Accessories Emojis & Symbols

⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠠⠤⠒⠈⠈⠀⠀⠰⠇⠠⠐⢁⠀⠀⠆⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⡰⠁⡀
⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠠⠀⠀⡠⠈⠑⠄⣀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⠀⠀⠀⡐⢊⡤⠈⠀⠀⢀⠄
⠐⠉⠀⠀⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠁⠎⠀⠀⡄⢂⠠⠋⠀⠀⢀⠔⠊
⠀⢀⣀⡀⠀⠀⠀⠀⣀⡐⢄⡠⠒⠀⠀⠀⠀⠀⠀⡄⠀⢀⠂⡀⠴⠗⠂⠂⡀⠀⠀⠀⠀⢀⣼⠘⠀⠀⠉⠀⠀⠀⠠⠒⢀⢀⣀⣀⡀
⠀⠈⠀⠈⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣴⠊⠘⠀⠂⠀⠀⠈⠀⠀⣀⠤⠋⡁⣀⠀⠀⠠⢂⠀⢰⣿⣿⡿⠹⣿⣿⡷
⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣶⠆⣄⢀⡄⠸⠀⡋⠀⠈⠉⠀⠒⠂⠀⠠⠴⠊⠁⡠⠚⠀⣿⡀⠀⠀⣿⠂⠈⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠀⠀⠠⠀⠀⢈⠀⠀⠄⠀⠈⠁⠒⠀⠤⠀⠀⠀⠀⣠⠔⠋⠀⠀⣼⣿⣷⣶⣾⣿⣧⠀⠠⠀⠀⠀⠀⠠
⠀⣀⠀⠀⠨⢀⠀⠀⠀⢀⠃⠀⡄⠀⠀⠰⠀⠠⢀⠄⠀⢀⣀⠀⠄⠤⠄⠄⣀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏⠀⠀⢂⠀⠀⡐⠀⠃
⠀⡀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⢀⣿⣿⣿⣿⣿⠀⠈⠀⠀⠁⠐⠀⠀⠂
⠈⠸⣿⡿⠀⠀⠺⣿⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⡰⠀⢰⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⡀
⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠛⠿⣿⣿⡿⠿⠇⠸⡀⠀⠀⠁⠀⠀⡸
⠀⡈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠐⠀⠈⠁⠎⠀⠀⠀⢀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠤⠀⠄
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⡀⠀⠀⠐⠀⠂
⠈⢀⠀⠀⠀⡇⠀⠀⠀⠐⠀⠁⠐⠂⠀⠒⠈⠠⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⡐⠀⠀⢂
⠀⠀⠈⠀⡈⠈⠀⠀⠀⣀⡀⠀⣴⣶⣆⠀⠀⠄⠀⠁⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠡⠀⠀⡜
⠀⡀⠀⠀⠀⢀⠑⠀⠻⣿⠿⠀⠈⠛⠁⠰⡁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠂⠀⠀⠈⠀⠀⠒⠀⠐⠂⠀⠁⠀⠅⠀⡆⠀⠀⠀⠃
⠀⠑⠠⣀⠀⠙⠃⠠⡀⠀⠠⠄⠀⠀⠀⠐⠈⠂⢨⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠜
⠀⡄⠀⠈⠑⠠⠄⣀⠨⠀⠀⠀⣀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⢠
⢀⠈⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀⠀⠀⡄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠘⢃⠀⠀⠀⢁⠀⠀⣀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠆⠀⠀⠀⢀⠆
⠀⠀⠠⡀⠀⠀⠀⠀⡌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠆⠀⠀⠈⣀⡀⠀⠤⠄⠀⠀⡤⠠⠀⠤⠀⠀⠀⠂⠀⠀⠀⡄
⠀⠀⠂⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠈⠀⠀⠘⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠃⠘⠀⠀⠀⠀⠁⠠⠠⠄⠠⠂⠀⠀⠀⠑⠂⠀⠘⠁⠀⠒⠈⠁⠀⠀⠀⠁⠈⠈⠀⠈

⠀⠀⠀⣠⣤⣶⣿⡦⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣻⠀⣛⠀⣻⠀⠀⠀⠀⠀⢸⣿⠀⣀⡀
⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⡸⠿⠿⢿⣀⡀⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠘⠛⣷⣿⣿
⠀⠀⠻⡿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠿⠀⠻⠀⠻⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠒⠒⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣶⢶⣶⣶⣶⢶⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠤⡷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠻⠿⠃⠀⠀⠀⠠⠿⠿⠯⠽⠿⠷⠀⠀⠀⠀⠀⢸⣿⣿⣿


⠀⠀⣴⣶⣶⣶⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡟⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠘⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢾⠷⠋


⠀⠀⣀⣖⣒⣒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⠒⠒⢶
⠀⠀⣿⡿⢿⢿⣿⡇⠀⠀⠀⠠⣷⣶⣾⣷⣤⣀⡀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠋⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠉⠉⠙⠛⠉⠁⠀⠀⠀⠀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⡀⠀⠄⠀⠀⣠⠀⠀⠚⠉⠛⠛⠒⠢⠀⠉⠑⠉⠈⠈⠈⠀⠉⠡⠀⠒⠚⠛⠋⠛⠂
⠀⠀⠀⠀⠀⠀⣵⣶⣶⣶⣽⡅⠀⠀⠀⠀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⢷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁⠀⠀⠰⣏⡯⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⢠⣿⣷⣦⣻⣷⣿⠻⠿⣷
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀⠀⠀⣨⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠙⠛⠻⠿⣿⣿⡆
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣀⠤⠤⣄⠀⠀⠈
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣟⡷⢰⡷⣀⠃⠀⠀⡞⠁⠀⠀⢸⡆
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢰⣆⠀⠀⠀⠙⠃⣼⣧⣿⠁⠀⠀⣇⠀⠀⢀⡸⠃
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢿⣆⠀⠀⠀⠀⣿⠉⠃⠀⠀⠀⠈⠓⠛⠉⠀⠀⢰⠀⣅
⠀⠀⠐⠿⠿⠛⠋⠙⠟⠛⠉⠁⠀⠀⠀⠀⠈⠁⢀⡤⠶⣦⡀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠺⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢚⣂⠀⠀⠀⣾⠀⠀⠀⣷⠀⠀⠀⢰⣿⠻⡀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⣿⣆⠀⠀⠙⣦⣠⠴⠃⠀⣠⣤⣾⠇⠀⠇⠀⢤⣤⣾⣷⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⣿⠁⠀⠀⠚⠛⠉⠁⠀⠀⠀⠀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⢸⣓⠆⠀⠀⠀⠀⠀⢀⣴⠿⠒⠺⢧⣄⠀⠀⠀⠀⠀⠀⣶⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣄⣀⠀⠀⠀⠀⠀⢀⡴⠶⠶⢄
⠀⠀⠀⡰⠛⠉⠛⢦⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢀⣿⡀⣸⣇⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⢻⡟⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⣧
⠀⠀⠀⣇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠻⣧⣀⠀⢀⣠⡿⠀⠀⠀⠀⠀⢸⣛⡧⣟⣻⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠻⣄⡀⢀⣠⠇
⠀⠀⠀⠈⠓⠒⠚⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠓⠆⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⢸⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⣠⣽⣧⡀⠀⠀⠀⠀⠀⢀⣠⣟⣉⣉⣳⣄
⠀⠀⠀⠀⢰⣧⡎⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⣀⡠⠄⠊⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⡀⠀⠀⠀⠀⣘⠛⠿⠧⠼⠿⠛⣃
⠀⠀⠀⠀⣮⣿⠇⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠘⢍⠝⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠟⠁⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡆
⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣤⣶⣶⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡐⠉⠰⡄⣤⠊⠑⢆⠀⠀⠀⠀⢠⠖⠛⠛⢦
⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠸⠟⠋⠉⠙⠛⠟⠀⠀⠀⠠⣦⣭⣝⣛⣛⣭⣥⡦⠀⠀⠀⠑⠤⠔⠀⠘⠠⠴⠃⠀⠀⠀⠀⢿⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⢀⣤⠤⢤⣀⣤⠤⢤⡄⠀⠀⠀⠀⡰⠚⠛⠓⢦⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹
⠀⢸⣿⣿⡿⠁⢿⣿⣿⡇⠀⠀⠘⣧⣀⡼⠉⠳⣄⣠⠇⠀⠀⠀⠐⡗⠀⠒⠀⢸⡇⠀⠀⠀⠀⠀⠐⣿⢊⣾⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⣦⣤⣴⠋⠀⠀⠀⠀⠀⠀⠰⢿⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⣷⡖⢶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⢠⠖⠉⠙⠛⠋⠉⠒⡄⠀⠀⠀⠀⣫⠹⠙⠩⣹⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡿⣟⡽⢿⠀⠀⠀⠀⠀⠀⢠⡶⣶
⠀⠈⠣⡄⠀⠀⠀⢠⠴⠁⠀⠀⠀⠀⠀⠀⢰⠀⢘⠀⠀⠀⠀⠀⢠⡏⠉⠉⠉⠉⣧⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⢸⠀⠀⠀⠀⠀⠸⣄⣘⠦⢮⣀⡼⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢷⣈⢙⣶⡀
⠀⠀⠀⠳⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠸⠀⠿⢄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣠⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⣀⡴⣶⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠙⡄⠀⠀⠀⠀⠀⠀⢰⠖⣶⣶⠲⡆
⠀⢰⡋⠁⠙⠩⠛⠈⠙⡆⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⠶⢖⢲⠀⠀⠀⠀⠀⠀⡠⢶⣄⣠⠧⣄⠀⠀⠀⠀⠀⢸⠔⠃⠘⠢⡇
⠀⠀⠛⡇⠀⠈⠀⢸⠛⠀⠀⠀⠀⢏⣁⣉⣀⡉⡲⣆⠀⠀⠀⠀⠀⠘⠈⢀⠀⠘⠀⠀⠀⠀⠀⢰⢀⠀⠈⠀⢀⠸⡀⠀⠀⠀⠀⢸⠃⢸⡄⢸⡇
⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⠒⠊⠒⠚⠀⠀⠀⠀⠀⡇⣼⣠⠆⠠⣸⡇⢇⠀⠀⠀⠀⠸⠁⣸⠇⠈⡇
⠀⠀⠀⠓⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⠹⠥⠤⠤⠽⠹⠼⠀⠀⠀⠀⠘⠒⠋⠙⠒⠃

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⡯⣿⣿⠀⠀⠀⠀⠀⣶⣦⣶⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⣦⣤⣤⣴⣶
⠀⠀⠰⠮⣭⣭⣭⡵⠖⠀⠀⠀⠀⠀⡿⢿⣟⡿⠿⠀⠀⠀⠀⠀⠾⠿⠟⠛⠿⠿⠿⠁⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋

⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⣸⣿⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠛⢳⡀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣠⣀⡀⠀⠀⠀⠀⣾⣿⡧⢾⣿⡷
⠀⠀⠀⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡇⠀⢀⠀⠀⣇⠀⠀⠀⠀⠹⣿⡿⠋⠹⣿⣿⠃⠀⠀⠀⠀⢿⣿⡇⢺⣿⡿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠸⠧⠤⠾⠦⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣾⠆⠸⣶⠇
⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣎⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⡹⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢐⣋⣘⣸⣉⣀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢀⠂⡆⢡⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⣍⢸⠀⠀⠅⠈⠀⠀⠀⠀⠳⠂⠄⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⠚⡔⡇⠜⢸⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠘⠒⠂⠃⠂⠘⠊⠀⠀⣾⣷⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡴⠢⠆⠀⠲⣄⡀⠀⠀⡘⠉⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⡔⠉⠉⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⠀⠀⢀⢸⠃⠁⠀⠃⠀⠀⢀⠡⠀⠀⢠
⠀⠀⠀⠀⠀⣥⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⢀⠈⠀⠀⠀⠀⢀⠀⠉⢉⡱⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒
⠀⠀⠀⠀⣄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠷⠋⢯⣄⠀⠀⢠⣦⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠍⠿⠹⠇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢼⠀⠠⣻⠈⢌⡆⠀⠀⢰⣦⢤⢠⠄⠀⢠⢤⡤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠊⠀⠀⠀⠈
⠀⠀⠀⢹⠈⡌⣤⡺⡃⡡⠐⠀⠀⠀⠘⠛⠂⠈⠇⠀⠛⠾⠥⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⣸⡔⡏⣟⣓⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣯⡧⡏⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣸⠼⠽⠼⣌⣧⠀⠀⠀⣗⢰⡄⣀⡀
⠀⠀⠀⠉⠙⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⣦⡆⠀⠀⠀⠀⢰⣦⡤⣦⠀⠀⠀⢠⣯⠃⠀⠀⠀⢠⣽⡀⠀⠀⠉⠀⠷⣿⡅⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⡀⠄⠀⠀⠀⠤⠄⣀⡀⠀⠀⠀⠦⠤⠤⠆⠀⠀⠀⠀⠸⠤⠤⠴⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢳⠀⣨⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠄⠠⠁⠀⢀⠛⠱⡶⠁⠀⠀⠀⠰⠶⠶⠟⠀⠀⠀⠀⠹⠶⠶⠾⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣮⢭⣵⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢺⣭⣻⢶⣒⣫⣵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠓⠋⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡏⠀⢠⡷⠶⠴⣏⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠇⠀⡇⠄⠌⢷⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣅⣠⠸⡄

⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀
⠀⠀⠀⣸⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣝⣿⡿⠀⠀⠀⠀⠀⠸⣿⡆⣴⣿⠇⠀⠀⠀⠀⠀⠻⣿⠟⠺⢿⠿
⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⠤
⠀⠀⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠈⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠼⠿⠃⠙⠿⠧⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣀⣆⡀⠀⠀⠀⠀⠀⠀⢰⣲⣾⣤⣿⣗⡆⠀⠀⠀⠀⠀⠐⢗⣣⢜⡾⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈
⠀⠀⣾⢧⣷⢿⡄⠀⠀⠀⠀⠀⠀⠉⡏⡇⡏⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡾
⠘⠛⠛⠋⠉⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢀
⠀⠀⠛⢷⡄⠀⠀⠀⠀⠀⠀⠰⢂⡐⢪⠴⠲⢤⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠑⡄⠀⠀⠀⣸⣿⣗⠀⣀⣀⡀
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠉⠟⠉⠀⠀⠀⢸⠄⠀⠀⠀⢸⠀⠀⡆⢰⠀⠀⡇⠀⠀⡞⠁⠀⠈⢳⡏⠙⢿
⠀⠀⠀⠈⣿⣿⣦⡄⠀⠀⠀⠀⠀⠈⠀⢀⠀⢀⣸⠀⠀⠀⠀⠈⠳⣄⣀⣀⣠⠜⠁⠀⠀⠳⣀⠀⢀⡼⠑⣄⢈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢀⡀⣐⠀⠀⠀⠀⠀⠀⣴⣆⣾⣿⠀⠀⠀⠀⠴⣾⣿⣿⣿⣷⣦
⠀⠀⢻⣷⣄⣀⢠⣤⡀⠀⠀⠀⠀⠀⠉⠛⠛⢻⡟⠀⠀⠀⠀⠀⠀⢹⣟⣿⡇⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⡿⣧
⠀⠀⠸⠀⠙⢿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⡆⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠰⣉⣟⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣸⠶⢤⠀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⢒⣟⣳⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠖⠋⠉⠉⠉⠉⠉⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠇⠀⠙⢟⢤⠚⣽⠎⣒⣏⣹⣒⡁
⠀⠀⡠⢚⠭⠟⠛⠛⠛⠯⣕⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡇⢀⡤⠴⠒⠒⠒⠒⠒⠦⡄⢹⣽⠀⠀⠀⠀⠀⠘⢄⠀⠈⣼⡆⢠⡿⠓⠒⠒⠒⢽⣆
⠀⠀⣧⠇⠀⠀⠀⠀⠀⠀⠈⢳⣱⠀⠀⠀⠀⠀⠀⠀⢸⣤⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⢨⠁⠀⠀⠀⠀⠀⠈⠙⠚⠋⠀⠸⣄⠀⠀⠀⠀⢀⡟
⠀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣠⡏⣳⠦⣤⠤⠤⣀⣤⠾⡇⣸⠏⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠈⠙⠛⠛⠋⠁
⢀⡗⢁⡐⠀⠀⠀⠀⠀⠀⠩⠂⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢯⣀⣿⣤⡀⢸⣺⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⡜⠁⠘⣰
⢸⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣍⣻⠟⠉⠀⠀⠀⠀⠀⠀⡤⣤⣄⠀⠉⣀⡼⠃
⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣨⡄⠀⠀⠀⠀⠀⠀⢸⡈⠀⢙⡀⢰⢏⣀⡀
⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⢇⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⢁⠞⠾⠂⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣸⠀⠀⠀⠀⠀⠀⢀⣀⣸⣷⠸⣄⠀⠀⢚⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠀⠲⣄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠿⠿⡀⠀⠀⠀⠀⢠⠋⠀⠻⠟⣆⠈⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⢀⢶⡋⣉⡩⠓⣯⣽⠞⢯⣉⣉⡷⡄⠀⠀⠀⠀⢠⣁⣀⣀⣀⡇⠀⠀⠀⠀⠐⢄⡀⠀⣼⠟⠀⠀⠀⠀⠀⠐⡖⠒⠒⠂⡖⡆
⠀⠀⠀⠀⠀⢀⡴⠃⡼⢁⣽⣠⣞⣋⣉⣻⣄⣩⡈⢱⠹⡄⠀⠀⠀⢸⠛⠛⠛⠛⢳⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢰⣧⣀⡀⣀⣅⡁
⠀⠀⠀⠀⢠⡮⠤⠾⠀⢤⣬⣭⣭⣭⣭⣭⣭⣥⣤⣤⣧⣼⡄⠀⠀⣦⣤⣤⣤⣤⣤⣇⠀⠀⠀⣴⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⠁⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠉⠁⠀⠀⠀⠀⢹⠄⠀⢸⣞⣟⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠦⠖⢺
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢲⣶⣶⣶⣶⣶⠋⠀⠀⢈⡿⠿⠿⠧⣄⠀⠀⠀⠀⠀⠀⠀⣧⢀⡀⡀⣸
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠱⣄⣀⡴⠁⠀⠀⡴⢡⠂⠉⠙⠒⢄⠳⡄⠀⠀⠀⠀⢀⡇⠀⠉⠁⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⣧⣷⣶⣶⣶⣾⣼⡆
⠀⢀⡤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⡤⠴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠠⡄⠀⠀⣠⠜⡴⠃⠀⠀⠀⣾⡿⢋⠀⠀⣠⣍⢻⣷⣠
⢠⡏⡶⠈⢁⡈⠛⣶⡙⢿⠉⣤⠀⣀⠛⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⠴⠶⠂⠀⠀⠀⠀⢸⣿⠇⠘⠻⠾⠟⠁⢸⢿⣿
⠘⣇⠠⡦⢈⣅⢉⣹⣬⡿⣀⣶⢀⡉⠸⠇⡟⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡣⡀⠀⠀⠀⣠⢪⠏
⠀⢻⡇⢀⣌⣩⡜⡻⠁⠘⢏⣓⢾⣁⣴⡞⠁⠀⠀⢀⡴⢚⣩⣼⠗⠀⠀⠀⠀⠀⢀⠴⣒⣢⡀⠀⣠⣒⠢⡀⠀⠀⠀⠀⠀⠀⡟⣮⣤⣶⣭⢶⣹⠃
⠀⠀⠙⢯⣍⣉⠟⠀⠀⠀⠀⠙⠺⠯⠚⠀⠀⢀⡴⣫⢖⡯⡴⠁⠀⠀⠀⠀⣠⣞⠕⠈⢸⣇⠇⠀⣏⡇⠑⠻⡦⡀⠀⠀⠀⠀⠙⡇⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠞⠁⢸⢰⠃⠀⠀⢀⡠⢊⣜⣁⣀⣀⠈⠁⠀⠀⠈⢁⣀⣀⣘⣎⡢⡀⠀⠀⠀⡗⠚⠉⠓⢺
⠀⠀⠀⠀⠀⢀⡠⠔⠒⣿⡀⠀⠀⠀⣠⢞⡵⠛⠲⢄⠘⢸⠀⠀⣠⠟⣻⣿⣶⣿⣷⣶⣽⣆⠀⡔⣭⣶⣾⣿⣶⣶⣭⣻⣦⠀⠀⣅⣀⢤⣀⣸
⠀⠀⠀⢸⠉⠀⠀⠀⠀⠘⣷⣄⣠⠞⣡⠎⠀⠀⠀⠈⢧⢸⠀⠀⠳⢬⢿⣿⣿⣿⣿⣿⣿⡏⠛⢹⣿⣿⣿⣿⣿⣿⡿⣣⠎⠀⠀⡇⠀⠀⠀⢸
⢷⡾⠿⡿⣶⠶⠶⠶⠶⠶⠛⣋⠴⠋⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠈⠳⢝⡛⠿⠿⠿⣟⠷⠉⢯⡻⠿⠿⠿⢛⡫⠔⠃⠀⠀⠀⡷⠒⠒⠂⢸

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠒⠲⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠤⠁⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⢤⡄⠀⠀⠀⠀⠤⠀⡇⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀
⠀⠀⠀⠀⠘⣄⠐⡀⠂⢠⠞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠤⠀⡇⠀⠀⠃⢠⠄⠀⠐⠀⡇⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠈⢣⡁⠀⠁⠀⠀⠀⠘⠀⠀⠀⠰⠀⠒⠀⠀⠄⠀⠀⠠⠔⠀⡄⠀⠀⠀⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⡀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠈⠀⠀⡐⢄⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠄⠄⠀⠀⠀⠒⠒⠒⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠃
⠀⠀⠀⠀⢀⠟⠛⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠐⠉⠀⠀⢀⣄⡠⠄⠂⠀⠁⠀⠀⢀⠄⠁⠀⠀⠐⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡀
⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠒⠛⡀⢢⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁
⠀⠀⠐⠂⠈⠀⠀⡵⠞⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠁⠀⡠⠀⠀⠘⠀⠀⠀⠀⠰⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆
⠀⠀⠆⠀⠀⠀⠐⠒⠒⢂⣀⣉⠁⠄⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣤⣃⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠠⠒⠀⠠⠶⠖⠠⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⣱⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⡴⠊⠉⢢
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠳⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⣄⣀⠸⡄
⠀⢠⡤⠀⠀⠰⡇⠰⠆⠀⠈⠁⠀⠆⣐⢢⠆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢧⠇⣸
⠀⠈⢡⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⢠⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⠾⠃⠐⠒⡆⠀⠀⠀⣾⣫⡿⢀⠃
⠀⠀⠈⠀⠀⠀⣇⠈⠀⠀⠀⠀⢀⠂⠀⠄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠇⠂
⠀⠀⡃⠀⠀⠀⢻⡄⠀⠀⠀⡰⠃⠀⠀⡂⠀⠀⠀⠄⠀⠀⠀⠠⠀⠐⠚⠀⠀⠀⠄⠀⠒⠐⠀⠂⠆⠀⡟⠀⢸⠆
⠀⠀⠈⠒⠀⠀⠀⠙⠓⠒⠚⠀⠀⠐⠂⠓⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠉⠀⠀⠉⠁⠁⠀⠳⠴⠋

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠂⡄⢠⠀⡀⢠⠆
⠀⠀⠀⠄⠒⡃⡀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠐⠁⠂⣠⢀⠄⡀
⠀⠀⠀⠤⠤⠴⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠐⡰
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠞⠲⠦⠄
⠀⠀⠀⠀⠀⡾⠋⠉⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⢠⠟⠂⠀⠐⢿⠀⠀⠀⠀⢀⠀⠀⡜⠀⢀⡀⠀⠀⣀⣀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠸⡃⠀⠀⠀⢸⠄⠀⠀⠀⠈⠀⠈⠀⠀⠉⠉⠈⠁⠀⠹⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠘⠀⠉⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠤⣵⠀⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠳⠃⡂
⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠖⠰⠶⠶⡄⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠔⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠃⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠄⢠⠋
⠀⠀⠀⣀⣀⣀⠈⠀⠀⠀⠤⠴⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠐⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠉⠁⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠐⠒⠒⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠰⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡆⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⢠⣴⣾⣷⣦⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣸⣅⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣆⠁⠀⠁⠀⠻⡀⠀⠀⠹⣛⡻⠏⠀⠀⠀⠀⠐⠚⠂
⠀⠈⢿⢀⠀⠀⠠⠆⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠂⡄⡊⠔⠀⠀⠀⠒⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣹⣿⣛⠛⠷⣤⠀⠀⠀⠠⢾⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣟⠁⠀⠙⠄⠘⠇⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⣛⣿⡿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠰⡤⡀
⠀⠀⠀⠀⠈⡀⢀⠀⠘⠁⠀⠀⠀⠀⠘⡛⠿⢷⣬⡷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡄⠈
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠉⢀⡍⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⠌⠄⠀⢀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠂⠀⠋
⠀⠀⠄⠒⠀⠆⠰⢀⡀
⠀⠈⠀⠀⡠⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠤⠤⠮⠤⡴⠀⠀⠀⠀⠀⠀⠤⢤⠀⠀⠀⠄⣤⠀⠀⠀⠉⠜⠀⠀⡀⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⣶⢓⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠀⠀⠄⠀⠐⠖⠀⠀⠀⠀⣾⡟⠛⣷
⠀⠀⠄⠀⠈⠋⠄⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠹⢷⠾⠟⢠⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⡀⠀⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⣹⠀⠀⠀⠀⠀⠀⢰⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠉⠉⡆⠀⠀⠀⠀⠀⠀⡦⢴
⠀⠀⠐⠈⠁⠀⠀⠈⠉⠉⠙⠆⠀⠀⠀⠀⠀⡰⠁⠁⠀⢂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠼⢀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠢⡈⠑⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⠒⠒⠒⠀⠐⠒⠒⢆⠀⠀⠀⠓⠒⠒⠒⠒⠒⠂⠚⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⢠⡁⣄⣈⣤⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⣀⣀⣀⠀⡼
⠀⠀⠀⠀⢀⠊⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠶⠔⠒⠒⠀⠀⠀⠀⠀⠀⠔⠋⠉⠉⠑⢂⠀⠀⠀⠀⠀⠀⠛⠛⢻⠙⠓⠃
⠀⠀⠀⠐⠁⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⡠⡴⠚⠒⠢⢄
⠀⠀⢐⠀⡀⠀⠤⠤⠀⢤⠀⠀⠀⠀⠀⠀⡠⠒⡚⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠌⡐⠀⡆⠀⠡⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠰⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢅⣀⣅⣀⣀⣄⠼
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⠀⢤⡀⣀⡀⣠⣀⣸⠀⠀⠀⠀⢰⣒⣀⣀⣀⢰⣿⣶⠀⠀⠀⠀⠤⠄⢐⡲⠈⢰⠨⠆⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠚⠀⠐⠒⠚⠀⠀⠀⠀⠈⣄⣂⣐⣈⢹⠟⠉⠀⠀⠀⠀⡂⠀⠀⣀⡀⠸⠧⠀⣔⣀⠀⠄
⠀⠀⡰⠀⠀⢠⡀⠠⠐⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠪⠁⠀⠀⠀⠀⠀⠀⠤⠒⠄⣀⡀⠀⠀⠀⢀⡠
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡜⠁⠉⡦⠀⠀⢴⠁⠈⡃⠀⠀⠀⠀⢀⠀⠀⠰⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢠
⠀⠀⠗⠒⠒⠒⠒⠒⠒⠂⢳⠀⠀⠑⠀⠐⢁⣀⣀⠀⠙⠻⡄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⡺⠋⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠤⠬⠆
⠀⠀⠒⠤⠤⠤⠤⠄⠐⠒⠚⠀⠀⠀⠀⡔⠑⠒⠚⠓⠀⢠⡇⠀⠀⠀⠀⠀⡀⠀⠛⠂⠀⡸⠀⡀⠀⠀⠀⠀⠀⡘⢠⠠⠴⠶⠛⣣⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠖⠁⠠⠁⠀⠉⠁⠉⢄⡀⠈⡀⠀⠀⠀⠀⠤⢤⣤⠔⠒⠋⠁⠀⡱⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠎⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡚⠁⠀⠀⠀⠂⠚⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠈⡇⡸⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⢠⢅⡀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠂⠁⠈⠚
⠀⠀⠀⡤⠒⠦⡀⢠⠧⠄⢨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢼⠛⠛⠚⠒⠚⢹⡇⠀⠀⠀⢀⡀⠀⠀⣠⡀
⠀⠀⠀⢋⡂⢈⡡⠘⠀⢂⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠉⠉⠀⠀⠄⠀⠀⠠⠇⠀⠓⣀⠀⠀⢀⣀⣘⣀⣀⣀⣀⣠⣤⣧⣀⠀⠀⢸⣿⣷⣾⣿⡇
⠀⠀⠀⠂⠡⠎⠀⠀⠉⠉⠀⠀⠀⠀⢰⠉⠑⣄⢀⠀⠈⢉⠀⠀⠐⠀⡀⠈⠉⠉⠐⠒⣐⣂⣀⣀⡴⠃⠀⠀⣁⠀⠈⠀⠉⠉⠉⠁⠀⠀⠀⠁⠀⠈⠛⠁⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⡠⠤⠀⠀⠀⡆⠀⡙⠚⢅⠀⠠⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠒⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠀⠀⣳⣰⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡻⡿⠻⢷⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣿⣦⣤⣬⣶⡶⣾⣷⣤⡄⠀⠀⠀⢀⢿⣀⣸⢆⠀⠀⠀⠀⠀⡬⢅⡈⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⢂⠀⠀⠈⠒⠤⠤⣄⣐⣁⣈⣍⣨⠥⠟⠊⠀⠀⡴⠁⠂⠀⠀⠀⠑⡄⠀⠰⣊⡀⠊⠑⢄⣀⠄
⠀⠀⢀⠄⠀⠁⠄⠠⠃⠀⠀⠁⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⢶⢶⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⠀⠠⠤⠤⠤⢼⢄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠠⡐⠈⠁⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⡉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⣀⣀⣀⣀⣀⡘⠠
⠀⠀⠀⢲⣐⣒⣒⣒⣈⠭⠕⠊⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊

⠀⠀⠀⠔⠀⠀⠐⠚⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠒⠖⠠⠤⠶⠐⠚⡛⠂⠐⠂⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⡉⠉⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠐⠃
⠀⠀⠀⠀⠀⢀⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠊⠀⠀⠁⠘⠷⠀⠀⠀⠀⠀⠠⠤⠄⠤⠤⢠
⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠚⠃
⠀⠀⠀⠑⣄⢀⠀⠀⡠⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢦⣟⡋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠣⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉
⠀⠀⠀⠈⠆⠀⠀⢀⠄⠀⠀⠀⠀⠀⠛⠐⠘⠉⠀⠀⠀⠀⠀⠁⠀⠀⣰⠀⠀⠀⢀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠘⠰⠁⠀⠀⠀⣇⣠⣤⣤⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠐⠢⠴⠂⠀⠀⠀⠘⠛⠧⡼⢳
⠈⠢⠄⣀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠐⠊⠁
⠀⠀⠀⠠⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠄⠀⠀⠀⡠⠐⠀⠈
⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⠀⣤⣤
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠤⠀⠀⠒⠒⠒⠒⡀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠁⠀⠀⠠⠠
⠀⠀⠀⠀⡸⠆⠀⠬⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠠⠀⠂⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⠄
⠀⠀⠀⠀⣠⡶⠖⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠸⠟⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠤
⠀⠀⠀⠈⠀⠀⡠⡘⠁⠀⠀⠀⢀⢼⢄⠠⡉⢜⠸⠔⡗⠡⠊⠅⠂⠊⠘⠀⠀⠀⡃⠀⠀⠀⠀⠈⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂
⠀⠀⠀⠀⢸⡾⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⡄
⠀⠀⠀⠀⠈⠐⢳⣞⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣷⢀⠀⠀⣮⡇⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠀⠠⠍⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠈⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⡄⠄⠄⢠⡤⢄⣠⠄⣤⣨⣩⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠹⣚⡛⠀⣂⠀⠀⠀⡆⠂⠆⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠁⠉⠀⠈⠅⠓⠁

⠀⠀⠀⠀⠁⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠸⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢀⠀⠰⠀⠀⡆
⠀⠀⠠⠄⠀⠇⠘⠀⠀⠀⠀⠀⠀⠀⡎⠀⡞⠁⠀⠃⠀⠀⣁⠦⣉⠀⠀⠀⡀⠀⠀⠶⠁⠀⠀⠀⠀⠻⡇⠈⠃⢐⠁⡠⠁⡄⠀⠠
⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠀⠀⠀⠘⠩⠣⠠⠠⠤⣀⡁⡠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠂⠀⡎
⠀⠀⠘⠀⠀⠐⢄⠐⠎⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠐⠐⠒⠀⠀⠀⢀⣁⠠⠀⠀⠀⠂⠉⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢉⣉⠉⠁⠀⣀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢀⡔⠁⢂⠀⡤⠐⢆⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⣠⣿⠟⡴⠀⠀⠄⠀⠀⠀⠀⠀⠄⠆
⠀⠀⠀⢀⠀⠀⠀⠃⠀⢀⠀⠀⠸⠀⣀⠇⠐⡇⠀⡼⠀⢰⠀⠀⠁⡜⠀⢠⠀⠰⠚⠿⢏⣼⣿⠋⠀⠀⠀⢀⠐⡦⣄⠀⠀⠠⠀⣀
⠀⠀⠀⠎⠀⠘⠀⠃⠀⠘⠀⠀⠀⡒⠁⠀⠀⠠⠈⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠖⠋⠟⠀⠀⠀⠂⠀⠶⠾⣻⠣⣝⣶⡄⠘⠁⡀
⠀⠀⠀⣀⠀⠃⠀⠐⠒⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠈⠤⠚⠋⡉⠉⠙⠉⠉⠈
⠀⠀⠀⠉⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄
⠀⠀⠀⢠⠀⠀⠀⢰⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠌⠀⠈⠀⠈
⠀⠀⠀⡎⠀⠀⡁⢠⠀⠀⠠⠀⠀⠠⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠐⠀⠄⠄⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠊⠀⡐⠀⢀
⠀⠀⠀⢥⣶⣤⠃⠸⡀⣀⠆⠀⠠⠀⠀⠐⠶⠒⠒⠒⢀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⣴⢾⠤⠤⠤⠤⣷⡧⠤⠀⠀⠂⠀⠁⠀⠘⠁
⠀⢀⠀⢸⡟⠛⠂⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠂⠀⠈⠠⠤⠀⠀⠤⠄⠤⠡⠀⠁⡀
⠀⠀⢀⢰⠐⠿⣾⡛⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⡂⠀⠄⠀⡄⠭⠄⠬⠅⡭⠨⡭⠌
⠀⠀⠘⢰⠀⠀⣿⣧⠀⠀⠀⢠⡄⢤⠐⠀⠀⠀⠀⠀⠀⠠⠀⠂⢠⠀⠰⠀⠀⠣⠾⠾⠄⠡⠀⠉⠈⠂⠬⠩⢡⠀⠀⡀⠄⢀⠄
⠀⠀⠀⠀⠄⠀⢻⣿⠀⠈⠀⢀⠈⢠⠀⣁⡐⠀⠀⠀⠀⠂⠀⠒⠀⣤⡄⡄⠀⠈⠩⢭⠥⠰⠂⠉⠑⡆⣏⠾⠂⠀⠀⠀⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢺⣿⠆⠀⠀⠀⠀⠀⠐⠐⠉⠐⠀⠀⢠⣸⣾⡀⢠⡿⠷⡀⠀⠀⠀⠀⢀⡠⠠⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠉⢳⠈⠄⠀⠀⠀⠀⡄⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠠⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠲⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠉⠑⠒⢤⡀
⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠈⣖⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠲⢄⣀⠀⠀⢀⡠⠤⠤⠄⢀⣀⡔⠲⡎⠁⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⡉⠓⢺⠀⠀⠀⠀⠀⡀⠷⢾⠛⢄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⢦⣀⡠⠔⠊⠀⠇⢠⠡⡀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡸⠀⠙⠒⠠⠼⠆⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⡴⠶⠶⠶⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣛⣉⣭⣭⣤⠤⠤⢤⣤⣤⠀⠀⠀⢤⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠕⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⡩⠥⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠤⠶⠒⠉⠀⠀⢠⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠉⠙⢏⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⠶⠶⠶⠶⠶⢶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠁⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡥⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⡤⠸⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡴⠶⠞⠛⠋⠉
⠀⠀⠀⠙⠛⠲⠶⠦⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠉⠉⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⡶⠶⠿⠟⠛⠛⠻⠿⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⢿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣄⡀
⠀⣠⣾⠟⠁⠀⠀⠀⢠⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡇⠈⠙⠻⢷⣤⡀
⣰⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠻⢷⣄
⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠶⠶⣶⣶⣶⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠿⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⡇⠀⣢⡴⠀⠀⠀⠀⣽⡿⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⡇⠀⢠⠦⡀⠀⢠⡔⣾⠛⠁⠀⢶⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⡃⠀⠈⠚⠁⠀⠎⠀⣿⣿⡀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⡀⡧⠀⠀⠀⠀⠀⠂⠀⣿⡇⠉⠀⣴⠙⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡏⠁⠀⠀⣇⠀⢀⢀⠀⠀⠀⠀⣭⡅⠀⠀⠉⡆⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢸⡇⠀⣨⣋⡀⠀⠀⠈⠉⢹⡁⡄⣿⣧⠄⠀⠀⢷⣦⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⡄⢸⡇⠀⢸⣧⣷⡄⠀⠀⠀⠀⡁⡇⣿⣿⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⡇⠀⠻⣽⣿⣤⣤⣤⡤⣤⠷⠃⢸⣿⠀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣧⠀⠀⠀⠈⠻⣿⠏⠀⠀⠀⠀⠸⣏⣸⣻⡦⠤⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣭⡿⣿⡿⢆⣠⢀⠀⠀⡙⣻⠇⠀⠀⠀⣀⣿⢟⣩⡴⣿⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⣯⣴⣾⣥⡴⠋⠙⢧⡀⢠⣾⣿⣾⣻⣿⡾⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⣀⠀⠀⠙⢷⣆⠀⠀⠈⢻⣄⠹⣿⡿⠏⠛⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠙⠃⠀⠀⠀⠙⠷⢦⡀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠲⠼⢂⢀⠀⠀⠹⢦⡀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣏⣀⣻⣦⣼⣿⣿⣿⡇⠀⠀⠀⠙⢾⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠟⠁⠀⠀⠀⢠⡆⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠢⠼⠋

⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⣈⠀⠈⠘⣿⣿⡇⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⢉⢑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡌⢈⡉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⢻⣿⣿⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠓⠚⠋⢸⣿
⠀⠀⡠⠖⢒⣛⣛⣛⠒⠲⡄⠀⠀⠀⣾⣿⡿⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡦⢐⣷⡆
⠀⠀⡓⠶⠤⠭⠭⢭⢤⠔⣻⠀⠀⠈⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⡂⠀⠐⠹⠆⠀⠀⠀⠈⠢⡑⢄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠇
⠀⠀⢏⠒⠦⠤⠤⠤⠀⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠗⠷⠚⠛⠒⣄⠀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⢸⣿⣶⣿⡿
⠀⠀⠀⠁⠒⠀⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠸⡇⢠⠤⠔⠒⢲⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠸⡜⢋⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢹⠀⠀⠀⠀⠀⠀⢻⡈⠉⠁⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠄
⠀⠀⠀⠀⠀⠰⡶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣀⣰⢶⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠈⠻⣏⣀⡇
⢀⠤⠚⠆⠀⠀⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⢠⠑⠁⠀⠈⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⡒
⠀⠀⠄⠀⢃⠀⠀⠀⠀⠀⠈⠉⠛⢦⣘⣷⠀⡀⣠⣛⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠰⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣿⣿⣿⣦⠀⠀⠀⠘
⢂⠉⣀⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠂⠁⠀⠀⠀⠀⠀⠀⠀⢷⣺⣿⣿⣿⡿
⠀⢣⠄⢀⠈⢸⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠛⠛
⠀⠀⠳⡤⢤⠊⡧⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⢀⠀⠰⠷⣶⣶⡶⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠘⡝⢶⡆⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠊⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠤⠒⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡉⠢⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠑⠒⠀⠉
⠀⢰⠀⠀⠀⠀⠀⠤⢂⠔⠁⠀⠀⠀⠀⠀⠀⠀⣠⠊⡀⢀⠀⠼⠂⣈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡾⠑⠒⠓⠒⠬⣉⠹
⠀⠀⠓⠀⠀⠀⠀⡀⠙⢄⡠⠀⠀⠀⠀⠀⠀⡔⠁⢠⠀⠈⡀⢀⢠⠀⢑⡬⠂⠀⠀⠀⠀⠀⠀⠁⣀⣠⣶⣒⣓⣓⣶⣀
⠀⠀⠀⠀⢀⡴⠛⠷⡤⠊⠀⠀⠀⠀⠀⢠⠎⠠⠀⠀⠠⠄⠀⢠⡤⠒⠁⠀⠀⠀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠢⡀⠀⠒⢀⡤⠚⠁⠀⠀⠀⠀⢀⣸⡍⢆⠀⠀⠀⠘⣿⣿⣉⣉⡉⠛⠛⣿⣿⡇⠀⠀⠀⢠⣤⡴⢦
⠀⠀⠘⢄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡒⢈⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⢧⣠⠏
⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣁⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠴⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠖⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠀⠀⠀⠀⠠⠔⠒⠚⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⠄⠀⠀⠀⠀⢀⣀⣁⣤⣤⣽⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠉⡛⠷⣤⣀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠚⠉⠁⢀⣀⣀⣠⣤⠤⠶⠖⠚⠛⠋⠉⠉⠀⢀⣀⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣹⣦⣈⠓⢬⣙⠻⣦⣄⠀⠀⠀⠀⠀⣠⠶⠚⢛⡉⠭⠥⠄⢒⣂⣀⣤⣤⡴⠶⠶⠟⠛⠋⠉⣛⠛⢶⡄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⠳⢦⣌⠓⠦⣙⠳⣦⣀⢀⡾⠁⠀⠀⠠⠖⣒⣛⣋⣭⡭⠥⠤⠤⠤⠀⢀⣀⣀⣠⣤⠈⠃⠈⣿
⠀⠀⠀⠀⢰⡏⠀⠀⠈⠙⠶⣤⡉⠻⢶⣄⡁⠊⠙⠻⢧⣄⣀⣀⣀⣤⣤⣤⣴⡶⠶⠶⠶⠟⠛⠛⠛⠉⢉⣁⡠⠄⢀⣼⠇
⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠙⠳⣤⡈⠛⢶⣤⡀⠀⠈⣩⡭⠭⠤⠄⠀⠀⠐⠒⠒⠒⢒⣒⣊⣉⣭⣭⣤⡶⣾⠋⠁
⠀⠀⠀⠀⠀⢀⡿⠷⣦⣄⠀⠀⠀⠀⠀⠉⠓⠦⠈⠛⢷⣤⣠⣤⣤⠶⠶⠶⠒⣚⣛⣛⣿⣭⡿⠿⠿⠟⠛⠛⠛⣻⡇
⠀⠀⠀⠀⠀⠈⢧⣈⠲⢭⡛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠉⢀⣉⣥⠶⠶⠚⣛⠛⠉⠉⠉⠀⢀⣀⣀⣤⣤⣴⡶⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣉⠳⢮⣙⢷⣤⡀⠀⠀⢠⠞⠉⠀⠒⣈⣉⣥⡤⠤⠶⠖⠛⠛⢛⣉⣉⠉⠀⠀⠀⠲⣎⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣌⠛⠮⣿⢶⣄⣿⠀⠀⠀⠈⠀⠀⠒⢚⣛⣉⣉⣉⣭⣭⣤⡶⠶⠶⠞⠛⢀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠈⠙⠻⠶⠶⠾⠛⠛⠛⠛⠉⢉⣉⣉⣀⣀⣤⠤⠤⠴⢒⣊⣥⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠒⠋⢉⣉⣁⣀⣤⣤⣤⡤⠤⠶⠶⠖⠒⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⡧⠀⠀⠀⠀⠀⠀⠀⡊⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⠂⣴⣿⠃⠑⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢣
⠀⠀⠀⠀⠀⠀⠀⣞⠉⠉⡧⠀⠀⠀⣴⠟⠇⠀⠀⠀⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠊⣿⡿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠁⢰⠁⡼⠿⠂⠹⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠠⣟⣁⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⡟⠉⠀⠀⠒
⠀⠀⠀⠀⡔⠀⠂⠀⠀⠀⠀⠀⠀⣿⣟⣡⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠘⠀⠀⢀⠇⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠈⢾⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠠⠘⠉⠀⠀⠀⣠⠊⠀⡀⠀⠀⠀⠹⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠷⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢸⣾⡞⠟⢻⣤⠖
⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠋⠙⠟⠀⠀⣄⣀⣍⡹⠄⠀⠀⠀⠀⠷⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠠⠴⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⣞⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠲⠚⠁
⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⠀⣤⡾⠆⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠐⡀⠀⠈
⠀⠀⠀⠸⡀⠀⡗⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠋⠀⢻⣧⡀⠀⠐⢄⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠹⣧⡻⠦⣴⠤⡀⠀⠀⠀⠀⢰⡏⣧⠀⠀⠀⢸⣿⡇⠀⠀⠈⠂⠀⠀⠀⠀⢇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹⠳⠶⠞⠁⠀⠀⠀⠀⠀⢻⣌⠛⠶⠒⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠟⠛⠇⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⣽⣛⣛⣛⣛⣻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠍⠉⠉⠋⠙⠭⡆⠀⠀⡠⠤⠤⣤⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⣰⠂⠀⠰⠂⠀⠀⠀⠀⠋⠁
⠀⠀⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢲⡐⣀⣿⠀⠀⠈⢹⠁⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠄⠁⠀⣠⢀⡀⠀⠀⠈⠀⠁⠁⠀⠀⠀⢸
⠀⢀⡴⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠈⠉⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠠⠆⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠰⠃⠀⠀⠐⠀⠀⠀⠠⣂⠄⠀⠀⢰⠀⠀⠃⠀⠀⠰⠘⡄⠀⠀⣗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡠⠄⠈⠁⠀⠀⠀⠘⠀⠀⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡀⠀⠀⠀⠀⢀⡠⠒⠉⣠⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⠀⡀⠀⠁⠀⠌⠂⠀⠀⠀⣀⠔⠉⢀⡴⠊⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠄⠂
⠀⠀⠀⠄⠈⠀⠠⠀⠀⠀⠀⢀⠤⠊⢀⡠⠞⠁⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⡠⡠⠁
⠤⠈⠀⡀⠄⠀⠀⠀⠀⡠⠖⠁⣀⠔⠋⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⠂⠀⠀⠀⠒⠀⠀⠀⣴⣾⣧
⠘⠁⠀⠀⠀⠀⣀⠔⠊⢀⡤⠚⠁⠀⠀⠂⠀⠀⢀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠀⠸⣿⣿⡡
⠀⠀⠀⠀⡠⠞⣡⢀⠖⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⣠⠺⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢈⠀⣀⠔⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⣀⡀⡄⠀⣀⠈
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣤⣤⠤⠔⠒⠈⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠶⠶⠶⠶⠶⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⣀⣴⠶⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢀⣴⠟⠋⠀⠀⣼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡟⠷⣦⣄
⠀⠀⣰⠟⠁⠀⠀⠀⠀⡇⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠖⠊⠁⠀⡇⠀⠀⠉⠻⣦⣄
⠀⢠⡿⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠒⠒⠒⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠚⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠉⠉⠁

⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⣰⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠴⢿⣿⡟⠋⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⢀⣽⣶⡶⠆⠀⠀⠀⠀⠐⠞⣿⣿⠿⠂
⠀⠀⠀⢨⡟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣄⡀
⠀⣼⣿⣿⣿⣷⡆⠀⠀⠀⢠⣶⣾⣿⣷⣶⡄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⢰⣿⣿⣿⣿
⢠⡟⢿⣿⣿⣿⡇⠀⠀⠀⣾⠛⣿⣿⣿⠙⣧⠀⠀⠀⢀⣿⣿⣿⣿⡟⠀⠙⢷⡄⠀⠈⢿⣿⣿⣿
⢸⡇⠘⣿⣿⣿⡇⠀⠀⠀⣿⠀⣻⣿⢛⡀⣿⠀⠀⠀⣸⡇⢹⣟⣛⠁⣠⡴⠛⠁⠀⢠⣾⣿⡿⢿⡄
⠀⢻⡀⢼⣿⣿⣧⠀⠀⠀⠘⠷⢀⠉⠐⠄⠇⠀⠀⢰⡟⠀⠀⠈⠉⠘⠉⠁⠀⠀⠀⣸⣿⣿⣷⠈⣷⡀
⠀⢸⡇⢨⣿⣿⣿⠀⠀⠀⠠⠂⠀⢄⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣷⡈⢠⣶⠀⢀⣿⣿⣿⣿⡄⠙⣇
⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠑⡆⠀⠀⠁⠀⠀⠘⠇⠀⠀⠀⠀⠠⣿⣷⣸⠃⠀⣼⣿⣿⣿⣿⣿⠀⠙⠁
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⢻⣿⣿⣿⠿
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿
⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⣸⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣿⢹⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣴⠇⣼⡇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄
⢸⠟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠔⠁⡀⠙⢢⠀⠀⠀⠀⠀⢠⠃⣀⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇
⠀⠀⢨⠀⠠⠋⠓⠀⢣⠤⡄⢠⠒⣼⠘⠋⣤⡀⠀⢹⠀⠀⢀⡀⠤⢤⠐⠒⠒⣦⠀⠠⢠⣀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⡠⠀⠀⠀⠈
⠀⠀⢈⠀⢀⡾⠓⠀⢸⠀⣿⢨⠄⡟⠀⠠⣋⡉⠀⣼⠀⠀⡌⠀⡄⠀⠈⣦⠀⠀⠁⢄⠀⠀⡤⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⡀⠀⣰⢦⡀⢸⠀⡇⠀⠇⡇⠀⠴⣫⡓⠀⣿⠀⠀⢰⠀⠈⢢⠂⠀⠑⡄⠁⠀⢣⠊⠈⢴⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⡡⠶⠄⢸⡞⠀⠀⠈⣇⢀⣘⠥⢥⣀⣹⠀⠀⠀⠐⡄⠈⠑⣤⠊⠈⢢⡄⠈⠁⡠⡎⠀⠀⠰⠶⠦⠤⢤⣄⣀⡀⠀⠀⠀⠆
⠀⠀⢰⡗⢚⠃⠉⠉⠙⡇⠀⠀⠀⠸⡅⣠⢠⢠⡆⣸⠀⠀⠀⠃⠈⣦⠂⠀⢡⡀⠀⠈⢂⠈⠑⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠼⠤⡄
⠀⠀⠀⢿⣾⣼⣾⣇⣧⠇⠀⠀⠀⠀⠣⠽⠧⠼⠾⠟⠀⢀⣤⣧⡀⠀⠑⡤⠀⠉⢢⠄⠈⢣⣠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣩⣀⣸⢧⣀⣀⣀⣀⣀⣀⠀⢠⣾⠉⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠄⠀⠀⢀⠀⠀⠀⠀⢽⠒⢻⡵⠊⠁⠀⠀⠉⠉⠉⠉⠛⣌⡿⠽⡇⠀⠀⠀⣴⣂⡤⢄⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⣜⣛⣉⣉⣉⣉⣛⣛⣒⣒⣒⡒⠒⠾⠷⠴⡇⠀⠀⣸⠇⣏⠑⡞⠉⣴⡂⢀⡀
⠀⠀⠀⢀⠐⠷⠶⠶⢤⣤⣤⣤⣤⣀⣤⠞⢀⣆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⡏⠀⠀⣿⢠⢎⣩⠓⢠⠧⣸⠁⠲⢇⡴⢠⡄
⠀⠀⡀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠈⢆⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⠟⠲⠤⣍⠸⠁⠶⢥⣝⣉⠖⢀⡟
⠀⠀⢆⡀⠛⠛⠛⠛⠓⠒⠶⠤⠤⠄⠠⣶⣦⡄⠼⡄⠀⢻⢻⡟⠉⠁⠀⠀⠀⠀⠒⠒⠒⠶⢲⠋⠀⢰⡏⠘⠢⣤⣀⠛⢱⠆⣼⠈⡏⢘⡏
⠀⠀⠀⠈⠁⠒⠈⠉⠁⠀⠀⠀⠀⠀⠠⠤⠤⠀⠠⠔⠀⠘⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢀⡴⠋⣤⠋⠰⢠⡍⢉⠓⠲⠤⣤⣁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⣟⡶⠒⠂⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢤⣈⠑⠂⠠⠊⡨⠓⠦⢦⢨⠏
⠀⠀⠀⠀⡠⣶⣶⠯⠷⣻⣿⡿⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⢔⢢⠆⠐⠒⠬⡈⠓⠒⠤⠧⣏⡐⠀⡌
⠀⠀⠠⠊⠙⢯⣿⣾⣻⣯⠟⠁⠀⠤⢀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠌⡀⠴⠋⡀⠀⠀⠀⠈⠆⡀⠀⠀⠀⠙⠛
⠀⠐⠀⠀⠀⣀⠀⠉⠁⡠⢀⡾⡻⣷⣦⣄⣀⠀⠙⠺⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠠⠀⠀⣶⡟⣽⣷⡀⠈⠀⠈⠳⣕⣦⡟⠁⠈⠁⠉⠉⠁⠊⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠱⡀⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⣀⠀⠀⡰⠃⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢄
⠀⠀⠑⣯⠉⠁⠀⠀⢧⠀⢦⡀⠀⠀⠀⠈⣉⠽⠪⣍⣀⠴⠊⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢌⠀⠀⠈⠻⠀⠀⠀⠈⢂
⠀⠀⠀⠙⠀⠀⠀⠀⠈⢧⠀⣈⠥⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠂⠀⠀⠀⠀⠐⢤⠔⠁⠠⡀
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠄⠀⠀⣀⡀⣀⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊
⠀⠀⠀⠀⠈⢆⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠶⠤⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠛⠛⠒⠶⠶⠤⢴⣶⡶⠾⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠑⠦⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣒⠲⣤
⠀⠀⠀⠀⠀⠀⢀⡏⠈⠑⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠚⣧⠀⠀⠈⣷⠘
⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⢏⠉⠁⠀⠈⡇⠀⠀⠀⢸⡄⢀⡴⠃⢠
⠀⠀⣠⠶⠛⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⠀⠀⠀⣀⡷⠋⠀⠀⣼
⢠⠞⠁⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣀⣆⣴⠞⠉⠀⠀⠀⣠⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠓⠒⢋⣭⠟⠋⠀⠀⠀⢀⣠⠞⠃
⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠞⠋⠀⠀⣀⣠⠴⠚⠋
⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⠶⢟⣛⣋⣥⡤⠴⠖⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣤⣀
⠀⠀⠀⠀⠀⠀⠠⠬⠭⠤⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡤⠀⠁⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠘⠣⣄⡀⠀⠀⠀⢀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⢷⣄⢀⣼⠢⠀⠀⠀⠻⠦⠤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⢀⠁⠀⠀⠀⢼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠐⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣦⡄
⠀⠀⠀⠀⣠⣴⣾⣿⣷⣄⠀⠀⠀⠀⠀⢧⠈⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣤⣾⠿⠗⣀⡀
⠀⠀⠀⡾⢿⣿⣿⣿⣿⣿⣷⡶⣄⠀⠀⠈⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⡺⠋⢁⡤⠖⠋⠀⢀
⠀⠀⠀⠻⣮⣿⣿⣿⣿⣿⡿⣷⠹⠦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠒⠈⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠐⣜⣿⣿⣿⣿⣿⣟⡵⠃⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠎⠓⠍⣩⠽⠛⠁⠀⠀⠀⡙⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⠶⠗⠓⠋⠁
⠀⠀⢷⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠉⠑⠒⠐⠀⠁⠀⠀⠀⠀⠀⠀⢰⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠚⠦⠀⠀⠀⠀⠀⠀⠀⣠⠂

⠀⠀⣄⣺⠗⠁⠀⠀⠠⠀⠉⠁⠉⠉⠀⠷⡿⠀⠁⠀⠁⠀⠀⠉
⢰⠿⠉⠁⠀⣀⠀⠀⠂⠠⠀⠀⠐⠋⠀⠋⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⠇⠀⣤
⠀⠀⠀⠀⢈⠻⠈⠀⠀⢀⡄⢰⡄⠐⠂⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠁⠰⡇⢰⡾
⠀⠀⠀⠀⡎⠀⡄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⠀⠀⠐⣃⠠⡆
⠀⠀⠀⠀⠩⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⡨⠖⠺⠛⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⣀⡄⠐⠋⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡿⠿⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⠐⠃⢀⣠
⡀⠀⡄⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⢠⣟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠄⠐⠋⢀
⠀⠀⠄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠃⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡙⡁⠀⠀⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠒⠃⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⡷⠰⠂⣇⣸⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠢⠀⠀⠀⠀⠤⠆⠐⠃⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⠀⠀⢘⣿⣿⣿⣿⡇⠀⣳⠿⣿⣿⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⠀⢠⣶⣶⠀⠀⠀⢀⣖⣂⠸⠯⠌⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢜⣭⣽⣙⠃⠠⠘⠀⡿⠻⠄⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠈⠀⠈⣸⣿⣠⠴⠉⠀⣿⣇⠐⢃⡘⠉⣀⣀
⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠈⠘⠙⣬⠂⡶⠀⣿⡻⠃⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀⠀⠀⠀⠀⢸⣿⣴⡖⢻⡟⣯⡍⢨⣯⢨⣿⡇⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⠛⣧⡿⠺⣧⡤⢾⠳⠄⢀⡆⠀⠀⠐⡆⠀⠀⢤⡾⢶⡿⠿⡿⡆⠇⢹⠇⠘⡇⠸⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠊⠣⠀⠻⠇⠀⣸⡗⣾⡧⠒⠀⠐⠀⠀⠐⠐⠒⠀⠈⠀⢈⣡⣤⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⠫⡹⣆⠔⡀⠳⡄⠀⠀⠊⠸⠃⠱⠠⡤⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣃⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣽⡔⢱⡷⠀⠙⢜⣌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠁⣽⣇⠴⠆⠊⡹⠅⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⣃⠞⣹⠾⠆⠀⠀⢡⣡⣜
⠀⠀⠀⠀⠀⠀⠀⢰⠇⣦⢻⢃⠘⠃⠀⠀⠀⠀⠀⠣⣿⣣⣎⡀
⠀⠀⠀⠀⠀⠀⢠⡿⢚⣀⢃⣾⠄⠀⠀⠀⠀⠀⠀⢰⡀⣳⣵⠰⡄
⠀⠀⠀⠀⠀⠀⠀⡼⢡⡟⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⣱⢎⡁⢤⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠳⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡙⢼⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡴⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠘⠂⠇⠀⠀⠈⠈⡃⠀⠀⠀⠃⠀⠀⠀⢀⠄⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⠀⠄⠂⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣤
⠀⠀⠴⠒⠒⠒⠒⠲⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⢱⡆⠀⠀⠀⠀⠀⠄
⠀⠀⡇⢀⠖⠉⠁⠉⠢⡀⢰⠉⠉⡆⡊⠀⠙⠄⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠞⠃⠀⢀⠀⠀⠀⢀
⠀⠀⡇⡌⠀⠀⠀⠀⠀⠱⠈⡲⣒⠁⢙⡶⡊⠀⠀⠀⠀⠀⠀⠀⣀⠀⣃⠀⠀⠠⢀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠄
⠀⠀⡇⠡⡀⠀⠀⠀⠀⡔⢸⠀⠀⡇⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⡅⠀⠬⠀⠀⢀⣀⣀⡀⠀⠠⠀⠰⠀⠀⠀⠀⠁⠤⠀⠄
⠀⠀⣇⠀⠑⠢⡤⠄⠊⠀⠀⠉⠉⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠀⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⠌⡆⠀⠀⠀⡇⠘⠀⠀⠀⠀⠅⡀⠀⠀⠀⠀⡈⠂⠀⠰⠰⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠁⠀⠀⢮⡰⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡾⢩⠏⢿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢤⢀⠠⢄⡀
⠀⠀⠀⠆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⡅⡆⠀⠹⢍⡘⢹⠀⢀⠔⠛⠋⠲⡄⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⢻⡀⢀⢈⡬⢷⡾⠀⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⡇⠀⢠⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠢⡉⠓⠛⠛⠉⠀⠀⠀⠓⠤⠤⠖⠁⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⢢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠠⢄⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠀⠘⠀⠀⠀⠀⠸⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠀⠀⡇⠀⢸⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠄⠀⠀⠀⠀⡀⠀⠀⠡⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠦⠶⠶⠶⠶⠶⠤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠉⠓⠒⠒⠒⠒⠒⠚⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠤⠤⣄⡀
⠀⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⢾⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢖⡡⠃⠀⠀⠀⠉⠢⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠓⠤⣈⡉⠓⠒⠒⠒⠚⢛⣉⣉⡥⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠦⠤⠤⠤⢤⣤⣤⣀⣀⣠⡤⠤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠿⠟⠛⠛⠛⠛⠛⠿⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣳⠄⠈⠉⠑⠲⠤⠤⢤⣤⣤⡤⠤⠤⠶⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣓⠲⠿⡧⢤⣄⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠦⣌⣹⣖⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣝⡲⠭⠍⠙⠒⠒⠀⠠⣤⣤⣤⣀⣀⣀⣠⣄⣀⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⢀⠴⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⠲⢭⡙⠀⠰⠤⠀⠀⢀⣀⣀⣀⡀⠀⢀⠀⠀⠀⣴⠶⠦⣄⠀⠸⡇⠀⢀⡾⠁⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠮⣍⡓⠠⢤⣀⣀⢀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠀⣼⠃⠀⠀⠈⠳⣄⣷⣰⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣗⡶⢤⣉⡁⠀⠀⠀⠉⠉⠋⠉⠙⠒⠒⠒⠒⠂⠀⢿⣄⣀⠀⠀⠀⢈⣻⣯⣀⣤⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⣟⣡⡈⠙⠳⠮⣭⣛⣒⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣛⣩⣿⣿⣿⡿⢦⣄⣀
⠀⠀⢀⣀⣀⣤⣤⡶⠶⡟⠻⣝⠯⣕⠮⠉⠙⠓⠦⣤⣀⡀⠉⠉⠛⠓⠾⠿⠿⣿⣿⣿⣶⣶⣿⣟⡋⠩⠽⠛⠛⠉⢸⡏⠙⢦⡀⠉⠛⠳⠶⢤⣄⣀⡀
⣶⢿⡉⠯⣉⠙⠦⣙⠢⣌⠓⠎⠉⠲⢤⣀⣀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠲⢦⣤⣤⡤⠤⣤⣠⡤⢤⣤⡤⠴⠒⠃⠀⢸⡇⠀⠀⢳⣠⠞⠀⠀⠀⠀⢩⡍⠙⢻
⠙⣦⡙⠢⠈⠑⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⠀⠀⠀⠀⠙⠲⠤⠶⠶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠀⢈⡗⠚⠁⠸⠏⠀⠀⠀⣠⠖⠋⢀⣴⡟
⠀⠈⠛⠶⣦⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠈⠙⠛⠒⠒⠦⠤⢀⡀⠀⠀⠈⠉⠀⠀⠈⠙⠋⠁⠈⠉⠉⠁⠀⠁⠀⠀⠾⠃⠀⠀⢀⣠⡤⠖⠋⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⢶⣮⣝⡛⠛⠛⠒⠲⠤⠤⠄⠠⢤⣤⠤⠴⠤⠤⠂⠀⠀⠒⠚⢉⣀⣀⣤⣴⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⠶⠶⠾⠿⠛⠛⠛⠉⠉⠁
⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠠⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⠀⡀⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠚⠃⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠯⠸⠟⠋
⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠈⠻⣿⡭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣀⡐⠦⠄⠀⠰⠟
⠀⠀⣶⣿⣧⣈⣉⣉⣀⣤⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠄⠀⠐
⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣂⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣤⣤⣴⣾⣧⣿⣾⣿⣿⣶⣤⣤⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣻⣿⡛⢿⡏⢿⣿⣿⣿⣿⣋⣿⠿⣿⣹⡿⣤⣤⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡔⠢⣄⠨⣿⠛⢟⠋⣙⡧⣿⣭⣿⠉⡿⢇⠉⡾⠈⣉⡄⠈⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⢻⠀⠈⠁⠙⣧⣿⣦⣩⣄⠹⠿⣇⣠⠓⡌⢻⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸⣿⣿⣿⣏⠺⣙⣿⣙⠏⣰⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠡⣼⣏⣳⢻⣾⠩⣾⣥⡟⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⡜⢻⣗⣽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠡⢟⣿⣽⡟⣿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡁⢾⡏⣓⠮⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠞⠻⢿⣟⢹⠶⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢾⠈⠻⡿⠛⠓⠲⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡻⠋⣤⠀⣬⣥⡄⢤⡀⢨⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣓⡢⠴⠧⠼⠿⡷⠤⠣⡔⣪⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠲⡏⢙⡛⠛⢿⡟⠓⠓⣹⠓⠦⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣨⡯⢬⣽⣗⣻⣝⡛⡻⣛⣠⣘⣁⣠⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠭⠑⣖⠡⡜⠻⣿⣿⣿⠋⠴⠄⠡⠤⠔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠳⠟⠛⠳⠚⠛⣿⠁⠓⠞⠳⠾⠷⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢀⡴⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣿⣾⣷⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡐⣿⣿⣿⣿⣿⣿⣆⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⣿⣟⢿⠙⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠗⢰⡿⠏⠹⠙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠋⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠘⢦⡀⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⣀⡀
⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡯
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢵⡪
⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣖⢽⡪
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡫⢕⢽⡮
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠽⣪⣕⢕⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⢠⡿⢖⡭⡪⣿⢕⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠭⡛⢗⢦⣄⣀⣟⣻⢕⣿⡪⣚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡺⢕⡪⡕⡜⡼⡜⠄⠈⠉⠺⢕⢽⣪⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⣴⡫⢕⢪⣳⣹⢱⡱⠑⠈⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⣠⣖⠯⣓⢬⢢⢧⢇⠣⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣍⡎⡞⣎⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢻⠿⠋⠀⠀⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⡠⠶⠖⠀⠖⠀⠆⠀⠆⠀⠛⠒⠠⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⣀⣈⠁⠀⢠⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⣀⠀⢐⠀⠀⠁⠀⠀⠄⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢀⡯⠖⠀⠀⢹⠁
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⢸⠉⠃⠀⠀⠀⠀⠀⠀⠀⠓⠀⢒⠒⠐⠂⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠓⠋⠉
⠀⠀⠀⠀⠠⡀⢰⠀⠀⡆⡆⠘⠀⠀⡇⠀⠀⡏⠀⠀⡔⢸⣽⢲⡄⢁⣈⠀⠀⢀⡀⠐⠃⠀⢀⠉⠀⠀⠘⡁⠀⠒⠒⢀⡀
⠀⠀⠀⠀⠀⠁⠈⢀⠟⠛⢻⡁⠀⢠⡇⠄⢠⠃⠀⠸⣚⣚⣗⣰⡇⢀⠀⠀⠀⠈⠀⠀⠀⣰⠛⢿⡄⣴⠀⠀⠀⠀⣄⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢸⡇⠀⠈⠁⠀⠀⠙⢋⠏⠃⠄⢀⠁⠀⡀⢠⠀⠀⠀⠘⠳⠾⠃⢸⠀⠀⠀⢰⡟⠊⠃⠀⢠
⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⣿⠀⠘⠓⠀⠀⢸⢠⡖⠀⠸⠀⢰⠀⢸⠀⢀⣇⢀⠀⠀⢰⠛⠉⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠈
⠀⠀⠊⠀⠀⠀⠀⠈⠆⠀⢰⠏⣀⠯⠀⠀⠀⠈⢸⡇⠀⠀⠀⢸⠀⠈⠀⠐⠶⢺⡀⢀⡀⠧⠔⠰⠶⠆⠀⠀⠐⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠐⠀⠀⠀⢒⡋⣀⢹⠀⠀⡄⠀⠀⠠⠁⠆⡏⠀⢸⠀⠀⢠⡆⠀⠀⠀⠈⢱⢸⠀⠀⢆⠉⠀⠀⠀⢰⡇⠀⠁
⠀⠀⠛⠒⠋⠁⠀⠀⠀⠸⡝⠹⢸⡀⠀⠳⠀⠀⡄⠀⠀⠁⠴⠞⠀⠤⢹⠀⠘⠌⠀⠀⠈⢘⠀⠀⢸
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠑⠃⠀⢡⣤⣤⡄⢰⠁⠀⠀⠀⢠⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠇⠀⠀⠀⣀
⠐⠒⠒⠒⠒⠒⠒⠀⠒⠒⠓⠒⢢⣤⣤⣤⡄⢸⠀⠀⠀⠀⠘⡇⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⡄⠀⢀⡃⠀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠘⠀⠀⠂⠀⠀⠏⠀⠀⠀⠀⠀⠋⠀⠀⠄⠀⠃⠀⠀⠳⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣒⣂⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠆⣯⠀⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⡦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⣟⡇⠀⡇⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⠚⠷⣶⣤⣤⣤⣴⡺⠍⠒⠁⢶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣄⡄⢈⣈⣀⣀⠠⠄⠀⢀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠰⠬⠤⠄⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⡀⠀⠀⠀⠀⠀⢀⣆⣰⣴⣶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡈⠁⠁⠀⠉⠉⢀⡈⣡⣿⣿⣧⣠⣁⢰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⣩⣿⡟⢿⣿⡿⣿⢿⣿⡿⣿⣿⢯⣍⣩⡄⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠰⠃⡌⠀⠀⡇⠀⠟⠀⠸⣣⠈⠍⠂⠙⢿⣥⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠃⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠁⠈⢄
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢢⠀⠀⠐⠄⠀⠈⣢⡀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠂⠀⠀⣀⡆⠀⠠⠔⡀⠈⢳⡀⠀⠌⢦⠀⠀⠹⣄⠀⡱⡀
⠀⠀⠀⠀⠀⢀⠁⠀⠐⡊⠀⠀⢀⠀⠀⠄⡇⠀⠀⢺⠀⠀⠀⠤⣵⠀⠀⠖⠃⠀⠨⣥⠀⠀⠂⢷⡀⠀⠽⡄⠀⡱
⠀⠀⠀⠀⠀⡈⠀⠐⣨⠁⠀⠀⡈⠀⠀⢨⠁⠀⠘⢹⠀⠀⠀⠀⢺⠀⠀⠀⢲⠀⠀⠘⣇⠀⠀⠌⣇⠀⠂⢹⡀⠀⢣
⠀⠀⠀⠀⠀⠁⠀⠀⡞⠀⠀⢁⠇⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠀⠂⢿⠀⠀⠀⢸⡄⠀⠈⣇⠀⠌⡄
⠀⠀⠀⠀⠀⠄⣊⢼⠃⠀⠐⠘⠃⠀⡈⠍⠀⠀⠠⡍⠀⠀⢀⣁⣸⠁⠀⠀⢸⡆⠀⠈⢸⡇⠀⢈⣘⡇⠀⠀⣻⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠁⠘⠄⠐⣋⣛⠀⠀⠔⠶⠀⠀⠒⢲⠀⠀⠠⠄⢼⠀⠀⣀⢨⡅⠀⠐⢸⠇⠀⠰⢸⡇⢀⡐⠾⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠒⠄⣀⣀⣹⠀⠀⠐⢂⡜⠀⠀⢀⣼⡁⠀⣀⠾⠂⠀⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⢰⣤⣄
⠀⠀⢀⣴⣞⢿⣿⣿⡿⣣⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤
⠀⠀⠘⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⠙⢦⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⣦⡶⣄⣐⢶⣴⣤
⠀⠀⠀⠘⣿⣿⡏⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠸⠟⠋⠓⠚⠓⠛⠐⠻⠂
⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⡤⠟⠀⠀⠀⠀⠀⠀⠀⠉⠷⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡤⢄⡤⢤⡀
⠀⠀⠀⣿⠉⠀⠀⠄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⡝⣆⢠⣿⢻⣶⠀⠀⠀⠀⠀⠠⡮⢤⡮⠤⠤⢵⡤⢵⡄
⠀⠀⠀⢹⣆⡴⠛⠢⡀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⢹⣼⣿⡏⣸⣸⠀⠀⠀⠀⠀⠀⠙⢆⠱⡀⠀⡜⡠⠋
⠀⠀⢰⣯⣤⣤⣤⣤⣤⣽⡆⠀⠀⠀⠀⠀⠀⠀⢸⡏⢧⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡿⣿⣠⢯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⣧⣼⠞
⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠷⠾⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠐⠈⠁⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣉⣹⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⡏⣣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠱⠎⠀⠈⢳⢹⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠻⠋⣽⣦⠟⠀⠀⠀⠀⠀⢠⣶⣶⣿⡿⢸⣿⣶⣶⡄
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣙⡻⠗⠀⠀⠀⠀⠀⢸⣻⡶⣤⣤⣤⣤⢶⣟⡇
⠀⠀⠀⠱⣄⣀⣶⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠸⡞⢣⡀⣠⠚⡺⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⠷⠟⠛⠉
⠀⠀⠀⠀⠈⠉⠯⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠠⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠿⠿⠿

⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠈⡋⠀⠀⠀⠀⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⠦⣀⣤⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⣿⡟⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣮⣏⡙⣿⡷⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡤⠖⠋
⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠉⢹⣿⣿⡄⠉⣶⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣤⡞⠛⠉⣷⣶⣾⠛⢣⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣇⣀⣀⡿⣿⣿⣀⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢸⣿⣿⡇⠀⠀⣿⣿⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢱⣶⣾⠛⠛⠳⣴⣶⡏⠉⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡼⠿⠿⣀⣀⠀⣿⠿⠿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡀⠀⣹⣿⣿⡆⠀⢀⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣏⠉⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠈⣹⣦⣶⣾⣉⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠿⠛⣿⣿⣏⢙⠿⣷⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢾⣿⠉⠙⣶⣶⡟⠛⢻⣿⣇⣠⣶⡿⠛⢳⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠁⢸⣶⣶⡉⠀⢀⣼⣶⣾⠿⠿⣧⣴⣾⠉⢀⡿⠿⢧⣤⡼⠿⢿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣤⣾⡋⠉⢹⣿⣿⠉⠙⢿⣤⣤⡹⠟⠻⣾⣿⣇⣀⣸⣿⣇⣀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⣻⠟⢳⣶⣾⠛⠉⣶⣶⣾⠋⠉⣷⣶⣶⠉⠀⣿⣿⡇⠀⣹⣿⢇⣤⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢹⣿⣄⣀⡿⠟⣦⣤⡟⠛⠻⣤⣤⡿⠛⠻⣶⣶⡏⠉⢹⣿⡏⢹⣞⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⡾⢿⣏⣿⣧⣀⣽⣿⣷⣀⣀⣿⣿⣇⣀⣸⠿⠿⣧⣤⡞⠛⣷⣿⣿⣷⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⣧⣀⣿⡇⠘⣿⡇⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⣿⣿⣧⣴⣿⣿⣇⣨⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⠿⣿⣁⣼⣿⡏⠙⣶⣿⠉⠉⣷⣶⡟⠉⢹⣿⣿⡇⠀⣿⣿⣸⣏⣿⠿⢧⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢿⣀⣸⣿⠟⠛⢳⣶⡟⠛⣤⣤⡿⠿⢧⣤⣼⠛⠛⣷⣾⠋⢹⣿⣿⢿⣀⣸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣼⢿⣧⡈⠀⢲⣾⠿⣇⣀⣿⣿⡇⠀⢸⣿⣿⣀⣀⡿⠿⣶⣾⠙⢇⣨⡿⠿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠿⣇⣀⣿⠇⠀⠻⢃⣀⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⡇⢀⡿⢿⣄⠈⢿⣇⣠⡝⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⣀⣼⣿⡇⠀⠀⣀⣼⣿⠉⠹⣶⣶⠟⠛⢻⣶⣶⡏⠉⣹⣿⣇⢸⡿⠀⢠⣹⠿⠿⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⣿⠁⠀⠉⠀⠀⣿⠉⢹⣦⣼⠿⠿⣇⣠⣼⠿⠿⣧⣤⡟⠋⣿⣿⣄⠀⠈⣿⣦⣤⣟⠋⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣇⣀⣸⣿⡿⠁⠀⠀⢸⣶⡾⠿⢯⣀⠀⣿⣿⡏⠀⠀⣿⣿⣧⣤⡟⠙⣿⠆⠀⠀⢿⠟⠛⣶⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢿⣃⣀⠁⠀⠀⢰⣿⠻⣇⡀⣸⣿⣿⠀⠀⢸⣿⣿⡇⠀⣸⡿⣷⣶⣟⠀⠀⠀⠘⣷⣶⡟⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⣿⡟⠀⠀⠀⠈⢡⣤⣿⣿⡏⠉⢹⣶⣶⡌⠉⠉⣿⣿⡏⢀⡾⢿⣿⡀⠀⠀⠀⠘⠋⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣤⡟⠻⣯⣄⠀⠀⠀⠀⢠⣾⠿⡇⠀⣿⣶⡾⠛⠛⣧⣤⣶⠛⠉⣿⣿⣇⣸⠟⢇⠀⠀⠀⠀⠸⣿⣇⣈⡏
⠀⠀⠀⠀⠀⠀⠀⢨⣧⣤⠿⠋⠀⠀⠀⠀⠺⡇⠀⣿⣿⠏⠛⢳⣤⣤⠛⠛⢻⣶⣶⠏⠉⣿⣿⣤⣼⠀⠀⠀⠀⠀⠀⣸⠿⠿⣦⡄
⠀⠀⠀⠀⠀⠀⠸⡏⠉⣿⡆⠀⠀⠀⠀⠀⣰⣿⡿⠉⠙⣶⣶⡞⠛⠛⣤⣤⡜⠛⠛⣷⣾⡏⠀⢿⣿⡄⠀⠀⠀⠀⠀⠻⢧⣴⣿⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⡗⠉⠁⠀⠀⠀⠀⢠⡿⠉⢳⣶⣶⠛⠛⣧⣤⣤⠛⠛⢣⣤⣴⠛⠛⢳⣶⣎⠉⣿⠀⠀⠀⠀⠀⠀⣴⣏⠁⣈⣿⣀⣰⣄
⠀⠀⠀⠀⠀⣤⣀⣸⣿⡆⠀⠀⠀⠀⠀⠈⣥⣤⠿⠿⢧⣤⣤⡿⠿⠿⣤⣤⡾⠿⠿⣤⣤⡼⠿⠻⣿⣇⠀⠀⠀⠀⠀⠀⠉⠉⢻⡿⠿⣿⣏⠙⠇
⠀⠀⠀⠰⣿⠿⣿⣀⣀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣀⣀⣸⠿⢿⣄⣀⡰⠿⠿⣇⣀⣠⠿⣿⣇⣀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⢿⡿⢧⣴⣿⠁
⠀⣠⣆⣠⣶⣦⠾⢿⣯⡀⠀⠀⠀⠀⠀⠿⢁⠀⣿⣿⣧⠀⣀⡿⠿⢷⣀⣠⡿⠿⢿⣀⣀⣼⣿⣿⣁⣸⠁⠀⠀⠀⠀⠀⠀⠰⣿⣦⡾⣉⠹⠷
⠀⠉⠙⠋⢙⣿⣶⡾⠛⠁⠀⠀⠀⠀⠀⢀⣿⣿⡏⠉⠙⣿⣿⣇⣀⣼⠿⠿⣤⣄⣼⣿⣿⡁⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠇
⠀⠀⠀⠻⠿⠉⠉⠀⣴⡄⠀⠀⠀⠀⠀⣿⡏⠉⢳⣶⣾⠁⢀⣽⠿⠿⠀⠀⠛⠻⣧⣀⣀⣿⣿⡏⠀⣿⠏
⠀⠀⠸⠃⢀⣾⡿⠀⠈⠁⠀⠀⠀⠀⠀⠈⢱⣦⣼⠛⠉⣿⣿⣧⣤⠀⠀⠀⠀⢰⡿⣿⡟⠉⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠻⣦⣤⣮⠁⣹⠇⠀⠀⠀⠀⠈⣥⣀⣿⣷⡾⠛⢹⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢇⣀⣼⠟⠻⣾⣿⠇⠀⠀⠀⠀⠀⠻⣿⠉⠙⣷⣶⡟⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⠿⣤⣴⣏⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣀⣀⡿⠛⢻⣿⠀⠀⠀⠀⠀⠀⠈⠻⣈⢹⣶⣶⡋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⠿⠿⣧⣶⣧⡀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⠉⠛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣀⣤⠟⢉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⣁⣈⣷⣶⡏⣉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⣩⣽⡟⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠿⢿⣥⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠛⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣧⣤⠚⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢉⣻⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢻⣶⡎⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡿⠿⣄⣈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⡽⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠿⣯⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣶⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣧⣴⠛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⠏⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣍⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠳⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠉⢙⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⣤⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⢿⣿⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠱⣶⠤⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⠟⠃⣶⡀
⠀⠀⠀⠀⠀⠀⡀⢠⣾⠇⠺⣿⡷⠶⠿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⣾⣿⢠⣤⡀
⠀⠀⠀⠀⠀⣼⣋⢀⣿⣷⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⣬⡟⠛⣢
⠀⠀⠀⠀⠀⠻⠿⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠛⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠐⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠴⠶⠒⠚⠛⠓⠦⣤⠶⠖⢲⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣸⣦⣀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⡒⠊⠉⠉⢉⣽⠉⠉⠉⠙⠛⠒⠻⢷⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢒⡎⠉⠁⣀⣀⠤⠕⠒⠊⠉⠉⠛⠓⠒⠲⠶⠤⢤⣤⣼⣇
⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⣀⡠⠄⢲⡎⠉⢀⣀⠤⠬⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄
⠀⠀⠀⡼⠉⠳⢤⡀⠀⡰⠁⠀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠶⠒⠛⠉⠙⡇
⠀⠀⠀⣇⠀⠀⠀⠉⠓⣧⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⣠⡤⠤⠶⠶⢺⡇
⠀⠀⠀⢘⣦⣀⠀⠀⠸⠀⢨⠓⢦⡀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠀⣀⣀⣠⡤⠴⠶⠒⠚⠛⠉⠉⠁⠀⣀⣀⣤⠴⠖⢻⡄
⠀⠀⠀⣾⠀⠈⠓⢦⣵⠀⢸⠀⠀⠉⠳⣄⡀⢠⡏⠀⠤⠖⠚⠋⠉⠉⠁⠀⢀⣀⣠⡤⠴⠶⠒⠛⠋⢉⣉⣀⣤⡤⠤⢾⡁
⠀⠀⠀⢻⡄⠀⠀⠀⡸⠳⢼⡀⠀⠀⠀⠀⠉⠛⣧⣤⡤⠤⠶⠖⠒⠛⠛⠉⣉⣁⣤⡤⠤⠶⠒⠛⠉⠉⠁⣀⣀⣠⣤⡞⠁
⠀⠀⠀⠀⠙⠳⣄⡀⡇⠀⡘⠉⠓⠦⣄⡀⠀⢰⡇⠀⠀⢠⡤⠴⠖⠒⠛⠉⠉⠀⢀⣀⣠⡤⠶⠖⠚⠋⠉⠉⢀⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠇⠀⠀⠀⠈⠙⠶⣼⣄⠀⢀⣀⣀⣠⣤⠤⠶⠖⠚⠋⠉⠁⣀⣀⣠⡤⠴⠖⠛⠋⠉⠁⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⠀⠀⠀⠀⢠⠏⠉⠉⠉⠀⠀⣀⣀⣤⠤⠶⠒⠛⠋⠉⠀⠀⢀⣀⣠⡤⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⢸⠀⠀⠐⠒⠛⠉⠉⠀⣀⣀⣤⡤⠤⠶⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠷⠤⠤⠶⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⣾⣿⣿⣶⠤⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠐⣛⣉⣤⡀
⠀⠀⠀⠀⠋⢻⣿⡿⠀⠀⠀⠀⠀⣾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⠋⠁
⠀⠀⠀⢀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣻⣯⣀⣀⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⣴⣾⣿⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡆⠀⠀⢀⣶⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣾⡿⣿⣿⣿⣿⣿⠀⠀⠀⢠⠛⠿⠿⠰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠙⢿⣦
⠀⢀⣿⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡜⢿⡇⠀⠀⠀⠀⠀⣠⣿⣃⣈⣿⣿⣿⡿⠁⣿⡀⠀⣸⡏⢹⣿⣿⣿⠁⠀⢀⣴⡿
⠀⠈⢿⡄⠈⢛⣿⣯⣿⠄⠀⠀⢀⡴⢀⠘⠄⣸⡇⠀⠀⠀⠀⠐⠛⠛⠉⠙⣿⣿⡿⠁⢀⣼⠇⢠⣿⠁⠸⠛⠷⣖⣤⡶⠛⠁
⠀⠀⠈⣷⠀⢾⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀⠐⠤⣀⠀⠀⠀⣠⣿⣿⣿⣧⡾⠛⠁⢀⡿⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣿⡄⢀⣿⣿⣿⣿⠀⠀⠘⠘⠀⠀⠀⣿⡀⠄⠀⠀⠈⠙⣷⢰⣿⣿⣿⣿⣿⠇⠀⢀⣾⠁
⠀⠀⠀⠈⠁⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠀⠈⠙⠀⠈⠢⣄⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠈⠃⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⡀⢠⣤⣿⡀⠀⣀⡤⠂⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⢠⣿⡟⠀⢤⣴⣤⠄
⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⢰⣿⣏⠙⠀⠉⠁⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠻⠅⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣸⠏⣿⠇⠀⠀⠀⠀⢸⠏⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡿
⠀⠀⠀⣠⡏⣠⣿⠀⠀⠀⠀⢀⣿⠀⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿
⠀⠀⣰⡿⠠⢻⡿⠀⠀⠀⠀⢸⡏⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⡄
⠀⠘⠟⠁⠀⠸⣇⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠃

⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡝⠿⢋⣴⣦⡀
⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠠⠂⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠋⣉⠀⠉⠀⢉⠙⠀⠲⠢⡀
⠘⢫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡝⠃⠀⠀⠀⠀⠀⠀⠀⣠⣦⠖⠀⠀⠀⠲⢦⣦⠀⠀⠀⠀⠀⠀⠀⢰⡇⠊⠁⠘⠧⣤⣀⣠⣀⣤⠼⠃⠀⠁⢸
⠀⠈⢱⣶⠄⠀⠀⠀⠀⠀⠀⠀⣶⡎⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢮⣔⡀⠄⠀⠀⠀⠀⠀⠠⢀⣢⡵⠞
⠀⠀⠀⠁⢾⣿⢆⣴⣦⡐⣿⡷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠛⠓⠛⠚⠛⢻⢻⡅
⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠂⠒⠒⠒⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡴⣆⡡⠤⠬⣀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠊⠉
⠀⠀⠀⡸⠀⢁⣠⣄⣄⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠏⠈⠀⠉⠘⣏⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⡄⠀⠀⠉
⠀⠀⣸⠁⣰⣿⠿⣿⡿⣻⣦⠀⢣⠀⠀⠀⠀⠀⠀⢀⣴⣫⣤⣠⣏⣀⣠⣄⣄⣀⣘⣇⣠⣌⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⡛
⠀⠀⣯⠀⣽⣿⣷⣬⣿⣿⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠙⢦⡑⠈⢣⠀⠀⠀⠀⠀⣰⠃⢘⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆⠀⠀⠀⢠⢿⡀
⠀⠀⠘⡄⠈⠿⣿⣿⣿⠿⠃⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢷⠀⠀⠀⣴⠃⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⣿⡂⠀⠐⣾⠸⣗
⠀⠀⠀⠘⡄⡤⣀⣀⣀⣠⣄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣣⠀⣰⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣾⡧⠀⠸⣿⣴⣿⠄
⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠉⠋⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⡄⢲⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡾⠻⣶⡢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠃⠒⠀⠥⣑⡂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⡃⢙⣿⣦⡾⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⢀⡤⠞⠁
⠀⠀⠀⣿⣿⠆⠈⠉⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠙⢿⣿⡟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋
⠀⠀⠀⢸⣿⠀⠀⢀⠤⠭⠿⠻⠯⠥⢄⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣦⡛⠉⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣻⡖⠾⠆⣟⣇⠆
⠀⠀⠀⠀⠿⠆⠀⠈⠉⠉⢬⣿⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⣷⣴⡟⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⢾⠿⣿⡷⡷⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⠃⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠷⣟⠾⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢐⣛⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣾⡥⣄⠀⠀⢄⠀⢀⣠⠀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠁⠀⠀⢦⠀⠀⠱⠂⠀⢀⣀⣀⣨⠀⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⠖⠁⠀⠙⠛⠁⠀⢀⣀⠁⠊⡠⠂⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣸⡇⠈⠀⠀⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠉⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣼⡇⠀⠀⠐⠒⠉⡄⠀⠸⣠⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠸⠿⠇⠀⠀⠀⠀⠀⠸⠆⠀⠛⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠁⠀⠀⠀⠡⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡀⠀⠀⠀⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠃⠀⠀⠀⠈⠀⠀⣀⡜⠁⣀⠆⠀⠀⠀⠀⠀⠘⣄⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠆⠘⠀⠀⠀⠀⠀⢄⡀⠀⠌⠀⣶⡄⠀⠀⠀⠀⠀⢀⠀⡀

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠀⡄⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⣠⣤⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠂⠀⠀⠀⠹⠉⠛⠋⢁⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡞⠻⣤⣶⣿⣁⡆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢀⣤⠀⠀⡄⣄⡝⢃⡼⠷⠃⠈⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⣧⠄⠠⠀⠹⣶⠁⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠘⠡⣀⠀⢠⣿⣟⡀⠠⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣷⠂⠀⠀⢸⣏⢷⠈⢢⣜⣳⢆⣠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡀⠀⢰⣿⡇⠀⠀⠈⣿⢸⡇⡄⠙⢣⣴⠋⠑⢆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⣾⠿⠃⠀⠀⠀⠈⢸⠇⡇⠀⢈⠁⢀⣉⡋⠓⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠙⢷⣼⣥⠀⠀⠀⠀⠀⠀⣸⠀⡇⢀⣼⠟⢩⣤⣿⠓⠀⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠌⢻⡀⠀⠀⠀⠀⢀⡇⠀⠁⢹⠿⠉⠉⠛⠋⢦⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡘⠀⡀⢠⠌⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠰⣤⠠⠉⢹⣰⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣀⣀⣀⠴⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢰⠆⠀⠄⠀⡤⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠀⠸⢇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠆⠹⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡜
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⣀⣠⡀⡄⣠⣀⡀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠤⡄
⠀⠀⠀⠛⣿⣿⣼⣿⡟⠃⠀⠀⠀⣠⡤⠖⠳⠤⣄⠀⠀⠀⢠⣶⣾⣶⣶⣷⢶⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠁⢸⣿⣿⣿⠈⠁⠀⠀⢸⣷⣭⣕⣨⣭⣿⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠻⠿⠿⠿⠃⠀⠀⠀⠀⠀⠸⠿⠿⠟⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠷⠶⠶⠇

⠀⠀⠀⢀⢠⡄⡀⣤⢀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⢨⣅⣬⣭⣄⣭⠀⠀⠀⠀⠀⣠⠖⠲⢤⠀⠀⠀⠀⠀⠀⣮⣴⣮⣴⠀⠀⠀⠀⠀⠀⢰⣾⣶
⠀⠀⠀⠀⠻⡼⡿⡼⠃⠀⠀⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⣤⣾⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃

⠀⠀⠀⠀⣴⣦⣤⣶⡄⠀⠀⠀⠀⣤⣤⣄⣀⣤⣤⠀⠀⠀⠀⠀⡠⠴⠤⢄⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⣿⣿⢻⣿⡇⠀⠀⠀⠀⠛⣿⠟⠻⣿⡟⠁⠀⠀⠀⡜⠀⠀⠀⠈⡇⠀⠀⠀⠀⣾⢻⣿⣿⢻⡆
⠀⠀⠀⠀⣿⡿⠸⣿⡇⠀⠀⠀⠀⠀⣿⣶⣵⣿⡇⠀⠀⠀⠀⢲⣄⠀⠀⠀⠛⠀⠀⠀⠘⠋⣿⣿⣿⡏⠛
⠀⠀⠀⠀⠛⠃⠀⠛⠃⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁

⠀⠀⠀⠀⢰⣆⢀⣶⠀⠀⠀⠀⠀⢀⣴⣶⣦⡰⡄⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⣀⣴⣦⣶⣄⡀
⠀⠀⠀⠀⢸⡟⠛⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⢠⣶⣶⣰⣢⣶⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⠀⠀⠀⢸⣿⣿⡟⢻⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠘⠛⠛⠛⠁⠋⠀⠀⠀⠈⠛⠛⠀⠈⠛⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠀⠔
⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠳⠀⠀⠀⠀⠀⠠⠧⠴⠀⠀⡄⣀⠆⠀⠀⠀⠀⠀⢈⠀⣤⡄⠈⠀⠀⠀⠀⢠⠘⠈⠀⡠⠻⡇⠐
⠀⠀⠀⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠙⠬⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠆⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⢦⡀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠽⠩⡇⠀⠀⢏⠹⡇⠀⠀⠀⢀⠈⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⢀⠎⠂⠰⠀⢰⠁⠀⠁⠀⠀⠀⠰⠚⠀⢻⠀⠔⠛⠀⢧⠀⠀⠀⠘⢴⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠈⠁⠋⠁
⠀⠀⠀⠘⠄⠀⠐⡇⠈⠀⠀⢰⠄⠀⠀⢸⠛⢿⠞⠀⡘⠳⡷⠞⠀⠀⠀⠐⠀⠀⠀⠠⠈⠀⠈⠁⠀⠀⠀⠀⠀⠈⣠
⠀⠀⠀⠀⠀⠋⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠠⡎⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠤⠀⠁⠀⠀⠀⠀⠀⠀⡠⠼⠮⡀⠴⡷⠅⠀⠀⠀⠀⠀⢄⠔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠶⠀⠀⠀⠀⢐⠀⠂⠘⣀⠁⠀⠀⡀⠀⠀⠀⠀⠒⡀⡤⢈⠂⢄⠄⠀⠀⠀⠀⠐⠁⣄⢸⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠀⠀⠠⡞⡳⡖⣔⠏⢱⢶⠺⡹⠄⠀⠀⠀⠀⠒⠲⣧⡀⠀⢐⠀⠀⠀⢀⡤⠆⠙⠛⠰⠴⣤
⠀⠀⠀⠀⠀⠀⠘⠶⠽⠃⠀⠀⠀⠀⠀⠁⠀⠄⠁⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢼⠀⠉⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢐⣀⢀⠀⠀⠀⠀⠀⢀⠀⠐⡡
⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠈⢿⠤⠚⠉⠁⠈⡷⢌⠖⠀⠀⠄⠠⠛⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃⢠
⠀⠀⠀⠀⠸⠀⠂⢰⠀⠺⠀⠠⠀⠀⠀⢨⠁⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⢢⠀⡀⠀⠀⠀⠀⠈⠛⠂⢀⣷⡁
⠀⠀⠀⠀⠀⠈⠠⠁⠵⠀⠀⠀⠀⠀⠢⠇⠙⠃⠘⠉⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠁⠑⠐⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⣠⣤⣠⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢻⡿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⣿⣿⡇⠀⢰⡇
⠀⠀⠀⢸⣷⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠅⠀⠀⠀⣿⣿⣷⠀⠸⠇⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣾⠀⠀⣶⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡏
⠀⠀⠀⠀⣿⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡞⠂⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡷⣿⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇⡇
⠀⠀⠀⠀⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⣴⣧⠀⣿⡇⠀⠀⠀⠀⣿⣇⡀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣷⣿⢰⣾⣷⡆⠀⠀⢀⣘⣿⣧⣇⡀
⠀⠀⠀⠀⢿⣿⣿⠃⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⢠⡇⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇⠀⠀⠀⢸⣿⡇⡇⢸⣿⢈⡇⠀⠀⠘⣿⠂⠀⠀⠀⣿⣿⡇⠀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠈⣿⣿⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣠
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⣀⣤⣄⣀
⠀⠀⠀⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢹⣶⣾⣿⣿⣿⣿⣷⣶⣶
⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢀⡾⠋⠀⠀⠙⢷⡄⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣋⣠⠀⠀⠀⠈⠻⠟⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣾⠁⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣿⣿⢶⣶⣶⠀⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠉⠉⠉⠉⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢹⡄⠀⠀⠀⢀⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠻⠲⠒⠓⠓⠚
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠙⢶⣤⣾⡷⠏⠀⠀⢀⣤⣤⣤⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣿⣿⢚⣛⣾⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⣈⡇⠀⠀⠀⠀⠀⣾⠉⠙⠻⣿⣿⠟⠋⠉⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠘⡆⠀⠀⠀⢠⣾⣿⣿⣧⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠦⣄⣰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠘⢷⣤⣀⣀⣀⣀⣴⡾⠃
⠀⠀⠀⠿⠿⠛⠛⠛⠁⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠙⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠐⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠠⣶⣿⠇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⢰⡀⠀⠀⠠⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀
⠀⠀⠀⠀⠙⠒⠀⠀⠀⠁⠀⠠⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠠⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣶⠀⠀⢈⣡⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡄⠀⠆
⠀⠀⠀⠐⠀⠨⠀⠀⠀⠀⠀⠀⣀⢂⠄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡄⠀⡀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠈⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⠀⠁⡈⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⢓⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⣾⠟⠛⠀⣰⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡈⠁
⠀⠀⠀⠀⢸⠞⠃⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⣠
⠀⠀⠀⠀⠀⠂⠀⡀⠄⡄⡿⠁⠀⠀⠀⠀⠀⢲⠄⠔⢂⡐⠂⡴⢰⣂⢔⣠⢒⡄⡖⢠⠁⡴⠂⠶⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⠊⠊⠒⠈⠐⠚⠓⠁⠃⠚⠀⠉⠀⠉⠀⠀⠈⠀⠊⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠔⠐⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⣯⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠿⢁⣅⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡞⠛⠿⠿⠃
⠀⠀⠀⠀⢀⠀⠄⠘⠹⣾⡉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠤⣄
⠀⠀⠀⠀⠈⢈⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⣠⣸⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠁⠀⠀⠀⠀⢓⡀⠈⠉⠱⠟⠀⠁⠀⠀⠙⠛⠤⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠂⠀⢰⣾⣷⠀⠸⠿⠟⠀⠀⠀⠄⠀⠀⢀⣀⣀⠀⡀⠈⠉⠉⠉⠉⠉⠨⠍⠩⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⢄⠒⡐⢒⠀⣶⣐⣀⣐⡂⢰⣖⡴⠦⠆⠀⠀⠄⠄⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⢓⡓⡂⢐⠀⠀⠀⠀⢐⣂⣐⢰⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣾⣿⠄⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠮⣷⡂⢐⡒⠒⢒⠲⢸⣒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⡿⠻⣿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢠⣶⣦⣄⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⣾⣿⣿⣿⣷⣶⣿⣿⣿⣶⣄⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣇⠙⠛⠿⠛⠛⠁⣸⣿⣦⢠⣴⣶⣶⣿⣛⣛⣛⣛⣫⡅⣶⣦⣄⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠙⠻⠿⠿⠿⠿⣿⣿⣿⣧⡀⠀⠙⠻⣿⣷⣦⣤⣴⣶⣿⣿⠟⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣦⡄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣴⣶⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣴⣿⠇
⠀⠀⠀⣀⠿⣿⣿⣿⣿⣿⣿⠿⣀⠀⠀⠀⢀⣠⣌⠙⠛⠛⠛⠛⣠⣀⡀⠀⢀⣴⣶⣶⣦⣤⣤⣀⣉⣁⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢾⣿⣦⣄⣉⣉⣉⣉⣠⣴⣿⡷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠿⠋⠁⠀⠀⠙⠻⣿⣿⣿⣿⣷⠄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠠⣄⡀⠀⣠⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣙⠿⠿⠿⠿⢟⣃⡀⠀⠀⠈⠻⣿⣯⣛⢿⣿⣿⣿⠂
⠀⠀⣠⣄⠛⠻⠿⠿⠿⠿⠛⢉⣿⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠈⠻⣿⣷⣮⣟⠋
⠀⠈⠻⢿⣿⣶⣶⣶⣶⣶⠾⠛⠁⠀⠀⠀⠀⠉⠙⠛⠉⠉⠛⠻⠿⠿⠿⠋⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠷
⠀⠀⣠⣾⠛⠛⠿⠿⠿⢿⣻⣤⡄⠀⠀⢀⣸⣿⡿⠿⠿⠿⠛⠛⠛⢉⣀⡀⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⣾⣶⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣄
⠀⠐⣿⣿⣶⣤⣤⣴⡾⠿⠛⠋⠀⠀⠀⠘⠻⠿⠿⠟⠚⠛⠛⠛⠛⠉⠉⠉⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠙⠿⠿⠿⠿⠛⠛⠛⠻⠿⠿⠛⠁
⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⣀⣀⣀⣀⣾⣿⣿⣿⣿⣦
⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣀⡀⠀⠀⠐⢤⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠉⠛⠶⣍⡻⢿⣿⣿⡿⠁
⠀⠠⣿⣿⣧⣄⣈⣉⣉⣉⣠⣿⣿⡇⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣟⣄⣀⠀⠀⠻⣷⣬⣭⣭⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠛⢶⣬⣉⡁
⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠂
⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⠿⠻⡿⠛⡿⢿⡿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢀⣁⣴⣏⠀⠈⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠞⠻⠿⠿⢿⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⡀⠀⠀⣀⢀⣿⣿⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠃⠀⠘⠗⠘⢾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⢀⣀⠀⢠⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠁⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢦⠀⠀⠁⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠟⠯⠉⣇⠀⠀⢸⠑⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠄⠀⠠⢿⠠⠁⠀⠈⡆⠀⡼⢃⠀⢈⡄⠴
⠀⠀⠀⠀⠀⠀⠀⢺⡁⠈⢆⣼⠡⠈⢧⡈⡐⢀⠚⣦⡇⠠⢀⡼⠁⢀⡖⠀⠀⠀⠀⠀⠀⣰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⢸⣼⡀⠀⠀⠙⣧⡂⡀⢻⡀⢠⡞⢁⠀⣐⢇⣴⠄⠀⠀⠀⠀⠑⢥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⣿⡴⣠⣄⢄⡈⣷⢠⠋⢡⡿⢀⣤⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣹⣿⣿⣞⢸⡦⠌⣻⣢⣿⣿⣿⠑⣄⠀⠀⢈⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠈⢿⣿⡹⣿⢿⡍⣷⠇⣺⣟⣿⣹⠁⠀⠉⢄⡀⠈⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠿⣿⣿⡪⢛⣿⡚⢸⡧⣿⡏⠀⠀⠀⠀⠑⢤⡀⢠⠈
⠀⠀⠀⠈⠢⡀⠀⠀⠈⠀⠀⠀⠀⠈⠩⢿⣗⠀⡺⡏⡁⡟⣯⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠢⡀⢀⣴⡾⡛⡊⡈⢉⠉⠉⠙⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⣆⠂⠂⠂⠐⠐⡀⡂⢀⠠⠈⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠛⢓⢛⠛⠓⡡⠠⠀⠄⠄⠐⠀⣧⢀⢨⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢪⡆⠠⠀⠀⢰⣾⠈⠁⠁⠨⠀⢀⣿⡀⠹⡦⡓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢪⠀⠑⡃⢈⠈⠀⣑⣗⡀⡂⢀⠀⠀⠁⣿⣇⢱⣿⠐⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠂⠚⠙⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠔⠛⠉⠹⠶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢲⡉⠠⠤⠀⠒⠒⠀⠀⠀⠀⠐⠀⠄⠉⠀⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠤⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡗⠸⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠨⡗⢀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠳⣟⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣫⠾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣽⠀⢀⠑⠺⠯⢵⡶⢒⡶⠾⠙⠓⠉⠁⢀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠳⢤⡤⢀⣀⣀⣀⣀⠠⠄⠀⠀⡸⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⣁⣢⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠤⡤⢀⠀⢀⣤⣀⠀⠀⣤⢠⣿⣿⡛⠛⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣀⠀⠀⠀⠀⠀⣄⣀⣀⣼⣿⣿⣷⣴⣤⣔⡿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠑⠛⣩⣯⡿⠻⣿⢿⡿⣿⢿⣿⣿⡻⣿⣷⢿⣭⣡⣤⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢰⠋⢀⠁⠀⠘⡄⠀⡿⠀⠁⠿⡅⠹⠈⢢⠙⠻⣿⣄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⡇⠀⢰⠀⠀⠸⠁⠀⠰⠀⠃⠀⠉⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⡴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⢲⡀⠀⠠⣑⡀⠀⠠⡱⣄⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠤⢇⠀⠀⠱⡀⠀⠀⠈⢆⠀⠀⡈⢆⠀⢉⠱⡀
⠀⠀⠀⠀⠀⠀⢀⠁⠀⢀⠠⡄⠀⠀⠤⠀⠀⢀⠠⡆⠀⠀⠸⡇⠀⠀⢀⡁⢡⠀⠀⠠⠼⠀⠀⠀⢳⠀⠀⠀⠈⢷⡀⠀⠈⣧⠀⠁⣡
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⣚⠀⠀⠀⢐⠁⠀⠀⢘⠀⠀⠰⠒⡇⠀⠀⠀⠀⠸⠆⠀⠐⠂⡦⠀⠀⠄⢧⠀⠀⠀⡘⡇⠀⠠⠘⣇⠀⠄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⠃⠀⠠⠎⡛⠀⠀⠀⣙⠀⠀⢈⣩⡇⠀⠀⠈⠀⢘⡂⠀⠀⠀⣿⠀⠀⡁⢸⡇⠀⠀⠀⢹⡄⠈⠁⢻⡂⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⡠⠀⡌⠀⠀⠐⢸⡇⠀⠀⠤⠆⠀⠀⠀⠴⠁⠀⠀⢈⡁⣉⡅⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⢀⠘⡇⠀⠠⢨⣇⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠂⠤⢚⠇⠀⠀⣈⣨⠀⠀⠐⠒⠂⠀⠀⠀⠲⠀⠀⠀⠠⠀⢰⡆⠀⠀⠈⢸⠆⠀⠀⠀⣿⠀⠀⠐⠠⣏⠀⠀⠐⣿⠀⠀⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⡤⣤⠀⠀⠘⠛⠅⠀⠀⣉⣙⡀⠀⠀⠒⠒⢺⡇⠀⠠⠤⢼⡄⠀⢈⠒⠾⠀⠀⠘⢰⣯⣀⣤⡸⠷⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠈⠓⠳⠄⣀⡠⢨⡇⠀⠀⠈⢁⣼⠀⠀⠀⢀⣾⡀⠀⣀⠸⠛⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠂⠠⠀⢀⠢⠀⠀⠀⠠⠀⠀⠄⠂⠐⠄⠠⠐⠁⠀⠐⠔⠠⠂⠄⠀⠊⠐⠁⠂⡠⠀⢀⠆⠈⠀⠀⡐⡁⠀⠀⠌⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⠁⠲⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠁⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣷⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠿⡿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠉⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⢿⣿⣿⣿⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣮⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣋⣱⣾⣿⡿⠏⠙⠛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣾⡿⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣾⣟⣿⡟⠙⣻⣿⣏⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣭⢠⣿⣿⣿⣟⡏
⠀⠀⠀⠀⢠⣾⣿⣾⣿⢱⣿⣿⣿⣿⣿⣿⠟⠉⣁⣿⣿⣷⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⠏⣿⠉⠉
⠀⠀⠀⠀⠈⠻⣿⣿⣿⡜⣿⣿⣿⣿⣿⣴⡶⣾⡿⣡⣿⣿⡿⠿⢿⡿⠸⣿⣹⣿⢍⣀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⢸⠿⣿⢷⣼⣿⡟⠻⢷⣿⣄⣿⣿⠿⠛⣁⣀⣀⣉⣀⣤⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠻⠄⠀⢠⣿⣿⡿⠶⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⠀⠙⢉⣿⠛⢿⠿⢿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠿⢿⣿⣦⠴⠟⠁⠀⠀⠀⠈

⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡄⡴⠄
⠘⠟⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡤⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁
⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠤⠀⠠⠄⠀⠰⠀⠀⠐
⢀⠘⠀⠀⠀⢀⢀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠁
⡌⠂⠂⠀⠀⠀⠀⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠜⢡⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠅⠀⠈⠀⠈⠀⠉
⢤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠸⡟⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣤⡄⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠏⠀⠀⠂⡄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠓⠶⠦⢤⣤⣤⣄⣀⣀⣠⣤⡤⠤⠶⠚⠃⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⡟⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⡷⠦⢤⣄⣀⡀
⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⢸⡇⠀⠀⠉⠙⠓⠲⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠶⠒⠛⠉⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠛⠶⣄
⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠻⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠴⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⡅⠐⠄⠂⠈⠀⠀⠀⡠⠐⡠⠀⠁⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠉⠀⠀⢀⠄⡊⠐⡉⡀⠀⡈⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠂⢁⣨⠀⠔⠂⠀⠉⠀⠀⠀⢄⠁⠀⠰⣄⠁⠒⠀⠀⠀⠂⠈⠤⠅⣀⡀⠀⠀⠂⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠄⢬⡁⠙⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⡇⠀⠀⠀⠀⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠂⠂⠐⠠⢄⠀⠀⢻⠀⢀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⢀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⣀⡀⠀⠀⠀⢘⠤⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⢅⡆⠀⠀⢠⠞⡟⣙⣯⡟⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣋⣻⣽⠻⠙⠆⠀⠀⢘⠖⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡄⠀⢁⢀⠀⠈⠐⠬⠺⢡⠪⠒⠁⠀⠀⢀⠤⠀⠐⢠⡀⠀⠘⠢⢉⠛⠑⠡⠀⠀⠀⠄⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠀⠈⢣⡑⠄⣀⡀⣀⣀⣀⡀⠤⠒⠈⠀⠀⠀⠈⠁⢈⠒⠤⣀⣀⠀⠀⠀⠀⢀⠈⡐⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠃⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠤⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠆⢠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠤⣤⣀⣀⠂⠂⢀⣊⡈⡤⠲⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠩⢀⠌⡡⢋⠔⡐⠁⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠁⠈⠀⠂⠌⠀⠀⠈⠀⠑⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠐⡐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠊⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢦⡉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢁⠔⠀⠀⠀⢀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢌⣀⠂⠀⠀⠀⠀⠀⣈⠤⠀⠊⠀⠀⡀⡀⠠⡀⠊⢀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠠⠂⠄⠠⠠⠀⠄⠀⠀⠈⠉⠀⠀⠉⠀⠀⠂⠂⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣠⣠⢤⡶⠖⠻⠟⣶⠖⡰⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣜⠱⠞⣥⠤⣏⡴⠗⢋⡼⢥⡾⣆⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣸⢿⡴⣋⡵⣾⣩⣥⣾⣍⣴⡾⠖⢿⡆⠀⠀⢀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣏⠸⣱⠟⠋⠉⠀⠀⠀⠀⠈⠉⠑⢻⣧⠀⠀⢸⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡄⢰⣿⣿⣿⣿⣶⣦⡀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡇⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠃⠈⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⠀⡄⡼⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠘⣯⡉⠉⠉⠉⣹⡏⠈⣿⣉⠉⠉⢉⣸⠇⠀⢰⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⡛⠷⠞⠛⠋⠀⠀⠀⠉⠛⠛⠋⣥⠂⠀⡞⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣉⣣⠀⠀⢠⣶⣶⣦⠀⠀⠀⠰⠣⠃⠀⡇⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠣⡀⠀⠙⠚⠉⠀⢀⠔⠁⠀⠀⠀⡇⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣦⣤⣤⡴⠶⠛⠛⠉⠉⠉⠃⠃⠀⣾⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢂⡄⠛⠉⠁⠀⠀⠀⠀⠀⣀⠀⡸⡦⣤⠸⣆⣀⢀⣠⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣀⣀⡼⠃⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⢀⣀⣠⣴⠞⠋⠁⠁⢀⡘⠀⠉⠛⠛⠁⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣴⣾⡿⣿⣿⣿⡇⣀⠴⠖⣸⢧⣤⡀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⣀⠀⢀⣀⡀⠀⠒⢻⠃⢀⣠⣼⣿⣿⣿⡯⠑⣿⣿⠜⠿⠛⠿⠷⢿⠦⠖⠶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢿⠟⠉⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⡧⢈⣾⡿⠞⡓⢞⠃⠲⡛⡄⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢴⣿⣿⢇⣠⠞⡗⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡛⠀⠧⠀⢤⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣓⣦⠢⠶⠻⢦⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣆⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢸⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢀⠆⠐⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⡎⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠒⠀⢒⣂⠺⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠜⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠁⠀⠀⠀⢰⣤⣄⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠔⠒⠚⢲⢐⣦⣤⣲⢸⣡⠰⣿⣿⣿⣯⣙⡠⠿⣉⠙⢰⡃⠀⠀⠀⠀⣀⠄⠒⠈⠉⠚⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⢸⢈⡱⢶⠯⡸⣦⢤⣿⢿⣿⣻⣿⣇⣤⣶⣶⣤⣿⡉⠀⠀⠉⠀⢀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢀⣀⣨⣆⣯⣻⣟⢃⣻⡾⠟⣻⠿⠿⠟⠿⠓⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣭⣥⣤⣤⣤⣤⣬⣥⣭⣭⣭⣭⣥⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠋⠉⠉⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠚⠋⠉⠉⠉⠛⢢⡀⠀⣀⣠⢤⣶⠶⠞⠛⠛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⣉⠥⠒⡙⠀⡰⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⣀⣠⣴⣾⠟⠁⠀⡰⠁⡐⠁⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠋⠀⠀⠀⢀⣠⠴⠒⠋⢉⣀⣠⣤⣴⣶⣿⣿⠿⠋⠁⢀⡠⠊⣠⠊⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⠖⣋⣠⣴⣶⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⠠⠐⠁⡠⠊⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢶⣺⣿⣶⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⣀⠠⠒⢈⣀⠤⠒⠁⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢖⡭⢖⠉⠀⠉⠉⠉⡉⣉⠡⠤⠐⠒⠂⠈⣁⠠⠐⠊⠁⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⣠⣴⡯⠚⢍⡀⠀⠈⢉⣉⡉⠀⠀⠤⠤⠀⠀⠐⠂⠁⠀⣀⣠⠤⠖⠚⠉
⠀⠀⠀⠾⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁
⠀⠀⠀⠀⠈⠓⠦⠤⠤⣤⣤⣄⣠⣤⡤⠤⠶⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠭⠉⠉⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠏⠉⠋⠹⠿⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠿⠋⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀⠀⠙
⠀⠀⠀⠀⠀⠈⠹⣶⣄⣀⣀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⣴⣷⣄⣀⣀⣤⣶⠟⠀⠀⠀⠀⠀⠀⢾⣿⣷⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣧⡤⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠃
⡿⢿⢿⠿⠿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠀⣠⣬⣿⣿⡿⠛⠛⠛⢛⣛⣛⣋⣉⣉⣉⣙⡛⠛⠛⠻⠿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⢿⣿⡁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣝⡻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⣫⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣾⣿⡿⣡⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣸⣿⡿⣴⣿⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣳⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣿⣿⣿⣿⠃⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣰⣿⣿⣿⠟⠁⠀⠀⠉⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠚⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⢹⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣸⣿
⠀⠀⠀⠀⣸⡿⠋⢹⡟⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⡏⠻⣿⡄
⠀⠀⠀⢠⣿⠁⠀⢸⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣿
⠀⠀⠀⠘⣿⡀⠀⠸⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠏⠀⠀⠀⠀⠀⢰⣿⠀⠀⢰⣿
⠀⠀⠀⠀⠹⣷⣄⡀⣿⡆⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⣾⡏⢀⣠⡿⠃
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄⠀⠘⠋⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⣼⣿⣿⣿⡏
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣆
⢀⣀⣤⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠈⠻⣿⣿⣿⣿⠟⢡⣾⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠉⠉⠀⠲⠿⠟⠛⠁⣰⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⢹⣟⠉⠉⠛⠛⠛⠉⠉⣿⠋⡉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠛⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⡏⠀⢻⣦⡀⠀⠀⠀⢀⣼⠟⠀⣿⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣩⣿⠃⠀⠀⣼⠃⠀⠀⠙⠿⣶⣶⡾⠟⠃⠀⠀⢸⣇⠀⠀⠘⣿⡄⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢀⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠉⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣹⣧⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣾⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣿⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⡟⠙⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉⢻⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠛⠲⠶⠤⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠴⠶⠛⠁⢈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣤⣀⣀⣈⠉⠉⠉⠁⠀⠈⠉⠉⠉⣁⣀⣀⣤⣤⣶⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠙⣿⡄⠀⠀⠀⣸⣿⠙⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⠇⠀⠀⠀⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣿⡿⠀⠀⠀⠀⠹⣿⣷⣶⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠚⠭⠍⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠠⠍⢉⡋⠒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣸⠀⠀⠲⠴⠆⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣷⣶⡶⠿⢿⣋⣭⣬
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠏⠀⠒⠒⠒⠂⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⠒⡊⠅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠆⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠙
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠦⠤⣤⣀⡀⠀⠀⠀⠄⠀⠈⠢⡀⠀⠀⠀⠀⠈⠑⠀⠀⠠⢢⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠋⠂⠒⠒⠒⠒⠒⠒⠒⠒⠤⠤⢤⣀⣰⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠂⠘⠃⢀⠈⠖⠀⠀⠰⠆⠀⠀⣤⠀⠀⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠁⢀⠀⠉⠀⠀⠀⢸⠁⡏
⠀⠀⠀⠀⡀⠀⠂⠦⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠘⡇
⠀⠀⠀⢤⠄⢂⠈⠉⢁⠐⠀⣠⡳⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠛⠛⠒⠲⠶⢤⣤⣤⣀⣀⣀⣀⠀⠀⠂⠉⡇
⠀⠁⢠⠀⠀⠀⡀⠀⠀⠀⠂⠈⠀⠐⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⣹⣿⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠢⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⡀⠀⠀⠉
⠀⠀⢃⠠⡀⠀⠀⠀⠀⠠⠂⡀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉
⠀⠀⠀⠱⡤⣀⣀⠀⠀⠄⠊⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣶⠦⠤⠴⠶⠶⠶⠤⠤⠤⠤⠤⠴⠶⠶⠒⢒⣺⢏⣿⠳⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠿⣦⠈⠳⣶⠶⠶⠶⠶⠖⠒⢶⣶⠒⠒⡿⠋⢉⡵⢃⡎⠸⠃⠀⠀⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⡈⠳⢤⣀⠀⠀⠀⠀⠀⠀⢀⣡⠴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣈⠉⠛⠒⠒⠚⠉⢁⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⣠⡾⠃⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⢾⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠘⢷⣄⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠷⠤⢤⣀⣀⡄⠀⠀⢀⣀⣠⣤⠷⠴⠴⠧⣤⣄⣠⣤⠴⠧⠤⠤⠤⠤⠤⠶⠶⠲⠶⠶⠒⠚⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⠋⠉⠉⠉⠉⠛⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⣀⡠⠤⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠶⣄⡤⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⢴⣺⠃⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣠⢖⠟⠋⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⡏⠓⠢⢤⣀
⠀⢀⠞⠁⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡷⠖⠛⠛⠛⠛⣲⠤⣄
⢀⠏⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠚⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱
⡼⠘⠀⠀⠀⠀⠀⠀⠀⣸⢤⣀⣀⡀⠀⠀⠀⠀⢀⡠⢞⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⡇⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠬⠭⠭⠭⢭⡭⢋⠔⠁⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠋⠉⠉⠉⠉⠉
⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⠝⠊⠀⣀⡤⠖⠊⠉
⠀⠙⢆⡀⠀⠀⠀⠀⠀⢀⠤⢚⣓⡥⠴⠒⠉⠁

⠀⠀⠀⢠⠊⠢⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⢀⠀⢀⣀⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢰⠾⠿⠿⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⢀⡞⠠⣋⢿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠊⠱
⠀⠀⠀⠘⢄⠀⠘⠀⠀⢾⡄⠀⠀⠀⢸⢿⣷⣞⣽⠇⠀⠀⠀⠀⠀⢀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣼⣅⠀⠀⠲⣔⠐⣸⣣⠀⠀⠀⠈⠳⡭⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢡
⠀⠀⠘⣟⢄⠀⠀⠀⡐⠃⠋⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠂⠊
⠀⠀⠀⠸⠄⡇⠒⠎⡄⠃⠀⠀⠀⠴⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠙⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣴⣶⣶⣦⣤⣀⠀⠀⠈⠂⢄⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡞⠙⣴⣿⠧⠤⢄⠉⠻⣷⡄⠀⠀⠀⠜⠻⣟⠒⠆⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣧⣁⣿⠁⠀⠀⠀⢣⠀⠘⠗⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣘⢿⣷⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⡀
⠀⠀⠀⠀⠄⠀⠔⠀⡀⠀⢔⡲⠀⠈⠀⠀⠀⠀⠈⣿⢾⣿⣽⡌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠁⠀⠹⠂
⠀⠀⠀⡀⠄⢐⣠⠤⢐⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⣝⠿⡟⠣⠤⠄⠀⠀⠀⠀⢠⡄⠄⠀⠀⠀⠀⠀⡀⠀⢠⢤⠀⠂⠀⠃⠀⢦
⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⣀⣀⢀⠄⠀⠀⠀⠀⡚⠛⠳⠆⠐⠴⠒⠆⢰⠃⠀⣿⣿⡿⠓⣊⣴⡀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡁⠠⠂⠀⠆⠀⠀⠁⠻⠀⠀⠙⠻⠥⠿⠿⠿⠼⠟⠃
⠀⠀⠀⠀⢄⡀⢠⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠈⠉⠀⠀⠀⠈⠁
⠀⠀⣌⠁⠆⠀⢀⠀⠨⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⢠⠉⢣⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣞⢇⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⢀⣈⠆
⠀⠐⠀⠠⡤⠬⠭⠥⠤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠠⢤⡆⠀⠀⠀⢠⡄⣴⡄⠀⠀⠈⠈⠔⠋⠀⠀⢄⠀⠀⠀⠀⢀⠠⢀⣀⠀⢁
⠀⠀⠀⠠⠂⣶⡴⠤⣄⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡤⠀⠀⣤⠀⠀⠰⡶⠆⠀⠀⠀⢠⢡⣾⡿⠿⣶⣆⠑
⠀⠀⢢⠀⠀⠜⣦⡴⠃⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⣇⠀⠀⠀⠀⠸⠐⡿⣧⣀⣼⣟⠀⡆
⠀⠀⠈⠀⠀⠀⢀⠑⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠁⢉⠛⠍⢛⠡⡠⠃
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢸⣿⡆⠀⠀⠈⣹⡇⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⡄⠀⢸⡇⠀⡀⠀⢿⣿⠂⠀⣴⣶⣶⣶⣦⣴⣶⣶⣶⡄
⠀⠀⠀⣼⣿⣧⡀⠀⣾⣿⣿⣆⠀⠘⣿⣿⣿⣿⡇⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣶⠀⠀⡇⠀⢸⡇⢰⡇⠀⢸⡟⠀⠀⡿⠉⠙⡟⠉⠙⡟⠉⠙⡇
⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢾⣿⠀⠀⣿⡇⠀⣿⠀⠀⡇⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠻⠦⠶⠿⠦⠾⠷⠦⠾⠃
⠀⠀⠘⣿⣿⣿⠃⠀⣿⣿⣿⣿⠀⠀⢿⣿⣿⡿⠀⠀⢸⣿⡇⠀⢸⣿⡆⠀⢺⣿⠀⠀⣿⡇⠀⣿⠀⢠⣷⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠐⠀⠐⠒⠒⠒⠒
⠀⠀⠀⢻⣿⡿⠀⠀⢿⣿⣿⡟⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⠀⣿⠇⠀⣿⠀⠐⣿⠀⢸⡇⠸⡇⠀⠀⡇⠀⠀⠚⠂⠚⠛⠛⠛⠒⠒⠒⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣾⣯⡀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⢀⣿⣿⡟⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⣿⡟⡇⠀⠀⢠⣤⡹⢿⠃⠀⢰⣿⣦⣤⣤⣴⣾⣷⣶⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡄⠀⠀⠀⠀⣬⣬⡉⠀⠀⠀⣿⣿⣿⣿⠿⢿⣿⣿⣿⡇
⠀⠀⢠⣿⣿⡇⠀⠀⠼⠿⠇⠀⠃⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣷⠀⠘⢠⣶⣿⣿⣷⣤⠀⠀⣿⣿⣿⣿⣶⣾⣿⣿⣿⡏
⠀⠀⢸⣿⣿⡗⠀⢁⠰⠶⠀⡇⠈⠀⠀⠈⠻⢿⡿⣿⣿⣿⣿⣿⠀⠀⣼⣇⠀⠀⣼⣷⠀⠈⡏⠀⢠⣿⡈⠄⠀⢸⣿⣿⣿⣿⣿⠀⠀⣀⣀⣀⣀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠿⠿⠇⠀⠸⠦⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠟⠁⠀⠸⠿⠿⠃⠘⠿⠿⠃⠀⠁⠀⠻⠿⠗⠀⠀⠘⠿⠿⠿⠿⠟⠀⠀⢿⠿⠿⠿⠷⡿⠿⠿⢿⡇
⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢀⣄⣄⣄⣤⣠⣀⣠⡀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⢹⣟⢸⠠⠀⠆⠀⠀⠀⣿⣿⣧⣤⣼⣿⢿⡃⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣴⡿⢻⡟⡝⠙⢻⣷⡀⠀⠀⠀⠀⣼⣿⣄⠀⠀⠀⠀⠿⠶⠶⠶⠶⠷⠶⠶⠾⠇
⠀⠀⢸⡇⢸⢐⠀⡇⠀⠀⢸⡏⠈⡉⠀⠉⠁⢹⡇⠀⠀⠀⣿⣿⣄⠀⠀⠀⢸⣿⢠⡿⡱⠀⢀⡿⢻⡷⠀⠀⠀⢀⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣄⡀
⠀⠀⢸⡇⢸⢈⠀⡇⠀⠀⠘⡅⠀⠁⠀⠀⠀⢨⡇⠀⠀⡆⢡⣠⡌⢰⠀⠀⠘⣿⣿⡱⠁⢀⣾⣣⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣞⣩⣶⠟⠋⡲
⠀⠀⢸⡇⢸⠘⠀⠇⠀⠀⠀⡟⠈⠉⣿⣿⣿⣿⠁⠀⠀⣇⠈⠉⠀⣾⠀⠀⢀⠈⢻⣿⣶⣾⣿⣿⠋⣀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡿⠛⠁⢀⣤⡇
⠀⠀⠈⠃⠘⠈⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠒⠛⠋⠀⠀⠈⠛⠛⠓⠒⠒⠚⠛⠛⠋⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⣀⠴⠚⠳⠦⣴⡋⣸⠁
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⣦⣄⠀⣀⡴⠛⠁
⠀⠀⢈⣩⠿⠛⠻⢯⣉⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣾⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⢠⡟⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢰⣿⢿⢏⣤⡄⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣷⣶⡆
⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣰⠋⢋⣼⣿⣧⡀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠘⣧⡀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⣿⣦⣤⣄⣀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠔⠁⠀⠘⣿⣿⣿⠆⠀⠀⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠙⠲⠦⠶⠚⠋⠀⠀⠀⠀⠻⠿⠛⠤⠬⠿⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠿⠿⠿⠃⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⡍⣿⠛⠿⠿⠿⠻⠟⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿