Zoning laws Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣶⣶⢦⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣠⢴⡴⠇⠈⠋⣹⣿⢏⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠘⠓⠉⠁⠙⢹⠉⠈⢰⠀⠀⢈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣰⠋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⣀⡀⢀⣠⠴⠁⠀⡄⠀⢐⣒⣦⣄⡀⠀⣾⣁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣾⣟⣿⣿⢻⣇⣛⣿⣷⣶⣤⣤⣄⣸⣿⣿⣽⡇⠀⠹⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⣴⣿⣿⣿⣽⣿⣟⣿⣿⢿⣿⡟⣹⣣⣿⣿⣿⠿⠛⣿⣷⠄⢈⠏
⠀⠀⠀⠀⠀⠀⠋⠀⢤⡛⠓⠊⢹⣿⠃⠚⠳⢿⣿⣿⣟⣲⣾⣿⣇⠉⠃⣭⣿⡇⠀⠶⣿⡟⢻⠁⠒⠸
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠄⠼⠛⢲⣶⣾⢿⣿⢉⣿⡿⡿⠄⡁⠈⠀⠈⢻⡇⠴⠃⠿⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠃⣻⠇⠀⠀⠘⠛⠛⠊⣿⣷⣿⣿⣷⠀⠻⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠻⣾⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢀⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⢀
⠀⠀⠀⠀⠀⠀⢸⡖⠙⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⣌⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠉⣾⠇⠠⠆
⠀⠀⠀⠀⠀⠀⢸⣷⡧⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣦⣤⣰⣆
⠀⠀⠀⠀⠀⠀⡀⠳⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠋⠙⠛⣯
⠀⠀⠀⠀⠠⣄⣠⠀⡿⠹⡄⠀⠀⠀⠀⠀⠦⠤⠀⠈⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⢣⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠆⠀⠦⠃⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠈⠂⠀⠶⠠⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢬⡟⠛⠂⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠐⠀⠄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡤⠔⠉
⠀⠀⠀⠀⠀⠠⠒⠲⣾⣁⠀⣢⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠏⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠤⠦⠀⠀⠀⣠⠙⣿⣾⠿⠋⠘⠀⠀⠀⠀⠀⠁⠡⢄⣾⣤⣀⣀⣼⣄⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠃⠐⠊⠉⠀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡤⠄⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⡀⣀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠇⠀⠀⠀⠉⠹⠀⡉⠃⠀⠀⠀⠬⢀⠀⢠⠁⠀⢤⠀⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠈⠁⠈⢁⠀⠀⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠅⠀⠉
⠀⠀⠀⠀⠀⠀⢀⠀⣠⡄⣢⡚⣥⣶⣼⠆⠀⠀⡐⠈⠨⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠁⢀
⠀⠀⢠⢤⣴⣿⣭⣼⣶⣼⣣⢸⣽⣿⣿⡆⠀⠁⠀⡀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠐⠀⠐⠀⣀⡀⠠⢷
⠀⠀⢦⣐⣷⣦⣦⣆⣱⣓⣩⣜⣿⣽⣿⠏⠀⢐⠂⠀⠀⠆⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⣠⠎⠀⠀⠀⠀⠀⠈⠛⡶
⠀⠀⠀⠉⠻⠲⢿⢾⣿⣿⡣⠸⠛⡉⣀⠠⠀⠁⠁⢀⢀⣈⣀⣊⣤⣜⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠄⢀⡤⠔⠢⡀⡁⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡃⢧⠥⠏⢻⠀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠑⠐⠁⠘⠡⠴⠤⠤⠼⠁⡠⠤⠀⠁⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣣⡄⣖⣕⡢⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠢⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡠⠒⠈⠀⠀⡀⠀⠀⠀⠀⢀
⠠⡂⠀⠂⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠂⣁⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠠⠀⠀⠘⡋⠀⠀⠈⠧⠆⡀⠀⢀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠱⡆⠄⡀
⠀⠀⠀⠀⠀⢀⡈⣆⠀⠀⠀⠰⠌⣀⠀⠀⡴⠀⠀⠁⠲⢤⡐⠈⠓⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⢀⠤⠒⠩⣽⢿⡄⢠⠀⠄⡑⠁⠀⠌⢈⡀⠀⠄⠀⠹⠀⢀⠄⠐⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣉
⠔⠊⠁⠀⡠⢐⣿⡄⡏⠀⢸⣰⢓⡀⣼⠤⡀⠀⠀⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈
⠀⠀⠀⢊⠎⣀⢖⠺⠇⡂⢼⢸⢨⠀⠁⠀⠀⠀⠀⠁⠀⠚⠂⠀⠄⢀⡠⠔⠊⠁⠀⠂
⣀⡀⠀⠉⠠⠟⡁⠠⠄⠋⠀⠉⣛⠁⠄⣂⡀⠀⠀⠁⡀⠐⣈⠅⠊⠁
⠀⢜⡒⠤⣀⠀⠀⠀⠠⠀⠁⠀⠉⠉⠉⠁⠀⢀⢀⠥⠐⠉
⠐⠀⠀⠀⠀⠑⠲⢦⡀⠀⠀⠀⠀⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠔⠊⠁
⠐⠠⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢻⠀⠀⢠⡂⣀⠠⡃⢨⠓⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⢁⠦⠚⠡⢀⠡⠀⠀⠈⠥⠁⠰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⢿⠈⠁⠋⠀⠀⣠⠘⠃⠀⠀⠀⠀⢀⠀⠐⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠴⣀⠂⠀⠀⢠⠀⠀⠶⣀⠴⠚⠁⠀⠀⣰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠂⠀⠀⠀⠁⠀⡏⠀⠀⠀⢀⡉⣖⠀⠀⠀⠀⠀⣇⡔
⠀⠀⠀⠀⠠⢶⠀⠺⠃⠐⠠⠀⠀⠀⠀⢴⠥⠀⢀⣀⣀⠀⠉⣬⣟⠒⠀⠉⢴⣀⣭⠀⠀⠿⠀⠘⠠⠁
⠀⠀⠀⠀⠀⠈⠀⠘⠃⣀⠁⠀⠀⠀⠀⠄⡙⠀⠀⢸⡁⠀⠐⣞⣗⠀⡀⢄⡴⠒⠛⠀⠀⠶
⠀⠀⠀⠀⠀⠀⡀⠀⣠⠄⠀⠀⠀⠠⠃⣾⠤⣤⣄⣀⣀⣤⣄⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠠
⠀⠀⠀⠈⠀⠀⠀⠊⡉⠙⠀⢉⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠶⢤⠤⠤⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠠⠂⠉⠃⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⢾
⠀⣀⠀⠀⠀⠀⠉⠁⠈⠓⠒⠒⠂⠤⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠶⠀⠀⢀⡀⠒⠘
⠀⠠⠤⠀⡀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⣤⠆⠄⠀⠀⠀⡠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⠉⣀⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠀⡆⠀⠀⠀⠀⠇⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠈⠈⠱⠀⠀⠋⠈⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠐⠀⡀⠀⠀⠘⠃⠀⠀⠀⠑⠀⢸
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠄
⠀⠐⠀⠴⠀⠠⠤⢤⣀⠀⠀⠀⠀⠀⠠⢠⠴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠀⠂⠈⠀⠈⠀⠒⠀⠈⠐⠀⠀⠁⠀⠃⠐⠂⠀⠃⠂⠐⠂⠐⠐⠃⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠂⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠠⠀⠐⠠⠀⠂⠠⠐⠐⠀⠐⠀⠐⠀⠒⠠⠐⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠲⠐⠐
⠀⠀⠀⠀⠀⠠⠀⢀⠠⠀⠄⡄⡀⠠⠀⡄⠀⠄⠀⢀⡀⢀⠤⢠⠠⠀⠄⠄⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠠⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢀⣴⠏⠀⠀⢠⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄⠀⠀⠹⣦⡀
⠀⠀⢀⡾⠃⠀⠀⠀⠀⠙⠛⠛⡿⣟⠛⠛⠛⠛⠛⠛⢻⡟⢻⡟⠛⠛⠛⠛⠛⠛⣻⢿⠛⠛⠉⠀⠀⠀⠀⠘⢷⡀
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠹⡄⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢠⠏⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢻⡀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢸⡏⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢹
⣾⠃⠀⠀⠀⠀⠀⠀⢠⡾⠤⠤⠤⠤⠤⠬⣧⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⣼⠥⠤⠤⠤⠤⠤⢷⡄⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⡼⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠚⠉⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠉⠓⠶⠶⠖⠋
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠼⠧⠼⠧⢤⣀⠀⢀⣠⠴⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⣹⣠⠞⠁⢀⣠⣀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⠀⠀⣏⠀⢸⡆⠀⣹⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣆⠀⠈⠛⠉⠀⢠⠏⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠞⠁⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⣤⡶⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⠓⠂⠀⠀⣾⣿⠋⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠾⠉⠉⠋⠉⠋⠒⠚⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠙⠻⢽⡉⠉⠚⠛
⠀⠀⠀⠀⠀⢀⡠⣴⣤⢶⡀⡠⢶⣆⣀⡀
⠀⠀⠀⠀⢀⢞⣶⢿⣿⣿⣿⢐⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡞⢼⡇⣾⣿⡿⣿⢸⣧⢙⣿⢹⡆⠀⠀⡇⠀⠀⠟⠻⠟⠛⠛
⠀⠀⠀⠀⣟⣠⡧⠈⣻⠋⠿⢺⣿⡼⣿⡜⡇⠀⠀⡇
⠀⠀⠀⠀⠙⠉⠒⠇⠻⠴⣿⠎⠉⠳⡿⠾⠏⠈⢈⡇⠀⠀⠀⠀⠀⠀⢲⡆
⠀⠀⠀⠘⡄⢠⠒⣰⠃⠀⠄⠤⠀⣾⢰⡶⡇⠀⠉⡁⠀⣶⠀⠀⠀⠀⠈
⠀⠀⡜⢱⠧⠈⠜⠉⢀⠈⢷⠄⠈⠋⠦⠤⠒⠋⠀⠆⣰⢿⡌⠁⠀⠀⠀⣀⡠⡤⠤⠲⠘⠀⠀⠁
⠀⡜⣀⣿⣁⣟⡀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠖⠈⠀⠘⠛⠀⠀⠂⠠⠰⢶⠆⠀⠀⠀⠀⠀⣀
⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠁⠙⡀⠀⠐⠋⠉⢙⣿⣿⣷⣄
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠈⠉⠻⠷⠄
⠘⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⠔⠲⠤⠤⠤⠤⢔⣒⣈⣁⣀⣈⠁⠄⠐⠒⠀⠀⠀⠀⠠⠤⠄
⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠉⠩⠭⠉⠉⣒⠒⡎⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢚⠀⠀⠈⠀⠉⠉⠀⢲⠶⡖⢢⣤⡤⠄⠄⠀⡠⠴⣿⢸⣧⣧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⣨⠬⢽⣿⣷⣶⣶⣶⣤⣤⣤⣼⣤⣇⣸⣀⡇⠀⠀⠀⡄⢛⣵⢸⢗⣷⡬⣿⣿⡟
⠈⠀⠉⠀⠂⠀⠘⠿⠿⣿⡿⣿⠀⠀⠀⠀⢸⣻⣿⠉⠛⢻⠿⡿⣿⣿⡿⣿⣍⣉⣩⡷⣯⠟⢸⣿⠉⠉⠉⠈⠉⠂⠀⡀
⠀⠀⠀⣀⠄⢂⡡⠔⢊⠥⠒⣉⠷⢒⡲⠶⠼⠿⣿⣄⣀⣸⣄⡇⣇⢈⡇⠀⠀⠀⠹⢞⣵⡇⢸⠏⠀⠈⠀⣀⠶⠒⠀⠠⠄
⠀⠀⠀⠀⠀⠉⠀⠚⠀⠰⠉⢠⣒⠉⠀⠣⠀⠀⡞⠀⠀⠈⠉⡏⠙⡿⠲⡶⡤⢤⠶⣿⣿⠇⠿⠀⣀⡔⠊
⢀⣀⡀⠀⠀⠀⢀⣀⡀⣀⠤⠄⠀⣂⣙⣃⠀⠤⠃⠄⠤⢆⣀⣁⠀⠛⠛⠅⠷⢾⣀⡿⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠂⠠
⠀⠦⠍⠽⠡⠌⠓⠚⠓⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⢤⠨⡙⢟⠲⡶⢤⠤⣤⣀⣀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⣘⢦⢳⣜⣦⢷⣸⠆⡇⠀⠀⠈⠉⠉⠀⠒⠀⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⣸⣿⡿⡯⢿⢺⠀⡇⢀⣀⠀⠤⠄⠠⠤⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣠⡾⠋⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠙⢷⣄
⠀⠀⠀⣼⠏⠀⠀⠀⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠀⠀⠀⠹⣦
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢠⠏⣧⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⣼⠹⡄⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡏⠀⠘⣆⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⣰⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠘⣧
⢰⡏⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠹⡄⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⢠⠏⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢹
⣾⠁⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣽⡄⠀⠀⢸⡇⢸⡇⠀⠀⢠⣯⣤⣤⣤⣤⣬⣧⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡸⠃⠀⠀⢸⡇⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⢀⡞
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠋⠁⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠈⠙⠲⠶⠒⠋
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠾⠷⠾⠷⠦⡄⠀⣠⠶⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣀⣀⣀⣀⣀⣀⣧⡞⠁⢠⠤⢤⡀⠘⣆⠀⠀⠀⠀⠀⠀⣸
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠻⣄⣰⠃⠀⡿⠀⠀⠀⠀⠀⢠⡟
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⣆⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠏⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠐⠛⠹⣷⠿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠀⠻⣿⣿⣿⣿⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣢⣤⣦⣼⣿⣿⣿⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⠰⣶⠶⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢿⣤⠤⠴⠞⠛⣻⣿⣿⣿⣿⡿⣿⠯
⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⠛⠁⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠠⠖⢿⠀⠸⣿⣿⣿⣿⠛⠛⠄⡠⢜⣷
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⣾⣿⢉⣿⣟⡿⠶⠶⠷⠾⣿⡆
⠀⠀⠀⠀⠈⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠉⠈⠁⠛⠿⠙⢿⡿⠀⠀⠀⠀⠀⣿⣿⣶⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡅⠽⢃⠀⠀⠀⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠐⠐⠂⠈⠁⠀⢾⠯⠐⠐⠙⢦⣴⣿⣿⣿⢿⠿⠷⠆
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡈⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠏⠈⠀⠈⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣸⠿⠛⢿⣿⠋⠘⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠛⠙⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣀⠀⠁⠀⠀⠀⠼⢋⠠⠀⠀⠁⠂⠀⠀⠀⢉⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠉⠀⡂⠜⠀⠀⠀⠀⠀⠚⠈⠆⠀⠀⢈⡍⠲⢄⡀⣠⣉⠻⠛⢿⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢠⡂⣰⣇⡀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿⢿⣖⠻⢿⣿⣿⣿⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢰⡿⢁⣭⠛⢶⣍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣨⣿⣦⡙⠻⠟⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⠀⠈⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⢻⣿⣿⣷⣦⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠐⠋⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠀⠐⠒⠒⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⣿⣿⣷⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⣦⣤⣀⣀
⠀⠀⠀⢰⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣯⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣂⣠⣀
⠀⠀⡀⠈⣇⡸⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣧⡛⠻⠁⠻⠿⠿⣿⣿⣿⡿⢿⣿⡯
⠀⠀⠆⢀⢻⡇⠉⠀⠖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣆⠀⠀⠀⠀⠲⣿⣿⡟
⠀⠀⠘⠀⠘⠒⠀⠀⠀⠭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⠀⠔⠠⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠩⣿⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡇⢀⢄⣘⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⢐⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⢿⣿⢾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⣿⣿⣿⣷⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡻⣬⣽⣻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠿⠀⣀⣀⡀⠀⠀⠈⠛⢿⣿⣿⠏⣿⣶⣠⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠺⠊⠋⠉⠉⠁⣿⣦⣤⣀⡀⣾⣧⣿⡚⢷⣶⢿⣿⣻⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣠⣉⣭⠿⠆⠻⠿⣷⡯⢷⠈⢿⣿⣿⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣏⣹⣷⣶⣗⠀⣾⣿⣿⡎⣧⢐⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠈⣿⣿⣿⡽⡦⣱⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢻⡌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣙⣿⡿⣿⢽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠹⣦
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⣰⡿⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⢿⣆⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⣼⠃⠀⠀⠀⠀⠀⠀⢠⡿⠀⠹⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠏⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣧
⢰⡏⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢻⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡟⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢹
⣾⠁⠀⠀⠀⠀⠀⢀⣘⣃⣀⣀⣀⣀⣛⡀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣛⣀⣀⣀⣀⣘⣃⡀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣃⣀⣀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠀⢠⣾⡿⣛⡻⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠿⢟⣼⣿⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠛⣛⣛⣛⣛⣛⣛⣃⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣿⡿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⣿⣟⣛⣛⣛⣛⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡷⠶⠶⠶⠶⢾⣿⡇⠀⠀⠀⠀⠈⣿⣿⠀⣿⣯⣭⣭⣭⣭⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⣟⠛⠛⠛⠛⢻⣿⡇⠀⠀⠀⠀⠀⠸⣿⠀⣿⣯⣤⣤⣿⣿⢛⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⣿⣟⣛⣛⣻⣿⠿⠿⠇⠀⠀⠀⠀⠀⠀⢻⡀⢿⣿⣿⣿⣿⡿⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡇⢸⠟⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣶⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡏⣩⠭⠭⠭⠭⠭⠭⠭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⣀⣀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠒⠒⠒⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⢠⠖⠚⠁⡇⢈⣉⣉⣉⣉⣁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠐⠒⠒⠒⠒⠂⠀⡇⠀⠀⠀⠀⠈⣇⠀⠀⡇⠠⠤⠤⠤⠤⠤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠒⠒⠒⠒⠒⠒⠀⡇⠀⠀⠀⠀⠀⠸⡄⠀⡇⠀⠖⠒⠀⠀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣿⢸⠀⠘⠙⠛⠋⠛⠃⠀⡇⠀⠀⠀⠀⠀⠀⢳⠀⣇⣀⣀⣀⣀⣀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠃⣿⢸⠀⠉⠉⠉⠁⠀⡖⣶⠇⠀⠀⠀⠀⠀⠀⠈⣇⠀⣀⣀⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠉⠀⠀⣉⠉⠉⠉⠛⠛⠛⠛⠛⠳⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⣉⣩⡽⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠛⠋⠉⠀⠀⠀⠀⠠⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣡⡴⠶⠻⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣶⣶⠿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⣿⣷⠾⠿⠷⠶⠶⢶⡶⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣻⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⣀⣴⣿⣿⣵⣶⣶⣶⣶⣾⡿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠀⢀⠈⠙⠻⣿⣶⣤⣀⠀⢄⡀⠀⠉⠙⠋⠁⠀⠀⠀⣠⣶⣿⣾⣥⠶⢍⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢶⣿⠛⠛⠛⢛⣛⣛⣛⣛⣛⡛⢿⣟⡶⣌⡁⠀⠀⠀⠀⢀⣠⣾⣿⠿⠛⢉⡰⢜⠃⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⣧⣤⣬⣤⣀⣀⣀⠒⠀⠒⠤⠻⠶⣹⣦⣄⢀⣴⡟⠯⢑⢠⡔⠊⠁⠈⠀⣀⡭⣷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣠⣤⣤⠠⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡭⣿⣁⣤⡶⠿⠃⣀⣤⡶⢾⡛⠉⠀⠼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡍⠻⡶⢦⣌⣉⠛⠛⠛⠶⢶⣦⣤⣤⣀⣒⣰⣟⣉⣤⣴⣶⣟⡋⠁⠀⢀⣹⣶⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠶⣿⡀⠈⠄⠈⠉⠛⠷⢦⣤⣀⠀⠈⠙⠛⠿⠿⣿⡿⣿⡿⠛⢉⣠⣴⠾⠟⣛⣫⡭⠴⠶⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⡈⢿⡀⠀⠀⠀⠀⠀⣀⣀⠉⠛⠶⣤⣀⠀⠀⠀⢉⣠⣴⣾⣿⣿⣷⠾⣿⣿⣶⣦⣀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢳⡈⠛⠛⠛⠛⠛⠙⠛⠛⠛⠷⠶⣤⣍⣛⣶⠶⢛⣽⠟⠋⣉⣤⣤⡒⠀⣀⣤⢼⡏⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣀⣀⡐⠒⠤⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣤⣼⣿⣿⡿⠷⠛⢋⠛⢉⣠⣴⠾⢻⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣉⣉⠉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣴⠏⠉⢹⡇⡄⠀⢀⣴⠶⠟⠋⠉⠀⠀⠘⡿⠛⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡈⠉⠙⠓⠶⢶⣭⣍⣛⠶⣦⣄⣴⣿⣧⣴⣶⣾⡧⠶⠚⠉⠀⠒⠒⠒⠀⠀⠀⢠⣷⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡹⠛⠛⠛⠓⠶⠦⣤⣌⣉⡛⠛⠿⢷⣿⡃⢄⡸⢦⣑⣲⠿⠿⡛⠛⠛⠛⠻⠶⣦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⣶⣤⣀⠀⠀⠀⠙⣯⠙⠛⠳⣶⣟⡉⠛⠿⢿⣶⡵⠞⡩⠐⢉⠄⠂⠀⢀⣠⠿⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⡍⠛⣷⣤⣄⠘⠓⠛⠛⠉⠉⠙⠷⣦⣤⣀⠀⠀⠀⠊⣁⣤⣶⣿⣯⣉⣠⠬⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣠⠟⠙⠛⢷⣤⣾⣿⣿⣶⣤⡀⠀⢀⣤⠾⠿⠬⣿⣷⣶⣶⣿⡿⠟⣋⡩⢬⡐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣀⣀⠉⠛⠻⠿⣷⣾⣿⢾⣏⣁⣀⣠⣴⡾⠜⠛⣉⠵⢞⣋⣽⣾⣃⡴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⣻⣿⢿⣶⡶⢦⣤⣤⡴⠟⠉⠛⣻⣗⠤⠔⠒⢊⣽⠿⢋⣵⣯⣼⠻⡶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢸⠁⠈⣷⡈⠙⠛⠷⢦⣤⣀⢖⣚⣿⡍⠑⣲⢛⣻⠶⣞⣛⣭⠴⠾⠃⠘⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⠲⢤⣀⢻⣤⣴⠶⠋⠉⠉⠹⠷⢮⣿⣿⣭⠷⠞⠛⣉⣥⠄⠂⠀⠀⠀⢹⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠐⠦⢄⡈⠛⠿⣤⣀⠀⠀⣰⡷⠲⣤⡉⠉⠀⠀⠐⠉⠁⢀⣀⣤⡶⢾⣛⣛⣡⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣤⣀⠀⠉⠓⠀⠀⠉⠛⣶⣟⠀⠀⡏⢻⣄⠀⣀⣤⡶⠿⠟⠛⠋⠉⠉⠉⢨⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⡝⠳⢦⣄⡀⠀⠀⢰⣿⠙⣿⠸⣧⠀⠹⠿⠋⠁⠀⣠⡀⠀⠀⠀⠀⠒⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠈⠱⠤⠉⠛⠷⣦⣼⣿⣿⠃⠀⣹⠆⠀⠀⠈⣉⣡⣤⠴⠖⢊⡽⠋⠁⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣿⠃⠀⠀⠀⠀⠀⣀⡀⠀⢁⡀⠀⠀⣿⡤⠴⣚⠋⠉⠁⢀⣠⠞⠋⠠⣦⡴⠴⣿
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣤⣍⣛⠶⢦⣤⣀⠀⠀⠈⠉⠙⢶⢧⣤⣾⢁⠤⠄⠉⠓⠾⠋⠁⠀⠉⠉⢀⣰⣤⣿⠃
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⡿⠿⠿⣶⣮⣭⣻⣶⣄⣀⠀⠉⠑⣺⣏⢀⡀⠒⣀⡠⠤⠔⣒⣠⠶⢟⡛⠉⠁⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣷⣦⣄⡀⠀⠀⠀⠀⠙⠻⢿⣶⣦⣬⣿⣠⣄⣠⣤⠴⠖⠋⠡⠔⠊⣁⡤⠐⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣶⣤⣀⠀⠀⠀⠈⣙⢛⣿⠛⠛⣯⠳⣄⠀⠀⠀⠀⠊⠁⢀⣠⠤⠚⠋⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣦⣤⣈⣉⢻⣀⣤⣬⢷⡌⣳⡀⠀⠀⠔⠚⠉
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠾⠛⠋⠐⠉⠉⠁⠛⠊
⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⡉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠙⠻⡿⠿⣿⢿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⡄⠨⠄⠀⠿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠿⠿⣿⡿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠿⠀⢀⠀⠀⠀⠀⠂⠘⠿⠿⣿⣿⢿⠶⠎⠙⠿⠿⠹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠭⠉⠋⠽⣶⡖⠒⠞⠠⡈⠀⠀⠀⠀⣀⡀⣀⣀⠐⠤⠤⠴⠲⠤⠄⠀⠠⠼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠔⠒⠒⠉⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠚⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠋⠉⠉⠙⠛⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠉⠉⠉⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣤⣀⣀⣀⣤⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠿⣄⡀⠀⠀⠀⢸⡇⠀⣴⠶⣄⠀⢰⡟⢯⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢸⡇⠀⠳⡴⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢀⣀⣸⣧⣤⣠⣇⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠁⢀⣀⣀⡀⠈⠉⠓⢾⣇⠀⠀⠀⠀⠀⠀⣾⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⣰⢞⣭⠷⠮⣭⡳⣄⠀⠀⠈⢳⣄⠀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠸⣅⣼⠛⠛⠛⣿⠋⠀⠀⠀⣸⢣⡏⠀⠀⠀⠀⢹⡜⡇⠀⠀⠀⠙⣦⠤⠤⠤⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⠧⣄⣀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⣿⣸⣀⣀⣀⣀⣀⣸⣇⣗⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⠀⠀⠀⠀⡿⠲⠲⠒⠒⠲⠲⣯⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢶⣠⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣸⠏⠉⠉⠉⠙⠳⠦⣄⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠶⠿⣄⠀⠀⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⣰⣏⣀⣀⣴⠞⢦⠀⠀⠀⢷⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠘⢦⣀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⣀⡼⠋⠀⠀⠀⠙⠲⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢹⡆⠀⠀⠀⠀⠀⠀⢹⡷⢦⣄⣀⡀⠀⠀⢀⣀⣠⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢹⠉⠙⠙⡏⠉⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣼⡀⠀⠀⡇⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⣀⣽⠀⠀⡇⠀⠀⠀⠙⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣄⢸⡇⠀⠀⠉⠀⢠⡞⠙⡆⠀⠀⠀⠀⣿⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠟⠉⠁⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠈⠉⠁





⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⢀⣠⠔⠙⠓⠛⠀⠀⠀⠰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠄⠀⠀⠀⣀⣴⣋⠀⠈
⠀⠀⠀⠀⠀⠂⠈⠀⠀⠈⠁⠒⠀⢤⢀⢀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠈⠀⠀⡠⢔⡾⠋⠁⡠⢔⡫
⠀⠀⠀⠀⠀⠀⡀⠄⠒⠤⢄⣀⠀⠀⠀⠀⠁⠉⠉⠋⡉⠀⠠⠀⠀⠀⣀⠠⠂⣩⠔⢁⡠⢒⠍⢚⠵⣺
⠀⠀⠀⠀⠀⠀⠀⠐⢠⣄⢀⢀⠉⠒⠠⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⢊⡠⠖⡁⢔⡪⠔⠉⢀⡤⠖⠋⠩
⠀⠀⠀⠀⠀⠀⠤⣀⣀⣀⠀⠈⠈⠙⠒⠒⠤⠤⣍⣑⣒⡋⢁⡠⢖⡡⣐⠥⠒⠁⣀⠴⠚⠉⠀⣠⡠⡇
⠀⠀⠀⠀⠀⠀⠗⠀⠒⠂⠈⠭⠅⣒⣀⠤⠄⣀⠀⠀⠈⢈⠤⣒⠅⣊⢄⣨⠵⠊⣁⣠⢤⡺⠟⣋⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠈⠩⠀⠚⠩⠭⠕⠊⣔⡯⠑⠉⢥⢴⣛⡽⠚⡹⢖⡯⠗⣻⠃
⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠁⢀⣨⠴⢞⠍⠀⣀⠥⠚⡡⠔⡋⢸⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢺⣷⡾⣫⠕⠋⠄⠒⠉⣠⡔⠬⠐⠁⢠⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠐⠆⣭⠝⠊⠁⠂⢀⣠⠶⠛⠁⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠦⣄⣀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠄⠂⠀⢀⠤⠚⠉⡀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠢⠄⣀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠠⣐⡼⠞⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠄⣰⠿⠭⠄⠀⠀⠀⠀⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠵⠋⠀⠒⠒⠒⠒⠦⠄⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠈
⠀⠀⠀⠀⠀⢰⠊⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠀⢘⠀⠀⠠⡤⠤⠤⠤⠤⠤⢤⣄⠀⠀⠀⡠⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⢲⡄
⠀⠀⠀⠀⠀⠈⡇⠀⠀⡤⠤⠤⠤⠤⠤⣀⠀⠀⡠⠊⣠⠶⠖⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢃⠀⠀⣤⣤⣤⣤⣤⣤⣤⡴⠎⣠⠞⡡⠒⠶⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣀⣀⣀⣀⣀⣀⣤⠞⡡⠊⠀⠀⠀⠀⢀⠐⠂⠉⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⣤⣀⣤⣤⣤⣤⡤⠚⢠⠞⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⣤⠤⢤⠤⣤⠤⠞⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠰⠶⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢻⣚⠛⠛⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⣏⣉⣉⣉⣓⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⣄⣀⣀⣀⠑⢆⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠹⣤⣤⣌⠳⣄⠑⢄⠀⠀⠀⣎⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠘⣄⣈⠳⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠈⢯⠳⣌⠳⢌⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠑⢌⠳⣌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⠊⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠣⡈⠓⠚⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠑⠦⣀⢀⠴⠋⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠈⠁⠀⢀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⡠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⣶⣿⣿⣿⣿⣿⠟⢛⡛⠻⣿⣿⣿⣿⣿⣶⠀⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⣾⣿⣿⣷⡈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⣿⣿⣿⣿⡈⢿⣿⣿⡿⢁⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠺⣿⡿⠐⠛⠂⢿⣿⣿⣿⣿⣿⠆⣬⣥⠰⣿⣿⣿⣿⣿⡿⠐⠛⠂⢿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⡀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠦⠘⢿⣿⣿⡏⠘⠛⠛⠃⢹⣿⣿⡿⠃⠴⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢉⡀⢉⣉⣁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠞⡶⢄⡶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡤⢏⠉⣠⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢠⡤⢉⠤⡴⡩⠏⣀⠠⡾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡕⢠⠤⠤⢠⠄⢐⣈⠃⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⢀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣄⡈⠋⠴⠨⠛⠐⠒⠏⠠⣄⢎⡟⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡶⣧⡤⠃⡒⢠⠔⢲⣠⡦⠜⠒⡒⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⡖⠤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡜⠁⠀⠀⠉⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣴⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⣶⠀⠀⠸⣧⣼⠇⠀⠀⣶⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢷⠀⠀⠛⠾⠻⣄⠀⠀⢸⡇⠀⠀⣠⠟⠷⠛⠀⠀⣠⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠟⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠹⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢙⣷⠤⢤⣄⠀⠙⢦⡀⠀⠀⠀⣸⣧⣤⣼⣧⣤⣼⣇⠀⠀⠀⠀⣠⡾⠋⠀⣠⣤⣤⡞⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠙⢷⣄⠀⠙⣦⡶⠛⠉⠁⠀⠀⠀⠀⠉⠉⠛⢶⣤⡾⠋⠀⣠⠞⠁⠀⠈⠛⠞⠋
⠀⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠀⠀⠀⠙⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠞⠁⠀⠀⠀⠀⠀⠀⣤⢤⣄
⠀⠀⠀⠀⠀⠀⢿⣤⣾⡃⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣠⡶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢘⣷⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣷⠶⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠀⣴⠶⣦⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⣰⠞⠛⠛⠛⠛⠛⠛⠳⣆⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣴⠶⣦
⠀⠀⠀⠀⠀⠻⠶⠟⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢾⡷⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⢿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠸⠇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡿⠶⠶⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⣾⠛⢿⡅⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠾⠋⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⢨⡿⠛⣧
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣄⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⡀⠀⢀⡴⠋⠀⣠⡾⠛⠷⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⠾⠻⣄⠀⠙⢷⣄⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡼⠛⠛⠋⠀⣠⡾⠋⠀⠀⠀⠀⢹⡟⠛⢻⡟⠛⢻⡏⠀⠀⠀⠈⠳⣄⠀⠙⠓⠒⢿⣅⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣆⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣴⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠋⠀⠀⣤⢶⣴⠋⠀⠀⢸⡇⠀⠀⠙⣦⡶⣤⠀⠀⢷⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⡿⠀⠀⢰⡟⢻⡆⠀⠀⠿⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⠿⢿⣷⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⡿⠿⠿⠛⠋⠉⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣦⡀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠈⠻⣿⣿⣦⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠈⠿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣦⣄⡀⣀⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣷⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢳⣰⡏⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠋⠄⠸⠿⠿⠿⠛⠙⠛⠛⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣆⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⠿⡃⢸⣿⣿⣿⠿⠿⠿⠿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡈⠈⣤⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣴⡇⢠⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠂⠁⢂⠘⠛⠛⠛⠉⠉⠉⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢧⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢜⣛⠅⢸⣻⣿⣿⠛⠛⠛⠛⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠋⠉⢀⣠⣾⣶⣄⡀⠉⠙⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⣶⣯⣾⣿⣿⣿⣿⣷⣦⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢰⣟⣿⠿⣿⡝⠛⠻⡿⣿⡄⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⣿⣭⡉⣻⡿⠋⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣁⡀⠀⢀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡤⠶⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠛⢿⣿⠀⢀⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣠⣴⣖⢿⣿⣿⣿⡆⢀⡿⣷⣏⢠⠟⣛⡲⣦⣤⣀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢠⡞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⠟⣄⠈⢛⣽⣿⡿⣷⡄⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡟⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣩⢿⣤⣼⣭⣿⣿⣿⣷⠸⣿⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠙⠳⠞⢚⣿⠛⠛⠛⢻⣿⠀⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠿⣿⠁⠀⠀⠀⢀⣒⣂⣿⣿⣶⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢾⣿⣶⣿⣦⣤⣴⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠋⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⠉⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠀⠀⠀⠀⣀⡀⠀⠐⠁⣀⣈⡠⡤⠶⠥⠚⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢉⣹⣋⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⡠⠊⠉⠀⡼⠁⠀⢈⠆⡷⠖⠒⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠧⡠⢤⠞⠙⠓⠒⠛⠚⠧⢤⡀⠒⠠⠀⠒⠠⡁⢶⣀⡂⠤⠬⠍⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠒⢏⣀⡀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⣄⢀⠀⠀⡀⠍⠀⠀⡀⠀⠀⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠰⠁⠀⠀⠀⠃⠀⠉⣹⡖⢒⡒⢠⣖⢚⡛⠲⠦⢄⣂⢭⣀⣒⠢⠭⡅⠹⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⣀⠀⠀⠀⠀⠀⠀⢰⠦⠬⠃⠀⢀⠇⠀⠀⠀⠈⠀⢀⡴⢉⠁⣿⡏⠹⠼⠁⢹⣶⣤⣤⡈⠁⠀⠀⠀⠀⠈⡦⠤⠄⣀⡀
⢹⡿⣭⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⢢⣤⠀⠀⠈⠒⠒⠣⢄⡜⠀⠀⠀⠀⡷⠖⠉⠀⢸⠀⣿⡇⠀⠀⠀⣸⣿⠀⢸⡿⠀⠀⠀⣤⣀⠀⠇⠀⠀⠀⠙⡇
⠈⣿⠷⣿⣷⣦⢄⡀⣀⣀⣠⢤⣴⠶⢮⣛⠯⣻⠆⠀⠀⠀⠀⠀⢰⠁⢀⠠⡴⠶⠁⠀⠀⢠⡎⢸⣿⣧⣤⣶⣶⣿⣿⠀⣼⠇⡄⢸⠙⠛⠈⣠⠀⠀⠀⠀⢀⠁
⠀⢻⢔⠽⣿⣝⠑⢫⣉⡢⠼⠓⠂⠉⠀⠀⠀⢘⡇⠀⠀⠀⠀⢀⠃⠀⢀⠜⠁⠀⠀⠀⠶⣡⠁⣾⣿⣿⣿⣿⣿⣿⣿⢀⣿⢠⢠⠺⡄⠀⠀⢙⣤⠀⠀⠀⡜
⠀⢸⡗⠦⣦⢝⣳⠜⢢⡄⠀⠠⢄⡀⠠⠤⣀⣻⠀⠀⠀⢀⣀⡎⢀⠔⠁⠀⠀⠀⠀⠀⣠⡞⢸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇⠆⡌⠀⠓⢒⣋⡅⠀⠀⠀⢠⠃
⠀⠀⣇⡈⠀⠝⢿⣛⡴⢶⠛⠻⢟⣛⠛⠋⢭⡿⠀⠀⠀⢹⠟⠴⣿⠄⠀⠀⠀⠀⠘⠊⣰⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⣇⣀⣀⣈⡅⢿⠀⠀⣠⠃
⠀⠀⣯⢻⢮⣔⣽⣯⠑⠒⠛⠉⠀⠀⠈⠉⢻⡇⠀⢀⠤⢿⠂⢴⠁⢀⡀⠀⠀⠀⠀⢠⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡷⠛⠁
⠀⠀⣟⠡⡳⢊⣛⡲⠤⠄⠒⠢⠤⠬⣤⣀⣿⡇⢀⡟⡧⡇⠀⣿⠀⡸⠀⠉⠒⠂⠤⠧⢈⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⣉⣉⠁⠈⠁
⠀⢈⡷⣮⣮⢥⡿⠿⠛⠛⡛⠛⠒⠒⠶⠴⣿⠀⡸⣤⡽⣤⡤⢭⡶⠥⠤⠤⠔⠊⠙⢦⣀⠙⠶⢦⣬⣉⣙⡛⣿⡿⠿⠾⢄⠀⡠⠊⠀⠀⠉⠒⠠⠄⣀
⠀⢸⢟⠗⡻⣷⠮⣍⣓⠒⠤⠉⠉⣉⣈⠀⣿⡀⠁⣈⣵⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⣆⡀⢋⠉⠁⠀⠀⠀⠀⠀⠫⡀⠀⢀⡀⣀⠔⠓⠂⠬⣀
⠀⣿⡭⡫⢺⠶⢿⡶⠾⠟⠛⠓⣂⣀⠌⠭⢿⣇⠼⠿⣦⣞⠳⣄⣀⣀⣀⡤⠤⠴⠂⣺⡋⠠⢚⡅⠈⠉⢣⡀⠀⠀⠀⠀⠀⠀⠙⢶⡁⠀⠉⠑⠒⠦⠤⣄⣉⠒⢠
⠀⠀⠀⠀⠻⠛⠲⠜⠛⢛⣛⡉⠥⠖⠓⠚⠋⠉⠑⢤⡀⠙⠯⣢⣄⣉⣑⣦⣤⣀⡴⣍⠂⠉⠉⠉⢁⠟⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⣠⡚⠕⠊
⠀⠀⠀⠀⠀⠀⠈⢫⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠉⠁⠀⠀⠀⠀⠀⣉⡵⢂⡴⠁⠀⠀⠰⠀⠑⢦⣀⣀⣠⡤⠀⠂⠂⠉⡀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣀⠀⠀⠀⣀⣀⡠⠴⢒⠩⠒⠙⠢⣀⣠⣤⠴⢖⡒⠉⢀⠔⠉⠉⠙⠲⣖⠃⠀⠀⢀⡨⣖⠉⠈⠁⠐⠛⠁⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠙⢏⠉⢉⡡⠐⠛⠀⡀⠀⠀⠀⠈⢁⡠⠔⠚⠉⠛⠁⠀⠀⠀⣠⠊⠈⠲⡤⠚⠁⠀⠀⠈⣁⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠳⣤⠔⠊⠉⠁⠒⠒⠤⠄⣀⠀⠀⡔⠣⡀⠀⠀⢀⣀⠠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠙⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣄⡀⠀⣀⠀⢹⠁⠀⠀⢠⣚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡇⠸⣭⠃⢸⠀⠀⡴⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀⣇⡠⠷⠴⠾⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠁⠀⠀⣠⠞⠁⢀⣤⠶⠶⣦⡀⠈⠳⣄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⣶⠁⠀⠀⣾⠁⠀⠀⠈⣷⠀⠀⠈⢏⠉⠙⠶⠃⢠⠖⡄
⠀⠀⠀⠀⠀⠀⠠⣏⡷⠤⠤⠤⠴⡇⠀⠀⣰⣿⣶⣶⣶⣶⣿⣦⠀⠀⢸⠒⠒⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⡤⡇⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⠀⠀⢸⠶⠶⠶⠶⠶⣎⡱
⠀⠀⠀⠀⠀⠀⢮⡹⠉⠀⡤⢄⣀⣹⡄⠀⢿⣿⣿⣷⣼⣿⣿⡿⠀⢠⠯⠤⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠘⠦⣈⠉⠉⠉⠉⠉⠉⣁⡴⠃⠀⠀⠀⣠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠓⡖⠒⣶⠉⢹⠀⠀⠀⠀⠀⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⡇⢠⠾⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠏⠀⠀⣴⢳⡈⠙⠁⢸⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠓⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢀⡠⠀⠂⠉⠐⠐⠀⠉⠛⠻⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠂⢐⣶⡶⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢬⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⢀⡖⠈⠉⣍⢳⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣄⢁⡀⠤⡀
⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠺⠶⠶⠀⠠⠘⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⣄⡀⠀⠀⠀⠠⠆⠠⠀⠄⣀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣓⢾⡧⠀⠀⠀⠀⣺⣿⣿⣿⡿⢿⣿⣿⡀⠀⠀⠀⡀⣀⣀⣭⣭⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⢠⠤⠤⠤⡇⠀⠀⠀⠁⠭⢾⣷⠶⠷⠛⣛⢹⠶⠠⠀⠉⠉⢛⣭⡶⠯⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢔⣀⡀⠈⠧⠀⠢⠤⠀⠀⠀⠤⢄⣀⣶⣶⣿⡃⠀⢈⠀⠤⠒⣒⠚⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠍⠉⢅⣲⣇⠀⠀⠀⠀⠩⣔⣟⣻⣯⠽⣾⣿⣤⠀⣪⢠⡀⢠⠄⠬⠔⠓⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠛⠛⠛⠛⠛⠚⠰⠆⢰⣿⣿⣿⣛⠛⠉⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣤⣤⣠⣤⣤⣼⣿⣿⣿⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⢀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷⡀⠀⠀⠀⡀⠀⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⠀⠿⠟⠛⠓⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠛⠿⠿⠂⠙⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣤⣴⣶⡤⢸⡏⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⡇⢠⣤⣴⣶⣤⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⡧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢹⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠙⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣤⠠⣾⣷⣶⠆⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⠴⢶⣷⠀⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠁⠀⠀⠀⠀⠀⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁






⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⢐⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⢠⣶⢖⣶⡶⠶⠶⠋⠰⢯⠗⠈⠳⢶⣶⣖⣶⣲⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣿⡽⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣫⣿⠁⣠⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢟⣽⠀⣿⢼⣹⠆⡏⠀⠀⠉⠉⠉⠛⠀⠀⢸⡵⡳⡧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡟⠊⠉⠓⡇⠀⠘⠋⠉⠉⠁⠀⠀⢸⣞⢟⡷
⠀⠀⠀⠀⠀⠀⠀⣼⣣⣿⠀⠙⠛⠋⠉⢁⡀⠐⠛⠛⠛⠓⠀⠀⢸⣫⢞⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡫⣿⠀⣰⢶⣲⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢟⡿⠀⠙⠚⠋⠐⠒⠒⠒⠒⠒⠒⠒⠒⠀⢸⢟⣼⡇
⠀⠀⠀⠀⠀⠀⠀⡷⣫⡇⠀⢸⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢟⡇⠀⠈⠉⢩⠄⠛⠛⠛⠛⠛⠒⠂⠀⠀⣿⣿⢿⠇⠀⠀⠀⠀⢀⣤⣶⠆
⠀⠀⠀⠀⠀⠀⢰⡿⢻⡇⠀⣾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣿⠀⠀⠀⣀⡴⠋⣠⡏
⠀⠀⠀⠀⠀⠀⢸⡷⣻⠁⠀⢉⡉⠁⢉⡿⠟⠓⠒⠒⠒⠒⠀⠀⣿⡫⢿⢀⣠⠞⢁⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⢸⡟⣽⠀⠀⣿⣽⡶⣋⣀⣀⣀⣀⣀⣀⠀⠀⠀⣟⣴⡿⠋⣠⠶⠟⠋
⠀⠀⠀⠀⠀⠀⢸⣟⢾⣤⣤⣬⣭⣤⣄⣉⣉⣉⣉⣉⣉⣀⣀⣠⠟⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢸⣧⣫⢎⣞⡵⣱⣫⣫⢞⡝⡵⣱⣣⣫⣯⠞⣁⣴⣋⡿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡧⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣲⠶⠛⠉⠉⣉⣈⠭⢟⣠⡀
⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⡤⠖⠋⠀⢰⡇⢀⡠⠔⠊⣡⠴⢒⣉⣼⠃
⠀⠀⠀⠖⢻⡷⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⡤⠤⣤⣤⣤⣤⣤⣤⣤⠴⠯⠬⠷⣖⣋⣻⡏⠉⣉⣉⠽⠋⡡⠴⠚⣉⠴⠊⠁⡗⡏
⠀⠀⢰⠶⠟⠒⠒⠒⠚⠋⠉⠍⠍⠀⠀⠀⣀⠀⣐⣂⣀⣀⣀⡀⢒⣀⣀⣀⣐⣒⡒⠒⠀⠤⠭⠭⠭⣶⡡⠔⢂⠩⢛⠨⢙⡩⠷⢇⣀⣀
⠀⠀⢸⡄⠀⢀⢀⣀⣀⠤⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠬⠭⠭⢉⣉⣙⣻⡂⢩⣰⠼⠒⠊⠁⠀⠀⠀⠀⠈⣉⣳⡦
⠀⠀⣼⠀⣀⣉⣁⣤⠤⠤⠤⠶⠶⠒⠒⠒⢒⣛⠛⣛⣛⣒⣒⠒⠒⠒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠴⠶⠾⠗⠉⠀⠀⠀⠀⣀⣤⣤⠒⠚⠉⠁
⠀⠀⠉⡠⠋⠁⣀⣀⣀⣀⣠⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠬⠥⠭⠭⠽⢶⣶⣶⣦⣤⢤⣄⣀⣀⡀⠀⠀⠀⠀⣀⠤⠖⠩⢑⡒⠊⣻
⠀⠀⠚⠉⠉⣩⠉⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠐⠒⠒⠒⠒⠒⠛⠂⠀⠀⠀⠉⠉⢹⡲⠭⢀⣒⠤⠍⠀⣒⣀⡽
⠀⠀⠀⠒⠂⡇⠀⣀⣀⣀⣀⠀⠈⠉⠉⠉⠉⣉⣁⣒⣛⣛⣒⣒⣒⣒⣒⣒⣶⠦⣤⣤⣤⣭⠍⢉⡀⣼⠐⣊⡡⠴⠒⠊⡉⠉⠀⠠
⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠭⠛⠉⠉⠉⠩⠭⠍⠁⠈⢨⠔⠂⠀⣈⠠⠀⠀⠀⡇
⠀⡰⠁⠀⠤⠤⠐⠒⠒⠒⢈⣉⡉⣉⣉⣉⣉⠉⠉⠭⠷⠶⠶⠶⠶⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠄⠒⠀⠠⢀⣰⣇
⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⠤⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⢸⠀⠀⠐⠚⠣⠤⠤⣼⣄⣱⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠒⢺⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠙⠛⠛⠋⠙⠋⠡⠤⠤⠤⠤⢀⣀⣀⡀⠀⠈⠉⠉⠉⡝⠀⢸⠀⢈⡀⠄⠀⠂⢁⡏
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠬⠭⢍⣉⣙⣛⣁⣀⣼⢈⠠⠀⠀⠈⢁⣰⠇
⠀⠀⠀⠀⠄⠚⠑⠠⡤⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣈⣙⣛⣛⣁⣒⠒⠒⠒⠢⠤⠤⠄⣇⢀⣀⠤⣔⡻⠿⡟
⠀⠀⠀⠀⠀⠀⢹⢎⡀⢤⡤⠄⠒⠒⠒⣊⣩⠭⠽⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⡉⢉⣙⠛⣋⠥⢒⣋⡁⠄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠉⠓⠀⠈⠁⠀⠀⠀⠀⠀⢠⣤⡤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⣈⡥⠤⠖⣂⢹⠇
⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⠤⠤⠄⠰⠶⠶⠶⠶⠶⠒⠐⠲⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⠁⠀⠐⠘⠋⠉⡟⠀⠀⠀⡀
⠀⠀⠀⢀⡠⠀⠀⢳⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⣶⡶⠶⠶⢶⣶⣤⣤⣄⣀⡀⠀⣽⠀⣀⣡⣤⣤⣶⡧⢀⡴⠊⡀
⠀⠀⣉⠤⢒⣩⠔⢊⡹⠗⢒⡲⠖⠒⣶⠶⠶⢶⡶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⠶⠶⠦⠶⠤⣤⠤⢤⡿⠭⢗⠟⢉⠵⣪⠔⣉⠴⢊
⠀⢀⠥⠒⣉⠤⠚⢡⠔⠊⠉⠀⠔⠉⠀⠔⠊⠁⠀⠂⠁⠠⠐⠉⠀⠠⠐⠁⠠⠒⠁⣀⠔⠊⣠⠖⠉⠠⠊⠡⠚⠵⠊⡤⠊⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠚⣩⡤⠶⠦⣬⡙⠂⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⢀⡀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠁⠴⢚⠲⠄⠁⠀⠀⠀⠀⠀⢀⠂⠀⠋⣹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣇⣀⣠⣿⡇⠀⠀⠀⢀⠀⠀⠤⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠽⠿⠿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠼⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠽⠿⠿⠀⠒⠐⠃⠐⠂⠿⠿⠿


⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣒⣒⠴⠶⣂⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⣲⠁⢈⠆⢘⣒⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⣍⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀⡢
⠀⠀⠀⠼⠷⠤⢤⡾⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣤⡆⠀⠀⠀⠀⠀⢸⣿⣟⣉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠪⠭⣕
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠟⠿⠛⠛⠃⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⣶⣤⠚⣿⠳⣴⣶⠀⠀⠀⠀⣀⣤⣶⣶⣄⣀⠀⣤⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⣶⠖⣿⣿⡿⢶⡶⠀⠀⠀⠘⠿⠿⢻⠟⠿⠟⠈⠛⠛⢻⡟⠛⠛⠀⠀⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠸⠛⣿⣧⣠⣄⣀
⠀⠀⠀⠀⢠⣤⣭⣄⡄⡀⠀⠀⠀⠀⠀⢀⣐⢴⠀⠀⠀⠀⠀⣀⣲⠀⠀⠀⠀⠀⢸⣦⣍⣉⣵⣿⠀⠀⠀⠀⠀⠀⢸⡟⠿⠿⢿⣿
⠀⠀⠀⠄⢤⢤⡤⡤⡌⠄⠀⠀⠀⠀⠀⠀⠀⡭⠀⠀⠀⠀⠀⠁⠭⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⡩⡀⠀⠀⠀⠀⠀⠾⡷⠤⠤⢬⣷⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⡟⠙⢂⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣙⢒⠂⣾⣿⠈⢳⠀⠀⠀⠀⠀⣖⢂⣐⠁⢤⠤⠐⢂⡁⠇⠀⠀⠀⠀⢸⠐⠩⠃⡇
⠀⠀⢀⣴⣆⣿⣿⣿⣿⣴⣦⠀⠀⠀⠀⠀⠀⠲⣒⣆⢇⠀⣿⡟⠀⠀⠀⠀⠀⢄⠀⡶⠔⠒⠀⢀⠁⡦⠆⠀⠀⠀⠀⣸⢖⠤⡖⠇
⠀⠀⠀⠙⠁⠈⠙⠋⠁⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠈⠒⠚
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⡶⠟⢋⣡⣉⠻⠷⣦⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡏⢉⣉⣉⣉⣉⣉⣤⣴⠾⠛⠉⠙⠻⢶⣤⣬⣉⣉⣉⣉⣉⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⢸⡇⠀⠀⠀⠀⠀⣠⣶⠿⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⣴⣾⣿⣶⣶⣶⣶⣶⣾⣿⣶⡄⠀⠀⠀⣿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⡇⠀⠀⠀⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣧⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢻⣆⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇⠀⢀⣼⠃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢻⣆⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⢀⣾⠃⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠛⢷⣄⠀⠀⠀⠀⠀⢀⣴⠞⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠙⠷⣦⣀⣠⡶⠟⢁⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣌⠙⢉⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⣰⣿⠋⠉⠉⢻⣷⡀⠀⠀⠀⠐⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠨⠂⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠪⠂⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⠀⠂⣀⣀⢀⣴⣿⣷⣤⣤⣤⣴⣿⣷⣄⣀⣀⡀⠂⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠕⣈⡀⠚⢂⣿⣿⣿⣿⠉⢹⣿⣿⣿⣇⠘⠃⡈⠐⠅⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠔⣤⡐⣿⣿⣿⣿⠃⢻⣿⣿⣿⣗⣠⡔⠄⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠒⠒⠒⠀⠒⣿⣿⣿⣿⣤⣼⣿⣿⣿⡗⠒⠒⠒⠒⠢⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⡞⠙⠢⣀⠀⠀⢠⠏⠱⣤⠎⠈⠙⠲⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠑⢦⣸⠁⠀⠀⠈⠳⢤⡏⠀⠀⠈⠑⠦⣀⠀⠀⠀⠈⣉⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠂⠠⡉⠳⣄⡀⠀⠀⠀⠉⣻⠂⠀⠀⠀⣨⠗⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠢⣈⠳⢄⡉⢓⡆⠀⢰⡟⠀⠀⠀⢰⠃⠀⠀⡾⣄⣀⠀⢀⣀⣀⡤⠔⣄
⠀⠀⠀⠀⠀⢠⣖⠒⠒⠒⠳⣄⠐⢄⡑⠢⡀⢸⡶⠀⠈⣧⠀⠀⠀⣿⠀⠀⢸⣇⠀⠉⠉⠉⠁⠀⠀⠀⠈⠑⠢⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣶⣄⣀⠈⠓⢤⣈⠓⠄⠸⣧⡅⠀⠈⠳⣄⠀⢻⡀⠀⠈⣏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢮⣟⣿⣿⣦⣄⠈⠙⠲⣄⡈⠳⣄⣀⠀⠙⢦⣀⠱⣄⡀⠘⢎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣤⣶⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢝⣿⡿⣿⣦⣄⠀⠉⠙⠚⠻⠿⣶⣤⣬⣟⣶⣿⣶⣦⣽⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⡶⠶⠾⢿⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⡺⣷⣝⢷⣤⣖⠭⢭⣿⣿⣿⡿⣿⡿⢿⣿⣿⡿⠷⠶⢟⣛⡶⠾⠿⠛⠛⠚⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢽⢵⣛⣚⢩⣭⣦⡶⠮⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠋⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠘⢦⠞⠀⠀⠀⠀⢰⠖⢦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢲⡀⠀⠀⠀⠀⠰⡶⠀⠀⠉⠀⠀⠀⢸⠀⠀⢠⡦⠀⠘⢶⠋⠀⠘⡟⠀⠀⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⢄⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⡔⠁⠀⠀⠹⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣶⠶⠶⠷⠶⠶⠶⠾⠶⠶⠾⠶⠶⠶⠷⠶⠶⠾⠶⠶⢷⣆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠒⠒⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠵⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢸⣯⠤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣷⠤⠤⠴⡦⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢿⣀⡿⠒⠒⠒⠒⢺⣿⠀⠀⠀⠀⢰⡟⠛⠛⠉⢉⠉⠙⠛⠛⣷⠀⠀⠀⠀⢸⣿⠒⠒⠒⠒⠺⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⠇⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⢀⠤⠤⢖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠀⠀⢘⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣈⡁⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⣿⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢸⣯⣀⣀⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠾⠖⠒⠊⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠈⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⠛⠛⡟⠛⠛⢻⠛⢻⠛⠛⠟⠛⢻⠛⠛⡟⠛⠛⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢀⡼⠀⠀⣇⠀⠀⡸⠀⢸⠀⢸⡇⠀⢸⠀⠀⠑⡄⠀⠀⠀⠀⣠⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠟⠒⠒⠒⠋⠀⠀⠈⠊⠀⣸⠀⠀⢸⠀⠀⠀⠀⠻⠂⠀⠀⣥⠀⠀⠀⠀⠻⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢰⡋⣳⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⡠⠒⠉⠙⠛⠉⠙⠒⢦⡀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠉⠐⠂⠶⠈⣀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠈⠉⠐⠲⠤⢀
⠀⠀⠀⡠⠚⠠⢐⣀⡞⠁⠀⡀⠤⠊⢡⡄⠀⠀⢹⡿⡎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⠴⢛⠢⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣴⣶⡂
⠀⢀⣼⠀⠀⢀⠚⠋⠐⠒⠀⠀⠀⡀⢉⣦⠀⠀⣸⣿⡧⢀⢀⠠⣂⣵⣶⣾⡄⣀⢔⠩⣶⠿⠟⣁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⣿⣿⣯⡥⠔
⠈⠀⢬⣑⠈⠁⠀⠀⠀⠙⠲⠒⠋⠁⠈⠉⠂⠰⢿⣿⣷⣏⣵⣾⣿⢿⣿⣿⢻⣫⠵⣾⣶⣿⣟⡍⢿⣦⣤⣴⣶⣿⣿⣿⣿⣟⣽⣿⣿⣿⠗⠊
⠀⠀⢚⠾⠷⣦⣄⣀⠀⠀⠀⠀⣀⣠⢴⣶⠶⠴⠒⣘⡿⣿⣿⢿⣧⠸⡿⠿⠾⣛⣲⣋⣫⣭⡖⠌⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠟⠛⠛⠛
⠀⠀⠀⠠⣒⣲⣦⣉⠝⠒⠦⣝⡫⠶⡅⣴⣢⠾⢛⣋⣐⣼⣤⠬⠽⠿⠷⠖⠛⠛⠛⠛⠉
⠀⠀⠀⠸⠶⠾⢭⣟⣢⠤⣄⠀⠚⣳⢞⡩⢒⡽⠿⣿⠿⠛
⠀⠀⠠⣠⡍⢙⡛⠒⠚⠉⠓⠦⠄⠖⠁⢈⣡⡾⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠉⠁