Wind blowing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠒⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣎⣀⣀⣀⣀
⠀⠀⠀⠀⣀⣠⣤⣄⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠠⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⣾⠋⠉⠀⠉⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡠⠴⠖⠒⠒⠒⠒⠒⠒⠶⠦⢤⣄⡀
⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⠤⠤⠤⠤⠴⠶⠒⠒⠂⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠈⠻⣦⣤⠀⠀⠀⡀⠤⠴⠒⠒⠛⠛⠋⠉⠀⠀⠀⠀⠐⠲⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣤⣀⣀⡀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟
⠀⠀⠀⠙⠷⣤⣤⣤⣤⡄⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠶⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣟⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⡀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠈⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢤⣄⣀⣤⠠⠤⠐⠀⠀⠀⢀⡴⠋⠉⠙⠶⣄⠙⢆⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢪⠁⠁⠀⣹⠆⠈⠆⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠈⠐⠲⠤⠤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣌⠓⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⠤⣄⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⡄⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣉⣀⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠉⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠶⢤⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣤⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣀⡀
⠀⠀⠀⣠⣾⠟⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠻⣦
⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠒⢦⡀⠆⠀⠀⠀⠀⠀⠘⣧⣄⡀
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⣾⣣⣙⢶⣦⢠⣐⣠⢞⠃⠁⠀⠙⢷⡄
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡘⠛⢒⠾⠃⠀⠀⠀⠈⣿
⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠈⢻⣦⣄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠁⢀⣄⠀⢠⠀⠀⠀⠀⠴⡎⠁
⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡾⠋⠀⡀⠺⠛⠶⢼⣄⣀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⣀⡄⠀⠀⠉⠁⢀⣠⠀⠐⠿⠂⠀⢀⣄⠈⢻⣝⡒⢭⣀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠙⠳⠶⣶⡶⠾⠛⠷⢤⣤⣤⠤⠖⠁⠉⠉⠉⠁⠙⢦⡈⠙⠲⣭⣑⠲⢤⣄⣀⡀⠀⠀⠀⢠⠋⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠃⠙⡄⠀⢢⢅⠫⠒⢌⠙⠯⣟⢶⣶⣜⠳⠖⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠀⣈⡇⠁⢹⡀⠀⠈⢕⢤⡁⠉⠢⡀⠀⠀⣀⣀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣑⠈⠀⣠⣾⠃⠀⠀⠀⠱⡿⠆⠈⠦⣁⠀⠈⠻⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⣔⠆⠶⣄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⡀⠤⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠁⠒
⠀⠀⠀⠀⢀⣀⡤⠠⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠶⠒⠲⠤⣀
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⢀⡤⠶⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢀⡆⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠤
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣓⡟⠀⠈⢻⠊⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⢀⡀
⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠲⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⡄⠈⡆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⢀⣶⣦⡂⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠔⠁⠠⠃
⠀⠈⠓⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⣿⡛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠒⠤⠀⠀⠀⢀
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠐⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡂
⠀⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠙⡔⡀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠶⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡈⠔⠀⠀⠁⠀⠀⠀⠀⠐⣈⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒
⠀⠀⠀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠉⠐
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡄⠠⡆⠀⢸
⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠤⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢠⣿⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⠒⠂⠐⠒⠂⠀⣀⣀⣀⣀⣠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣦⣄⡀⣀⣀⡀⠀⠀⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠦⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠳⣾⠋⠀⣀⠀⠈⠟⠋⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⣀⠀⠈⠀⣰⡟⠀⣀⣤⠄⠀⠀⣸⡇⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠉⠛⠀⠀⣿⠀⠀⢰⣟⣠⡾⠋⠁⠀⠠⢶⣿⡀⠀⢀⣀⣀⣀⡀⢀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢰⡿⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠈⠉⠉⠉⠁⠈⠁⠈⠋⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⢸⡇⢀⣾⣯⣤⣴⠶⠶⠶⠿⠀⠀⠀⢸⡇⠀⢀⠀⢀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠀⠀⠀⢸⣧⡿⠋⠉⠀⠀⠀⠀⠀⢀⢀⣀⣴⠟⠀⠀⠈⠁⠈⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⢻⣆⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠛⠋⠁⠀⠀⠰⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣿⠀⠀⣼⠇⠀⣀⣤⣤⣤⣀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⢹⣇⢰⡿⠶⠟⠋⠁⠀⠈⠉⠀⢀⣼⠇⢠⣤⣤⣤⣤⡄⢠⠄⢠⣤⠄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⣦⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠻⣦⣼⣏⣀⣴⣦⣀⠀⢀⣠⣾⠃⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⠉⠁⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠘⠃⠘⠛⠃⠐⠃




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢸⡶⠶⠶⠶⠶⢶⣤⣶⡟⠛⠛⠛⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠈⠙⠳⣄⠀⠀⠀⠀⠻⣧⣠⣴⣶⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⠖⠂⠀⢀⣠⣴⡶⠿⠿⠿⠿⠿⠿⢿⣿⣶⣤⣄⡀⣠⣿⠟⠉⠁⠀⠀⠀⠉⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣼⣿⣇⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠉⠙⠻⢿⡿⠋⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⠟⢉⡉⢻⡆⠀⠀⠀⣠⣶⠶⣶⣄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢼⠰⣿⣧⢼⡇⠀⠀⢠⡟⣁⡀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣚⣛⣛⡛⠻⠇⠀⣤⣼⣻⣿⡥⢠⣟⣠⣤⠤⠴⠦⢤⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣠⣴⡾⠛⠛⠛⠛⠛⣾⡿⠛⠉⠉⠙⠛⠲⠀⠀⠀⠉⠻⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣾⡿⠁⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⢛⣿⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠐⠦⣤⣀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣼⢟⣭⣭⡁⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⠀⠈⠉⠉⠉⠉⠉⠛⢛⣿⣼⣿⣿⣿⡄⠀⢀⣀⣠⣴⣿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠘⢿⣧⡀⢀⣀⣤⠴⠖⢛⣩⠼⣞⡻⢿⢿⣡⠿⠛⠋⠉⠈⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⡤⠴⠖⠛⢿⣿⣅⣠⣶⣚⣩⣄⡴⢋⡝⣻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣤⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠘⠛⠉⠉⠉⠉⠉⠁⠀⠸⣷⡄⢀⣠⠴⠛⠉⠛⠛⠛⡹⠋⢀⡾⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⢿⣦⣄⣀⡀⠀⣠⠞⣁⣀⣼⠟⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠙⠛⢛⡟⠛⠛⠛⢹⠇⠀⠀⠈⢻⣿⣿⣶⣤⣄⣀⣀⣤⣴⡿⠋⠙⠻⠿⣿⣷⣶⣤⣤⣄⣠⣀⣀⣠⣤⣶⡿⠋⠁
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠹⣌⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠦⣶⠶⢶⢲⢲⠀⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⢲⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⡄⢀⡀⠀⠧⡆⠀⠀⠐⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠈⠁⠐⠄⣀⠤⠋⡈⠀⠀⠀⠀⠀⢀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠠⠂⠈⠁⠀⠀⠉⠁⢀⠊⠀⠀⠃⠀⠁⢀⡆⠀⡷⠈⠁⠀⠆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⡷⠀⠀⠀⠀⠀⠀⠀⢪⢀⠀⠀⠀⠀⢀⠤⢀⡀⠔⡒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠘⡁⠀⠀⠀⠀⠀⠀⢠⠏⠀⣉⡛⠥⠚⠁⣠⡀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡶⠋⠀⠈⡀⠀⠀⠈⠉⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠁⠑⢚⠀⠈⠁⠀⡴⠃⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠉⠉⠓⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡽⢯⣀⠀⢈⡹⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠑⢦⡀⠀⠀⠀⠳⣀⠈⠉⠁⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣍⣱⡄⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠙⠒⠒⠒⠋⠉
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣀⣀⠘⠯⠭⠖⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠈⠣⠤⠷⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⡦⣄⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣠⠤⢤⡀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⡶⠶⠤⠤⣍⣲⡉⠲⣄⠀⠀⠀⢀⠏
⠀⠀⠈⠓⠒⠋⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠭⠷⠦⠀⠀⠈⠁⠀⠈⠳⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠶⠲⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⣴⣊⣓⠆⠀⠀⠈⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢰⡄⠀⠷⠘⣆
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡴⢦⡀⠀⠀⠀⣠⠗⠦⣽⡀⠈⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠖⠊⠀⠀⠉⠓⠒⠚⠁⠀⠀⢸⠇⠀⠀⢸⠙⡆⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⠶⠃⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠒⠒⠒⠒⠒⠒⠒⠛⠋

⣿⢿⠿⡿⡿⡟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⡤⣤⣠⠞⠋⠛⢦⠖⠒⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣰⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢷⠀⠀⠀⠀⣴⠛⠙⡇⠀⠀⠀⣠⡞⢳⡄
⠀⠀⢠⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠳⣦⠀⠀⠙⠞⠛⠁⠀⠀⠘⣇⣤⣸⡇⠀⢀⡴⢦⡀
⢠⠖⠺⠃⠀⠀⠀⢀⠶⠄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣤⠤⡄⠀⠀⠀⠉⠀⢰⠏⠁⠈⢹
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡼⠇⠀⢿⠀⠀⠀⠀⠀⠈⠛⠳⠶⠛
⢸⡀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠱⠀⠀⠀⠸⡆⠀⠘⠧⠴⠶⠞
⡞⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢰⣟⡁⢾
⠀⣼⠁⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠘⠶⣤⠀⠀⣴⠲⠤⣄⡴⠚⢢⡴⠶⣄⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠘⠷⢤⡞⠂⠀⣀⣤⡄⢀⡀⠀⠉⣉⣳⣤⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠋⠉⠁⣼⠀⢸⠙⠳⢤⡽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠳⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⡄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢳⣄⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣶⠛⠲⣴⠞⠲⠟⠓⠚⠉⠈⠛⠋⠉⠉⠈⠹⠻⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⣷⠀⣼⢀⡴⠎⠀⠀⠀⠀⢐⢺⡏⠄⠀⢀⠉⢲⠀⠀⠀⠀⠀⠙⠛⢶⣄⠀⢰⠟⠀⠘⣆⢣⣈⣴⢀⡔⠀⠀⠐⣿⣄⠀⠀⠀⢀⣹⣧⣤⣤⣤⣾⠟
⠀⠀⠀⠈⢷⣼⣼⣷⢟⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠻⣦⠓⠀⠐⡖⣲⠀⢟⢃⣿⡵⠂⠀⠀⢸⣿⣤⣶⣿⠿⠟⢛⠉⠉⠉⠁
⠀⠀⠀⣀⠀⠙⠿⠟⠛⠉⠁⠀⠈⢻⣏⡀⠨⣧⠄⠀⢆⢀⡀⠀⠊⠵⠀⠀⠀⠲⠀⠀⣟⠀⠀⠀⠐⠈⡖⣆⢨⠄⠁⠀⠀⢀⣼⣿⡿⠋⠀⣀⣤⣬⣷⣷⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⣿⡠⠐⣷⠄⠘⣾⣫⠄⠀⠉⠐⣀⠀⠀⠀⡆⠀⠀⠈⠡⠀⠀⠘⠿⠿⢃⠀⠀⠀⢴⣿⣿⠏⠀⠀⣀⣿⣿⣿⣿⡿⠓
⠀⠀⠀⠀⢁⠄⠀⢀⠀⠀⠁⠀⠀⠀⠠⠿⣬⣿⠊⢱⡿⠄⢀⠀⠀⠀⠉⠀⠤⠀⠈⣀⠠⠲⠀⠀⠀⠰⠖⠚⠟⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣹⠛⠂⢠⡉⠦⡒⠤⠄⠀⠐⡸⠐⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⣀⢀⡀⡀⠀⠀⢱⡄⠀⠇⠀⠀⠈⠿⠉⠁⠀⠰⢐⠣⠼⠀⠆⠠⠈⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠛⣿⡇⠀⣴
⠀⢀⣀⡀⠀⢀⡀⠁⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⣀⣤⣄⡀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣀⠀⠀⠀⠐⠂⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⡿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡀⠸⣿⣾⣷⠀⢨⣶⢾⣭⢴⡍⠀⢀⣛⣓⣉⣵⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠠⡄⠀⠐⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠⠀⠄
⠀⢹⣿⣿⠇⢠⣿⡿⠃⠀⠀⢰⣿⡿⡦⠀⠀⠘⣿⠿⠷⠾⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⠿⢀⡤⠁⠀⠀⠀⠀⠀⣭⣻⡰⡞⠁⠀⢰⠶⢖⣻⣯⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣿⡇⠀⠀⠀⠀⠀⠎
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⠏⠋⠀⠀⠀⠘⢿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠃⠀⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⣶⣾⣷⣀⠀⢀⡀⠴⢃⡄⢀⣠⡄⠀⠦⠀⠀⠀⠐⣄⠀⠄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠑
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣴⡇⠀⡆⠀⠀⣿⣿⣿⣿⡀⢲⡙⡘⣆⣃⠀⡁⡦⢀⡃⠈⠀⠀⠠⡀⢂⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢶⠘⡁⠈⠁⠀⠘⡛⡴⠁⣠⣶⣤⠀⠈⠆⣡⠀⠠⢀
⠀⢠⣭⣏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢿⣿⣿⡏⠀⣀⠈⠁⠀⠈⠀⠀⠁⠀⢸⣿⣿⣿⡇⠀⠀⠈⠛⠟⠋
⠀⠈⠖⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⠀⠀⢹⣿⣿⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄
⠀⠀⠍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠠⠄⠀⢸⣿⣿⣿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⣼⣦⠀⠀⠀⠐⠀⠛⡛⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣤⢀⡀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⢠⠰⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⣸⣿⡼⠇⠀⠀⢸⣇⢀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⡆⠉⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣀⡏⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠸⣿⣿⡯⠀⠀⢀⠀⢨⣷⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠖⠀⠀⠀⠸⣄⣧⢰⡄⣿⠃⡏⣤⠀⠀⠀⡄⢀⡠⠂⠀⠀⢀⣤⢄⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⢷⣘⣏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡄⣇⣿⢠⡇⣿⠀⠀⠀⢃⠀⢀⠀⠀⢀⠿⠇⡋⢿
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣶⢿⠃⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⣇⠰⠄⠀⠀⠀⢣⢹⣿⣸⣇⠇⠀⠀⠀⡎⡀⣻⠀⠀⠈⡆⠃⠠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣌⡁⠀⢫⡔⡮⠁⠀⠀⠀⢻⣿⣿⠞⠀⠀⠀⠀⠰⣃⣿⠀⠀⠀⠑⡀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠠⠀⢀⡿⡿⢗⢐⡱⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣻⣿⠀⠀⠀⠀⠱⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣇⡶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠻⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠒⠒⣦⣵⣸⡟⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢆⡁⢂⠘⠈⡌⠘⢀⠠⠆⠀⠀⠀⠀⠔⢁⠄⠊⡁⠄⠂⢘⠻⣜⣻⠶⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢤⡀⠙⢦⡸⣿⡤⠋⠀⠴⡳⣖⠠⣄⡎⠠⢂⡤⠊⠀⡠⠊⠁⢠⢹⣮⣳⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⣢⣌⡙⣿⣿⣿⣾⠧⠒⢖⠾⠎⢣⠀⠱⣧⠊⠀⢀⠜⠀⠀⢀⠃⠈⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢦⡤⠀⣡⢚⡟⢇⡉⣗⠢⡎⡄⠀⢡⠀⠘⣤⠐⠁⠀⢀⠀⠁⡰⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠃⡼⡵⠛⠁⡎⢁⠈⠁⣾⠀⠀⠰⠀⠀⢣⠀⠰⠄⠄⠀⠁⡠⠞⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠭⠭⢉⡚⠀⠀⢡⠀⠲⠀⠈⠟⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⣶⣤⣢⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠤⠤⠀⠀⠀⡅⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠂⢤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢫⡁⠒⠠⠤⠄⢚⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣁⡂⠐⢒⡩⡆⠇⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠈⠀⠀⢸⠀⠀⠸⠀⠀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⠰⡀⠠⠀⠀⠀⠇⠀⢸⠀⠀⡄⠀⢠⠁⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣄⣥⣀⣆⠀⡀⢰⡀⢨⠀⢀⣇⣀⣼⣤⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠷⣧⣭⣩⣍⣿⣍⣏⣉⣋⣍⣩⣥⣤⠴⠟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠔⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⢰⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣧⢸⣿⣇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣶⡄⢀⢰⡇⢠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡄⢰⢀⡇⡇⠀⠀⠀⢿⣿⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⡇⣼⠈⣷⣼⠀⣶⣦
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣧⢸⣸⣿⠃⡇⠀⠀⠈⠛⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⣿⡏
⠀⠀⢸⠀⠀⢰⣿⠁⠀⠀⢸⣿⣿⣿⠏⠸⠇⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣾⣾⣦⣼⣿⡇⠀⠰⣸⣿⣿⣿⠀⢤⣼⠀⠀⠀⣸⣿⡿⡇⢸⣿⣇⢀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡓⣿⣿⡖⣿⣿⣿⣿⣿⣿⣾⣿⣷⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⢟⣷⣿⣿⣿⣿⡿⢯⣬⢄⡹⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⣭⠞⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡬⣯⣡⣽⠂⡽⠏⠟⣟⣷⣾⣇⡀⠀⢹⣿⠛⠻⣿⡿⢋⣹⣿⡁⠁⠐⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⢻⠅⣈⣥⠹⡇⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⢾⣻⣿⣿⣿⣷⣾⡶⢶⡿⠿⠿⢿⠿⡿⠿⠿⠿⣿⣿
⢸⣿⠷⠀⠈⠉⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿
⠰⠆⠒⠤⠤⠠⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠿⢷⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⠀⠀⢸⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⣿⠀⠀⠸⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⠋⢿⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡇⣿⠀⣷⠀⣿⠀⣴⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠈⠃⢸⡷⠘⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡂⡼⠀⠛⠀⣻⡄⠀⠀⣠⣾⣮⣴⣆⠀⠀⢰⠀⣿⡀⢰⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⡇⢹⣾⠆⣼⠛⡇⠀⢀⣛⣹⣿⣿⣿⣤⠀⠈⢠⠏⠃⠈⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡇⢹⣇⣼⣡⣤⣀⣶⡄⠀⢹⣿⣿⣿⣿⣠⣿⢠⡀⢸⠀⠆⢸⡇⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⢻⣿⡿⢿⠞⣷⠀⣆⣿⢹⣿⢻⡉⣿⠿⠁⠸⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢻⣼⡏⣧⣸⠁⠈⠀⠆⢾⣿⣿⢸⣿⢹⣷⣿⡀⠀⡾⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢸⣿⠃⠟⢹⠀⠀⠀⢰⠸⣧⡏⣸⣿⣸⣧⠿⠧⢘⡇⢠⢠⡿⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⠀⡀⢙⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣶⣿⡿⣦⣸⡇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⠀⠁⢸⠀⡄⢰⡆⠀⢸⣇⣿⣿⡧⡻⢇⣿⡛⡧⠙⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⠀⠀⢸⡀⠀⠈⠇⠇⢸⣿⣿⡟⠁⡇⢈⢸⠁⡇⠸⢻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠃⠸⡇⢠⠀⡆⠀⢸⢻⣿⡇⢀⠃⠘⢌⠀⠁⠘⢸⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠁⠀⡇⠀⠀⢿⠀⢸⣿⣿⡇⠸⠀⠀⠈⠀⠀⡆⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⠐⡄⢿⠀⠀⣼⠀⠸⢿⣿⡟⠀⠂⠀⡜⠀⠀⢸⣿⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢱⠸⡇⠀⢸⠀⢸⣿⣿⡇⠈⠀⢸⡇⠀⣀⢰⣿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠘⡆⢰⠀⢸⠀⠸⣿⣿⣧⠈⡀⠐⡆⠀⢉⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠁⠘⠀⢮⠀⣸⣿⣿⣿⠀⡇⢰⣇⠀⡄⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣿⡄⢀⠟⣸⠀⢿⣿⣿⣿⡆⡗⣸⡏⣰⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣿⣿⣿⣿⠈⣐⢻⣥⣾⣿⣿⣿⣿⣴⣿⣷⣿⣿⣿⣿⣿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⡾⠟⠟⠯⠬⠭⠍⠿⢭⠭⠍⠉⠉⠙⠛⠛⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡙⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠦
⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣽⣿⡿⠿⠧⣽⣿⣿⣿⣿⣿⢿⣿⣷⣶⣶⣦⣤⣤⣄⣽⣿⣷
⠛⢻⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠶⠶⠀⠀⠀⠀⠁

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀
⠀⠀⠀⠈⠚⠉⠳⠀⠀⠀⠀⢀⢪⠉⠋⠄⠀⠀⠀⢠⣵⠌⠦⢡⠸⠀⠀⠀⠀⠊⢠⠀⠀⠀⢠⡾⣿⢆
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠗⠁⠀⠀⠀⣸⡑⡆⢰⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⢠⠁⡍⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡴⠀⠂⡄⢚⣧⣥⣬⡴⡏⠀⠠⠀⠁⠀⠀⠀⠀⠀⠂⡅⡇⣷
⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⢰⠀⡠⡀⠀⡃⠀⢠⠃⠀⠀⠉⠉⠀⠀⠀⠠⠀⡀⠀⠀⡀⠀⡀⠐⣡⣇⡇
⠀⠀⠀⠀⢱⠀⠇⠀⢠⠃⠀⠀⠑⠤⠒⠒⡌⠀⠀⠀⢀⣠⣶⣀⠀⠀⠀⠐⠄⠀⠀⠏⠀⠀⠀⠹⠿⠁
⠀⠀⠀⡀⠙⠀⡤⠠⠃⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⡜⢡⠊⠉⠑⠙⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⢀⠞⠁⠉⠢⠀⠀⠑⠌⣄⣀⡠⠖⠁⠀⠀⢠⠀⠀⣠
⠀⠀⠀⠀⠈⣦⠃⠀⢀⡠⢅⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠙⠀⠀⠐⡤⠊⠉⠈⠑⡄⠤⠚⠀⠀⠀⢠⠂⠢⠀⠀⠀⠀⠉⢀⠀⢀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠆⠀⠬⠇⠀⠀⠀⠀⢆⠀⠀⣰
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⢄⡀⠀⡰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠃
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⣩⣴⡀⠀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠟⡀⠀⠀⠀⣀⠴⣈⡷⠖⡢⡄⠀⠀⠲⠃⠀⠈⡋⠀⠀⠀⠀⠐⠂⠀⢠⡀⠜⠄⡀
⠀⠀⠀⢠⡌⣷⡄⠃⠀⠀⡜⠁⠂⠀⠁⠀⠈⠸⠀⠀⠀⡠⠄⠀⠁⠀⠀⠀⠀⠀⠀⠠⡀⠺⡇⡼⣂⠂
⠀⠀⠀⠘⠹⠇⡅⠀⠀⠀⡇⠀⠀⠀⠈⠀⢀⢀⠃⢀⡠⣷⢣⠀⠄⠀⠀⠀⠀⠀⠀⠀⠋⠁⠛⠋⠉⠁
⠀⠀⠀⠀⢰⠀⠇⡀⠀⠀⠰⡀⠂⠀⠀⠀⡌⡜⠀⠃⠀⠈⢣⢠⠀⠀⠀⣀⠀⣀⠀⣀⠴⡶⡄⢀⢠⠒
⠀⠀⠀⠰⣎⠀⢸⡷⠀⠀⠀⠑⢄⢆⢐⣰⠜⠀⠀⢃⠀⠀⢸⠸⠀⠀⠸⣇⢀⠾⡖⣇⡄⡇⢇⣸⢨⣱⠄
⠀⠀⠀⠀⠚⣧⣸⠃⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠠⡀⢙⡆⠀⠀⠀⢀⠀⣄⣦⣀⠀⠄⢀⠀⡠⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⡴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⢽⣤⡀⠀⠀⠀⠀⠀⠀⣠⣶⠽⠋⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢝⢦⡀⠀⢀⡤⡺⠛⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⣽⣿⡵⠋⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⢔⡫⠚⠛⢮⡢⡀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⣾⠗⠉⠀⠀⠀⠀⠙⢮⣢⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣯⣄⡉⠁⠀⠀⠀⠀⠀⠀⠙⠪⡲⣄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠨⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠈⠪⡳⣄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣈⠪⡳⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠾⣇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠜⡿⡟⢙⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣤⣶⣵⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠈⠚
⠀⠀⠀⠀⠀⠀⢰⡿⣻⣯⣵⣿⣿⡏⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⣠⣃⣤
⠀⠀⠀⠀⠀⠀⠸⣿⠻⣿⡿⣿⣿⢃⣾⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠏⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡾⠿⠿⠿⠊⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠤⠴⠃⠈⠓⢢⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢁⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡟⡗⠚⡇⠀⠀⠀⠀⣠⡶⠶⠂⠐⣧⢒⡶⠃
⠀⠀⠀⠀⠀⠀⠀⢄⣏⠸⣇⣇⣀⣙⣲⡄⢸⣾⢟⣶⣄⣀⠚⢉⣀⣀⣀⣀⣀
⠀⣁⡀⠤⠒⠚⠃⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠒⠀⠸⠖⠠⢀
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠋⡝⠁⢹⠉⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡘⢠⠀⡎⠀⡈⡻⣧⡀⠀⠀⠀⠀⠀⠀⢠⣴⠟⠻⠛⢷⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⠇⠀⣇⠈⢰⡇⠀⠁⠱⢈⣷⠀⠀⠀⠀⠀⣤⡿⡼⠀⠀⡆⢸⠛⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡇⠃⢸⡇⠀⢠⠰⡏⠸⡷⠁⠀⠀⠀⣾⠁⡇⢰⠀⢁⠀⡇⢹⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⣄⡇⠀⢸⡇⠀⠎⢠⡆⠀⣿⠀⠀⠀⠙⣿⠐⣧⠀⠀⢸⠰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⢸⡀⠉⡇⠀⢸⡇⠀⡆⢐⠇⠀⣿⠂⠀⠀⠀⣿⠀⢸⠀⠈⠸⠀⠘⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⢶⢷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠃⠀⡇⠃⠀⠃⠀⠀⢀⡇⠀⢹⠀⠀⠀⠀⣿⠀⠻⡀⠀⣀⠇⠘⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠃⢸⡆⠹⢳⡔⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⡇⠀⠀⣴⠇⠀⢸⠇⡔⣸⡇⠀⠀⠀⢹⡄⠀⡅⠠⢫⠀⣼⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢾⡁⢰⡄⣿⣄⡤⠀⠀⠠⣼⡇⠈⠀⢰⡇⠰⠀⡇⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⣸⡗⠀⡆⠀⢸⠀⣯⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⠀⡘⠁⢸⠇⡏⣿⠀⠀⠀⠀⢸⡇⡀⠀⠀⡇⠀⠀⡇⢀⠆⠀⠀⠀⣾⠀⠀⠀⠀⢸⣇⠀⡝⠀⢸⢀⡗⢠⡗
⠀⠀⠀⠀⠀⠀⢠⣯⠀⢹⠀⠇⡠⢟⠀⡇⣿⡀⠀⠀⠀⢸⡇⡇⠲⠀⡇⢀⠀⡀⠀⠀⠐⠀⢀⣿⠃⠀⠀⠦⣸⠏⢶⠀⠀⡜⢻⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⡃⠀⠸⠀⡷⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠈⠀⡅⠀⠀⢰⡀⠀⣿⠀⠀⠀⣨⡟⠀⡜⢀⣴⠃⡬⢠⡿
⠀⠀⠀⠀⠀⠀⠰⣧⠀⢸⢢⠙⡆⢀⣄⡆⣿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠓⠀⠃⠀⠀⣸⠇⠐⣿⣀⣤⠾⠋⣠⡎⠀⣠⠃⡰⢁⣾⠁
⠀⠀⠀⠀⠀⠀⠰⣿⠀⢰⠀⢰⡀⠘⡇⠆⣿⠀⠀⠀⠈⢺⡇⡿⢆⠀⡇⠀⢠⡄⠇⠀⣧⠀⢠⡿⠭⠼⠒⢉⡳⠤⠚⣃⠟⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⣆⠘⣱⠀⠇⢰⢿⡄⠀⠀⠀⢸⡇⡇⠀⠀⡇⠂⢸⡇⠀⠀⣿⠀⢸⡟⠒⢻⠋⣉⡹⠶⢺⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢣⠀⢻⠀⢸⠘⡜⢷⡇⢠⣠⣸⡇⡇⠀⢠⣇⠀⢸⡇⡄⠀⣻⡄⢸⣏⣹⣯⣥⣴⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣇⠘⢦⠈⢧⡈⠫⠿⠿⠿⢹⡇⡇⠀⠀⠏⠀⢘⠃⠈⠀⣿⠁⢸⡭⠍⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⡗⠈⠳⢄⣉⠚⠳⣆⡉⠨⣷⡇⠐⣄⠀⠀⠀⠀⠀⠀⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠘⠷⣤⡤⢉⣉⣉⡩⠴⣲⣿⡇⠀⢹⠀⠀⠈⣦⠂⠀⡹⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⣄⣀⣀⣀⣴⠶⠛⠁⢸⣿⠀⢸⠀⡄⠸⠏⠀⠀⢷⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢿⢸⠀⢀⠀⠁⠰⠀⢠⠀⠼⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠀⠸⢦⠀⡀⠙⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠐⠈⠀⣷⠀⢰⠸⡆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠀⢸⠀⠀⠿⠀⠀⢸⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢘⠀⠀⢰⡄⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣀⠀⢸⠁⠀⢸⠀⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠰⠈⠆⠘⠀⠘⢸⠀⣿
⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢸⡀⠀⠿⠀⠀⣈⠀⣿⠆
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⢾⣿⠀⢸⠃⠀⣟⠀⡔⡏⠀⡿⢶⣤⢤⣤⣀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠚⠋⣩⡀⠀⠁⢸⣿⠀⠈⠀⡄⣿⠀⠀⡇⢸⡇⠀⠰⠄⠠⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠀⠒⠂⠻⢿⡷⠂⡆⠀⡿⢀⣀⣷⠟⠀⠠⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠙⢻⡷⠶⠿⠟⠋⠀⡀⠀⠙⠀⠰
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⢀⡀⠀⠈⠥⠤⠀⠀⠀⠤⠄
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠈⢳⣤⣤⣤⣤⣤⣄⣴⠾⠿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠙⠳⣄⠀⠀⠀⠙⢿⣄⣤⣴⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠖⠂⠀⣠⣴⠶⠿⠿⠿⠿⠿⠿⢿⣷⣦⣄⣀⣼⠟⠋⠉⠀⠀⠈⠙⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣧⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⠀⠉⢻⡟⢁⣤⠶⣦⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⣾⣡⣦⠘⡧⠀⠀⢀⡾⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠛⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⡼⠿⣿⣇⠀⠀⣸⣵⣶⡀⣸⠃⣀⣀⣀⣀⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⡶⠶⠶⠶⠶⣤⣿⠿⠛⠳⠶⠤⠀⠉⠙⠻⢏⣰⠿⠋⠉⠉⠀⠈⠉⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡿⠋⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⠀⢀⡀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢋⡽⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣄⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡶⠋⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠶⠦⠤⠤⠤⣤⣤⡿⢱⣶⣶⡄⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣿⣆⠀⠀⠀⢀⣀⡤⠶⣻⡽⣿⣿⡇⣴⡶⠶⠿⠛⠋⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡬⠿⣷⣖⣋⣩⡴⠖⣋⣡⢟⡶⡗⠚⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠒⠒⠒⠚⠛⠋⠉⠉⢿⣆⠀⣀⡬⠟⠛⠛⠟⣻⠟⢁⣞⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠿⣧⣤⣀⣀⢀⣼⣁⣀⡼⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠙⡻⠋⠛⠉⢹⠇⠀⠀⠘⢿⢿⣷⣶⣤⣤⣤⣶⠟⠋⠉⠛⠿⢿⣷⣶⣦⣤⣤⣤⣤⣶⡾⠟⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣾⠀⠀⠀⠀⠈⢣⡈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠹⠄
⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠐⠒⠁⠂⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠈⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠐⠀⠀⠀⠀⢈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⢀⡠⠰⢀⠤⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⣠⠂⠁⠀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢌⠀⢠⠃⢜⡂⠀⠀⠠⠀⣠⠖⠊⠀⠂⠀⡀⠈⠠⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠢⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠉⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⢀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐
⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣄⣀⣤⣤⢠⣤⠀⣠⣄⣠⣀⣤⢤⣤⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣇⠄⠀⠀⠀⠀⠟⠟⠛⠳⠸⠚⠀⠳⠐⠛⠛⠆⠘⠘⠟⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⠶
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⡀⠀⠀⠸⡆⢸⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠨⠀⠀⠀⠛⠿⠘⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⢠⡄⢿
⠀⠀⠀⠀⠇⢀⠰⠀⠀⢀⣸⠋⠀⠀⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠆⠀⢐⠀⣾⠀⢾⡇⠀⡇⢲
⠀⠀⠀⠀⠛⠈⠓⢀⠚⠻⠿⠀⠀⠀⠄⠀⠂⠉⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠘⠓⣾⡿⢹⢲⣼⡇⡆⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠁⠸⣼⢸⣿⢹⣡⡇⡄
⠀⠀⠀⠀⠀⠀⣀⡀⣀⡲⡄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⠠⠴⠀⠄⠠⠐⠚⠂⠀⠀⠀⢀⡀⠀⢀⡹⠎⠋⠈⠋⠾⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠋⠁⠈⠉⠉⠠⠀⠖⢊⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠦⠄⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⢋⣠⣤⣤⣀⠀⠀⠰⠶⠂⠀⠀⠀⠀⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠶⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠠⡀⣤
⠀⠀⣀⠀⠤⠀⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⢀⣤⠀⠤⠆⠀⡀
⠒⠁⠀⠀⠑⠈⠩⠖⣨⡥⠔⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠁
⠀⠐⠊⠁⠈⠔⣊⠁⢀⡴⠖⢉⡤⠄
⠆⡠⠖⣂⡴⠏⣡⡶⠋⣴⠞⢉⣴⠞⢋⣡⣤⠀⢀
⣉⡤⠞⠡⠤⠖⠋⢀⡼⠁⠔⢉⡴⠚⣉⠥⠴⠚⢋⣠⠴⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠟⠀⣁⠖⢚⣩⠶⠋⣠⠶⠒⣩⡤⠶⠒⣠⡤⠞⠛⢁⣴⡶⠗⠋⣉⣤⠔⢂⠄⢀⣀
⣤⡿⢃⡴⢋⣤⠶⠛⣉⡤⠞⣋⠴⣠⡿⢋⣤⠾⠁⣸⠟⠀⣠⡾⠋⣠⡾⠋⣠⡾⠋⢠⣼⠃⣠⡤⢀⣠
⣩⣔⣯⣖⣋⣴⣞⣉⣡⣶⣛⣡⣞⣩⣴⣛⣈⣴⣚⣁⣤⣞⣉⣤⣾⣋⣠⣾⣛⣡⣴⣛⣀⣜⣡⣾⣋⣡⣤⣟⣃⣤⣶⣂⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠆
⠀⠀⠀⠲⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆⡼⢠⠆
⠀⢀⠀⠢⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⠇⠀⠉⠁
⠀⠀⠀⢆⠆⠀⠀⣸⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⡅⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⢠⠀⠰⡄⠀⢀⢀⡎
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠹⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡆⠀⡇⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢘⢣⡄⢠⡀⠀⠘⠆
⠀⠀⠀⢤⣠⡄⠧⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣰⠀⠀⠀⠀⡿⠛⡷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠈⠻⡄⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⢦⠀⠀⠈⠁⠀⠀⢀⣠⠁⠀⢸⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⡇⢠⡆⠀⣰⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸⣆⠀⠀⠀⡈⣤⣀⣰⠇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠱⣌⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠙⠓⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠰⠀⠀⠀⠀⠀⠀⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠃

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⣠⣾⣿⣿⣧⡀⠀⠀⠀⡔⠒⢂⠀⠀⠀⢀⣴⣿⣿⣿⣄⠀⠀⠀⣰⣾⣿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦
⠀⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⠀⠑⠄⠢⠀⠀⠀⠘⠛⠛⠛⠟⠛⠀⠀⠘⠛⠛⢿⠟⠛⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢰⠂⠀⡄⠀⠀⠀⠀⣴⣼⣆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣠⣶⣾⣤⣀⠀⠀⠀⠀⣰⣾⣿⣿⣆
⠀⠀⠀⠸⣧⣄⣀⠄⠀⠀⠀⠙⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣾⣿⣿⣿⣷⠄⠀⠀⠀⠘⠛⡻⡛⢟⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀
⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⠀⠠⠀⠄⠀⠄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠋⠉⠃⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣈⣠⣧⣊⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⣲⢭⡵⡢⡄⠀⠀⠀⠀⢀⣴⣧⡀⠀⠀⠀⠀⠀⠀⣴⣿⣀
⠀⠀⠀⠠⠊⡇⠢⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠛⠙⠁⠈⠚⠘⠀⠀⠀⠀⠀⠈⠃⠀⠺⠂⠀⠀⠀⠀⢀⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡀⠀⠀⣼⠀⠀⠀⣀⡠⠒⠉⠀⠉⢳⡀⡀⢀⡀⠤⢄
⠀⠀⣀⠠⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠠⠠⠄⠀⠀⠀⠉⠀⠀⢀⡨⠀⢠⠊⠀⡡⠤⠤⡀⠀⠈⠁⠈⡇⠀⠀⠀⠗⠢⡀
⠀⠉⠉⠁⠀⠀⠂⠀⠌⡑⠂⠤⢀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠪⣀⠠⠔⠀⠀⢸⠀⠀⠓⠀⠀⠹⠀⠀⠀⠴⠃⢀⣀⠀⠀⠀⠚⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⢀⠈⠒⠠⠄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣣⣀⠠⠄⠐⠁⠀⠀⠀⢀⠀⠈⡸⠀⠀⠐⠀⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣐⠀⠀⠄⢀⡀⠉⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣀⠀⠀⠈⠉⠉⠀⣠⣤⡤⠶⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠒⠤⠤⢌⣁⡀⠒⠒⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣒⡒⠒⠬⣔⠄⡀⠀⠀⢠⠀⠀⠀⠈⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠢⡀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⡶⠶⠦⠤⣄⡀⢀⣸⡄⠀⠈⡆⠀⠉⠉⠁⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠐⢤⡀⢀⠤⠶⠦⣄⡀⠀⠀⢱⠄⠀⠖⠀⡹⠁⠈⠳⠤⠖⠁⠠⣄⠀⠀⠈⡧⠤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠤⠉⠒⠀⠀⠒⢿⡀⠀⡆⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆⠀⢀⡴⠄⠊⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠴⠦⠀⠤⠞⠉⠉







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠋⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡺⠋⠋⠛⢂⠀⠀⠀⠀⠀⢠⢡⢋⠉⠇⢡⠣
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠐⢸⠀⡇⠁⡄⠀⠀⠀⠀⠀⠀⠐⢀⠁⡆⠀⢰⠘⠀⠀⠀⠀⠀⠆⡆⠘⢰⠸⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠈⢠⢸⠀⡇⢀⢠⠀⠀⠀⠀⠀⠀⡇⠸⠀⠁⠀⠈⠀⡆⠀⠀⠀⠘⢠⠀⠀⠘⠀⡀⠇⠆
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠈⢸⠀⡇⠸⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⢸⠀⠀⢀⠀⡇⢠⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠄⡄⢀⠀⠀⢸⠀⡇⠀⠀⠀⠀⢸⠀⡇⠘⠀⡇⢸⢸⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠘⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⡀⡇⢸⠀⠃⠸⠀⠇⠀⠀⠀⠀⢸⠀⠇⡁⢠⠀⢸⢸⠀⠀⠀⠀⠰⠹⠀⢁⢩⠣
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⡇⢸⢠⠀⠀⠀⠀⠀⠀⠀⠂⠘⢠⠀⠃⠸⠀⡄⠘⠀⠀⠀⠀⡇⠀⢨⢸⠈⠀⡇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢰⢸⠀⡇⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⠀⡄⠀⠀⠀⡄⡆⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⢸⠀⠀⠇⠀⠀⠀⠀⠀⡀⢁⠈⡀⠆⠸⠀⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠃⡄⠈⠘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⡇⠈⠀⠀⢠⠀⠀⠀⠀⠀⠆⠸⠀⢁⢸⠀⠇⠠⠀⠀⢸⢰⠀⡇⠀⠀⢸⠀⢠⠀⡄⠀⠀⢠⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠃⠀⠀⠃⢸⠀⠀⠀⠀⠀⠰⡀⢣⠸⡀⠆⠸⡀⠣⡀⠀⠀⠀⠃⠀⡇⠀⡄⠈⠀⡇⠀⠀⠸⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⢠⠀⢰⠀⡄⢸⠀⠀⠀⠀⠀⠀⠱⡀⢆⠱⡈⢆⠑⢄⡈⢣⠀⠀⢠⠀⠁⠀⡇⢠⠀⡆⠀⠀⡄⢀⠀⠸⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠂⢀⠀⡇⢸⠀⢸⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆⠱⣄⠑⠠⠌⣹⠀⠀⢸⠀⠀⠀⡇⢸⠀⡇⠀⠀⠇⢸⠀⡆⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⢌⡑⠢⠄⣸⠀⡆⠀⠀⡇⠀⡇⢈⠀⠀⠀⢠⠀⡆⢠⠀⡆⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠘⠀⢸⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢈⡐⠂⠰⠀⡇⠀⠀⡇⠀⠀⢸⢀⠀⢠⠃⡘⠀⡆⠀⠁⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⢸⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡆⡇⢠⠀⠃⠀⠂⢸⢀⡦⠁⡰⠃⡘⠀⡐⠀⠇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⡸⠊⢀⠎⢀⠜⠀⡰⠁⡜⢠⠃
⠀⠀⠀⠀⠀⠀⡀⢠⠀⢠⠀⡇⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⢸⠀⠀⢀⠖⢁⠔⠁⡠⠋⠀⡔⠁⡸⠀⠎
⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢁⠊⡔⠁⡠⠊⠀⢠⠊⠀⡰⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠾⡘⢀⠎⠀⢀⠔⠁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⡀⣧⢂⡠⠒⢁⠠⠊⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⡝⠻⡄⣉⠠⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⡇⢰⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⢸⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡄⢸⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠃⢸⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠣⠀⠀⠀⠃⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠈⣀⠀⠀⠀⠀⡆⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⠃⠀⠁⠀⠀⠈⠀⠀⠀⢀⠀⠈⠁
⠀⠀⠀⢀⠀⡏⢱⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡜⣙⣎⣸⢇⡇⡀⠀⡀⠆⠀⡔⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠀⢠⠖⢦⠀⠀⣀
⠀⠀⠀⡋⣇⡇⢸⣠⢏⡇⠀⠀⠀⢠⠶⡄⠀⡇⠉⢩⠦⢊⡀⠘⢆⣡⡠⠜⣀⡔⠉⢀⠀⠠⠖⠀⠀⠁⢀⠀⢸⠁⠸⠀⡰⠁⠱⡀⠀⠠⡄⢀⡀
⠀⠀⠀⠳⠤⡄⢰⠓⠊⠉⠉⠉⠓⢣⠀⡧⢬⡇⠦⣿⢰⢳⠈⢲⠊⠀⠀⠀⠀⠙⣏⠥⠒⠐⠒⡀⠀⠉⠁⠀⠸⡄⠆⢧⣇⠀⠀⡇⠀⡦⡇⢨⠀⢶
⠀⠀⠀⠀⠀⠁⢸⡄⠀⠀⠀⠀⠀⠈⣆⠉⠒⠁⠀⠻⠞⣸⢅⣣⠀⢀⣀⠤⠔⠒⠛⠂⠉⠉⠀⠀⣫⡄⡿⠋⠉⠙⠤⢠⡀⠀⠀⠳⢖⣡⢇⣈⡄⡇
⠀⠀⠀⠀⠀⠘⠈⠀⠀⠰⠷⠆⠀⠀⠈⠑⠒⡄⠈⡴⠉⠁⠀⠉⠙⠢⠤⢀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠈⠁⠠⠄⠀⠀⠀⢣⠀⠀⡏⠉⠀⠀⠈⠇⠀⢤⣀
⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠃⣶⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠁⠒⠀⠒⠀⢠⠀⢠⢸⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⠈⠁
⠘⠚⠚⠓⠚⠒⠒⠛⠛⠛⠚⠒⠒⠚⠒⠚⠒⠓⠂⠛⠓⠚⠚⠚⠓⠓⠚⠓⠒⠚⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠛⠚⠒⠓⠛⠒⠒⠓⠛⠒⠒⠒⠒⠚⠛⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⠴⡖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⣉⣁⣤⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠚⠁⠀⢀⡠⠤⠒⢊⣉⢥⣐⣶⣿⣿⣿⣿⣿⣿⢿⡟⣿⡇
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣤⣴⣮⣵⣾⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⡿⠇
⠀⠀⢸⠀⠀⠀⠀⠐⠒⠀⠠⢄⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣟⣻⡿⠿⡟⠋⠉⢸⣿
⠀⠀⢸⠀⢀⡴⣣⢣⣈⠐⠀⢸⠀⠀⡄⠀⠀⢸⣿⣿⡿⣿⠿⠟⠛⡟⠉⣿⣴⣾⡆⠀⠉⠘⣿
⠀⠀⢸⠀⠘⡀⠃⢃⣋⠠⡄⠈⠀⠀⡇⠀⠀⠘⠿⣷⠉⠀⠺⠿⢿⡗⢿⣿⢼⣽⣿⠀⠉⠁⣿⢸
⠀⠀⢸⠀⠀⣷⣀⡀⠁⢀⠃⠀⠀⠀⡇⠀⠀⠀⢸⣿⠒⠚⠈⠁⢸⠿⣾⣃⡞⣴⠇⠉⣀⣘⣿⢸
⠀⠀⢸⠀⠐⠫⡀⠀⢆⣁⠀⢰⠀⠀⠃⠀⠀⠀⢸⣿⣶⣞⣻⣿⣿⣷⣼⠏⠛⢉⡴⣋⣿⣹⣿⢸
⠀⠀⠈⠀⠀⠀⢺⠟⡀⠘⠁⠀⠀⠀⠀⠀⠀⢠⡟⣡⣿⣾⣧⣶⣿⣿⣿⣷⠂⣿⣤⠿⡿⢿⣿⢸
⠀⠀⠀⠀⡄⢀⣨⣉⠁⣠⡄⡤⠀⠀⠀⠀⢠⡿⣼⠟⢚⡩⠅⠀⠤⠤⣀⣉⠻⣿⠁⠂⡁⢸⣿⢸
⠀⠀⠀⢀⡟⣿⠟⠻⠿⠿⠓⠚⡆⠀⢰⠀⣼⠛⠋⠚⠑⠒⢫⠷⠉⠭⠭⢿⣿⡇⠀⠀⠀⢸⣿⢸
⠀⠀⠐⢇⠀⠠⠀⠀⠀⠒⠂⠉⠀⠀⣸⣾⡇⠀⠀⠰⠀⢀⠌⠁⣀⡄⡈⢻⣿⣷⢶⣶⣶⣾⣿⢸
⠀⠀⠀⠀⢀⠠⠀⠒⠒⠈⠉⠉⠁⢲⣿⣿⣧⠀⠈⡞⠄⢀⣾⣿⣿⣿⡄⢸⣇⠀⡀⠰⠀⢸⣿⢸
⠀⠀⠠⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡀⠀⠸⣮⣛⠿⢿⣿⣿⢷⠟⠉⠀⠑⡐⠀⠘⣿⢸
⠀⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⢸⡿⢶⣄⢹⣯⣿⣿⣿⣷⣿⡞⠀⢠⠇⣡⠷⣶⣿⢸
⠀⠰⢄⠈⠻⣿⣶⣚⣁⣀⣠⠎⠁⠀⠀⠀⠸⣷⣀⢙⣿⣿⣿⡟⣛⣿⡏⠀⢀⣤⠊⠁⠉⠀⠒⠚
⠀⣼⡀⠑⣶⣟⣿⣿⣟⣿⠃⠀⠀⢀⣄⠀⠀⡸⠟⠻⣿⣿⣿⣟⣭⣽⡟⢰⠿⠇⣆⣀⡠⠤⠴⠶⠒⢀⢤⡀
⠀⠻⣯⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⡆⢰⠃⠀⣾⡟⠉⢻⣿⣿⣿⠿⣶⣲⣭⠥⢖⠲⠝⠭⢙⡋⡀⢸⠇
⠀⢸⣿⣳⣿⣿⣿⣿⣿⡇⠐⠀⠀⣆⠀⡇⣼⣀⠀⣿⣧⡀⠈⠛⣿⣷⢯⢋⣴⠖⣿⠀⠀⠀⠀⠀⠀⡀⣿
⠀⠈⠛⠻⣻⣿⣿⣿⣿⠀⠏⠀⠀⠘⣆⢳⡜⠠⠄⢹⣿⠆⢴⣾⣿⣿⠐⡶⠀⠐⠉⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠈⠛⠿⣿⡏⠀⣠⡴⠖⠂⠸⣾⡇⠀⣀⣻⣿⣬⣭⣴⣿⡿⠀⠁⠀⠀⠀⠀⠀⠀⠠⠿⠋⢸⡗
⠀⠀⣠⠤⠒⠒⠒⣛⣓⡒⠃⡀⠀⠀⠀⠈⢻⣾⠓⠚⠛⠉⠙⣿⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⡒⢐⠬⣾
⠀⠛⣏⠘⡀⠀⢾⣿⣿⣿⡧⠈⠳⡄⠀⣀⣤⣌⣷⣤⢦⡜⢧⣺⣿⢳⢰⠁⠀⠀⢀⠀⢀⠀⢌⣠⡼⠃⡀⠐
⠀⠀⣽⣆⠘⠦⡀⢍⠹⠭⢤⡐⣀⣾⣲⡋⠛⠨⠙⠛⠻⣾⡧⣿⣿⠨⣼⡢⢠⠖⣨⣷⡴⢿⣿⡿⠁⠄⠈⠺⢄
⠀⠀⠙⣿⣷⣄⣿⢟⢛⣛⣛⡛⣛⣿⣿⡁⢉⡐⢆⢻⡧⣘⢽⡿⣿⣦⣦⣾⣿⣿⠿⣵⡚⢅⠀⠹⡆⠀⢀⣤⠞
⠀⠀⠀⠈⢿⣿⣿⣿⣿⠛⣛⣻⣿⡿⠿⣿⡮⣱⡌⢧⣣⠈⣩⡛⠒⠚⠋⠉⠁⣈⠤⠽⢷⣜⣤⢄⣷⠴⠋⠐
⠀⠀⠀⠀⠀⠙⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠌⠉⠈⢉⣀⡤⠜⠀⠀⠀⠀⡈⠀⠀⠀⠀⠙⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⡻⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠶⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢇⡄⠀⣰⠆⠀⠀⣺⠁⠀⡀⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠹⠿⠦⢤⣴⡞⠀⠙⠉⠁⠀⠀⢸⠃⡆⠘⣷⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢸⣇⣧⠐⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢢⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣶⣧⡟
⠐⠀⠀⠀⠀⠀⠀⣿⣁⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠗
⣸⠇⠠⠄⠀⠁⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡦
⠁⠀⣧⠀⠋⠀⡀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣀⠀⠦⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⡀⠀⠀⠈⠉
⠀⠀⢸⡖⠂⠈⠀⡼⠀⠀⠀⠀⠀⠀⠰⢼⣦⠀⢸⡇⠀⠀⢀⠇⠀⠀⠀⢨⠁⢢⢠⠀⠀⠀⢸⣀⠀⠀⠸⠶⠃
⠀⠀⠀⠀⠰⢪⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⢾⣧⣼⠷⠃⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡤⠚⠋⠀⠀⡆⢠
⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠘⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⢛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⢸⠀⠀⠀⠈⠋⢀⠠⠀⠀⠰⣄⡴⠀⠓⠂⢀⣀⣀⠰⠁
⠸⡤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⣆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢰⠀⡀⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⡄
⡀⠀⣀⡀⠀⠀⠀⢠⠂⠀⠀⠀⣠⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠧⢀⠈⣇⠀⠘⠠⡇⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⢦
⢷⣸⠀⠹⠃⠀⠀⠁⠀⠀⢠⢏⡆⢰⡞⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢀⠠⡁⠀⠀⠀⠀⠀⡀⠀⢸⠇
⢀⠹⠀⢠⡄⠀⠀⠀⠀⠀⣹⣼⡆⣾⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⢡⠀⣇⡿⠀⠀⠀⠀⠀⠀⣘⠟⠀⢀⠠⠀⠀⠙⣿
⠾⠃⠀⡾⠛⠀⠀⠀⠀⠀⠻⣿⣷⣷⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠳⠷⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈⠀⣀⠀⠂⠀⠀⢻
⡅⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠀⠀⢠⡜⠀⠀⠈
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣥⠞
⠐⠀⠚⠛⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⠀⠀⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⠑⢀⠔⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠑⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠈⠇⠀⠀⠿⢸⡇⠀⠀⣄⠀⣷⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠞⠀⡇⠀⠀⡁⢠⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡄⠑⣤⠀⢀⠀⢰⠀⠀⠀⠀⡇⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠛⠀⠈⠀⢠⠀⠀⠀⠀⠁⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠂⠀⣿⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⢤⡀⠀⠀⠀⠀⡄⠀⡇⠀⠠⠀⡇⠈⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⣈⠀⠇⠀⠀⠀⠀⠀⠀⢀⠀⣠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠸⣇⠀⠀⢿⠀⠄⠀⠀⠀⠀⣆⠀⠀⣠⡟⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⣄⡈⠃⠤⣈⡲⢀⡀⠀⠀⠀⠁⠀⠾⢋⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣌⣀⣀⣀⡀
⠀⠀⠀⠐⠃⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣾⠿⠿⠿⠿⠟⠿⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡿⠾⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⣲⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠋⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀⠊⠀⠈⠙⢦⡀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠰⠀⠀⠀⠀⣾⣿⡏⣴⡆⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⡧⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡶
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡿⢀⠀⠀⠀⠀⣿⡟⢡⣿⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⢸⠀⠀⠀⠀⣿⠀⢹⣿⠀⠀⢿⣿⠟⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⢀⠀⣿⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⣿⠀⡄⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠆⠀⠀⣿⣧⣿⣇⠀⠈⣿⡇⠀⠘⠀⠀⠀⣿⡀⠸⣿⠀⠈⣿⠇⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡃
⡄⠀⠀⢻⣿⢿⣿⠀⢁⢻⣧⠀⢸⠀⠀⢰⡟⠃⢸⡟⠀⢰⡟⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⡀⠰⠀⠀⠀⠀⢰⡇
⠰⡆⠁⣸⣿⣆⠙⣧⠘⠀⣿⡀⢸⠄⠀⢸⡇⠀⣿⠃⠀⢾⠁⣴⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠸⣄⠛⢿⣿⣧⡈⢣⠀⠸⢧⠈⠀⠆⢸⡇⢰⡟⠀⠀⠀⣴⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠂⡀⠙⢿⣦⠠⠖⠀⠈⠀⠠⠀⠀⠁⡞⠃⢀⣠⡾⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠈⢦⣀⠙⢷⣄⡀⠈⢤⠀⠀⠰⠂⠀⠀⠛⠉⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠁⠐⠒⠈⠉⠱⠦⣬⠻⠷⡄⠡⠀⠰⠀⢀⣤⠶⠚⠁⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣶⣿⣶⣤⣤⣤⣼⣿⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⣿⣀⢀⣀⣨⣿⣿⣷⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠻⠿⠿⠿⠿⠿⠿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠓⠘⠛⠈⠉⠃⠐⠀⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢾⣄⣱⠖⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⣄⡠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡖⢠⠚⠑⠶⠚⣯⣹⡖⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⢢⠜⠉⠀⠈⠀⠀⠠⠀⠀⠈⠁⠐⠠
⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⡐⠈⠀⠁⠠⠎⣿⠙⣏⡉⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠰⠃⠀⠈⠀⠰⠁⠈⠁⠀⣉⠰⡏⠘⠃⠈⠱⠞⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠆
⠀⠀⠀⠰⠂⢰⡁⠀⠸⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⢠⡆⠀⡉⠛⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⢧⡤⠐⠇⠐⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⢠⡄⠀⠀⠀⠀⢠⠀⠆⠀⢢⠀⠁⠀⠈⡀⠐⠂⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⢁⠀⠰⠏⠀⠈⢃⠀⠀⠀⢀⠀⠀⠀⠱⠀⠀⠀⠀⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠦
⠀⠀⠀⠘⠃⠀⠰⡶⠀⠈⠡⣄⠀⠀⠃⠀⠀⠰⠀⠶⠘⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡄⠈⠂⠀⠀⠘⢄⡀⠀⡄⠀⠰⢀⡀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠰⡷⠀⠀⠀⠀⠀⠀⡇⠀⡀⠈⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠻⠀⠈⠻⠀⠀⢀⣁⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣾⣿⣷⣶⣷⣶⣿⣿⠿⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⢸⣿⣀⣴⡿⠀⠁⡀⠀⠀⠋⢁⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠈⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿⠟⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣿⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢻⣿⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⣿⡇⠀⠀⠀⣾⣇⠀⠀⣠⣴⠟⢫⡀⠀⠰⢋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡏⠀⣸⣿⣹⣷⣾⡇⠀⠀⢈⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⠏⣹⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹⡇⠀⢻⡿⣡⡈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣻⡿⢿⣄⡼⣧⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⡇⠀⣼⢧⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⡀⠘⠧⠶⢋⡌⠉⠙⠛⠒⠒⢲⣦⣤⣴⠄⠀⢘⡇⢀⡟⣼⢻⡿⣿
⠀⠀⣀⢠⣤⠴⠚⠉⢀⡴⠛⢷⡄⠀⠀⣸⠏⠳⠦⣄⡀⠀⢼⠟⠛⠇⠀⠀⢸⡇⢸⣧⠇⢸⣿⣿
⠀⠈⠙⠻⣇⠀⣠⡴⠋⠀⠀⣠⣿⣷⣛⡛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢻⣯⣤⣼⣯⣿⣀⡀
⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢸⡁⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣷⡀⠀⠀⠘⠟⠻⠛⠛⠛⠛⠛⠛⠗⠲⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡏⠈⣿⣿⣟⣿⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣿⣶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣤⣤⣤⣴⣿⣿⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠛⠛⠓⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠴⠶⠒⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠙⢳⢏⣠⡄⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠞⣉⠁⠀⢀⣤⣉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠀⠀⠀⢀⡎⠈⡇⢠⡏⠀⠘⡆⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣠⠖⠒⠚⢿⣆⡇⢸⣦⣄⡠⠟⠋⠉⠁⠀⠈⠉⠂⠀⠀⠀⠐⠋⠉⠀⠀⠀⠈⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠉⠀⣇⠀⠀⠀⠀⠩⠤⢬⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠘⢦⣀⡀⠠⢤⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠒⠀⠲⠤⠤⠀⠄⠀⡀⣾⣀⡀⠀⠀⣰⠛⠓⠚⠛⠃⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠨⣉⣡⡽⢀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠤⠤⢶⡀⠈⠁⠈⠳⠶⠛⠦⣤⣀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠂⠁⠁⠀⠀⠀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⠲⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⢤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣸⠷⣄⠀⠀⠀⠀⠀⣀⡤⠟⣆⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠶⠛⠁⠀⠈⠙⠲⠶⠒⠛⠉⠀⠀⠈⠓⠶⠤⠤⠶⠋⠁

⠀⠀⠀⠄⠄⡀⠀⠀⡠⠀⠀⢀
⠀⠀⠀⠀⠄⠀⢆⠊⠼⠛⢩⠇
⠀⣤⠀⠀⠠⠀⢨⠴⠀⠀⣀⡄⠒
⠀⠀⠐⠃⠀⠂⣴⠀⠀⣄⣀⠀⢤⡀⠀⢀⢠⡄
⠀⠀⠀⠀⠄⠋⢿⡡⠀⠽⠉⠉⠂⠐⣔⠡⠛⣀⠆
⠈⠉⠀⠀⠀⠀⠀⠘⠂⢠⢤⡤⠂⣠⡏⠐⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠛⠱⠀⠘⠁⠁⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⢐⠀⠀⠀⠁⠀⠀⠀⠀⢠⡼⢏⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠦⠀⠀⠀⠀⠀⣠⣴⣗
⠀⠘⠧⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠟⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠏⠀⠉⠐⠃⡒⠰⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⢛⡁⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠄⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠖⠒⠀⠤⠂⠀⠀⠀⠐⠂
⠀⠁⠀⠀⠀⠒⠃⠀⠀⠀⠨⠥⠄⠀⠀⠀⠠⠀⠁⠒
⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢀⠀⠀⣀⠀⡉⢀⠁⠀⠀⠀⢀⠀⠁⠀⠐⣾⣣⣠⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⡀⠈⠉⢀⡀⢠⣠⣀⢀⣀⣹⣄
⠋⠡⠀⣀⠀⢀⣠⣷⣿⡾⠵⠞⠛⠓⠒⠛⠉⠉⠉⠀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠶⠶⠤⠶⠾⠻⠿⠛⠛⠛⠟
⠛⠛⠛⠛⠋⠉⠉



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⢀⡀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠍⠐⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠺⠆⡿⠥⠞⠚⠃⠀⠀⣥⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠰⠦⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠤⠀⠀⠛⡷⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠺⣦⣶⣷⡀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠠⠀⣠⠀⠀⠀⠀⠀⠈⠉⠃⠉⠈⠛⠄⠠⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠀⠀⠀⠀⠈⢣⣁⡀⠀⠀⠀⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠁⠀⢨⠄⠀⠂⠀⠀⠀⠀⢠⡋⠀⠀⣀⣄⠀⠀⠀⣠⢟⡀⣉⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⢃⡀⠀⠀⠀⠀⠀⠀⢠⠈⢤⡄⡂⢨⣿⣿⠀⡃⢀⠚⠃⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣏⡉⢠⣀⣤⡀⠀⠀⠈⣷⣾⣦⣷⣾⡿⢿⠛⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⠌⠐⠀⠘⢦⡦⣄⠀⡜⠁⠀⠀⢿⣿⡇⠀⡀⠈⢀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⣀⠏⠍⢀⡀⠀⠀⠈⢹⣇⢼⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠣⡴⠗⠀⠀⣾⠃⠀⠀⠀⠀⢻⡄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠀⠈⢠⢀⡴⢰⡟⠀⠀⠀⠀⠀⠨⣧⠀⠀⢨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣶⡟⠋⢻⣿⣇⡼⠁⠀⠀⠀⠀⠀⠀⣹⢀⡖⠼⠞⣩⡘⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⠱⠀⠈⢻⠟⠁⠀⡄⠀⠀⠀⠀⠀⣿⣸⣿⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⣤⠖⠈⠀⠘⠆⠀⠀⠀⠀⠀⠀⣸⣿⠟⢿⣽⡛⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣥⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠴⠄⠀⣽⣧⣤⣀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⣿⠛⠶⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢳⡀⠄⠀⠀⠀⠀⢠⡴⢿⠀⠘⠂⠀⠈⠉⠃⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣈⣿⣷⣶⣷⠾⠟⠋⠀⠘⣠⠘⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡭⣸⣮⢛⣿⠛⠿⣧⠀⠀⠀⠀⢰⣿⣰⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠐⠤⣄⠈⠾⣧⠃⣴⣾⣿⠁⢲⡟⠀⠀⠀⠀⠸⠿⣿⣧⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠁⠈⡀⠁⠐⣻⣽⠿⠿⠏⠰⠂⣿⡁⢰⣀⠃⠀⠐⢸⣧⡟⠀⢢⡰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⢒⡡⢦⠤⢀⡒⣷⣾⣏⡁⣸⣏⣤⠗⠺⠈⢁⠠⠀⠘⠞⠯⠉⠐⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠠⠛⠚⠙⠛⠋⠙⠛⠉⠁⠀⠒⠀⠒⠀⠂⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣤⠤⢤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠿⣾⣶⣦⡀⠀⠀⠀⠀⠀⣠⣼⡟⡭⠒⢿⣶⣻⢄⣀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⡀⠀⠀⢨⣿⣿⣷⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⣿⣛⡿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠁⠀⠀⠀⢘⣿⠿⣷⣄⠀⠀⠀⠀⣿⡟⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣡⡄⠀⠀⠀⠀⠀⠈⠻⣿⣷⣮⣿⣷⣄⠀⠀⠘⣷⠸⡏⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠙⣿⣿⣿⣇⠀⠀⠸⣇⠙⡌⢿⣿
⠀⠀⠀⠀⠀⠀⣼⠃⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⢿⣿⣿⣿⡄⠀⠀⣿⠀⢹⡜⣿
⠀⠀⠀⠀⠀⣰⣿⠃⢸⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣤⠘⣿⣿⡿⣿⣦⣴⡏⠀⠈⣷⣿⡄
⠀⠀⣀⣠⡶⠋⢿⡀⢸⣆⢻⣷⣄⡀⠀⠀⠀⠀⠀⢸⡿⠠⠹⣧⠘⣿⡇⠠⣍⣉⣠⠀⢠⣿⣿⠁
⠀⣾⣿⠁⠀⠀⢸⡇⢸⢿⣦⡙⢿⣿⣶⣤⣤⣤⣴⣿⠃⠀⠀⠙⢠⣿⢻⣴⡹⠿⠏⢀⣼⣿⡟
⠀⠹⣿⣿⡄⠀⢸⡇⢸⣰⠟⣿⣷⣿⣿⣿⣿⣿⣋⣼⣆⡀⠀⠴⢠⣿⢨⣿⣿⣶⣶⣿⠿⠋
⠀⠀⠘⠿⠁⠀⡿⡇⣼⡏⠀⢿⣿⣿⡿⠉⠉⠉⠉⠛⢿⠁⠀⠀⣿⣷⢿⣷⣶⡶⢿⡁
⠀⠀⠀⠀⠀⠀⣧⢀⡿⠀⠀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠸⡜⢰⡅⡿⠃⠈⠛⢯⣙⠀⠳⡀
⠀⠀⠀⠀⠀⢠⣟⣼⠁⠀⢠⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⠀⠀⠀⠀⠉⠙⠿⣉⡢⡀
⠀⠀⠀⠀⠀⣿⠀⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡇
⠀⠀⠀⠀⠀⢸⣼⠁⠀⠀⠹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⢀⡿⡿⠀⠀⠀⠀⢱⡽⡄⠀⠀⠀⠀⠀⠀⠀⣇⢀⡇⠀⠀⠀⠀⠀⠀⣰⠋⡟
⠀⠀⠀⠀⣾⡄⡿⠀⠀⠀⠀⠀⢇⠘⡆⠀⠀⠀⠀⠀⠀⢿⣸⠁⠀⠀⠀⠀⠀⣠⡏⢸⠁
⠀⠀⠀⠀⡼⠀⡇⠀⠀⠀⠀⠀⠈⡧⠈⣲⣄⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢷⡤⣾
⠀⠀⠀⠸⡧⣴⡼⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠀⣏⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⣿⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠴⠒⠀⠀⠀⠀⢤⠁⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢠⡄⠸⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢂
⠀⠀⢀⡀⣘⣧⣼⢿⡧⠀⠀⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣷
⠀⠀⢸⣗⣿⢷⠊⠁⢳⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡓⠩⣥⠎⢻⡿
⠀⠀⣘⢻⡟⠀⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣄⠀⡜⣠⠛⡅
⠀⠀⠷⠚⠇⠀⠘⠙⢂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢙⡗⠀⠙⣇⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡈⠁⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠈⠁⢦⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣖⡶⣤⠤⡆⣲⣋⣀⡤⠀⡀⠁⠀⠴⢀⠐⢀⠀⠀⠀⠀⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠉⠓⠚⠋⢁⠀⣤⣤⣦⡛⠔⠀⢀⠀⠀⠀⠄⠂⠠⠀⠒
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠈⢹⡟⣿⣿⠇⠀⣀⠂⠄⠀⠀⡀
⠀⠀⠀⠄⠂⠀⠀⠀⠀⠄⠀⠀⠠⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡹⠇⣯⡍⠀⠀⠊⠈⠀⠁⣸⡅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠈⢆⠀⠀⠀⣵⢀⣻⠁⠀⠀⠀⠀⠀⢠⣿⡷⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⢀⠀⣶⡛⠀⣠⡄⠀⡀⢹⡀⣇⠀⠀⠀⠀⢀⠀⣸⣯⡇⠑
⠀⠀⠀⠀⢀⣤⡀⢀⠀⠈⠀⠀⠀⠀⢸⡤⠰⠤⠁⠉⠀⠀⠀⠊⠀⠸⣇⢹⡞⠃⠘⠖⠀⠾⡋⠉⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⢆⠁⠀⠀⠸⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣿⡈⣷⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⣀⣤⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠁⠀⡠⠄⠀⡄⠐⡡⡀⡈⠁⢉⢀⣄⡰⠿⢿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣼⢀⡐⠒⠀⠐⠠⠘⢳⠞⠓⠦⣊⣉⣉⠉⠀⠀⠀⠀⠀⠀⣀⠈⠉⠁⠒⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠆⠉⠛⠿⢤⠴⣤⡴⠶⠞⠋⠀⠀⠽⠿⠟⣃⡤⠶⠦⢘⠀⡀
⠀⠀⠀⠀⠀⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⡤⠁⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠲⠾⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠠⠄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢥⣀⣀⣀⡀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⡠⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠉⠓⠒⠶⠒⠋⠁⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⢃⣤⣀⣀⡠⠤⠔⠊⠁
⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⣿⠟⣍⡿⠶⢤⣤⣤⣤⠤⢴⡀⢰⡟⠁⠀⣔⡠⠾⣯⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⢰⡏⠀⢀⣠⢾⣿⡏⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡼⠛⠦⡀⠈⢧⡀⠀⠈⠹⣿⣆⣀⣠⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⠞⢁⠔⠉⠀⢸⣿⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡼⠁⠀⠀⠈⢢⡀⠱⡄⠀⠀⠘⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠁⡰⠃⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠁⠀⠀⠀⠀⠀⠙⠀⠙⡀⠀⠀⠀⠀⣴⠟⠻⣏⠁⠉⠀⠙⣿⠻⣧⡀
⠀⠀⡀⠰⠁⠀⠀⠀⠀⠸⣆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⢸⠃⠀⠀⢻⠀⠀⠀⢀⠟⠀⠈⣇
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⡀⠀⠰⠃⠀⠀⠀⠸⠃⠀⠤⠋⠀⠀⠀⠸
⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣹⡄
⢰⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⡀⠀⠀⠀⠀⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠂

⠀⠀⠀⠀⠀⠤⠤⠴⠴⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⡽⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠑⠒⠒⣺⠗
⠀⠀⠀⠀⠤⠴⠶⠶⠲⠴⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⠤⢤⢤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣼⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣴⣚⣉⣡⣄⠀⢸⠀⢀⣈⣉⣉⣉⣲⣄⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠴⠧⠤⢼⠤⠤⠤⠤⠤⠒⠒⠃⠀⠐⠉
⠀⠀⠀⠀⠀⠘⠉⠉⠙⠉⠉⠘⠀⠋⠉⠈⠛⠁⠀⠀⢸⠀⠀⠒⠒⠃⠒⠒⠂⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⣾⠏⠁⠈⢹⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠉⢻⣇⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠙⣿⣆⠀⢻⣄⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢀⣼⠏⠀⣼⡿⠋⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠙⠋⠀⠀⠉⠛⠛⠛⠋⠉⠋⠉⠙⠋⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠛⠃⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠖⠲⠶⠶⠶⠾⠷⠾⠛⠁
⠀⠀⠀⠀⠀⢀⣤⡶⢶⡶⠶⠶⠶⠦⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⢀⣿⠁⠀⠀⢠⣤⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣠⣄⣀⣠⣀⣠⣤⣤⣤⣀⠀⠀⣠⡄⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠈⢿⣦⣀⣠⣾⡟⠀⣰⡟⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠙⣧⠀⠹⣿⣄⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⢹⣧⣀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⢀⣰⡿⠀⠀⠈⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢳⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠞⠋⠀⠠⠞⠃⢴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠉⠙⠋⠁⠶⢄⡀
⠀⠀⠀⠀⠀⢀⡾⠭⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆
⠀⠀⠀⠀⠀⠸⢤⣒⣠⣤⢄⣀⠀⠀⣀⡠⠂⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠙⢿⣏⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⣀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢰⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⢨⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣾⡀⣀⣠⣤⠴⠾⠧⡀⠀⢦⣄⣤⣤⣤⣿⠟⣸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣼⠉⢏⠉⠉⣿⠀⠀⠀⠙⢄⠀⠙⠻⠟⢻⡿⣏⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣼⠃⠀⠈⡇⠀⢻⡀⠀⠀⠀⠈⢧⠀⠀⠀⢸⡇⠈⠳⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠈⣧⠀⠀⠈⡇⠀⠀⢧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣼⠁⠀⠀⠀⠳⡄⠀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠈⢧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠏⠀⠀⠀⠀⠀⢳⠀⢷⠀⠀⠀⠀⠀⠀⡇⠀⢰⡇⠀⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠸⡆⠘⡆⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣷⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡆⠀⠀⠀⠀⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⢸⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⠀⢠⡇⠀⢸⠀⠀⠀⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⢸⡀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡀⠸⡇⠀⠀⠀⠀⠀⣸⠄⠀⣸⡆⠀⠀⢀⡟⠀⠈⡇⠀⠀⠀⠀⠀⣸⠃⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢁⣴⡿⠀⠀⠀⠀⣰⣃⣀⡼⠋⠀⠀⠀⢸⠁⠀⣠⡷⠀⠀⠀⠀⢰⣇⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠎⠀⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠀⠀⠀⠀⠀⠀⠀⡆⠉⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡿⡖⣄⠀⠀⠀⠀⠀⣇⢀⣀⠀⠀⡄⡾⠀⠀⠀⠀⠀⠀⢀⣀⣠⠒⡘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠟⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⣿⣆⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⣄⢠⢄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⡄⡀⠆⠘⠀⣳⠀⠀⠀⠃⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠈⠁⠀⣄⣃⣌⠏⣄⡈⠀⠱⠄
⠀⠀⠀⣰⡀⢸⡽⠁⠈⠦⣽⡉⣿⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠐⠶⠇⠐⡆⠸⣄⣸⠖⠃⣦⠇
⠀⠀⠀⠙⣍⡩⢀⡀⢤⠀⣼⠀⡆⠀⢀⡀⠀⠀⠀⢀⢤⡀⠀⠀⡤⣤⡄⠀⠀⠀⠀⣟⣉⣀⣇⠖⠈⠩⣤⣴⠁
⠀⠀⠀⠀⠀⣇⠀⠈⡿⢺⣼⣿⠗⠀⠈⠁⠀⠀⠁⠋⠉⢳⠄⠁⣄⠀⡇⡰⠙⠂⠀⠈
⠀⠀⠀⠀⠐⠚⠛⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠼⠤⠤⠞⠚⠁⠓⠀⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⣿⣿⣶⢿⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣰⣟⢩⣭⢿⣷⠋⣶⣾⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠞⣁⣴⣿⡿⠛⡯⢚⣿⣿⣿⣟⣻⣻⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣰⣿⣿⣿⣿⣿⣶⣿⡿⣬⡟⠛⠛⠟⠛⠦⠐
⠀⠀⠀⡀⠀⠻⢱⠜⣿⣿⣿⣿⣿⡿⢿⠋⣽⠛⠓⠃
⠀⠀⠀⠸⠷⢸⣿⣼⣿⣿⣿⣿⡿⢶⠖⢛⡇
⠀⠀⠀⠀⠀⠹⠿⣿⡿⢿⡛⢿⡷⣬⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠈⠁⠀⠀⠈⢻⣷⡠⢀⣀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠤⠄⠀⠀⠚⠛⠚⠻⠿⠶⠿⠿⠿⠷⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠙⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣝⣴⠶⠀⠐⠻⢷⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠺⠀⠀⠀⢈⡔⢢⠀⡴⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡤⠤⠼⣦⢸⠀⣧⡀⣨⠷⠒⠒⠀⠐⠂⠄⠀⠀⠠⠒⠋⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠉⢹⠀⠀⠀⠈⠧⠤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⡳⢤⣀⡐⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠐⠒⠀⠐⠀⠀⠸⠤⠄⠀⠠⢏⠉⠉⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢶⣚⣠⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠉⠀⠀⠀⠂⠈⠁⢈⢧⡀⠀⠀⠉⠀⠈⠙⠒⠦⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡶⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠓⡤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⠞⠳⢄⣀⠀⣀⣠⠴⠋⠳⣄⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⡇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣝⣿⡇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡈⠉⠙⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⠀⠀⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠘⡇⢘⢧⠀⠀⠀⠀⠀⠀⠀⡿⠟⠛⢛⣿⡄⠀⣿⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⡇⢀⣿⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢻⢸⣿⣷⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣉⣀⠀⠞⠃⠀⠳⠀⣠⣠⢀⠆⡶⡒⠛⠛⠛⢰⠸⠿⢿⣧⠀⢿⣄
⠀⠀⠀⢁⣀⣈⣭⣁⣛⣾⣿⣿⣭⠭⠭⠟⠉⠁⠼⡾⣬⡿⣽⣟⢆⣷⣶⣿⡷⠿⡟⣻⣿⣿⣿⡇⠴⣶⠶⢶⣾⣷⡷⠆
⠀⠀⠀⠀⠀⣐⠺⠶⣶⠦⣶⠶⠤⠢⢶⣶⠶⡶⣾⢿⠗⣿⣶⣶⣬⣽⣷⣶⣶⣶⣿⣿⣶⣿⣿⣿⣿⠿⠿⢶⡿⡿⠟⠓
⠀⠀⠀⠀⠀⠀⢠⠤⠦⠀⠀⠒⡖⡗⣶⠃⠀⠒⠻⠲⠄⠉⠭⠛⠛⠛⠘⠁⠉⠋⠉⠉⠉⠓⠊⠁⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⣤⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠁⠈⣁⡴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⠲⣄⠀⠀⠀⠀⠀⠀⡼⠇⠀⡰⠉
⠀⠀⠀⠀⠀⢀⣴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⢳⠈⠳⠦⠤⣤⠴⠊⠁⠀⡠⠃
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣤⡤⠤⠖⠋
⠀⠀⠀⠀⢀⣿⣿⣿⣦⠀⠀⠀⣿⣧⣀⣀⣀⡀⣀⣠⣀⣰⠀⠀⠀⠞
⠀⠀⠀⢀⣾⠟⢙⡝⠁⢣⡀⢀⠇⠉⠙⠛⠛⠛⠉⠁⠀⣿⣷⠖⢄⡈⠢⡀
⠀⠀⠀⡼⢃⡔⠁⠀⠀⠀⣧⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠛⠀⠀⠙⠢⡈⠢
⠀⠀⢺⣰⠋⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠃⠜
⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠈⠲⡰⡀⠀⠀⠀⠀⠀⠀⢸⡘⠀⠀⠀⢀⡾⠂
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⢳⠃
⠀⠀⢿⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣦⣀⠀⠀⠀⢸⣑⢄⡀⠀⠙⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠘⢿⣿⣤⣀⡀⠀⠀⣿⡇⠀⠙⣿⣯⣄⠀⠀⢸⡀⢠⡄⢠⣶⡄⣿⡇⢀⣤⣿⣿⢠⣿⣿⡆⣴⡆⢰⣷
⠀⠀⢾⣿⣿⣿⠋⢰⣧⣿⡇⠸⣦⣹⣿⣇⣰⡦⠘⣇⢸⠅⠀⢿⣷⣿⠀⢸⣿⣿⡏⠀⠀⠈⢷⣿⡇⢸⣿⣶⣦
⠀⠀⠈⠛⢛⠃⠀⢸⣿⣿⡇⠀⢸⣿⣿⣿⡏⠀⠀⠿⠼⠀⠀⠸⣿⠟⠀⠸⣿⡿⠁⣠⣄⡀⣸⣿⡇⠸⣿⣿⡇
⠀⠀⠀⠀⣾⡇⠀⠘⠛⠉⠁⠀⠸⣿⣿⣿⡇⠀⠀⣜⡞⣇⡞⣠⠀⢀⣀⣀⣀⠀⢺⣿⣿⠁⣿⣿⡇⠀⠉⡉
⠀⠀⠀⠀⢻⡇⠀⢰⣧⢰⣿⡄⣠⠈⠙⡉⡀⢀⡄⠀⣿⣿⣿⡄⠀⣾⣿⣿⣿⡇⢸⣿⣿⡄⠈⢋⣀⠀⢸⡇
⠀⠀⣸⡄⣼⡇⠀⣀⠙⢿⣿⣿⡿⠀⢱⣿⣿⣾⣠⠀⢻⣿⣿⠁⠀⠙⠿⠿⠿⠁⠈⣿⣿⣿⡀⢸⣿⡄⢸⡇
⠀⠀⢿⡇⣿⣇⠀⣿⡇⠸⣿⠀⠀⠀⠲⣿⣿⣿⠃⢀⠀⠙⠁⡴⣿⣳⠄⢠⣤⣤⣀⠸⣿⣿⠇⠘⣿⡇⣿⡇
⠀⣀⢸⡇⣿⣿⠀⣿⡇⠀⢀⣤⣤⡄⠀⠈⢉⠁⠀⣿⣷⣶⠆⠈⠁⠋⠀⢿⣿⣿⡗⠀⠉⢁⠀⢳⣿⣧⣿⠃
⠀⢻⡏⢿⣿⣿⠀⣿⠇⠀⠘⣿⣿⡛⣀⡀⢿⠇⢀⣾⣷⠁⢰⣿⣿⡆⠀⠘⣿⣿⠇⠀⠀⣾⡇⣎⢻⣿⡿
⠀⠘⣿⣼⣿⣿⡾⠟⢠⣾⡆⠁⠀⠀⠿⠷⢾⣦⢸⣿⡟⠀⠀⠛⠉⠡⡄⠀⠘⠃⠀⣿⢠⣿⣿⣿⠀⠀⣤⣤⡄
⠀⠀⠀⢸⣿⣿⠀⠀⣼⣿⣿⡆⠀⣴⣷⡄⠀⣿⣿⣿⡄⢠⣴⣧⠞⡀⣴⣾⣷⣦⡀⢸⣿⣿⢿⣿⠀⠀⣿⣿⡁
⠀⠀⠀⠘⣿⣿⠀⠀⠸⣿⣿⠇⠸⣿⣿⡿⠀⢿⣿⣿⠃⠰⣿⣿⠏⠐⣿⣿⣿⣿⡅⠘⣿⣿⣼⠏⠀⢠⣿⣿⡇
⣀⣀⣀⣀⣉⣁⣀⣀⣀⣈⣁⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣉⣁⣀⣀⣈⣉⣁⣀⣀⣀⣉⣉⣀
⣿⣟⣟⣛⣝⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⡄⠀⠀⠀⠀⠀⢀⡜⠁
⠹⣤⡀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠒⠒
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠦⠤⠤⠤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⣿⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢠⡞⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠳⣄⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠈⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠈⠉⠓⠲⠦⠤⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣄⠀⠀⠀⠀⠀⣷⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠒⠖⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡄⠀⠀⠀⠲⡦⠀⢠
⠀⠀⢀⠀⠀⠀⢀⡆⣰⠃⡀⠀⠀⠀⠀⠀⢠⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⢼⣣⢀⡓⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠈⠳⠥⠅⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢠⣉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠁⠀⠀⠀⢙⣋⠠⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠂⠀⠀⢀⠠⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⢢⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠌⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⡴⠀⠀⢰⣿⠃⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⢀⠠⠋⠀⡈⠈⠀⠀⢁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⡀⠀⡇⠀⠀⢀⣸⣀⠀⠀⣱⢶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠎⠀⠀⠀⠀⡀⢠⠸⡇⢀⡇⠀⠀⠀⠉⠉⠀⠀⢹⢸⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇⢐⣠⡗⠚⠁⠰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠆⡄⠀⢄⠀⠀⠜⢀⠄⠈⢺⢸⠁⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠽⠿⠟⠀⠀⠀⠁⠁⢀⠁⠀⠀⠸⢼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⣙⡁⠀⠸⠶

⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠠⣄⣀⡼⡠⢄⠀⠀⠀⠀⠀⢀⠜⠀⣀⡈⢀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡠⠭⡙⢢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⡀⠱⡒⢄⣀⡠⠃⠀⠀⠀⠀⠀⠀⢠⠊⠉⠓⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⢀⡸⠈⠀⠀⠀⠀⠀⠀⠠⠉⠐⠛⠉⠉⢱
⠀⠀⠀⠀⠀⠀⠳⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⠜⠀⠀⠀⠑⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠐⠢⡌⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠤⣄⠀⠀⠀⠀⠀⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢
⠀⠀⠀⠀⠀⠐⡂⠤⠞⠀⠤⠊⠀⣹⠀⠀⠀⠀⠀⠐⠉⠐⠈⠐⡄⠀⠁⠀⠀⠀⠀⠀⠁⡢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢕⠢⠤⠞
⠀⠀⠀⠀⠀⠢⠋⠀⣈⡆⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡠⢃⠆⠀⠀⠀⠀⠀⠀⠀⠮⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠈⠒⠁

⠀⠀⠀⠀⠀⠀⠐⠉⠑⡄⠐⠈⠠⡉⢢⠀⠀⠀⡀⢠⠖⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠆⠀⠀⠀⠀⠀⢠⠊⠉⠲⣀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠴⠃⠀⠀⠀⡸⢀⠇⠀⠰⡆⠇⠊⠓⡲⡕⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢤⣀⡸⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⡀⣈⡤⠊⠀⠀⠀⠑⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⣀⠜⠘⠀⡰⠀⢠⠂⠀⠀⠀⠀⠀⠀⠐⡆⢄⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡄⠀⡔⠒⠤⣀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠌⡇
⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠂⠐⢒⣉⠤⠀⠀⠀⠀⠀⠈⠑⠦⣀⡀⠈⠀⠀⠐⠤⣉⣀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠔⠃⠀⢢
⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⡢⣀⠀⠑⣄⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠁⠂⠲⡜⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⡀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠬⢉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡰⠃⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠄⠔⢈⡁⠀⠀⠀⠀⠀⠒⠂⠉⢲⠀⠀⠀⠀⢱⢸
⠀⠀⠀⠀⠀⠈⠐⠒⠒⠊⠁⠐⠈⠁⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠼⠀⠀⡀⢀⡡⠊

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠚⠛⠀⢀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠅⢻⣿⣷⠶⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠻⠿⠃⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠣⣤⣴⣾⣟⣁⣀⣈⠀⠐⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠁⠀⠀⢀⡏⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⠟⠀⠀⡇⠀⣠⣿⢡⡄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⢠⣷⣾⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⢣⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧⠀⠀⠙⣿⣿⣿⠇⢸⣿⣀⣀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠘⡇⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⣿⣿⡿⠀⢺⣿⣿⣿⣿⣶⣶⣿⣷⡀⠀⠀⠀⠀⠀⢀⡇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣿⣿⣧⣄⢸⣿⣿⣿⣿⣿⣟⣻⣿⢿⣿⣆⠀⠀⠀⣼⠇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣷⡄⢸⡟⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡿⠿⠶⣾⣿⠿⣿⣿⠛⠳⣿⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⢿⣷⡸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠉⠁⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠘⣿⣇⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⢨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠰⠀⠀⠀⢻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⣼⣷⡆⠀⠀⠀⠀⠀⢀⣄⡀⢤⠀⠀⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢄⣤⣤⣶⣿⣿⣶⣿⣿⣧⣀⣀⣀⣀⣠⣬⣉⠉⠹⠤⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠉

⣤⣶⣶⣴⣶⡶⠶⠶⠶⠶⠒⠒⢂⣀⡒⣒⣂⣰⣆⣠⣤⣤⡤⠤⠤⠤⠤⠤⣤⣄⡠⠄⠀⢀⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣷⣶⣤⣤⣤⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣯⣽⠛⠛⠻⠏⠡⢤⡤⠄⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣤⣤⣀⣀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢤⢢⡰⡀⣠⢠⡄⣄⢠⡀⡀⣄⣀⣀⣀⣀⣀⣤⣀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣏⣎⣷⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠳⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠦⣬
⠀⠀⠀⠀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⠟⠛⠛⠉⠉
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢿⡀
⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠟⠀⠀⠀⠀⢀⣘⣷
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠋
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⢸⡆⣤⠀⠀⠀⠀⠀⠀⠈⢱⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠤⢤⣤⡤⠴⠶⠛⠁
⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠉⠛⠓⠲⠶⠶⠶⠶⡖⠀⠀⠐⠀⠀⠀⠀⣼⠋
⣿⠀⢠⣧⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡤⠀⠀⠀⣼⠃
⠙⢶⡿⣿⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⡇⠀⠀⣸⠃
⠀⠀⢀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⡇⠀⢠⡏
⠀⠀⢸⠇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⠀⠀⣼⠁
⠀⠀⢻⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⠀⢰⡏
⠀⠀⠀⠻⣄⠀⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡏⡿⠀⣼
⠀⠀⠀⠀⠹⡆⢸⣇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⡇⡇⠀⡟
⠀⠀⠀⠀⠀⢿⠀⢿⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⢘⡆⠘⢿⠇⢰⡇
⠀⠀⠀⠀⠀⠘⡇⠀⢀⣀⣀⣸⠗⠀⠀⠀⠀⠀⠀⢾⣁⠀⠀⡀⠸⣧⣀⡀
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⠀⠀⠈⣹⡆
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡤⠿⠤⠤⢮⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⠿⠲⠶⣄⠀⠀⠀⣴⣠⠞⡋⢀⡄⠠⠀⠀⠀⡈⢻⡍⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⡁⢠⠀⡆⢼⠃⣀⣀⡾⢁⡜⢀⡞⢠⠁⠐⠘⡆⢱⠀⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇⡆⠀⡇⢸⠀⢀⡿⢀⡞⢰⡞⠀⡏⠀⡇⠀⣇⠘⡇⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⡇⢰⣇⡇⠀⣼⢀⡞⠀⡾⠀⡸⠀⢸⠁⠀⣷⠄⣿⠀⢸⠉⠁⠀⠀⠀⠀⡀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⢿⠈⢸⠁⢳⡇⣸⠁⢰⠃⣤⠇⠀⡘⠀⠀⣿⠀⢸⡄⢸⡇⣰⠂⠀⢀⣠⠿⠟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡆⢷⡘⣧⢸⡀⣾⢀⡏⠀⡾⠀⡞⠀⠀⡇⠀⠀⢸⠃⢸⡇⢨⡟⠁⢀⡴⠋⣀⣀⡴⠄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠈⢷⣌⡁⠳⡟⢸⡇⢸⠃⣸⠃⠀⢸⠇⠀⠀⢸⠀⠘⡇⠀⡷⢀⡞⣠⠞⣵⠋⠀⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣉⣉⣠⡇⣼⠀⡾⠀⡿⠀⠀⣸⠀⠀⠀⢸⠀⠀⡇⠀⡇⣼⢳⠏⣰⠃⣼⢁⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⢉⡇⣿⠀⡇⢰⡇⠀⠀⣿⠀⠀⠀⣿⠤⣼⣇⣸⠁⡇⣸⠀⡟⣰⠏⣼⠃⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡏⢸⠁⣼⡇⠀⢸⡏⠁⠀⢠⣟⠀⣒⠮⢭⣽⡷⣏⣼⡵⠋⣴⠋⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣿⡇⢸⠀⢻⡇⠀⢸⠃⠀⠀⢺⡍⠀⠈⠉⢒⣒⣾⠿⢋⣠⠞⢁⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡇⢸⠀⢸⡇⠀⢸⣤⠄⠀⢸⣆⠒⢦⣭⣉⣭⡴⢖⣫⡵⠞⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⡇⠸⡇⠀⣾⠁⠀⠀⣾⠈⢉⡏⠛⠛⠛⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠘⡇⠀⣷⠀⣿⠀⠀⢰⡇⠀⣸⠁⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣇⠀⣿⠀⣿⠀⣿⠀⠀⡾⠀⢠⡏⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢸⡄⢸⡇⣿⠀⣸⠃⠀⡾⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠲⠶⠚⠻⡇⣿⠀⠘⡇⠘⣇⠻⢠⡏⠀⡼⠁⣾⠭⠦⣄⣀⡤⠖⠒⠛⠛⠓⠒⣦⠀⢀⣀⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠃⢸⡦⠀⣿⠀⣿⠀⣾⠀⡼⠁⣸⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠦⣄⡀⡧⠀⣿⠀⡿⢠⡏⣼⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⢦⣼⠇⣸⠃⢸⠇⡟⢀⣉⡤⠤⠤⠤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠤⠴⠶⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙



⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠠⢄⠀⠀⠀⣀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠀⠒⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡼⠁
⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⡿⠉⠓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀
⠘⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠈⢿⣅⡀⠀⠠⠀⠀⠅⠀⠒⠠⠄⠀⠀⠀⢀⡀⠀⡐⠁⠀⠀⠈⠑⠀⠀⠀⠐⠢⣀
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⢌⠐⠀⢈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠢⡈⠂⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠑⢄⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣉⣁⠂⢀⣠⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⡧⢸⠁⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠓⠚⢁⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢁⡎⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣊⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⡘⠠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠁⠀⠉⠉⢹⡆⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢠⠄⠀⠀⠀⠀⠀⠀⢼⠁⠀⠲⠤⠀⠀⠀⢸⠷⠛⠛⠛⣦⠀⠈⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠙⡆⠀⠀⢀⡖⠻⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠸⠶⣄
⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠈⠓⠋⢁⠆⠀⢸⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠾⢤⡀⠂⠒⠒⠢⣄
⠀⠀⠀⠀⠀⠘⣆⣰⢠⠀⠀⠀⠀⠀⠀⡰⠋⢀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣀⢀⣴⣾⠶⠿⠓⠒⠦⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠉⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢠⢷⡄⠀⠀⠀⣸
⠀⠀⠀⠤⠤⠒⠚⠉⣀⠤⠒⠀⠀⠀⠈⠉⠑⠒⠲⠶⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠤⠐⠁⠀⠓⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⢀⡖⠀⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠐⠋⠒⠒⠶⠦⠤⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⣀⠈⠀⣠⡟
⠀⠀⠀⠀⠀⡠⠔⠊⠁⢀⣀⠠⢤⣀⠀⠀⠀⠀⠒⠢⢄⣠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠺⡝⢠⣄⠈⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡙⢦⠀⠀⠀⠀⠀⠈⠑⠄⠀⠐⠶⠖⠂⠀⠀⠀⠀⠀⢹⡆⢸⣧⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡔⠀⢹⠄⠃⠀⠀⠀⢸⡋⠉⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣘⠒⠊⠀⠀⠀⠀⠀⠀⠻⣈⡠⢆⠀⠀⣶⡄⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠹⣄⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡀⠀⣆⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣿⣿⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⣁⣉⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⠀⠉⠀⠀⠀⠠⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠒⣶⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡱⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠃⠀⠀⠀⠨⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⡴⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠘⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠰⢶⠇⠀⢠⣾⣧⠀⣀⣐⣀⡀⣴⣦⣄⣀⣀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠉⠛⠦⣤⣠⣄⣀⢀⣀⣦⣔⣴⣼⣯⠿⡄⢿⣩⡿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠁⠀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠁⠛
⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡄⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠼
⠀⠀⠀⠀⠀⠀⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⠁⠛⠂⠂⠀⠀⠀⠐⠐⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠈⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇⠀⣿⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⢸⡇⢸⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢱⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⠀⠈⣿⢸⡇⢰⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⢸⡀⠀⣿⢸⡇⢸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⡆⣇⠀⣿⢸⣇⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢟⣜⢦⣿⢸⢿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⡰⡀⠘⢮⡪⢗⡏⢸⢸⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⣀⣈⠂⢈⠆⠀⠈⠳⡇⢸⢸⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⢄⡀⠈⡍⠀⠁⣤⠀⠀⠀⣿⠘⢸
⠀⠀⠀⠀⠀⠒⣄⣈⡄⠀⠀⠀⠀⠠⠂⠉⠁⢺⡏⠉⠁⠀⠀⣆⢀⠀⠀⠀⡿⡄⣾⡀
⠀⠀⠀⠀⠓⠚⠋⢀⠂⠀⠀⠐⡄⠫⠤⣄⣀⠬⠀⣠⡼⡿⠿⢛⠛⣃⠤⢄⡇⣇⣿⡇⠀⠀⠀⣀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠉⠁⠉⠛⠚⠛⠁⠀⠀⠀⣰⡤⢀⡨⠞⠁⠀⠈⠙⠤⠤⠶⣧⣹⣿⡇⠀⠀⣨⠴⠒⠧⣄⠀⢈⡆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠂⠀⠳⢤⣄⣀⣈⡟⠉⠁

⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡄⠀⠀⠀⠀⠀⠀⠀⠐⢡⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢆
⠀⠀⠀⠀⠀⠈⠙⠀⠀⠛⢿⣦⣁⠲⢦⠀⠀⠐⠇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⡄⠈⠁⠀⠀⡤
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠈⠛⢿⣷⣤⡳⡄⠀⠀⢀⢀⠇⡀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠆⠀⠈⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠈⢿⣷⣼⡄⠀⣹⠂⣸⡅⠀⢻⠦⢊⠶⠶⢦⡀⠀⡐⠠⣄⠀⠀⣀
⠀⠀⠀⠀⠀⣤⠀⠀⠹⣷⡀⠀⠀⠀⠀⢻⣿⡇⠈⣧⢂⡿⠀⢸⣇⠀⣾⠞⠷⣆⣧⠰⣇⠛⣿⠋⠊⠁⠀⠀⠀⡄⢤
⠀⠀⠀⠀⠀⣿⡆⡀⠀⠙⢿⣷⣤⡁⢄⠈⣿⣇⡿⠗⠛⠷⡄⣼⠃⢸⡟⢓⡤⠟⢔⡙⠿⡟⠃⠀⡀⢀⣆⣰⠏⠀⠉
⠀⠀⠀⢠⠄⠹⣷⣘⠆⡀⠀⠙⢿⣿⣄⢠⣿⡵⢛⣼⣿⣶⡀⣿⠞⠨⠐⠉⢀⡜⠻⣿⠋⠀⠀⡤⠚⠉⠈⡿
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣆⠑⠄⠈⠻⣿⣴⡟⠁⢾⡻⣽⠿⢁⣵⣦⣸⠀⢠⡾⢷⡶⣁⢀⣄⠘⠧⠶⣄⣴⡥⠤⣤⣤⡀
⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣷⡄⠂⠀⢹⣿⠇⠀⠀⣥⣌⠰⣿⠀⠈⣿⡆⢸⠁⠨⡟⢁⠁⠸⣀⣀⡼⢿⢷⠊⠀⡔⠀⠈⠁
⠀⠀⠀⠀⠀⢹⣶⡄⠀⠈⢻⣿⡌⠀⢸⣿⠀⠰⢬⠏⡹⣄⠛⠠⣄⢿⡷⣾⠀⠁⢹⡎⠈⠀⡿⠛⠀⡔⠙⠶⠟
⠀⠀⢤⡀⠀⠀⢻⣷⠀⠀⠀⢿⣧⢀⡾⠃⢰⣷⢃⡜⠱⡜⢿⡆⠸⢺⣏⣹⡄⠀⠀⣡⣴⠒⢢⣄⡾⢷⠒⡶⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠟⠉⢘⣲⢁⡾⠒⠶⣿⡌⢷⣍⠺⣿⣭⡶⠀⠎⠑⢿⣀⣀⡞⠛⢠⣿⣀
⠀⠀⡤⠄⠀⠀⠸⣿⣧⠀⢀⡿⠃⠐⢦⢺⡏⣸⠃⠀⣸⣟⣼⠘⣿⡀⡋⡭⢰⠟⣘⣶⠼⣿⠿⣦⣤⣽⣄⡧⠛⠁
⠀⠀⢀⡀⠀⠀⠀⠹⣿⣆⡎⢴⣿⣟⡷⢻⡃⣿⠳⣴⣿⠏⢸⡃⣿⣄⢡⠘⣄⠘⢁⣨⠔⢻⠒⢿⣆⣠⡙⡷⢠⡀
⠀⠀⠈⢀⠀⠀⠀⢀⣸⣿⣧⣸⡊⠉⡄⠻⡇⢻⣼⣿⠃⡞⢸⡇⣿⣡⢺⡶⡻⣟⠶⣿⡄⣷⢸⣿⠅⢈⠱⡆⠈⠁
⠀⠀⠀⠛⡴⠂⠀⢦⡁⢄⡄⣻⢉⠧⡠⡋⣧⡘⣿⡉⢸⡃⣸⢹⣷⡄⠙⠷⠟⣳⣭⣾⣿⡝⡇⣿⢛⠷⣶⠂⠛⠐
⠀⠀⠀⠀⠀⡸⠉⠓⣿⢞⣷⣿⣋⠀⡿⠇⡛⣷⣹⠧⠜⠲⡿⠿⠩⠀⠊⣀⡶⣩⣿⣿⣹⣧⣰⢛⡞⡷⠚⠓⠀⠂
⠀⠀⠀⡆⠀⣀⣒⣛⢿⡿⢿⠯⣉⡸⡃⠄⠙⢠⡈⠀⣰⡄⠀⣀⣤⠼⠚⠁⠄⢉⣿⡿⣿⢿⣻⣾⡟⠘⣁⡀⠀⢀
⠀⠀⠀⠶⠀⡧⠶⠶⣿⣻⠚⠓⢋⠛⠃⣤⡠⠚⠋⡉⣤⡤⠞⡉⡄⠄⢆⣂⡵⢿⡿⣶⢏⣼⠻⡣⠚⣉⣠⢿⡆⢸⡇
⠀⠀⠀⠀⣠⣆⠀⢹⣿⣟⠀⣸⠁⣀⡠⢋⠠⢈⣠⡶⠉⡔⢇⣀⣬⠶⠟⣫⡝⢯⡽⢃⠘⠳⢎⢙⡀⠸⢈⡾⢃⣾⢣
⠀⠀⠀⢸⣽⣿⣔⣺⣯⣷⠐⠦⠀⠘⠠⠉⣼⠿⡯⢱⠝⣴⠛⣡⡠⣶⣛⣤⣶⠿⠝⠋⠀⠈⢹⢀⣡⠶⢋⣴⠟⡱⠁
⠀⠀⠀⣸⠾⣯⡿⣯⡼⣿⡶⠀⢲⢁⠂⣼⠏⠘⡇⣷⣼⣤⢿⡱⠞⢛⣋⣈⣿⣶⠚⣄⢷⠟⢀⡉⠁⠀⠘⢿⠞
⠀⠀⢸⡿⣷⣙⣿⣿⣷⣿⣟⣤⣼⣨⣾⠿⣶⣬⣷⣿⣿⣿⣿⡴⠛⠏⠉⠉⠄⢿⡧⢠⠜⡀⡀⣠⢉⠑⠳⣤
⠀⠀⠘⢿⣿⣿⣦⣏⠿⣿⣿⠋⠉⠻⠁⠀⠀⠁⠀⠀⠹⠛⠛⣷⡈⠀⠄⠐⠀⣸⣟⠐⢂⠋⠁⣘⠏⠞⢛⣽⠀⣠
⠀⠀⢀⣼⣿⣼⣿⣿⡿⠛⠁⢄⠀⠀⣀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠻⢶⣦⡄⢠⣿⢃⡀⠼⡤⠀⡜⠛⢛⣫⣤⣶⠋
⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⠀⢠⡀⠀⠀⠀⠀⠀⠂⠀⢀⣿⣷⣿⣹⢄⡌⠀⠀⠤⢦⡀⢿⠗⠊
⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠰⡤⠈⠣⣨⣶⡾⢷⣷⣎⣠⠂⠀⢤⠄⠀⠀⠈⣿⡡⠊⠉⠁⡴⠾⢧⣿
⠀⠀⠀⠀⠀⣩⠟⠀⣀⠀⣀⠀⢴⡿⢫⠔⢈⣉⡉⠻⡻⣿⣄⠀⠀⠀⢀⠀⠹⣷⣀⡠⢌⣙⡚⣛⡡⠂
⠀⠀⠀⠀⠈⠻⡤⠀⠀⠀⠈⠛⡿⠴⠁⠜⠁⠀⠈⠧⠘⠻⡗⠂⠀⠂⠁⢀⣴⠿⠃⠐⠚⠛⠋⠉

⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣧⢙⣍⢋⣿⣿⡇⠀⠀⠀⠻⢧⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡿⣯⣿
⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠘⣿⣿⢧⣿⣿⡸⠿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣼⡇⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠨⣿⢿
⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣭⣭⣽⣫⣽⣭⣭⣶⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠰⢶⡶⠿⠿
⡇⠀⠀⠈⣻⡋⠀⠀⠀⠀⠀⢀⣾⢯⣿⣽⣟⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢿⣿⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⣿⣟⣿⣿⣽⣿⣽⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠘⠿⠿⠿
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢿⡧⣿⣿⣼⣿⣺⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣿⣺⣟⣻⣗⣛⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣬⣀⠚⠂
⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣟⡛⠋⠀⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⡍⢰⣿⣿⠂⠁
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⢸⣿⣿⠅⣉
⠀⢀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣇⣸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠂⢺⣿⣿⠂⠆
⠀⠀⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⠋⣿⣿⣿⠃⠀⣼⣿⡿⠃⠀⠀⠀⠀⠖⢺⣿⣿⡉⡁
⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣾⠟⠉⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣧⣤
⠀⠀⠀⠻⠿⠿⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣀⣈⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠹⠿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⣤⣤⣤⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢠⣶⣷⡆⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⢹⣿⣽⣭⣽⣿⡏⠉
⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⡇⠀⢸⣿⣿⠏⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⢠⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣶⠀⠀⠀⠀⠀⣶⣶⣘
⣭⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣿⣿⣟⣯⢷⡄⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠟⣿⣿⠀⠀⠀⠀⣀⣀⣈⠻⠿⠿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣷⣿⣿⢿⣟⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣯
⣿⣷⣷⣿⡇⠀⠀⠀⠀⠿⢿⣿⣛⣛⣛⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⢿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⣿
⣯⣭⣭⣽⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠰⠀⣠⡀⠀⠀⢠⣾⣷⣿⣿⣾⣯⣽⣽⣿⣦⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢰⣾⣿⣭
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣿⣶⡀⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⣿⠄⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⢿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⣈⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⣁⣸⣿⣿⡑⡂⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣶⣿⡆
⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⡂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⢀⡀⣿⠃⠀⣼⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿
⣿⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡶⣶⡆⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠃⠀⠀⣶⣶⡙⣿⣾⣿⢠⣤⠀⠀⠀⢻⣿⣷⣠⣶⣯⡻⠟⠀⠀⠀⠀⣿⣻⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠠⠦⠠⠀⠈⠚⠀⠮⢗⠀⠀⠀⠀⠀⠐⢋⠄⠪⡇⠀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⡠⡈⠈⠀⣠⡀⠀⠀⠀⢔⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⠇
⠀⠀⠀⠀⠀⠈⠁⠙⠑⠊⠀⠀⠀⠀⡀⡀⠀⠙⠓⠁⠀⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠇⠰⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠨⠆⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠗⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠧⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠄⠀⠆⠀⠀⠀⠐⣅⠹⠍⡆
⠀⠀⠐⣃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⠐⠓⠔⡄
⠀⠈⢂⠘⢁⡂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢀⠉⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠪⠂⠟⠆⠉
⠀⠐⠑⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡸⠁⠀⢪⣼⡿⠋⠉⠉⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠈⠀⣀⣠⣴⡒⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣶⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⠀⠀⢠⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⡇
⠀⠀⠀⣠⣔⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⣀⣀⣀⣠⡿⠀⠀⠀⢠⠇
⠀⠀⠀⣸⠋⢸⣄⠀⠀⠀⠀⢠⣿⣷⡀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⡟⠋⠉⠛⠋⠀⠀⠀⣠⡟
⠀⠀⢰⣿⠀⢸⠙⠀⠀⠀⠀⣾⣿⣿⣿⣶⣾⣿⣶⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⢂⠀⠀⠀⠀⣠⣼⠟
⠀⠀⠸⣾⡆⢸⠀⠀⠀⠀⢰⣿⡟⠛⠉⠙⠻⢿⣿⣿⣿⣷⣶⣴⣶⣶⣶⣦⡄⠀⠀⠀⠀⣼⣿⣿⣿⠿⠶⠶⠶⠚⠋⠁
⠀⠀⠀⣿⡇⢸⡇⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣷⡇⠀⠀⠀⣸⡿⠋⠁
⠀⠀⠀⣿⡇⢸⡇⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⡆⠀⠀⢸⠛⠁
⠀⠀⠀⣿⡇⣾⡇⠰⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⣾
⠀⠀⠀⠁⢠⣿⡇⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡇
⠀⠀⠀⢀⣿⡿⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣿
⠀⠀⢠⣾⠟⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡷⠀⣿
⠀⠀⢸⣿⡞⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣇⢀⡿
⠀⠀⢸⣿⢿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⢿⠇
⠀⠀⢸⣿⡸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⢸
⠀⠀⢸⣿⡇⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⡇⢀⢸⡀
⠀⠀⠸⣿⣇⣿⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢻⣇⣸⠈⢃
⠀⠀⠘⢿⣿⣿⡆⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠿⢿⡇⠙⠲⠦⡄
⠀⠀⠀⠀⠀⠀⠉⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠁⢀⠀⠀⠀⠀⠀⠀⢀⡄⠈⢹⡋⠈⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣀⣧⡤⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠈⠁⠀⡀⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠃⢺⡜⠀⠀⠀⠀⠀⠈⠾⠐⠒⠂⠀⠀⠃⠑⠉⠀⠀⠤⢄⡀⠀⠀⠀⠒⠒⠚⠀⠚⠈⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣿⠀⠈⠀⠀⣤⢘⠑⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢢⠀⣿⡇⡀⢀⢰⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⡄⠀⠀⣄⣄⣀⢠⢸⠀⠀⠀⢤⡀⢠⣦⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠈⠀⣿⠀⡄⠈⢸⠀⠘⠃⠸⡇⠀⠀⠀⠸⠠⠐⠛⠉⠳⠤⠤⠤⠄⠀⠤⠄⠀⠈⠘⠃⠀⣀⠺⡰⠙⣞⡁⢄⠁⠀⢙⡀
⠀⠀⠀⠀⢠⠀⠠⡤⣶⠂⠈⢦⡀⢿⠓⢧⠂⡤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢠⣀⣦⠀⣀⣄⠘⡟⠉⠻⣁⣽⣊⠤⡄
⠀⠀⠀⠀⣞⡧⢤⡽⠋⠀⠀⠈⠙⣿⠂⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣸⣅⣴⠐⡇⢀⠙⠦⠼⠋⠀⣸⠋⠁
⠀⠀⠀⠀⠀⢧⡤⠂⠢⢄⠺⡇⠀⣿⡂⣸⠀⠀⣤⡆⠀⠀⠀⡀⢠⣒⣢⠀⠀⢀⠲⠹⢷⣆⠀⢀⣀⠀⠀⢭⡴⠴⣤⡧⠞⠀⠀⠐⢶⠾⠗
⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⢻⠀⣣⣻⣷⠟⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⢲⠌⠈⢤⠀⢸⡇⢰⠂⠃⢣
⠀⠀⠀⠀⠀⠠⠼⠿⠶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣯⣀⣀⡤⠧⠾⠃⠿⠀⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣀⣀⢀⢀⣀⣀⣀⣀⣀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣀⡀⢀⢀⢀⣀⠀⢀⢀⠀⡀⡀
⠠⠀⣀⡤⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠈
⢠⢀⣀⣀⢀⢀⣀⡀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛