Foam Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⣿⠁⣹⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⢀⣤⡶⠶⢶⣄⡀⠀⠀⠀⠀⠈⠛⠛⠿⠋⠀⢀⣤⣤⣄⠀⠀⢠⡟⠉⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠈⢿⡄⠀⢀⣠⣄⡀⠀⠀⠀⢰⡟⠁⠀⠙⣷⠀⠘⢷⣄⣀⣴⣿⣄⢀⣀⡀⠀⠀⠀⢀⡶⢶⡄⠀⠀⠀⠀⢺⣅⣀⡿
⣤⣀⠀⠀⢿⡅⠀⠀⠀⠀⠀⢸⡇⠀⣾⡉⢙⣷⣤⣄⣀⠘⢷⣄⣀⣴⠟⠀⠀⢠⡿⠋⠀⠀⠉⠛⠉⠻⣦⠀⠀⠈⠻⠞⠃⠀⠀⠀⠀⠀⠉⠉
⠀⠉⠻⣆⠘⢷⣄⠀⠀⢀⣠⡾⠁⠀⣼⠟⠋⠁⠀⠈⠙⢷⣄⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣴⠟
⠀⠀⠀⢹⡆⠀⠉⠛⠛⠛⠉⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣠⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣠⡴⠶⢶⣤⡀
⠀⠀⠀⣼⠃⣠⡴⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡶⠶⢦⣄⠀⠉⠉⢀⣤⠶⠾⠛⠷⢶⣤⡀⠀⠀⠀⠀⢿⣼⣿⠋⠀⠀⠀⠈⢿⡄
⣠⣤⠾⠃⠀⠻⠶⠟⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣾⠃⠀⠀⠀⠘⣷⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣼⠇
⠉⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠶⠞⠋⠀⠀⠀⣿⡀⠀⠀⠀⢀⣿⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣠⠾⠛⠶⣤⡶⠞⠃
⣴⠟⠋⠉⠀⠀⠀⠀⠉⠙⠻⣦⣤⡶⠟⠛⠶⣦⣀⣠⣴⠶⠶⠛⠛⠻⠿⢦⣤⣶⠟⠁⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢰⡏⠀⠀⠀⢸⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠻⣦⡀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣤⣤⣄⠻⣦⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⠻⠶⣤⣤⣴⠶⠛⠁⠀⣿⡀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⢠⡶⠷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⢀⣴⠶⠶⣤⠀⠀⠈⢳⡾⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⣇⠀⠀⣹⣧⡴⠶⠟⠷⢤⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠛⠛⣿⠏⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣀⡀⠹⣦⡀⠀⠀⠀⠀⣰⠟⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣬⡛⠷⠶⠶⠛⠉⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⠶⠶⠶⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⣄⠀⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠏⢀⡤⠴⠦⢄⡀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⡤⠖⠋⠀⠀⠀⠀⢱⣙⢚⣠⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠓⠒⠢⣄⠀⠸⣁⡹
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠉⠲⠤⠖⠀⡤⠒⠛⠒⢦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠸⠦⢄
⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⣀⣤⡴⠒⢺⡀⠀⠀⠀⠀⠀⠀⠉⢳⡴⠚⠉⠉⠒⢀⠀⠀⣷⣀
⠀⠀⠀⠀⢀⣠⠇⠀⢠⠎⠀⠀⠣⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠘⠂⠀⢀⡬⢷⡀
⠀⠀⠀⠀⡇⠀⠙⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣹⡄⠀⠀⠀⠀⣀⠀⠀⣀⡀⢀⡟
⠀⠀⠀⠀⠈⠛⠉⠓⠚⠙⠲⠤⠴⠚⠲⠤⠤⠞⠉⠙⠒⠒⠋⠁⠈⠓⠒⠒⠊⠁⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⡎⠀⠀⠂⠉⠢⠀⠀⠦⢉⠀⣁⠠⠈⢤⠦⠅⠀⠀⠀⡀⠀⠀⠐⠀⢓⠠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠁⠀⠀⠀⠀⠀⠀⠂⠂⠀⢁⡨⠀⢁⠀⡠⠀⣞⢑⠰⢂⠀⠀⢀⡂⢡⢌⡀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣄⣀⠀⠐⠃⢤⠀⣊⢦⣭⣠⠒⠻⡁⢠⠂⡀⠠⠺⡈⠁⠠⢁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠢⣄⠀⠈⠉⠁⠈⠙⣦⠓⠀⠀⠤⠠⣭⠘⠤⠤⡁⠈⡂⣁⡄⠀⡠⠰⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠦⠀⢠⢀⠈⢙⠈⠟⢺⠀⠈⡉⣉⠀⠦⠀⠎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠐⠚⢀⠀⠀⣀⠔⠈⠣⠀⠀⠀⠀⡁⢠⢥⠰⠱⠀⠁⠈⣤⠈⠀⣄⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢀⡀⠠⢀⠀⠀⠀⠀⠀⠀⡀⢀⡐⠗⠀⢀⡄⢀⠄⠂⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠸⢄⡀⡜⠁⠀⠀⠀⢢⠔⠚⠓⠢⡀⠀⠈⠁⠀⠀⢀⣀⡊⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠑⠄⠀⠀⠀⠀⠀⠀⠀⢀⠽⡉⠀⠈⠑⠂⠁⠀⠈⠀⠔⠉⠁⢀
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠠⠀⡀⠀⠀⠀⢆⠢⡀⠀⡀⢀⠆⠀⠀⡀⠀⠀⠸⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣠⠾
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠔⠋⠢⢀⡀⠷⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣤⠴⠊⠀⠀⠙⠑⠉
⠀⠈⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁



⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠢⠀⢀⠠⢀⠀⠀⠀⠀⠀⡀⠀⠆⠐⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠀⠀⠀⠀⠀⠀⠐⠤⣶⠿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠐⠀⠨⠴⠔⠆




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⣀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣠⠴⠒⠒⠒⠦⣄⢀⣀⡼⠁⠀⠀⠀⠀⠀⠙⡦⠖⠒⠲⢤⡀
⠀⠀⣠⠖⠋⠉⠀⠀⠉⠓⢶⠋⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⢀⣠⠶⠛⠛⠛⠲⢦⡀⠀⠀⠀⠹⡤⠖⠛⠉⠛⠲⢤⡀
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⢤⣄⡀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠹⣦⣤⠶⠶⠦⣄⡀⠀⠀⠀⠀⠱
⡴⠟⠛⠋⠛⠛⠲⣦⣀⡴⠋⠁⠀⠀⠀⠀⢀⠈⠙⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⣦⣀⣤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠈⠩⣶⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⣠⠶⢦⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡡⣄⢠⣀⡀⢜⠁⠀⠀⠀⢸⢱⠊⠠⢧⠞⡁⢤⡀⡇
⠀⠀⠀⠀⠠⢤⢄⣠⢀⠀⣠⢢⣀⣠⠲⣄⣠⡿⣀⣑⠐⠂⠋⢷⠃⠀⠀⠀⢸⡐⠀⠀⠀⡔⠁⢸⠀⡇
⠀⠀⠀⠀⠀⠐⢸⣻⢠⠉⠁⢀⠉⢁⡀⠠⡏⠂⠎⣇⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⡟⢰⠃
⠀⠀⠀⠀⠈⠐⠊⢹⢸⠀⠀⢸⠀⠘⠁⠀⠉⣤⠒⠃⠀⠀⠀⣸⠁⠀⠀⠀⠀⠹⣌⣀⡴⠃⢸⠃⠌
⠀⠀⠀⠀⠀⠀⠀⣾⠘⠀⠀⠀⠀⠘⠀⠀⠠⣋⠀⠀⠀⢀⠞⠁⠀⣴⣦⠄⠀⠀⠀⠉⠀⢀⠎⣰
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡇⠀⠀⠀⠂⠖⠊⢀⡼⠀⠀⠀⠀⠀⠀⡼⢰⠃
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢾⣟⠁⠒⠒⠉⠀⠀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠱⡗
⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢳⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠀⢰⠁⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠁⡄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⠀⠀⠀⠀⡆⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠓⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⣄⠀⠀⡇⢸
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠠⣴⠀⠀⠀⠀⠘⠀⠀⡇⢀
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣴⣤⣄⣧⣸⣀
⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⣠⣤⠴⠶⠚⠛⠋⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠐⡂⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢂⡴⠏
⠀⠀⠀⡇⠀⠀⢀⡤⠞⠋⠁⠀⣀⣠⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⢘⡀⠀⠘⠧⣄⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⡏⠓⠒⢄
⠀⠀⡰⠋⠀⢀⠄⠀⣟⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⣶⠇⠀⠀⠀⠁⠐⠤⡀
⠀⠰⠇⠀⠀⠉⢀⡞⠁⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣤⣠⣯⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠡⡀⠀⠀⠈⢣⡄⢺⣍⣁⣀⣀⣠⣤⠤⠴⠶⠒⠛⠋⠉⠉⠉⠉⠉⠀⠒⠙⠥⠥⠜⠁⠀⠀⠀⠀⢀⡀⠔
⣀⣀⣀⣀⣀⣀⣀⣈⣉⣭⣄⣀⣀⣀⣀⣀⣒⣂⣒⣒⣒⣀⣀⣀⣒⣈⣉⣉⣉⣉⣈⣉⣁⣀⣀⣀⣉⣉⣉⣀⣀
⣿⣿⣿⣿⣯⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣭⣯⣿⣯⣽⣿⣭⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⣠⣤⣄⢾⡷⣰⣶⣦⡄⢠⣤⡀⣾⣿⡇⠀⢀⣤⣤⢠⣾⣿⣿⣿⣷⣄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣮⡻⣿⡇⣾⣿⣿⣿⣿⠘⣛⣁⢬⢉⡀⡄⣿⢟⡋⣿⣿⣿⣿⣿⣿⣿⢚⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣵⣿⣷⡝⣿⣿⡿⢱⣿⣿⣿⣷⡌⣵⣶⣰⣿⣿⣜⢿⣿⣿⣿⡿⣫⡜⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣯⡍⢿⣿⡿⢧⡶⢘⣦⣽⣛⢿⣿⣿⢧⣿⣿⡼⣿⣿⣿⢗⣬⣭⣵⣾⣿⣿⡎⣻⢟⣵⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⢰⣶⣾⡟⣴⣿⣿⣿⣿⣷⠉⣑⣊⡛⠟⣵⣶⣶⣶⣾⡽⣿⣮⡛⣫⣵⣶⣶⣬⡻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⠿⠿⢋⣨⣭⣯⣥⡻⣿⣿⣿⡿⣱⣿⣿⣿⣿⣷⡽⣿⣿⣿⣿⡿⣙⣛⣙⠿⣿⣿⣿⣿⣷⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⣾⣿⣿⣿⣿⣿⡜⠿⠿⠇⣿⣿⣿⣿⣿⣿⡇⠿⠿⢿⣟⣾⣿⣿⣿⣿⣎⣿⣿⣿⡿⣠⣭⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡏⣿⣿⣿⣿⣿⣿⠧⠋⢉⣵⣾⣷⠮⠻⠿⣡⣾⣿⣿⣷⡼⣿⣿⣿⣿⣿⡿⠸⠟⣫⣥⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣬⢻⠿⠿⢟⣫⣶⡄⢸⣿⢏⣶⣿⣿⣿⣮⣻⣿⣿⣿⣿⡝⠻⠿⠿⣛⣵⣄⣠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⡇⣤⣛⢾⣿⣿⣿⣿⣿⡇⣿⣿⣿⡿⣁⣀⣴⣿⣼⠿⣿⡏⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣎⠻⠿⣿⠿⣛⣾⣿⣿⣌⠿⣿⣿⣿⢟⣤⣽⡉⠁⣾⣿⣿⣯⣽⣷⣤⣾⣷⣄⣀⣴⣿⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠛⢻⣿⡿⣶⣶⣾⣟⣿⣿⣿⠾⣿⣿⣿⣏⣹⣿⣿⡟⠙⢿⣿⣿⡿⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡹⢿⣿⣧⣀⣼⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡟⣿⣷⣴⣿⣿⢟⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣭⣟⣛⣛⣻⣭⣭⣽⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣯⣭⣟⣛⣛⣻⣭⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀⣀⣴⠟⠋⠉⠉⠉⠉⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠋⠙⠻⢷⡿⠛⠛⠋⣀⣤⣤⣤⣄⠀⠀⠀⢸⣷⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠾⠿⠁⠀⣤⣤⡤⣤⠀⠀⠀⢀⣾⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠋⠉⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠀⠀⠀⢀⣠⣤⣤⣄⣤⣤⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠛⠛⣷⣤⣄⠀⠀⠀⠀⠈⣉⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠁⠀⢀⣾⠋⠁⠈⠹⠏⠀⠀⠀⠀⢀⣴⠿⠻⠟⠁⠀⠀⠀⠀⠘⠋⠉⠀⠀⣴⡟⠿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⣴⣾⣿⣧⣤⡀⠀⠈⢿⣦⠀⠀⠀⠶⠚⠂⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⡶⠶⠖⠀⠀⠀⠀⠉⠁⠀⢲⣷⣾⣿
⠀⠀⠀⠀⠀⣿⡏⠙⠻⠿⣿⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠰⣶⣶⣶⠿⠟⠛⣿⡇
⠀⠀⠀⠀⠀⢿⣧⣀⠑⠂⠀⢿⣧⣤⣴⣿⣀⣠⣴⣿⣄⣀⣴⡿⠿⠿⠿⠿⠿⠿⠿⠛⠛⢿⣤⣀⣀⣠⣿⠁⠀⣀⣀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠉⣿⡿⠷⣶⣦⣭⣭⣁⣉⣉⠉⠁⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣭⣭⣽⣿⡷⠾⠟⠛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠠⢀⠍⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⢿⣿⡟⣿⣻⣿⠋⡉⠉⠉⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣴⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣿⠃⠀⣿⡀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠸⣿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠘⢿⣦⣼⣇⣀⡀⠀⠀⣀⣀⣀⣀⣤⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣅⣀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠙⠻⣿⠋⠉⢻⣷⡀
⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠘⣿⠀⠀⣠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠀⠀⣾⡇⠛⢷⣤⡀⢠⣤⠈⠛⣻⣇
⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠙⣷⣾⡇⣀⠹⠻⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⣶⡾⣷⣤⣶⣶⣆⣠⣿⠟⠉⣿
⠀⠘⢧⣤⣤⣤⡤⠴⠶⣶⡶⠀⢿⣤⡟⠉⠿⠶⠀⣸⣇⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⢦⣤⠘⠷⠿⠶⠶⠶⠞⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣻⣶⣿⣤⠴⠶⠶⠚⠛⠛⠛⣹⠇⠀⠀⣀⣀⣤⡴⠶⠚⠛⠋⠉⠉⠉⠈⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠻⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡴⠠⠤⢤⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣤⡇⠀⠀⠀⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠳⣄⠀⠻⣷⣶⣄⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡆⠀⠀⠀⠈⢧⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠰⢤⠨⠃⠀⠀⠀⠣⣀⡀⣀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠄⠒⢲⣤⡀⠀⢠⣏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠴⠶⠦⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠈⠀⠉⢹⠀⠀⠙⠯⠉
⠀⠀⠀⡀⠒⢶⡀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⠤⠚⢉⡉⠉⠓⢦⡻⢦⣀⣀⡠⠂⠀⠐⢲⢀⡄
⠀⠀⠘⢦⣀⠔⠁⢀⡞⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠘⠀⠀⠀⢳⡀⠀⠀⣀⣀⡙⠂
⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⡎⣴⠉⠉⢙⡷⠀⠀⠄⢀⡀⠀⠀⢰⣶⡀⢉⣥⣤⣤⡀⠀⠀⣧⠀⠀⠀⠀⠈⠱⡄⠸⠍⠂⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⠿⠶⠶⠶⣤⣄⠀⣶⠽⠷⣦⣀⡟⠘⣷⠈⣿⣀⣙⣿⠄⠀⢹⠀⠀⠀⢀⡤⠤⡀⠀⢀⣀⠁
⣄⠉⠇⣀⠀⠀⠀⠸⡆⠀⠀⠀⡤⢶⡄⠀⠙⣷⡇⠀⠀⢸⣿⡧⠤⢿⡄⣿⠿⠗⠋⡀⠒⡮⠤⣄⡀⠀⠀⢀⡽⢄⡙⠊
⠈⠹⠝⠹⠤⠤⠀⠀⢷⠀⠀⠸⣧⡈⠀⠀⣠⠟⢷⣤⠤⠊⣸⣄⠀⢸⣇⣿⡄⠀⢀⢷⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⢱
⠀⠀⣶⡀⠀⠀⠀⠀⠘⣆⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢦⣀⡳⢤⠀⠀⠀⠀⠀⠀⠀⣠⠖⣄⡀
⠀⡀⠈⠃⠀⠀⠀⠀⠤⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣌⠁⠉⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠉
⠰⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠉⠙⠛⠿⠷⣶⣶⣶⣟⣛⣛⣛⣛⣩⠭⠽⠒⡇⠙⠒⠀⣠⡢⠀⡆⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠹⣄⠀⠀⠀⠀⢙⢶⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣨⡉⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠂⠈⠳⠤⢧⣠⠤⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣿⣿⣃⣀⡀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⣶⣷⡆⠀⠀⠀⢠⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⡿⣫⣭⣛⣿⣿⣿⣿⣿⣿⣦⣤⣬⣭⣝⠇
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⣤⣦⣛⣟⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣣⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣵⣭⡻⣿⣿⣿⣿⣟⣭⣭⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣭⣭⣻⣿⣿⣿⣿⣇⢿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣭⣻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⣿⡿⢛⣛⡻⢿⣿⣿⣿⣷⣿⣿⣿⣿⢛⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠑⠻⠿⠛⢹⣿⣿⣿⣿⡿⠿⣿⣿⡿⠳⣿⣿⣿⢾⣿⡿⠋⠻⠿⠿⠟⠃⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⣀⡀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣧⡃⠀⠀⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠉⠀⠀⠈⠙⢦⠀⠹⢷⣆⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢠⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⢄
⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠓⠤⠄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠄⠀⠩⠳⢄⠀⢺⣤⡄⠸
⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢀⠴⠂⠉⠉⠉⠉⠉⠳⣄⡀⠀⠀⠀⢀⠤⠤⠤⢄⡸⣆⠀⠀⢀⠄⠀⢀⡈
⠀⠀⠀⠀⢰⡄⢀⠇⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⡀⠀⠱⠀⠀⠙⡌⠉⠉⠁⠀⠢⠀⠁⠁
⠀⠀⠀⠀⠀⠈⠀⠀⢰⠁⢠⣆⡔⠋⠙⡷⠀⠀⠐⣀⠀⠀⢰⣦⠈⣡⣤⣄⡀⠀⢸⡄⠀⠀⠉⠉⢦⠰⠜⠂⣀
⠀⠀⠀⣀⠀⠀⠀⠀⢺⡀⠘⠻⠿⠶⠶⠶⣤⢰⡾⠻⢶⣄⡇⠸⡇⢹⣠⡽⣿⠀⠈⡆⠀⠀⠠⠴⢦⠀⢀⣄⠁
⠀⠀⠪⣈⣃⡄⠀⠀⠀⡇⠀⠀⣰⠛⠆⠀⢸⣿⡀⠀⢠⢿⠓⠚⣷⢸⠟⠋⢁⡎⠹⠒⠶⠄⠀⠀⠴⠂⢌⠁
⠀⠀⠀⠈⣡⠉⠉⠁⠀⢹⡀⠀⠙⠷⣤⡤⠞⠉⠛⠛⠁⠘⠓⠀⠟⠚⠃⠀⡄⢹⡀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠛⠆⠀⠀⠀⢀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠚⠫⠁⠀⠀⠀⠀⠀⠈⠡⠓⢲
⠀⠀⠀⡇⠀⠀⠀⠀⣄⠀⠀⠈⠙⠓⠲⠶⣶⣦⣤⣶⣶⣖⣲⣖⣛⣿⠭⡏⠳⠄⢀⣤⠀⡀⠀⠀⠀⠀⠂⠀⠘
⠀⠀⠀⠹⣄⠀⠀⠀⠘⠶⣀⡀⠀⠀⠀⠀⠀⣀⠀⢉⡍⠉⠉⠁⠀⠀⠀⠘⠒⠀⠀⠛⠦⢧⣤⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⢀⡀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣎⡁⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣥⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠚⠛⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣴⡟⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢧⣄⣠⡾⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣼⣟⣵⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢠⡿⢻⣅⣀⣀⣰⠏⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣤⡀⠀⢀⣤⣴⣶⣦⣄⠀⠀⠀⣠⣶⡄⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢸⡇⠀⠈⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⢺⣿⣄⣀⠙⠃⠀⣿⡏⠀⠀⠈⣿⡇⠀⢠⣿⠙⣷⡀⠀⠈⣿⡀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣾⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣀⡉⠙⠛⢿⣦⠈⣿⡇⠀⠀⠀⣿⡏⢀⣿⣧⣤⣽⣷⠀⠀⣿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⡾⠏⠀⠙⢿⣦⣤⣾⠟⠁⣼⡟⠉⠉⠉⢿⡧⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⢸⡿⠚⠶⢦⣄⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⢠⣿⠂⠀⠀⠀⢹⡆⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠤⠤⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠶⣦⣿⠇
⠀⠸⣎⠁⠀⠀⢀⣼⣥⣤⣀⠀⠉⠛⠻⠷⠶⠶⠶⠶⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠈⢿
⠀⠀⠉⠛⢻⠟⠉⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⠀⠀⠀⣠⠟
⠀⠀⠀⢀⡏⣼⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠤⠤⠤⠤⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿⠟⠋⠁
⠀⠀⠀⠘⣷⣝⠃⠀⠀⠀⢀⣰⣷⣶⣴⣶⣶⠶⠶⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠷⠶⣶⣶⣶⣶⣶⡶⠾⠟⠋⠁
⠀⠀⠀⠀⠈⠛⠿⠶⠶⠶⠛⠁
⠀⣀⣀⡀
⠀⡃⠀⡁⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⣀⠠⠔⠒⠉⢹⣻⠆⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⣀⠄⠒⠉⢀⣠⠴⠂⠉⠀⠀⠀⠀⠀⡞⠁⠓⢄⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⣀⠄⠒⠉⠀⣀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⠑⢄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⣀⠔⠊⠁⡀⠤⠖⠀⠀⢀⢀⢤⠠⠄⠀⠀⠀⢀⣤⡴⣶⢶⡀⠀⠱⡄⠈⢦⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡀⠀⠈⠀⡠⠔⠊⢀⠀⢄⠠⢐⠢⠉⠀⠀⠀⠀⠀⠘⣯⠁⡆⣨⣿⠇⠀⠀⠘⢄⠈⠇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⠄⠊⣀⠤⠂⠁⠀⠀⢀⠘⠢⠈⠁⠀⠀⠀⠀⢠⣤⡀⠀⠀⠘⢷⣀⣟⠁⠀⠀⠀⠀⡈⠀⢸⠀⠀⠆
⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⡞⡁⠀⠉⠀⠀⠀⠀⠀⠜⠂⠁⠀⠀⠀⠀⠀⠀⠀⢸⡷⣼⣷⣄⠀⠀⠻⣿⡆⠀⠀⠀⠀⠓⠐⠃⠀⠀⢸
⠀⠀⠀⢀⣴⠏⠀⠀⠀⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣋⣙⢓⢄⠀⢸⠛⣰⣿⢾⣭⣶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⢠⡾⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⡄⠀⢾⠄⡇⠈⠳⣬⠆⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡑⡆⠀⠀⣸
⠀⢠⣏⠀⢹⠀⠀⠀⡏⡍⢳⠀⠀⠀⠀⠀⣼⠁⠀⢈⣁⣀⡘⣧⡘⠤⣀⡿⣦⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⠁⢀⣾⡟
⠀⡞⠀⠀⠀⡆⠀⠀⡇⠈⠘⣆⠀⠀⠀⠀⠻⠾⠉⠓⠒⢀⣻⠈⠛⠶⠾⠟⠁⠀⠀⠀⠀⠀⣀⢠⠲⠒⠂⡠⠔⢊⠔⠁⢀⣴⣯⣿⡇
⢸⡇⠀⠀⠀⠸⡀⠀⠹⡀⠀⠘⡄⠀⠀⠀⠀⠀⢀⣠⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⣰⢅⠩⠑⠙⢀⠤⠊⢁⠔⠊⢀⣤⣾⣿⣿⣿⡿
⠈⡇⠀⠀⠀⠀⠱⡀⠀⢣⠀⠀⠘⣄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⠤⠋⠀⣁⡠⠌⢁⠄⠀⢀⣤⠾⣽⣹⢿⣾⣿⡟⠁
⠀⢧⠀⠀⠀⠀⠀⠹⡄⠀⠳⡄⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠐⠉⢀⠤⠊⢁⣤⢾⣿⠁⠜⣵⣱⣾⡿⠋
⠀⠈⣆⠀⠀⠀⠀⠀⠙⢆⠀⠈⠢⣀⠀⠭⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠊⠁⣀⠔⠊⢁⣠⢾⣿⣛⠛⣋⣿⢿⢷⡿⠋
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠳⡀⠀⠈⠙⠂⠁⠀⠀⠀⢀⠀⡄⠘⠁⢀⡠⠐⠀⣀⣤⢶⣿⠏⣴⢧⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠒⠈⢁⣠⢶⢛⡿⣏⡨⣃⡜⣸⣣⣳⠿⠋⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣗⣢⢾⣿⣽⣉⣻⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠐⠠⠀⣼⢫⡫⠋⢯⣽⣿⣿⣿⣻⣿⣿⣯⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⡀⢀⣾⣱⡰⢫⣿⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠪⢶⣄⣜⣳⣆⣼⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠐⠤⣄⡀⢀⣀⣠⡤⠤⠷⠶⠶⠒⠲⠒⠳⠶⠤⣤⣀⣀⣀⡤⠊⠀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⣀⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⡀⢀⣀⠄⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡴⠋⠀⢀⣀⣀⣀⣀⣠⠊⠁⠀⠀⢀⣤⠶⠶⠀⣠⡴⠆⣄⠀⠀⣠⣤⡀⠀⢠⡴⢦⡀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⢹⠁⠀⠀⠀⠀⠘⠳⢤⡄⠀⣏⠀⠀⣿⠀⣼⠷⠾⢷⠀⢸⡗⠛⠁⠀⠀⠀⠀⠀⢷⡤⡤⠤⠄⠀⠀⠀⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⡬⢧⡀⠀⠀⠀⠀⠶⠞⠁⠀⠈⠛⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⣟⢧⡀⠀⠀⠉⠁⠀⠀⠀⠉⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠛⠦⡀⠀⠀⠀⠀⠀⣠⠞⠁⡇
⠀⠀⠀⣷⠀⠙⢦⡀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠉⠙⠓⢶⠲⠶⠶⠶⠶⠶⡶⠶⠒⠒⠛⠉⠉⠱⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡤⠞⠁⠀⢀⡇
⠀⠀⠀⣿⠀⠀⠀⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠛⠋⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣉⠛⣛⢛⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡾⠀⠀⠈⢳⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠒⠒⠲⢤⡀⠀⢳⣷⣀⡀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠙⠛⠷⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡴⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠁⠀⠀⠀⠈⠓⠦⠴⠄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⠆⠀⠠⠭⠷⣄⠀⠸⣷⣤⣀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡤⠒⠚⠉⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⡀⢿⡆⠀⠀⠀⠀⡌⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢠⠀⠈⠙⡆⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠤⠤⠄⠒⠉⠀⢦⡀⠀⠙⢦⠙⠶⠦⠔⠊⠀⣄⠈⠙⠀⠖
⠀⠀⠀⠀⠀⠘⠷⠤⠊⠀⢀⡎⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠁⠀⠀⠈⢧⠀⠀⠠⠤⠤⢌⡁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣾⣰⡇⠀⠀⠽⠃⠀⠀⢀⣠⡄⠀⠀⣸⢿⡄⢀⣶⡶⣶⣦⡀⠀⢸⡆⠀⠀⠀⠀⠀⠘⠄⠙⠂⠁⣤
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠙⠛⠛⠟⠛⠷⢶⣄⢰⡿⠛⠻⢶⣤⡏⠀⣿⡀⣿⣠⡤⢻⡇⠀⠀⡇⠀⠀⠀⠠⠐⠲⡄⠀⢀⣤
⠀⠀⠠⣇⣈⡇⡄⠀⠀⠀⠈⡇⠀⠀⠀⣠⠺⣶⠀⠀⢹⣿⡁⠀⠀⢸⣿⠗⠶⢾⡇⣿⠟⠛⠉⢠⠒⢺⠗⠶⣤⠀⠀⠀⢠⠜⢤⡉⠁
⠀⠀⠀⠈⠸⠟⠹⠆⠶⠀⠀⢸⡀⠀⠀⢿⣦⡀⠀⣀⡼⠛⠷⠶⠔⠋⣹⡥⠀⢸⡧⢼⠤⠀⢀⠸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣜⠦⠄⠀⠀⠀⠀⠀⠀⠀⡤⢛⣆⣀
⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⠰⠙⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⡁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠉⡇
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠉⠛⠻⠿⢷⣶⣾⣿⣟⣟⣓⣚⣋⣩⡭⠽⠖⢿⠈⠓⠂⠀⡔⡆⢠⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁
⠀⠀⠀⠀⠳⡀⠂⠀⠀⠀⠘⢦⣂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠳⠖⠐⠀⠙⠦⠼⣆⡠⠤
⠀⠀⠀⠀⠀⠈⠓⠒⠀⠂⠀⠀⠈⠙⠓⠒⠂⠀⠀⠀⠈⠛⠒⠒⠛⠓⠒⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠀⠐⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡻⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⠀⠀⠀⠀⠀⠈⡀⡀⠄⠀⠀⠃⠠⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⢠⢇⡓⢤⡄⠐⠒⠐⡞⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⠁⠀⠀⡘⠈⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠐⠁⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⠀⠀⠀⠀⠀⠆⠀⠘⠀⠀⠀⠀⡐⠹⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠐⠦⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠙⠉⠉⢣⠰⢎⣠⠀⠀⠀⠀⠄⠀⠘⡀⠀⠀⠀⠈⠂
⠀⠀⢰⠁⢅⠀⠀⠀⠀⠉⠉⠉⠛⠓⠂⠠⠶⡈⠀⠀⠀⡀⠀⣷⠀⠈⠢⣀⣠⡤⣤⠤⠤⢷⡶⠒⠃⠇⠴⢠⡠⢀
⠀⠀⠠⠀⠀⠑⠢⢤⡤⠤⠤⠤⠔⠀⠄⠠⠤⡁⠀⡀⠚⡐⠚⠸⡍⠢⡀⢁⠘⠀⢤⢠⡄⠼⠀⢐⡀⠯⠷⠠⣄⠱⠍⡄
⠀⠀⠀⠗⠢⢄⡀⠀⠀⠉⠑⠂⠲⠤⠤⣀⡀⠱⡄⣈⣠⠔⠒⠀⠁⠀⣄⣈⣦⠂⣠⣊⠠⠌⠄⠂⠚⠉⠈⠁⠀⢀⣠⠃
⠀⠀⠀⠘⡀⠀⠀⠉⠐⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⣀⣀⡀⠤⠄⠐⠂⠉⠀⠆
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠂⠀⠀⠀⠐⠒⠀⠒⠒⠂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⡠⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠉⢳⠣⢀⠀⠑⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠠⠄⠒⠨⠋⠉⡱⠈⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢁⠤⠊⠐⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠶⠓⠒⠒⠊⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠃⡀⡄⠀⠀⠀⠀⠀⠈⠓⠒⢦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠀⠈⠀⢄⠃⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠁⢠⠡⠙⢆⠀⠀⠘⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠗⠀⠀⠀⠀⠹⡖⠼⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⢀⠀⠓⠒⡤⠂⠈⠀⠀⠹⢶⠼⡦⡴⠀⠀⠠⢂⠆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⡀⣠⢀⠀⢤⠀⣠⠀⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡰⣂⣽⢦⡀⠀⣡⣶⡄⡀⢀⣠⣌⠀⠉⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⣃⣠⡈⠉⠁⠀⡐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡁⠀⠂⠂⣀⠙⠋⠙⣀⠈⠛⠋⠀⠠⠃⢦⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⡁⠀⢀⢀⡄⠈⢀⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢠⠂⠀⠈⢻⣷⣠⠀⠀⢀⡀⠀⠀⡄⠐⡌⢢⡃
⠀⠀⠀⠀⠀⠀⠘⠀⢀⢤⣳⠥⠬⠦⠥⠴⣫⢖⡄⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢀⢄⡣⡧⠬⠴⠌⣴⡥⣶⡀⠀⡸⠁⠀⠈
⠀⠀⠀⡀⠀⠀⠀⢀⠮⣗⠯⠭⠭⠭⠭⠽⠉⡷⢖⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠫⡳⢻⠭⠭⢽⣿⣿⡟⢔⡻⠄⠈
⠀⠀⠀⠀⠆⠀⠀⠶⡽⠃⣏⣉⣉⣋⣉⣙⠛⢭⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠳⠝⠀⣬⣭⣭⣭⣭⣭⣇⠈⢪⠽
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⠉⢉⣩⢉⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⠀⠓⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⡄⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠰⠟⠀⠨⠅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠰⠠⠳⠜⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠽⠈⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠨⠽⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡇⢀⣀⣀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⠃⠀⠀⠈⡷⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠒⠓⠲⠦⣄⠀⠀⢹⣹⣄⣀⡀⠔⠁⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠙⠿⢷⡶⠶⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢹⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄
⠀⠀⠀⠀⠀⠺⣤⡀⠏⠀⠀⠀⠀⠻⣄⣀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⡤⠒⠒⠲⢤⡀⠀⠀⣾⡅⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣭⠤⠤⠤⣤⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⡏⠀⠀⠉⠉⠉⢹⠀⠀⠘⠿⠿⠀⠈
⠀⠀⠀⠀⣀⠤⣄⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⢀⡴⠷⠖⠒⠲⢤⡈⢿⣄⠀⠀⠀⢀⡜⠀⠀⠤⡄
⠀⠀⠀⣴⠀⠀⢈⠇⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠋⢁⠀⠈⠱⡄⠀⠀⠘⣦⠉⠛⠛⠛⠁⠀⠰⣀⠀⠉⠘⠁
⠀⠀⠀⠘⠓⠒⠈⠀⠀⡾⠀⠀⢀⠀⣠⡤⢴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠦⠄⠀⠁⠀⠀⠀⠘⣇⠀⠀⠠⠔⠰⠦⢄⡀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⡇⣾⡁⠀⠀⡨⠏⠀⠀⠐⢀⣠⡄⠀⠀⢠⡿⣷⡀⢠⣶⠶⢶⣶⣄⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⢹⠀⠓⠂⠁⣤
⠀⢀⠀⠀⠀⠀⠀⠒⠺⡇⠀⠈⠛⠿⠿⠶⠶⠶⢶⣤⡀⢴⠷⠚⠻⣶⣄⣾⠁⠸⣷⠀⣿⣀⣤⣹⣿⠀⠀⢸⡆⠀⠀⠀⢠⣄⠶⢦⡀⠀⢀⣄
⣔⠉⢻⠀⡔⠀⠀⠀⠀⢿⠀⠀⠀⠀⣠⢶⣦⠀⠀⠙⣿⣿⠀⠀⠀⢈⣿⣿⠤⢤⣿⡀⣿⡿⠾⠚⠁⡠⠲⢾⣡⣄⣀⠀⠀⠀⠀⣀⠧⣀⠛⠊
⠉⠻⣟⠆⣧⣀⣀⡀⠀⠸⡄⠀⠀⠰⣿⡀⠋⠀⠀⢀⡿⢿⣦⣀⣠⠞⢹⣇⠀⠀⢹⡇⣿⣀⠀⠀⠐⣧⡄⠁⠀⠀⠉⠁⠀⠀⠀⠁⠀⠈⢳
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠙⠻⠶⠶⠖⠋⠀⠀⠉⠉⠁⠀⠊⠉⠁⠀⠛⠉⠉⠉⠀⢀⡎⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⠀⠀⠸⢷⠄⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠚⠲⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠗⠲
⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠛⠷⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡴⠶⢶⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⣧⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⣯⣿⣭⣭⣭⠭⠶⠖⠛⠋⢹⡀⠈⠉⠁⢰⣽⠇⢰⠁⠀⠀⠀⠀⠀⠌
⠀⠘⢧⡀⠂⠀⠀⠀⠀⡳⢮⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠈⠙⠲⠼⢧⣤⠤⠄⠀⠀⡀
⣤⣤⣤⣭⣷⣶⣶⣦⣥⣤⣤⣬⣭⣷⣶⣶⣶⣶⣬⣥⣬⣷⣶⣶⣿⣷⣶⣶⣬⣷⣶⣦⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⡄⠈⡀⠀⠀⠀⢀⠄⠒⠔⠀⠐⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢀⢶⣶⣶⣶⡖⢁⣾⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠉⠁⠀⠀⠀⠑⠒⢦⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠱⡤⠒⠄⠴⣱⠞⠁⠀⠀⠀⠀⠀⠀⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡞⠁⠀⠀⠀⢠⡀⠀⠂⢠⠀⡀⠈⠑⠒⠢⢄⠠⠤⢤⠔⠚⠃
⠀⠀⠀⢀⣤⣴⣎⠉⢳⡞⣦⡀⠀⠀⠀⠈⠀⣜⠀⠀⠀⠜⠁⠀⠀⠐⠀⠀⠠⠄
⠀⠀⠀⠈⢶⣾⣟⡛⢚⣿⣩⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠙⠚⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢖⡐⢤⢀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠀⢤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⠊⠐⣤⢏⣀⣞⡂⠀⠐⢿⣿⠿⠷⠂⠀⠀⠾⠟⠁⠀⠀⠐⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠈⢜⠷⠞⠚⠒⠓⠺⢭⣨⡅⠀⠀⠸⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠕⠐⠀⠆⡌⠀⠀⠀⠀⠀⠿⢿⣶⣿⣶⣶
⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⢦⠇⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡂⠠⢀⡀⠠⠄⠀⠠⣔⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠤⡂⠠⠶⠂⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠂⠚⠉⠉⠀⠦⠀⠀⠠⠌⠃
⠀⠀⠀⠈⠂⢀⠈⠁⠀⠀⠠⣁⠖⡀⡡⢀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⠄⠙⢁⡦⠀⠀⠀⠽⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠈⡆
⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⣤⣤⠷⢶⡶⣄⣨⡵
⠀⠀⠀⠀⢠⠄⢄⠀⠀⠀⠀⠀⠀⣴⣦⡴⣶⡶⡆⠀⠀⠀⠀⣠⠄⠒⠂⠉⠉⠻⣶⡀⠀⣼⡟⠀⠀⠀⠀⢻⡏
⠀⠠⠢⢀⡈⣆⠈⠖⠐⠀⠀⠀⣴⣾⣿⣿⣾⣿⣿⣤⠀⠀⠸⣯⡀⠀⠀⠀⢀⢸⡟⠀⠀⠙⣧⠀⠀⠀⣠⣾⠇
⠀⠀⠉⠄⠘⠀⢆⠓⠀⠀⠀⠀⠈⠁⠈⠓⠋⠋⠙⠛⠧⠀⠀⠈⠻⠶⠚⠑⠺⠛⠁⠀⠀⠀⠈⠛⠛⢷⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⡄⠀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖
⠀⠀⠀⠀⠀⠀⣖⣚⠑⣒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⣠⠤⠐⠒⠒⠤⣄⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠓⢄⡀⣀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⠒⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡞⠁⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠑⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⡄⢀⡀
⠀⠀⠀⠀⠀⣰⠖⢆⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠊⠠⣐⡄⠠⠄⠀⠀⠀⠀⠀⠈⡀⠬⠖⠦⢄⡀⠀⠀⠀⠀⠰⠥⢤
⠀⡤⠒⠲⠎⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠑⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠢⡄
⠘⢦⢀⡤⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢱
⠀⠀⠈⠀⠀⠉⠉⠋⠹⣁⣀⠉⠈⠉⠁⢀⣀⠉⠛⠀⠛⠉⢁⠘⠒⠐⠂⠒⠁⠉⠘⠛⠋⡛⠒⠻⠭⠭⠤⠔⠒⠙⠒⠂⠐⠒⠛⢯⣲⠤⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠉⠀⢽⣉⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠄⠃⠀⠀⢄⢀⡀⣀⠀⠀⠀⢀⡠⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠑⠒⠒⠚⡩⠽⠖⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠚⠻⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢼⡉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗
⠀⠒⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠤⠊⠁⠀⠀⠈⠢⠤⠀⠀⡀⠉⠉⠋⠉⠉⠁⠈⠉⠁⠈⠉⠒⠒⠒⠉⠙⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢂⣀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡤⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡠⠠⡔⠒⢄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⣀⡤⢄⣀⣀⢄⣀⣀⣀⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣒⣢⣤⣔⣒⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣤⣶⣾⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠻⠿⢿⣿⠟⠉⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⠀⠀⢀⠀⠀⢀⣠⣶⣿⠿⠋⠉⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠙⠳⣦⡙⣿⣦
⠀⠀⠀⠀⣀⣤⣤⣄⣀⠙⠻⢿⣿⣿⣿⢿⣷⣶⣿⠟⠋⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠈⢷⡘⣿⡇
⠀⠀⣠⣾⠿⠛⠛⠛⢿⣷⡀⠀⠀⠀⢠⣾⡿⠛⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⢿⡀⠀⢸⡇⣿⣿
⠀⠀⣿⡏⠀⠀⠀⠀⠀⣿⣿⠀⢀⣴⣿⠏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠘⣧⠞⠁⠀⠀⢸⡇⠀⣸⠇⣿⡏
⠀⠀⢿⣷⡀⠀⠀⠀⣠⣿⡟⢠⣾⡿⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⣿⢙⣷⣄⡘⠷⠀⠀⠀⣾⠁⠰⠟⣸⣿⠃
⠀⠀⠈⠻⢿⣷⣶⣾⡿⠋⢠⣿⡟⢀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣾⠉⠀⠈⢻⡄⣿⠋⠀⠈⠁⠀⠀⠀⣼⠃⠀⠀⣴⣿⠃⣠⣾⡿⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢠⡟⠀⣸⠃⠀⠀⣴⡋⣁⡀⢻⣄⣀⣀⡼⠁⠈⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣾⡿⠃⣼⣿⠋⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⠀⠀⢻⡀⠀⠀⠈⠉⠉⢹⡆⠈⠉⠉⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⣿⣿⣅⠀⢿⣿⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⡄⠀⠘⢷⡀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⣀⣴⣿⠟⠉⠙⢿⣷⡌⢿⣷⣤⣤⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⠻⣄⠀⠀⠙⠶⣤⣄⣀⣀⣀⣀⣤⣤⠶⠞⠋⠁⠀⣀⣴⣾⡿⠋⠁⠀⠀⠀⠀⢻⣿⠀⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣍⠛⠆⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣴⣶⣾⣷⣤⣀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠛⠿⢿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠤⠒⠈⠉⠁⢰⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⠉⠀⣰⡤⠤⠔⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠔⠒⠒⡇⠀⡇⢛⠉⠙⠐⠒⠒⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣄⡀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠙⠓⠲⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠒⠒⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠖⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣭⣶⣶⣦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣶⣶⣤⡀⠀⠀⠀⠀⣰⡿⠛⢍⠉⠻⠁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⡇⠀⢿⣷⣤⠾⣦⡴⣿⣿⠀⢸⡆⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⠲⠶⠞⠁⠀⠀⠙⠶⠦⡴⠚⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡴⠚⠋⠙⠳⣦⡀⠠⡀⡇⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠙⠛⠹⠙⠒⠚⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠃⠀⠀⠘⠒⢲⣀⣀⠀⠀⠀⠀⢰⠉⠉⠑⠂⠐⡄⠀⠀⠀⠀⣀⣀⣰⠋⠀⠀⠈⢀⣀⣀
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢷⡀⠀⠀⢫⠀⠀⠀⠀⠀⠀⣰⠀⠀⡸⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠒⠐⢄⡀
⠀⠀⠀⠀⠀⠑⠤⠤⠤⠶⣤⣤⣤⣴⠴⠦⠤⠴⠞⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠉⠀⠀⠉⠛⠒⠒⠲⠶⠶⠶⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠚⠉⠁⠉⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠢⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⡀⠀⠀⠀⠀⠀⢀⡄⠒⠁⠀⠀⠀⠀⠀⠀⠉⣠⠵
⠀⠀⠀⠀⠀⠀⡀⢠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⠀⠀⠀⠀⠙⠒⠒⠠⠔⠒⠢⠤⠚⠉⠉
⠀⠀⠀⠀⠀⠈⠒⠀⠠⠤⠤⢤⣀⣀⣀⣀⣀⡤⠤⠤⠤⠟⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢤⠋⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣦⣀
⠀⠀⠀⠀⠀⠀⢠⠴⠚⠀⠀⠀⠀⠹⠒⢦⠖⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠀⠀⠀⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠘⠦⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⠐⠁⠀⠀⠀⠈⠒⠂⠀⠤⠤⠤⢄⠀⠀⠀⢀⣤⡤⣄⠀⠀⠀⣠⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠔⠒⠚⠐⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠈⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⢿⡀⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⣀
⠀⠀⠀⠀⠀⡀⣴⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠼
⠀⠀⠀⠀⢯⠟⣴⢦⠀⢀⡤⢄⠀⠀⠀⢠⣦⠀⠀⢀⡠⠴⠒⠒⢶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠳⠊⠀⠀⠀⠀⣁⠴⠚⠉⠀⢀⡀⠀⠈⢧⠀⠀⠉⠳⡀
⠀⠀⠀⠾⠇⠀⠰⣋⠇⠀⠀⠀⢀⡠⠖⠋⠀⠀⢀⡀⠔⠉⠀⢱⠀⠈⡆⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⡠⠐⢤⡁⠈⠳⡄⢰⠉⠀⠀⠸⡄⠀⠀⠀⣧
⠀⠀⠀⢰⡋⢳⠘⠷⠀⡏⠀⢀⠎⠩⣶⡁⠞⢨⡧⠟⠒⠉⠉⠀⠀⠀⡠⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠉⠁⠀⠀⠀⢳⠀⠀⢑⠆⢀⠗⠒⠁⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢼⡆⠀⠰⠔⠊⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⣀⠔⣋⡀
⠀⠀⠀⠀⣠⠊⠉⠁⠀⠀⢱⡀⠀⠀⣀⣀⠤⠒⠉⡀⣀⠴⠖⠒⠐⣎⠁⠀⠙⢿⠆
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠐⠉⠉⠓⠁⠀⠉⠒⠊⠉⢆⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⡹⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠒⠒⠒⠒⣒⣦⠤⠤⠤⢄⣀⡀
⠀⢀⣸⠤⡄⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡶⠤⠤⠤⣄⣉⣒⠆⠀⠀⠀⠀⠹⡀
⢮⣁⣀⠀⠉⠈⠈⠀⠉⠉⠈⠉⠉⣀⡬⢭⠉⠁⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡩
⠀⠀⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠦⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠂⠉⠁
⣀⣀⣈⣓⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣒⣒⣒⣒⣒⣚⣉⣉⣉⣉⣉⣣⣤⣴⣒⣊⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣟⠉⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⠿⠛⠋⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠰⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⢘⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠀⠆⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂
⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⣟⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⢪⠐⠇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠛⣠⠞
⠀⠀⠀⠀⠀⠀⡞⠓⢤⡜⠀⠀⠀⠸⡆⠀⠈⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢸⠃⠀⠘⠦⣄⡀⠀⠀⢳⠀⠀⢻⠀⡏⠀⠈⠉⠉⠙⠛⠲⣤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠙⡆⠀⠈⣇⠀⠸⡆⢹⠀⣰⢲⠶⠤⣤⠟⠁⣀⡴⠋
⠀⠀⠀⠀⠀⡇⠀⠀⡠⠐⠢⠄⢸⣀⡠⠞⠉⠙⢧⡏⢠⡏⢛⡶⠞⢁⡴⠮⡉⠳⡀
⠀⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠈⠄⢫⠀⢠⠖⠉⠁⠀⠈⠳⣏⡠⠴⠿⠓⠒⠛⠉⠉⠱⡄
⠀⠀⠀⠀⠀⠈⢧⠀⢇⠀⠀⠀⢸⠈⢆⡜⡔⠉⠉⠒⠢⠀⢸⠀⣀⠤⠴⠒⠒⠒⢄⠀⣧⡤⠖⠲⢤⣀
⠀⠀⠀⠀⠀⢀⣸⡄⠈⢦⠀⠀⣸⠀⠘⣤⠁⠀⠀⠀⢠⠀⢸⠀⠇⠀⠀⠀⠀⠀⠈⡄⢏⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠰⣅⠀⡱⠀⠀⠉⠉⠁⠀⠀⠈⡀⠀⠀⠀⠸⢀⡏⡀⢀⠀⠀⠀⠀⠀⠀⠇⢸⠀⡠⠖⢆⠐⡆⢳
⠀⠀⠀⠀⠀⢹⠂⠉⡑⠒⠒⠒⠒⠒⠠⠤⠼⠤⠤⠤⠧⠼⠽⠧⠼⠤⠤⠤⠤⠤⠤⠼⠤⠯⠔⢀⡸⠀⠇⠈⣇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⢸⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣧⠀⢸⢦⣠⠇
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠶⢻⡀⡸⠀⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠛⠛⠛⠋⠉⠈⠻⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠛⠛⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢰⡒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠶⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣠⠖⡄⢸
⠀⠀⠀⠀⠀⢀⠤⢤⡰⠊⠁⠀⠈⠙⠁⠀⠀⠀⠀⢡⡔⠊⠉⠉⠐⠖⠒⢢⣀⠤⠤⣄⢀⠠⢤⡀⠀⡠⣇⠸⠧⢤⣄
⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠙⢫⢣⠜⢰⢀⣦⢼
⣠⠊⢉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⣈⣀⢏⠈
⡇⠀⠣⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠒⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡤⠖⠁
⠀⢸⡉⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⢸⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⣆⡀
⠀⠀⢀⡽⠀⠈⢉⠗⠒⠲⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠊⠉⣳⠀⠀⢀⣹
⠀⠀⠘⠤⣀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⢣⡀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠀⠀⠈⠁⣹⡆⠈⣇⣀⣀⠀⠀⣉⠁⠀⠐⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⣀⣠⣶⡶⠈⡙⠻⣿⣿⡄⢸⡏⠉⠐⠤⠙⠻⣿⣿⣶⣦⣬⡛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡌⠳⢿⡹⣿⠥⢉⣉⣁⡐⢩⡿⠚⠛⠛⠀⠐⠲⢄⣠⣽⠟⡉⡽⠇⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⣶⣤⣉⡙⠛⠛⠾⠛⠟⣀⣶⣿⣋⠁⠁⠓⠘⢛⣉⡉⠀⢰⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣷⣼⣦⣀⣉⡉⠙⠦⢤⣠⠶⠶⠊⠀⠉⣉⣉⣦⡶⠊⠉⣟⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⢛⢿⣿⣿⣿⣟⡿⢿⠟⠟⡿⠿⣿⣿⣿⠗⡄⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠏⢹⣿⣿⣿⣋⣹⢿⡉⠁⠛⠾⠓⠂⣠⢼⣿⣿⡟⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⠂⢲⣾⣯⠂⠀⠁⠙⣧⢀⣠⣤⣤⣤⣴⣾⣿⣿⡆⠀⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡃⠹⡇⢙⠤⠀⠀⠀⣈⡻⠿⣿⣿⣿⣿⣽⣿⣷⠋⠀⠀⠠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡃⠀⣝⡦⠄⠈⢁⣠⣌⣶⣤⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠈⢳⣤⣴⣴⡟⢳⣾⠋⠉⠩⠦⢈⣭⣿⣿⠂⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⠀⢠⡟⠹⣿⣿⣿⡿⢁⡀⠀⠀⠰⢤⢼⣿⣯⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⢸⣀⠈⠐⣿⣿⡇⠉⢉⡀⠀⠀⠟⣿⣿⠋⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⠉⠻⣷⣾⡿⣿⠀⠌⠁⠀⣠⠈⣿⣿⡇⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠀⠀⢸⡿⠚⣻⣄⠉⠀⠂⠻⡆⣽⣿⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⠀⠀⣼⣷⠀⠀⠻⢛⣟⣿⠿⣾⣿⣯⠈⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⠀⠀⠀⣩⣿⡆⠋⡐⠠⠄⠠⠈⣼⣿⡿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⡀⢸⣿⣷⣄⣘⠀⣤⣤⣴⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⡀⠀⠀⠐⣿⠟⠻⠻⢏⡓⠫⠿⢿⣿⠗⠀⠀⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢿⡷⠀⠀⠋⠸⠃⠂⠀⠰⠇⢠⣼⣿⣿⠃⠀⠀⢠⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢾⡅⠂⠀⠀⡜⠉⠀⠀⠀⠈⠀⠼⣿⣿⠀⠀⠀⠘⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢀⡀⠘⣠⣤⡾⣦⣶⣶⢾⣶⣿⣧⣀⠀⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣿⠋⠁⢀⡟⠡⢙⡁⠀⠉⢘⣻⣾⣿⡇⠀⢈⣿⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣹⣷⣤⣭⣻⣶⣈⣷⣤⣸⣿⣿⣿⣿⣷⣤⣿⡏⣠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣌⣉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣀⣯⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠀⠀⠒⠒⠒⠛⠋⠉

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢨⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠤⠤⠤⠤⣤⠤⠤⠤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⡤⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠄⠀⠠⠀⣠⠕⠒⠘⠒⠤⡁⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢠⠒⠉⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠦⠔⠒⠬⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠠⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣬⠉⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠸⡀⢸⠛⠈⠺⡇⠀⠀⠀⠀⢠⠦⠄⠤⠔⠉⠓⠒⢲⢸⠗⠁⠋⣧⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⢀⠞⢁⠆⠀⡠⠊⠀⢰⠢⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢄⠀⠹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡸⡀⡜⠀⡰⣳⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⢸⠀⠸⡆⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠁⢸⠀⠀⡿⣹⠀⠀⠀⠈⢦⣤⠴⠃⠀⠘⣲⠀⠙⠲⠒⠃⠀⢰⢱⠀⠈⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⢇⢈⢆⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠀⠀⡀⠀⢀⢀⠎⡟⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠄⢀⠈⠘⡆⠀⠈⢢⡈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⢋⡔⠁⠀⢰⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠈⠒⠱⠦⢄⣀⣀⡀⢀⣀⣀⣀⠤⠶⠏⠒⠁⠀⠀⣠⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠰⠀⠂⠘⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠘⠀⠈⠀⠐⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠁⠠⠀⠁⠀⠀⠃⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢸⡇⠀⠀⢀⠘⠀⠀⠀⢈⠀⡀⢀⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠂⢀⠀⠀⠀⢀⡀⠈⠀⠈⠀⡀⠀⢀⢘⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠴⠶⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠶⠶⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⣶⣿⣝⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣖⠚⠉⢡⠶⢦⡸⣧⡴⠋⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣶⣟⠉⢠⡟⠉⢰⡄⢸⡗⠋⠓⠈⣃⣤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠀⠸⣧⣤⣤⡘⠳⠦⠞⢁⣀⡥⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡇
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠶⢞⣣⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢸⡇⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⢸⡇⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠓⠲⠦⢤⣤⣀⣀⣀⣠⣤⣤⠤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁
⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣄⣀⣀⣀⣠⣤⠤⠶⠚⠋⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣏⣏⣼⣩⣽⣥⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⡆
⠐⢶⣶⣿⣷⣤⣤⠄⠀⣀⣄
⠀⢀⣿⣿⣿⡏⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠘⠉⠀⠈⠳⠀⠀⢀⣷⣶⠃⠀⡀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡀⠀⢀⡀⢸⢱
⢠⡄⠀⡀⠀⢀⡀⠀⠉⢻⠟⠓⢀⣽⣿⣇⡀⠘⠃⢀⣦⣠⠀⣳⣾⡀⠈⠁⣤⠀⠛⠃⠀⠙⠃⠈⡌⡄

⠀⠀⢀⣿⣷⣿⠀⠀⠀⠀⠀⢠⡄⠈⠟⠀⢀⠀⠈⢙⡿⠧⠀⠀⠃⢀⣤⡀⠀⢀⡀⠘⠗⠀⠀⠀⢣⣧
⠀⠈⠉⠹⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣶⠂⠀⠀⠀⠀⣀⠀⠀⢉⡀⠀⠹⠛⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠁⠀⠶⠆⠀⢦⣿⡶⠀⠀⠀⠀⠉⠉⠀⢠⣀⠄⢹⡿⡏⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⡀⢀⡄⠀⠀⠘⠉⠁⠀⠀⠠⡶⠀⠀⠈⢻⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣹⣿⡧⠄⠀⠀⠀⡀⢀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠈⠁⠙⠀⠀⠀⠛⢠⣿⣿⠦⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢀⣤⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠘⢳⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡱⠀⠀⢀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⣀⠤⠤⠤⣀⡀⠀⠀⣠⡔⣃⠙⠃⢀⢤⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⡇⢀⣤⣀⡀⠀⢱
⢀⠔⠋⠙⠲⢤⡀⢀⡐⠉⠙⠞⠀⠀⠈⠖⠉⠀⠀⠀⠀⠀⠙⢆⠀⠀⠿⠛⠁⠀⠈⢛⡀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠑⠊⠀⠀⢹⡀⢸
⡌⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⢿⠀⠀⠀⢸⡇⢸
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠰⠆⠉⠉⠳⡁⠀⠀⠀⠀⠀⠀⠀⡷⠒⠒⢄⠀⠀⠀⡀⣔⢀⢸
⠈⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⢱⠯⣷⣊⣨⣧⣤⣀⡀
⠀⠀⠈⢇⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢸⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⠐⠈⠂⠒⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠂⠩⢥⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⡀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠠⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠁⠀⢀⡸⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⡜⠀⠀⢀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡜⠀⣄⣸⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢡⠀⢹⣤⠃
⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣴⣼⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣽⣾⣧⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣥⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠦⣄⣀⣠⠴⠒⠶⠶⠒⠋⠳⠤⣀⣀⣀⣠⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡆⣿⣷⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡋⠋⠛⠛⠛⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⣿⣿⣿⣿⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⣿⣿⣿⡿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⡉
⠀⠀⠀⠀⠀⢠⣾⣷⣆⠸⡆⠀⡿⠁⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⡏⣿⣿⡏⠀⣷⠀⡇⣀⣤⣤⣶⠀⠰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣶⣧⡘⣧⡀
⠀⠀⠀⠀⠀⠸⣻⣿⡟⢀⡇⠀⣿⢻⣿⣟⣻⣄⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡘⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡶
⠀⠀⠀⠀⠀⠀⠈⠁⣠⠞⠀⠀⣿⣸⣗⣷⣹⣽⣿⣿⠁⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡘⣿⣆⠀⠀⠀⠀⠀⠀⠀⣇⢠⡇
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡘⣿⡄⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠙⠛⠛⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡘⣷⠀⠀⠀⠀⠀⠀⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⡘⡇⠀⠀⠀⠀⠀⠙⠙
⠀⠀⠀⠀⠓⠒⠶⠶⠶⢤⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡈
⠀⠀⠀⠀⠤⠤⠶⠶⠶⠟⠛⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡏⣾⠂⠀⠈⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⡏⠀⠀⠀⢃⠀⠀⠁
⠀⠀⢀⣀⣤⣤⣤⣤⣴⣾⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣴⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠚⢃⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠸⠟⠿⠟⣿⣿⠿⠿⠿⠟⠻⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠀⠀⠀⠀⣀⣾⠁⠀⠀⠀⠈⠛⠿⢿⠿⠿⣿⠟⠛⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠠⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⢁⠀⠛⠋⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢀⡀⠀⠀⠀⠀⣿⣟⠀⠐
⠀⠀⠀⠀⠠⣤⣤⣼⣶⣿⣿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡄⠀⠀⠀⠀⠀⣒⣶⠶⠶⢶⣖⠀⢠⠀⠀⢸⡏⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠴⠶⠾⣿⣿⣿⣿⣶⣤⣤⣶⣴⣧⣤⠾⠯⠍⠀⠀⠀⠀⠀⠀⠀⡪⠭⠭⠭⠭⠵⠀⠈⢧⡀⠀⠻⠶⠂⠀⠀⠹⣿⣄⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⣽⣯⡭⠭⠳⠶⠞⠓⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⣤⣤⣀⣀⣀⠁⠰⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠚⠉⠉⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠁⠒⠖⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠁⠠⠄⠒⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣙⣦⣀⣀⠀⠀⠀⠀⠀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠄⠠⢶⢶⣶⣶⡶⠖⠶⠴⠶⠤⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢖⣋⡉⠄⠐⣶⣻⡭⠁⠀⠠⣮⠄⠈⠉⠉⠉⠉⣉⣙⣒⣶⡤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⣸⣿⡈⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⢉⣉⣉⣉⣉⣀⡤⠤⠶⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡴⠋⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⢥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⠚⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠈⠉⠛⠒⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠋⠉⠁⣠⠤⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⡤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⡼⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⣀⡀⠈⠉⠀⠀⣴⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡏⠉⠉⣷⠀⠀⠀⠙⠒⠚⠁⠀⠀⣠⡤⠖⠚⠛⠛⠛⠛⢉⣁⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣎⣱⠆⠀⠀⠀⠀⣸⠁⠀⢠⡞⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⢠⠇⠀⢀⡞⠀⠀⠀⠀⢾⣀⣨⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⣤⠟⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⠞⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⢀⣠⠴⠒⠒⠒⠒⠒⠋⠁⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠋⠀⢀⣠⠤⠤⠶⠒⠒⠚⠉⠀⠀⠀⠀⢠⡞⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢳⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠉⠓⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠖⠉⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠤⠤⠤⡤⠤⠤⠤⠶⠶⠒⠒⠛⠉⠁

⡿⢿⠿⠿⡿⡻⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⡿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠡⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠀⠀⣈⡖⢂⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⠀⠈⡆⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⢀⣤⠀⠀⠀⠀⠑⢤⡀⠀⠀⠈⠁⠀⠀⡁⠐⠐⢦⡀⠀⠀⠁⢢
⠀⠀⠀⠀⠀⢀⢠⠖⠃⠀⠤⠀⢅⣄⠀⠀⠀⠐⠂⠀⠚⠲⣄⠀⢀⣤⠀⣀⣀⣄⣀⣀⣀⣰⠤⡀⠓⢀⡀
⠀⠀⠐⠒⠓⠒⠒⠲⠢⠴⠚⠒⠒⠒⠤⢤⣀⣤⣉⡤⠤⠤⠤⠭⠡⠑⣟⡠⠠⠀⠀⠀⠀⠀⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⣠⣼⠽⠿⠦⠼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠛⡍⠀⢠⠭⠁⠀⢐⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠬⠶⡄⠀⠈⠚⠁⣀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⠢⣄⣀⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠈⠊⠓⢾⣆⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⠽⠃⠀⠀⠀⠀⠀⢀⡀⠁⠀⠙⣆⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡞⠁⠀⡤⣶⠻⠀⠀⡔⠁⠈⡆⢠⠀⠸⡄⠀⠀⠀⠸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⡀⠀⠳⡇⢀⣀⣼⠔⠂⠀⡇⡾⡁⠀⠽⠦⠄⣀⣠⣤⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠹⣄⣀⠷⢚⡄⠸⢄⣀⡴⠁⡿⣜⡂⠤⢀⡀⢡⠊⣄⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢴⡋⣁⣤⢴⠟⠲⣄⣀⣀⣀⢧⠀⠉⠙⠲⢆⡽⠤⢿⣤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡝⠋⠉⢸⠀⢰⡏⢁⡄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠘⠁⠀⠀⠈⠳⡈⢣⣾⠆⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢰⢹
⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣶⣄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠏⡄
⠀⠀⠀⠀⠀⣠⠞⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢳⠈⡓⠀⠀⠀⣸⠀⠀⠀⠀⠀⢓⢡
⠀⠀⠀⢀⡞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣇⠀⢀⡌⢠⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⣸⠀⢀⠀⣄
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⣾⢀⡏⣀⣀⣀⣐⣳⠐⢯⠍⣰⠖⠀⢱⠀⠈⢟⣉⡓⢲⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⣳⣜⠯⣝⣓⠠⠤⠬⣓⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠴⠋⠀⠀⢈⡉⣉⠍⢥⡀⠀⠀⠀⡤⠶⠋⠛⠒⢲⡄
⠀⠀⠀⠀⠈⠙⠲⢤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠀⡅⠙⠄⠀⣀⠅⠀⠀⠘⠓⠒⠢⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠐⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠚⠚⠋

⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⡄
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⡴⠒⠚⠒⠲⡄
⠀⠀⢸⡇⠀⠀⠀⠼⠥⠤⠤⠤⠤⠼⠄
⠀⠀⢸⡇
⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⠀⠀⡀⠉⠉⠉⠒⠒⢦⠞⠉⠉⠙⢦⣀⣀⠀⣀⣀
⠀⠀⢸⡇⠀⠀⠀⣠⠖⠒⠲⠴⣒⠃⠀⢠⡦⢀⡈⠋⠀⠘⠃⠀⠀⠶⠆⠀⠰⠆⠀⡀⠈⠋⠁⠈⠙⢦
⠀⠀⢸⡇⢀⡤⠚⠁⠰⠇⠀⢀⣍⠀⠀⢀⡀⠈⢁⡀⠠⡦⠀⠀⢠⡄⠀⢀⣄⠀⠈⠛⣀⠀⢤⡄⠀⢉⡉⠓⣄
⠀⠀⢸⡇⡏⠀⠀⠀⠀⠠⡦⠀⠁⢤⠄⠘⠁⣤⠈⠉⠀⠀⠴⠆⠈⠀⠶⠀⠁⠠⡦⠀⠛⠀⠀⠰⠆⠈⠁⠀⠚⠒⠲⣄
⠀⣠⠚⠓⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⢢
⠀⠙⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠜⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⡖⠒⢲⠶⡶⠶⠶⢶⠶⡶⠶⢶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⢶⣶⣶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠒⠻⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠐⠚⢻⡿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠚⢿⠟⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⡀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠐⢺⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⠂⠐⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⣰⡄⠘⠃⠀⠀⠀⠀⠀⠀⠄⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠤⢾⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠠⠴⢾⣷⠶⠤
⠀⠀⠀⠀⠀⠁⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠰⡦⠈⢻⡿⢁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠇


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠾⠁⠀⠀⢳⡤⣤⠀⠀⢠⡞⠁⠀⠀⢛⡆⠀⠀⢀⣠⣤⣤⡾⠋⠀⠀⠀⠉⢳⣀⣀⡀
⠀⠀⠀⠀⠀⣰⠞⠛⠂⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠉⠉⠛⠉⠉⠁⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢧
⠀⠀⠀⠀⠀⠹⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⠃⠀⠀⠀⠀⠀⣠⠖⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⠞⢦⣤⡤⠶⠶⠞⠉⠁⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠛⢦⡄⠀⢹⣆⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⡀⢀⠀⠀⢛⡆⠀⠙⠳⠶⠴⠞⠦⣄⣀⣀⣹⣄⠀⠀⠀⠀⢀⡰⠦⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣤⣀⡤⠤⣄⡈⠉⠓⠚⠛⠋⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠛⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⣀⣰⠁⠀⠀⠀⠛⠀⠀⠀⢷⣀⠀⠀⠀⠀⣴⠒⠏⠉⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠓⣄
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢳⡄⠀⠰⣏⣠⠀⠀⠀⣁⣹⠇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠁⠀⠀⠀⠸⠦⣄
⠀⠀⠀⠀⠀⠘⢦⣄⣤⠀⠀⠀⢠⡄⠀⢀⣄⣠⡼⠁⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⣠⣤⣀⠀⠀⠀⠀⠹⢦⣄⣀⣀⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠞⠛⠒⠋⠀⢀⣀⣠⣤⣄⠀⠀⠀⠀⠀⢀⡴⠚⠀⠀⠉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠿⠀⠀⠀⠈⠛⣧⠀⠀⠀⠘⢧⣄⠀⣄⠀⣲⡼⠇⠀⠀⢀⣤⠶⢦⣤⠤⣤
⠀⠀⠀⠀⠀⣠⠟⠉⠁⠉⢳⠀⠀⠀⠀⠈⠷⣤⣤⣤⣤⣤⡤⠼⠃⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⡞⠉⠁⠀⠀⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠙⠚⠦⠶⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠛⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠳⢴⡀⠀⠀⣀⠀⣠⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠀⠇⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢴⡞⠉⠀⠈⠻⣤⠤⣤⡀⠀⢷⣀⡆⠀⠀⡀⠀⠀⠀⢀⣸⠇⠀⢀⡴⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⣠⣴⠇⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⢻⡆⠀⠈⠳⣤⣤⠷⣤⣤⡴⠋⢀⣀⣴⠋⠀⠀⠀⠀⠙⣧⠴⠶⣤⡀
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠻⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠹⣧⡀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢀⣴⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣄⠀⠀⣀⣀⠀⣀⡼⠛⠛⠉⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡶⠑⣀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠐⡐⠀⠀⠀⡀⢀
⠀⠸⡀⣤⡸⡀⠀⠀⠀⠰⣄⢉⣚⡅⣀⠆⠀⠀⡉⡠⠀⠀⡅⡀⠀⠀⡚⠀⢲⡀⣀⢃⠈⠁⠀⠠⠀⣋⢹⠀⠄
⠀⠀⠻⢁⠓⠀⠀⠀⠀⠀⠉⠛⣟⠝⠋⠀⠀⠚⢀⡄⠿⢂⡂⠒⠀⠘⠏⠈⠻⠀⠰⠃⠀⠀⢀⠀⠀⣳⣾
⠀⠀⢸⡷⠀⠀⠀⢀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠀⠰⠂⠉⠀⠦⠀⠀⢀⠀⠀⠀⢹⡃⠀⠀⠀⣨⣄⠀⢀⡀⠀⡔⠪⡅
⠀⠀⢸⢠⠀⢀⠀⠿⣧⠀⠀⠀⣄⡀⢀⠠⢠⠠⡀⠀⠙⠀⠀⢀⡀⠉⢀⡀⠀⠐⣆⢀⡀⢨⠊⡼⠁⠘⠁⠀⢖⠄⠀⣀⡀
⠀⠀⢀⣏⠀⠠⠀⣸⣿⠀⠘⠀⣀⡄⠈⢼⠋⢹⡆⠆⢤⠀⠀⠀⠀⠄⠀⠁⠀⠀⢻⠉⠀⠀⢪⡖⠀⢠⡇⠀⠀⠉⠲⠈⠁
⠀⠀⠈⠉⠀⠙⢌⣯⣝⠌⠁⠀⢈⡀⠘⠌⣛⢋⠐⠀⠀⠀⠀⠐⠂⠀⠐⠢⠀⠀⣼⠀⠀⠀⠸⠆⠀⠀⡇⠀⠀⠀⣶
⠀⠀⠀⠀⠀⡤⠀⠁⣯⠀⠀⠀⢈⡀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⡗⠀⠀⠀⢸⠀⠀⠀⡃⠀⠀⠀⢈
⠀⠀⠀⠂⠀⠀⠀⢠⢿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢨⠀⠀⠈⠛⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⢘⠉⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⡗⠀⠀⠀⢘⠀⠀⠀⠆⠀⠀⠀⠸
⠀⠀⠀⠓⠀⠀⢠⠀⡸⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⣧⡀⠀⠀⠈⡁⠀⠈⠂⠁⠀⠀⠠
⠀⠀⠀⠚⠀⠀⠀⠀⢰⠀⠀⠀⠐⡤⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠃⠀⠐⢰⣐⠆⠀⠀⠀⢠⠄⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣤⣤⣤⣤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣿⣿⣿⡿⠿⠿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠠⠀⠴⡾⢶⣶⣶⡄⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢠⠒⣶⣶⣶⠻⣃
⠀⠀⠀⠀⠀⣌⣀⣁⣸⣿⣿⠃⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⡷⠀⢠⡌⣸⣭⣯⣤⡄⣿⡇
⠀⠀⠀⠀⡀⠉⠉⠻⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠛⠋⠀⠀⠀⠃⠀⠘⠁⠸⠙⢿⣿⡇⣹⡇
⠀⠀⠀⠀⠀⠀⠋⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⡻⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠀⡀⢀⣠⢄⡀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⢷⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣛⣛⣛⡋⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠚⡇⢺
⠀⠀⠀⠀⠠⠀⠀⢀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠉⠄⢰
⠀⠀⠀⠀⢠⣠⡀⢀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⠀⢐⡀⠙⣶⡀⢼
⠀⠀⠀⠀⠀⠙⠛⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠚⠁⠀⠀⠀⠀⠀⠑⠚⠦⠼⠧⠾⠿⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠿⠿⢷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣤⣶⢟⣫⠶⠛⢛⣻⠿⢃⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠿⠿⢟⣛⣛⣛⣛⣛⣛⣉⣉⣉⣩⣟⣛⣿⡿⢟⣥⣜⡻⠶⢛⣫⣵⣾⣿⣿⣥⣄⣀
⠀⠀⠀⢰⣿⠟⠋⢩⣶⣾⣿⣿⠿⠿⠟⠛⠛⣛⣫⣭⣭⣽⣿⣿⣿⣏⣘⣻⠷⣟⣥⡾⠿⠛⠿⣿⣿⣷⡍⠛⢿⣷⡄
⠀⠀⠀⠘⢿⣷⣦⣤⣈⣉⡙⠛⠛⠿⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⣛⣉⣡⣤⣴⣾⡟⠁
⠀⠀⠀⣰⡿⠁⠉⠉⠛⠛⠻⠿⠿⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠟⠛⠛⠉⠁⠈⢿⣆
⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⣿⡟⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⢿
⣿⡇⠀⠈⠙⠛⠿⠷⣶⣦⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣶⡶⠿⠟⠛⠉⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠹⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠋
⠀⠀⠻⣿⣿⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⢿⣿⣿⠏
⠀⠀⠀⠈⠻⢷⣦⣍⣙⠛⠿⠿⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⡿⠿⠛⣋⣭⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣶⣤⣤⣍⣉⣉⣉⠙⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣉⣉⣡⣤⣤⣶⣾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⡟⢰⡿⠿⢿⣦
⠀⠀⠀⠀⠀⢠⠄⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢿⣄⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⠁⢰⡶⣌⠻⢿⡿⠏
⣤⢶⡀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠛⢻⣆⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣆
⠛⠚⠁⠀⢀⣼⣿⣿⣿⣿⣿⣷⣶⣾⡿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⢨⣿⠄
⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⡀⠈⣿⣤⡄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⣿⣯⣀⣼⠇⠘⢿⣤⣿⣦⣬⣷⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠛⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠸⣏⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣼⣿⣿⣷⣼⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣧⣤⡍⠈⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣦⣤⡀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⡇⠙⠿⣿⣿⣿⣿⠁⠀⠀⢻⣿⣿⣿⣷⣦
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧⣬⣿⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣧⡀⣀⣿⣿⣿⣿⣧⡀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠃⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢻⣿⣤⣴⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠟⠉⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣼⡿⠁⡀⠀⠀⠀⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣻⣿⣿⣿⣿⣿⣶⢿⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⣿⡿⠿⢛⣿⡿⣯⣱⡟⠉⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠁⠀⠀⣿⡿⠁⢀⣿⣿⣶⣤⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠻⣷⣴⣿⡿⢹⡿⠉⠉⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⢿⣿⣿⣿⣿⣿⡿⣿⠟⠀⠀⠀⠀⢸⣟⢛⣦⢿⣧⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡍⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠘⣿⣿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠙⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⣀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⡿⢿⣷⣤⣤⡄⠀⠀⢸⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣄⣼⣿⣿⣧⡿⠀⠀⣿⣿⠉⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠻⣿⣦⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢙⣿⣿⣿⣿⣷⣦⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠋⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠙⠋⠀⠀⠈⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡖⠁⠀⢠⢤⠀⠀⠀⠀⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢚⠀⠀⡜⢀⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣭⠃⠀⠙⠋⢁⠀⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠸⣦⣀⡼⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡞⠀⠀⠀⡀⠀⡉⠑⠒⡄⢀⠀⠀⠀⡰⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢒⠏⠻⠤⠕⠀⢾⣿⣿⣿⢖⠝⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣴⣶⣤⣴⣿⣿⣿⡷⡍⣴⡁⠀⠀⠀⣀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣯⢟⠞⠱⡄⠈⠓⣖⠉⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⣿⣿⣿⡿⡣⢯⠶⠚⠙⠦⣤⡼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣹⠊⠀⢀⢞⠞⡔⠛⠿⣬⡉⠁⠀⡶⠒⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠰⣇⢀⡰⡻⠃⠀⢸⠀⢀⣨⣿⡆⣸⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠙⢦⠌⡐⣟⠀⠀⢠⠃⠀⢻⣿⡿⠙⠋
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⣢⠾⠁⠀⡰⠁⠠⣾⣿⡟
⠀⠀⠀⠀⢠⡏⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠜⠁⠀⢀⠜⠀⠀⣤⣾⣿
⠀⠀⠀⠀⢸⡇⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡡⠋⠀⠀⢠⣾⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠘⣇⠀⢸⠀⠀⠀⠀⢀⠤⠒⠤⣾⠝⠀⠀⠀⠐⠛⠛⢻⠉⠙⣯⠉⠙⣇
⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⢀⠔⠡⢄⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⡀⠀⡇⢇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠄⠀⠑⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢣⢀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠠⠴⠚⣉⠄⢀⠅⠀⡠⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⢣⢸
⠀⠀⠀⠀⠀⠀⠠⠭⠒⠭⡀⢄⣪⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠈⠟

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣾⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⠤⠀⠀⠹⠉⠀⠀⠀⠀⢠⣿⣧⡀
⠀⠐⠒⠺⢿⣿⣿⣿⣿⡷⠶⠆⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠾⣿⣿⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⠹⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠻⠋⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣀⠀⠀⠀⠀⠀⠀⠈⢿⡏
⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣇⠀⢘⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⣠⠀⠀⢠⣼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢈⠿⠿⠛
⠀⠀⠛⣿⠟⠀⠀⠹⠃⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀
⠀⠀⠀⠈⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠙⣿⠛⠁⠀⠀⠀⠐⢦⣠⣿⣧⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⡉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠈⢿⡏⠉⠓⠀⠀⣰⣿⣶⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠻⠓⠠⢴⣿⣯⠄⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠈⠛⠁⠀⠀⠀⢀⣀⣼⣧⣀⡉⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⢡⣤⣾⣧⣤⠄⠀⢤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢹⡿⣿⡇⠀⠀⠀⠀⠀⠉⠉⣿⣿⠏⠉
⠀⠐⠒⠒⠿⠿⠿⣿⣿⠿⠿⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⠀⠀⠀⠀⠀⠚⠻⠿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠰⠶⢾⣿⣿⡶⠶⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠤⣤⣿⡤⠤⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠀⠀⠀⠀⠀⠐⠶⢾⣿⣿⠷⠆⠀⠀⠀⠀⠀⠀⠲⠾⢿⣿⡿⠿⠒⠂⠀⢸⡇
⠀⠀⠀⠤⠤⣾⡦⠤⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⡄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣿⣿⣦⡤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠠⢤⣼⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⣀⣤⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠶⠶⣿⣿⡷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡐⢤⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢁⣀⣱⣮⡀⢸⡀⠀⠀⠀⠠⠝⠿⣄⠁⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡁⠀⠀⠈⢁⡨⠿⠯⠀⠀⠀⠀⠀⠀⠀⠛⣇⣀⣠⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠟⠃⠀⠀⠀⠻⠀⠀⠀⠈⢈⡧⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠐⣀⣠⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⣤⣦⡀⠀⢀⣄⠀⠀⣸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣶⣶⣤⣶⣾⣿⣶⣶⣦⣀⣠⣴⣿⣿⣷⣶⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⢿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠿⠛⠋⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⡀⠄⠀⠀⠘⠓⠲⣾⣿⣏⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠒⠇⠀⠀⠀⠐⠚⠃⠀⠀⠀⠀⠀⠀⢼⣿⣿⠟⠉⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢈⣿⣇⣀⣀⣠⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⢶⣿⣶⣾⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠊⠉⠁⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⣄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣥⠶⠲⣆⠈⠛⢦⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⢴⠳⣤⡙⢷⣴⠋⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⣁⠀⢸⠛⢷⡀⠸⡟⠉⠙⠆⠉⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠹⡆
⠀⠀⠀⣠⠋⣇⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⢿⣀⣤⣜⢧⣄⡽⠀⠉⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⣿
⠀⠀⢠⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣤⠼⠃⣀⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⢀⡴⣿
⠀⠀⢸⣇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⡤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠀⠀⠀⠀⣠⠴⠋⣰⠏
⠀⠀⠸⡏⢧⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⢀⣠⠴⠋⢁⣠⠞⠁
⠀⠀⠀⢳⡀⠹⣦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⢀⣠⡴⠞⠋⢀⣠⠖⠋
⠀⠀⠀⠈⢳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠙⠒⠤⢤⣤⣤⣤⣤⠴⠶⠛⠉⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉⠀⠀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠉⠛⠲⠶⠶⠒⠚⠋⠉⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠉⠁

⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢴⠷⠀⠀⠀⠀⠀⣤⠀⠰⣶⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣠⠤⠖⠚⡟⢛⡛⠓⠒⠶⠤⢭⣶⡦⢤⣀⠰⠆⠀⠛⠁⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡬⠛⢉⠀⣴⠧⠀⠄⠀⠰⠆⠀⠘⢃⡀⠀⠉⡳⢬⡓⢦⡀⠠⠦⠀⣠⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢗⣰⠋⣠⠋⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠿⢀⣝⢦⡙⢦⠀⢀⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡴⣁⡀⢀⡏⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠟⢿⠀⠠⠀⠀⠈⠋⢀⣹⣌⢳⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠓⢸⠁⣸⢁⠉⠁⣸⠀⠀⠀⠳⠶⠖⠒⠒⣶⠐⠋⠉⠹⠯⣗⠦⣄⠀⠂⠈⠉⠸⡟⢻⡄⠠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⢠⡄⡟⢠⡷⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠘⠓⠐⠻⠆⢀⠱⣌⢳⡐⠶⠀⠀⢹⡀⢷⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡇⢸⠉⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⢈⣠⡜⡆⢷⠐⠀⢀⠘⡇⠘⡇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡗⠙⢸⢀⣠⣴⠾⢻⠀⠀⠀⢀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢋⡁⢹⢸⠀⠀⢿⠒⡇⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣤⣾⠟⢋⢡⡄⢸⠀⢀⡴⠋⠙⠓⠲⠤⡧⠀⠀⠀⠀⠐⠶⠈⠁⡾⢸⠐⠒⠀⠀⠃⠾⢺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡯⠟⠉⠈⢇⠘⣆⠀⢸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⣰⢃⠟⠻⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣚⠽⠚⠁⠀⣤⠄⢀⡌⠳⣾⠳⣤⡄⠀⠈⠀⡀⠀⠀⠀⠀⠀⡀⠀⠠⠆⣠⠞⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⡫⠗⠋⠁⠀⠀⠀⠀⠉⠁⠀⠁⢀⡈⠳⣎⡿⠦⢤⣊⡟⠃⠄⠐⢦⣀⣡⣾⣶⣊⡥⢊⠉⠻⠇
⠀⠀⠀⠀⠀⢀⣠⠴⣚⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠉⠓⠒⠤⠭⣭⣭⣭⣭⠥⠴⠚⠋⠱⠆
⠀⠀⣀⡤⠖⣉⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⡲⢦⡄⠐⠶⠀⣤⡌⠋⠀⠈
⣶⠋⢁⡴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⡔⠉⠀⠉⠁⠀⠀⠑⣄⠀⠀⠀⠀⢀⠔⠒⠢⠤⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠒⠠⡄
⠀⠀⢀⡴⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡠⠼⠀⠀⠀⠀⠀⠀⠑⠒⠦⠒⠢⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠎⠁⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠆⠀⠀⠘⠛⠛⠦⠰⢄⠀⠀⠀⠀⠀⣀⢀⡠⠬⠭⠭⠕
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠁⣁⠤⠤⡀
⠀⠀⢠⠊⠉⠉⢢⣀⣀⠤⠒⠤⡀⠀⠀⢀⠤⠤⠊⠀⠈⢳⠀⠀⠀⠀⣀⠤⠤⠤⠔⠉⠉⢢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠁⠀⠀⠈⠦⢄⡀
⠀⢀⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠳⡄⠀⡇⠀⠀⠀⠀⠀⠸⡁⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⡀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢
⠀⠀⠓⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠁⠀⠈⢇⠀⠀⡀⠀⠀⡇⠀⠘⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⡧⠀⠀⠱⢄⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠜
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠢⡀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠓⠠⠔⠊
⠀⠀⠀⡰⠉⠉⠋⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⢀⠔⠊⠉⠒⢄⠠⢄⡀⠀⠀⠀⢀⣀⡔⠁⠀⠈⢢⢀⡀⠀⠀⠀⠀⠀⣀⢀⠔⠉⠉⠑⢄
⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⡰⠉⠀⠉⠀⠀⠀⠀⢸⠒⠒⢯⣉⡉⢡
⠀⠈⠢⢄⣀⣀⣀⣀⣀⣀⣀⣀⠴⠃⠀⣏⣁⠀⡀⠀⠀⠀⠀⠀⠀⢀⠇⠸⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠱⣀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠁⠈⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠀⠒⠉⠒⠊⠁⠀⠀⠀⠀⠑⠒⢆⡀⢀⡠⢀⣀⣀⠜⠀⠀⠈⡀⠀⠀⣀⠀⠀⢀⠆⠀⠀⠀⡤⠃
⠀⠀⠀⡠⠒⠠⣀⣀⡰⠊⣉⠵⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠉⠘⠣⠤⠒⠤⠴⠃
⠀⢀⠜⠀⠀⠀⢈⠔⠈⠒⠁⠀⠀⠈⣆⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⢁⠔⠋⠑⠒⠉⠉⠐⢄⠀⠀⠀⠀⢠⠂⠉⠑⠴⠊⠉⠲⡄
⠀⠈⠢⠤⠤⡔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⢴⠊⠀⠀⠀⢀⡔⠊⠋⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⡤⠶⠤⠴⠉⠉⠑⣄⣀⠱⠒⠢⠔⠒⢢
⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠉⠉⠉⢳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⣀⡀⣀⡀⡉⠉⢢
⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠂⠀⠀⠈⠉⠀⠀⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹
⠀⠀⠀⠀⠀⡠⠴⠁⠀⠀⠙⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠂⠁⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠒⠒⠢⡀
⠀⠀⢠⠔⠊⠀⠀⠀⠀⡠⠤⠎⠁⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡤⠒⠓⢤⡀⢀⡠⢄⡀⠀⠀⠀⠀⠀⣀⠤⠀⠤⡎⠀⠈⠀⠀⠀⠀⠥⠤⡀
⠀⠀⡇⠀⠀⠀⢀⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡀⠀⠀⠀⠈⢲⠀⡠⠜⠀⠀⠀⠀⠁⠉⡆⠀⠉⠙⡆⠀⠀⢀⠃⠀⠀⠀⠘⠒⠢⡔⠋⠉⠉⢢⠀⢈
⠀⠀⠘⠦⢀⠰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠇⠀⢠⡤⣤⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠦⠤⠾⣁⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡎
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠓⠔⠢⢄⣀⠤⠊⠈⠁⠀⠀⠀⠀⠉⠉⠑⠈⠢⠄⠀⠤⣀⡠⠆⠔⠊⠉⠉⠉⠉⠀⠀⠓⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡙⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⣾⣏⠈⠉⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣿⠿⢟⣛⣿⣮⣛⠻⠿⠟⣿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣾⣿⡟⢡⡾⣫⡿⣿⣿⢿⡿⣿⡿⣯⣻⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣭⣳⣤⣽⣿⡿⢱⣿⣿⡟⣰⢏⣿⣹⣗⣿⢷⡙⢿⣮⣛⠶⣿⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣩⣽⣿⣿⣿⠃⣼⡿⣹⡇⣿⣿⢿⠙⣿⣽⣆⣿⢦⡙⢿⣷⣮⠻⣿⣷⡶⣆⠀⠘⠻⠶⠶⠾⠟
⠀⠀⠀⠀⠀⣠⣤⠖⠛⠉⢱⠞⢻⣿⡽⢟⣡⠞⣽⣿⣿⡇⣿⣿⣿⡆⣿⣿⢿⣧⣾⠻⣆⠹⣎⢷⠘⣯⠻⣟⠛⠛⢶⡄⠀⣤⠶⠖⠛⠻⢦⣄
⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠘⠻⣯⣭⠶⣻⣿⠾⢋⡾⣡⣿⣿⣏⣼⠇⣿⣿⡘⣏⢹⣧⣹⠌⣿⢿⡆⢿⡛⠋⠀⣴⣟⣁⠀⠙⠛⠛⠛⠛⠛⠋
⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⣰⣟⣫⡾⢿⡏⣿⣿⡟⣰⡏⣿⣇⢿⡿⣿⣿⠀⣿⣌⢳⣼⣿⡆⠀⠀⠀⠉⢻⡆⠀⠰⣾⣿⠆
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢻⡆⠀⢾⣿⣧⠾⠷⠞⠻⣷⢿⣟⣱⢿⡇⢿⣿⣎⢻⣿⢿⡶⣷⠾⠀⠉⠋⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⣀⣀⣹⣾⠟⠋⠀⣿⣼⠁⣿⢻⡇⠘⠷⠛⢀⣀⣠⣤⡴⠶⠛⢉⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠛⠓⠒⠛⠛⠛⣋⣉⣩⣉⠛⠦⣤⣤⣤⣬⣅⡀⢙⣋⣡⡤⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣤⠴⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠅

⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠴⢌⠚⣀⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢂⠒⡃⠦⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠴⡈⠒⡄⠄⠄⢀
⠀⠀⠀⠀⢸⣿⠁⠒⢈⡙⠑⠉⠓⠜⠓⠒⠦⣬⡆⠀⠀⠀⠀⢰⣿⠃⠒⢂⡉⠑⠉⠻⠜⠓⠒⠦⣤⡆⠀⠀⠀⠀⢾⡿⠀⠒⢈⡉⠀⠙⣇⠞⠒⠲⠤⣼⡄
⠀⠀⠀⢀⡌⠙⠓⠻⠿⢿⣶⣶⣿⣶⠶⠶⠒⣆⠡⠀⠀⠀⢀⡌⠉⠛⠻⠿⠿⣶⣶⣟⣶⠶⠤⠒⢮⠁⡀⠀⠀⢀⠎⠙⠛⠿⠿⢿⣶⣶⣷⣶⠶⠖⠒⢎⢁
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠂⢱⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠂⠑⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠣
⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠤⠐⠨⠀⠀⡋⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠐⠈⡁⢸⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠬⠐⢈
⠀⠀⠀⡆⡠⠤⡀⠀⠀⠀⠀⠀⠀⢀⠖⠲⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣷⠁⠀⠅⠀⣀⢄⡀⠀⢀⠇⠠⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡟⠀⣀⠘⠴⠁⠀⠱⢄⠌⠀⠀⠁⠘⠂⠀⢸⠀⠀⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⢸⡏⢳⠀⡴⢦⡄⢰⡤⢤⡄⠂⢸⣇⠀⢸⠀⠀⡇⢰⡏⢻⠀⣴⢶⡄⢠⣴⢦⡄⠀⢸⣇⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠘⣷⡄⢸⡇⠀⣿⢸⡇⠈⣿⠀⡎⣿⠀⢸⠀⠀⡇⠈⣷⡌⢸⡇⠀⣿⠀⡇⠀⣿⠀⡏⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⢠⠈⣿⣸⡇⠀⣿⢸⡇⠀⣿⢰⣧⣿⡆⢸⠀⠀⡇⢠⡈⢿⣼⡇⠀⣿⠀⡇⠀⣿⢠⣧⣾⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠘⢦⡾⠘⣧⣠⡟⢸⡇⢠⡏⣸⡁⠼⠗⠘⠀⠀⡇⠘⠧⡾⠉⣧⢀⡟⢘⣇⢠⡟⣸⡅⠸⠷⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠀⠘⠛⠉⠀⠉⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠀⠘⠛⠉⠀⠉⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢇⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠈⠑⢶⡤⣄⣀⡀⠀⠀⠀⢀⣀⣀⣴⡤⠂⠁⠀⠀⠀⠙⢶⡤⢄⣀⡀⠀⠀⠀⢀⣀⣀⣠⡤⠂⠁⠀⠀⠈⠛⢶⡤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⡔⠊
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠈⠭⠉⠙⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠈⠭⠉⠙⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠨⠭⠉⠙⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠒⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⣇⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠳⠋⢴⣢⠀⢠⠖⡄⠀⠀⠀⢶⠄⠀⣀⡤⠖⠚⠙⢻⡓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠈⠛⠁⠀⠀⢀⡠⠖⠋⠁⠀⣀⠀⡀⠀⢣⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠥⠃⠀⠀⣀⡤⠚⠉⠀⠀⡠⠤⣐⠀⠀⣸⠀⠀⢇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⡴⠊⠁⣀⣄⢠⢊⡐⣆⢀⣈⠧⠸⠀⠀⠀⠘⠆⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠘⠧⠼⠉⠉⠀⡇⠀⠸⣀⠘⢺⣈⡡⠟⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡜⢁⠜⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠞⠉⠙⠆⠀⠈⠀⠀⠀⢀⡠⠔⠈⠀⣀⣀⣀⡠⠞⠁⢶⢦
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⠼⠦⡤⠐⠒⢎⡡⠠⢆⠐⠁⠀⠀⠀⠱⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢹⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣳⣀⣀⣀⡤⢄⡀
⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡀⢀⣀⠐⠪⢍⠉⠉⠉⠉⠓⡄
⠀⠀⠀⢠⡒⠉⠉⠑⠀⠒⠉⠒⠒⠑⠂⠂⢐⣒⡒⠒⠤⠔⠒⠒⠊⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⢒⡄
⠀⠀⠀⠀⠉⠉⢳⠄⠀⠀⠀⠀⠀⠀⠀⠸⡩⣀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠳⠤⠤⣤⣄⣀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠴⠶⠒⠒⠒⠋⠉⠙⢦⡤⠤⠔⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠒⠚⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠀⠲⢄⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠓⣐⡃⠀⢸⢵⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠯⠠⠜⠁⠀⠁⠸⡤⢤⠏⠓⢤⡀
⠀⠀⠀⠀⡰⠋⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⣄⡀⠀⠉⠲⣄
⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⠀⠀⠀⡔⠂⠒⠐⠁⠈⡇⠀⡦⣈⠓⢄⡀⠀⠑⠦⣀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠑⢴⠉⠉⠀⠀⠀⠀⠀⠐⠃⠀⠣⠌⢃⠀⠉⠢⣄⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡀⠉⠢⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠢⡀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⠈⠑⢄⡀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⠆⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣸⠆⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠁⠀⣰⣄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠉⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠁⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⡀⠀⠀⠀⠀⠀⣀⠠⠔⠊⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡄⡔⢂⣤⠀⠀⠀⢀⣀⣠⠴⢶⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠰⡋⠉⠉⠉⠁⠀⠀⠙⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠚⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⢤⣶⠾⣉⣂⣈⡉⠉⠀⠾⠍⢀⣲⣄⡀⠀⠀⠀⠀⡠⢒⡫⠋⢁⣠⣎⠀⡨⠃⢁⣲⠄
⠀⠀⠀⠀⢰⠛⠮⣀⣘⢛⣿⠟⠓⠀⢀⣐⣁⣀⣈⠿⢻⠀⠀⠀⡠⠛⠒⠲⠥⢭⣭⣥⡭⠥⠀⠒⠂⠓⣄
⠀⠀⠀⠀⡼⠛⠒⠢⠤⠄⣀⣤⣬⣤⣤⡤⠤⠤⠖⠒⢻⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⡀⠀⠀⢀⣠⡀⠀⢀⡀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢳⠀⠀⢰⡏⢸⢧⡞⣿⣸⢃⡿⣰⢿⡇⠀⢰⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠇⠀⣈⠓⣶⣾⣡⣿⣿⡼⢳⠟⢾⠃⠀⡆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⡀⠉⠉⠁⠈⠁⠈⠁⠀⠀⠀⠙⠀⠸⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⢺
⠀⠀⠀⠀⠀⠠⣘⠆⠀⠈⠂⠀⠀⠀⠀⠀⠄⠀⢀⡔⠀⠀⠀⡇⠠⠄⣀⡀⠀⠀⠀⢀⡀⠤⠒⠉⠀⡀⠤⢸
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠘⢷⡦⠤⠤⢀⣀⣀⣀⡀⠀⠤⠤⠀⡴⠋⠀⠀⠀⠀⠙⠽⢒⠶⠤⠤⠤⠤⠤⢒⡲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠐⠒⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉



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

⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢨⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠞⠃⠀⠀⠀⠐⢤⣤⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⠀⠀⠀⣱⢀⣀⡤⠖⠁⠀⠀⠀⠀⠐⢀⠀⠀⠀⢀⡴⠁⠀⠈⠉⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⠜⠁
⠈⠲⠤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠒⠤⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠅⠤⢴⣠⠆⠈⠖⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢲⠁⠀⠀⠀⠀⠀⢠⠄⠀⡀⢠⠀⠀⢀⢀⠀⢀⡼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⡈⠁⠁⠈⠁⠁⠀⡜⠉⠉⠀⠀⠑⠦⠴⠀⠀⠀⠀⠀⠀⠠⠃
⢄⢀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⢀⣀⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⢄⠀⠀⢸
⠀⠉⠑⠒⠓⠒⠉⠀⠀⠀⠀⠀⠱⣄⣀⣠⡼⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠠⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡀⠀⢄⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠐⠦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡼
⠀⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠔⠚⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⢤⡀⢀⡠⠐⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣇⠀⣠⠀⠀⠀⢠⣤⠀⠀⠀⠔⠀⠉⠁⠢
⠀⠀⠓⠃⠀⠀⢰⠁⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⢁⣀⡀⠀⠉⠉⠀⠀⢀⡀⠈⠀⠀⢘⢀⡄⠀⠀⠀⠀⡔⠁⠉
⠀⠀⠀⠀⢠⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⠀⠀⠀⠀⢀⡜⠢⡠⠚⣄⠀⠀⢀⡴⠥⠄⠠⠤⢄⡀
⠀⠀⠀⠀⣈⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠥⢀⠀⠀⠀⠀⠀⠃⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠒⠈⠀⠀⠀⠀⠒⠎⠀⠀⣠⣒⡒⠦⠔⠒⠢⠤⡄⠀⠈⠑⢄⠒
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡇⠰⡞⡵⣶⡦⠀⠀⣬⣭⣁⠁⠀⠀⠀⣸
⠀⡏⢉⠉⡉⠉⡉⢉⠉⣀⣀⡄⠬⠤⠄⢀⡀⠀⠀⠁⠀⠇⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⢹⢶⠀⢏⡻⡇⠀⢸⡸⣿⠁⢃⠒⣄⡴⠃⡖
⠀⡇⠀⠀⢀⢸⡀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠛⢭⠭⠍⠀⡥⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⢸⠈⢆⠀⢰⡥⠤⣴⠉⠁⢀⡌⢴⠉⠀⠆⡗
⠀⡇⢀⠀⡰⠊⠀⠀⠤⠤⢤⣄⠀⠐⠒⣠⢄⡀⢣⡠⠀⡇⠰⠐⠒⠐⠂⢲⠒⠂⠀⠀⢸⠀⠨⠷⡦⢭⣨⡥⡴⢚⠉⡹⢋⢧⣁⣤⣷
⠉⠀⠉⠀⡇⠀⠀⠀⠉⠐⣚⣧⠀⠀⢴⣻⡄⢃⡿⢤⠀⡇⢀⠀⠀⠀⠀⢸⠀⢀⠀⠖⠁⠁⠐⡞⠀⢰⠀⠅⢀⢸⠊⠐⠁⠈⡇⡐⡒
⣀⡄⠉⠁⠳⢦⠃⡵⠇⠀⣌⢫⠇⠀⣩⡛⡣⢸⠃⠜⠀⠃⢸⠀⠀⠀⠀⢸⠀⠈⠀⠐⠂⠈⠀⠳⠄⣨⡀⢘⢇⣀⠉⠒⠒⠘⣧⠆⢇
⢀⣠⣤⠦⠄⠠⠛⢦⠀⠀⠈⡵⢦⣤⣷⠍⠀⠌⠀⣁⠀⡁⢸⠀⠀⠀⠀⢸⡔⠁⠠⠔⠀⣰⢯⢻⡄⢙⡷⢡⠞⡀⠈⠑⠒⠒⠙⡀⢸
⠈⡆⠀⡬⢤⢰⣪⠞⠓⢤⣀⠘⠂⢐⣋⣤⠞⢋⡡⠜⡇⡀⢸⠀⠀⠀⠀⢸⠐⠤⢄⣀⣄⣀⡄⠀⣠⢈⣱⡁⠀⣣⣀⣀⣀⠠⠔⡇⠸
⣀⣿⠀⠇⠲⡼⡅⠀⠀⡇⠉⢛⠫⠚⡩⠔⠊⠁⠀⠰⠁⡀⠗⠠⠦⠠⠄⣸⠄⠂⠌⠣⠸⠄⢤⠔⡹⡏⢸⠁⠀⠀⢳⠀⠀⠀⠀⣭⢉
⠤⠘⠀⡇⡘⢰⣀⡀⠠⢼⢠⠋⡝⠁⠀⠀⠀⢀⠠⠺⣒⣊⡉⠔⠓⡄⠢⠔⠢⡀⠈⡉⠤⠶⣭⠊⠀⡆⢸⠀⠀⠀⢸⡇⠀⠀⠀⢸⠄
⠒⠉⠀⢹⠁⠈⠲⠒⠛⢋⡇⠸⠀⢀⡠⠔⢊⡡⢐⠩⠐⠉⡠⠔⠊⢳⠴⠒⠛⠩⠀⠀⠀⠀⣿⠈⠀⠉⢸⠀⠀⠀⡞⠹⡄⠀⠀⢸
⠀⠶⠄⠱⢤⣀⡀⠑⠢⢄⡑⠦⣮⣅⠴⠮⡔⠊⣀⠤⠂⠁⠀⠀⠀⠸⡄⢀⣀⠀⠀⠀⡐⠀⢸⠠⠶⠄⠸⣽⣖⣱⠇⠀⢳⡁⢮⡼⢀
⠀⠀⠀⡐⠁⠀⠈⠉⢲⠚⠻⣄⣠⣏⠀⠂⠓⢎⠀⠀⢠⠊⣿⠽⠂⣄⢗⠝⠁⠀⠀⠠⠀⠀⣴⠀⢀⣄⢰⠃⠄⢇⠀⠒⣂⢇⡀⣇⠈
⠀⠀⠀⡇⠀⠀⠀⢰⡟⠈⠀⠘⢟⠋⠀⠀⠀⠈⠄⠀⠠⢡⠀⢀⡶⣼⠚⡤⠖⠤⠒⣦⣐⠊⡿⠴⣥⠤⠥⠤⠤⢬⡖⠛⠚⠀⠀⢈⡆
⠀⠀⠀⡇⠀⠀⠀⠘⢹⠀⠀⠀⠘⡣⡀⠀⠀⠀⠈⠀⠘⢯⣉⡜⠂⠁⠀⡛⢄⢠⡾⠜⣹⡦⣤⡔⠉⠉⠈⠈⠁⠉⠓⠀⠈⠉⠓⠒⣁
⠀⠤⡄⡇⠀⠀⠀⡇⠈⡆⠀⠀⠀⡗⠓⢄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠜⠉⠛⠉⠙⢎⠀⠀⢙⢆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⡧⠤⠤⢤⡇⠀⢸⡄⠀⠠⡇⠀⠈⢢⡀⣀⠀⠈⡄⠀⠀⠀⠀⠎⠀⡘⠀⠀⠈⡈⢣⠀⠀⠁⢻⠉⠙
⠀⠀⠀⢹⣁⣹⣉⡀⠀⠀⠹⠤⠽⡥⢄⠀⠋⣕⢄⠱⡀⠘⣄⣀⠤⢸⠀⢠⠀⠀⠀⠀⠰⠈⡆⢀⠈⠈⡆⠀⠀⠀⠀⠀⠐⠓⠶⠳
⠀⠤⠤⢾⣀⠀⠁⣈⣧⠒⢷⢄⣀⣀⠠⡧⠡⣑⣀⡤⠋⠀⠉⠀⠀⢸⠀⠘⠄⠀⠀⠀⠀⠀⢡⣀⣙⣀⣱⣄⡀
⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣐⣲⣆⣀⣀⣀⣀⣀⣘⣙⣁⣘⣒⣒⣔⣒⣒⣚⣒⣒⣚⣃⣀⣀⣈⣁⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣡⠤⠤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢹⡄⠀⠀⣠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠃⠀⠀⠘⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠊⠀⠀⢸⠁⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⢸⠀⠀⠀⡰⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠳⠤⠤⠊
⠀⠀⠀⠀⠀⠀⢰⠃⢹⢸⠀⢸⢠⠒⣦⠙⠋⡴⡀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢦⠀⢀⡠⢄⡀⠀⠀⠀⠀⣠⠖⢦⡀
⠀⠀⠀⢠⠖⠋⠉⠉⠉⠙⠒⠚⠺⠤⢼⣀⣘⣷⡃⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣸⣀⣼⡀⣀⡏⠉⠑⡶⠒⠳⣄⣴⡃
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦⣀⡴⠃⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⢳⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣠⡤⠤⢾⣉⠗⡞⠁
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡰⠋⠙⠒⠒⠲⠶⠦⠤⠴⠶⠖⠒⠚⠉⠁⢹⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⢀⠀⠀⠀⠀⢠⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣸⣿⠀⠆⠀⠀⠀⠀⠙⠋⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠶⠾⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠀⠀⠀⡵⠀⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⡇⠀⢿⣿⠟⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢉⠀⠁⠀⠀⠀⠁⡀⢸⣿⡀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠃⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡜⠃⣤⡄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠂⠀⡀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⣆⠐⠀⠀⠀⠀⠀⢀⣠⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠛⢠⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⡿⠋⠀⠀⠀⠀⠛⠛⠿⣿⡿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⡐⠈⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠟⠁⠀⠀⢀⣼⣿⣄⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀
⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣄⠒⢿⣿⣿⣿⠟⠂⠀⠙⠁⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠴⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠷⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠁⣰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠉⣻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠦⠖⠦⡀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣷⠀⠀⡷⡇⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⡯⡀⠄⣐⡑⡘⢦⡀⠀⠀⠀⠀⡼⢡⣤⡌⣧⠀⡇⡇⠀⠀⠀⠀⠀⣿⣿⣶⣄⣠⢤⣼⡟
⠀⠀⠀⢀⣰⠛⠉⠙⢦⡄⠀⠀⠀⠀⠀⠙⢶⣄⠉⣡⠽⠊⠀⠀⠀⠀⠀⡇⠈⢭⠀⣿⠀⣱⡇⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠙⠓⠴⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⠛⠚⣿⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠉⠉⠛⠋
⠀⠀⣠⠔⢒⡒⠒⢤⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⢶⣶⣤⣤⡄
⠀⢸⡇⡈⠀⠒⡃⠴⠃⠀⢸⠀⠀⠀⠀⣀⠴⢊⠅⣢⢟⠎⠳⡄⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡛⢑⡀⢃⢲⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⡧⢀⠋⠾⠓⡁⠔⣨⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣻⠈⠀⢸⢸
⠀⠸⡇⠀⠀⠀⠀⢠⣄⣀⡟⠀⠀⠀⠀⡷⣄⠑⣖⣡⠴⠋⠀⠀⠀⠀⠀⢀⣠⠔⣒⣿⡟⠉⢳⡆⠀⠀⠀⠀⠀⣷⣽⢀⠀⠀⣿
⠀⠀⠈⠒⠦⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣳⣄⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠙⠾⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⢠⣴⡳⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢴⠞⠓⡆
⠀⠀⠘⣎⢳⠘⠉⠸⣿⡀⠀⠀⠀⢀⡤⠴⠉⠀⠀⠀⠀⠈⢓⣢⠀⠀⠀⠀⡶⣯⣶⡯⠕⠒⠢⣄⠀⠀⠀⠀⠀⠀⡨⠷⠾⣄
⠀⠀⢴⡚⠂⠀⠀⠀⢻⠃⠀⠀⠀⢸⡕⠀⢄⡀⠀⢀⣠⠒⢁⣼⠀⠀⢀⡴⢇⣻⠀⠀⣀⣴⣾⣿⠆⠀⠀⠀⡴⠋⠀⠀⠀⠀⠳⡀
⠀⠀⠀⢹⠓⢄⠀⠀⠈⢳⡀⠀⠀⠸⣧⣄⠀⠈⢙⠁⣀⣴⠟⠋⠀⠀⣸⣻⣦⣤⣴⡞⣣⠟⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢼⣀⣈⣆⣀⣤⠾⠁⠀⠀⠀⠀⠙⠻⢶⣶⣶⠞⠁⠀⠀⠀⠀⠈⠙⠾⣽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⢀⢀⡞
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣠⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠘⣇⣀⡼⣏⠀⠀⠀⠀⢰⠛⢦⣀⣀⡀⠀⠀⠀⣠⢶⡄⠀⠀⢀⡤⠖⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢀⡿⠛⣧⣞⣲⣦
⠀⠀⠀⠀⠀⡿⠙⡇⠈⠀⠀⠀⠀⠈⣧⡾⠀⠈⠉⠉⠉⠉⢧⢸⠇⠀⠀⠙⡟⠒⠶⠶⠶⠒⡿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⡄
⠀⠀⠀⢠⣎⠀⠀⢙⡆⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢻⠢⠤⠤⠴⢺⡇⠀⠀⠀⠀⠀⢸⡏⠈⠉⠉⠁⠹⡇
⠀⠀⠀⢸⣇⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠳⠤⢤⡤⠞⠀⠀⠀⠀⠀⠀⢫⠢⠤⠤⠤⠤⠒⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠓⡄⢸⠁⠀⠀⢳⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣥⣭⢻⡇⣾⣿⣿⡜⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡠⠏⠘⠦⣤⠴⠋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⠿⢟⣼⣷⣙⣛⣛⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⠞⣋⣩⣉⡛⢦⡀⢰⠋⠙⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢛⣥⠶⠶⠶⣬⡙⢿⡏⣴⣮⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⢡⠊⠁⠀⠀⠈⠀⢻⡌⠓⠚⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢁⣟⣵⣿⣿⣿⣿⣿⡌⣷⣭⣵⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣧⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠸⠿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡼⠙⠀⠈⢳⡀⠀⢀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⣾⢛⣛⡊⣿⣿⡿⢿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢳⣀⠀⢀⡼⠳⢾⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡜⢿⣿⣯⢉⣭⣉⣭⣭⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠲⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⣝⣻⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⡴⠋⡠⠤⠀⠀⠀⡀⠀⠀⠀⠀⢠⢤⠀⠀⢀⡤⢤⡈⠳⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠘⣇⣀⣀⠀⢸⠁⠀⢸⡆⠀⣏⣈⡇⠀⡎⠀⢀⡇⠀⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣈⡇⠘⢆⣠⠜⠁⠀⠁⠀⠀⠀⠉⠈⠉⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠑⢤⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣠⠤⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠒⠶⠤⣄⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⣒⣛⣫⡭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠐⠂⠤⢄⡀
⠀⠀⠀⣠⠊⠁⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠘⠒⠤⠤⢤⣄⣀⣘⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⣖⣚⣋⣉⣉⣉⣉⣩⣉⣉⣙⣳⣶⣤⣤⣤⣤⣤⠤⠤⠤⠤⠶⠤⠶⠶⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣤⣤⣴⡄⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⠀⠀⠀⢨⠉⠉⣹⠀⠀⠀⠀⠀⠀⡄⠉⣻⡇⠀⠀⠀⠀⠀⢠⠀⠀⣼⠀⠀⠀⠀⠀⡄⠀⢀⡇
⠀⠀⠀⠀⠘⢀⠀⢹⠀⠀⠀⠀⠀⠀⡇⡀⠮⡇⠀⠀⠀⠀⠀⢸⢀⠀⢸⠀⠀⠀⠀⠀⡇⣀⣀⡇
⠀⠀⠀⠀⠌⠀⠀⠈⡆⠀⠀⠀⠀⠐⠀⠀⠀⢹⡀⠀⠀⠀⠀⡎⠀⠀⠈⡆⠀⠀⠀⢠⣿⣿⣿⣧
⠀⠀⠀⡜⠀⠀⠀⠀⠸⡄⠀⠀⣠⠃⠀⠀⠀⠀⢧⠀⠀⠀⡜⠀⠀⠀⠀⠸⡄⠀⢠⣿⣿⣿⣿⣿⣣
⠀⠀⠘⢀⡀⣀⢠⡀⢒⠛⠀⠀⠁⣀⢀⡐⣒⠒⡚⠃⠀⠘⢀⡄⣠⡄⡖⣲⠛⠀⠛⣻⢻⣿⣿⢛⡟⠃
⠀⠀⠀⢹⣽⣻⣿⡷⣿⡇⠀⠀⠈⣯⣿⣻⣿⢷⣿⠀⠀⠀⣾⢰⡇⣿⣇⣿⡆⠀⢸⠇⣿⢹⣿⣼⡇
⠀⠀⢀⠘⠁⠉⠉⠁⠉⢁⠀⠀⡄⠉⠈⠁⠉⠈⠉⡀⠀⢠⠙⠃⠙⠁⣿⡽⢃⠀⣈⣛⣘⣋⣿⣯⣋⡀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠂⠀⠀⠀⠀⠰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠇⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⢸⠀⣀⠤⠠⢤⣀⠰⠀⠀⢇⠠⠤⠄⠤⠤⣀⠆⠀⢸⠀⡠⠤⠤⠤⣀⢰⠀⢿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠉⠀⠀⠒⠀⠚⠁⠀⠀⠀⠉⠀⠉⠉⠒⠉⠀⠀⠀⠉⠂⠀⠉⠐⠚⠁⠀⠀⠉⠙⠋⠛⠛⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⡀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣤⣴⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣷⡄
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⢷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠕⠆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⡏⢡⡀⠑
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠉⠒⠉⠉⡠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⢐⠆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⢠⠂⠂⠒⠀⠀⠀⠀⠀⢤⢀⡗⠈⠢⠤⠄⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠉⢀⠽⡽⠋⠒⠂⠀⠀⠀⠀⠤⠐⡇⠀⠀⠀⠀⠀⠀⠈⠆⢄⠀⢄⢀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠲⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢠⡃⠀⢱⠂
⠀⠀⠀⠀⢬⠇⠀⠀⠀⠀⠀⢸⠌⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡶⢫⣜⠒⠊
⠀⠀⠀⠀⠂⠲⢁⠀⠀⠀⠀⠇⠀⠠⠒⠎⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡰⠡⠃⠀⠉⡆
⠀⠀⠀⠀⠀⠃⠈⡄⠲⠀⠴⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠰⠖⡐⠠⠁⠀⠀⠠⠁
⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⡰⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠏⡐⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⡠⠄⠒⠀⠈⠀⠈⢸⠄⠀⡠⠂⢸
⠀⠀⠀⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠀⢀⠼⠠⣀⣀⡀⠀⢠⡁⠊⠆⠀⠠⠀⠀⣉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄⠀⠀⠀⠀⣠⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⢰⠋⠉⠉⢧⠙⠚⠀⡴⢦⣸⡁⠀⠀⢸⠖⢲⡀⠀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠻⣤⠼⠹⣄⠀⢀⡼⣠⠞⠛⠳⣞⠁⠑⠶⠶⠛⠦⢼⣁⠘⢧⣤⢏⡤⣄
⠀⠀⠀⠀⣞⠛⠿⢿⣿⣒⣒⡶⠶⢾⣿⣭⣭⣤⣿⡀⠀⢀⣿⣀⣀⣀⣀⣀⣤⣯⣈⡷⠤⠶⢾⣗⣻⣿⠿⠿⠛⣷
⠀⠀⠀⠀⠉⠙⠳⡄⠀⠈⠉⠉⠛⠛⠓⠶⠶⠦⠤⠽⠿⠯⠭⠤⠤⠤⠤⠤⠴⠶⠶⠒⠛⠛⠉⠉⠀⠀⣴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣠⡤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⢤⣄⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄
⠀⠀⢀⡖⠛⢲⡀⠀⠀⠀⠀⠀⠀⢀⠏⠈⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⣆⠀⠀⠀⢐⡇⣀⡑⢄⡀⠀⠀⢀⣠⠤⢤
⠀⠀⠀⠳⣤⠜⠢⢄⡀⠀⠀⠀⠀⡞⡀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⣠⠴⠚⢤⡤⠋⠀⠀⠀⢸⡇⡇⠙⢦⡙⣒⡫⠥⢦⢀⡞
⠀⠀⠀⠀⢻⠀⠀⠂⠉⠲⣄⠀⣸⠁⠀⠀⠀⠀⠀⠀⢣⠀⢀⠴⠋⠅⠀⠀⢸⠀⠀⠀⢀⡠⠜⣡⠇⠀⠀⠈⠁⠀⢠⢃⡞
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠢⠑⠃⠂⠀⠀⢀⠀⠀⠀⡈⢗⠁⠊⠀⠀⠀⢀⣞⢀⡴⠚⢡⠖⠋⠁⠀⠀⠀⠀⠀⠀⣇⢸⡀
⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⠀⠀⠐⠀⠀⢰⠋⢳⠀⠀⠐⠀⠀⢀⡀⢀⡞⠉⠈⢻⡙⠒⠬⣍⡒⠦⡄⠀⠀⠀⠀⠀⠈⢣⡙⣄
⠀⠀⠀⠀⠀⢹⠀⠀⢺⠀⢳⠀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⢰⠉⢹⠸⡄⠀⠀⠀⡇⢀⡠⡎⢉⣧⢹⠀⠀⡴⢋⣭⣛⣚⣁⣈⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠈⠓⠊⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠘⠖⣋⡤⠧⠀⠀⢰⠷⠋⣠⠞⠉⠸⡜⠦⠊⡰⠋⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⣻⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣀⣀⣸⣅⡀⢀⣀⡴⣫⠤⠞⠓⠦⠤⣀⢇⡠⠞
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⡽⠋⢀⡜⠁⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠓⠲⠦⠤⠤⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⣤⠔⠋⣠⠖⢻⡁⠀⡼⠓⠢⠤⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡠⠚⠁⠀⠀⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⠒⠒⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢰⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢄⡞⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡥⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠓⠒⠲⠦⠤⣀⣀⠀⠀⠀⠀⣰⠚⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⣀⡤⠖⠀⠈⠒⢒⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⢳⡀⠀⠻⣄⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⢄⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣀⣉⡉⠉⠛⠒⠶⠤⢤⣀⣀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⣀⡥⠤⢤⡀⠋⠀⠀⠀⠉⢢⠀⠀⢀⣀⡀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠲⠤⡠⠞⠁⠀⠀⡠⠖⠒⢦⡀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⢣⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠙⢦⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠠⠒⠓⠢⠈⠀⠀⠀⡀⢻
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠇⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⣘⡃⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⡟
⠀⠀⠀⠈⢧⠀⠀⠀⡠⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢦⠀⠀⣀⣤⠖⠘⠦⣀⣀⣊⠀⠢⣀⣀⣈⠔⠐⠀⠒⠋
⠀⠀⠀⠀⠀⠙⠒⠒⠒⠀⣄⠀⠀⠀⢁⢀⡀⠀⠀⠀⢀⠜⠀⡀⠀⠀⠀⠀⠈⡇⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠋⠁⠀⠙⠲⠦⠤⠤⠖⠋⢄⡀⠀⠀⣂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣱⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⠀⠀⠀⠀⠀⠀⣰⠫⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⡰⡳⠃⠀⠀⠀⠀⠀⠀⠳⣀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣰⡳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⢀⡨⠟⠁⢀⣀⣄⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⢀⡪⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣴⠋⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠿⣷⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠉⠉⠙⠲⢤⠀⠀⠀⠉⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⢀⡴⠖⠛⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢙⢹
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⢜⠟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢌⢆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⡜
⠀⠀⠀⣀⣀⡀⠀⠈⠙⠲⠤⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠠⣪⠟⠁
⠀⢠⠊⠁⠈⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⢞⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠋
⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠤⣄⡀⠀⠀⠀⠙⠦⣄⣀⠀⢀⣰⠵⠋⠀⠀⠀⠀⢀⡔⠻⢷⣦
⠀⠀⠙⠲⢤⢶⣷⣤⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣻
⠀⠀⠀⠀⣏⠀⠀⢹⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠋⠆⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠲⠦⣄⡀⠈⠑⠊⠁⠀⠀⠀⠀⠀⢠⢴⣶⣤
⠀⠀⠀⠀⠈⠒⠴⠚⠁⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⣏⠃⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⣐⠵⠃⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⣀⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣸⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠛⢻⣧⠀⠈⠳⣄⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣠⠏⠀⠀⠀⠈⠙⠒⠶⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⠈⢁⠔⠒⠒⠊⠁⡘⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⣒⠂⢑⠀⠀⢓⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⣄⠀⠃⠀⠀⣀⣀⠀⠀⡁⠉⠁⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡗⠛⠀⠀⠀⠧⠘⠀⢀⠎⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⠁⢷⠁⠀⠀⢠⣄⡁⢔⢁⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣾⡆⢡⠐⢈⠀⠈⠁⠀⠀⠀⠀⢁⣬⡵⢻⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣧⡌⡇⡏⠁⠀⠀⠀⠀⠀⠉⠉⣡⣤⣾⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⢻⣿⡇⠁⠁⠀⠀⠀⠀⠈⠁⠐⣶⠀⣿⠃⣠⣄⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣬⣻⣶⣾⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⢯⣾⣿⣷⣾⣟⠛⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⣯⠿⠛⠛⠛⠷⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡳⠀⠀⠀⠀⠀⠀⠀⢀⡞⣴⣿⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⠁⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⡿⠷⢶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠃⠀⠀⠀⠀⠀⠀⢀⢞⣾⣿⣿⣿⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡠⣫⡞⠁⠀⠀⠉⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣠⣤⣴⣞⣿⣶⠶⠀⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠃⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁