⠄⠀⠀⣤⣦⣤⣄⡴⠾⣫⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⣉⡛⣉⣸⡇⣴⣤⣀⣉⣭⣥⣿⡯⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠄⢰⣤⣦⢿⡛⠋⢋⣬⣀⠈⠁⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠐⠟⠿⠛⢐⣣⣬⠐⠂⣤⣄
⠀⠀⠀⠀⡐⠄⠀⠀⠉⠹⠿⠻⠍⠂⠉⠻⠿⠗⣢⣀⣻⠿⠷⡀⠀⠀⠀⠀⠀⠀⢨⣫⡇⠐⠶⣾⣶⠄⠘⠛⠛⠁⠐⠈⠿⡧
⠀⠀⠀⢐⡇⠀⠠⠒⢀⣴⣶⡆⠀⢰⣶⣶⣄⠀⣄⡻⣽⣧⢸⣼⠀⠀⠀⠀⠀⠀⠘⢿⣷⣧⠴⣨⣍⠳⣄⠀⠀⣀⡀⠀⣤⡁⢱⡀
⠀⠀⠀⠸⣿⢄⡠⢐⠛⠛⠛⠂⠉⠀⣉⣙⡋⠁⠀⠀⣒⠄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡘⠻⠃⠘⠇⡅⣌⣿⡆⠙⠟⣰⡇
⠀⠀⠀⠀⠻⢿⣗⣤⠀⠀⠀⠤⠐⠿⠯⠛⠓⣂⣰⣭⣷⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣦⡠⢀⢑⡌⠁⣱⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠷⠿⢾⠿⠾⠟⠛⠉⠋⠉⠁⠀⣠⣤⣄⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠚⠿⠿⠼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠰⠾⠶⠈⠛⠁

⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⡀⢀⣠⣤⣶⣦⣤⣀⠀⣠⣤⣴⣦⣤⣀⠀⣀⣤⣴⣶⣤⣄⠀⣀⣤⣴⣶⣤⣄⡀
⠀⠀⠀⣰⣿⠟⠉⠉⠉⠛⢿⣿⠟⠉⠉⠉⠙⢿⣿⠟⠋⠉⠉⠙⢿⣿⡿⠋⠉⠉⠙⠻⣿⡿⠋⠉⠉⠉⠻⣿⣆
⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⢈⣿⣷⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⠁
⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⢿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⣠⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧
⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⡟⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀
⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠹⣿⣦⣄⣀⣀⣤⣿⣿⣦⣄⣀⣀⣤⣾⣿⣷⣄⣀⣀⣤⣾⣿⣷⣤⣀⣀⣠⣾⣿⣷⣤⣀⣀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠉⠛⠛⠛⠋⠁⠀⠉⠛⠛⠛⠛⠉⠀⠉⠛⠛⠛⠛⠉⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⠳⢤
⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⠂
⡰⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠙⠉⠀⠀⠀⣠⠶⠖⠲⠚⠲⡄
⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣿
⠘⢦⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠦⢤⡀⠀⠀⢰⠇
⠀⠀⠙⢦⡀⠀⠂⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⣇⣀⣤⣀⡟
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡞⠉⠉⠉⠀⠉⠷⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢳⣤⠴⠒⠋⠉⠳⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠦⣄⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠛⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠉⠉⠀⠀⠙⢦⡀⠘⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄
⠀⠀⣀⣤⡤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠲⢦
⠀⣾⠁⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰
⠀⡼⠋⠀⠀⠈⠑⠤⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠀⠀⠀⠈
⠀⠻⢦⡤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠔⢺
⠀⠀⡾⠀⠀⠈⠁⠒⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠤⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠐⠁⡆⠀⠀⠀⠀⠀⠀⡾
⠀⠘⣇⠀⠀⠀⠀⠀⠀⡇⠀⣎⠉⠀⠀⡏⠓⠀⡖⡆⠀⡠⠒⢂⣉⣐⡆⠀⠀⡠⠄⠂⢦⠀⠀⢠⠞⢉⡀⠀⠈⣆⠀⡇⢀⠃⠀⠀⠀⠀⠀⣸⠃
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠙⠒⢬⡉⢢⠀⠀⠂⢠⠁⡇⠚⠀⡴⠉⠀⠉⠀⠀⢀⠇⢀⣄⠘⡀⠀⠘⠀⠸⣉⠇⣀⠄⠀⣇⡜⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠅⢰⠀⡆⠰⠞⢠⠃⡇⠀⣇⢰⡆⠀⠤⠄⡸⠀⢘⠁⠀⢃⠀⠀⠀⣠⡀⠘⠣⡀⢀⣈⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠾⠤⠴⠖⠃⠀⠳⠤⠤⠎⠀⠘⢤⣈⣩⡀⠀⡗⢊⡇⠀⠏⢣⠀⠘⡀⠀⣀⣀⠰⣄⡴⠋⠘⠊⠀⠀⢀⡴⠏
⠀⠀⠀⠀⢰⠛⠒⠤⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠀⠀⠑⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠴⡿
⠀⠀⠀⠀⠘⢧⣄⡀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠦⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣛⣛⣓⣲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣒⣚⣋⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠋⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡟⢛⣿⠟⣛⣛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣤⣀⣶⣠⣤⣤⣀⣤⣄⠀⠄⠾⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡼⠿⠟⠛⠛⠉⠉⠉⠉⠉⠈⠉
⣿⣿⠿⢿⣿⣿⣿⣿⣿⣯⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠗⣴⣒⣞⣿⣿⣿⣿⣿⣿⣿⣿⣀⣄⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡆⠀⠂
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠴⣾⣶⡷⡆
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣇⣤⣼⣿⣿⣀⠀⠀⠠⣦⣴⣿⣷⣉⣷⡄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣻⣀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⣻⣾⡿⢿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣯⢽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⡬⠴⠻⣿⣿⠿⠜⢋⣿
⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢿⠋⠁⠀⣀⣿⣿⣿⣿⣧⢿⣿⣿⣿⣼⣇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣠⣶⣆⣉⣉⣠⡄⠀⢠⢸⣿⣷⣤⣼⣽
⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣀⠀⣰⣾⣿⣟⢿⣿⣿⣿⣾⡥⣠⣿⣷⡽⣷⣶⣶⣶⣶⣶⣿⣿⣿⣷⣶⣶⣤⣼⣿⣿⣬⠝⠛⣓⣤⣤⣰⣿⠻⣛⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣤⣘⣻⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⠨⡝⣃⣼⣿⠿⣶⣼⢿⣅
⣿⣿⣿⣿⣿⣿⣿⠇⢉⡉⠉⠙⠉⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠿⠿⠛⠻⣶⣿⣿⣿⠁⣼⣿⠿⡿⠃
⠿⠿⠿⠿⠹⢿⣿⠆⠉⠓⠀⢑⣀⢻⣄⣿⡀⣴⡿⣄⣰⠿⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⡀⠀⠀⠀⠘⣿⡿⠇⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣬⣿⣿⣿⣿⣿⡿⢿⣿⣶⣿⣶⣶⣿⣿⣿⣿⣄⣼⣥⣽⣋⡉⠁⣀⡼⠁⠀⠀⠀⠀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠛⠳⣶⣿⣿⣿⣿⠟⠙⠋⠙⠛⠛⠛⠛⠛⠇⠘⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣷⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠀⢸⣇⠀⠀⢬⣅⢄⣢⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣣⣠⠂⠀⢑⡃⡈⣠⡔⢭⣛⣾⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⣿⣿⣶⣤⣴⣿⣿⡷⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠢⠀⠠⠉⡉⠨⠑⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠁⢀⠀⣀⠁⠠⠖⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡄⠀⠦⠀⠀⠁⠀⠀⣀⣀⡀⠀⠠⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠈⠓⠤⣀⠀⠈⠀⠀⠀⠉⢉⠐⣁⣤⠊
⠀⠀⠀⠀⣀⠀⠀⠒⣀⠀⢐⠀⡄⠀⡀⠀⠈⠀⠀⡀⠐⠘⢀⢬⠁⠐⠒⠩
⠠⠊⡄⠀⠊⠀⠒⠀⠁⠀⠀⠀⠘⠦⡀⠛⠀⠒⠀⠀⠀⠀⡤⠤⠄⠐⢀⡴⠄
⠃⢰⠃⠀⠀⠐⠀⠀⠰⠖⠉⠀⡍⠘⠈⠙⠒⢀⠀⠤⠤⠀⣤⡤⡀⠈⠁⠠⠘⠒⠚⠉⠭⠙⠋⠑⠢⢄⡀
⢃⠫⠈⠚⠂⢀⠀⠰⠂⠀⠦⠆⣀⠙⣀⠠⠌⠀⠄⠀⢀⠀⠀⡀⠁⣀⡎⠠⠀⠈⠀⣀⠀⠀⠛⠀⠂⠀⠑⢄⡀
⠀⠉⠒⠜⠀⠀⠀⠀⠀⠀⡤⠂⠊⠠⡈⠁⠦⠄⣀⣀⣘⡀⢈⣁⣤⡍⠀⠂⡀⠒⠀⠁⠀⠂⠀⠂⠁⣀⠀⠀⢧
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠚⢣⡠⠀⠑⢂⠀⠀⠥⠠⠁⣄⠀⠀⠇⠠⡄⠀⠀⠀⠠⠄⠀⡀⠠⠄⡀⠀⠄⠐
⠀⠀⠀⠀⠀⢀⠤⠀⠀⡀⠀⠒⠶⠨⢅⣢⠬⠀⢀⣀⣀⣄⣉⡄⠤⠜⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⠆⠀⢰⢂
⠀⠀⡀⠊⠙⠀⡀⠈⠀⠀⠀⠀⡀⠀⠚⠃⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠒⢣⠀⠀⠀⠀⠢⠂⠒⡠⢜⡝
⠀⠀⠁⠀⠠⢀⡄⣈⠀⠀⠈⠁⠀⠀⠀⠘⠀⠀⠠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⠄⢀⣐⣇⣈⣀⡠⠔⠋
⠀⢐⠀⠀⠄⠀⠄⢀⡀⠀⠀⠀⠘⢁⠠⠀⠀⠓⢃⢴
⠀⠈⠦⡋⠀⢠⠀⠀⠀⠠⣒⣢⡄⠀⣀⠀⢀⡈⢱⠎
⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠀⠁⠀⠀⠀⣀⠠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠛⠛⠋⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠀⢀⣀⡤⠴⡖⠚⠛⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⢸⠉⠘⢳⡾⠭⣩⣽⣿⠿⣟⠷⣤⠄⣀⣀
⠀⠀⠀⣀⡤⠖⠊⠉⣀⣿⡇⠀⠀⠀⠘⠀⠀⠸⠇⠀⠇⢹⡏⠑⠒⠢⠬⣷⣄⠀⠈⠉⠒⠠⢄⡀
⠀⣠⡞⠁⠀⢀⡴⠋⠁⣿⣧⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠤⣀⠀⠀⢄⠀⠈⠳⣄
⠀⣿⡀⠀⠀⢸⣇⠀⠊⠀⠀⠉⠉⠛⠛⠷⠶⣦⣤⣤⣀⣈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠑⠂⠀⡧⠀⠀⠘⡆
⠀⠘⢿⣦⡀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⢶⣦⣤⣼⠀⠀⢀⣠⠞⠁⠀⢀⡼⠃
⠀⠀⠀⠉⠻⢷⣦⣤⣀⡉⠙⠓⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠬⠽⠒⠊⠉⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⠶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠤⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣠⠴⠊⠙⠋⠉⠉⠓⠶⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠂⣔⠒⡆⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⢀⠀⠀⠀⠀⠛⠃⢣⠀⠉⠉⠀⠀⠀⠠⣋⡹⠀⡽
⠀⠀⠀⢀⡞⠉⢢⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⢠⠟⠒⠉⠁⠠⠴⢏⣀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠛⠀⣀⣀⡜⠁
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢢⠀⠀⠀⠀⠀⢸⣀⡠⠔⠋⠁⠀⠑⠦⣄
⠀⠀⠀⣳⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⠒⠃⠀⠀⠀⡀⠀⡇⠀⠀⢀⣀⠀⠀⢀⠀⠈⡇
⠀⠀⠀⢿⠀⠀⠀⠀⡔⠓⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⢁⠜⠀⠀⠀⠧⠬⠂⠀⠀⠀⠀⡏
⠀⠀⠀⠈⢻⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠁⠀⠀⠀⠀⢀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⠀⡀⠀⡎⠁⠈⢧⠤⠔⠀⠀⢀⠿⠤⠤⠤⠤⠖⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠙⠺⢄⡀⠀⣉⠈⣉⠳⠤⢖⣁⣀⣠⠴⠚⠁⠀⠀⠀⣠⠖⣦⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠛⠂⠀⠈⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⠖⠂⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⡀
⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠇⠀⠠⠲⠏⠣⠀⣠⠤⠄⠀⠈⠀⠀⠀⠀⠁⠐⠠⣴⣇⠀⠀⣀⡠⠆
⠀⠀⠀⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⣇⠀⠈⠀⢀⣀⡀⠀⠀⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⣀⠀⢴⡇⢀⣶⠘⠦⡌⣀⣾⡧⠃⠀⣾⡧⠃⢀⣿⠁
⠀⠀⠀⠀⠀⢀⠤⠒⠈⠹⣿⡄⠀⢸⣇⠜⣿⠀⢠⠁⠀⢿⡀⢀⠜⠻⣀⡠⠊⣿⠀⠀⠠
⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣿⠁⠀⠀⠉⠀⢻⣠⠂⠀⣶⠀⠉⠁⡀⠀⠀⠀⠀⣿⠀⢠⠃
⠀⠀⠀⠀⠀⠣⣀⣀⡤⠟⠁⣰⡇⠀⠀⣼⠆⠀⠀⢀⡏⢀⣤⠀⣠⡄⢀⠀⣤⠘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡟⠀⠀⠀⠸⡇⢸⡏⠠⣟⠀⢾⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠃⠀⠀⠀⠀⠓⠀⠀⠀⠈⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣀⡀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⢠⣾⡿⠁⠀⣼⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢠⣿⠟⠁⣠⣾⠟⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠈⠁⢀⣴⡿⢁⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⣴⡿⠋⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠛⠛⠛⠿⢷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⣠⡄⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠸⠗⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠸⠗⠀⠀⠀⠙⠻⢿⣦⣄⡀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠀⠰⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣤⡀⠀⡀⠀⠈⠙⠿⣶⣤⣿⠃⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠀⠀⠀⠾⠎⠛⢿⣦⡀⠀⠀⣠⣿⠏
⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⣤⠀⠀⠠⣦⠀⠀⠀⢀⡀⠀⠀⣤⡄⠙⢿⣦⣼⡟⠁
⣰⣾⣿⣻⡿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠋⠀⢀⣤⠀⣤⡄⠹⣿⣿⣶
⣿⡏⠙⠻⠿⣶⣦⣄⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⢠⣦⠀⠈⠋⠀⠀⠀⠀⠉⣀⣬⣶⡿⠟⠉⣿⡆
⣿⡇⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⡶⠿⠛⠋⠁⠀⠀⠀⢻⣇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⣾⢿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠁⢸⣿
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢰⣶⣶⡾⠿⠟⠛⠉⠁⠀⠀⠀⠀⣾⡇
⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠃
⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⠿⢛⣿⡿⠁
⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠻⠿⠿⠛⠛⠛⠋⠉⢁⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣿⡉⠉⠙⣏⠝⠲⠦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠈⢳⣌⠡⠘⢿⣖⡢⢦⣬⣉⡛⠒⠒⠶⠖⠲⠒⣲⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠙⠷⣍⡀⠂⠍⢙⠒⠾⠭⣿⣒⣲⣶⠶⠚⡁⢪⡴⠋⠙⠲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⢤⣬⣤⣀⣀⣐⣀⣤⡴⠞⠉⠀⠀⠀⠀⠈⠛⣌⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠘⣇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢸⡀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⡄⠀⣿
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣧⠀⣿
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐⠀⠀⣼⠀⠀⠀⠀⠀⠄⠀⡿⠀⡹⡄
⠀⠀⠀⠀⠀⣧⣄⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣀⠀⠀⠀⢠⠀⢀⠇⠀⡇⢹⡄
⠀⠀⠀⠀⠀⢹⡄⠙⢦⡉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⡠⠂⡙⠳⣄⠀⠂⢀⠞⢀⡼⠁⣸⠇
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠹⣦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⡊⠊⡠⢋⡴⢃⠈⠳⡄⠀⢐⣫⡤⣾⠃
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠻⢦⡙⠂⠀⣀⣤⠶⠖⠋⡙⠷⡄⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⠻⣤⡁⠔⢁⢞⣤⡿⠞⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠉⢻⠏⠁⠀⠘⠘⠀⡡⢢⠹⣄⣀⣀⣀⣀⣀⣀⠀⠀⠙⢦⣈⢻⣆⢑⣯⠞⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣀⣠⣤⣿⠀⢈⡤⠴⠖⠊⠀⢸⢀⡏⠉⡏⠉⠉⢹⠉⡏⠉⡟⠛⢛⠛⢿⠛⢳⠶⠶⡶⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠹⡅⠐⡀⢸⣆⠸⠤⠤⣒⡶⠿⡟⠉⠅⢠⡇⢰⠀⢸⠀⡇⢠⠇⠀⠘⠀⡇⠀⡜⠀⣰⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢣⠀⠃⠘⠈⢱⠒⠛⠁⡇⠀⡇⠀⡆⣸⠀⡀⠀⣾⠀⡇⢸⠂⠀⡇⢀⠇⢰⠁⢰⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠆⠸⠀⡇⣸⣀⣀⣠⣁⣀⡃⢀⡇⡇⠀⣇⣀⣇⣀⣃⣸⣀⣠⣀⣜⣀⡃⢀⠆⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠚⠋⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⠒⠒⢦⡀⠀⠀⣠⠔⡒⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠢⢤⡀⠱⡄⢀⡗⠚⡟⣡⠋⡠⠔⠂⢀⣈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⢍⣉⡓⣦⠴⡷⠲⡗⢫⠀⣠⠷⡗⢾⠒⢶⠯⠥⣤⡄⠤⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠤⠒⢻⠁⢀⡆⢀⡜⠀⡇⣨⠇⠣⣀⠳⠈⠳⠘⠢⠀⠱⠌⠙⣂⡽⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣢⡤⠤⠥⠤⠬⠤⠤⠒⠚⠉⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⢤⡈⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠬⠓⠂⢈⣑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠤⠶⠒⢚⣋⣉⠥⠤⠶⠒⠚⠋⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣩⡥⠤⠤⠶⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣠⣤⣚⣁⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠴⠦⠤⠤⠤⠤⠤⠤⠴⠒⠒⡻
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠔⠋⠙⠒⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⢸⣀⣀⣀⣀⣀⣀⠠⠤⠤⠤⠤⠤⠐⠒⠒⠒⠒⠒⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠤⠤⠤⠤⠐⠁
⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠥⠤⠤⠤⠔⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠙⠛⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠁




⡿⠉⠙⡟⡻⠟⠟⠛⠻⣟⠛⡟⠿⠻⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣟⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⢒⡖⢲⠖⡤⢤⡤⢤⠄⣶⠲⡎⢻⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣯⣼⣇⣸⣘⣇⣸⣇⣸⣇⣿⣤⡷⠾⢿⡿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠺⢬⣷⣚⠛⠯⠽⢯⣍⣽⠿⢭⣥⠟⠛⢒⣫⡴⢾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⣎⡀⠰⠆⠈⠉⣛⠛⠳⠶⠶⠶⠶⠶⠶⠞⠛⢫⠉⠀⠈⣋⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠸⠟⢳⡶⣤⣤⣋⣀⣀⠀⠗⠀⠀⠙⣁⣀⣀⣠⡤⣶⠛⠏⠁⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⠀⠈⠋⠈⠟⠉⠻⠋⠙⠟⠙⠟⠉⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦
⠀⠀⡠⠚⢧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠟⢹⣿⣷⡄
⠀⡔⢷⡐⠎⠻⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣴⠟⢡⢄⣴⠿⣿⣧
⢀⣆⠀⠻⣦⡉⠀⣙⠾⣅⣀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠑⣞⠋⠰⢂⣴⠟⢁⣴⣿⣿
⣮⠞⣳⣄⡈⢻⣶⣌⡀⣠⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠈⠳⢞⠉⢀⣴⣞⢷⡼⠋
⠈⠺⣁⣾⣿⣿⡿⠿⠋⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠉⠉⠑⠚⠁
⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⣙⠛⠳⠾⠷⢶⣷⣤⣤⣶⣤⣤⣶⣤⣴⠷⠶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⡛⣿⠲⢶⡶⢦⡤⢤⣴⣶⡶⣶⠶⡶⢶⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣿⣤⣼⣦⣼⣧⣠⣇⣸⣤⣿⣤⣷⣾⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⢠⠪⠁⠀⠉⢳⡄⠀⠔⠋⢩⣟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⢰⡶⠛⠉⠀⡀⠉⠳⢝⡲⠤⣤⣤⡶⢋⠉⠓⢦⠀⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⢿⡿⢿⡴⠚⠉⠀⠈⠙⠦⣄⣈⣀⣠⣿⢳⡄⠳⡀⠈⢗⠈⣉⣉⠙⢦⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠹⡟⢻⣬⣔⣲⣤⣄⣀⡀⠻⠙⠦⣄⣀⡀⠀⣀⣌⠥⣪⣥⠀⢳⡀⠙⢦⣈⡳⡤⣄⠱⡜⣧⣶⡌⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⡍⠙⠿⠿⢿⣶⣦⣤⣄⣀⠀⠀⠀⠈⠻⠛⣆⡀⠙⠲⣴⡶⣿⣷⣬⣇⣷⠏⠉⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠉⢻⠛⠿⣶⣦⣤⣀⡀⠀⠉⠉⠉⣿⡆⠻⠟⠃⠉⠀⠀⠋⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠈⠓⠈⠻⢿⣷⡲⢄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢇⢹⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣲⠌⢏⠳⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⢤⣄⡀⠂⠀⠀⠀⠙⢯⠙⣔⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣺⣽⣟⡻⢿⣶⣀⠁⠘⡟⠋⠀⠀⠚⠿⣟⠶⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣟⠿⣶⣦⣵⣄⠀⠠⠄⠈⢱⡼⠂⠈⢑⣒⡲⡄⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣭⡻⢿⡷⣦⣤⣀⠠⠖⠉⠀⠈⠉⢻⡌⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣬⣽⣿⢿⣿⣷⣴⣬⣀⠸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⢒⣀⡥⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣯⣝⡒⠬⢕⡫⢽⣻⣷⢼⢿⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣬⣁⡒⠈⣟⡼⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣻⢦⡝⣿⡻⢽⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠊⠱⠟⣁⣾⠞⢿⠹⣶⠉⢦⠉⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠙⣆⣤⡞⣁⣁⣠⠾⢀⣿⠀⣿⠇⣹⠏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢋⣉⣩⣭⠭⢴⣞⠛⠋⠈⢛⡠⣯⠄⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣠⠔⠚⠉⠉⠁⣀⣠⣤⣥⣖⣈⣉⣀⣀⣥⣾⣿⣷⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⣠⣤⣶⠿⠿⡿⠛⠉⢉⣩⣥⡴⠛⣡⡾⡇⢸⣿⣮⢿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣤⠞⠋⢁⣠⠤⠄⠃⢉⣉⠠⠴⠚⠓⠋⢡⠋⣠⣿⣿⡿⢸⣧⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢳⡿⠁⣠⠴⠋⠀⣀⡴⠞⠋⠀⢀⣀⠤⠤⠖⠒⢛⣩⡾⠛⣡⣾⣏⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠈⢾⣇⢰⡏⠀⠀⡼⠋⠀⣀⠴⠊⠉⢀⣀⡤⠶⠒⢋⡭⠐⠉⠁⢁⣼⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠀⠈⠻⢌⣧⡀⢸⠁⠀⣼⠃⢀⣴⡾⠋⠀⠀⣠⣾⡯⣤⣤⣴⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣬⠙⠆⢤⠤⡈⡙⠛⠷⠾⠯⢴⡾⣿⣤⣶⣞⣻⣍⣿⣷⣼⣯⣿⡿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠃⠀⠀⠀⠀⠈⠉⠘⢷⠳⡚⠳⠾⢿⠿⡟⢻⡟⢻⣹⢩⡧⣼⢱⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠘⠂⢸⢀⡇⢸⠇⡿⣿⢸⡇⡟⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢄⠀⠀⠀⠁⠀⠘⡇⢸⠈⠇⣸⢠⠇⠓⡾⣼⢡⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⠐⡈⡄⡀⢀⠀⠀⡀⣧⢸⢰⠀⡾⢸⣤⣛⣧⣿⣼⣿⣿⣽⣿⣿⣤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⡦⣦⢢⣧⠰⡀⠧⢁⢹⣸⣼⢴⡧⡿⣿⣼⢸⣿⣿⣿⣿⣿⣾⣟⣿⣌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠻⠼⣾⣿⣇⢱⡸⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣟⣦⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡵⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠑⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠀⣂⠶⠒⣀⠴⠖⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⡠⠄⠂⢉⠠⠔⠊⠀⠀⢀⠀⠤⠐⠉⡻⢖⠠⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠋⠁⣀⠠⠊⣀⠔⠉⠀⠀⣀⠠⠒⢉⡠⠤⠐⠊⠁⡠⠊⣉⠬⠛⠀⠐⢄
⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠉⡠⠔⠊⠀⢠⠔⢈⠤⠠⡔⠊⠁⣀⣀⡠⠔⠉⠄⠈⠀⢀⡠⠄⠒⠂⢑⣀
⠀⠀⠀⢰⠁⠀⢀⠔⢁⠔⠉⢀⠠⠔⡞⠁⠀⠥⠖⠒⠻⣄⠔⠧⠬⡁⠂⠁⡠⠄⠂⣁⠤⠐⢉⡡⠒⠉⣆
⠀⠀⠀⣾⢀⠎⢡⠔⠁⢀⠔⢁⠤⢺⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⡠⠒⠉⢀⠠⠐⢁⡠⠊⠁⠘⡄
⠀⠀⢀⡿⠃⠰⣁⠄⠊⣁⠔⠁⠀⠈⢺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠⠊⡡⠔⠊⠁⠀⠀⢀⠠⡇
⠀⠀⠸⡨⠀⠉⢀⠔⠉⠀⠀⠀⡀⠐⢀⠠⠘⠉⠈⡉⠔⢀⠤⠊⠁⠀⢀⠀⠊⡠⠊⠀⢀⣀⠤⠀⠊⣀⠄⡇
⠀⠀⠀⢳⠧⡈⠁⠀⠀⠀⢠⠊⡠⠀⠁⡀⠄⠒⢁⠠⠒⠁⠀⢀⠠⠂⣁⠤⠊⠀⡠⠒⣁⠤⠔⠂⢁⡀⢀⠃
⠀⠀⠀⠀⢣⡈⠑⠢⡀⠀⠃⢰⡠⠊⡁⠄⠒⠉⠀⠀⠀⡠⠊⢁⠔⢊⣀⠤⠒⢉⠤⠊⠀⠀⣀⠔⠁⡸⠃
⠀⠀⠀⠀⠀⠑⢄⠀⠑⡄⠄⠈⡠⠊⠀⠀⠀⠀⠀⠀⠐⠀⣔⠅⠊⣁⠤⠐⠊⠁⠀⠀⠀⠊⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣸⠀⠀⢠⠐⠒⠒⠦⡀⠀⠀⠘⠤⠠⠐⢈⡠⠖⠉⠀⠀⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣠⠮⣄⡀⠀⠀⢡⠀⠀⠀⡴⠁⠉⠁⠀⠀⢀⣀⣄⢀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠦⡀⠔⠓⠒⠒⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⢈⠀⠄⠀⠀⠀⠠⣈⣢⣏⢐⣃⠀⠀⠀⡀⠂⠀⢀⠄⠀⠀⠂⠄⠀⠈⣂⠀⢀⡀⣀⣨⡀⠀⠀⠀⠀⠀⠠⡀⠐
⠀⠀⡄⠁⠀⠀⠀⠂⠀⠀⠭⢚⢹⣿⢟⢔⠀⠀⠂⠀⠀⡠⠉⠀⠀⣦⠀⠠⠃⠂⢘⠀⠠⠀⢿⣿⡿⢀⠁⠀⠀⠉⠀⠈⠁
⠀⠀⠈⠢⠤⠈⠠⠔⠁⠀⠀⠃⠆⠹⠗⠁⠀⠀⠀⠠⠈⠀⠀⠀⠀⠈⠓⠀⠦⠒⠁⠀⠀⠐⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⢀⡕⠠⠂⠀⠀⠀⠀⠴⣿⡟⡩⠄⣠⠀⠀⣚⠽⠚⠩⣖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢴⣶⡄⠈⡀⠀⠀⠀⣴⣄
⠀⠀⠀⠁⡀⠁⢈⡄⠀⠀⢃⠉⣽⢿⡾⡯⠀⠀⠵⠪⣔⡯⠷⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⢂⠈⠁⠀⡀⠀⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⢀⣠⡲⢄⣀⠀⠀⢀⠀⠀⠙⢲⠄⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡰⡆⢶⡀
⠀⠀⠀⢨⠇⠂⣉⡏⠀⠀⠀⡤⠀⠀⠀⡀⠀⠀⠀⠘⠿⠏⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢻⡈⡇
⠀⠀⠀⠀⠉⠩⠋⠁⠀⠀⠀⠂⠠⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠈⠻⣶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠩⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⡀⠀⢀⣀⡀⢀⡀⠀⢀⠀⠀⢀⣀⡀⠀⢀⣄⠀⠀⣀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⠁⠰⣿⡉⠋⢸⣿⠀⣿⡇⢰⡿⠙⠃⠀⣼⣿⡄⠀⣿⣷⡄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠙⣷⡄⢸⣷⠀⣿⠃⢸⡇⢺⣶⠀⣿⣾⣧⠀⣿⣿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠈⠀⠻⠶⠿⠁⠀⠻⡾⠏⠀⠸⣷⡿⠁⢸⡿⠀⢿⠆⣿⡿⣧⡀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡦⠓⠀⠠⢤⣤⣤⣤⠀⠀⠀⠀⠀⣤⡤⠤⠶⠒⠋⠁⠀⣼⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣀⣀⣬⣬⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣁⣁⣀⡈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⣰⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⢸⣿⠃⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠈⠉⠉⠁⠀⠀⠘⠟⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢰⣿⡏⠀⢀⣀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠘⠟⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⣴⣿⣿⣶⡀⠀⠀⢴⡆⠀⠀⣠⣶⣶⣄⠀⠙⣿⡗⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⢀⣼⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣄⣁⣀⣋⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠯⠿⠿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⠌⠉⠠⣃⠀⠀⠀⠀⠀⠸⠉⢶⠃⡇⠀⠀⠀⠀⠀⠐⡧⠶⠤⠴⠯⠭⠍⠠⠤⠬⠟
⠀⠀⠀⠀⠀⢏⠀⠉⠂⣾⢡⠀⠀⠀⠐⠂⠄⠀⣹⠀⠚⠀⣨⠃⠀⠀⠀⠀⠀⠑⢠⠞⠀⠀⢀⠀⡄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⡰⠁⢀⠀⣿⠀⡀⠀⡁⠀⡀⢀⡄⢸⣄⡈⠀⠝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡌⠀⠀⣀⡀⠀⠀⠠⠤⡀⠀⡇⠉
⠀⠀⠀⠀⠀⢈⡆⡀⢀⡽⢆⡀⠀⠀⣀⣀⣠⡤⠞⠀⠉⠓⠲⠚⠀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⠃⠀⡀⠣⢟⡀⠴⢐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠸⣨⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⢣⠈⡇⠀⠀⠀⠀⡜⠀⠀⠚⠀⠥⠝⠰⣉⠇⣴⠂⣷
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠒⠃⠙⠲⡄⠀⢠⡇⠀⢎⣨⠂⢜⠂⡶⠀⠘⠔⠁⢻
⠀⠀⠀⠀⠁⠀⠀⠀⣠⠀⠀⠀⠐⢮⡁⠀⢯⠀⠀⠀⠀⠀⠀⠀⢰⠒⠠⡀⢠⠀⠀⠀⠀⣰⠃⠀⠈⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⢔⠒⠁⠀⣰⠃⠀⠓⠶⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠖⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡨⠆⠀⠀⠀⠀⠀⠸⠧
⠀⠀⢐⡆⠀⠀⠉⢀⠴⠂⠉⠀⡤⠉⠙⠦⡀⠀⠀⢀⢒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠓⠁⠀⢀⣀⠀⣀⡀⠀⠁⠔⠒⢢
⠀⠀⠈⢠⢢⠄⡔⠁⠘⣀⡤⠤⣄⡀⠀⠄⠙⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠔⠢⡄⠀⢀⠔⠊⠁⠀⠀⠀⠈⠓⣎⠀⠀⡞⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠆⠀⡞⠀⠀⡼⠁⠀⠀⣄⠙⢦⠀⡤⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⢦⠏⡀⡜⠀⡐⡐⠀⡀⢀⢘⡇⠀⠈⠓⡆⠀⠀⣹⡗
⠀⠀⢰⠀⢸⡃⠀⠐⡇⠀⠄⠀⢸⠂⠘⡇⠀⠀⢸⡄⠀⠀⢴⡞⠀⠀⠀⣏⠅⠀⠐⢿⡔⡜⠀⡔⡰⠀⡰⢡⢃⣼⣁⠀⠰⡞⠁⠀⠈⠓⠃
⠀⠀⢸⠀⠈⣇⠀⠄⠈⠲⠤⠴⠋⠀⢰⠇⠘⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢈⡆⢈⠈⡴⠻⢤⣜⣜⣀⣔⣴⠷⠋⠀⠙⠣⣀⡟
⠀⠀⠀⢧⠠⡌⠦⣀⠀⠀⠀⠐⢀⡰⠋⠠⠀⢀⡟⠀⠀⠀⠀⣠⠀⠀⠀⢯⡐⣡⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠳⣄⠀⠈⠙⠒⠒⠛⠉⢀⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠖⠀⠀⠀⠀⠕⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡭⠴⠛⠁⠀⠀⠀⠀⣀⣠⠎⠉⠐⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣍⡉⠙⢳⡄
⠀⠀⠀⡰⠤⠆⠀⠀⢴⡄⢰⢸⠀⠀⠀⠀⠀⠈⠃⠀⠈⢆⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡞⠡⣠⡞⠉⠉⡇⠈⣿
⠀⠀⠘⠢⡤⠷⠀⠀⠀⠀⢸⢸⡆⢀⠀⠀⠀⠀⢀⣀⠀⠀⠖⠲⠶⠞⢣⡀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⣰⠋⣄⣰⠋⠀⢠⡞⠁⣸⡟
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢸⠸⡇⠘⠇⠀⠀⠀⠬⠄⠀⡐⠀⢀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣧⡜⠁⠀⠀⠈⠙⠛⠋⠀⠀⡀
⠀⠀⠀⠀⢠⢄⠀⠀⠈⠃⢸⡆⡇⠀⠀⠀⠀⠀⠀⢠⠞⠃⠐⣒⢋⣀⠀⢀⡆⢳⡀⠀⠀⠀⠀⢠⢾⠘⣦⠋⠀⠀⠀⠀⣠⡂⠀⠀⠀⠘⠃
⠀⠀⠠⠒⠇⢸⠀⠀⢀⠀⠈⡇⣧⠀⠀⠀⠀⠀⢠⠃⣈⠣⠐⠊⢀⠂⢂⢠⠀⣸⠃⠀⠀⠀⡰⢧⢀⡿⠃⠀⠀⠀⠀⢀⡽⣓⢦⡀
⠀⠀⠀⠁⠀⠞⠀⠏⢏⠇⠀⡇⢿⠀⠀⠀⠀⠀⠘⠦⣌⣃⡈⠀⠚⢀⣑⣨⡴⠋⠀⠀⠀⠀⠳⠼⠟⠁⠀⠀⠀⠀⠀⢾⡘⠀⡇⢱⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⢧⠜⠀⠀⠀⠰⡷⠂⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠫⠭⠴⠃⣠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣯⡼⣿⣿⣿⣴⣿⠷⣶⣄⣠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡼⠛⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⢹⡿⠋⠉⢹⣿⠿⠋⠙⠛⠛⠛⠛⠻⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⢨⣷⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⣾⣿⣶⣦⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⣤⣿⣿⣿⠏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡈⠛⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣤⣉⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⣩⣴⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⣦⣭⣭⣉⣙⣛⣛⣛⣛⣋⣉⣭⣥⣤⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣠⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡋⠀⠀⠀⠀⠛⠿⣦⣦⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣛⡿⣿⣿⣿⣾⣯⡛⠦⣄⡀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢏⣺⣿⣿⣿⣷⡍⠙⠻⢿⣷⣮⡛⠁⢤⡀⠀⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢈⢙⢿⠛⣟⣛⣏⣉⣹⡁⡜⢠⠃⡠⠩⠻⢿⣷⣌⠹⢶⡝⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣾⣿⣷⡿⠋⢿⣿⣿⣿⢿⣷⣿⣴⣃⡰⠁⡀⠙⢿⣷⣼⣏⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⡟⠁⠀⠀⠙⠷⢦⣄⣶⣤⣽⣿⣷⣾⡰⢁⠜⢻⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣬⣽⣿⣿⡿⣿⣿⣿⣯⡔⣠⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡽⠛⠛⠓⠀⠀⠀⠈⢉⣠⣀⣀⠁⠀⠉⠛⣿⣿⣵⡣⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢞⣿⣿⡖⡄⠀⠀⠸⡥⠿⠿⠿⠂⠀⢀⡿⣿⣿⣾⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠠⣄⠀⢀⣼⣴⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣿⣿⣇⠀⠀⠀⠿⣤⡴⠦⠀⠀⠀⠀⠹⢿⣿⣏⣙⣻⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣿⣿⣆⠀⠰⠠⣤⠄⠀⢠⡤⠓⠆⠀⠀⠈⣹⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣀⠀⠈⠭⠥⠖⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣄⠀⠀⠀⢀⣠⡴⠞⠉⣿⣿⢟⢻⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣽⢿⣟⡿⣿⣷⣟⠋⢁⣀⣠⢴⠛⣍⢦⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣸⠀⡇⡆⠘⢩⠁⡁⢣⠀⢷⣸⣿⣿⡿⠋⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣆⠈⠻⣿⣿⣿⣿⣷⣷⣶⣼⡦⢸⠸⡶⣿⣿⣿⠟⠁⠀⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⣼⡍⡏⢏⢹⠉⣇⣸⡶⣿⡿⠟⠁⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⠻⢿⣿⣿⣞⣻⣹⣽⠟⢋⠠⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠿⠛⠛⠛⠻⠿⠶⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠙⣷⡀
⠀⣰⡟⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢠⡿⠀⠀⠀⠀⠻⠟⠁⠀⣿⡿⠀⠀⠀⣶⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣾⣷⣤⣤⣄⣀
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⣿⠀⠀⠀⣾⣷⠀⠀⠀⠀⢴⣿⡆⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⢻⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⢻⣆
⠘⣿⡀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢻⡆
⠀⠘⣷⡀⠀⠀⠉⠀⠀⠀⠀⣀⣀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠻⠟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⣤⣤⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⢿⣇⠀⠀⠀⠀⠀⠀⢿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⢶⣦⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣠⣿⠁⠀⠀⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⣾⠋⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠰⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣼⡟⠀⠀⠀⠀⠈⠉⠁⠀⠀⢸⣷⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠲⢦⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠛⠳⣤⣤⡀⠀⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢀⣤⡞⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀
⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⢦⡀
⢠⠞⠻⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣦
⠈⢷⣤⠀⠈⠉⠙⠒⠂⠤⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠚⠉⠁⢀⣼
⠀⣼⠃⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠀⠀⠀⠀⣠⠖⠋⢙⡧⠀⢰⠒⡆⠀⢠⢤⠀⠀⣠⠖⠒⢲⠀⠀⠀⢀⡴⠶⡄⠀⠀⡴⠊⠉⠉⠉⠳⡀⢀⠀⡀⠀⠀⢸
⣿⠀⠀⠀⢠⡇⠀⡞⠁⠀⠀⢸⠀⣿⠀⢸⠘⡄⡼⠁⡴⠚⠉⠀⠀⠀⢸⠁⠀⢹⠀⠀⡇⠀⡶⢦⡀⠀⣇⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠣⣄⣙⣛⠒⠢⣼⡀⢿⠀⢸⠀⣷⡇⢸⠃⠀⠀⠀⠀⠀⣼⢸⣇⠈⡇⠀⣇⠀⠙⠚⠀⣠⠏⠀⠀⠀⠀⠀⢸
⢻⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⢸⡇⢸⣀⡏⢰⣿⡀⢸⠀⢴⡒⠒⠲⡄⡇⠘⠿⠀⢹⠀⢹⠀⢀⠀⠸⡁⠀⠀⠀⠀⠀⠀⣾
⢸⡄⠀⠀⠀⠀⢀⣀⣠⠼⠀⣸⡇⠀⠉⠀⡸⠈⣇⠈⠓⠖⡁⠠⡖⢻⠇⠀⡜⢧⠈⣇⢸⠀⢺⢧⠀⠱⡄⠀⠀⠀⠀⢰⠇
⠀⢳⡄⠀⠀⢸⣉⣀⣠⡤⠞⠁⠱⣄⣠⠴⠁⠀⠘⠳⠤⠖⠧⠤⠇⢸⠀⣼⠀⠈⣆⢸⡄⡇⢸⠈⢇⠀⣹⠀⠀⠀⣠⠏
⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠚⠁⠉⠉⠀⠈⠉⠀⠀⢀⡴⠋
⠀⠀⠀⢺⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠋
⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿