Recipe Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠄⢫⣱
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠠⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠀⠤⢀⡐⠆⠠⢆⡄⠠⡥⢀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢤⡰⣶⣒⣤⠂⠁⠀⠀⠀⠚⠐⠒⠢⠌⠢⣘⡸⠃⢠⡃⢠⠊
⠀⠀⠀⠀⠀⠀⢀⣠⣚⣿⣿⣛⣮⣷⣿⣾⣥⣆⣀⣀⣀⡀⣔⣃⣈⣀⢀⣀⣘⠄⠀⡰⡣⠚
⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠀⠀⠀⠤⠠⠠⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠠⠭⢽
⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⠀⠀⠀⠀⠀⠄⠀⡀⠄⠐⠂⠤⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠃⠀⠀⠀⠄⠀⠠⠂⢀⡤⠐⠒⠤⡀⠀⠀⢤⠀⠀⠀⠐⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠆⠀⠀⡀⠀⠀⠀⡎⢰⢉⣈⡆⡅⢸⠀⢠⠄⠈⠔⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠰⠀⣁⠀⠀⠀⢡⡈⠒⠓⢊⠔⠁⠀⡄⠈⠂⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠂⠀⠀⠠⠌⠉⠉⠀⠀⠀⠒⠈⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣙⣀⣛⣀⠘⠃⣘⣃⣚⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢠⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣀⠉⠉⠙⠛⠻⠿⢿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟⠋⠉⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠈⢿⡆⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣛⣛⣛⣛⡛⠛⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠤⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆⣣⣤⠾⠓⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⢱
⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠠⢀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠁⡑
⠀⠀⠀⡀⠀⠲⠀⠀⠐⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⢠⣤⣆⠟⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠄⠀⠀⠉
⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠈⠀⠀⠔⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠐⠐⠄⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⣠⠤⠀⠒⠁⢀⡁⠠⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠰⠐⠒⠐⠖⠒⠒⠒⠆
⠀⠀⠀⠈⠢⢈⠉⣉⢀⣠⡤⠆⠒⠈⠉⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠒⠐⠀⡀⠀⠀⢀
⠀⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠖⠂⠉⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢀⠀⠀⡆⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠃
⠀⠈⠆⠁⠆⠀⠠⠄⡔⠂⠉⠁⡬⣀⡀⠜⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠔⠁⢠⡄⠃⠀⠀⡇⠀⠀⡇⠀⠀⠒⠂⠛⠋⠈⠃⠁
⠀⠀⠈⠒⠓⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠠⠐⢀⠔⠁⢐⠀⠇⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠅⠈⠀⠀⠢⠀⠠⢭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠰⠀⠀⠤⠤⠈⠁⠀⠀⠀⡄⠀⢀⠀⠸⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠆⠀⠆⠀⠀⠀⠘⠀⠘⠋⠉⠀⠀⠠⠤⠤⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠊⠚⠓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠀⢀⡀⡇⡁⢇⡩
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠁⠀⠙⠁⠙⠓
⠀⠀⠀⡄⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⠛
⠀⠀⢠⠦⡤⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⡀
⠀⠠⠁⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⡀⠤⠤⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⢀⠀⡀⠤⠤⠤⠤⠀⠀⠀⡀
⠀⠐⠀⠀⠅⠀⡀⠀⠀⠐⠈⠀⠀⠀⠳⠠⠄⠀⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡸⠉⠀⠀⠀⠀⠐⠀⠀⠀⠉
⠀⢠⠀⠤⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⣆⠀⠾⠡⠄⠆⡰⠀⠀⠀⠀⠀⠀⣀⡀⠘⠫⠤⠤⠛⢀⣀⣤⠀⠀⠀⠀⠀⠀⠐⠛⠑⠘⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠈⠐⠂⠀⠐⠚⠁⠀⠀⠀⠀⠀⢠⠂⢈⡉⠉⠉⣉⢉⡉⠀⢸⠀⠀⠀⠀⠀⠀⡀⣰⠀⠐⢬⡄⠀⠀⢸⠀⠀⠀⠀⢀⠚⠉⠁⠀⠆⠔⠀⠉⠓⣄
⠀⠀⠀⠀⠥⣭⠈⠀⠀⠀⠀⠀⠀⠀⠀⠧⠑⠚⠞⠃⠸⠀⠄⠃⢼⠀⠀⠀⠀⠀⠀⠁⠋⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠰⠒⠂⠀⠂⠐⠔⠇⣸
⠀⢰⠀⠂⢀⠁⠉⢀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠲⣅⡁⠘⠓⠁⢀⣀⠴⠁
⠀⠈⢄⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⡀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⢲⣄⢀⡉⠉⠉⠉⠉⢁⣀⡴
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠛⣶⣿⣿⢿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠰⠋⠀⡠⠛⠛⢻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣅⠀⠔⠀⢀⠊⠁⢀⠼⠋⠙⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣷⣄⣨⠀⠀⠃⠀⣠⠊⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠾⣦⣠⡋⠀⠀⢛⣄⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢈⠻⣦⠀⠀⢰⣯⣴⣿⣿⣿⠛⠀⠀⠉⠷⣦⡤⠾⣷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠈⠻⣿⠛⠀⠀⠘⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⡑⠂⠀⣹⠇⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣾⣷⣴⣶⣄⣤⣀⣿⣆⠀⠙⢿⣟⢉⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣳⣿⡿⣿⠁⠀⢰⣤⣠⣿⣿⣿⣿⣿⣶⣶⣦⠀⣠⠴⠶⣾⣏⠉⠻⡏⠀⢹⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢿⣿⠻⣿⣴⠛⠃⢀⣀⣹⣿⣿⣋⣿⠿⣿⣿⢟⣿⣽⡇⣄⠀⠈⢋⠀⠀⡇⠀⡌⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⣤⡀⠀⠀⠀⠀⣼⠿⣀⠀⠀⢻⣿⣶⡏⠉⠻⡄⠈⢷⣾⠃⠀⠈⠻⡀⠀⢸⣤⣼⠷⢿⣶⣾⠋
⠀⠀⠀⠀⠀⠀⡞⠁⠀⢒⣈⠿⣦⠀⠀⠀⢿⡀⢈⡳⠖⢾⡀⠀⢹⡄⠀⢻⣀⡼⠛⠓⠷⡆⠀⣹⣾⣏⣩⣷⣤⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢿⡀⠈⠉⠁⢀⡿⣦⣤⠴⢿⠉⠈⠹⣆⠀⢹⡀⢀⣿⣶⠾⣻⣧⣠⣄⠀⠘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢹⡖⠒⠒⠉⢀⣼⡇⢀⠀⠱⡄⠀⢸⣀⡸⢿⣿⠋⠀⢰⡏⠀⠀⠈⠳⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠖⠋⠀⣧⢙⡇⠀⣶⣶⠋⡴⠛⣉⠛⠛⡷⠟⠳⣄⠸⠦⣄⣿⠛⠛⠛⡟⠁⣠⠴⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⠠⠄⠊⠀⡿⣤⡾⠋⠹⣾⡀⢰⠁⢀⡼⠀⢀⢴⠃⢀⣄⡈⣿⡆⠂⠤⣼⢾⡁⢀⡤⠖⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠔⠛⠁⣸⣧⡀⠀⠈⠛⠾⣄⣀⣥⠀⠈⢀⠀⠈⣻⣷⡿⠃⠂⠤⣼⡆⣹⣏⠀⣠⠒⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠲⠖⠋⠁⣸⢷⡀⠀⠀⠀⠀⠉⠉⠳⠶⠟⠶⠶⠛⠈⣷⠄⠤⣄⣸⡆⠻⣯⣿⣇⡞⠉⠒⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡆⠴⠚⠁⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄⣠⣈⣿⠀⠸⣿⣯⣭⣿⣦⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣶⡊⣰⠟⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠸⣧⣀⣀⡀⢹⡆⠀⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢠⡾⠛⢶⡾⠛⠉⠻⣦⣀⣀⠀⠀⠈⠻⣭⡴⠟⠁⠀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠂⠀⣠⣤⠜⠉⠁⠉⢿⣄⠀⠀⠀⣀⡀⠀⠀⠘⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣰⢿⡇⠀⣴⡶⠘⠋⠛⣿⠛⠻⠍⠙⣷⡀⠀⠀⠉⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⣹⡿⠿⣁⢀⣤⣂⠿⠤⣀⠈⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠻⠏⡉⠑⢀⠈⢻⠋⠀⣀⡀⠀⣷⡟
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢹⡆⠀⠐⠀⢸⣀⣰⡿⣿⠛⠙⠲⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠉⠀⣀⣴⣴⠟⠛⠋⠘⣷⣄⣀⡀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⢿⡉⠄⢀⡾⠃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠞⠋
⠀⠐
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣠⠖⣦⠀⠀⠀⠀⠀⠀⣠⠔⠢⣄⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣾⣤⠴⠶⠒⠛⠋⠉⠉⠙⣁⠙⢳⡞⠁⠀⠀⢿⡀⠀⠀⣠⣾⡁⠀⠀⠀⠙⢗⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡷⠀⠀⠘⠰⡇⠀⡜⠉⠈⠛⠦⣤⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡠⠂⣼⠃⠀⠀⠀⣸⡇⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠐⢁⡾⠁⠈⠀⠀⣀⠟⢀⡾⠉⠀⠙⢦⡀⠀⠀⠀⠀⢀⠔⠫⣻
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠄⢀⣴⣿⠀⢀⣠⠶⠘⠷⢤⣼⡷⢦⠀⠉⠀⣟⠀⠀⠀⢀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢀⠤⠊⠀⠄⢁⡴⠋⠁⡷⠈⡀⠁⠀⠀⠀⢀⠀⠰⣾⣀⣠⠞⠁⠀⠈⠛⠫⡉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠤⠈⠁⠀⢈⣠⠞⠋⠀⡀⠀⠙⣾⠀⠀⠀⠀⠊⠅⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢿⡀⠈⠩⠄⠐⢈⣁⡴⠞⠋⠀⣀⠤⢴⡦⢤⣀⣸⣛⣒⠒⠚⠛⠉⠁⠀⠀⢰⡖⠶⠲⠤⣤⡀⢀⣨⡧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠉⠁⠀⠀⠀⢰⠁⠀⠈⢀⠞⠁⠀⠛⠀⣱⡄⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠙⣯⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢘⣄⠀⠀⠀⢸⡏⠉⠉⠛⠲⠦⠶⠛⠀⠀⠀⠀⠀⠐⢸⣇⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⡠⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠶⠖⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⢸⡏⠉⠁
⠀⠀⠀⠀⠠⢴⡶⠖⠒⠶⣽⡆⠀⠀⠀⠀⣠⢤⠖⠲⠚⠲⠶⣄⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢀⠐⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣠⠟⡃⠠⠄⠀⠀⣠⠂⣠⠀⠄⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣏⠠⠀⠀⠀⠀⠀⢰⠏⣠⠏⠐⠋⠴⠁⠀⠀⠀⢰⠋⠛⢯⠀⠀⠀⠀⠀⠀⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣶⡖⠒⢦⠀⠘⡄⠀⢀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠂⠀⠀⠀⠀⠙⣆⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⠇⠀⠈⠳⠤⣌⣁⡤⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢸⣤⣀⠈⠓⠶⠤⣄⣠⣤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⣀⡴⠏⠀⠀⠀⠀⢀⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠶⢆⣀⣀⠀⡀⢠⡤⠞⠓⠒⣆⠀⠀⠀⠀⠀⠀⠀⣿⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠲⣦⠀⠀⠉⠉⠉⢉⣠⡴⠖⣻⠟⠁⠀⠀⠀⠀⢠⣴⠇⢀⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠞⣙⠛⠉⠛⠶⡄⠀⠀⠈⡇⠀⢀⣤⠞⠋⠁⠀⢼⣋⣀⣖⣠⣂⣰⡶⠞⣁⡴⠋⠀⠀⣼⣧⣀
⠀⠀⠀⠀⠀⠀⢀⡞⢉⠀⠈⠁⠀⠀⠀⣾⣥⣔⣀⡴⠃⣴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣩⡥⠶⠛⠉⠀⠀⠄⠁⠄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣸⢁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠁⠀⢸⡅⠀⠛⠶⠶⠦⠴⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉
⠀⠀⠀⠀⠀⢸⡏⠄⠀⠀⠀⠀⠀⢠⣞⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⣀⣀⠀⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢻⡀⠀⠦⠀⠀⠀⠀⠁⠈⠳⣄⣀⣀⠀⠀⠀⣠⡽⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⢄⡜⠀⠀⣼⠁⠀⠀⠈⠉⢁⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢿⡀
⠀⢠⠀⠀⠀⠀⠙⢶⣠⣴⠆⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠈⠳⣬⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⢀⡶⠛⢲⣤⠟⠻⠤⠶⣤⠼⠴⠋⠁⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢀⠞⠋⠉⠉⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠄⠀⣀⣀⣀⡀⠀⠠⠤⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠐⠀⠀⠀⠀⠀⠀⠈⡷⢟⡙⠲⠦⡴⠖⠛⠶⣄⠀⠀⠀⠀⢹⡇⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⢰⠀⠀⠀⠠⠽⢧⠤⣄⡀⠀⢳⡄⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⢀⣠⣄⠀⠀⠀⣠⠇⠀⠀⠈⢢⡀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢧⠀⠀⠈⠉⠓⠶⠤⠤⣤⡤⠤⠶⠶⠚⠋⠉
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠈
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠦⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠾⠃⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡀⢀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⢀⢤⠴⠆⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠃⠈⠂⠓⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⢀⠁⠄⠀⠀⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⢀⠀⢀⣀⡠⠀⠀⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠐⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢩⠀⢀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢘⠀⠀⢨⠁⠀⢀⠀⣀⡠⠄⡄⠤⠈⠡
⠀⠀⠃⣀⡁⠀⠂⠈⠅⠀⠀⡰⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢂⠘⠈⠀⠐⢈⠀⠀⠸⠀⠀⠈⣉⠀⠈⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠀⠈⠁⠀⢠⠘⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⢀⠀⠀⠀⠀⡄⢀⣡⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡍⠅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⢀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠊⠀⠁⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠇⠢⠠⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣄⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢰⡄⠀⡴⠂⠀⡄⡄⠀⢰⠀⠀⠀⠀⠀⠀⠾⠁⢈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠠⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⡄⠉⡁⠘⠒⢒⡓⢊⠉⠙⡆⠀⠀⠀⠀⠀⡀⢀⠀⠤⣁⡀⠀⠀⠂⠀⠀⠀⠀⠠⠒⠉⠀⠄⠠⠈⠉⠒⢄
⠀⠀⠀⠀⢀⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⠌⠥⠢⠳⠈⠁⠭⠄⢤⠄⠀⠀⠀⠀⠀⠁⠃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠤⠤⠀⠤⠠⠔⠆⢸
⠀⢠⠀⠀⢈⠑⠀⠀⠀⠄⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠈⣀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠇⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⢁⣀⣀⣤⣤⣤⣌⡢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⢀⣤⠴⠚⠋⠉⠀⠀⠀⠀⠙⣿⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⢶⣒⣒⣚⣿⣿⣷⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⣀⡤⢒⣩⠵⠞⠛⠉⠉⠉⠁⢀⣀⣈⠉⠉⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡀⢢⠀⠀⠀⢀⠄⠈⡠⠖⠋⠀⠀⠀⠀⢀⣀⣤⠞⠋⠉⠉⠙⢳⡶⢶⣄⣀⣀⠈⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣳⣄⠐⢁⠔⠈⠀⠀⠀⣀⣤⠶⠛⢻⡟⠁⠀⠀⢀⡤⠒⡡⠂⠜⠉⠉⠙⠛⢶⣄⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⡀⠁⠀⠀⢀⣴⠞⠉⠀⠀⠀⠘⡇⠀⠄⠂⠁⢀⠁⣤⡄⠀⠀⠀⡀⠀⠀⠻⢦⡀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⠎⣤⢶⠖⠛⠉⠙⠳⣦⠀⠀⠀⢀⡿⠀⠀⠀⠀⣾⣿⣿⣏⠀⣧⠐⠀⠀⢀⠀⣸⣇⠀⠀⠈⢿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢀⠎⢸⠁⠃⠀⠀⠀⠀⠀⠘⣧⣀⡴⠞⠃⣀⡂⢠⣶⣾⣿⣿⠿⠃⠁⢒⣒⠚⠡⠒⢿⡙⣷⡄⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡾⢀⠎⠀⢸⠀⡄⠀⠀⠀⡀⠀⠀⠈⣿⠀⠈⢀⣀⡀⣀⡛⢿⣿⣿⣿⠟⠀⠀⠀⠀⡀⠀⢸⠷⠾⠿⢲⡄⠀⢿⣷
⠀⠀⠀⠀⠀⠀⣸⠃⡌⠀⠀⢸⣧⣐⠊⡁⠉⠁⠀⡠⣰⠏⠀⠀⠀⠻⣷⣿⣿⣿⣿⡿⠻⣄⠆⢢⡀⡀⠆⣃⠄⠀⠀⢀⠸⣧⠀⠀⢻⡇
⠀⠀⠀⠀⠀⢠⡿⢠⠁⠀⠀⣼⠀⠹⢦⣄⣀⣐⣨⡼⢷⠀⡄⠀⠀⠘⠛⠿⢿⢿⣿⣴⣶⣟⠻⢷⣌⣁⠈⠁⠀⠀⠀⠈⠐⠘⣧⠀⡜⣿
⠀⠀⠀⠀⠀⢸⡇⠘⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠁⢀⡾⠃⢌⣂⣼⣿⣷⣆⣁⣼⠃⠀⠱⠙⣆⠀⠈⣇⠀⠀⠀⠀⠐⠠⠀⢸⡏⠀⢸⣿
⠀⠀⠀⠀⠀⣾⠁⡆⠀⠀⢀⡷⠞⠛⠛⠛⠛⠛⢶⡼⠁⢀⣿⣿⣿⣿⣿⡏⠀⠀⢠⠃⢀⠀⡿⠶⠞⢉⡂⠀⠀⠀⠐⠁⣠⣿⠁⠀⠈⢸
⠀⠀⠀⠀⠀⣿⠀⣷⠀⢠⡾⠁⠀⠀⠀⠀⢸⠆⠆⢡⠰⠻⡿⠿⣿⠃⠛⠃⡤⠔⠁⠘⣧⣬⣴⣖⡂⠀⠃⠐⠏⡒⠐⣟⠉⣿⠀⠀⡄⢠
⠀⠀⠀⠀⠀⢹⣷⣿⡀⣿⠈⠀⠀⠀⠒⠀⠺⠀⢀⡜⠄⠳⠤⣂⠀⠁⠤⣤⣵⠖⠚⠛⢹⣿⣿⣿⣿⣆⠀⠈⠢⡙⢄⣿⢰⡏⠀⠀⠃
⠀⠀⠀⠀⠀⠈⣿⡘⣇⢿⡘⢄⠀⠀⠀⠀⣀⠗⡙⠁⡀⠌⠓⠂⡇⢰⡞⠁⢀⡤⠖⣋⡹⢿⣏⠻⠿⠗⠀⠀⠀⠙⠸⣏⡿⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⠳⣤⣈⣀⣀⣩⣴⠊⠀⠀⠀⠀⠀⠈⣠⢙⣧⣤⠞⡡⠊⠀⠀⠀⠀⠑⡄⢤⣀⣀⣤⣄⣠⡿⠁⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡝⣆⠀⠉⠉⢻⣤⡿⠀⠀⠀⣀⠄⢂⡄⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠁⢸⠏⠉⠀⣨⡟⠀⠀⠀⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣞⢷⡀⠀⠀⠙⢧⣤⣀⡉⠄⠂⢁⠈⠂⠀⠀⠈⢂⠣⣐⢄⣴⠋⠀⡀⢡⡞⠀⢀⡼⠋⠀⠀⡔⠡⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣀⡻⣄⠀⠀⠀⠉⠻⣽⣓⠒⢻⡄⠀⠀⠀⠀⡀⠑⠌⠦⣌⣉⣁⡴⠋⢠⠶⠋⠀⠀⡠⢊⣼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡳⢄⡀⠀⠀⠀⠉⠛⠾⢷⣄⡀⠀⠠⠈⣀⠀⢸⣧⣭⠵⠚⠀⠀⠀⢀⡠⣊⣴⠿⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡙⠂⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠚⠋⠙⠛⠁⠀⠀⠀⢀⡤⠖⢋⠿⠋⠁⠀⠀⠹⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢄⡉⠒⠢⠤⠀⣀⣀⣀⣀⣀⣀⠠⢤⣴⣶⣿⡥⠖⠋⠁⠀⠀⠀⠀⠀⡸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠠⠀⠠⠤⣤⣤⡴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣎⠀⠀⠀⠀⠀⠀⠀⠊⣁⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⣦⣠⣤⡤⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⣄⢀⠀⡠⢠⣄⢀⢄⢀⢀⡄⢠⣄⡀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠑⠊⠐⠑⠊⠉⠃⠊⠈⠐⠂⠘⠋⠐⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠉⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢀⠀⠀⢀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡗⠀⠀⠐⠤⠤⡖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠂⣰⠉⠱⢄⣀⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠺⢄⡀⠀⠀⠀⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⢄⡀⠙⠊⠑⡆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢠⡀⠀⠉⠉⠉⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠉⠒⠒⠲⠛⠉⢣
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠑⢄⢀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⡖⠋⠀⠀⠀⠀⠀⠀⢀⠴⡄⠀⠀⠀⡗⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠰⡶⣀⠀⢸⠀⠀⠉⠙⠢⢅⢤⣀⣀⣠⠇⠀⠀⠀⠀⠀⠀⢳⣄⣀⣠⣤⠤⠖⢉⠁⠀⡇⠀⢀⣀⡇⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⢑⡜⢆⡄⠀⠀⡀⠀⠀⠀⠐⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠒⢉⠍⢣⣄⠀⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠺⠦⣀⠀⠀⠠⣀⡀⠀⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⣸⣆⠀⠀⣀⠄⠀⠀⢀⡰⠃⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢻⡎⠒⢦⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⠂⠀⠤⢔⣈⠽⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠐⠊⢧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⢀⡧⠀⣤
⠀⠀⠀⠐⠀⠀⠀⣀⡑⢊⠀⠀⠤⠠⠼⠤⠒⠀⠨⢀⠀⠀⣶⡰⣂⠀⠀⠀⠠⠢⠀⠤⠀⠠⠀⠀⢁⠠⠀⠀⠘⠀⣹⣁
⠀⠀⠀⠀⠠⠀⢼⡈⣿⡰⠁⢀⡀⠀⠀⡀⠤⢀⡠⠌⠀⠠⡞⠁⡌⠋⠛⠋⠀⡞⠻⡖⠶⠤⠀⠈⠉⠀⠀⠀⠀⠈⠀⠘⣞
⠀⠘⠀⠠⠤⠄⠀⠉⠇⠀⠀⠀⠀⠀⠀⠃⠀⢸⠓⠢⠤⠮⣤⠤⣀⣀⣀⡂⢤⡤⢼⠁⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⢨⠃
⡏⠍⠀⠀⠀⠀⠀⠐⠒⠂⠒⠒⡋⠀⠉⠉⠉⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠋⠈⠉⠉⠒⠂⠀⠒⢪⠉⠉⠉⠉⠉⠍⠉
⡆⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠠⠄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠚⠁⠀⠀⠀⠈⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠲
⠯⣤⣀⣀⣀⡀⠀⠃⠀⠄⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠰⠶⢭⣝⣒⣒⣚⣻⡭⠵⠂⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⠜⡀⠀⠀⠀⠀⡰
⡅⠀⠀⠀⠈⠙⠛⠦⠾⠦⠴⠟⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣶⡶⠾⠂
⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠂

⠂
⡶⣿⢿⢿⢿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣾⠀⠁⠠⠀⠀⠊⠀⢀⡴⢋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠂⠀⠀⡟⠀⠀⠁⠀⢀⣀⣀⡾⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⡴⢛⢡⡙⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡞⠉⠙⢿⡋⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⣏⠰⣌⢧⡹⣜⣧⠀⢂⠀⠀⠀⡇⠀⠀⣴⠏⠀⠀⢀⡼⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢷⡙⢦⠻⠍⠘⡇⠀⢂⠀⠀⣿⢠⡾⠁⠀⠀⢢⡞⠁⢀⠔⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠈⠀⠄⡀⠀⠙⠶⣤⣴⣾⡃⠀⠀⠀⠀⣿⠏⠀⠀⠀⣴⠏⠀⠀⠁⠀⠀⠀⠁⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⡾⠃⠀⠀⢈⡾⠁⠀⢀⣀⣠⣤⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠶⠶⠶⠶⠶⠖⠛⠛⣛⣻⣿⡄⠀⠀⠹⣦⠟⢀⣀⣠⣴⡿⠶⠞⡛⢉⣭⠤⡄⠀⢻⠀⣀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⠶⠟⢛⣉⣁⣸⣧⡤⠶⠞⣛⠛⢉⠉⣤⠶⣆⢸⣋⠁⠈⠓⠶⣤⠀⢸⡟⠉⠉⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣼⠷⠞⢛⣋⣉⠉⢠⡴⠂⢠⡞⠙⠃⣸⠀⣿⣴⠏⢸⣯⡤⠀⠓⠞⠋⠀⢸⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿⠀⠀⣿⠁⣹⠇⢸⣧⠀⢸⣇⣠⡆⠻⠀⠋⠀⠀⢄⣐⣠⣤⠴⠶⠖⠒⣾⠇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣁⣀⣤⣤⣿⡀⠀⣿⠚⢯⡀⠸⡧⠶⠀⢉⠉⣀⣠⣤⣶⡶⠛⠋⢹⡇⣀⣤⡶⠶⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⢸⡇⠀⠉⠀⠀⠀⣀⣠⣤⣷⣾⠛⠉⠁⣿⠀⢻⡄⠀⢸⡟⠉⠀⠀⢀⣀⣤⡤⠶⠶⠚⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠈⠷⠴⠶⠖⣿⠛⠉⠀⢰⡾⠁⠀⠀⠀⣿⠀⠀⢻⣆⠈⠓⠖⠛⠛⠉⠉⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠄⠀⢠⡞⠁⠀⠀⣰⠟⠀⠀⠀⠀⠀⣿⠀⠀⡀⢻⣷⡄⠀⠀⠠⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣝⡳⣄⣼⠋⢀⣤⠶⠚⠛⢓⣿⠀⠀⠰⠈⢷⡙⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣽⠷⠟⠁⠀⣿⣤⡴⠶⠟⢋⣿⠀⠀⠀⠁⠈⠻⠾⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⠀⠠⠀⠸⣆⠀⠀⣀⣾⠇⠀⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠋⠀⠀⠠⠁⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣀⣤⣀
⠀⠀⢿⠀⠈⠳⢄
⠀⠀⠈⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠑⢄⠀⠀⠀⠀⣠⠶⣤⣤⣴⡇⠄⣟⣉⡿⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠳⣼⡉⣳⡷⠤⡇⢂⣀⣿⡟⢠⠀⣱⠖⡚⠻⢟⠳⡤⠶⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⡩⠽⠲⢄⠈⠻⣁⠽⢦⡈⢣⡀⡨⠛⠉⢻⠟⡉⠈⡱⠞⠁⢣⡀⣀⣸⠢⡈⠉⢦
⠀⠀⠀⠀⠀⠰⡇⠀⠧⣠⣊⠉⠻⢾⢁⠤⡴⠋⠉⠙⣇⣀⡤⠷⠠⡴⠚⡓⢌⠀⡰⠋⢀⣈⠦⠃⣠⠟
⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠈⠉⠉⠛⠒⠒⠳⠤⠤⠤⠼⠧⠤⠶⠤⠞⠒⠒⠛⠚⠋⠉⠉⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠶⠖⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠏⠉⠙⡥⠀⠀⠀⣛⠛⠛⠛⠷⢤⠦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⠃⡀⠰⠀⠀⠀⠈⠉⠀⠀⠀⢀⡈⠀⠂⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠛⠉⠀⠠⠀⠈⠀⠀⠀⢀⡄⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⠂⠀⢰⠂⠀⠀⠰⠂⠈⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠈⠀⠍⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠚⠀⠀⠞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⠀⠀⡀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⢀⣤⢿⠄⣴⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠷⣄
⠀⠀⠀⠀⠀⣴⠋⢠⡟⠀⠰⡂⠀⠀⡉⠁⠀⠀⣀⡀⠀⠀⠀⠈⠃⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠰⠄⣿⠀⢸⣧
⠀⠀⠀⠀⠀⣿⡄⠘⢧⣉⠀⠀⠀⠘⠒⠀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⡼⢻
⠀⠀⠀⠀⠀⣇⠙⠶⣄⡉⠳⢦⣀⡁⠀⠘⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠂⠀⠀⠔⡆⠀⠀⣀⣠⡾⠋⣠⠞⠁⣼
⠀⠀⠀⠀⠀⢻⡀⠀⠈⠙⠲⢤⣈⡙⢦⡴⢶⣦⣤⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠾⢉⣠⡴⠚⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠤⣤⣉⣉⣉⡉⠙⠛⠛⠛⠛⢋⣉⣉⣠⠤⠶⠚⠋⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⡈⠉⠙⠛⠓⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠛⣉⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠦⠤⠤⠤⠤⠤⠴⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣒⠋⠭⠒⢂⣈⡀⢤⠀⣀⣀⣀⡤⣤⢤⠄⣀⡀⠉⠉⠛⠒⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢞⣫⡴⠞⠋⠁⣀⠐⣨⡤⠆⣹⢭⣋⡿⢶⣻⣵⣶⣦⣏⠉⠛⠏⡏⠛⡟⡖⡶⣄⠉⢷⣦⣀
⠀⠀⠀⠀⠀⣠⣟⠵⠛⠛⣇⣤⡦⢚⣕⡺⢏⣖⡺⠗⠻⢞⣫⠯⣗⣻⡔⢮⡿⣦⣄⣠⣄⣀⣠⣆⣩⠞⣻⡓⣌⢿⡳⡄
⠀⠀⠀⠀⢠⣿⡏⢀⡰⢭⡿⣤⢙⣆⣉⣿⠻⣿⡿⡿⣷⣾⣻⠽⣟⡼⠿⢏⣸⠏⠈⣿⣿⣿⣶⣓⣻⣍⡽⢣⢼⠘⢉⣿
⠀⠀⠀⠀⢸⡿⣷⢌⡻⣯⣽⡯⣟⠛⢷⡾⣷⠿⣲⡏⡼⢿⣭⡿⢭⣿⣳⣯⣤⠞⠋⠒⣿⡖⣫⠿⠭⣯⣵⣾⣗⡷⣺⣿
⠀⠀⠀⠀⠀⣿⠘⠻⢯⣗⡺⠭⠟⡕⣶⣶⠒⣫⣝⣺⣳⣿⣿⣿⣷⣯⣽⣟⣯⣀⠶⣎⡹⣗⣓⣶⢿⣝⣯⣽⣿⡟⢱⡇
⠀⠀⠀⠀⠀⢸⡆⠀⡀⠀⡏⢛⡲⠤⣝⣚⣣⣟⣨⣟⣿⣙⢍⡁⠻⡩⢟⣿⣞⣯⣵⣿⣬⣷⣾⣿⡿⠷⡟⠋⣧⠇⣾⠁
⠀⠀⠀⠀⠀⠀⢷⠀⢇⠀⠁⠈⠭⣛⣒⠢⠬⠉⠉⠙⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⢋⠩⠭⠁⠀⠀⠈⠁⢸⠋⣸⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⢚⣩⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠦⠤⣤⣤⣤⣤⡤⠤⠴⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⡲⣄⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣀⢀⡀⠐⠂⠀⠀⠔⢁⡄⢀⠀⠀⠿
⠀⠀⠂⠀⡤⢈⠀⡀⠀⠤⠀⠀⠀⠠⠀⠈⠐⠀⣠⣄⠄⠀⠀⠀⢈⠀⠀⠀⠀⠰⣇⡠⠙⠛⠨⠚⠁⠆⠀⠈⠄⠀⠈⠂
⠀⠃⠐⠀⡀⠘⢀⠁⠀⠀⠉⠀⠀⠠⠀⠀⠀⠈⢀⡀⠱⠤⡅⠀⢀⠀⠀⠀⠀⢸⠛⠿⣷⣦⣱⠈⠀⠀⠁⠀⡀⠑⠀⠞
⠀⠰⡆⠀⠀⠣⠀⠀⢂⠀⢀⠤⠍⠐⣀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠁⠀⠀⠀⠀⠻⣷⡢⢄⠉⠛⠈⠀⠀⠀⠈⠋⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠁⢀⡁⢤⠀⠀⠀⠄⠀⠀⠈⠀⠘⠻⠿⠀⠀⠀⠀⠀⠀⣀⠈⠛⢷⡽⢀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠂⢀⠃⠀⠒⠀⠂⠀⠀⠂⠀⠀⠀⠀⢠⠀⠄⠖⡀⠈⠐⠂⢁⠐⣄⠘⠛⠀⠀⠈⠀⠀⠀⠀⠄⠀⠠⠀⠀⠠
⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⠁⠁⠒⠂⠀⠠⠀⠀⠀⠀⠀⢡⠀⠀⠀⠂⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠
⠀⠀⠁⠀⠴⠆⠠⢠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠠⠀⢰⢹⡿⡏
⠀⠀⠄⠀⠀⠀⠀⠀⠙⢖⡂⢁⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⣤⣤⣤⣤⡀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⣸⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⡠⠀⠀⠀⣰⠻⢿⣿⣿⣷⣭⣭⣏⣨⣿⣿⣿⣿⠛⡆⠀⠀⠆⠀⠀⠀⠀⡔⠀⢿⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠙⠀⠀⠀⢿⢘⣻⠻⠛⣿⢸⣿⡇⠾⢛⠛⡍⠿⡃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣀⠀⠘⢼⣧⣄⣷⣾⣬⠿⠧⠿⠶⠿⠾⠷⢖⣁⠀⠀⠠⣀⠀⠀⡀⠴⠀⠀⠠⠢⡀
⠀⡐⠁⠄⠂⠀⢄⠀⠁⠀⠠⠀⢠⡾⠻⠎⠁⠠⠀⠀⠀⠤⢄⠀⢤⠀⠀⠀⠀⠊⠀⠌⠐⠀⠀⠤⠀⠘⠂⣀⣠⣤⣤⣤⠁
⢰⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠁⢳⡤⢈⢤⠀⠂⡀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⢀⠀⠂⠔⠀⠀⠀⠀⠀⢰⡷⠲⠴⠞⣩⡷
⠈⡀⠀⠂⠤⠀⠁⠀⢠⠃⠀⠀⠐⢀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠑⠀⠉⣠⠂⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠰⠀⠀⡔⠡⠘⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⢠⠓⠄⠔⠲⠒⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠁⠀⠀⢪⠒⢹⠂⡄⠀⠑⠲⠷⢦⣤⡤⠠⠜
⠀⠀⡀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⢨⠉⠁⠀⠀⡀⠘⢐⠀⠀⠅⠀⠀⠰
⠀⠀⠙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠙⠃⡀⠀⠀⠒⠀⠈⠀⠒⠀⠀⡀⠀⠀⢂⠀⠀⠒⠀⢀⠈⠀⠢⠤⠂⠀⠂
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⡰⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠀⠀⠁⠀⠰⠀⠀⠀⠀⢂⠀⠀⠀⠈
⠀⠀⠀⠀⣠⣄⡈⠘⠲⣄⣄⠞⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠿⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠄⠀⠀⢀⠀⠀⠀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⢄⠀⠀⠠⠀⠀⠀⡀⠔⠃
⠀⠀⠀⠀⠀⠈⠊⠀⡄⠄⠀⠀⠀⠀⠀⣥⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢇⠀⠀⠠⠀⠢
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠘⠒⠂⠀⠐⠂⠈⠀⠀⠀⠀⠈⠊⠠⠀⣀⣀⠁⠎⠀⠄
⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣱⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠘⣇⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠰⣷⣀⠤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⢁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠰
⠀⠀⠀⠀⠳⠄⠔⠊⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠂⠀⠀⡠⠄⠒⠂⠐⠀⠄⠀⠀⠀⠁⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠐⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⢀⡧⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢈⢘⡀⠀⠀⠆⢀⠀⡄⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠀⡰⠀⠀⠀⠀⠰
⠀⠀⠀⠿⢤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⢰⡀⢀⠄⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⣉⠉⠉⠉⠉⠉⠀⠀⢠⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⡒⠠⡀⠀⠄
⠀⠀⠀⠰⢀⡀⠀⠀⠀⠀⢦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⠀⠄⠠⠀⠈⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡉⠀⠀⠀⠈⣆⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⡀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠂⠀⠃⠀⠀⠀⠆⠀⠀⡀⣀⠀⠀⢠⠀⠀⠀⠀⠀⢸⣝⠠⠐⠓⠀⠒⠒⠊⠁
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⡈
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠉⠑⠚⠒⠋
⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠤⠤⠀⠀⠉⠀⠀⠐⠦⡀⠀⠀⢎⠀⣈⡀⠠⢀⣠⠀⠀⠀⠀⠤
⠀⠀⠀⡡⣈⢹⡒⠒⡢⡄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⠙⠃⠀⠠⢠⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠒⠚⠀⠈⠉⠉
⠀⠀⠀⠣⠈⠀⠂⠀⠤⠢⠌⡀⠁⠀⠀⢰⣀⠀⠀⡄⠀⠀⠀⠠⠀⠰⠀⠀⢉⢀⡘⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠳⢄⣇⡀⠐⠂⠂⢀⣆⠀⠄⠐⠁⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠑⠶⠕⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠁⠓⠁⠐⠁⠀⠀⠀⠰⠈⠀⠄⠀⠀⠀⢠⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚

⣰⣖⠀⣺⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⢀⡁⠀⠀⠀⠀⠀⢀⠄
⢨⠇⠀⢹⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⢡⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡤⣀⠀⡄⠀⠀⠀⠄⢘⠀⠢⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠉⠉⠃⠀⠀⠀⠀⠦⢀⡁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠈⠀⠀⠀⠆⠀⠀⠀⠘⠙⢐⠂⡀⠀⠀⠀⠀⡬⢁⡃⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⢀⣤⣦⢄⡀⠀⠀⠀⢈⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⢵⡅⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠋⠃⠃⠀⠀⠀⠀⠀⢐⡀
⣿⣿⠿⠿⠻⠿⡿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⢀⠀⠀⠀⡠⠀⠀⠀⡀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⣀⡢⠀⢂⠀⢀⠀⢂⠀⠀⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠄⢠⣂⡉⠦⠂
⠀⠀⢠⡀⠀⠀⠀⠑⠀⠀⠢⢀⠀⠀⠁⠀⢐⣓⡅⠀⠀⡐⡀⠀⠂⠀⠀⠀⠀⡀⠁⠀⠉⠂
⠀⢆⠀⢀⠀⠀⡠⠐⢂⠂⠂⠠⡀⠀⢰⠍⠘⣵⠂⠀⢠⠊⠀⠐⠀⠰⠐⡠⠊⠀⠈⠁⠒⠂⠀⠀⠈⠡
⠀⢀⢄⠈⠀⢈⠀⢀⠤⢀⡦⠦⠏⢀⠤⢄⡀⠻⠀⠀⠈⠂⠠⠛⠑⠀⠀⠀⠀⢀⡀⠁⠁⠀⠂⠁⠂
⠀⢸⠀⠣⠀⠉⠀⠡⠬⠅⠒⠊⠀⡘⠀⠀⡌⠀⢀⠀⠀⠦⠄⠀⣠⣤⢶⣞⣤⠀⢀⠀⠀⠀⠀⡄⠒⠆
⠀⠸⡐⢀⡇⠀⠀⠖⠂⠀⠀⢠⠆⠑⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⡈⠹⠉⠉⠉⡁⠀⢀⠘⠀⠈⠁⠈
⠀⠀⠈⠁⠐⠢⠀⠄⠀⠀⠀⡀⢀⡠⣶⠴⠀⠀⡀⠀⠀⠰⠳⠀⠀⠀⠀⠉⠀⠀⠠⠀⠄⢀⠄⠙⣈⣠
⠀⠓⠀⠀⠀⠀⠀⠀⡄⠀⠄⠐⠂⠉⠠⢊⠐⠃⢃⡲⠖⠀⠀⠀⠀⠤⠀⢀⡀⢈⡀⢀⠀⡀⠀⡀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠴⠔⠒⠂⢉⠴⠀⠀⠀⡀⠀⠀⠂⠅⠀⠀⠐⠈⠠⠈⠀⠃
⠀⢂⠀⠀⠐⡀⠀⠀⢴⡄⠀⠀⣠⠤⠤⠸⢇⣀⠐⠋⡀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⡠⢐⠂⠚⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠁⡀⠁⠀⠀⠀⠂⠠⠈⠁⠀⠀⠀⠂⠐⠉⢀⠀⠀⠀⠈
⠀⠀⠠⢀⠀⠀⡔⡄⠀⢀⠀⠄⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢄⠀⠲⠆⠈⠁
⠀⠀⢀⣀⠀⠀⢡⠁⡀⠠⠁⡆⠀⠂⠀⠀⢀⠀⢰⠂⡀⠀⠀⠀⠀⢀⠰⠂⠀⠐⢣⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠖⠀⠀⠀⡀⠐⠀⠾⠀⠀⠀⠈⠀⠠⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⢀⠜⡄⠀⠈⠿⠂⠁
⠀⠀⠂⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠄⠀⠀⠄⠒⠒⠪⠐⠂⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡐⡀⠈⠁⠠⠒⡀⠃⠀⡙⠀⠀⠀⠀⠀⢀⠀⠀⠠⡰⠠⢀⠆⠄⠂⠀⣀⠀⠀⢀
⠀⠐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠃⠀⠂⠠⠀⠀⠉⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⡉⠀⠀⠀⢩⠃
⠀⢰⢙⠡⠃⠀⠚⠀⠂⠀⠀⡐⠀⠀⡡⠐⠘⠂⠀⢀⡀⠍⠀⠀⠀⠀⠀⡙⠙⠁⠀⠀⠀⠐⠀⠀⠐⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣰⠛⠻⡆
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⢻⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣏⡸⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠦⠶⠛⢻⠶⣤⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⠲⢤⣤⠶⠛⠉⠀⢹⡆
⠀⢀⡾⣧⣀⣈⣇⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⢀⣴⣋⣙⣦⣭⣹⡟⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠘⣇
⣴⣯⣤⡟⠁⠈⠙⢷⣄⠀⠀⠀⠈⠉⠛⠲⢶⢺⠀⠀⠀⠀⣾⣼⣶⣫⡟⠉⠉⢳⣤⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⡏⠀⠀⠀⠙⣧⠀⠈⠛⢦⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣤⠤⠚⠾⠅⠀⠀⠀⢹⡀⠈⠉⣉⠛⠋⡿⠃⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠈⣷
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡴⣷⠀⠀⠀⠀⠀⢳⡀⠀⠉⢀⡼⠁⠈⠁⠀⠀⠀⢷⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⠴⠿⣄⡇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡞⠁⠀⠀⠘⠃⠀⠄⠘⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠈⠉⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠘⠃⠀⠐⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠁⠀⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄⠀⠈⠛⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳⣤⡏⢻⣆⣠⣯⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⢧⣄⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⣀⡈⢳⡏⠉⣻⣾⠙⣧⠈⢿⣹⠆
⠀⢀⡶⠒⠒⠒⠒⠚⠛⠛⠛⢛⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⣟⣉⣉⣉⣉⣹⠂⠀⠀⢿⠘⡇⣠⡤⣤⣴⣿⠟⠁⠀⠀⢸⣏⣉⡙⠳⢴⡃⣿⢰⡿⣧⠀⠻⡄
⠀⠘⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⡴⠟⠉⠉⠉⠉⠉⠲⣄⠀⠸⠀⠀⣿⡀⠁⢹⡇⠀⠀⠀⠀⠀⢀⣀⡿⢦⠀⠙⢧⣸⠃⣼⣆⣀⣽⡦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠛⠛⠻⣿⢦⡼⠃⠀⠀⠀⠀⠀⠈⢿⠙⠛⠓⠒⠚⠛⠚⠛⠉⠁⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣄⣹⣦⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠉⢻⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⠶⠛⠶⣿⣶⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⢁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⠷⠮⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⢀⣾⡭⠽⠧⠬⣍⡉⣿⣋⣽⣇⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡴⠶⠶⢶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡀⠀⠀⣤⠀⠈⠙⠳⢦⡀
⠀⠀⣠⠞⠁⡀⠘⠀⡀⠈⠙⢦⡀⣽⡛⢯⡉⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠰⢦⠀⣤⠈⠁⣠⠌⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠉⠛⠻⢧⣄⣀⡄⠀⠀⠙⢦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠉⠀⢠⠀⠙⣦⠙⣿⢛⣷⠘⡆⠀⠀⠀⠀⢾⠀⠞⠀⠀⠀⠈⣠⠄⠀⠴⠖⠈⢷⠀⠀⠀⠀⠀⠀⢸⣇⠊⣷⠀⠀⠦⠈⠙⠳⣄⣠⠆⠀⠹
⠀⠀⠹⣄⠉⠀⠠⠄⠀⠀⠀⠀⢠⠌⣧⠉⢻⣽⡆⡇⠀⠀⠀⠀⠈⡿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⢸⣏⡴⠏⢠⠖⣛⣉⣽⡳⣬⣻⣦⡤⠶
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠰⠆⠀⠀⠀⠘⡇⢸⢉⣷⠇⠀⠀⠀⠀⢰⡟⠖⠛⠛⠳⢶⠶⠛⠉⠳⠶⠞⣩⡷⠀⠀⠀⠀⠀⢸⡁⠀⠀⣟⢾⣙⣧⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠐⠀⠀⢻⠟⢫⠏⠀⠀⠀⠀⠀⠀⢻⡗⠛⠛⠛⠛⠻⢿⣝⡛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣾⠛⢳⣀⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣀⣨⡿⢦⠾⠃⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠰⠀⠀⠀⠀⠀⠀⢑⣄⠉⢠⠁⠔⠀⠈⢢⠀⠀⢀⠇⠠⠔⠀⠠⠝⠀⠁⠀⠀⠀⠈⠀⠄⠀⠐⠀⠐⢈⠀⠩⣎⡀⢀⠄⠒⣢⢠
⠀⠀⠀⠀⠠⠄⠒⠀⠒⣆⠀⠈⢆⠀⠰⠠⡀⢣⠀⠢⣀⣤⠠⠄⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⠁⠀⡀⢁⠎⠀⠤⡌⠀⠙⠒⠒⠊⠉
⠀⠀⠀⡦⠄⠀⠀⠀⠨⠐⠀⠀⠀⠑⠠⡐⢈⠐⠀⣀⢸⢞⠵⠀⠀⠀⠠⡡⠤⠀⠇⡀⠀⠁⠀⠀⡰⠁⢎⡀⠀⠀⠀⢀⠀⠀⣀
⠀⢸⡀⠈⢈⠀⠀⣀⠴⠲⢙⠌⠜⡐⠢⡀⠀⠀⣾⠆⠀⣧⣟⠀⢀⣢⡌⠀⠀⠘⠈⠀⠇⠐⡠⢊⠀⠀⢘⠈⠉⠉⠀⠀⠀⠀⠀⢤
⠀⠀⣀⡀⠈⠀⡘⢑⣠⡀⣄⡄⠰⣔⡢⠽⠀⣀⣁⡀⡀⠘⡇⠀⠀⠈⠒⠠⠤⠻⠑⠀⠀⠁⠀⠈⠜⢀⠈⠁⠉⠀⠰⠀⠁⠆
⠀⠀⡇⠘⣆⠈⠐⠂⠀⠊⠐⢒⣉⡠⠔⠁⠸⠇⠀⠈⣡⠂⢀⠀⠀⠀⢀⢈⠁⠀⠀⣀⣠⣤⣤⣌⠀⠙⠀⠀⠑⠀⠀⠀⠀⠄⣀
⠀⠀⡇⡔⠈⡆⠀⠉⠈⢉⠉⠁⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⠘⢐⡀⠐⠁⠈⠀⠀⠺⠿⣯⠿⠷⠽⢧⠀⠆⠀⠀⠆⠀⢰⣅⡠⠂
⠀⠀⠣⡈⣠⠇⢀⠀⠈⠧⣈⠁⠐⠈⡩⠃⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠤⠔⠁⢀⣀⠀⠤⠂⠁⠠⠒⠁⠀⢀⣀⠀⡀
⠀⢀⠀⡀⠀⡐⠑⠄⠈⠆⠀⠀⠈⠀⡀⢀⡄⢴⣯⠒⡄⢀⢔⡀⠄⠀⠠⢏⠝⠀⠀⣀⠀⠀⣀⢀⠀⠀⠔⠈⠄⠀⡴⠁⠈⣆⣄⡅
⠀⠓⠒⠀⡐⠀⠀⠀⠀⠀⣀⠀⠨⠌⠰⠖⠘⢁⡠⠊⠔⠗⠐⠠⢤⡶⠂⠀⠀⢄⠀⢠⡄⠀⢀⠀⠀⢁⠀⠀⠀⠐⠠⢀⠔⠁⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠚⠀⠐⠂⠀⠒⠈⠀⣀⣩⣄⠦⠔⠛⣡⡀⠀⠀⠀⢀⠇⠀⢀⠀⠮⠩⠠⠍⢡⠘⠂⡈⢒⣈⠦⠀⡀
⠀⢀⠀⠆⠊⠣⡀⠀⠀⠀⡰⠀⠤⠀⠀⠘⠃⠀⠉⢠⡄⠀⠀⣚⠭⠁⣄⡀⠐⢁⡀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠘⠦⠀⠀⠀⡤⠀⠀⠀⠚⡟⠠⠈⢀⡴⠖⠋⠃⠚⣳⣠⡄⠈⡀⠄⠈⠀⠀⠈⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠖⡄⡠⡄
⠀⠠⢄⡈⠡⠊⠀⠃⠀⠀⠀⠈⠂⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠈⠐⠄⠂⡄⠀⠂⡬⠂⠀⠁⠐⠒⠒⠒⠒⠊⠉⠃⡀⠀⠀⠀⠀⠃
⠀⠐⠀⡀⠀⢁⠀⢊⠔⡠⢄⠐⠀⠠⠄⠀⠀⡠⡴⠄⡈⠀⠀⢠⠀⠀⠀⢀⠋⡀⢄⠀⢠⠆⠀⠀⠀⠀⢀⢀⠀⠸⣰⠀⢨⠙⠈
⠀⠀⠂⠒⠈⠀⠀⠘⡌⠃⠈⠀⢑⠀⡄⠄⠠⡀⠀⠀⠀⠀⡀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠪⠩⠉⢬⡇⠈⠀⠠⡀⠀⠀⠂
⠀⢀⠀⡒⠒⡋⢆⠀⠣⠠⠊⠀⠁⡐⠁⣀⠄⠀⠀⠀⡐⠀⠀⠻⠀⠈⠐⠂⠀⠀⢀⠤⠊⠁⠀⢀⠤⠀⠘⢲⠔⠁⠀⠰⣶⢂⠡⠄
⠀⠈⠀⠀⡄⠀⢈⠀⠀⠊⣉⠢⠀⠈⠁⠃⠃⠀⠢⠀⠀⢀⣀⠄⠀⠀⠀⠃⢀⠄⢃⠀⠀⠠⢀⠀⠀⢀⡠⠃⡆⠀⠀⠄⠋⠉
⠀⠀⠈⠀⠉⢀⠀⠀⠀⡈⠀⢠⠀⢀⠀⠀⠀⠀⢀⣀⣀⠉⢀⠀⠀⠀⠕⠀⢘⠠⠂⠉⠁⠉⠡⠊⠛⠩⠐⠊⠀⣐⠀⠀⠀⠀⢠
⠀⠀⠀⠄⠀⠀⠀⠀⢀⠰⠀⣀⠉⠂⢠⠔⢠⠸⡁⠀⡩⠆⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⡴⣲⠀⠔⠢⢠⠐⡆⠀⠀⠀⢀⣀⡀⠀⠁
⠀⠠⠴⠀⢁⠈⠀⠀⠀⠑⡃⠀⢀⣀⡀⠙⠉⠀⠥⠤⠧⠀⠠⠀⣀⠈⠂⠒⠃⠀⢀⠀⠈⠁⠀⠂⠁⠀⠘⠀⠀⡚⠃⠀⠀⠀⠑⢲
⠀⠀⡴⡺⠀⡼⠃⢀⣄⡀⢀⠄⠁⠀⢘⠀⠀⡠⠐⠀⣂⣄⠀⠀⠈⠀⢠⠄⠀⠀⠈⠠⠄⠂⣤⣴⣴⠀⠀⠀⠀⠱⡀⠀⠀⠀⡠⠋
⠀⠐⣇⠤⠑⠁⢠⠀⠀⠀⡁⠀⠀⡠⢊⡀⠈⢠⠊⠁⡀⠀⠂⠤⠤⠄⠊⠀⠠⠀⠁⢀⣀⡠⠂⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⢴
⠀⠀⠈⠐⠒⠂⠚⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠉⠁

⠀⠧⠀⠀⠀⡠⠒⠉⠀⠀⠁⠐⢀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡈⢡⠀⠰⠁⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧
⠀⠀⠀⠀⢈⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠓⠦⣤⣤⠴⠋⠀⠀⠄⠀⢀
⠀⢀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⢃⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢈⠦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⢀⠀⠀⠀⢸
⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⡀⠀⢀⠠
⠀⠀⠀⠀⢀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢂⡶⠛⠲⡄⣴⠚⠳⣆⢰⡗⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢧⣀⣰⠇⢷⣄⣠⠟⢸⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⡀⢀⡤⣄⢀⣀⠀⣠⢤⠀⣤⣄⢀⡤⡀⢠⢀⠀⣄⢠⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠞⠳⠸⢤⡤⠸⠣⠀⠧⡶⠆⠿⠇⠻⣤⠟⠸⡼⠀⠏⠾⠸⡦⠇

⠀⢀⣀⣀
⠀⠘⡔⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠄⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠠
⠀⡡⠂⠀⠑⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠑⠂⠤⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠀⠀⠀⡠⠀⡀⠀⠀⣀⠀⠀⠀⠲⢁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠔⠁⠀⠀⠀⠀⠉⠐⡄
⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⢀⣠⠴⠶⠦⣄⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣄⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢳⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠀⠀⠁⠀⠀⠀⡘⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⡀⠑⠄⢀⠀⠀⢀⠠⠞⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠲⡄⠀⠀⢰⡷⠂⠁⠀⠀⠀⠀⠀⠀⠚⠈⡀⠀⠀⠀⠀⠀⢰⠒⢦⣤⣤⡴⠖⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢠⠀⠀⠀⢀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠲⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡒⠀⢠⠀⠀⠀⡠⠘⢩⢃⠀⠀⠀⠀⠀⠄⠀⠈⠉⠂⠀⠀⠀⠀⠀⠔⠇⢘⢁⠀⠀⠘⠢⠰⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠘⠠⠸⠁⠀⠀⠱⠀⢐⠄⠀⠀⠀⠀⠀⢄⠀⠀⣁⠎⠀⠀⠀⠀⠠⢆⢨⡉⠡⠀⠀⠀⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠰⢦⣤⣤⡶⠂⠂⠀⠀⠀⠀⠉⡙⠃⠀⢠⠊⠀⡰⠀⠀⠀⠀⣠⣤⣄⠀⠀⠘⠣⣄⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠶⠛⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠰⠋⠀⠀⠀⠀⢼⠁⡠⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄⠀⠀⠀⠁⠈⠀⠀⢠⡀⢈⣶⠀⠈⠃⠒⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⢀⠇⠀⠐⠂⠀⠀⠀⠀⠀⢡⡸⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢀⣠⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠀⡟⠀⠀⠰⣵⣷⢿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠁⡀⠀⠀⠀⡂⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠆⠀⠀⠁⠴⠊⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣂⠀⠀⣠⠃⠀⠀⠀⢃⡀⢺⠀⠀⠈⠻⠷⠴⠞⠋⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⢡⠆⠩⠄⠀⠀⠀⠀⠀⠀⠀⠓⠂⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡠⠤⣀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⡆⢀⣲⢺⡿⣦⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⢶⡁⠀⠀⠀⡙⠆⠀⢀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣵⣿⣿⣿⠋⠀⠀⠠⣶⣶⡶⠀⠀⠙⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⢀⡠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⡤⠠⠤⠠⡀⠐⠴⣔⡶⠤⠴

⠀⠀⠀⠆⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⡠⠐⡠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⣄⡆⣦⡤⠼⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⠟⠁⠀⠠⢂⡘⡄⠀⡘⠀⠀⠀⢠⡖⠒⠒⠛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠘⠁⠀⠚⠀⠀⠀⠀⠈⠙⠖⠀⠀⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠐⡤⠀⠀⠸⠃⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠸⠀⠀⠀⠀⠀⠀⢀⣀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡐⠂⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⠀⠀⠙⠀⠀⠀⠀⠀⠀⡀⢤⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠸
⠀⠀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠓⢎⡩⣄⠀⠀⠑⢌⠀⢡⠀⠀⠠⠈⠂⠀⠀⠀⢀⠀⠘⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠘⠨⠗⡀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉

⢀⠄⠀⠋⠀⠁⠐⠀⠀⠀⠠⣴⡄⠐⡤⣧⠄⠀⠀⠀⠀⠀⣄
⠀⠀⠔⠋⠽⣟⠐⠀⠀⠀⠀⠍⠉⢰⠛⠧⠀⠀⠀⢀⠄⠈⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⢀
⠀⠀⠀⠈⢰⠁⠀⠀⠀⠀⠀⢰⠀⠰⢀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠠⡐⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠈⠚⢻⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢂⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡀⠀⠀⠀⢀⢖⠃⠒⠒⢤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⣄
⠀⠈⠀⡀⣠⠤⠤⣀⡄⠀⠀⠀⠄⠠⡂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢣⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠠⠁⢠⠀⢰⠀⠠
⠀⠃⠀⠀⠀⠀⠀⠐⠀⠀⠀⠣⢀⡐⠀⠂⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠐⠈⠀⠀⠀⠈⠂

⢀⣀
⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⣴⣦⡄
⠀⠀⡀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡿⠟⠁⠀⠀⢀
⠀⠀⡇⠀⡆⠀⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢳⡄
⠀⠀⠃⠀⡇⠀⠁⠀⢠⠦⠤⠤⠤⠤⠤⠤⠤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⡀⠀⠀⠀⠀⠂⠀⠠⢉⠁
⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠤⢄⣔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠄⣀⡴⢶
⠀⠀⠀⠀⠀⠈⠀⠀⠸⠃⠒⠓⠚⠂⠀⠀⠀⠀⠀⠀⢐⠣⢰⡁⠀⠀⠀⠀⠀⠀⢀⣤⠒⠘⠃⠰⠉⣁⡼⠶⠒⢁⢅⡴⡋
⠀⣴⣢⣴⡀⠀⣤⣲⣼⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢚⢀⡒⠈⡓⠀⠀⠀⠀⢀⠊⣶⣄⡤⣚⡛⠋⢀⣆⡄⣤⣚⣡⢼⠏
⠘⠠⠴⠓⠐⠒⠀⠒⠋⠒⠒⠂⡬⠄⠃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠳⣌⠛⠻⠴⣇⣼⡥⠖⣪⠯⠥⠚⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠬⢤⣬⣭⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠀⠀⢀⣴⢶⣀⡔⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⡸⢁
⠀⠀⠀⢹⡟⠁⡄⢁⠀⠉⠑⡄⠀⠀⠀⠀⠀⣀⠀⢰⡦⣴⣉⡉⡳⠛⡅⠀⢀⡀⠀⠀⠀⠀⠀⡼⠙⠓⠚⠃⢆
⠀⠀⠀⢾⣓⣒⣒⣲⣖⣓⣒⣷⠆⠀⠀⠘⣁⢹⡽⣛⡛⠀⠀⢈⢷⠱⠟⣾⣞⡐⠀⠀⠀⠀⠀⢧⢤⠤⠤⢤⡿
⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢰⣹⣕⣸⡫⢓⢲⣬⢵⡛⠊⢑⣥⢟⡇⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠁
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⡟⠮⣍⣉⣙⣄⠁⠀⣩⣟⣫⠴⣺⠃⠀⠀⠀⠀⠀⠀⡅⠀⠀⣀
⠀⠀⠀⠀⠙⣶⠤⠴⠤⢶⠏⠀⠀⠀⠀⠀⠈⠲⢤⣌⣉⣙⢦⡴⣋⣩⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠤⠇
⠀⠀⡠⠖⡍⠙⠉⣻⣷⠏⣠⡻⣋⣵⠀⠀⠀⠀⠀⠉⠓⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⠁⣠⣓⣶⠟⠉⡄⣬⠉⠐⡏⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠚⠓⠢⡀
⠀⣿⡜⡻⣯⣏⠀⢮⣀⡨⠀⢠⣿⠀⠀⠀⠀⠀⠀⡞⡞⠲⠖⠒⢺⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢙
⠀⣟⠮⣿⣷⣮⣶⣶⣶⣶⣿⠿⢻⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⡸⢸⠀⠀⠀⢀⡀⡔⢉⡉⠉⠉⠉⠉⠉⠉⠙⠁⠈⢣⡀
⠀⠙⣷⠤⣀⣉⡉⠉⠉⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠑⠤⢽⣶⡯⠤⠊⠀⠀⠀⠀⠁⢂⢰⣿⣶⡦⠀⠀⠀⠀⢀⡅⠀⠐
⠀⠀⠈⠙⠲⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣤⣷⠄⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠦⠤⠤⠤⠤⠤⠤⠖⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⢠⡌⠀⠀⠀⠀⠀⣾⠶⡀⠴⢄⠠⠐⡆
⠀⢀⡈⣿⠀⠀⠀⢨⡙⡐⢈⠰⠚⣶⠖⢲⠁
⠀⠀⠐⠘⡾⢱⢄⠃⠅⢐⠨⠀⢁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢋⢉⠤⢝⢤⡛⠀⠈⡀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⠄
⠀⠀⠀⠈⣻⡣⣋⠓⢠⣈⣲⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠂⠀⢀
⠀⠀⠀⠘⠂⢈⠖⠨⠌⠀⠾⢀⠄⠓⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠐⠒⠂⠒⠀⠇⠘⡀⠀⡐⠃⠤⢀
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣤⡀⠁⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠠⢀⣁⠀⠀⡐⠀⡜⠀⠀⡷⠎⡀⠀⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⡀⠀⢠⣾⡟⢨⢤⣴⠎⠀⠀⠀⢠⠆⠀⠀⡔⠔⡀⢀⠊⡄⢀⡜⠀⠈⠀⠀⠀⠁⠀⠈⢃⠠⠊⠀⠀⡀
⠀⠀⣘⣖⠒⠦⠙⡒⢿⡟⣑⠭⣄⣀⡀⠀⠒⠁⠈⠄⠀⠢⠐⠀⢀⠎⠀⠊⠀⣀⡠⠄⠀⠀⠀⠀⢠⠂⠀⠀⠀⠔⠑
⠀⠌⠀⠈⠀⠈⠀⠬⠰⠎⠄⠀⠀⠀⠈⠢⡠⠄⠀⠘⡞⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠄
⠈⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠖⠁⣤⠶⠛⠉⠀⠐⠒⠂⠉⠀⠒⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠠
⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⡀⠀⢀⠙⢉⠉⠥⠀⠀⠀⠀⠔⠂⠄⠀⠀⡤⠆⠐⠄⢀⠔⠀⠄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⠉⠉⣚⡁⠀⠃⠀⠀⠁⠐⠀⣀⠀⠀⢀⠀⣀⠄⠀⠀⠀⠁
⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠁⠀⠀⠀⠀⢈⡄⠀⠠⠐⠀⠀⠑⠀⠂
⣶⣶⠶⠶⠶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣒⠋⠭⠒⢂⣈⡠⢤⠄⣀⣀⣀⡤⣤⢤⠄⣀⡀⠉⠉⠛⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢞⣫⡴⠞⠋⠁⣀⠔⣩⣤⠆⣹⢭⣋⡿⢶⣻⣷⣶⣧⣏⠉⠛⠏⡏⠛⡿⡖⣶⣄⠉⢷⣦⣀
⠀⠀⠀⠀⠀⣠⣟⠵⠛⢛⣇⣤⡦⣚⣕⣺⢏⣖⡺⠗⠻⣞⣫⠯⣗⣻⡖⢮⡿⣦⣤⣀⣄⣀⣠⣆⣋⠟⢻⡗⣜⢿⡷⡄
⠀⠀⠀⠀⢠⣿⡏⢀⡰⢯⣿⣤⢙⣖⣩⣿⠿⣿⡾⠿⣷⣿⣻⠿⣟⡼⠿⢏⣸⠯⠘⣿⣿⣿⣶⣒⣻⣍⡽⢫⢸⠘⢉⣧
⠀⠀⠀⠀⢸⡿⣷⢬⡳⣯⣽⡯⣟⠛⢷⡾⣷⠿⣶⡏⡼⢿⣭⡿⢭⣿⣳⣿⣤⠞⠋⠒⣿⡔⣫⠿⠭⣯⣵⣾⣗⡷⣺⣿
⠀⠀⠀⠀⠀⣿⠘⠳⢿⣗⡺⠭⠟⡕⣲⣶⠒⣫⣝⣺⣳⣿⣿⣿⣷⣿⣽⣿⣯⣀⠶⣎⡹⣟⣓⣶⢿⣿⣯⣽⣿⡟⢱⡇
⠀⠀⠀⠀⠀⢸⡆⠀⡈⠀⡏⢛⡲⠤⣝⣚⣣⣏⣸⣟⣿⣙⣍⡁⠻⡩⢟⣿⣞⣯⣶⣾⣼⣷⣾⣿⡿⠿⡟⠋⣧⠇⣾⠃
⠀⠀⠀⠀⠀⠀⢿⠀⢇⠀⠀⠈⠭⣓⣒⠢⠭⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⢋⠩⠭⠁⠀⠀⠈⠁⢸⠋⣸⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⢚⣩⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣤⣤⣤⡤⠤⠴⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣤⡶⠾⠛⠛⠉⠉⠉⠙⠛⠛⠷⢶⣤⣄⡀⠀⠀⠈⠲⣄
⠀⠀⢠⢀⡄⣠⣠⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⣾⣟⠥⠒⠈⠉⠁⠒⢤⡀⡰⠉⠉⠓⣄⠀⠉⠻⢷⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⣾⣿⣿⢻⡇⠀⠀⠀⢠⠊⠀⠀⢀⣾⢫⠊⠀⠀⠀⠀⠪⠕⠘⠓⢹⣧⠀⠀⠀⢨⠗⠲⣦⡴⠋⠙⣆⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠑⡄
⠀⠀⢸⣧⣿⣿⣾⡇⠀⠀⢠⠃⠀⠀⣰⡟⡱⠁⠀⠀⠀⠀⠰⠆⠀⠆⢰⡆⡟⠀⠀⠀⠈⢦⣁⣎⣣⣌⣰⠽⣷⡄⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠸⡀
⠀⠀⠘⣿⢿⠿⣿⠃⠀⢀⠃⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡲⠀⢀⠃⠀⣀⡀⣀⠀⣃⠤⠈⣧⠶⣀⣠⢿⡄⠀⠀⠱⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠈⢲⡖⠁⠀⠀⡎⠀⠀⢀⡿⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡉⢡⣒⡄⢍⠙⠶⡴⣿⡯⠟⠀⠀⢿⡄⠀⠀⠇⠀⠀⢸⠀⠀⡸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡳⠞⢔⡣⠈⠒⢁⠼⢄⣩⠧⠀⢀⡀⠘⣷⠀⠀⢸⠀⠀⢸⢀⠜
⠀⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠃⢞⡆⣀⡰⠽⠃⠀⠀⠀⠀⠀⠀⠘⡄⣿⡀⠀⠈⠀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⢿⢀⠎⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢔⡲⠣⠗⠭⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⡇⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢸⢰⠀⠀⠀⡇⠀⠀⡼⠋⠀⠀⠀⠀⢠⠔⠉⠀⠀⡴⠒⠲⢤⡀⠪⢵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⢸⠀⠀⢈⣿
⠀⠀⠀⠀⢸⢸⠀⠀⠀⢡⠀⠀⠑⣾⣄⣀⡀⢠⠃⢠⣊⠉⢆⠙⢅⠠⠀⠛⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡟⠀⠀⡆⠀⠀⠸⢨
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢇⢰⠒⠛⠀⡇⠈⠁⠀⡆⠀⠐⡎⣰⠫⢿⠒⠛⢁⢴⠦⢕⠢⢤⡀⠀⠀⠀⠀⢀⠞⢠⡿⠀⠀⡸⠀⠀⠀⡆⢸
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠈⢎⠒⠢⣀⣼⡀⠀⠀⣇⠄⢸⠃⡌⠀⠬⡆⠀⢂⢏⠔⣹⡤⡖⠸⡂⠤⠤⠔⠉⣰⡟⠁⠀⡰⠁⠀⠀⠀⡇⢸
⠀⠄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠣⡀⠀⠈⢿⣦⡀⠈⠋⠁⠀⠹⡀⣴⠀⢀⡤⠹⢏⠐⡤⠬⡷⡝⠀⠀⣠⡾⠋⠀⢀⠔⠁⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠁⠀⢺⡈⢆⣲⠇⠈⠑⢉⣠⣴⠟⠋⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠂⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣑⣶⣥⣴⠶⠞⠛⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡤⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⠙⣦⠀⠀⠀⢠⡾⠁⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢸⡇⠀⣠⠏⠀⠀⡀⠀⢙⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⠀⣠⠏⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡄⢿⡇⢷⡏⠼⠤⠦⠤⢤⣄⣀⢄⡀⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠀⠀⠷⡘⢧⣺⡔⢀⠀⠀⠠⠤⠀⠈⢁⡴⠻⢷⡤⡀
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⢈⢷⣿⣧⠠⠀⠀⠁⡀⠀⢠⡞⠡⠀⠀⠈⠢⠢
⠀⠀⠀⠀⠀⠀⢢⡀⢄⠀⠀⠁⠐⠀⠀⠉⠀⠀⠙⠛⠓⠈⠀⠐⠠⠈⠚⡀⠀⠀⡀⢁⢠⠞
⠀⠀⠀⠀⠀⠀⠈⢯⠓⠲⠤⣤⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣈⣁⡠⠴⠚⡟
⠀⠀⠀⠀⠀⠀⣀⡈⢧⠀⠀⠀⠀⠉⠉⠉⠙⠓⠓⠒⠒⠒⠒⠚⠉⠉⠉⠉⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⢮⡉⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⣘⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⣀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠭⣙⠛⠓⠦⠤⠤⠤⣤⣤⠤⠤⠤⠶⠶⢛⣻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠤⠔⠒⠒⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⠀⠀⠾⠂⠀⠀⠀⠛⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢀⡀⠀⢀⢄⣀⠀⠀⢧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣻⣿⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣣⡙⠃⠀⠀⢰⠀⠘⠲⠼⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⣧⠀⠀⠈⠙⠦⣀⣀⣀⣀⠴⠀⠀⡟⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⣀⠉⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣸⣯⢳
⠀⠀⠀⠀⠀⠀⠀⡴⠯⣀⣨⠟⠃⡏⠙⢦⣄⣀⡈⢀⣓⣃⡤⢾⣅⠀⠀⠀⠁⣽⢛⠿⣀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢉⣀⡂⠇⠀⠀⣼⠋⡏⠉⢫⠀⠱⠸⣏⢦⡀⠀⠘⣌⠷⢂⣩⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠯⢻⢩⢉⡟⣧⢀⣼⠃⠀⠃⠀⠘⡀⣄⢤⡹⣆⡛⣤⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢰⡇⡇⠘⢸⢸⡇⡎⢹⡃⠀⠀⢞⢢⣠⠁⠟⢌⡇⠙⢟⠁⠀⡸⠀⡇
⠀⠀⠀⠀⠀⢠⡏⡇⣧⠀⢸⢸⡇⠃⣨⡧⠀⢠⠈⡇⠁⠀⢀⣘⡵⠁⠈⡇⢠⠃⠀⢹
⠀⠀⠀⠀⠀⣸⡃⡇⢹⣧⢐⣨⡷⠟⢫⡀⠀⣸⣅⡇⢠⠞⠉⣡⣤⣤⡼⠱⡾⠀⠀⡼
⠀⠀⠀⠀⠀⣿⡇⡇⠀⢹⠻⣿⡄⠀⠀⣿⡛⢫⠟⢠⢻⢳⢻⣽⠀⠳⣄⢀⡠⠄⠰⠳⢤⡄⡀
⠀⠀⠀⠀⠀⣿⠁⠇⠈⢸⢀⠀⢷⡄⠀⠘⠷⠋⠀⣾⢸⢸⣹⡇⠀⠀⢠⠋⠐⠒⠀⣀⣠⠤⠈⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣿⠷⢿⣦⣼⣬⣀⣆⣻⣄⠀⠀⠀⣸⣃⣸⣴⣿⣡⣤⣶⠾⡎⠁⠐⠁⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠙⠛⢧⣀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠤⠤⠤⠔⠚⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠴⠶⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⣆⠉⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⣼⣿⣀⡀⠀⠀⠈⢷⡀⢿⢀⣩⣿⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⢦⡀⠀⠀⢳⣾⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡿⢫⣉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠶⠿⠿⠛⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⣉⣠⣤⣴⣶⠶⠶⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⠿⢋⣠⣴⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢶⠾⠿⠿⠶⣶⣦⣤⣤⣤⡾⠟⣁⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⣧⣂⠀⠂⠀⠀⠀⣀⣨⡿⠉⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣈⠉⠙⠛⠛⠛⢉⣉⣡⣴⡾⠟⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠉⠛⠛⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⡿
⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⣿⡏⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⢹⣧⠛⠋⠀⠛⠃⠈⠛⠁⠘⠛⠁⠘⠛⠛⠘⠛⠃⠘⠛⠃⠘⠛⠀⠛⠛⠃⠘⠛⠃⠘⠛⠃⠐⠓⠒⠒⣸⡟
⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣴⡞⠉⠹⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⢑⠙⠒⢤⡀⠀⢰⡏⡞⠀⠀⠀⢀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠃⠀⠀⠘⠀⠀⠈⢳⡆⣿⣼⠇⠀⠀⠀⠀⠂⠀⠱⡄⠤⣤⡤⠤⠄⣀⣀⡀
⠀⠀⢀⣀⠤⠐⠒⠂⠉⠁⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠘⣾⡿⣼⠀⠀⠀⠇⠀⢈⠀⠀⢣⠴⠃⠙⣖⢄⠀⠀⠈⠉⠐⠒⠢⠤⣀⡀
⠔⠊⠁⠀⠀⢀⣀⣀⠀⣤⣤⢼⡀⣤⠮⡤⠤⠤⠤⠄⠤⢼⣳⣿⠀⠀⠊⠀⠀⠘⠀⠐⢹⠀⢀⡠⠜⠋⠉⠉⠈⠉⠉⠒⢄⡀⠀⠈⠙⠢⢄
⠴⠖⠒⠈⠉⣀⠠⠤⣴⠁⠈⢉⣿⠃⠀⠈⢦⠀⠀⠈⡆⠀⠙⣿⠀⠀⠀⢀⠀⡐⠀⢀⣸⢎⣁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⠉⠒⠒⠤⠄
⢰⡤⣀⡔⠉⠀⠀⠀⠈⢻⣦⣼⣿⠀⠀⠀⠀⢣⡀⣤⠃⠀⢀⢏⠀⠀⠀⠀⡐⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⢠⠀⡠⠞⢠⣤⣀⣀
⠈⠈⢱⠁⠀⠀⠀⠀⠀⠀⠱⡽⣷⠀⠄⠂⢁⡠⠟⠈⠢⢤⣪⠤⠥⠤⣤⣊⠀⣼⣏⠀⠀⠀⠀⠀⠀⡀⠀⠈⠂⡠⠚⠙⣶⣪⣍⡥⢶⠏⠉
⠀⠀⣶⠄⡀⠀⠀⠀⠀⠀⠀⠹⣼⡄⢀⡔⠁⠀⠠⡀⠠⠀⠈⠢⡀⠀⠐⠉⢉⡿⠁⠁⠀⠀⣀⣤⣾⠶⠶⢶⣶⣥⡔⠚⠉⠁⠀⠀⣾⡄
⠀⠀⢸⡆⠈⠀⠀⠁⠀⠀⠀⠀⠹⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⠸⡇⠀⠀⢠⢞⡕⠋⢀⠀⠀⠀⠀⠉⠳⠤⣤⠘⠀⢀⣿⢸
⢷⡀⠘⡇⠀⠀⠀⠈⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢿⠒⠒⢦⡀⢀⣴⣯⡏⠀⠀⠀⠑⠀⠀⠀⠀⠀⢠⠇⠀⠀⡼⣸⣼⠤
⠒⠬⣁⡛⠠⠄⣀⡀⠀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢰⠀⠀⠀⠘⢾⣱⠇⠈⠀⠀⠀⠀⠀⠀⠀⠄⣀⣎⣀⠤⠜⣛⠥⠔⠊
⠀⠀⠀⠈⠉⠐⠂⠬⠍⣁⣒⡒⠤⠤⠇⣄⣀⣒⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡃⡀⢀⣀⡈⣀⠠⠤⣄⣒⡀⠭⠕⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠂⠀⠸⠏⠉⠉⠥⠠⠌⠁⠉⠉⠿⠛⠁⠙⠒⠒⠂⠈⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠉⠑⠒⠀⠤⠤⠄⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠔⠂⠉⢠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠒⠒⠂⠒⠲⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠒⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⢀⠎
⠙⣤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊
⠀⠈⠢⡀⠉⠁⠒⠂⠄⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠐⠂⢉⠜⠁
⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠂⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠂⠈⠉⠉⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⠤⣤⠤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣠⡤⠄⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⢤⣤⢤⣤⣤⣤⣤⣠⢤⡤⠶⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⡀⠠⠀⠜⠠⠆⢒⡀⠀⠀⠀⠀⠀⠀⠘⠀⢘⡆
⠀⠀⠀⠠⠀⠁⢲⠢⡠⢨⠀⡦⠀⠀⠀⠀⠄⣤⣤⠞⢷⣴⣦⡤⣄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡔⠃
⠀⠀⠀⠆⣹⠀⣠⡀⣁⢏⢐⢃⠀⠀⠆⠀⠀⠈⠀⠀⠀⠁⠀⢿⣶⣤⠀⠀⠉⠂⠒⠄⠄⠄⠤⠄⠊⠉⠀⠀⠀⠑⠠⡤⢤⡄⠐
⠀⠀⠀⠀⠀⢀⡘⣥⣄⡐⠋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⢤⡍⣹⠉⡓⠐⠒⠐⣆⣹⠏
⠀⠀⠀⠈⠐⠌⡃⠉⠈⠠⠰⠀⠀⠀⣄⠀⠀⡀⠀⠀⠀⠀⣰⣷⣿⡏⠀⠀⠀⠉⠙⠓⠻⠒⠛⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⡀⣷⡀⠀⠀⣰⣿⣿⣿⠃⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣷⣷⣻⣿⣿⣿⠏⠀⠀⠀⠆⠀⠙⠉⣃⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⡤⠒⢲⣦⡀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢤⣄⣄⡼⠀⠀⡜⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢠⠃⠀⠀⢹⡇⠀⠀⠀⠀⢠⣨⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠤⣾⠁⠀⠀⠈⠣⣤⣄⣠⣤⣼⡿⠃
⠀⠀⠀⠀⠘⡀⠀⠀⣾⠃⠀⠀⠀⠀⠘⠽⠀⠀⠀⠀⠀⢿⣿⣶⣿⡿⢃⡾⠀⠀⠀⠀⠀⢀⣼⠂⠀⠀⠀⠀⠈⠉⠋⠉⠁
⠀⠀⠀⠀⠀⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠥⠭⠖⠋⠁⠀⠀⠰⠂⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀
⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⢰⣀⠀⠀⠀⠀⠈⠀⢀⡿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠐⣨⡷
⠀⠀⠀⠀⠀⠘⠆⢠⡇⠀⠀⠠⣦⡀⢸⡀⣠⣾⡾⠀⡠⠀⢳⣟⣦⣿⣶⣶⣄⠀⠀⡆⢰⡇⠀⠀⠙⢷⣄⡀⠀⠀⢀⣤⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠁⢸⠁⠀⠀⠀⠈⠉⠙⠙⠋⠁⠀⠰⠉⠁⠙⢋⠎⠀⠀⠘⢻⣇⠀⠁⠘⣧⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠃⠀⠀⠀⣀⣤⠀⠀⠣⣄⠀⠀⠀⣠⣤⣴⡿⠃⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⣀⣤⡴⠋⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣠⣀⣀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣄⡀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⣷⠺⡏⢱⠄⠀⢈⠁
⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣻⣿⠀⠀⠘⠀⠀⠀⠀⠀⠘⠂⠀⠀⠁⠘⠁⠈⠁
⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⠿⠿⠯⠁⠀⠀⠈⠛⠶⠦⠤⠤⠤⠤⠴⠿⠶⠾⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠚⢛⣉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⣄⡀⠀⠀⢀⣠⠴⢚⣋⣭⠤⠶⠖⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡛⢭⢼⠖⠗⢋⢻⡶⠞⣫⡵⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠾⡖⠂⣍⣨⠷⢊⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣞⣉⣭⣥⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⠶⠶⠦⠤⠤⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠫⢅⡶⠬⠖⡀⠵⢠⡤⢈⡓⠦⠄⣉⣙⠓⠲⢤⣄
⠀⠀⠀⠀⠀⢀⣠⢞⠚⠣⡼⢑⣩⣄⢘⡀⠱⡶⠀⠆⡈⢁⡤⠤⡄⠨⢙⠊⢂⡉⡳⣆⡀
⠀⠀⢰⡶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⠓⠒⠒⠶⠶⠶⠶⠾⠿⢶⡆
⠀⠀⠀⠻⣔⠂⠒⠀⠒⠀⠂⠐⠂⠒⠂⠒⠀⠐⠀⠒⠀⠒⠂⠒⠀⠒⠂⠒⠀⠒⠐⠂⢒⡾⠁
⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⡤⠶⠶⠶⠤⣀⠀⠀⠀⠀⢀⣀⣼⣁⡀⠀⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀⣀⠤⣶⣆⣷⠯⡳⡄
⠀⠀⠠⣏⣀⣀⣀⣀⣀⣸⡆⠀⠀⠀⣟⣓⣛⣛⣻⠆⠀⠀⠀⢠⡗⠺⡆⠀⠀⠀⡼⣱⣋⢩⣿⣿⢿⣻⡁
⠀⠀⠀⣗⣒⣒⣒⣒⣒⣺⡇⠀⠀⠀⢸⡀⠀⠀⡏⠀⠀⠀⠀⢸⣉⡆⡗⠀⠀⠀⡇⡏⢳⠻⠖⣫⣍⡇⡇
⠀⠀⠀⠻⠽⢦⡀⡠⠯⠝⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⠀⠳⡙⢟⣣⣴⣭⢞⡜
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠁⠀⠀⠀⠀⠸⠶⠶⠇⠀⠀⠀⠀⠈⠓⠒⠒⠚⠉
⠀⠀⠀⣠⡴⣾⢳⢦⣄⠀⠀⠀⠀⠀⠀⢰⣰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⢤
⠀⠀⠰⡗⠷⠾⠾⠾⠚⡇⠀⠀⠀⠀⡤⠬⠭⠥⣄⣀⠀⠀⠀⡴⠋⠅⠀⠈⠑⢦⠀⠀⠀⠀⡞⠁⠀⠈⣻⠃
⠀⠀⠀⣇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣇⠀⠀⠀⣯⡼⠀⠀⠀⠹⡍⢻⠉⣿⢩⠏⠀⠀⠀⡸⢦⣂⣠⠖⠁
⠀⠀⠀⢸⣀⣀⣀⣀⡞⠀⠀⠀⢰⣒⠛⠒⡒⠚⢓⣲⠆⠀⠀⠀⢣⣸⣀⣇⡞⠀⠀⠰⣏⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣚⣲⡄
⠀⠀⠀⢀⡤⠴⠊⢧⡀⠀⠀⠀⢀⡤⠤⡤⠤⣤⠤⠤⡀⠀⠀⠀⠀⠀⠀⢀⣾⣙⡄⠀⠀⣾⣤⣼⣷⣼⡆
⠀⠀⠀⣞⣉⣉⣉⣉⣳⠀⠀⢀⣯⣤⣤⣥⣀⣈⣤⣤⣽⡀⠀⠀⠀⠀⡠⠻⣄⠈⡷⠀⠀⠘⣧⠴⢊⡽
⠀⠀⠀⢻⠈⡇⢸⠁⡾⠀⠀⠸⡯⣕⣻⣿⣉⣾⣿⣪⢽⠇⠀⢀⣠⡚⠳⡄⠀⢙⠇⠀⠀⠀⢹⣊⣽⠃
⠀⠀⠀⠈⣇⣧⣸⣰⠃⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠉⠉⠀⠀⠙⠦⠷⣤⠼⠒⠋⠀⠀⠀⠀⠈⢧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⣏⣯⣙⣇⠀⠀⢀⠜⡙⢄⡔⡙⢆⠀⠀⠀⢻⠛⡟⢴⣉⡦⠀⠀⠀⠀⠀⣠⣯⢯⠟⠲⡄
⠀⠀⠀⢀⡴⠋⠀⣿⠬⣿⠟⠀⠀⣾⢀⡟⠈⡇⡝⠈⡇⠀⠀⣸⠀⣧⠞⠀⠳⡄⠀⢀⡤⣞⣵⡷⠋⠀⢠⠇
⠀⠀⢰⡋⠀⢀⠔⢁⠔⠁⠀⠀⠀⠘⢌⢃⡼⢇⢃⡜⠁⠀⢰⠃⠀⢸⠀⠀⠀⡇⠀⠸⣯⠗⠉⠀⢀⡴⠃
⠀⠀⠀⠙⢶⣁⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠸⣅⣀⣸⣄⣀⣠⡇⠀⠀⠈⠢⠤⠖⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣄⣀⡀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⣋⣉⣡⡤⠤⠶⠖⠒⠒⠒⠛⠛⠛⠒⠒⠒⠶⠦⢤⣈⡉⠛⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⣉⡤⠶⠚⠋⢉⣀⣠⡤⠤⠶⠶⠖⠒⠒⠒⠚⠛⠛⠛⠉⠉⠙⠛⠛⠿⣷⡄⠀⠹⡄
⠀⠀⠀⠀⣠⠞⠉⣠⠶⠋⠁⢀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡿
⠀⠀⠀⡼⠁⢀⡞⠁⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⢀⡼⠃
⠀⠀⢸⡇⠀⠘⣇⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⣀⡴⠋
⠀⠀⠀⠳⣄⠀⠈⠛⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠶⠒⠋⠉⠀⣀⣠⡴⠚⠁
⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⠀⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣤⠤⠶⠚⠋⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣄⣀⣀⣀⣤⣤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠾⠛⢛⣋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢟⡛⢛⡯⡽⣧⣄⣀⣤⣴⠶⢟⣛⣋⣭⣥⡷⠾⠟⠛⢛⣉⣉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠋⣧⠅⠺⣥⢙⡈⢿⣿⠷⠾⣛⣛⣩⣭⣤⡶⠶⣾⣿⣛⣫⣭⣭⡽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠊⣥⠤⠅⣲⣀⣩⡥⠾⢿⣛⣛⣯⣭⣽⠶⠶⠟⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣴⣯⣭⡿⠷⠞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣼⡟⠛⠿⠛⠉⢁⠙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠾⠛⣋⡭⢀⠈⠋⣤⡤⠘⠃⠉⣠⡙⠷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⡶⠿⢋⣀⡴⠎⡉⢀⡘⠁⠐⠒⠢⣈⣋⡀⠐⠷⣤⡜⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣿⠆⢉⡤⠿⢉⠀⠛⣀⣥⠀⠻⠿⠋⢙⣉⠉⠷⢤⡃⠈⢛⣀⠈⠻⠶⣦⡀
⠀⠀⠀⠀⣀⣀⣾⣏⣁⣊⣁⣀⣈⣉⣥⣤⣬⣥⣤⣈⣳⣦⣬⣥⣤⣤⣤⣤⣄⣀⣀⣀⣈⣃⣹⣷⣀⣀
⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣀⣤⠀⢀⣀⠀⣀⡀⢀⣀⠀⣀⡀⢀⣀⡀⢀⣀⠀⢀⠀⠀⢀⡀⠀⢀⣀⠀⢀⣀⢀⣀⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠀⠈⠉⠀⠈⠉⠀⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⢀⣀⡀⡀⠙⠁⠀⠄⣀⠀⠀⠀⠀⢸⡁⣧⠘⢆⠀⠀⠮⠀⠀⠀⠀⠀⣤⣿⣮⡟⠀⠀⠀⠀⢀⣠⣄
⠀⠈⠉⠁⠘⠋⠃⠀⠐⠒⠒⠋⠀⠀⠈⣗⠈⣀⠜⠀⠀⠐⠒⢀⠀⠀⠘⠾⣽⠟⠀⠀⠀⠀⠀⠸⠧⠟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉
⠀⠀⢚⠉⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡰⡖⠃⡄⠀⠘⠛⠿⠟⠃⠀⠀⢂⡁⠂⢤⠀⠀⠰⢷⣾⠿⠄
⠀⠀⠀⢰⠄⠀⠀⢠⠐⠐⢃⠀⠀⠀⢀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠠⠄⠰⠋⠐⣂⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⣈⠁⢲⠄⡀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠉⢳⡄
⠀⠀⠀⠠⣦⡤⠀⠰⠁⠀⠀⠀⠺⠀⠈⠁⠀⠀⠀⠀⢠⣀⣀⣤⡄⠀⠀⠙⢀⣀⠀⠀⠀⠀⠀⠀⠒⠉⠁
⠀⠀⠀⠈⠛⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠈
⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⢠⠐⣀⡤⠀⠀⠀⡀⢠⠀⠀⢀⣤⣤⣤⢀
⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⡀⠀⣄⡸⠀⠠⠤⠤⠂⠁⠀⠠⠄⠄⢀⡀⠀⠀⠐⠄⠁⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠐⠒⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⡀⣂⢠⡀
⠀⠀⠀⠀⠀⠒⠁⠀⠈⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠿⠜
⠀⠀⠀⠓⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⡀⢠⡆⠀⠀⠀⠀⣀⠀⠀⣀
⠀⢤⣤⣀⣠⡤⠀⠐⠿⣵⣦⠽⠀⠀⠀⠊⠂⠀⠀⠀⠉⠁⠀⠉⠁⠀⠰⢁⢶⠶⣔⠢⡀⠾⢏⡹
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉
⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠰⡆
⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠀⠘⢻⡉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⣀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠟⠄⠀⠀⠀⠀⢦⣤⡤⠟⠁
⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⣠⡆⠀⠠⠄⠄⠒⠈⠀⠀⣀⣷⣌⡓⠀⠀⠀⢀⠀⢢⡀⠀⠀⠀⠀⠛⠃⠀⠀⢀⡤⡤⢠⠄
⠀⠀⠂⠘⠀⠐⠀⠀⢀⣀⠀⠀⠀⠠⠝⠹⠈⠗⠀⠀⢐⡘⢑⡋⠀⠀⠘⠛⣤⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠒⠂
⠀⠀⠆⣀⡀⠀⠀⢀⠀⠉⡄⠀⠀⢀⣠⡴⠶⠂⠀⠀⠄⠂⡀⠒⠀⠀⠀⠒⠒⠂⠤⠀⠀⠘⢃⠀⢴⢂⡄
⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢀⠀⠿⠁⠀⢀⣶⠤⠼⠦⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣧⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠿⠿⠟⠛⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠛⠻⠿⠿⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡠⢖⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⡲⢄
⠀⠀⠀⠀⡎⡔⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡴⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠈⢢⢳
⠀⠀⠀⠀⢇⠘⠦⣀⣤⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⢦⣄⠴⠃⡸
⠀⠀⠀⠀⠈⠳⢄⣀⠉⠒⠢⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⠉⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠈⢏⠉⠓⠒⠤⠤⠤⣄⣉⣉⣉⠙⠓⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠚⢉⣉⣉⣉⣠⠤⠤⠤⠒⠚⠉⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣤⠤⠤⠤⠤⠒⠒⠋⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⢀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⡀⣤⠀⢀⣤⠠⢆⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠔⠀⣀⠠⣤⣤⢝⣠⣮⠐⣣⣰⣆⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⢀⣠⣤⠾⠀⠐⠒⠃⠉⠁⣀⡀⣠⣤⡤⡶⣎⣩⡴⣀⠀⠀⠀⠐⠲⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠠⠖⠋⠉⣀⡤⡤⣴⣶⣶⢿⠿⠟⠻⠍⠃⠴⢲⣄⠁⣉⡉⢂⠲⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠂⠀⣀⣤⠔⠚⠋⠅⠒⠂⠉⠁⠈⠨⡷⡤⡄⠀⠐⠂⡔⢈⠭⠀⠈⣯⠀⠁⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠐⠞⢱⡆⠀⠀⠀⠂⠈⢿⣷⣀⣤⣤⢠⠀⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠐⢉⣠⡖⢕⡊⢎⡑⠎⠰⡌⢛⠒⠋⢀⡀⠀⠀⠀⠀⠐⠀⠂⠠⠀⠀⢁⠤⠀⠈⠅⠄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⠖⠁⠀⠒⠉⠃⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠛⠏⠿⠉⢿⠛⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠯⡁⠀⠁⠀⠃⠔⠄⠜⠡⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠋⠰⠠⠋⠔⠂⡰⢣⠠⣿⣿
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣧⡨⢀⠐⠃⢠⡚⡉⠻⠔⠠⢈⡖⣤⣿
⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠈⡈⠠⠂⣀⠢⡤⠃⠀⠺⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣦⡀⢀⠀⠌⠨⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣿⣶⣷⣾⣿⡿⠟⠁⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡧⡃⡆⣴⠂⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠶⠴⠾⠏⢈⡍⠁⠈⣭⢁⣗⠺⠦⢆⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠮⠟⠀⢀⠀⢴⠀⣘⣋⡾⠐⠀⠀⠉⣀⣀⢀⣌⠓⠲⠦⢤⡀
⠀⠀⠀⠀⡤⢚⣡⡟⠋⠛⢠⠀⠀⠑⠛⠀⡠⠁⠀⢠⢤⡠⠞⠃⢀⣌⠈⠋⠈⢆⣀⡀⠙⢷⡢⡀
⠀⠀⢀⡎⣰⠟⠋⠁⠀⢈⡼⠃⡀⠘⠂⢂⣺⢆⢤⠦⠀⠀⢀⣤⠀⠉⠀⢠⣄⠀⣈⠂⠘⠈⢻⣎⣦
⠀⠀⠸⡇⣿⣄⠺⠤⣀⠬⠀⢈⣉⣀⡥⠈⠉⠛⠀⢆⣴⣀⠨⠈⠀⠀⠒⠋⠀⠀⠀⣬⠀⠀⢰⡟⢸
⠀⠀⠀⣇⠬⡻⢦⣤⠸⠍⠀⠈⣀⠐⠆⠀⠀⠁⢒⠙⣦⡴⠐⢒⠀⡤⠀⠀⠀⢰⠤⢤⣤⡴⢋⡠⣿
⠀⠀⠀⢹⡀⠈⠲⢌⡛⠶⣦⣬⣑⣀⡂⠐⠶⠟⢆⠟⠏⡛⠮⠙⢃⣄⣚⣹⡦⢶⣚⣯⠵⠚⠁⢠⡟
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠀⠒⠺⠿⠭⠽⠽⣿⣿⣿⣿⣿⣿⠭⠭⠿⠿⠒⠛⠉⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⣄⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⠤⣶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠉⠉⠉⠉⠉⠉⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠚⠋⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⣤⡶⠶⠶⠶⣤⣴⣦⡾⢿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⠞⠋⣠⡙⠒⣠⣄⠐⣃⠀⢀⠀⠰⢦⣀⣉⡁⠙⠛⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⢈⡄⠉⣥⠏⠉⣉⠁⠤⠀⠉⠁⠛⠙⠠⢶⠀⠈⠃⠴⠰⠶⣤⣀⢭⡛⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⡙⡫⠶⡞⢃⣁⣴⢲⡀⢉⡀⠀⣛⡛⠂⠘⢂⡀⢀⡤⠤⠴⢦⡀⠤⠌⣉⠠⠅⣤⠨⡝⣿⣄
⠀⠀⠀⣤⣤⣤⣤⣿⣯⣥⣭⣤⣥⣬⣥⣤⣤⣤⣬⣦⣾⡦⠶⠾⠷⣶⣴⣾⠶⢶⠶⠶⠶⣾⣶⣶⣦⣥⣤⣤⣤⣤⣤⣤⣽⣷⣤⣤⡄
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢀⣼⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠀⠒⠂⠀⠀⠀⠀⠒⠂⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢺⠤⣄⣀⣀⣀⣀⣀⠀⠀⠠⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠚⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣀⡠⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠒⠋⠍⢀⡠⠚⣳⢦⡀
⢀⣀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⠀⠁⠀⠉⠀⠉⠙⠳⢄⡀
⠀⢆⣿⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠤⢀⣀
⠀⢌⠛⡙⢷⣦⣤⣠⡤⠄⠀⠀⠀⠀⢀⣀⣀⣬⢴⣯⢠⣼⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡷⠤⠒⣟
⠀⢀⣷⡊⠐⠶⠒⠿⣏⣹⣛⣻⠋⢭⣍⣡⣤⣀⣉⢩⣾⠁⠀⠈⠐⢄⠀⣠⠶⣾⡿⠋⣹⣏⣉⣉⡤⣤⡴⣞⣋
⠀⢸⠩⡓⠶⣄⣀⠀⠀⠀⠈⣑⠀⢀⡰⠀⠈⠭⠤⠎⣿⡀⡀⡄⠀⠀⣼⠉⠲⡌⠀⢮⡌⢿⠑⢺⢥⡂⠌⣓⡽
⠀⠈⠳⠄⠀⣄⡈⠛⠀⠤⡄⠀⣄⠉⣀⠀⠀⡀⢠⠞⢱⠙⢤⢣⠆⢸⣿⡇⢸⣌⣵⠪⠷⣘⡆⢘⠶⠼⠷⣧⡂
⠀⠐⡀⠀⠈⠉⠉⠉⠁⠒⠚⠃⠈⠛⠁⠀⠁⠈⠁⡀⠎⠀⠀⠙⢄⣋⠹⣧⠀⢿⠮⣉⡛⢒⠯⡴⣷⠒⠒⠓⠁
⠀⠀⠈⠁⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠙⡄⠹⡦⡞⢡⣈⢙⠆⠑⢌⣻⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⡐⡴⢳⠀⠀⠀⠀⠀⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⠈⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡽⠉
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢴⡟⠛⣌⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⠞⢫⠝⠀⢸⡇⠀⢹⡄⠀⠹⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡶⠟⠓⠄⠒⠁⠒⠖⠿⣿⣶⣿⠃⠀⠀⣿⡆⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠘⠛⠒⠶⠶⠶⠶⠒⣋⣥⠞⠁⠀⠀⣰⡿⠁⢀⣿⣷⣬⡙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣀⣤⣤⢤⣴⣶⡒⠚⠋⠉⠁⣀⣀⣠⡴⠞⠋⠀⣠⠞⠉⣿⡿⣿⣷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⡶⠶⠟⠛⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣿⣯⣍⣩⣤⣤⣤⣶⣮⣥⣴⣾⣿⠇⠈⢻⡇⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⢛⣿⠏⠀⢀⡾⠁⢀⣾⠁⠹⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⣤⣤⣤⣤⣤⠤⠲⠚⠊⠉⠁⠀⠀⢀⣀⣀⣤⣤⡤⠶⠶⠾⠓⠒⠉⣉⣀⣴⡾⠋⠀⣠⣾⡟⠀⠀⣿⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠋⠉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠚⠛⠋⠉⢀⣀⣤⣾⣿⠏⠀⠀⣠⣿⡆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼⠿⠛⠋⠉⢉⣽⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣠⣤⣠⡤⠶⠶⠶⢶⣿⣿⣿⡟⠋⠀⢀⣠⠞⣹⠟⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣷⠶⠶⠖⠒⠊⠉⠉⠙⣟⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠉⠻⢷⣤⣄⣀⠀⠀⠀⢈⣹⣿⡿⠟⠋⣠⡾⠋⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⣤⣖⣋⡉⠁⠀⠀⠀⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣿⡿⠿⠿⠛⠛⠉⠁⣠⡴⠟⠉⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢈⣩⡟⠛⠛⠛⠛⠋⠁⠉⠀⠀⠀⢀⣠⣤⣚⣋⡉⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⣀⣀⣤⣶⣿⣿⣿⠿⣿⠷⡄
⠀⠀⠀⠀⢠⣶⢻⣿⣦⣤⣤⣄⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣶⣾⣿⣷⣶⣶⣶⡿⡿⢟⣿⠙⣏⠳⡄⢍⠺⠛⡤⣿⡀
⠀⠀⢀⡠⣞⠫⣵⠍⣿⡟⢋⡉⠻⣭⢉⡿⣛⠏⠛⡿⢙⠟⡛⣩⠉⠛⠙⠛⢛⢏⡹⣹⣙⣏⠙⡏⢩⡈⠁⠈⢦⡔⢠⠀⠈⠙⢀⠈⡄⢁⠀⠄⢤⣑⢮⡄⢻⡀
⠀⣰⣟⡄⠹⠀⠇⠘⣡⠷⠈⡯⠆⠉⠌⠃⠉⡰⠀⢤⠃⠛⠸⢀⠋⠀⠋⠛⠈⠈⠁⠱⠉⡭⠀⡐⠃⠁⠀⠀⡘⠀⠂⣰⡄⠰⡆⠀⡿⠀⢱⠆⢠⡏⠐⠀⣼⣷⣦
⢨⡀⢟⠛⣴⡷⠶⠄⣹⠀⠘⠁⡼⠁⠀⠀⠰⠃⠀⢰⠂⡴⠀⢹⠀⢠⠂⠰⣀⠀⡄⠀⠶⠀⣠⡀⠈⢠⠀⠀⢰⡇⣀⣾⣀⣴⢀⣤⡇⣠⡟⡴⠟⠻⠧⣿⣾⠃
⠀⠳⠈⢄⢹⡀⠀⠘⡉⡴⠛⠉⠸⣆⣰⣦⣤⠷⠒⡴⢀⣡⠼⠚⠳⡄⢠⡖⠉⠈⠓⢤⣤⡊⠉⠉⠳⡄⢷⡏⠀⠈⠙⠏⠙⠀⠈⢙⠃⠀⢙⡎⠀⠀⢠⣸⠆⠀⣼
⠀⠀⢣⠘⣿⣡⠀⠀⢡⢀⡀⠀⠀⢫⣽⣮⠁⠀⠀⢻⣼⠁⠀⠀⠀⣿⡎⠁⠀⠀⠀⣶⣿⠁⠀⠀⠀⣷⡌⠀⠀⠀⢸⣼⠃⠀⠀⡟⠀⠀⡾⠀⠀⠀⣾⠋⠀⡰
⠀⠀⠈⠆⠘⣻⡄⠀⠀⣾⣧⠀⠀⠸⠟⢻⡄⠀⠀⢸⣥⡆⠀⠀⠀⢉⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣄⣤⠀⠀⠀⣈⡇⠀⠀⠸⠃⠀⣴⠁⠀⢀⣿⡏⠀⢠⠃
⠀⠀⠀⠐⡀⢡⣹⡆⠀⠸⣿⡄⠀⠀⡟⢸⡇⠀⠀⠀⣄⣿⠀⠀⠀⢸⠗⠄⠀⠀⠀⣿⢿⠀⠀⠀⢸⣿⠁⠀⠀⢰⣟⠇⠀⠀⡆⠀⢠⠏⠀⠀⡜⢣⠁⢀⠎
⠀⠀⠀⠀⠙⡀⣤⣷⠀⠀⢸⣣⠀⠀⢸⠤⣷⠀⠀⠀⢩⣽⠄⠀⠀⢸⣆⡶⠀⠀⠀⣵⣿⠀⠀⠀⠺⣿⠀⠀⠀⣠⡻⠀⠀⢀⠁⠀⡜⠀⠀⢰⣱⡆⢀⠟
⠀⠀⠀⠀⠀⢡⢠⡙⡇⠀⠈⣿⡄⠀⠀⣆⠹⡆⠀⠀⠈⢿⡀⠀⠀⢸⣽⣷⠀⠀⠐⠛⡛⠀⠀⠀⣾⡍⠀⠀⠀⣹⡏⠀⠀⠘⠀⢠⠃⠀⢀⠟⡷⠀⡜
⠀⠀⠀⠀⠀⠈⡄⢀⠸⠀⠀⢸⣧⠀⠀⢹⡾⣇⠀⠀⠀⢾⡇⠀⠀⢸⣀⣿⠀⠀⢸⢀⣿⠀⠀⠀⣷⡇⠀⠀⢠⣿⡅⠀⠀⡇⢀⡙⠀⠀⡞⣰⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢡⠌⡀⠧⠀⠀⣿⠆⠀⠀⣿⢿⠀⠀⠀⠸⣿⠀⠀⢸⣿⣯⠀⠀⠈⢘⡏⠀⠀⠰⠟⠀⠀⠀⢸⣿⠀⠀⢠⠀⣬⠁⠀⡜⠀⠇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢁⠐⡄⠀⢸⣧⠀⠀⢹⢘⡁⠀⠀⠀⣾⠀⠀⠸⣹⣿⠀⠀⠀⢸⡇⠀⠀⢀⣾⠀⠀⠀⣦⡟⠀⠀⠉⢠⠃⠀⢰⠁⣴⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠂⠀⠀⣷⡀⠀⠀⣿⣿⠀⠀⠀⢿⡀⠀⠀⣼⣿⠀⠀⠀⣾⡇⠀⠀⢘⡿⠀⠀⠀⣿⠇⠀⠀⢠⡟⠀⠀⠗⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠸⣇⠀⠀⢻⠍⡀⠀⠀⠘⡇⠀⠀⠃⣸⠀⠀⠀⠟⠁⠀⠀⢉⠁⠀⠀⢸⠈⠀⠀⠀⣿⠁⠀⡾⠀⠆⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⠀⠀⠈⢀⠃⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠘⡆⠀⠀⢀⠉⠀⠀⠁⠸⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⣀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⠢⠤⠤⡤⠄⠀⠀⣀⣀⡀⣀⣀⣀⣀⠀⠠⠤⣤⠤⠤⠤⠒⠒⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⣤⣶⣏⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⣿⣿⢿⣄⠀⠀⠀⣠⡿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⡟⣧⡆⣴⡏⡷⣿⡿⣿⡏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡽⢿⣿⣿⡟⣷⢿⣸⣿⣿⣿⢟⡴⣿⠁⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣙⡾⠿⠿⡇⢹⣷⣿⣿⡭⣿⡟⢰⣟⣠⡴⠞⠋⠉⠀⠀⠉⠛⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣛⣷⣦⣙⡌⢿⡇⠀⣸⣿⠶⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠉⠳⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣙⣻⣿⣿⣿⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣀⣌⣩⠿⠛⠁⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠂⣉⡿⠿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⡴⠞⠁⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢀⡀⠀⠠⠀⠀⣀⡴⠖⠛⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⢀⠐⠂⠀⠀⠐⠂⠀⠁⠀⠀⣠⣴⣛⠁⠀⠀⠀⠀⣀⡴⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⣄⣀⣀⣀⠀⢀⣀⣠⡤⠴⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⢀⣠⠶⢋⡉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠛⠋⠐⠚⠉⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠛⠶⠦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠶⠶⠦⠤⠤⡤⣄⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠾⠿⠴⠶⠒⠒⠒⠶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⢤⣤⣤⡤⠴⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⠶⠿⠿⠟⠻⠛⠛⠛⠛⠛⠻⠿⠿⠿⠷⢶⣶⣶⣤⢤⣀⡀
⠀⠀⠀⠀⣠⠴⢚⡭⠖⠋⠉⢁⣀⣀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⠉⠉⠓⠮⣝⠲⢤⡀
⠀⠀⠀⢰⡇⠀⣏⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣈⠇⠀⣷
⠀⠀⠀⢸⡏⠲⢬⣓⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⣖⣩⠴⠊⣿
⠀⠀⠀⠈⡇⠀⠀⠀⠉⠙⠛⠛⠿⠿⠷⠶⣶⣶⣶⣶⣤⣤⣤⣴⣶⣶⢶⡶⠶⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠒⠦⠤⣤⣀⣀⣀⣀⣀⣀⡤⠤⠴⠒⠋⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠚⠉⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠠⠔⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠶⠚⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄⠠⠔⠀⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠐⠋⢁⣀⡤⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⠀⢂
⠀⠘⠀⠑⠀⠠⠀⢒⠉⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠆⠃⠠⠀⠀⠀⢸⠀⠀⠓⠂⠉⠂⠉⢀
⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠊⠀⢸⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⡀⢀⠀⠀⠀⢈⡤⠤⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⢠⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠈⠘⠒⠘⠻
⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄
⠀⠀⡰⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⢀⡀⠈⠐⠀⠀⢰⠀⠀⠀⠀⠀⢀⡴⠒⢢⣄⠀⠀⠨⠀⠀⠀⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠃⣈⠁⠉⣈⠌⠀⠸⠀⠀⠀⡐⠢⠄⠭⠭⠬⠥⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠐⠒⠀⡒⠤⢄⡀
⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠐⡠⠰⠄⠒⠐⡠⢀⡇⠀⠀⠀⠀⠘⠢⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡈⢀⠀⣄⠄⢰
⠀⢀⠀⠀⠘⠑⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠄⠀⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠑⠒⠒⠒⠉⠁⣠
⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠿⣿⣛⢛⠻⡻⣛⢛⣛⡿⠿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⢟⣫⣭⣴⣼⣯⣩⣽⣜⠂⠓⠯⡜⡱⣋⢽⢒⡎⣭⣛⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⣫⠞⢋⢀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠙⣦⠙⢛⣉⣬⣥⣤⣤⣴⣮⡟⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠛⠅⣰⠋⢰⠋⢉⢀⠇⠀⠀⠐⠚⠀⢀⣤⡶⠟⣿⠉⡩⣤⣰⠶⢶⣶⢸⡇⣳⣝⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⡉⣼⠁⠀⠀⠀⠂⠋⡀⠐⠀⠀⢀⡴⠋⡕⢶⠀⣿⠀⡆⣝⠀⠂⣸⢻⢸⡇⣿⡶⣻⡽⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠐⠠⢀⡇⠀⠠⠀⠀⠐⠀⢼⣿⠄⣰⠟⡴⢖⡌⠨⡄⢸⡇⠣⠉⠠⠤⠁⠺⢸⡇⢿⣿⡽⢞⣎⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠈⠀⠄⢸⠀⠀⠀⢀⣀⣠⣤⣤⣄⣼⣏⡰⢜⣌⠖⠂⣃⣸⣷⡴⠶⠶⠞⠛⠛⠻⡟⠛⠷⣼⠋⠭⢆⢿⣿⡄
⠀⠀⠀⠀⠀⠀⣸⢻⡏⠐⠀⡀⠐⣘⣧⣤⠞⢉⡍⡤⢤⠀⣿⠉⡉⠛⢦⣩⡴⢻⢉⡄⢸⡆⠀⡚⢃⠋⢿⢸⡇⠀⢠⠀⠙⢦⡙⡜⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠁⣠⠔⠋⢉⠉⠻⡄⠋⢃⢓⢸⡆⢻⡄⠆⠀⠃⢻⡄⢠⢼⠠⠄⣷⠰⠦⣬⣉⡺⣸⠃⠀⠈⠀⠀⠀⠹⣦⢹⣿⡆
⠀⠀⠀⠀⠀⢸⣧⡟⣠⠈⢀⠐⠀⠀⠀⠀⠹⣆⠈⠀⢈⡴⠛⠻⣄⠑⢤⡌⡇⣀⣼⡦⠶⠿⠶⠶⢶⣍⣡⡏⠀⠐⠂⠀⣤⡀⣀⢸⡎⣿⠇
⠀⠀⠀⠀⠀⢸⣿⡇⠙⠄⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠋⡀⢒⠠⠊⠀⢠⣼⣿⡉⠔⠀⠀⠀⠀⡰⢀⡼⣿⠰⣿⠖⠐⠂⣈⣀⡍⠀⡇⣿⡄
⠀⠀⠀⠀⠀⠸⣿⡇⠀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠞⠙⢦⡐⠃⠀⢀⡴⠟⡉⢹⡙⠲⠦⡤⠴⣶⠟⡋⢀⠈⢷⠀⠀⠂⠀⠈⠉⠀⡼⠃⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠐⢀⠑⢄⠀⢀⡤⠞⠁⡄⠲⣤⠙⠳⣤⠟⠀⠀⠀⢸⡇⡀⠤⢀⡀⣿⢸⡇⠤⣛⡈⣧⠀⢠⡄⠀⠀⠎⣕⢸⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⢀⠸⢂⡿⣏⡠⠚⢜⡦⡱⢈⡱⠇⡿⠀⠀⠀⠀⣼⡁⠀⠚⢠⢠⡟⠸⢧⣅⡃⣇⠸⡆⠀⠀⣠⠌⢄⡄⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠥⡸⡇⠀⠑⠦⣌⣙⠂⠃⠘⠃⢷⡀⠀⢀⡼⠁⣉⠛⠒⠒⣾⠗⠶⢤⣌⣉⡉⢀⣇⢀⡴⣡⠐⡾⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠠⠸⠆⠀⠤⡀⠉⠉⠉⠛⣛⡛⢷⡚⢋⡠⢖⡍⢻⠆⢀⡿⠀⠆⠤⣀⣉⠙⢻⡟⣩⠾⢏⣙⣽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡠⢠⡧⠀⠀⠁⠀⠀⠂⠘⠿⠃⠈⠳⣌⠁⣬⣂⣝⠃⣼⠃⡘⠄⠉⢑⣾⠀⣼⢡⡏⢡⢬⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⣠⡱⡄⠀⠀⠠⠄⣰⢀⠐⠂⠀⠈⠛⢦⣝⣋⣼⠇⢰⣜⠒⠤⢼⠇⣰⠇⣶⢘⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣘⢦⡀⠀⡼⡀⠠⠀⠀⠐⠒⠀⠀⠀⣹⢟⠳⢦⣬⣉⣒⠋⣰⡟⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣯⣖⡦⠤⠀⠤⠤⠤⠴⠒⢒⢚⠱⠜⢙⡓⠆⠭⣉⣭⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠙⠿⣿⣿⣿⣶⣶⣤⣿⣴⣤⣮⣧⣬⣼⣶⣶⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⠀⠐⠚⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠁⢀⡀⠓⠒⠒⠒⠒⠒⠒⢀⡀⠀⠀⠀⣶⡷⣿⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡠⢺⢀⣁⠆⠁⠀⡂⡾⡀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⢠⡌
⠀⠀⠀⠀⠰⣀⠀⠇⢐⠈⠼⠀⠀⢻⡥⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠤⠲⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢨⣉⢿⡇⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠰⠒⠀⠀⢸⠀⠆
⠀⠀⠀⡠⠀⠰⢂⠛⢺⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠡⠄⠄
⠀⠀⠀⢉⣀⠀⠀⠌⠀⠨⠌⢻⠍⠀⠀⠀⠠⠄⠐⠀⠀⠁⠀⠀⠀⠈⠀⠀⢣⠀⠀⠀⢀⢀⠀⠠⠄⠤⣀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠰⢤⢀⠀⠈⠓⠂⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠰⡁⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠭⠙⢲⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠊⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⢀⣀⣄⣀⣀⡀⡀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠄⠀⠀⠠⠶⠀⠀⢂⠀⠀⠠⠄⠀⠀⠈⢀⠠⢀⣀⠀⠒⣤⡀
⠀⠀⠀⠀⠨⡉⠁⠙⠀⠛⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⠆⠀⢀⡀⠀⠀⠀⢀⠀⡡⠀⣁⢀⡴⠎⠁⡱
⠀⠀⠀⠀⠀⠱⡒⠲⠲⠒⠒⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⢠⠴⠙⠘⠀⠀⠀⡀⠋⢸⠅⠀⡀⡤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⢀⠉⠃⠀⠀⢒⠈⢡⠀⠠⠇⠀⠘⠀⠂⠁⠑⠀⠀⠀⢀⠀⠈⠀⠀⡀⡁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⢠⠀⢀⣄⠀⠀⠀⠉⠁⠀⢀⠐⢉⡀⠀⠀⠀⠀⢀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⡘⠀⠀⠠⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⣠⠰⠃⣀⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡘⡷⠀⢠⣄⠀⠀⠀⠀⢀⠨⠁⠀⠄⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠾⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢂⢀⣔⢴⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠈⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠁⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠒⢀⠀⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠉⠀⠀⠀⠈⠀⠀⠄⠀⠠⠠⠔⠲⢖⠒⠀⠥⠀⠀⠀⢢⢢⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⢤⡴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠰⢦⣾⠿⣾⠗⠿⠖⠓⠦⠀⠀⠀⠀⠀⠀⡿⠛⡿⠟⠾⣷⢿⣦⡴⠀⠀⠀⠀⠀⠀⣴⢾⣿⣧⣯⣿⣦⠀⠀⠀⠀⣀⣤⣿⣿⣺⡷⢿⣤⠆
⠀⠀⠀⠀⠀⠛⠡⠀⢀⠆⠔⡠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠿⠀⡑⠠⠘⠛⠀⠀⠀⠀⢀⡿⠏⠛⠁⠘⠀⠉⠁⢀⠀⠀⠀⠉⠉⠟⠛⢻⡟⠀⠙⡥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣴⣮⣷⡾⠷⠦⠀⠀⠀⠐⠏⡃⠀⠀⢧⠀⠀⡀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠂⢈⡌⠀⢀⡧⡂⠀⠀⠀⠀⠁⠐⡠⠀⠀⢄⢢⡥
⠀⠀⠀⠀⠀⣀⠧⣀⠀⠱⠈⢀⠀⠠⠀⠀⠀⠀⠀⠈⣋⠴⠁⠀⡆⠀⢠⡘⣾⠃⠀⠀⠀⠀⠀⢀⡦⡀⠘⠀⢀⠻⡴⠁⠀⠀⠀⠀⠀⠀⡇⢠⠐⠌⠴
⠀⠀⠀⠀⠀⣌⣠⠇⡀⠀⢡⡈⢀⠀⠀⠀⠀⠀⠀⠀⠌⣒⠁⡖⡇⢀⡈⣧⣫⠆⠀⠀⠀⠀⠀⣌⣠⠁⠀⠀⠀⣷⣋⠁⠀⠀⠀⠀⠀⠠⢀⢈⣂⣛⠉
⠀⠀⠀⠀⠀⢨⣅⠚⡡⠀⠈⡰⣮⠜⠀⠀⠀⠀⠀⠀⠠⠤⠼⣀⠠⠰⣙⢾⡀⠀⠀⠀⠀⠀⠀⢬⡰⢃⠀⢀⣸⠿⠃⠀⠀⠀⠀⠀⠀⠰⠈⠙⠀⠁
⠀⠀⠀⠀⠀⠶⢬⣎⠁⡶⢈⢀⡿⣸⠇⠀⠀⠀⠀⠀⢄⡀⠈⠉⠸⠀⣽⣾⡄⠀⠀⠀⠀⠀⠐⢮⣒⠃⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠲⠤⠤⢽⣀⢠⠀⡙⣫⠖⠀⠀⠀⠀⠀⠈⠷⣆⡆⠐⢀⡜⠁⠀⠀⠀⠀⠀⠀⠐⢤⣭⡞
⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⠳⠀⢻⣧⠆⠀⠀⠀⠀⠀⠀⢀⣋⣔⡀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢆⠀⠀⠀⠀⡀⢀⣦⣸⣆⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⠀⠇⣸⠟⠋⣴⠂⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⠟⠋⠟⠉⠉⠁⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠨⣌⣡⠄⡸⠁⢿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⣄⣰⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣏⠵⠀⠡⣈⣬⡭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⣿⣍⣿⣽⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠓⢂⡄⢠⠸⠋⠀⠀⠀⠀⠀⣰⢤⢠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡁⢂⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠁⠀⠀⠀⠀⠀⠀⠺⠿⠛⠟⢿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠠⡿⠾⠿⠟⠛⠃⠀⠀⠀⠀⠀⢁⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠀⠀⠀⠀⠀⢀⣓⠂⠒⠃⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣝⡸⢋⡡⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣕⡲⠄⣠⠖⢃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⡀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠐⡆⢀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⠖⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣉⡛⢃⡯⠥
⠀⠀⠀⠀⠀⠀⠠⣿⠋⢁⠀⠀⠀⠀⠢⣽⣄⠀⠀⠀⠀⠀⢻⡥⢃⡀⠀⠀⠀⢻⡸⠇⠀⠀⠀⢀⠻⣊⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⡘⠒⠦⢅⡩⠖⡂
⠀⠀⠀⠀⠀⣄⢷⣿⡷⠞⠁⠀⠀⠈⡓⠶⣛⠀⠀⠀⠀⢀⡚⠇⣹⠂⠀⠀⢘⡎⠙⢠⠆⠀⠀⠀⡣⠤⠀⠀⠀⠀⣀⢃⡜⠀⠀⠀⠉⠛⠲⢤⠴⠊⡁
⠀⠀⠀⠀⠀⢸⣎⣇⣀⣤⡼⠀⠀⠀⠉⣻⠅⣀⠀⠀⠀⠀⠙⢺⢋⡴⠀⠀⢨⠘⠟⢃⡀⠀⠀⣆⠡⢼⡅⠀⠀⠀⣝⠩⠞⠀⠀⠀⠀⣙⠓⠂⢒⡉
⠀⠀⠀⠀⠀⠠⣥⣙⠋⣀⣴⠀⠀⠀⠶⣈⡶⠃⠀⠀⠀⠀⢻⣜⢋⣤⠀⠀⡀⠛⠶⠋⠀⠀⠀⣄⡓⢋⡄⠀⠀⠰⣌⠔⠊⡄⠀⠀⠀⠤⣉⠋⠔
⠀⠀⠀⠀⠀⠀⢠⣉⣷⠟⠁⠀⠀⠀⠲⣿⣷⠀⠀⠀⠀⠀⠀⣼⣯⣡⠀⠀⠘⠳⢄⣰⠀⠀⠠⣌⡛⠉⠀⠀⠀⠤⣌⣱⠚⠀⠀⠀⠀⢉⣀⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣿⠖⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⣠⡟⠉⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⠑⡞⠀⠀⠀⠀⠠⠼⢴⠀⠀⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠉⠉⠁⠀⠀⠀⠐⠒⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣀⣀⣀⡠⠶⠾⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣥⣤⣤⣤⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠁⠁⠍⠻⡇⠀⠀⠀⠀⠀⢀⠤⢤⣀⡀⠀⠉⠹⢦⡀⠀⠀⠈⠂⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡇⠀⡀⠐⠉⠛⠛⠳⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣠⠶⠛⠁⠀⠀⠹⢦⣀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⣤⠄⠀⠠⠴⣤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠸⠿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠋⢀⡀⠀⠀⠀⢩⡿
⠀⠀⢠⣀⠀⠀⠀⠀⠉⠛⠲⢿⣆⣻⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠤⠀⠀⠈⠁⠀⣀⠼⠀⠀⠀⡞⠀⠀⢀⣿⠀⠀⠀⠀⣸⡅
⠀⠀⠼⢿⣗⡦⣄⣀⣀⡀⠀⣤⣀⣠⣭⣥⡿⠋⠁⠀⠀⠀⠀⠀⠤⢄⡀⠀⠉⠀⠀⠀⣀⣠⠴⠒⠉⠁⠀⢠⠾⠇⢣⣤⢀⠔⠀⠀⠀⠀⢀⡿
⠀⠰⣤⣄⣀⠀⠉⠈⠛⠃⢀⣿⠀⠀⠘⠁⠀⠀⠀⠀⠐⠒⠲⠤⠀⠀⠀⠀⣀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠁⠿⠀⠀⠀⢀⣠⡏
⠀⠀⠈⠙⠛⠛⠤⠶⣶⡄⠸⠃⠀⠀⠀⢀⣀⡀⠉⠉⠀⠀⠀⢀⡤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣷⢀⢀⡴⠚⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢞⡘⠇⠀⠀⠀⢀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠤⠀⠐⠒⢤⣀⡀⠀⠀⠀⠀⠀⠈⢂⣾⡿⠉⠁⠀⠀⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠈⠹⢿⣤⣤⡶⠶⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣶⣦⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣆⠀⠀⠀⠙⠻⢿⣾⣽⣛⠳⢦⣄⣀⠠⠔⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⠒⠦⣄
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠉⠛⠻⡷⢶⣏⠉⢠⣄⠴⠒⠛⠁⠀⠀⠀⡠⠂⠂⢬⣀⠀⠀⠀⠀⢈⡶⣄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠴⠛⠋⣿⠿⣶⡉⠀⠘⣇
⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡄⠀⠀⠀⠙⣾⠟⠀⠀⢠⡏
⠀⠀⠀⠀⠉⠻⠿⣶⣶⣀⣐⠲⣶⣶⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠘⢤⣠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠷⠶⠿⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠂
⠀⠀⠤⠔⢀⠀⠁⢀⡎⠈⠓⠀⠀⠀⠀⠀⠀⢀⠄⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠠⠀⠁⠒⠄
⠀⢡⡀⠦⠀⢈⣒⣀⠀⢤⡆⠀⠠⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⢇⣤⡍⠉⠀⠀⠀⡀
⠀⠈⢜⠧⡀⠀⠀⠀⠐⠀⠠⠀⡭⡐⢢⠀⠀⠀⢀⡀⠀⠠⠀⠀⡠⢔⠐⠀⠀⠀⠀⠀⠈⠉⡉⠀⠘⡄⠐⠆
⠀⠀⠐⠷⣌⣀⠓⡀⢀⢣⣤⣼⡭⠝⠋⠀⠀⠐⠏⢀⢄⠎⠥⣀⡈⣛⡛⠉⠉⠀⠀⠀⠀⡐⢀⡔⢀⠅⠀⡁
⠀⠀⠀⠄⠀⠉⠉⠀⠠⠈⠀⠀⠠⠄⠀⠀⠀⠈⠀⡇⢼⠁⠀⠀⢀⠉⠀⠀⢀⠀⢀⣠⠚⡀⠁⢠⠞
⠀⠀⠀⠀⠤⠂⢴⣂⣔⡒⡠⠀⠀⠀⠀⡀⠀⠀⠑⠃⣏⠀⠀⠀⠀⠀⣀⣀⣤⡶⢊⠡⢻⡥⠖⢁⢀⠴
⠀⠀⠀⠐⢦⠀⠀⠀⠙⢾⡁⠩⠢⡀⠀⠀⠀⢠⣄⡇⠁⠀⠘⠋⢉⡥⠡⠛⢈⠒⠀⠐⠂⠐⠂⢁⠔⠀⠀⠀⢀
⠀⠀⠀⢄⠀⠀⠀⠈⠐⠀⢱⠀⢟⡃⠀⠀⠀⠀⠁⠹⣤⣈⣙⣋⢁⣀⡤⠚⠷⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠘⢇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠤⠳⠄⠠⠄⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⠈⠉⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⡀⠔⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠀⠂⠀⠂

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

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠀⠀⠠⠀⠀⠈⠀⢀⡼⠋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠂⠀⠀⡟⠀⠀⠁⠀⠀⣀⣀⡾⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⡴⢛⢡⡙⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡞⠉⠙⢿⡋⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⣏⠰⣌⢧⡹⣜⣧⠀⢂⠀⠀⠀⡇⠀⠀⣴⠏⠀⠀⢀⡼⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢷⡙⢦⡻⠍⠘⡇⠀⠂⠀⠀⣿⢠⡾⠁⠀⠀⢢⡞⠁⢀⠔⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠄⡀⠀⠙⠶⣤⣤⣾⡃⠀⠀⠀⠀⣿⠏⠀⠀⠀⣵⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⡾⠃⠀⠀⢀⡾⠁⠀⢀⣀⣠⣤⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠦⠶⠶⠶⠶⠖⠛⠛⣛⣉⣷⡄⠀⠀⠹⣦⠟⣀⣀⣠⣴⡿⠶⠞⡛⢉⣭⠤⡄⠀⢹⡀⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⠶⠟⢛⣉⣁⣸⣧⡤⠶⠞⠛⠛⢉⠉⣤⠶⣆⢸⣏⠁⠈⠓⠶⣤⠀⢸⡟⠉⠉⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣼⠷⠞⢛⣛⣉⠉⢠⡴⠂⢠⡞⠙⠃⣸⠀⣿⣴⠏⢸⣯⡤⠀⠓⠞⠋⠀⢸⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿⠀⠀⣿⠁⣹⠇⢸⣧⠀⢸⣇⣠⡆⠻⠀⠋⠀⠀⢄⣐⣠⣤⠴⠶⠖⠒⣾⠇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣁⣀⣤⣤⣿⠀⠀⣿⠚⢯⡀⠸⡧⠶⠀⠉⠉⣀⣠⣤⣴⡶⠛⠋⢹⡇⣀⣤⡶⠶⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢸⡇⠀⠉⠀⠀⠀⣀⣠⣤⣶⣾⠛⠉⠁⣿⠀⢻⡄⠀⢸⡟⠉⠀⠀⣀⣀⣤⡤⠶⠶⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠈⠷⠴⠶⠖⣿⠛⠉⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⢻⣆⠈⠓⠖⠛⠛⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⢠⡞⠁⠀⠀⣺⠟⠀⠀⠀⠀⠀⣿⠀⠀⡀⢻⣷⡄⠀⠀⠠⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣝⡳⣄⣴⠋⢀⣤⠶⠚⠛⢓⣿⠀⠀⠐⠈⢷⡙⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠷⠟⠁⠀⣿⣤⡴⠶⠟⢋⣿⠀⠀⠀⠡⠀⠻⠾⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⠀⠠⠀⠸⣆⠀⠀⣀⣼⠇⠀⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠾⠋⠀⠀⠠⠁⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⠉⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⢤⡴⠶⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⣤⢶⣫⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⠀⠁⠀⠈⠀⡀⠈⠈⠷⠶⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⢀⣀⡤⠶⣒⣫⠽⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡞⡛⠠⠂⠠⠆⠐⠀⠈⠀⠀⠀⠈⠃⠈⠉⠳⢦⣀⣤⠶⠚⠉⠀⠀⠀⢀⣠⠴⠖⣋⣭⠴⠒⠋⠁
⠀⠀⠀⠀⠀⢀⡼⠁⠀⡤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠉⠀⢈⢷⠀⠀⠀⠀⣀⡴⢚⣩⠴⠚⠋⠁
⠀⠀⠀⠀⡶⠋⠀⠀⠀⠈⠀⡀⢀⡀⠲⠀⣀⠀⠀⠀⠀⣀⠀⠀⠘⣿⠀⢀⡤⠞⣡⠖⠋
⠀⠀⠀⠀⣷⠰⠀⠲⠂⠀⠀⠀⠉⠋⠀⠀⠁⠀⠀⠀⠘⠁⣀⢀⡼⢃⡴⠋⣠⠞⠁
⠀⠀⢀⣴⣿⠂⢤⠀⠀⢠⠄⠀⠀⠀⠀⠠⡖⠀⠘⠁⢀⡤⠞⣩⠞⠋⢀⡾⠁
⠀⠀⢸⣿⣇⠡⡀⠀⠠⣄⢀⣀⡘⠂⠴⠂⢀⣠⠴⢚⣩⠴⠋⠁⠀⣰⠋
⠀⠀⢸⠙⣮⡛⠶⣤⣄⣀⣤⣬⡤⠴⠒⢋⣩⡤⠖⠋⠁⠀⠀⣠⠞⠁
⠀⠀⠘⢧⡀⠙⠓⠶⠬⠭⠤⠤⠴⠖⠛⠉⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠒⠚⠋⠉⠁

⠀⠄

⠐⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡀⢰⣶⠁⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐
⠂⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠐⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠂⠀⠀⠀⢂⠀⡈⠀⠀⠄
⠀⠐⡆⠀⠀⠀⢀⠀⠈⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠘⠀⠀⠀⢈⡰⠀⠀⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⢀⣀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠄
⢄⡄⠀⠀⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢠⣀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⡘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠃
⠰⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⡄⠒⢢⠀⠿⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠖⠄⠀⠀⠁⠀⠀⠀⠆⠆⠀⠀⠀⢀⠀⠈⠀⠠⠀⢠⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡀⠀⢄⡰⠀⠀⠀⠄⠄⠀⠀⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠠⠴⠀⠀⠀⠂⠂⠀⠀⠈⠀⠀⠀⠀⠠⡠⠀⠀⣖⣀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠐⠀⠠
⠀⠀⠀⠀⢀⠀⠀⢀⠂⠀⠀⡀⠌⠀⠀⠀⠀⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠐⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⣌⡅
⠀⠀⠈⠐⠂⠀⣀⣀⠀⠀⠠⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣖⠑⡢⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠮⠁⠽⠀⠉⠁⠀⠀⠀⢀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡯⠀⠀⠀⠀⠀⠈⢿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠟⢛⣛⣁⣀⣀⠀⠀⠀⠉⠉⠘⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⣿⣿⣿⡒⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠤⠀⢰⠂⠀⠀⣀⢀⡀⠀⢀⠀⠀⠀⢸⡏⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⣀⠀⠀⣿⡀⠏⢢⡿⣿⡟⢠⡎⠀⠀⠀⠘⣷⢹⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⡇⠈⣿⡆⢇⢹⠀⠀⣿⣿⠀⠀⠀⢸⡇⠨⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣷⣄⢹⣇⣾⡄⡅⡀⢹⡏⠀⢸⣷⣿⠁⢠⡀⠀⠀⠀⠀⢻⡗⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢿⡸⣿⣿⣻⣧⡀⣷⢸⠇⠀⣼⣿⠇⠀⣼⣧⣤⠄⢰⡄⠚⠓⠼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣼⠷⠛⠛⠉⢻⣿⣿⣾⡰⢠⣿⣿⣶⣦⣿⣿⣿⣴⣀⣤⣐⣴⣦⡀⠘⠿⡃⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠻⠿⡿⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋⠛⠉⠉⠁⠀⠀⠀⠉⠉⠙⠟⣿⣿⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⠸⣿⠉⠁⣀⡤⠴⠶⠶⣶⠶⡶⠖⠲⠦⠤⠤⠴⠃⠈⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠘⢦⡨⢛⣩⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⠐⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡈⠉⠘⡿⠿⣛⣋⣻⣍⣉⡋⢉⡉⠙⣛⣻⣛⡛⠛⠃⠲⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⢁⣶⣾⣿⣿⣿⣿⣿⠿⠿⠷⢶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣠⣈⠻⢿⣍⣍⡀⠀⡀⠆⠁⠈⠀⠀⠀⠈⠈⠉⠑⣢⣦⣠⡴⠏
⠀⠀⠀⠀⠤⠤⠶⣶⣾⣿⣿⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣴⠿⠶⠞⢛⣟⣓⣛⣛⣻⣟⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣻⣟⣿⣿⣿⣿⣷⣶⣶⣶⣷⣿⣾⣿⠿⠿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠙⠛⠿⠿⠿⠿⠟⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠄⣤⣄⡀⠀⠀⢀⡠⠊⠀⠀⠀⢀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠫⠀⢻⣻⡟⣼⠈⡷⣴⣯⣤⣀⢀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠂⠀⣸⣿⢀⠉⠈⣯⠘⢃⣾⣏⡽⣿⣯⡖⡽⣏⠉⠑⠠⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠆⠀⠀⠀⠀⢻⠈⣆⠂⠀⠘⣦⡎⠱⠛⣱⡿⢾⣿⡇⢻⠀⠀⢀⢄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣥⣀⠀⠀⠈⠷⠮⠧⠤⢴⠌⠧⠤⠧⠿⠋⠽⠿⠶⣞⢧⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣆⠀⠀⠈⠙⢯⣍⢀⠀⠈⠁⠈⠈⡁⣄⠀⣠⣼⣿⠆⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣿⠤⠀⠀⠈⠓⠀⠀⠀⠀⠀⠠⡾⠏⢐⣽⣿⠋⣠⠟⠛⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠬⠈⢍⡋⢁⠀⠀⠀⠀⠀⠀⠐⠞⠂⢠⣬⠥⠳⠋⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡚⠇⠀⠀⢀⢬⠉⠁⠀⠈⣠⠶⠋⢈⠙⢃⠀⠀⠀⠀⠀⠁⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣿⡆⠀⢀⣀⡉⠀⠀⠠⠮⠞⡀⠀⠀⠔⠁⠠⢂⠠⠀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠛⠃⠉⠀⠻⣽⡆⠂⠀⠀⣁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⡀⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣀⠀⠐⠀⢀⠀⠀⡀⠀⠀⠒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠪⠉⠁⠈⠁⠀⠀⠀⠀⡠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠘⠾⠁⢆⡒⠐⡆⡄⢄⡀⡎⠂⠂⠀⠂⠐⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⢂⠃⠀⡉⡁⠀⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙

⠀⠀⢀⡀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠐⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢢⣤⠀⠀⠀⠬⡄⠀⠀⠀⠀⠀⠘⠛⢩⡁⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⠀⠀⠀⠉⠀⠀⠀⠀⠉⠐⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠴⠿⠟⠫⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠁⡀
⠀⠀⡎⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢤⡄⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠅⠒⠂
⠀⠀⠘⢄⠀⠠⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠃⠄⠅⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠈⠒⠀⠄⠀⠀⠠⡀
⠀⠀⠀⠀⠂⡺⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠳⠀⠀⠀⡀⠆⠀⠀⠄⠃⠀⠌⠀⠀⠐⢂⡀⡔⢀⡀⡄⡠⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠌⠄⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⢈⠆⠀⠀⠀⠀⠀⠀⠛⠱⢃⡙⡾⠜⢗⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠆⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡰⠀⠀⠀⠀⠀⠀⠄
⠀⡀⠀⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⡄⣠⠡⣶⣦⠀⡀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⢸⢇⡴⢁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠄⠀⢺⣿⣷⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢨⠁⢹⠄⠈⠉⣴⠁⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⡐⣮⠀⠁⠀⠠⠀⠀⢀⡀
⠀⠲⢦⡀⠛⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣈⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣹⠇⡜⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢐⢳⡌⠀⠀⠁⠀⠀⠚⡇⠐
⠀⠂⠀⣈⣆⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠬⢽⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠁⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠂

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡠⣫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡜⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⢎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⡰⢃⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢀⡜⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⢎⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⡠⣔⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢠⣿⠏⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣠⠴⣚⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⡿⠃⠀⠀⠀⠀⢀⣤⠞⣋⠤⣚⡭⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⢤⣀⠀⢀⣤⠴⠶⣤⡀⢀⡞⠁⣴⠟⠀⠀⠀⢀⣠⠞⡫⢔⣫⠵⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⢀⡴⠞⠛⠋⠀⠀⠀⠀⠈⠳⠋⠀⠀⠀⠀⢙⠟⢀⣼⣋⠀⢀⣠⢖⣫⣷⡽⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢎⣠⠞⢀⣩⣗⣯⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠿⠛⠁⢻⣤⣤⡀
⠀⠀⠀⠀⣠⠖⠛⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⣠⣤⣤⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡛⠛⠛⣷
⣾⠁⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠰⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⢠⣤⠟
⠈⢻⡆⠀⠀⠉⠑⠒⠀⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⠔⠒⠉⠀⠀⠀⣼
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡆⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿