Wool Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣠⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠞⠓⠘⠛⠃⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠰⠃⠀⠸⡄⣶⠘⡂⣀⣀⣄⢁⠤⠔⠒⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⡈⢀⠹⣿⡿⠋⠀⠀⠀⠀⠀⠈⠉⢀⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠊⢈⠣⠍⡀⢀⠀⠐⠁⡀⡤⠖⠊⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌⠈⣔⣾⠊⠀⡀⠈⠀⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠑⢄⡀⣤⡀⣀⠀⠂⠿⠋⡠⢊⢖⠔⡻⠃⠊⠋⡐⠶⠀⠰⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠊⢰⠰⠁⠀⢡⢃⠄⢊⡄⡀⢰⢾⠇⠂⠐⠀⠀⠆⡀⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠃⠆⠀⡽⠀⠀⡜⠃⠀⠀⠀⠀⠀⠐⡔⠂⠁⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠐⣤⢴⣽⣤⡀⠀⠀⠀⠀⠀⠀⠈⣂⢐⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠚⡀⠀⡄⣿⢶⣌⠉⠁⠃⠀⠀⠀⠀⠀⠀⢨⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠐⠀⠀⠉⠓⠦⠀⠀⢶⣤⠀⠀⠈⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠋⠄⡀⠈⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡀⠀⠀⣠⠟⠁⢲⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣐⣚⢥⠁⠀⠃

⠀⠀⠀⠀⣀⠠⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡀⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠒⠲⠄⠒⠀⠐⠒⠦⠀⡀
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡆
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠐
⠀⠑⡄
⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠒⠙⠂⠒⠒⠒⠢⠤⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠤⠀⠀⠀⠂⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡆⢀⠀⠀⠀⠁⡇⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⢢⠞⠉⠠⠶⣴⢄⠀⡅⢀⠐⢠⡇⢠⡄⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠚⠁⠈⢉⡰⠚⠀⠠⠅⠂⠀⠉⠐⠢⠆⢳⡟⠁⠂⠈⠘⠋⠠⢀⠔⠀⠀⠀⠀⠈⠰⠄
⠀⠀⠀⢀⣀⠀⣠⠤⠚⠓⠲⢤⣀⠀⠀⢨⠀⠢⠄⡀⠀⡇⠀⠀⠀⠄⢀⢠⡏⣀⡀⠀⠀⠀⠳⠉⠈⢂
⠀⠀⠀⠈⢭⡞⢁⠀⠀⠀⠀⡀⡘⢣⡀⡀⠀⠀⠀⠋⠺⡇⠐⢀⠀⠀⠀⠀⠀⠓⣧⡀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠈⠀⠴⠂⠀⠀⠉⢱⢇⢀⣧⠈⠒⠆⠀⡸⢳⣟⠀⠀⠀⠀⠀⠀⠃⠀⠸⣗⢦⡴⠆⠀⢂⠎
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣠⣿⣿⠏⣹⠠⣼⣀⡴⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣁⣉⠷⠔⠁
⠀⠀⠀⠀⠈⠠⡀⢀⠀⢺⠟⠋⢁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⠴
⠀⠀⠀⠀⠀⠀⠈⠑⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣀⠂
⠀⠀⠀⢰⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⢴⠴⠀⠀⠐⠁⠀⠂⠀⠂
⠀⠀⠀⢀⠀⠀⠈⠐⠠⠀⠀⢄⠄⠀⠈⠀⠀⠀⠀⠈⠀⠁⢄⠁⠀⠀⠈
⠀⠀⠀⠈⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄⠀⠂
⠀⠀⠀⠀⠐⠈⠢⣠⠎⠀⠀⣠⡴⠆⠀⠀⠀⠀⠶⠦⣄⠀⠀⠀⠀⢉⠄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠁⢾⣶⠀⠀⠀⠀⠀⣡⡄⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⡀⠆⠐⠿⡧⠄⠤⠴⠀⠚⠛⠀⠠⢀⠀⠀⠈⢤⡤⠀⠀⠀⠀⠄⡀⠌
⠀⠀⠀⠀⠴⢟⡄⢀⠔⠀⠀⠀⠀⠀⠁⠀⢀⠐⠁⠀⠀⠀⠀⠀⣯⠀⠬⠙⠁⠰
⠀⠀⠀⠀⠀⠉⠁⠘⠂⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⢀⡀⠐⠃⢀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⢄⠈⠋⠋⠉⠀⡘⠒⠁⠈⠐⠐⠃⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⡔⠀⢸⣄⠁⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠡⡤⠊⠐⡩⢊⢓⠆⠀⠈⠉⠛⠋⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⠀⠀⠀⠀⡀⠀⡜⠀⠀⢍⠀⣀⠀⣠⡠⠺⠀⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⠳⡀⠀⠀⠀⠁⢸⠀⠠⢨⠀⢀⠜⠡⠀⠀⠈⠀⠀⠏⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⢀⡠⠚⡅⠀⠀⠀⢠⣄⢢⠀⡘⣢⠦⠀⠤⣈⠆⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠤⢤⠟⠀⢿⣷⡀⠉⡀⠄⢀⡄⠀⠁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⠀⠀⠀⡶⠁⠈⢻⠒⠨⠤⠮⠤⠄⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣒⣈⣠⡤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠉⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣼⣯⣀⡀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠻⣯⡁⢰⡟⠻⣦⡀⢨⡿⠛⠷⣤⣠⡶⠟⠉⠙⠻⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣹⣇⣤⣬⣿⣾⡷⠶⠾⠿⠾⠷⠶⠶⢾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣴⠶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⣀⣀⣤⣤⣤⡶⠶⠶⣶⠶⠶⣶⡶⠶⠶⢶⣶⢶⣤⣤⣤⣸⡇
⠀⠀⠀⠀⠀⢀⣠⡶⠟⠙⣿⠉⠉⠀⢿⡀⠀⠀⠀⣿⠀⠀⠘⣷⡀⠀⠀⢻⡆⠀⠀⢈⣿⠁
⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠘⣧⡀⠀⢸⡇⠀⠀⠀⢿⡄⠀⠀⠘⣷⡀⠀⠀⢿⡄⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢻⣄⡘⣷⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⢈⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠈⠻⢿⣄⣀⠀⠈⣿⠀⠀⠀⠀⣹⣧⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠷⠶⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠒⣾⠟⢻⣿⠟⠛⢻⡿⠶⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡟⠉⡿⠃⠀⣼⠁⠀⢸⡇⣀⣠⣾⡶⠶⠶⠾⠿⠿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⣴⠏⠀⢰⡇⢀⣰⣧⡴⠶⠛⠋⠉⠁⢀⣀⣀⣠⣤⣤⣤⣤⣬⣝⣛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣽⠃⠀⣼⠃⠀⣀⡼⠷⠛⠉⠀⢀⣀⡤⠴⠶⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⡟⠀⢠⣿⡴⠞⠉⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⠶⠶⠶⠶⠶⢦⣤⣤⣙⣷⡄
⠀⠀⠀⠀⠀⢀⡴⢻⡟⠀⠀⡇⠀⢸⡏⠀⠀⢀⡴⠞⠉⠀⠀⠀⢀⣀⠤⠖⠚⠛⠋⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠙⠛⠿⣦
⠀⠀⠀⠀⢠⣾⠃⢸⡇⠀⠀⡇⠀⢸⡇⣠⠾⠋⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠶⢤⣄⡀⠙⣧
⠀⠀⠀⢠⢿⡿⠀⢸⡇⠀⠀⡇⠀⠸⣿⠁⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢾⣧
⠀⠀⠀⡿⢸⡇⠀⢸⡇⠀⠀⣷⠀⠀⣿⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣀⠀⢹⡆
⠀⠀⢸⡇⢸⡇⠀⠀⣿⠀⠀⢻⡄⠀⠸⣧⡴⠋⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⢀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿
⠀⠀⣼⡇⢸⣇⠀⠀⢹⡆⠀⠘⣷⠀⠀⠹⣇⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠈⢻
⠀⠀⣿⡇⠀⣿⠀⠀⠈⣷⠀⠀⠸⣇⠀⠀⢻⡄⢠⡞⠁⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⣬
⠀⠀⣿⣧⠀⢹⣇⠀⠀⠸⣆⠀⠀⠹⣆⠀⠀⢻⡟⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⢤⣤⣤⣀⣀⠀⠘
⠀⠀⣿⢸⡆⠀⢻⡄⠀⠀⠹⣆⠀⠀⢻⡄⠀⠀⢻⡄⢀⡞⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⣀⣤⣴⠞⠛⠋⠻⣯⠀⠀⠙⢦⣄⡈⠉⠙⠛⢾
⠀⠀⣿⠈⣧⠀⠈⢿⡀⠀⠀⠘⣧⠀⠈⢿⡄⠀⠀⢻⡏⠀⠀⠀⣠⡶⠋⠀⠀⠀⢀⣴⡞⠉⠈⠹⣆⠀⠀⠀⠈⢷⣄⠀⠀⠈⠙⠓⠶⠶⣾
⠀⠀⢹⡆⢹⡆⠀⠈⢳⡄⠀⠀⠈⢷⡀⠈⢷⡀⠀⠀⠹⣄⢀⣴⠋⠀⠀⠀⢀⡴⠋⠀⢻⡀⠀⠀⠙⢧⡀⠀⠀⠀⠈⠳⠶⢤⣤⣤⣤⣤⣼
⠀⠀⠈⣷⠀⢿⡄⠀⠀⠹⣆⠀⠀⠘⣷⡀⠈⢷⡄⠀⠀⠘⢿⠁⠀⠀⢀⣴⣏⠀⠀⠀⠀⢳⡄⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⢹⡆⠈⢿⡄⠀⠀⠘⢧⡀⠀⠘⣷⡀⠀⠻⣦⡀⠀⠈⢳⣄⣠⡞⠉⠹⣆⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠉⠛⠶⠶⢦⣤⣤⣴⣶⣾⠃
⠀⠀⠀⠀⢿⡀⠀⢻⡄⠀⠀⠈⢳⡄⠀⠘⣷⡀⠀⠈⠻⣄⠀⠀⠙⢿⡀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠈⢷⡄⠀⠙⣦⠀⠀⠀⠹⣄⠀⠈⢷⡄⠀⠀⠈⠳⣄⠀⠀⠙⢦⣄⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⠳⣄⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠈⠳⣦⡀⠀⠉⠛⢦⣄⣀⠀⠀⠉⠙⠛⠓⠶⠶⣶⣤⣶⣤⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠘⢷⣄⠀⠈⠳⣄⠀⠀⠙⢶⣄⡀⠀⠈⠛⢶⣄⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⣀⣀⣀⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⠙⢷⣄⠀⠈⠳⣄⠀⠀⠈⠙⠶⣤⡀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣿⣷⣄⡀⠈⠳⢦⣄⠀⠀⠈⠙⠷⣄⡀⠈⠙⠳⠶⠶⠶⣶⣶⣶⠞⠛⠁
⠀⠀⠀⠀⣀⣤⠞⠛⠿⠶⣦⣄⡀⠀⠀⠈⠉⠛⠛⠻⠶⣦⣌⣷⣦⣀⣀⠀⠈⠙⢶⣦⣤⣤⣴⡶⠛⠉
⠀⢀⣴⠞⠉⢀⣤⠶⠶⠶⣤⡈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣿⠻⣿⠋⠁⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠛⠛⠓⠶⣤⡀
⢠⠟⠁⣠⡾⠋⠀⠀⠀⠀⠀⠙⠶⣄⡈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣼⠀⠀⠀⣀⡤⠖⠋⠉⣀⣠⣤⣴⣶⣦⣤⣄⠀⠹⣆
⣼⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠈⠙⠲⣤⣀⠀⠀⠀⢀⣠⡴⢟⣡⡾⠋⣠⡴⠛⠁⢀⣤⠶⠋⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹
⣿⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣉⣛⣛⣋⣉⣥⠶⠛⣡⡴⠛⠉⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢉⣀⣴⠞⠉⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⣰
⢻⣄⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠁⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⣴⠏
⠀⠙⠷⣄⡈⠙⠳⠦⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠖⠛⠋⢉⣀⣤⠶⠛⠁⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠞⢋⣡⡴⠞⠁
⠀⠀⠀⠈⠛⠷⠶⠶⢤⣬⣅⣀⣀⣀⣀⣀⣤⣤⡤⠶⠞⠋⠉⠁⠀⢀⣠⠶⠚⠋⠉⠉⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⡴⠋⣁⣤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠂⠀⠐⠻⠿⣟⣛⣦⣝⠓⢯⣙⣛⣄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣐⡚⣻⣍⠻⣿⣷⣦⣤⡤⠾⠛⢉⣉⣻⣄⠻⣤⡼⢷⡈⠹⣽⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⢸⣿⠋⢹⣿⣆⠈⢷⣤⠼⠿⠡⠴⠒⠞⠉⠙⠛⠛⢷⡈⢳⣶⠷⣄⠘⣥⠴⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⣾⡇⠸⡟⠀⠿⠛⠛⣧⡀⣧⣤⣤⣶⠶⠖⠲⢶⣶⣾⠊⢛⣿⣄⠱⣦⢾⡄⠘⠋⠲⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠿⠿⡇⠀⠇⠀⣿⣿⠟⠉⣇⠈⢿⣿⣿⣷⣦⣠⣤⣟⣁⣴⣿⣿⠟⣤⠈⣏⣉⡄⠘⠷⣦⣌⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⣀⣠⣴⣿⡀⡇⠀⡿⠷⠖⠛⠻⣆⠈⣿⡏⣉⣉⣉⣉⢉⣉⣉⣉⣛⣚⣻⣄⠘⣟⣻⡄⠐⡶⠧⣝⣾⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⣷⣿⣯⠴⠛⠛⢿⡇⠠⣧⡶⠲⣾⠛⢻⡄⠈⣏⢙⡟⠉⢁⣾⣿⠟⠉⣽⣿⡍⢿⡄⠙⣿⣧⠀⢹⡆⣦⢬⣽⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢹⠋⣀⣤⢶⣾⠛⣇⠀⣟⡛⢶⡋⢰⠻⢿⡄⠘⣿⠁⢀⣿⣿⣋⢠⡾⠿⠿⠿⠲⢿⡄⢹⡿⡄⠈⣟⠛⠓⠛⣷⠀⢷⡀
⠀⠀⠀⠀⠀⠀⡀⢈⣽⠀⠘⣿⣿⣆⠜⢁⣼⣧⠐⡎⣗⠀⠙⢿⣷⣤⠷⠀⠹⣏⠈⡁⣈⣁⣀⣤⣤⣤⠄⡶⣾⣇⠘⡿⢷⠀⢹⡈⠀⠁⠉⡇⢸⡷⡄
⠀⠀⠀⠀⠀⠈⡁⢸⠿⢧⠀⠸⣿⣯⣠⣾⣿⣿⠄⡆⢹⣧⠴⠛⠁⣀⣴⣧⠀⠸⣏⠙⣉⣉⣤⣤⠆⠰⠋⠉⠀⢨⡁⢐⣸⡆⠘⢷⣶⠒⣿⣷⠘⡿⣧
⠀⠀⠀⠀⠀⢰⡆⠈⡷⢾⡆⠀⢷⢤⣤⣀⣀⣹⡆⢸⠀⣇⡠⠔⠛⠉⢉⣀⣅⠀⢻⡹⠋⠉⠀⣀⣀⣤⢦⠴⠶⢟⣧⠈⣿⣷⠀⢇⣻⣤⠿⡇⢠⣷⢿
⠀⠀⠀⠀⠀⢸⣷⠀⠹⣧⡻⡀⠈⢿⣧⠀⡸⠟⢣⢈⡇⠈⣦⣴⣓⠙⠫⠦⢼⡆⠀⣷⡶⠻⠿⠿⣿⣷⡓⣶⣤⣼⣿⡀⢴⣾⠀⢘⠋⣀⣴⣡⠾⢋⡼⡇
⠀⠀⠀⠀⠀⠀⠻⣆⠀⢿⠙⠳⣀⠀⢿⡋⢁⣤⣾⡀⢇⠀⢻⣴⠟⠻⢶⣄⡀⠱⡀⠈⢷⣦⣀⣀⠀⢈⣉⣭⠿⠟⢛⡇⠈⣶⠇⢸⡿⠗⠋⣡⣶⡏⢘⡇
⠀⠀⠀⠀⠈⢦⡀⠙⣇⠈⢿⣄⣸⣇⠈⢳⣟⠛⠛⣷⠘⣇⠘⣯⠤⣴⡿⢿⣛⡷⣿⠀⠘⡦⠀⠙⠛⢿⣁⣤⣤⣶⠾⠷⠈⢻⡆⠀⣦⡴⠋⡝⢹⠇⣼⠁
⠀⠀⠀⠀⠀⠘⣷⣄⠘⢧⠈⢿⣋⡼⠷⡀⠩⢷⣄⣹⣦⠸⡆⠘⣆⡀⠐⠈⠉⠉⢙⡇⠀⠹⣶⣄⠀⠀⠉⠻⢥⣀⣠⣼⠀⢺⡇⠀⣿⠃⣰⣷⡌⢠⠇
⠀⠀⠀⠀⠀⡀⠹⣟⢳⣤⡑⣆⠙⢷⣄⣽⣆⠀⠻⣿⣿⡄⠱⡀⠹⣿⣷⣶⣶⣤⡤⣷⡄⠀⠻⠉⠑⣤⣄⡀⠀⠉⠙⠿⣄⢸⣇⠀⠃⠐⠛⣹⢁⠞
⠀⠀⠀⠀⠀⠑⢦⣘⢏⣴⠿⠾⣿⣄⠈⠯⣍⣹⣄⡈⠣⠌⡄⠻⡀⠙⣧⢀⣀⣀⣀⣠⣧⡀⠀⢳⣯⣤⣬⣍⣻⡦⢤⠀⢿⠀⣿⠀⣶⣀⣤⡷⠋⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠶⢴⣿⣿⣷⣦⡈⠫⢟⠳⣄⠀⠹⣆⠙⡄⠈⢏⡈⠈⠋⠁⡈⢳⠀⠀⢻⡟⠋⠉⠁⠀⠀⣨⣿⠀⣟⣀⣿⠟⠋⢀⣠⣾
⠀⠀⠀⠀⠀⠀⢰⣤⣀⡀⠀⠀⠉⠉⠉⠋⠛⠓⠘⠟⠻⠓⠢⠬⠳⡷⠤⢄⣿⣿⡿⠟⢛⣋⢣⣀⣀⣧⣤⣤⣶⠾⡿⠣⠼⠛⠛⠁⠀⣠⢴⡟⣯⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣝⠛⣍⠓⠲⣦⠶⢤⢤⣤⣁⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⡀⣀⣀⣀⣠⠴⣶⠉⠏⣰⣯⣀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣙⢾⣷⣄⠈⠻⣷⣶⣶⣷⠟⠿⢻⣧⣄⡘⠻⣿⣏⠉⠛⣿⣟⠙⠛⠛⣿⡏⠉⢻⡋⣹⣽⣿⡿⠟⠀⣿⢀⡿⠟⠿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣤⡀⠙⢿⣿⠶⠖⠛⠛⠋⠉⢛⣷⡌⢳⣤⣀⠈⠻⢶⣿⡶⠛⣄⠀⠳⣷⠛⠉⢀⡍⠀⡂⣸⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠤⣤⡝⣢⣀⡈⠳⠶⣴⣶⣶⣟⠉⠙⣷⡀⠻⣮⣝⠶⣤⣀⡉⠙⠛⠧⠤⣽⣶⣾⣿⣇⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣄⡀⠉⠉⠛⠳⠶⠮⢿⡄⠙⡏⠉⠳⠦⠉⣉⡒⠦⠤⠤⠤⠤⠴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣯⣤⣬⣾⣷⣤⡤⠤⠤⠤⣽⣆⠈⠳⣤⡶⣶⣍⡉⠛⢿⠷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠭⡤⠶⠖⠛⠛⠛⢳⣤⠈⢻⢿⣿⠿⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢀⠴⠒⠊⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⡆⠀⠀⢀⠔⠁⠀⣠⠔⠁⠀⠀⠀⢀⣠⣤⠶⡖⡖⡲⠲⢖⢴⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⡇⠀⣰⢃⡠⠔⠊⠀⠀⢀⣠⡴⢾⢋⠁⠀⠀⡇⣧⣗⠬⢖⡮⢃⠭⢛⠭⢛⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⡰⠋⠁⠀⠀⠀⢀⡴⡏⢸⠇⣾⡄⡀⣇⡶⡫⢋⡵⢊⡥⠊⡡⠂⣡⢖⠥⡊⠝⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⡾⠁⢀⠔⡆⠀⣰⠛⡀⠇⢸⢸⡏⢇⢧⢟⠞⡱⠋⡐⠋⡠⠊⡠⢊⠵⣛⠩⠔⣪⠔⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠱⣾⢁⡴⠁⡰⠁⡰⡏⠆⠱⡸⡈⡎⡿⣼⢧⢃⠎⣠⠊⢀⠞⣠⢊⣴⣛⡭⠅⢒⡩⠔⢊⡤⢚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠀⣏⡞⠀⡴⠁⣰⠇⢿⡜⢆⢱⠳⡸⣽⠏⡏⠸⢠⠃⢠⠋⡰⢡⠾⣅⣐⠲⠬⠅⠒⣊⣥⣐⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢃⠀⣿⡠⠞⠀⠀⡏⡄⡿⠹⣌⢢⡳⡙⣼⢰⠀⠇⡌⢠⠃⡼⢡⢿⣥⢤⡶⣄⠲⢎⡋⠹⢖⣒⣒⣚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡄⡇⠀⠀⠀⠘⣇⢡⢷⢇⢯⡷⡝⢮⣷⢸⢸⠀⡇⡎⡰⢡⡟⢆⢫⡑⢭⣛⠓⠶⣈⣑⣶⣶⣤⣤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⡇⡇⠀⠀⠀⠀⡏⢂⢮⢎⢾⠃⡜⡷⢼⣾⡘⡀⡅⡇⠇⡿⡜⢆⠣⡙⢄⠙⢍⡒⢦⠠⣭⠭⣽⠿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⣼⠀⠀⠀⠀⢹⣌⢪⣮⢮⡟⡸⢡⠎⡽⣯⡻⢟⠷⢦⣟⢮⣢⡳⣜⠦⡑⠦⣙⢢⣵⣾⣛⣉⣩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⠀⠀⠀⠀⢏⠣⡹⣷⣷⡇⡎⡜⢰⠁⡜⣳⢽⣢⢍⣻⠭⣙⡛⠿⠿⠷⣞⣛⣹⣤⣤⡴⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⣆⠘⢮⡫⣿⢀⠃⠇⡘⢰⠁⡾⣿⣓⠾⢭⣒⡭⢕⣒⣒⣒⣒⠢⠶⠶⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠘⢕⠦⡙⠪⢿⡐⠀⡇⠸⢸⣍⣥⡐⠪⠥⠖⡋⠵⣒⠶⣲⠶⣲⡿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢌⣳⣌⡓⠢⠽⣇⡇⢸⢸⡓⠒⠒⠢⠍⠡⣒⠩⢔⡪⢔⣩⡯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠂⠻⠶⠾⠷⢒⡂⠀⣬⡥⠴⠨⠥⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠃⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣠⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⣤⣤⣀⣰⠟⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⡻⣻⡿⠯⣛⣚⠿⣭⣭⣓⣛⣿⠏⣴⣄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢫⢞⡴⢯⣉⣓⠲⠬⣍⡒⠬⣛⠶⣏⣌⣻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡱⢣⡾⠤⣄⣀⠈⠉⠒⠤⣉⠲⢌⡓⢬⡻⣿⠭⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡽⣰⢡⡿⣒⡭⠭⠛⣛⣓⣦⣄⠈⠑⢦⡙⢦⡙⢮⠻⣖⠯⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⠃⡞⣋⠥⠒⣋⣩⠥⠖⣒⣚⣷⣦⡀⠙⢦⡙⢦⠱⡝⣯⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⡜⢸⣏⡠⠖⢋⡡⠔⢚⣉⣥⣾⢟⣓⣛⣦⡀⠙⣄⠳⡘⣞⣯⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⠦⣍⡛⠣⠤⢾⣉⣴⣿⢃⣉⣠⠤⠔⠛⣆⠈⢦⠱⡘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡇⣿⢶⣤⣈⡉⢓⣶⢿⡿⠣⠤⠶⠶⠒⠚⢉⡽⢧⠈⣆⢳⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⡳⣝⢦⣽⣟⣓⡾⠁⠶⠶⠒⠒⠒⣋⡽⢡⠏⣧⠸⡜⣮⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣞⣾⡿⢝⣲⡿⣁⣉⡙⠛⣋⣉⣩⠞⡱⢃⠜⣹⡆⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡛⢮⣳⡿⣡⠭⣛⡿⠭⣭⡴⣣⢞⡵⣫⣾⣿⡿⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⢷⡿⣑⡮⢝⣒⣫⢟⡥⣚⣵⣯⣾⣿⠿⠋⠐⠛⠛⠛⠛⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠛⠛⠻⠷⠿⠿⠟⠛⠋⠉



⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡔⢲⢶⠂⠤⢀⡀⡠⢊⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠥⠀⠐⠀⡎⡌⠀⡄⢠⠈⠓⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣒⠀⠈⡝⢰⢰⠁⣸⠁⡞⠀⠀⢿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠐⡀⢐⡲⢠⢃⠂⡴⡏⡼⠁⠀⡀⡸⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠣⡰⢈⡔⡡⢃⠊⡼⢁⡅⡀⠀⠰⢀⡋⠀⢸⠀⠀⠀⢀⠴⠚⠉⠉⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠁⡵⢊⠔⡡⠃⡜⠀⡜⢡⠁⠁⠁⠘⠀⠀⠸⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⠔⢁⠜⢁⠊⢀⠞⠀⠂⠈⡄⡬⠭⠉⣩⢃⡴⠋⠀⠀⠀⣠⠄⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⢶⠁⠔⢁⠔⠁⠆⠀⠀⡔⡘⠩⢄⡰⠋⠉⠀⠀⠀⠀⠀⠙⢦⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⠃⠀⠙⠶⣅⣀⡜⢀⠄⠜⠂⡠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡠⠊



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⡽⠂⠀⠀⠀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⢠⠏⢠⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡼⠀⠀⠀⡰⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠚⢉⣙⠒⢤⡀⢰⡇⡇⠀⠀⡴⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡴⠉⠈⠉⠲⣝⣼⣱⠃⢀⡞⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠃⣀⣴⡒⠉⠹⡉⠻⡉⢻⡺⣅
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⢏⠞⠓⠦⣍⣉⡉⠙⣄⠙⢦⡙⢦⡑⣄
⠀⠀⠀⠀⠀⠀⢠⠋⡴⠋⠉⠙⠢⡹⡄⠀⠀⠀⢀⡠⠊⣀⠴⢣⣏⠙⠒⠦⠤⢤⣭⣭⠭⠷⣄⠙⠢⣌⠛⣆
⠀⠀⠀⠀⠀⠀⢫⠀⡇⠀⠀⠀⠀⡇⡇⣀⡤⠖⣋⡤⠚⠁⠀⣼⣨⠟⠒⡤⢤⣄⣀⣀⣤⠤⡼⠓⢤⡀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠓⠬⣑⣒⣒⢚⣋⣩⠥⠖⠋⠁⠀⠀⠀⠀⢻⣀⠤⠊⢀⡠⠊⣠⠎⢀⣾⣛⣫⠭⠜⠓⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣠⠔⢋⡠⠞⢁⡴⣟⡒⠤⠴⠒⠒⢋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠒⢉⣠⢶⡉⠢⣄⡉⠉⠓⠒⣺⠏
⠀⠀⠀⠀⠀⠀⢀⡴⢋⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠯⣼⣄⠑⢤⣀⣉⣑⠶⠚⠁
⠀⠀⠀⠀⠀⢠⠋⠀⡎⠀⠀⠀⠀⠀⠀⠀⡴⠁⣀⣈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡇⡰⠁⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠳⡀⠙⣄⠀⠀⠀⠀⠀⠀⣇⢱⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⡑⠦⠤⠤⠤⠤⠜⣦⡙⠯⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠊⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠊⠉⠀⠉⠓⠦⢤⣈⣉⣉⡉⢉⣉⣉⣀⡠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢤⡠⢤⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣾⣟⠷⣶⣤⡤⠽⠛⣛⣳⡝⢯⡽⢆⠘⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⣿⠃⣾⣷⡌⢷⠒⠋⣒⣛⣋⣈⣉⣙⣦⠱⣟⢣⠈⣶⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⢸⣿⡇⢹⠀⣧⣶⠟⡌⢿⣿⣿⣍⣈⣹⠟⣠⣾⡷⡘⠿⠧⠀⣬⣝⠿⣆
⠀⠀⠀⠀⠀⠀⡀⡼⢋⣠⣴⣷⠠⠀⡿⠗⠚⢻⡈⢿⣋⣉⣉⢉⣉⣉⣛⣒⣳⡘⣟⣧⠐⡿⠽⣾⡄
⠀⠀⠀⠀⠀⢸⡇⢸⡿⠒⢉⣩⣷⠐⣷⣏⡿⢩⣧⠘⢯⡟⢀⣾⡿⢃⣼⣿⣌⣧⠘⣿⡄⢹⣷⣖⣿⡀⣆
⠀⠀⠀⠀⠀⢘⣃⠀⣶⣯⡩⢋⣼⠠⣟⡌⠳⣿⣍⣧⠘⣧⠚⠛⣂⣉⣁⣨⢡⣬⡇⢳⢧⠀⡇⠀⠚⣇⢸⣆
⠀⠀⠀⠀⠁⢸⡿⡀⢸⡿⠤⢾⣿⡆⠎⣷⠖⢋⣠⣼⠆⠸⣏⣉⣭⠤⠖⠐⠉⠀⣩⠀⣮⡆⠻⣶⠲⣿⠸⢿⡄
⠀⠀⠀⠀⣷⠀⣯⢷⠀⢫⣶⠀⣾⣇⢰⠰⣆⡩⠤⣴⠒⡄⠹⣁⣠⣤⣶⣞⣟⡛⢻⡆⢙⣇⠸⡼⠛⡋⣸⠟⣇
⠀⠀⠀⠀⠹⣆⢸⡟⠦⡈⢿⠞⣀⣼⠸⡀⢻⡽⠶⢤⣈⠹⠀⢻⣤⣀⡉⠙⣚⡿⠿⢷⠈⣭⠀⡷⠞⢋⣵⠎⡷
⠀⠀⠀⠐⣄⠙⣆⠹⣦⡿⡈⠻⣍⠙⣧⢳⡈⣷⠲⠟⢿⣟⣧⠈⣶⡈⠙⠻⣤⡶⠶⠛⡀⣹⠀⣶⡞⣹⠹⢡⠇
⠀⠀⠀⠀⠹⡷⣌⢣⡙⢾⡉⣦⠘⢷⣾⡆⢃⠸⣦⣤⣀⣀⣘⡄⠈⠿⠦⣀⠀⠙⠒⢾⡇⢹⡄⠟⢰⢿⠇⡜
⠀⠀⠀⠘⢦⣙⣏⡷⢿⣦⡙⢏⣓⣆⠙⠍⡄⢆⠙⣍⣉⣉⣁⣽⡄⠐⣶⣭⣝⣲⡤⠀⣹⢸⡇⣰⣠⣼⠊⢀
⠀⠀⠀⠀⠀⠉⠉⠓⠺⠿⣿⣦⣍⢻⣳⣄⠘⢆⣃⠈⢧⣥⣁⣠⣹⡀⠘⡟⠁⢀⣀⣤⢿⣠⡧⠿⠛⣡⡴⠇
⠀⠀⠀⠀⠈⢛⠶⣆⠤⣄⣠⣀⣀⠀⠁⠉⠉⠉⠉⠁⠚⠙⠋⠓⠒⠛⠒⠛⠋⠋⠉⠁⢉⣠⡄⠶⣫⡏⢙
⠀⠀⠀⠀⠀⠀⢩⡿⣶⣌⠳⢶⣾⣿⠿⢻⣯⣄⣛⡷⡂⠓⠶⣗⠛⢻⣷⠘⢿⢙⣿⡿⢟⠈⡇⡾⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⣙⢛⠳⢤⠙⠻⣟⣉⣉⣁⡬⢿⡌⢷⡦⣌⠛⠿⢋⣦⡈⢻⣉⣤⡾⢠⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠶⣌⡉⠛⠻⠦⢬⣿⡌⢻⠓⠿⠓⢂⠠⢌⢉⣹⣟⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢯⣬⣿⣶⠦⠠⢠⣽⣆⠙⢦⣶⣮⣉⡻⠷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠉⠉⠛⠂⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⡤⣖⠒⠒⠒⠂⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀
⠀⠀⠀⠀⢀⡔⠫⢍⣢⣙⠦⣹⢦⠀⠑⣝⢦⡀⠀⠀⣀⡠⠤⠐⢤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⠟⡙⣿⢉⣭⣟⡻⠲⢤⡀
⠀⠀⠀⢀⠜⠒⠈⣙⢿⣛⢶⣞⢯⣳⣳⣽⣿⡷⠀⠛⡂⠈⠓⢦⢢⣳⣢⢯⢳⣄⠀⠀⠀⠀⠀⣀⡔⠛⢹⢻⢸⢣⢧⢹⢸⣿⠋⠻⣦⣙⣦⡀
⠀⠀⠀⠘⠕⢒⣃⣲⣤⣬⣲⣼⣿⣿⠿⣿⣥⣌⣐⣊⠺⢴⣕⣆⢫⢷⣹⢸⠀⢼⢷⡄⠀⠀⣰⢟⡀⢄⣿⡇⡎⢟⠎⡮⣿⣖⡭⣔⡦⣝⣿⣷⡀
⠀⠀⠀⠂⢈⠴⢻⠿⢻⠋⢩⣹⣯⠀⠰⣤⠪⢙⡿⣯⣽⣦⣹⣾⣮⣸⣿⣿⢜⡾⣭⢿⠀⠀⣿⣯⣿⣿⣿⡟⢣⡞⢠⠃⣿⡲⠬⣕⡫⢺⢽⣿⡇
⠀⠀⠐⣦⢋⡄⣼⡆⣏⢮⡸⡈⢮⡫⣦⣖⣭⣲⣽⣿⣿⣷⣿⣿⣿⡿⠿⠿⠥⠖⠽⢻⡆⠀⣿⢿⡟⣹⢽⡇⢿⠞⢸⣷⢻⣄⣶⡿⣿⢶⣽⣿⣿
⠀⠀⠀⠹⣩⢽⣻⡧⣌⠗⢽⣝⡲⢍⡢⣿⢾⣾⣿⣿⣿⢿⢋⠙⢍⡛⠓⠲⣶⢻⣴⣿⠀⠀⢻⣧⢟⡿⣿⣿⣾⡇⠘⢻⢸⣿⢋⠔⢡⢮⣿⣿⠇
⠀⠀⠀⠀⠙⠿⣅⢷⡉⢷⡾⣦⣭⣷⣿⠶⠻⣿⢿⢋⢿⢸⡯⣿⣿⠲⢌⢳⣗⣿⣾⠃⠀⠀⠈⢿⣿⣹⣵⣿⡘⣧⠄⣿⡾⣿⣿⡖⣩⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠘⠾⣾⣻⢸⣿⣾⣭⡛⣿⣿⣿⣿⠋⠀⠀⠀⠀⡈⠳⣿⣶⣿⣷⣟⢼⣷⣧⢛⠉⢞⡛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣸⠿⠿⠿⢿⣿⠽⠋⠀⠀⠀⠠⠂⠉⠀⠀⠀⠙⠻⠿⣿⣼⣿⣷⡾⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠐⠒⠂⠀⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⠯⢋⣡⡾⢟⠍⡨⢍⣷⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⣒⢖⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⢊⢽⡿⠃⣠⢞⣥⠞⠑⣩⣞⣡⣽⡀⡌⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⣵⣲⠿⢿⣿⣿⠏⣨⣾⠟⣦⡀
⠀⠀⠀⠀⠀⢠⠎⠁⣸⠏⢠⠞⣕⠴⠃⣠⢟⣳⠦⣍⡻⢧⡹⠘⡌⢧⡀⠀⠀⠀⠀⠀⢠⣾⣿⡭⠴⣂⣤⣭⠷⠾⠷⡿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢠⣥⣤⣶⠃⣠⢋⢞⡕⠀⡼⠭⣴⣦⣉⠓⠯⣲⢝⢦⣁⢸⣧⠀⠀⠀⠀⠀⣞⣯⡹⣞⡯⣗⣚⣿⣭⣭⠷⡿⣭⣹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣙⣿⢃⣰⠃⡂⡜⢀⣾⡷⣶⣤⣄⢯⠷⡶⣾⣕⢥⡝⢦⣿⡆⠀⠀⠀⢰⣿⣷⣝⡶⣝⡿⣿⣽⣱⣶⣷⡾⠾⣿⣷⣽⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣧⡏⣼⡏⡜⣸⠁⣼⡿⠞⢋⠔⣩⡞⢯⣉⢻⢭⡳⢧⣌⣿⡇⠀⠀⠀⢸⣿⢿⣿⣿⣾⣽⡲⠯⠟⠳⠿⣯⢭⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡇⣿⢸⢣⡇⢠⣟⠭⢂⡏⣾⢋⡞⣡⣿⢳⣝⢽⡻⣝⢿⡇⠀⠀⠀⠘⣟⢷⣌⡉⣛⡛⢣⣤⡦⠤⠨⠽⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⡇⡏⣯⢿⢳⢸⣧⣞⣽⢸⣵⣿⡼⢿⢇⢸⣿⢳⣽⣾⡟⠀⠀⠀⠀⠀⠙⣿⣷⣧⣥⣍⣛⣛⣛⣋⣉⣛⣫⣽⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠹⡇⡇⠀⢸⢸⣸⣷⡿⣻⡞⢟⡝⣄⡿⡸⢸⡎⣼⣻⡟⠁⠀⠀⠀⠀⠀⠀⠙⢯⣿⣷⣿⣿⣿⣟⣶⣿⣾⣿⣿⣿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⢧⣿⣼⣸⡿⣿⣾⣯⣳⡹⣿⡿⢡⢳⠏⣴⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣿⣿⣿⣿⣿⠎⣻⣌⠳⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡩⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⢉⠴⠆⠖⠂⡀⠈⣁⣈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⣀⣈⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢒⠒⠛⢉⣍⠉⣩⡉⠙⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠈⠀⠀⠉⠀⠀⢸⠈⠀⢧⠀⠀⡇⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⠀⡀⠀⠀⠘⠃⠀⠘⠀⠀⣠⡿⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠙⠒⠬⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠁⣤⡶⠀⠉⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡤⠴⠞⠋⠁⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢣⣼⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣀⡀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣟⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣥⣤⡤⠤⠤⠴⠦⠐⣒⣒⣒⣢⣬⠩⠉⠛⠉⢿⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠦⠀⡿⠤⠤⣤⠶⠶⠾⠿⠭⢽⠟⠒⠒⠒⠒⡾⠋⠉⠉⠉⠉⠉⠙⢦⡀⠀⠒⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣟⡰⠊⢀⡴⠞⠛⠳⣄⠈⢷⡀⠈⠀⡸⠁⣠⠖⠃⣀⠢⣄⠀⠀⠱⣄⠀⢂⡴⢻⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⢀⡴⠋⠒⠀⢀⡀⠘⡀⠀⠙⠒⠚⠁⠀⠁⠠⠄⠀⠀⠈⢢⠀⠀⠈⠉⠉⢀⠼⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡇⡼⠁⠀⠀⠀⠈⠀⠀⠡⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣀⢳⡀⠀⠀⡰⢁⠀⡇⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣡⣇⣀⣀⠁⠀⠀⠀⠀⠀⠙⢦⣤⣎⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠼⠶⣆⠀⠐⠒⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢸⡤⣬⣉⣉⣩⡭⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠶⠶⠒⠒⠒⠚⠛⠋⠉⠉⢩⡍⠉⠉⢹⡀⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢰⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠠⢴⣿⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⣤⣄⣀⣀⡇⠀⠀⠀⠀⠀⠀⠈⠶⠦⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡄⡇⡉⡝⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⣠⢾⢶⠛⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠞⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣋⡟⠚⠎⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠤⣤⣀⣀⣀⣀⣀⡀⠀⠀⢀⢀⣀⣀⣠⡤⠶⠛⠉⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣿⣿⠟⣽⣿⠋⡩⢹⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣇⣾⣿⡇⢠⣿⡇⢀⣴⣳⡟⣛⠉⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⡿⠋⢿⣿⢻⣿⢂⣾⡟⡞⣼⣿⣿⣋⣭⣭⣥⣜⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣾⣿⣿⢷⣰⣤⣇⣷⡏⣼⣿⣹⣱⣿⣿⣿⣿⣿⣭⣼⢖⣶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣏⣿⣿⣬⣶⡿⡻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⠭⠷⢾⣿⣶⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⡏⣿⣿⣿⣽⡇⣧⢻⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣷⣖⠬⣐⢶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣿⣶⢬⣉⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡝⣷⣬⣯⡻⣿⢿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣶⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡷⢶⣍⠛⢧⣹⣿⣿⡗⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣾⣝⠻⢿⣿⣿⣷⣤⣉⣹⣿⣿⣿⢿⣿⣿⣿⣿⣷⣦⣌⡒⠭⢿⣿⣿⣼⣼
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠙⢮⣛⠿⣆⣬⠉⠉⠉⢉⡁⣀⣤⣶⣿⡿⣺⣿⣿⣿⣿⠛⠳⣤⣶⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⡙⢿⣶⣮⣽⣯⣽⣿⣮⢿⣿⣾⣟⣽⣿⣿⣿⣿⣿⣷⣼⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⢿⣷⣾⣭⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⣿⣿⡿⣿⣿⣿⢿⣻⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⣀⡀⠁
⠀⠀⠀⠀⠀⠀⣤⠀⢀⠃⠀⠀⡀⠐⠐⠀⡀⠆⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠆⠄⠆⠂⢐⡶⠨⠆⡉⢧⠐⠇⠩
⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠚⠁⠠⠓⠆⡀⠁⠀⠀⡀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠢⠄⢁⠠⠠⠁⠆⠠⡜⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠐⠀⠀⠀⠂⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⢢⠀⠀⠀⠀⠀⠀⠀⠘⠧⠯⠿⠿⠇⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⡀⠀⠀⠀⠀⠦⢀⡘⠀⠀⠀⠀⠀⠀⠀⠠⡇⡐⣼⣯⠂⠀⠀⠀⠀⠀⠀⠔⠠⠠⠀⠐⠂⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⢬⡙⢞⠉⠙⠋⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⡈⢆⠳⣠⠔⠁⠀⠀⠀⠀⠀⠀⠠⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⢠⠟⠉⢢⠱⡀⢰⣄⠀⠀⠀⡠⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⠴⡻⡀⠀⠀⠣⡑⢄⢢⠙⠦⡔⠁⢠⠃
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⣄⡤⠊⠁⠀⢇⢣⠀⠀⠀⠙⢮⣓⡵⠼⠤⠔⢛⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⡈⡄⠀⠀⠀⠀⡨⢶⡀⣰⡊⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢰⠀⣀⠠⠐⠒⠒⡇⣇⠀⠀⠀⣠⠋⠳⡝⡻⣼⢆⠀⠑⢄⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡞⠋⠀⠀⠀⠀⠀⡇⡏⠙⠢⡾⠢⣱⣼⡶⡷⠃⠀⠑⢄⠀⠑⣀⠀⠁⠑⠤⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠢
⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⣀⠀⠀⣤⠧⠄⡲⠥⢤⣏⣴⡖⠁⠀⠀⠀⠀⠱⣄⠈⠢⡀⠀⠀⢀⡽⠖⠢⠤⣸⡀
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⡡⠋⠉⠀⠠⡊⠀⠀⢠⣃⠾⡀⠀⠀⠀⠀⠀⠀⡼⠒⠲⣮⢦⡞⠁⠀⠀⠀⠀⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠱⡴⢩⠏⠀⣱⡀⠀⠀⠀⠀⠀⣇⠀⠀⠈⣣⠈⠒⠤⣀⠀⢀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⠜⡾⠧⡀⠀⠸⡱⡀⠀⠀⠀⠀⠘⣄⣠⠊⠀⠀⠀⠀⠀⠻⠉⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣰⣧⠞⠀⠀⠈⠢⣄⣹⡧⠀⠀⠀⠀⠀⡎⢳⠀⠀⠀⠀⠀⠀⠀⠹⡓⠒⠪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⣈⠜⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣧⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣤⠤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠉⣸⠃⢀⡏⠀⡿⠀⢸⠋⢹⡗⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣾⠃⢠⡏⠀⣼⠃⢰⡇⠀⣾⠀⣼⠀⠀⡟⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢷⣠⡟⠀⢰⠇⢀⡾⠀⢰⡇⢀⡟⠀⢸⠇⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠹⡆⠈⣿⠀⣰⠏⠀⡼⠁⢀⡟⠀⣼⠁⠀⡿⢀⡟⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡀⢻⡄⠈⢷⡏⢀⡼⠁⢀⡾⠁⣰⠇⠀⣸⡃⣼⠁⢰⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡀⢳⡀⠹⣄⠀⢻⡾⠁⢀⡾⠁⢰⠏⠀⣰⠏⠙⠳⠦⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢷⡀⠻⣄⠈⣷⠟⠀⢠⡞⠀⣰⠏⠀⣰⠏⠛⠦⣤⣀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⢳⣄⣹⠟⠁⢀⣴⠋⢀⡴⠃⠀⣴⠋⠳⢦⣄⡀⠉⠙⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡴⠟⠁⠀⣠⠞⠁⣠⠞⠁⢀⡾⠛⠦⣄⡀⠈⠙⠓⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⠞⠁⣠⠞⠁⢀⣴⠛⠦⣄⡀⠈⠙⠳⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣾⣁⣀⣠⡞⠛⠦⣤⣀⠉⣛⣶⡴⠛⠁
⠀⠀⣠⠶⠛⠛⠛⠓⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠈⠉⠛⠛⠛⢒⣾⠟⠋⠉
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣤⣤⣤⣤⡽⣞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠉⠛⠲⠶⠤⠤⠤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠋⠁

⠀⠀⢀⡶⠚⠋⠙⠛⠃⠂⠀⠀⠉⠉⠀⠉⠁⠈⠀⠘⠛⠛⠛⠉⠛⠛⠃⠀⠀⠈⠉⠀⠀⠉⠀⠀⠐⠊⠛⠛⠋⠙⠛⠙⠂⠀⠀⠈⠉⠁⠉⠉⠁⠀⠀⠒⢦⡄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐⠠⠀⠀⡀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⠀⠁⠂⠶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠈⠁⢀⠀⠘⠀⠠⢄⡀⠈⠉⠓⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⢀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠀⠉⠓⠢⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠚⠖⢠⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠰⡀⠠⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⢀⠀⢀⢀⠀⠀⠈⠄⣠⡀⢌⣠⣀⣌⣠⣡⠄⢄⡠⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠁⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡎⠀⠀⠀⣴⡀⠀⠀⠀⢀⡴⠀⠀⣠⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⠋⠀⠀⠀⠀⠋⠀⠠⠀⠂⠀⠀⠀⠁⠀⠀⠄⠊⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠘
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⢸
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠙⢦⡄⢀⣀⡀⠀⠀⠀⠀⡀⣀⠀⣀⣁⣈⣀⣀⣀⣀⣀⡀⣀⠀⢀⠀⠀⠀⢀⣀⢀⣀⣀⣀⢀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⢀⢀⣀⣀⢀⣀⣀⣀⢀⡴⠋
⠀⠀⢀⠀⠀⡀⠀⡀⠈⠉⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠉⠁⠀⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠉⠁⠀⢀⠀⠈⠉⠉⢉
⣿⡟⣉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⡴⠊⠀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡡⡀⠀⠀⢀⠀⣁⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡜⣇⣀⣀⡉⡐⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⢁⡴⠋⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠐⠂⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⢀⠀⠂⠀⠀⡠⠀⠀⠀⠀⢈⠲⠀⠁⠀⣀⡀⠤⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣌⣈⠉⠙⠉⠉⠁⠀⣀⣀⣀⠀⠀⡀
⠀⠀⠀⣀⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⡤⠴⠃⠀⠀⠀⠤⠤⠀⠀⠄⠀⣀⠉⠙⠉
⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⡈⠑⠒
⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⢴⣒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠠⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠑⠄⠀⠀⣀⠨⠓⠤⡀
⠀⠀⠀⠐⢄⠈⠢⡀⠀⠀⠰⡈⣖⡉⠔⢂⡠⠒⠉⠢⡀
⠀⠀⠀⠀⠀⠈⠉⠑⡀⠀⠀⢡⠘⢢⣔⣁⣀⣀⣠⠀⠱⡀
⠀⠀⠀⠀⢀⠀⢀⠀⠱⠀⠀⠀⠀⡀⢢⠠⠤⠤⠀⠒⠂⢳
⢐⡀⢢⢄⡂⠌⣐⠊⠩⢧⠀⠀⡄⡇⠈⢧⠤⠤⠄⠀⠀⠈
⢨⠀⠌⠄⠈⡱⢲⠬⣥⣒⣆⠀⠀⠹⠀⠘⡍⠉⠁⠀⠀⢠
⠈⡶⠀⠀⢀⢃⠎⡰⠃⠀⠸⠀⢆⢸⠀⠀⡏⠀⠀⠀⢐⡞
⠀⠐⡄⠀⠀⡜⢠⠁⠀⡀⠀⡆⠈⢆⠣⠀⡇⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠘⢄⠀⠀⢆⢂⠌⠀⠀⡄⠀⠈⠁⠀⡂⠀⡠⠓⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢀⡇
⠀⠀⠀⠀⠑⠢⢏⣈⠀⠀⠀⡆⠀⠀⠀⡠⠔⠋⠀⠀⠀⠙⢄⠑⠄⡀⠀⢀⡠⠊⠁⠀⠀⠀⠈⢀⠠⠔⢂⡡⠄⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠤⠒⠁⠀⠀⡀⠤⣒⡉⠄⠒⠉⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠀⠀⠒⠒⠒⠒⠂⠚⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠭⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣠⣶⣿⡄⠀⠀⠀⠀⠀⡟⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠰⣿⣿⣮⣭⣿⣿⣿⠧⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠠⣾⣿⣿⣿⣿⣷⠀⠀⠀⣰⠀⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣶⣾⣗⣾⣷⣷⠀⠀⠀⠀⠀⠀⣾⣫⣿⣿⣿⣧⠀⠀⠀⢹⡟⠋
⠀⠀⠀⠈⢻⣿⣿⡿⣿⡁⠀⠀⠙⠀⢸⠀⠻⡀⠸⠄⣇⢰⡇⣸⢠⡇⠀⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠘⣿⣻⢿⣿⣽⠏⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠁⠙⠿⣿⡁⠀⠀⠀⠀⢸⢀⠀⠈⡄⢰⡄⠈⠀⠓⠀⠉⡠⠳⠀⠀⠀⠀⠀⠀⠀⣛⡻⣿⣽⣾⣷⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠉⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠁⢸⡇⠀⡇⣸⠀⡀⢀⠀⡀⢠⠃⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣝⢿⣿⡿⢀⠠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⢸⡇⢸⠀⠿⠐⠧⠸⠾⡀⢸⣰⡃⠀⠀⠀⠀⠀⠀⠛⠷⠶⠾⠶⠾⠶⠟⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠀⠀⠀⠀⠀⠀⢀⣀⡤⠀⠀⠀⢀⣀⠤⠔⠊⢁⣀⣀⣀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣼⡦⠀⠀⠀⠀⠀⠈⢧⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠟⠋⠁⠀⠀⠀⢰⠋⠀⠀⢠⣶⣿⣿⣿⣿⣿⣷⡀⠀⠈
⠀⠀⠀⠀⢸⡆⢀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⡆⢸⣷⠘⣇⡄⠀⢨⠁⠀⠀⠀⢀⣤⣤⣴⣶⣿⣿⣿⠿⠛⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⣀⠀⣀⡀
⠀⠀⣄⣿⠀⣿⢸⣿⡇⡤⢾⡀⣀⡀⠀⢾⣿⣿⡧⠛⠉⠁⠀⠀⠀⣠⣶⣦⠰⣿⣿⠆⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣾⣿⠇
⠀⠀⢻⣾⡄⣿⡸⣿⡍⢧⡾⢿⣀⡿⠀⠀⠀⠁⠀⠀⠀⢀⣶⣿⣷⣽⣷⣿⣿⣿⣿⣿⣿⣾⣯⡾⣷⣶⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⢁⠀⠀⠀⠀⠻⡿⠃
⠀⠀⠈⢿⣧⣿⣿⣿⢿⣰⣁⡞⠉⠀⠀⠀⠀⡀⠀⠀⠀⠘⠿⣷⣿⡋⣙⠻⣿⣿⢻⡟⣿⣿⢛⣿⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣾⣷⣷⣾⣷⣾⠂⠀⠀⠀⠀⠰⢄⠀⠀⣰⣿⣾⣿⣿⡇⣿⣷⡜⣿⢸⣷⡘⢏⣾⣿⣿⣷⣿⡆⠀⢀⣠⠖⠓⢶⡄⠈⠀⠀⠀⠀⠢⠀⠠⠐⠀⠒
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣄⡀⠀⠀⠹⣿⢿⣿⣿⡇⣿⣿⢇⣿⢸⣿⡇⢸⣿⣿⣿⡿⣿⠏⠀⣾⠁⠀⠀⠀⣿⠀⣠⡶⠛⠲⣄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⢿⣀⠀⠀⢠⣶⡿⣿⣅⣬⣴⣿⣿⣸⣿⣇⣸⣿⣿⢿⣶⡄⠀⠀⣇⠀⠀⠀⢠⡟⢰⡏⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣘⠟⠁⠀⠈⠿⢿⡿⣻⡿⣿⣿⣿⣿⣿⣿⢿⣟⢿⡿⠿⠁⠀⠀⢻⣄⡀⢀⣾⢁⡿⠀⠀⠀⠀⣾⠁⠀⠀⣠⣶
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣤⡼⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠰⣿⣿⠖⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡏⣼⣷⣄⣀⣤⡾⠃⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠠⠿⠿⠿⠿⠯⠀⠠⣶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⢱⡿⠋⠉⠉⠁⠀⠀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⢰⡇⡾⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠛⢃⠀⠀⠀⠀⠀⠀⣀⡀⢠⡀⠀⠀⢀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣾⣽⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠸⢿⣿⣿⣿⠿⠀⠀⠀⢀⣀⡁⠀⢡⡀⠀⠀⠻⡇⢸⡇⡀⠀⣰⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠨⠀⠀⠀⢳⡈⢃⠀⠇⠈⡇⠀⠀⡟⠀⠀⠀⠀⠀⠻⠿⣿⣿⡿⠟⠁⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⢂⠘⠀⢣⠀⢸⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⣷⣾⣶⣦⣤⡀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡄⠀⠀⣸⠃⡀⠀⠀⠀⢀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⢠⢦⡄⢀⡄⣠⢀⡏⢠⠁⣤⡄⡠
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⣧⠀⠀⣾⠸⡇⠸⠄⣯⠸⠇⠿⠈⠗⠸⣇
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦
⡇⠀⠀⠀⠀⠈⠀⠰⠟⠔⠗⡴⠷⠜⠷⡔⠷⠼⠗⡴⠾⠔⠿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⣄⡀⠀⠀⠉⠁
⡇⠀⠀⠀⠀⠀⠀⢈⣉⣊⣉⢊⣉⢊⣉⣊⣉⢊⡉⢊⣁⢊⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠻⣯⣣⢻⣿⢏⠳⡀
⡇⠀⠀⠀⠀⠀⠀⠠⠔⠕⠔⡅⠄⡕⠴⠕⠄⡁⠔⡕⠔⠕⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⠾⢾⡗⡋⠭⠂⣠⣴⢿⠀⠀⠀⠀⣴⣦
⡇⠀⠀⠀⠀⠀⠀⢈⡉⢊⣉⣊⣉⢊⣁⡂⣡⢊⣉⢊⣉⢊⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣩⣴⣫⣤⣴⣞⡻⠕⢿⠀⠀⠀⠀⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠐⠒⠕⠒⠕⠒⠕⠒⠕⠒⠕⠒⠕⠒⡕⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢯⣿⠇⣿⣮⡩⣿⡿⠃
⡇⠀⠀⠀⠀⠀⠀⠈⠉⠊⠉⠊⠉⠊⠉⠋⠉⠊⠉⠊⠉⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠘⠛⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇
⡇
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡇
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣖⠒⣶⠶⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣴⡞⣭⡻⣗⡆⠓⣭⡶⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢂⠁⠀⢦⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⠛⠛⠏⡉⠄⢊⣩⣵⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢺⣛⡭⢶⡘⡕⢀⠠⢼⠩⠽⡦⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿⣿⣶⣯⣴⢮⡶⠿⣭⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠫⣍⢂⡭⢗⢎⢹⡬⠕⣲⡭⢯⡘⢭⡚⢕⡪⡝⢶⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⢧⣟⣨⣙⣧⣜⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⣂⢍⡱⡈⣑⣺⠭⣆⠼⠙⠒⢏⡶⣐⣾⡒⢑⡾⡙⠂⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠡⢘⣦⠭⠖⠂⠉⠀⠀⠀⠀⠀⠀⠓⠼⡡⢜⠎
⡇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠐⠘⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠓⠒⠋⠈⠉⠉⠉⠀⠒⠂⠀⠀⠰⣿⠇
⡇
⡇
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣴⠿⠾⢷⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢠⣿⡋⠀⠀⠈⡇⠙⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣤⡖⠁⠀⠘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢿⢿⣫⣀⡰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢰⠅⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⣄⠀⠀⠀⠀⠀⢠⠟⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⣿⠉⣤⣉⡙⡣⠀⠀⠀⣶⡟⠃⣠⡏⠀⠀⣀⣀⣤⣄⡄⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣤⠼⣷⡗⡇⣀⣾⣿⠃⢀⡿⠀⠠⠚⢙⢩⠉⣿⡷⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⠃⢀⡾⠁⠀⡀⢀⠈⠐⠺⡓⠶⢔⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⣻⣧⡿⠀⣸⠁⠀⠀⠈⠛⠀⠀⠀⠛⠘⢋⡽⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡗⣯⡍⢿⡟⠠⡇⠀⠀⠀⠀⠀⣠⢰⠫⣶⣠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢘⣵⠚⠷⢭⡵⠿⢏⢰⠆⠀⠀⠀⡀⣧⡽⣿⠾⠏⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣾⡅⠀⠀⢤⠀⠀⠈⢾⡃⡠⣰⣊⡣⡙⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠄⢰⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠀⠍⡝⠓⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⣀⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⢌⠐⠊⠉⠀⠀⠀⠀⠀⠀⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠰⠀⢀⣧⣬⡤⠀⠀⠀⠀⠀⢀⣈⣳⣻⣷⠞⠷⠶⠦⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠨⢿⡃⠀⠀⠀⠀⠀⠐⡈⠁⠉⠻⡼⠆⠀⠀⠀⠀⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠁⠀⠀⠈⣿⡿⠂⠀⠀⢈⣌⣻⣶⣤⠼⣇⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡴⠀⠀⠠⠆⠘⠷⠀⠀⢠⡞⠉⠙⠛⢳⣼⠋⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣀⣀⡀⠀⠘⠀⠣⡤⢽⣇⠀⠁⢀⣸⢷⡶⣚⡴⠀⢀⠼⠙⢋⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢾⣧⣶⣶⣾⡟⠙⠻⢿⡿⠛⠛⣿⣋⠀⠀⣮⢒⠗⢠⢸⡟⢇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠀⠘⢗⡀⠀⠘⠣⡄⠀⠙⠷⡴⠞⡟⠁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⣀⠃⣢⣤⣤⢪⡐⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠸⠾⠀⠀⠘⠿⠃⠀⠀⠀⠉⠁⠀⠀⠀⣦⡄⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⢀⣴⣿⢣⠂⠀⠀⠈⠛⠽⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⡈⣥⠄⣴⠁⢂⠩⠀⠐⠂⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡄⣻⠟⠃⠀⠀⣠⠄⠀⠀⣦⡛⠟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢣⢗⣍⡠⠀⠀⢁⣀⣤⢊⠽⡿⠛⠛⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⢀⣤⠶⠺⢿⡀⠈⠀⠀⠐⢒⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⢺⡟⢧⡁⠀⠀⠀⠀⠀⣀⣠⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠓⣶⣆⣦⣄⠀⠀⠀⠀⠀⠙⢿⣅⢀⠁⠤⠀⠀⠚⠒⡰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡟⣿⣽⠘⡟⢱⣦⠀⠀⠀⠀⠀⠀⠛⠛⠾⠷⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠋⠀⠀⠀⠀⢀⡟⡸⢿⡿⠛⠀⠒⠚⣁⡳⠦⣼⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⢼⢇⡷⠋⠀⠀⠐⠉⢁⠤⣶⣿⠧⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠘⣧⠟⠉⣀⣠⠴⢿⣁⠘⠀⠀⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢧⣕⣾⡿⡅⠀⠀⠁⠠⢄⣀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠛⠿⣄⢊⠡⢤⢴⠞⣲⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠟⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⠃⠀⡎⠉⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣠⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⢴⣶⣶⢶⢶⢶⢤⣄⣰⠃⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡎⢏⣧⢃⢷⡟⣱⣟⣕⣵⣩⣾⣿⣦⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢿⣿⢸⣿⡾⠟⣋⣭⡥⠷⣒⣶⣾⣫⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⢿⢯⡻⡼⠞⣡⠦⣕⣾⠷⣛⢟⠿⣫⣵⣾⡱⠾⢋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣶⠏⣌⣾⢏⣴⠞⡡⡪⡪⢗⢝⠕⣡⣾⣿⣿⡷⢾⣛⣲⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢿⡄⡧⢡⡾⢡⢊⢎⢎⡴⡡⣢⣾⣿⡿⢛⣵⢾⡻⡇⠅⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢿⢧⢡⢻⢡⢃⢆⢏⡞⣴⣿⡟⣱⢟⣵⣿⣵⢸⡄⣿⠀⡄⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣼⡏⡆⡎⡘⣬⢎⣾⡿⣱⣿⢣⠯⢙⡻⠿⠟⢶⢷⡞⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣾⡇⡇⡇⣿⡏⣾⢧⢣⣿⡇⡾⠭⠅⣐⡛⠉⠀⠠⣭⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⣷⢸⢻⢹⠸⡡⣧⣷⡫⠄⠠⠄⠒⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠺⣼⡜⡕⠟⡿⣿⣯⡫⣛⠝⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣷⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡱⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⢂⡔⠐⡻⠀⠧⢤⣀⡀⠀⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠉⠁⠀⣨⠒⠃⡀⠀⢀⡅⢸⠁⠀⠂⠉⠲⣤⠞⢡⠞
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠄⠃⠀⠀⠀⠄⢈⢤⠁⣨⠀⠀⣀⠀⡾⢁⢴⠃⡀
⠀⠀⠀⠀⢀⡼⠁⠀⢢⠌⠁⠀⠀⠠⠀⡠⠀⢀⠼⠀⣇⠐⢀⡡⠊⣠⠏⠀⠠⠁⣄
⠀⠀⠀⢀⠞⠤⢀⠘⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⡄⢠⠅⢠⠎⢡⢾⠁⠀⠆⠀⠐⠈⣆
⠀⠀⠀⡜⠀⠀⠀⠀⠂⠀⠊⡀⠀⠀⠀⠀⠠⢊⠁⢾⡜⢁⡔⠁⢀⠃⠠⠀⠃⠀⠀⢸⡄
⠀⠀⢀⠇⠀⠀⠀⠀⠔⠀⠊⢀⠀⠀⡠⠈⠀⠀⠑⢄⠐⠋⠀⠀⡈⠀⠀⠰⠀⠃⠀⠈⢣
⠀⠀⢸⡼⠀⠀⠀⠀⠀⠁⡀⠁⠀⠾⠀⠀⢢⠀⠠⡀⠑⠀⠀⣀⠁⠐⠀⠆⠐⠀⠀⠀⣼
⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⢠⡗⢁⡴⣀⠀⠀⠀⢠⠋⠀⠀⠐⠀⠃⡈⠀⠀⡿
⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⠀⠁⢀⡠⠊⡠⢿⠀⡏⢂⠀⢀⡈⠀⠀⢀⠁⡈⠠⠀⠄⢀⠇
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠏⠀⣀⠞⢡⡎⢀⡆⢀⠃⠀⢠⡘⠀⠀⠀⠀⠐⢀⠂⡸⡄⡜
⠀⠀⠀⠀⠸⣆⠀⢠⠄⢀⡴⢁⡔⠁⠀⢸⠇⢸⡐⢡⡀⠀⠀⠀⠀⠀⠁⠂⠰⢇⡞
⠀⠀⠀⠀⠀⠈⢢⣘⡤⠋⣠⠋⠀⠀⠀⢸⠀⡟⠀⠄⠀⠀⠀⠀⠀⢀⠄⡰⣤⣊⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠟⢠⣎⠀⠀⠀⠀⠀⡈⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠤⠤⠤⠤⠤⠄⠀⣉⡁⠒⠠⣀
⠀⠀⠀⠀⠀⡔⢁⡔⠁⠈⠙⠢⠦⣀⣀⠇⢸⢁⠐⢀⡀⢀⡤⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠈⢂
⠀⠀⠀⡠⠊⡠⠃⠀⠀⠀⠀⠀⠀⠀⢨⠀⡌⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠀⡸
⠀⢀⠞⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠒⠘⣉⠤⠚⠁
⢠⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⢉⣁⠠⠤⠐⠒⠈⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⡤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⠀⠀⠀⢘⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠑⠢⠄⣀⣀⣀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣨⡉⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠠⠤⠒⢁⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢆⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⢎⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢔⣠⣀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡞⠡⢩⠏⣉⠢⢄⡀⠏⠱⠲⠄⣀⡴⡱⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢩⠁⡜⠠⢁⠣⢀⠂⠍⡢⠈⢳⠀⠂⣠⢋⠾⣄⠀⠀⠀⠀⢀⡠⠔⡪⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠆⠐⢀⢃⠏⠒⠄⠑⠢⡈⠢⣙⠀⡖⡵⠉⡆⠤⡑⣄⢔⡢⠵⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡄⠀⠸⠀⡅⡄⡸⢈⠢⢕⠈⡢⡈⠢⣈⣯⡞⢰⠀⣅⠁⠢⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⡀⢀⠀⢠⠑⡈⢅⠢⡑⢌⠪⠢⣸⠁⠀⠘⠀⠉⢍⠢⣄⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡆⡇⠸⠀⠸⡄⠘⡄⠢⠈⠢⡑⡀⡎⠀⠆⡄⢀⢇⠈⢓⢄⠑⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⠀⠃⠇⠀⠀⢠⠈⢄⠈⢢⠑⢄⠐⣼⠁⡸⠀⠀⡘⢀⢂⠈⣃⠑⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢣⡀⢠⠘⠀⢠⠑⢄⠑⣄⠑⢄⣰⠂⠠⠁⡄⢠⠣⠈⡀⠄⢙⠢⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⠄⢳⡈⡀⠀⢸⡑⢄⠐⢄⠓⣤⠃⠠⠁⡜⢠⠟⡀⠂⢠⢰⢀⢷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢜⡷⡈⠦⠑⣼⡐⡀⠅⢠⡉⢢⡕⠀⡔⢁⠌⡠⠋⠰⢁⢀⡠⠚⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡊⠕⠂⠁⠈⢊⠢⣱⢄⠛⢥⠘⢠⡨⠋⡠⠊⡠⠃⠜⠁⡠⠤⠚⡉⢐⣠⠇
⠀⠀⠀⠀⠀⠀⢀⡠⠔⣊⠥⠒⠉⠀⠀⠀⠀⠀⢀⠝⣡⠊⡑⠢⡙⠣⣤⠎⠠⠞⠐⡓⠈⠁⠀⠂⢁⡂⠔⠁
⠀⠀⠀⣀⠴⣊⠥⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡔⣣⠎⠀⠈⠂⠕⣤⣑⠢⢍⠛⠥⠄⣒⣀⢠⣴⡶⢋
⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠛⠂⠉⠉⠀⠀⠈⠀⠀⠀⠀⠤⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠀⠀⠀⠐⠒⠀⠀⠀⣀⠀⡀⠈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠠⢀⡀⠀⠀⠀⠀⠀⢀⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠅⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⣲⣿⣨⣿⣎⠡⣲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡀⠀⣨⡄⡬⠽⠿⣗⣿⣿⡀⠈⠿⣿⣿⣆
⢀⣼⣦⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⠀⢆⡟⠀⠈⣀⣀⣀⣀⣹⣿⣫⣿⣧⣀⣠⣬⣭⣿⡄
⠀⠉⠀⠀⠈⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⡴⠾⠛⠉⠉⠉⣹⣿⣽⣿⣿⡉⠉⠁⢀⣸⣃
⠀⠀⠀⠀⠀⣽⣺⣯⣿⣿⣾⣮⣿⣿⣿⣿⣝⠂⠠⣀⣀⣭⣭⣽⡇⣿⢸⣿⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣱⣄⣀⡀
⠀⠀⠀⠀⠀⢺⡯⣿⣻⣿⣿⣿⣿⣿⣿⣿⡀⣏⠅⠠⢙⢳⣿⣿⣇⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣿
⠀⠀⠀⠀⠀⢨⣏⡿⣿⣿⣿⣽⣷⣳⣿⣿⣧⣈⣂⣴⣿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⠉⠉⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠘⣿⢿⣷⣿⣾⢿⣾⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡿⡿⣿⣿⣯⣹⣷⠄
⠀⠀⠀⠀⠀⠀⢿⣺⢿⣿⣕⣿⣯⣛⣿⣷⣻⣿⣿⣟⣵⣯⣯⣿⢜⣷⣿⡾⡵⣟⠷⡫⣕⡿⣿⣮⣽⣿⣻⣿⣿⣿⣧⢀
⠀⠀⠀⠀⠀⠀⠘⡧⡛⣿⢿⣝⣿⢿⡾⣿⣵⣷⣯⣮⣾⡵⣽⢷⢮⡷⣭⢮⠿⡳⢟⢎⡯⣾⣑⡯⢚⢶⢽⡙⡫⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⠫⠿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣟⣿⢻⣿⡿⣻⢿⢿⡿⡾⣿⣿⣿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠉⠁⠛⠛⠚⠛⠚⠛⠓⠛⠚⠛⠛⠛⠛⠛⠓⠓⠛⠛⠛⠻⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠘⠃⠒⠂⣄⣀⠎⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠁⢳⠀⠀⠀⡃⠀⠀⣷⡵⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠣⠀⠀⡄⠀⠀⠋⣴⣊⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠄⠀⠀⠀⠀⠱⣺⠁⠀⡰⠀⠽⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⢄⠀⠠⡀⡴⠁⠠⠀⠀⢠⠃⠐⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠈⢢⣀⠞⠀⠀⠀⠀⢠⢅⡐⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠙⠤⣀⠊⠄⡐⡀⠀⢠⠎⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠤⠄⠊⠀⠀⠀⠀⠉⠃⠚⠔⠰⠰⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⠁⠂⢈⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⣄⠬⠒⡁⠁⠠⠀⣉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡅⠄⠘⠀⠄⠁⠖⡽⠰⢄⣚⠓⢉⢩⣀⠀⡁⠀⠂⠀⠈⠀⠂⢸
⠀⠀⢀⠴⡘⡈⠁⠆⠦⠀⠁⠉⠐⢄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⠆⡁⢀⠢⣀⡑⠀⠀⠢⠀⠰⠧⠀⠂⢈⠁⡄
⠀⠀⢏⠣⣻⢖⢄⡤⠒⣰⠀⠀⠀⠀⠡⡀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠠⠀⠀⠈⠄⠑⡀⠱⡀⠀⠀⡄⠄
⠀⢸⠜⣲⠡⢡⠆⣍⠠⠒⠇⠀⠀⠀⠀⠐⠄⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⡀⠀⠀⠐⠀⠰⠀⠡⠀⠂⠠⠄⡘
⠀⠀⠣⣃⢠⣁⠬⡀⢉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠌⣀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢂⠃
⠀⠀⠀⠈⠙⠐⠚⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠌⠀⠄⠀⠐⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⣇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠌⠀⠒⠀⠀⠉⠀⢐⠀⢂⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠤⠤⢤⠀⡈⠀⠀⢀⠁⠀⠄⠀⢀⡡⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢅⡀⡀⠈⠀⠀⠀⠄⠀⠀⠂⠀⠐⠀⠀⠠⠀⠑⠒⠂⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠑⠂⠒⡄⠀⠀⠈⡁⠀⠁⠀⠀⠁⠀⠀⡐⠐⠐⠀⢂⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⢀⠟⠒⠲⠂⠪⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣿⣷⡆⢰⣶⣶⣶⣶⣶⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣾⡟⣡⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠏⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⠃⣀⢀⡀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢿⣿⡇⣿⣤⣿⣼⣧⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢃⣦⠹⣿⣿⣿⣿⣿⣿⢰⣶⣍⠁⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⢏⣾⣿⣷⡙⣿⣿⣿⣿⣿⢸⣿⣿⣿⡌⣛⣛⣛⣛⣛⣛⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡈⣿⢃⣾⣿⣿⣿⣷⡘⣿⣿⢟⣿⡘⢿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠉⣾⣿⣿⣿⣿⣿⣷⠜⠃⣾⣿⣿⣶⣄⠴⠆⡹⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⣋⣭⣤⣭⣥⣬⣭⣭⣭⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⢉⣭⣭⣭⣭⣽⣿⣿⣿⣿⠇⠛⠟⠛⣛⣛⡛⠿⠿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠷⠙⠻⠿⠿⠿⠿⠿⠿⠇⢾⣿⣿⠿⠿⠿⠟⢠⡀⠸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⠇⣷⡰⣌⣛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣥⣤⣶⣶⣶⠹⠇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⣭⣭⣤⣄⢺⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣦⢶⣷⡟⣾⣼⣣⣶⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢻⣿⣿⣾⣿⣷⣿⢿⣷⣿⡿⣫⣖⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣾⡏⣏⣿⣿⡽⣾⣟⣵⣿⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⣾⣿⣿⣿⣿⣿⣿⢿⣿⣵⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣯⣿⣇⣿⡿⡷⣿⢿⡿⣿⣼⢟⣯⣿⣿⣿⡿⢿⣻⣽⣾⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡳⢿⣭⡿⢿⣟⣿⣿⣿⣿⡿⣺⣿⣿⣿⣿⣷⣿⣿⢹⣷⣿⢿⣿⣟⣳⠧
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣻⣭⣷⣿⣽⣷⢿⣿⣿⣗⣿⣿⣽⣿⣿⡺⣿⣿⣿⢸⣿⣿⣽⣟⣿⠯⣍
⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡟⣿⣿⣟⣾⢿⣳⣯⡻⣾⣿⣻⢽⣿⣿⣿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣯⣾⣿⢯⣿⣿⣷⣟⣿⣿⣾⣿⣿⣗⢿⡻⣕⣌⣳⣽⣯⣷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⡻⣷⣿⣿⣿⣿⣏⣿⢯⣯⣻⣿⣿⣛⣻⣿⣯⣭⣿⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣼⣿⣿⣮⣻⣿⣿⣿⣿⣿⣯⣳⡳⣽⣟⢷⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣮⣻⢿⣟⣿⣧⣧⣿⣿⣿⣿⣷⣿⣝⢾⣿⡻⣿⣿⠿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣝⣾⣿⣿⣿⡼⣝⡻⣟⡿⣻⣟⢮⡻⡿⠟⠂⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣷⣷⣻⣽⡳⢽⠛⠛⠃⠁⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠛⠛⠓⠲⠦⢤⣄⣀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣤⣤⠴⠖⠛⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉


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

⠃⢠⡏⠀⣀⠀⠹⡄⠈⠋⠀⡼⠁⣀⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢳⠀⠹⠃⢠⡏⠀⣠⠀⢹⡄⠈⠏⠀⡜⠀⣀⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢳
⡄⠈⣧⠀⠙⠀⢼⠁⢠⡤⠀⢹⠀⠘⠁⢠⡏⠀⣤⠀⢸⡆⠈⠃⠀⣞⠀⢤⡄⠈⣧⠀⠙⠀⣼⠁⢠⡤⠀⢹⠀⠘⠁⢰⡏⠀⣤⠀⢸⡄⠈⠃⠀⡎
⠀⠰⡇⠀⢶⠂⢸⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢼⠀⠰⡶⠀⣸⠀⠈⠀⠰⡇⠀⣶⠂⢸⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠉⠀⢼⠀⠰⡶⠀⣸
⠊⢀⡟⠀⣀⡀⢺⡀⠘⠟⠀⣸⠂⢀⠀⠘⣇⠀⠿⠀⢸⠃⠀⣀⠀⢿⠀⠹⠃⢀⡟⠀⣀⠀⢺⡀⠘⠟⠀⡸⠀⣀⠀⠘⡇⠀⠿⠀⢸⠃⢀⡀⠀⢣
⡀⠈⣇⠀⠻⠀⣰⠁⢀⣀⠀⢹⡀⠹⠃⢠⡏⠠⣀⡀⢹⡄⠈⠋⠀⡼⠀⣀⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢳⠀⠹⠃⢠⡏⠀⣀⠀⢹⡄⠈⠋⠀⡜
⠁⢠⡇⠀⣤⠄⢘⡆⠀⠃⠀⣞⠀⢤⡄⠈⣧⠀⠙⠀⢼⠁⢠⡤⠀⢹⠀⠘⠁⢠⡇⠀⣤⠀⢸⡆⠈⠃⠀⣞⠀⢤⡄⠈⣧⠀⠙⠀⢼⠁⢠⡤⠀⢹
⠆⠀⡷⠀⠈⠀⢼⠀⠰⡶⠀⣸⠄⠈⠀⠰⡇⠀⣶⠂⢨⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢾⠀⠰⡶⠀⢸⠀⠈⠀⠰⡇⠀⣶⠂⢸⠆⠀⠁⠀⢇⠈
⠀⠘⣇⠀⠿⠀⢸⠃⢀⢀⠀⢳⠀⠹⠃⢀⡟⠀⣀⠀⠺⡀⠘⠟⠀⣼⠂⢀⠀⠘⣇⠈⠿⠀⢸⠃⢀⣀⠀⢣⠀⠻⠃⢀⡟⠀⢀⠀⢺⡀⠘⠟⠀⡸
⠁⢠⡏⠀⣀⡀⢹⡄⠈⠋⠀⡼⠁⣠⡀⠈⣇⠀⠛⠀⣸⠁⢀⣀⠀⢳⠀⠹⠃⢠⡏⠀⣀⠀⢹⡄⠈⠋⠀⡜⠀⣠⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢳
⡄⠈⣧⠀⠙⠀⢼⠀⢠⡤⠀⢸⠄⠘⠁⢠⡇⠀⣤⠄⢸⡆⠈⠃⠀⣞⠀⢤⡄⠈⣧⠀⠙⠀⢼⠀⢠⡤⠀⢹⠀⠘⠁⢰⡇⠀⣤⠀⢸⡄⠈⠁⠀⡎
⠀⠰⡇⠀⢶⠂⢨⠆⠀⠁⠀⢟⠀⢲⠆⠀⡷⠀⠈⠀⢼⠀⠰⡶⠀⣸⠀⠈⠀⠰⡇⠀⣶⠀⢸⠆⠀⠁⠀⢏⠀⢲⠆⠀⡷⠀⠈⠀⢼⠀⠰⡶⠀⢸
⠃⢀⡟⠀⢀⠀⢺⡀⠘⠟⠀⣼⠂⢀⡀⠘⣇⠈⠿⠁⢸⠃⢀⣀⠀⢷⠀⠹⠃⢀⡟⢀⣀⠀⢺⡀⠘⠟⠀⡸⠀⢀⠀⠘⣇⠀⠿⠀⢸⠃⢀⢀⠀⢣
⡠⠈⣧⠀⠛⠀⣰⠁⢀⣀⠀⢱⠀⠹⠃⢠⡏⠀⣠⠀⢹⡄⠈⠋⠀⡼⠁⣠⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢱⠀⠙⠁⢠⡏⠀⣠⠀⢹⡄⠈⠋⠀⡜⠁
⠁⢠⡇⠀⣤⠄⢘⡆⠀⠃⠀⣞⠀⢤⡄⠀⣧⠀⠙⠀⢼⠁⢠⡤⠀⢹⠀⠘⠁⢠⡇⠀⣤⠄⢸⡆⠈⠁⠀⣎⠀⢤⡔⠈⣧⠀⠙⠀⢼⠀⢠⡤⠀⢹
⠆⠀⡷⠀⠈⠀⢸⠀⠰⡶⠀⢸⠄⠈⠀⠰⡇⠐⣶⠂⢸⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢾⠀⠰⡶⠀⣸⠀⠈⠀⠰⡇⠀⢶⠂⢸⠆⠀⠁⠀⢇
⠀⠘⣇⠀⠿⠁⢰⠃⢀⣀⠀⢻⠀⠹⠃⢀⡟⠀⣀⠀⢺⡀⠘⠟⠀⡼⠂⣀⡀⠘⣇⠀⠿⠀⢸⠃⢀⣀⠀⢣⠀⠻⠃⢀⡟⠀⣀⠀⢺⡀⠘⠟⠀⡸
⠃⢠⡏⠀⣀⡀⠹⡄⠈⠋⠀⣼⠁⣠⡠⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢻⡀⠹⠃⢠⡏⠠⣠⠀⢹⡄⠈⠋⠀⡜⠀⣀⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢱
⡄⠀⣧⠀⠙⠀⢼⠀⢠⡤⠀⢹⠀⠘⠁⢠⡇⠀⣤⠀⢘⡆⠀⠁⠀⣞⠀⢤⡄⠀⣧⠀⠙⠀⢼⠀⢠⡤⠀⢹⠀⠘⠁⢰⡇⠀⣤⠀⢸⡆⠈⠁⠀⡎
⠀⠰⡇⠀⢶⠂⢨⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢺⠀⠰⡖⠀⣸⠀⠈⠀⠰⡇⠀⢶⠂⢸⠆⠀⠁⠀⢏⠀⢲⠆⠀⡷⠀⠈⠀⢺⠀⠰⡶⠀⣸
⠋⢀⡟⠀⣀⠀⢺⡀⠘⠟⠀⡸⠂⣀⠀⠘⣇⠈⠿⠁⢸⠃⢀⣀⠀⢳⠀⠹⠃⢀⡟⠀⣀⠀⢺⡀⠘⠟⠀⡼⠀⣀⠀⠘⣇⠀⠿⠁⢸⠃⢀⣀⠀⢣
⡀⠈⣧⠀⠛⠀⣸⠁⢀⣠⠀⢱⡀⠸⠁⢠⡏⠀⣠⠀⢹⡄⠈⠋⠀⡾⠀⣠⡀⠈⣇⠀⠻⠀⣸⠁⢀⣀⠀⢳⠀⠹⠁⢠⡏⠠⣠⠀⢹⡄⠈⠋⠀⡜
⠁⢰⡇⠀⣤⠄⢨⡆⠀⠁⠀⣞⠀⢤⡄⠀⡧⠀⠙⠀⢼⠀⠠⡤⠀⢹⠄⠘⠁⢰⡇⠀⣤⠄⢸⡆⠀⠁⠀⣎⠀⢤⡄⠈⡧⠀⠙⠀⢼⠀⢠⡤⠀⢹
⠆⠀⡷⠀⠈⠀⢼⠀⠰⡖⠀⣸⠀⠈⠀⠸⡇⠀⢶⠀⢸⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢼⠀⠰⡖⠀⣸⠀⠈⠀⠰⡇⠀⣶⠀⢸⠆⠀⠁⠀⢯
⣀⠘⣇⠀⠿⠁⢨⠃⢀⣀⠀⢳⠀⠹⠃⢀⡟⢀⣀⠀⢻⡀⠘⠟⠀⣸⠀⣀⣀⠘⣇⠀⠿⠁⢸⠃⢀⣀⠀⢳⠀⠹⠃⢀⡟⠀⣀⡀⢻⡀⠘⠟⠀⡸
⠁⢠⡏⠀⣠⠀⠙⡄⠈⠋⠀⣼⠁⣠⡀⠈⣇⠀⠛⠀⣸⠁⢀⣤⠀⢹⠀⠘⠃⢠⡏⠀⣠⠀⢹⡄⠈⠋⠀⡜⠀⣤⡀⠈⣇⠀⠛⠀⣸⠁⢀⣠⠀⢱
⡄⠀⣧⠀⠙⠀⢼⠀⠠⡤⠀⢹⠄⠘⠁⢰⡇⠀⣤⠄⢸⡆⠀⠁⠀⣞⠀⢤⡄⠀⣧⠀⠙⠀⢼⠀⢠⡤⠀⢹⠀⠘⠁⢰⡇⠀⣤⠀⢸⡆⠈⠁⠀⣎
⠀⠰⡇⠀⢶⠂⢸⠆⠀⠁⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢺⠀⠰⡖⠀⣸⠀⠈⠀⠸⡇⠀⢶⠀⢸⠇⠀⠀⠀⢯⠀⢲⠆⠀⡷⠀⠈⠀⢾⠀⠰⡖⠀⡸
⠃⢀⡟⠀⣀⡀⢺⡀⠘⠟⠀⣸⠂⣀⡀⠘⣇⠀⠿⠁⢰⠃⢀⣀⠀⢳⠀⠹⠃⢀⡟⢀⣀⡀⢺⡀⠘⠏⠀⡸⠀⣀⡀⠘⣇⠀⠿⠀⢸⠃⢀⣀⠀⢣
⣠⣈⣧⣀⣻⣀⣰⣁⣤⣤⣀⣱⣀⣸⣁⣠⣏⣠⣠⣄⣹⣄⣈⣏⣀⣾⣠⣤⣠⣈⣧⣀⣻⣀⣸⣁⣤⣀⣄⣵⣀⣹⣁⣠⣏⣠⣠⣄⣹⣄⣈⣋⣀⣼⣠
⣿⣏⠬⣟⣛⣛⣛⣛⣛⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣽⣧⣧⣧⣧⣧⣿⣼⣾⣼⣒⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⡶⠓⠀⠀⠀⠒⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠃⠀⢸⣿⠄⠀⠀⠀⠀⠉⠉⣪⣿⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⣄⣀⠀⠀⡤⠀⣠⡄⠀⠀⣸⠁⠀⢀⣤⢴⣖⡿⠋⢹⣿⣽⣻⣿⣆⠀⠀⠀⠀⠀⣾⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⣷⣜⡿⣿⡿⠂⠀⢾⣽⠃⠀⠀⣿⠶⡿⢟⠀⣁⠲⣅⠀⣰⣿⣿⣿⠟⣋⣴⠀⣀⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⡔⠀⠈⢲⢿⣝⣿⠃⠀⠀⠊⣿⠁⠀⠀⢹⠀⠀⡀⠃⠬⡱⣿⣿⣿⠿⣋⣴⠞⣉⡴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢱⠄⠙⠒⣶⡆⣰⡷⣠⢾⣿⡟⠀⠀⠀⠾⢿⡀⣆⠀⡘⡀⠘⠁⢀⣶⣷⠞⣋⣵⠿⣋⣵⣾⣿⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡈⠀⠀⠀⣻⣴⣟⣺⣷⣌⣻⣧⠀⢀⠂⠀⠄⡀⢿⡀⠰⢹⣼⣷⡟⣫⣴⠿⣫⣴⣾⣿⣿⣿⣿⣿⢫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢋⣀⣘⣉⣥⣶⣿⣿⠿⠛⠛⢿⣄⣾⣌⠂⠂⣧⣷⣥⠀⢷⣻⣷⣿⣯⣷⡿⣿⣷⣿⣿⣿⣿⣿⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡙⣿⣿⣿⣿⣿⠛⠀⢀⠀⠀⠠⠂⠙⢿⣿⣷⣾⣿⣿⣇⠘⢿⣿⣿⣿⣯⣷⣫⣿⣿⣿⣿⣿⣿⡇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣯⣿⣷⣿⠁⠣⠀⢡⣀⣠⣶⣄⣀⡠⠟⣫⡴⢛⣽⣿⣿⣾⠿⠛⢻⡿⠛⣛⠛⢻⣿⣿⣛⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠇⠠⣄⡲⠄⢉⣛⣠⠿⣋⡴⢚⣩⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⡏⣘⣿⣿⣯⡹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⢷⡤⢋⣥⠞⣩⣶⠛⢿⣿⣿⣿⢑⠰⠀⢂⣤⡄⢀⡀⡼⢿⣿⣟⣟⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣀⠾⢋⠴⡯⠞⠃⠀⠀⠈⠙⠛⠋⠁⠐⠁⢇⠀⠈⠘⢡⢏⣟⣻⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣶⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠾⠄⣼⣿⣿⢏⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⢿⣛⣿⡶⢟⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠾⠛⠛⠋⠉⠁⠙⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⣸⣽⡵⠮⠶⠷⠷⠶⠦⣄⠀⠀⠀⠀⢀⡴⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣝⢮⡻⣷⣒⣒⡩⠭⠭⠭⠭⠭⣒⣛⠦⣠⠖⠉⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⡙⢮⡓⢝⠢⣝⠶⣖⣒⣒⣒⣒⣒⢒⣤⠾⢵⡀⠀⢀⣠⠴⠿⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠽⣛⣦⣙⠦⣙⠢⣝⣦⡿⣻⣻⣏⣷⢏⢫⣙⣯⣷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢴⡻⣯⡌⡸⡳⢌⣱⠞⣩⢞⡵⢃⢽⡜⡜⡆⠇⢷⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢣⠱⡜⢧⣇⡷⢞⡡⢊⡵⢋⠔⢁⣴⣳⢱⢹⢸⣸⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣳⡼⢞⣩⠖⣩⠖⣡⠖⣡⣴⣿⡾⣿⡏⡞⡖⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠵⢚⣉⣴⣿⠵⣋⡥⠾⠯⠿⣒⣫⢭⣿⡇⠇⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⣹⢝⢛⣩⠵⠿⠭⡭⢭⠭⠭⢖⣚⢭⣿⠱⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠊⠁⠀⠉⠋⢛⣟⡛⠿⠛⠿⡛⠿⡵⠋⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⢀⣠⠤⠖⠒⠒⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⢤⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣤⣴⠟⠻⣷⣾⠛⢻⣦⡶⣾⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣿⡿⠁⣠⡿⠁⣠⣾⡟⠁⣠⡾⠋⢀⣿⠀⣾⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣀⣼⠏⠀⣴⡟⠀⣴⣿⠏⢀⣼⡟⠁⣠⣿⡏⢸⡟⢹⡏⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣿⣿⠏⢀⣾⡟⠀⣼⣿⠃⢠⣾⠟⠀⣴⢿⣿⠀⣾⠃⣿⡇⠀⣿⡟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⢸⣿⡏⠀⣾⡟⠀⣸⣿⠃⢠⣿⠏⢀⣾⣷⣼⡏⢰⣿⣰⣿⠇⢀⣿⠁⢸⣿⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣿⠀⢸⣿⠀⣸⣿⠁⢰⣿⠇⢀⣾⡟⠀⣼⠏⠻⣿⠁⣼⠟⢿⣟⠀⣼⡿⠀⣼⠋⢹⡇⠀⠀⠀⠀⣠⡾⠏⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⢹⡇⠀⣿⠀⣿⡇⠀⣿⡟⠀⣼⡿⠀⣸⡿⣷⣼⡟⢰⣿⣦⠀⠻⣶⣿⠃⢠⡿⠀⣸⣧⣄⣀⣴⠟⢋⣠⠾⠛⠛⠋
⠀⠀⠀⠀⠀⠀⣿⠉⢻⡆⠈⣷⡀⠸⣿⣿⠁⢰⣿⠇⢠⣿⠇⢠⣿⡀⠙⣿⠃⣾⠻⣿⣧⡀⠹⣧⢠⣿⠃⢠⣿⣴⠿⠋⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⢹⡆⠈⢿⡄⠘⣷⡀⠙⢿⡀⢸⣿⠀⢸⣿⠀⢸⣿⣿⣼⡏⢠⣿⡀⠹⣿⣷⠀⢹⣿⢃⣠⡾⠛⢁⣴⠞⠋
⠀⠀⠀⠀⠀⠀⣸⣿⣦⡘⣿⡄⠘⢿⣄⠈⠻⣿⣿⠀⢸⣿⠀⢸⡇⠹⣿⠃⣼⣿⣷⡀⢹⣿⣧⣠⡿⠟⢉⣤⣾⠿⢿⡄
⠀⠀⠀⠀⠀⠀⢿⣄⠈⠛⢿⣿⣄⠈⠻⣷⣄⠈⠙⢷⣼⣿⠀⢸⣷⣀⡇⢀⡟⠈⣿⣧⢀⣿⠟⠋⣠⣶⣿⠟⠁⣀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⠈⠛⠷⣦⣌⣻⣿⣦⣄⡈⠙⠻⠾⣿⣿⣧⣼⣿⣀⣼⣿⣋⣥⣴⡿⠟⠋⢁⣠⡾⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡈⠙⢿⣶⣤⣀⡈⠙⠛⠻⠿⢿⣷⣦⣤⣤⣭⣭⣿⣿⡿⠿⠟⠛⠋⢁⣀⣤⠾⠛⣉⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠛⠛⠛⣿⣍⡛⠷⠶⣦⣤⣠⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣿⣿⠿⠶⠾⠛⠋⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡶⠖⠶⢿⣏⠻⢶⣤⣀⠉⠛⠿⢿⣿⣭⣭⣉⣉⣉⣈⣉⣉⣁⣀⣀⣠⣤⣤⣶⣾⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⠶⢿⣆⠀⢿⣿⣿⣶⣤⣄⣼⠏⣹⡏⠻⣿⡛⠛⠛⠛⠛⠉⠉⣀⣠⠟⠁⣀⣄⣀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⢶⣿⣦⡼⠟⢁⣤⡾⢿⣿⠀⣿⢷⣄⠈⠛⢶⣶⣶⣿⣿⣿⡿⠁⣠⡾⠋⠉⠙⠻⣦⣀⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢋⣠⣶⡛⠻⣦⣼⠇⣸⣯⡀⠙⣿⣦⣄⡈⠉⠛⠛⠉⣀⣴⠟⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⣠⣴⠟⠉⠉⠛⠿⢻⡿⠀⣿⠟⠻⠶⠟⠛⠋⠛⠻⠶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⢁⣴⠞⠋⠀⠀⠀⠀⠀⠀⣼⠇⢸⡏
⠀⠀⠀⠀⠀⣠⡴⠟⢉⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠁
⠀⠀⢀⣴⠞⠋⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡟
⣠⡾⠋⣁⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠁
⠻⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⠁
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣠⠴⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠥⠤⠒⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⣲⠶⠟⠻⣿⣿⣿⣾⣿⣿⣿⡿⠟⢰⠋⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠊⠉⠀⠀⡀⠀⠀⠉⠙⠛⠛⠉⠛⠒⠦⠾⣖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷
⠀⠀⠀⠀⡇⠀⠹⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠒⣤⢧⣠⡬⠿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⣤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠉⠙⠙⠋⠉⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠙⠿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡄⠀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛
⠈⠁⠉⠁⠒⠂⠤⠄⣁⣲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣖⣛⣉⣁⣀⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⢛⣻⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣉⠁⠐⠒⠀⠀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⣤⠴⠶⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠂⡤⢂⠖⣠⢆⠆⣰⠛⡴⣠⣠⢀⡴⢃⡄⡀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠆⠀⠑⠉⠁⠈⠉⠉⠈⠀⠁⠀⠈⠁⠈⠁⣩⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠦⠀⣀⠀⠀⠀⠀⠀⠀⢸⠿⠏⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⠀⠀⠀⠀⠘⠣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡔⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢧⣜⡵⠞
⠀⠀⠀⢸⣧⠀⠀⠘⠻⠶⠆⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠋
⠀⠀⠀⠘⠛⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡤⠀⠈⠀⠀⠀⠀⠀⠠⣀⠀⠀⠉⠀⠀⠀⠀⠀⢴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠐⠒⠋⠀⠴⠆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢰⡀⠀⠠⠀⠀⠀⠀⠐⠆⠀⠀⣻⣀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡤⢄⠀⠈⢹⡏⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠘⠃⠀⠀⡰⠁⠀⠀⠀⠀⠀⠠⠋⠉⠄⠀⠀⠀⠀⠀⠒⠀⠀⠣⠞⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⡈⠄
⠀⠀⠀⠀⠀⠲⠀⡐⠁⠀⠀⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠳⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡼⠁⠀⡀⢀⣀⠀⠀⠀⠈⠡⠔⠀⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠆
⠀⠀⠀⠈⠀⡼⠁⠀⠘⠋⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣰⣴⠾⠁⠀⠀⠀⠠⠤⠀⠀⠤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠼⠁⠀⠀⠄⣀⠀⠄⠐⠀⠀⠘⠁⠀⠀⠀⠉⠀⠈⠋⠁⠐⣦⣤⣖⠂⠀⠀⠀⢠⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠠⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡜⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠠⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠸⠿⢷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠛⠃
⠀⠀⠀⢶⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢄⠀⠀⠀⠘⠀⠀⢠
⠀⠀⠀⢸⡆⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠈⠛⢉⣉⠠⣿⣖⠀⣤⠄
⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠋⠓⠀⠀⠀⠀⠰⠋⠠⠄⢁⠀⠀⠀⢠⠀⠰⠃⠠⠀⠀⠀⠀⠀⢾⡣
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⢎⠸⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠌
⠀⠀⠀⠹⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠓⠾⢤⡀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⡤⠴⠒⠒⠛⠛⠒⠺⢷⣄⠀⠀⣠⠇⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣫⠥⠒⢊⣉⣉⣉⣉⡙⠒⢤⡙⣦⠞⡡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣩⠴⢒⡩⠟⢉⣡⠤⢾⡉⠑⡦⡙⢾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡴⠋⣠⠖⣉⡤⠔⢺⡇⠀⡇⢹⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣠⠊⡠⠊⢁⡤⠖⢺⠁⢰⠃⣞⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⡞⡠⢾⢡⠇⠀⡞⢀⡞⣰⠏⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡞⣸⣤⡼⠥⠞⠋⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠇⡏⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡥⢺⡼⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⠄⠀⠀⡀⠀⠀⡄⠀⠀⠁⠀⠄⠀⠀⡀⠐⠀⡄⠀⠀⠁⠀⠄⠀⠀⡀⠐⠀⠄⠁⠂⠡⠀⠄⠀⠀⡀⠐⠀⡄⠁⠀⠡
⠀⡀⠀⠀⠀⠂⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰
⠄⠈⠀⠀⠀⢀⢀⠀⠄⠈⠀⠄⠈⠀⠀⠀⢀⢠⠀⠆⠀⠀⠀⠈⠀⠀⠀⢀⢀⠀⠆⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠄⠈
⠰⠀⠀⠀⠀⠁⠀⠀⠰⢄⠀⠰⠀⠀⡀⢀⠁⢈⠀⠰⢄⠀⠰⠀⠀⠀⢀⠁⢀⠀⠐⢄⠀⠰⠀⠀⠀⠀⠁⢀⠀⠰⢄
⠀⠀⠀⠁⠀⠈⠈⡀⢀⠈⠀⠀⠀⠀⠁⠀⠈⡈⡀⢀⠈⠀⢀⠀⠀⠁⠀⠈⡈⡀⢀⠈⠀⠀⠀⠀⠀⠀⠀⡈⡀⢀⠈
⠀⠀⠀⠂⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠀⠀⠀⠀⠠⠀⠈⠀⠀⠂⠐⠀⠀⠀⠀⠠
⢠⠀⠀⡀⠠⠀⡀⠆⠀⡀⠀⢠⠀⠀⡀⠠⠀⡀⠆⠀⡀⠀⢠⠀⠀⠀⠠⠀⡀⡄⠈⡀⠀⢠⠀⠀⠀⠀⠀⡀⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠐⠀⠀⠂⠀⠀⠀⠰⠀⠁⠁⠰⠀⠀⠂⠈⠀⠀⠰⠀⠁⠀⠰⠀⠀⠂⠈⠀⠀⠰⠀⠁⠁⠐⠀⠀⠂⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠠⠁
⠐⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠐
⢠⠀⠀⠰⠀⠀⠠⠠⠀⠀⠀⢠⠀⠀⠸⠀⠀⠠⠠⠀⠀⠀⢠⠀⠂⠰⠀⠀⠠⠠⠀⠀⠀⢠⠀⠀⠰⠀⠀⠠⠠⠀⠁
⠀⠐⠀⠀⠀⠀⠀⢰⠀⠀⠁⠈⠐⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠨
⠘⠀⠀⠠⠀⠀⡁⠀⠈⢀⠀⠘⠄⠀⠠⠀⠀⡀⠀⠘⢀⠀⠀⠄⠀⠠⠀⠀⡁⠂⠘⠀⠀⠘⠀⠂⠠⠀⠀⡁⠀⠀⠠
⣀⠀⠀⠀⠘⠐⠐⠀⠀⠀⠀⣄⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⣄⠀⠀⠀⠐⠐⠑⠀⠀⠀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠱⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠁⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠡⠀⠀⠀⠀⠁
⠄⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠆⠀⠀⠂⠀⠀⠂⠀⠀⠄
⠰⠀⠃⠄⠰⠀⢀⠀⡀⠀⠀⠰⠀⠃⡄⠐⠀⢀⠀⡀⠀⠀⠰⠀⠃⡄⠐⠀⢀⠀⡀⠀⠀⠰⠀⠃⡄⠐⠀⢀⠀⡀
⠁⢰⠀⠀⠀⠀⠈⠄⠀⠂⠀⠁⢰⠀⠀⠠⠀⠈⠄⠀⠆⠀⠁⢰⠀⠀⠀⠀⠈⠀⠀⠆⠀⠁⢰⠀⠀⠠⠀⠈⠀⠀⠆
⠄⠈⠀⠁⠀⠀⠀⠀⢀⠈⠀⠌⠈⠀⠐⠀⠀⠀⠀⢀⠈⠀⠌⠈⠀⠐⠀⡄⠀⠀⢀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠀⢀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢲⠒⡽⠫⢍⡉⠉⠉⠁⢲⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⣰⠃⣠⠃⣼⣙⠲⢄⡈⠑⠦⣄⠀⡆⠈⡆⢛⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⡎⠀⢰⠃⣰⠃⡾⢄⡈⠙⠢⣍⠓⢤⡀⠙⠓⠀⢻⠈⡇⠀⢫⣝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡹⠀⡸⠀⢠⠇⢰⠇⡼⢤⡀⠉⠓⢄⡀⠙⠢⡉⠢⣌⠀⢸⡄⢓⠀⢸⣀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡯⢀⠇⢀⠇⠀⡜⢀⡏⣰⣙⠢⣌⠓⢤⡀⠉⠢⣄⠈⠳⣬⠀⠈⡇⢸⠀⠀⣧⡙⠲⢄⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢰⠇⢸⠀⠸⠀⢠⠃⣼⢁⣧⡈⠑⢦⡑⠦⡉⠢⣀⠈⠳⣄⠈⠀⠀⡇⢸⠀⠀⣇⠈⠑⠦⣈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣸⠀⡇⠀⡇⠀⡘⢀⡇⣸⢇⠙⡷⢄⠈⠳⣌⠲⣌⠣⡀⠈⢲⠀⠀⡇⢸⠀⠀⡿⣗⠦⣀⠈⠑⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠀⡇⠀⡇⠀⡇⢸⠀⡏⠘⣆⠘⢆⠙⢦⡈⠳⣌⠳⡈⢦⡸⠀⢸⡇⢸⠀⠀⡇⠈⢆⠈⠓⢄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⠃⠀⠀⢠⠁⡸⢰⣆⠀⠈⢆⠈⢦⠀⠙⢦⡈⠣⡘⢦⡇⠀⢸⠀⡘⠀⢠⠳⡀⠈⢷⢤⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠃⠀⡃⠀⡀⢸⠀⡇⢸⠉⢦⠀⠈⢣⡀⠱⡄⠀⠙⣄⠙⣾⠀⠀⡏⠀⡇⠀⡸⡄⢱⡀⠈⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠸⣇⠀⡇⠀⡇⢸⠀⡇⢸⣆⠀⠳⡀⠀⠙⢄⠈⠢⡀⠈⢳⠇⠀⠸⠀⣸⠁⢠⠃⠘⡄⢣⠀⠸⣌⠢⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡀⠹⡄⢇⠀⡇⠸⠀⡇⢰⠈⢣⡀⠘⢦⡀⠈⠳⣄⠈⢢⡎⠀⢠⠃⢠⠏⠀⡜⡆⠀⢱⠈⡆⠀⢟⠢⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⡀⠱⣸⠀⢸⠀⡆⢁⢸⠷⣄⠙⢦⡀⠙⢦⡀⠈⢳⠎⠀⢠⠏⠀⡞⠀⡸⡆⠸⡀⠀⡇⢸⠀⠸⢦⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠳⡄⠙⣇⠈⡆⢃⢸⠀⣇⠈⠳⣄⠙⢦⡀⠙⢢⠏⠀⢠⠃⢀⡜⠀⡼⢧⢱⠀⠇⠀⢸⠈⡆⣠⠟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡑⣄⠙⢄⠈⢣⣰⠸⡈⡆⢋⠱⣄⠈⠑⢤⣈⡶⠃⠀⡰⠃⢀⠎⠀⣴⢹⡘⡌⡆⢸⠀⢈⡤⠛⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠈⠳⡄⠙⢧⣃⢳⠘⣆⠈⠑⢤⣠⠏⠀⢀⠞⠁⡠⠋⢠⠎⠘⡎⡇⢇⣡⡼⠖⠉⣠⠖⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡑⢄⠈⠢⡀⠙⢾⡆⢫⠑⣤⠞⠁⢀⡴⠃⢠⠞⢁⡔⠁⠀⣀⡷⠟⠊⢁⡠⠔⣋⢴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡑⢤⡈⠳⣄⠈⠺⢟⣀⣀⡔⠉⣠⣴⣁⠴⠯⠐⠒⢉⣀⡤⠔⣊⡡⠔⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣙⠢⣄⠙⠢⣄⡉⠻⢭⣥⡠⠤⠤⠶⠒⢚⣊⡭⠴⠒⢋⣡⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠽⣦⣄⡉⠒⠦⢄⡉⠒⠶⢍⣉⣥⠤⣒⡮⠿⡏⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠚⠛⠒⠒⠒⠉⠉⠀⠀⠀⠈⠓⠠⠤⠭⢉⣁⡒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡩⠶⠂⠲⠶⠦⠬⠭⣭⣍⣛⣒⣒⣒⣒⣒⣒⣫⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣠⠔⣫⠜
⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⣋⡩⠭⠥⠶⠶⠶⠦⠬⠭⠭⠭⠭⠭⠭⠭⠥⠒⠋⠁
⠀⠀⢀⡠⠔⠊⣁⠤⠖⠊⠉
⣠⠔⢉⡠⠔⠋⠁
⣷⣶⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⣲⢣⣣⢫⢋⠞⡴⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡠⡰⣴⣴⡰⡜⡌⢏⣎⣞⣟⢧⣣⢯⢏⡞⡴⣱⢣⢃⢄⠀⠀⠀⢀⣀⣤⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣜⢄⠱⣝⢮⡪⣟⢷⢱⢹⡘⡞⡜⡼⡷⣝⢯⡜⣰⢡⢣⢃⢎⠎⡦⠶⠚⠋⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡪⡳⣕⢮⡑⢬⡲⢝⣇⢧⢧⢱⢹⣹⣹⣮⡳⣝⢧⡇⡎⡞⡞⡜⡼⡀
⠀⠀⠐⠒⠒⠒⠒⠶⠶⠶⠶⠶⢆⢽⣿⣮⡢⣕⠪⣓⠬⣑⠺⡜⡞⡆⢇⢧⢣⢷⣝⢮⠫⡻⣼⢸⢱⢱⢳⢣⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⣕⢽⡮⡒⢵⡢⢝⡲⠭⣷⢹⢹⡸⡜⡎⡞⣮⡣⡑⢜⢮⡻⣼⣜⡟⣟⠟⠛⠛⠛⠓⠒⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣼⡜⡷⣝⠪⣗⠮⣑⠪⢽⣚⣧⢇⢇⢧⢳⢹⣻⡑⢌⢮⡣⡱⣜⢿⣿⣿⡄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠿⣿⢃⢇⢯⠟⢦⣙⠢⢍⣒⠒⠽⡜⡸⡼⡌⡆⣏⣿⣮⡳⣝⣎⢮⣣⡹⡇⠇
⠀⠀⠀⣀⣠⠤⠖⠛⠉⠁⠀⠀⠸⢻⢸⢸⢸⢸⢸⢨⢻⢲⠮⣭⣭⣷⢣⢣⢳⢹⠙⢙⣙⠙⢎⠻⡛⣝⠝⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⢸⢸⢸⢸⢸⢸⢸⢰⣸⣾⢸⡜⡞⡎⣿⣟⣛⣋⣫⣫⡃⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⢸⢸⢸⢸⢸⠀⣸⢿⠇⠃⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢀⡈⣹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣀⣿⣵⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠠⢇⣨⢿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⣰⣆⠻⢥⣾⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠓⠀⢀⣿⣿⣄⠛⣿⣏⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢸⣿⣿⣿⣧⢿⣿⡘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢍⣷⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⣿⣿⠛⣏⣧⠷⣨⣿⣎⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⣿⠛⢾⠋⠀⠀⡌⣹⣿⢸⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⣿⣄⠈⠦⠀⠀⠙⠁⠟⣎⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⣿⡟⠳⠄⢀⠀⠀⠀⠈⠉⡇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠀⠀⠀⢸⣿⣷⡀⠀⢸⡆⠀⡔⢉⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠸⣿⣿⣧⣬⣾⠛⢾⡟⠑⢠⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠀⠀⢰⣿⣿⣿⠇⢸⣦⣽⠟⡶⠾⡟⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⠃⠀⠀⠀⢰⡏⠁⠀⠀⠉⠱⠿⣻⣿⣾⣽⠇⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡘⠀⡘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡴⢿⣿⣟⢡⣀⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⠁⢀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠃⠀⣸⠓⣿⣿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⡈⠀⢸⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡏⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠇⠀⢠⡇⠈⣿⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⢀⣴⣇⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠁⠀⠙⢿⣿⣿⡏⠉
⠀⠀⢀⣀⣀⣠⣤⣀⣿⡿⠉⠉⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡏⣿⣷⣀⣀⣀⣀⣀⣀
⠸⠯⠟⢉⣍⡈⣣⡿⡿⡥⠀⠤⠤⠼⠄⠠⠤⠄⣰⠎⣁⡀⣧⣠⣤⣤⣤⣧⣾⣿⣿⣿⣿⣿⣿⣿
⢰⡶⠦⠀⠈⣙⡛⠿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣴⡻⠧⣬⣠⣟⣒⣒⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠁⠀⠈⠙⠛⠛⠋⠀⠈⠀⢁⣀⣀⣈⣉⣉⣉⣛⣛⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣟⣻⣿⣻⣿
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣿⣿⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣻⢋⠟⡹⢋⡝⣹⢛⡷⢶⢤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⣇⢸⡘⣧⢋⡜⣡⢋⡜⣡⠋⡴⣱⣿⠟⣽⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⡇⣇⢻⠀⡇⢿⢞⡼⢡⢎⡜⢡⣮⢮⡾⣣⣾⡿⣫⢎⢷⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣛⣿⣧⢹⠘⡆⢹⢸⣿⣲⣧⣏⣴⡿⣵⣿⢟⣿⢟⢞⡵⡳⣫⣿⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣗⣒⣲⣿⡜⡇⢿⠘⡏⣿⢿⣿⣿⣿⣿⣿⣿⣟⣵⣵⣿⣿⣾⡿⡿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⣿⣿⣧⢹⡘⣇⢻⢹⣿⣶⣿⣷⣿⣿⣿⣿⡿⣛⢟⣽⡛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡿⣧⡇⡏⣿⡆⣧⢹⡌⣇⢿⣫⣾⣾⢟⢽⡿⡫⢞⣵⡻⣗⡷⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⢇⡇⣧⣏⣷⠸⡆⢷⢹⡜⣿⣪⢔⣵⡿⣫⠔⡿⢛⢿⣶⢭⣲⢭⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣼⠸⡼⣽⣇⢻⡈⣇⢳⢻⣶⣟⡭⢚⡥⣪⠖⡡⣪⠜⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⢹⣿⣧⣻⣧⡽⣋⢽⣆⢳⡸⣎⢯⢿⡽⣚⡽⢊⡴⣫⠖⣡⢞⡵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡫⢕⡪⣗⣽⣿⣦⠳⡙⣞⣾⣟⡡⢖⡥⢚⡡⣚⠕⣩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠒⠒⠶⢾⣿⣯⣾⣿⣻⡿⠹⢧⡹⣜⢾⢿⢷⡩⢖⡩⠚⣡⠞⠁
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⡿⢷⣭⣉⡛⣮⣮⣻⣿⣷⣭⠴⠋⠁
⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠠⣿⠁
⠀⠀⠀⠻⣦⣀⡀
⠀⠀⠀⠀⠀⠈⠉⠙