Vacation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠱⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⣤⠴⣤⡁⠂⢄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡤⢾⣦⡰⡟⠻⡉⠉⠙⢦⢌⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⠁⠈⠁⠈⠛⠒⣻⢏⠎⣂⢰⠀⠀⣼⠀⠑⡈⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠒⡄⠀⠀⠀⠀⠎⢀⠇⠯⡀⠘⠔⠁⠀⠀⠀⠈⡄⢂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⠀⠀⠀⠀⠉⠀⠖⠺⠀⠀⠀⠀⠀⠸⣮⠿⡀⡀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⢀⠀⠀⢄⠀⠀⢀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠾⡇⠁
⠀⠀⠀⠀⡀⠨⠰⠉⠉⠉⣷⠨⠀⡀⠈⠓⢄⣇⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡄⡀⢀
⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⡉⡄⠀⠀⠀⠙⠶⠒⠂⠀⢀⠀⠀⠀⠀⠀⠑⠂⢲⢁⠁⠈
⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠵⠤⠤⠤⠤⠤⡧⠾⠴⠓⠲⢟⣚⡛⢍⠉⠙⠛⠛⢋⠆
⠀⠀⢰⠀⠘⠠⡷⠀⠀⠀⠰⡧⠈⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠈⢻⡆⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⠄⠁⠰⢢⢀⠀⠀⠀⠀⠰⠀⠀⡠⢄⠙⠒⠚⠁⠃⠀⠀⠀⠀⡔
⠀⠀⡄⠀⡠⠐⠒⠒⠒⠒⠒⠒⠠⠀⠀⡷⢤⡁⡐⠂⠀⠒⠀⠒⣘⡜⡠⠀⠡⠄⠀⠬⠅⠀⠀⠈⢆⠀⠀⠠⠀⠀⠀⠀⠀⡠⠂
⣆⠀⠀⠀⠃⠤⠤⠤⠤⠤⠤⠤⠄⡆⠀⠂⢀⠧⠀⢀⡀⠀⠀⡀⠠⠖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠦⠀⡖⠐⠀⠂⠈⠀⠠
⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠠⠀⣠⠑⠶⣷⣴⡀⠀⠀⠀⠀⠀⡔
⠣⣘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡠⠂⠐⠒⠓⠒⠒⠓⠒⠀⢀⠀⠀⠀⠀⠀⢀⡤⠊⠈⠁⠐⠃⠀⡀
⣀⣈⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣌⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣎⣶⣶⣶⣦⣬⣤⣦⣤⣖⣒⣒⣚⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡠⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠂
⠀⡤⢊⠄⠀⠀⠀⡀⠠⠀⠀⠀⡡
⠀⠄⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⡆⠄
⠀⠠⠀⠀⠀⠀⠀⠈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⡇⡄⠀⢀⣶⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣷⠁⠀⠀⢿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡾⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠃⠢⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠤⡤⠒⠒⠒⠒⠂⠐⡖⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠖⠂⢩⠶⠿⠙⠉⠀⠀⠘⠟⠛⠙⠉⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢂⡀⡄⠈⠀⠤⠤⢤⡤⠤⠤⣤⢤⡀⡆⠈⠀⣉⠁⠐⠂⠳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡄⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠰⢀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡠⠀⠀⠀⠃⠈⠀⠉⠈⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠁⠀⠀⢀⠠⠓⠖⠁⡀⠉⠀⠀⠀⠀⠀⢀⡀⠤⢀⡤⠶⡶⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠀⠀⠀⢀⠄⠈⠀⣠⠞⠁⠀⠂⠀⠀⠀⠙⢦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠃⠀⠀⠀⠀⡰⠁⠀⠀⡜⠁⠀⠀⠌⠀⠀⠀⠈⠀⠀⢣⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠂⠀⡀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠀⠘⠀⠀⠀⠰⠄⢀⣀⡀⣀⠀⠀⠀⡇⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠰⢷⡴⠻⡿⠿⠦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠐⠦⠤⠀⣀⣀⠁⠀⠀⠈⠁⠐⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⠼⣦⡀⣿⠉⢹⣿⠗⠀⠢⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⠘⣡⠆⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣈⠙⠉⠘⣿⣷⣼⡋⠈⠋⢀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⠇⠀⡾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⠀⠙⠶⠶⠶⠛⠿⠿⠷⠦⢀⠀⠁⡀⠀⠀⣤⠀⠑⠀⠞⡈⠀⠀⠀⡀⠀⢘⡄⣪⠃⡜⠁⢙⠃⢆⠅
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⣌⣉⡀⢈⠀⠀⠈⠀⠀⠀⠀⠑⡄⢋⠜⢁⡞⠁⡠⢞⡴⠁
⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠁⠀⠀⠀⠀⠐⠶⣀⠀⢞⣐⡭⠞⢟⣤⠞⠁⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠂⠀⠀⠀⠀⡀⠠⢼⢝⠳⢯⡐⠦⣞⣪⠦
⠀⠀⠀⠀⠀⠀⠐⢀⡃⠐⠀⢲⡎⠉⠉⣶⡎⠉⠙⣦⣀⣤⣤⣤⣤⣤⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡬⠑⠂⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠒⠊⠉⠙⠒⠺⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢀⡐⠈⠏⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⡰⠁⠀⠀⠀⢀⠘⢝⣂⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⠂⠍⠀⣵⣀⠀⠀⠀⠈⠿⠁⠀⠂⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠚⢀⣼⣿⣿⣿⣦⣄⣠⠂⠣⡈⡴⠑⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⡀⢄⠔⠥⠂⠰⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠑⠢⡀⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⢠⠀⠀⠂⠀⠀⠹⠤⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠺⠟⣿⡀⠘⡟⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣐⠀⠈⠶⢤⠢⡀⠀⠆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⠇⠤⡉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠓⢁⣀⣘⡆⠀⠘⢀⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠀⠀⠉⠚⠠⠟⠀⠀⠟⠛⠉⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠎⠉⢹⣿⡖⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢂⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⢁⠀⠀⠆⠀⢠⣤⠀⠀⡻⢃⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠁⠀⠀⠀⠈⠀⠀⢢⠀⡇⠀⣠⠀⠀⢀⠠⡀⠈⡄⠀⢦⠀⠀⠐⠶⠔⠁⠸⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⢈⢢⠁⠞⠁⠀⢀⠌⠀⢳⡀⠀⠀⠀⠇⠀⡌⢀⠐⠀⢀⡄⠀⢠⣃⣠
⠀⠀⣀⣤⣤⣤⠃⠀⢠⣼⣀⠇⠀⠀⠀⢀⠀⣮⡜⠀⠀⠀⠀⡌⠀⠀⠀⠱⡄⢀⡀⣀⠐⠀⣰⠀⠀⢀⢙⣈⢉⣴⠟
⠀⠘⠻⠿⠿⣧⣤⣶⣿⣿⣿⠀⠒⣻⣿⠁⢀⣿⡇⠀⠀⠀⣼⣿⣷⣦⡀⠀⣈⠃⡈⠀⡤⠊⠑⢄⣀⣤⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢠⣿⣷⠀⢾⣿⡇⠀⠀⢰⣿⣿⣿⣟⡁⠀⠀⠀⠀⠂⠋⡆⢠⠞⠛⢿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢷⣾⠛⠇⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠴⠃⠘⠀⣠⠂⠈⡁⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠢⣄⠒⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠁⢀⠀⠈⠲⢤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡁⠰⠃⡡⠄⠀⠀⠀⠀⠑⣄⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣱⠀⠤⠄⠁⠀⠀⠀⠀⠀⠏⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠁⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⢶⣦⣤⣄⡀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠘⣧⣀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⡙⠁⠀⢠⠀⣈⢙⠛⠿⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡀⠼⠞⠒⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣚⡁⠀⠀⠠⠌⠐⢄⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⣀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣼⠀⠨⠀⠀⠉⠃⢤⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠂⠀⠀⢆⡄⠀⢀⣈⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣅⡼⠃⢠⠐⠃⠀⠀⢀⣿⡖⠁⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠗⡐⠀⠀⠀⠀⠘⠙⢢⢀⣄⠈⡄⠶⡀⠀⢀⠚⠁⠀⡀⠐⠀⠀⢀⣀⣤⡠⠛⢂⡀⠀⠚⠁⠀⠰⡖⠠⠦⠀⠀⣠⠜⢋⡿⠂
⠀⠀⠀⠀⠀⠀⢀⠆⠭⠀⠈⠀⠀⠠⠔⠀⠀⢁⣤⠾⠯⢤⡨⠀⠉⣵⡆⠀⠀⠘⠿⠂⣶⠠⠛⠁⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⠃⠰⠀⡈⣥⠞⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠠⠎⠀⠀⠀⣰⢫⠁⠀⠀⠀⢹⠀⠀⠀⠈⢂⡀⠀⠐⠀⣀⠀⠀⠀⠀⠐⢀⠤⠀⡄⡀⡤⠀⠈⠠⢉⡀⠆⣀⠘⠠⠀⢠⡀⢠⠼⣍
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⠀⠠⣲⠶⡯⠀⠠⡄⣦⣄⣚⠤⠀⠀⠀⠀⠁⢠⠀⠀⠀⢡⠀⠀⢀⣀⢈⠱⠚⠁⠀⠀⢀⠀⠀⠰⠃⠀⠉⢎⣀⡊⣉⠁⠁
⠀⠀⢀⠄⠒⠒⣀⠉⠋⠀⠀⠔⠈⠁⣀⠄⡤⠄⠀⠈⠋⠤⢧⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢠⠇⠸⠡⠀⠒⣃⠀⠃⠉⠀⠪⢀⠈⡀⠀⠀⢴⠶⠁⠀⠀⠆
⠀⣀⠛⠛⠋⠱⠚⠄⠀⠀⡠⠞⢹⠶⠋⠀⢀⣶⡆⠀⣴⣶⠇⠕⠀⠀⠀⠀⠀⠀⠀⠘⠌⠃⠈⠁⠉⠩⡑⠀⢀⠀⠀⠀⠈⠐⠀⠀⠀⠃
⢀⠀⣐⡀⠀⠀⠀⢰⡔⡀⠑⠠⢀⠦⡀⠀⠈⠉⠄⠀⢁⠘⠉⠐⠂⠀⠴⠤⣤⠦⠴⠂⠀⠀⠀⠀⠀⠀⠈⠂⢠⡑⢄⡀⠀⡹⠄⠀⠁⡠⠀⠀⠀⠀⢀⠌
⡔⠀⠀⡥⣀⣌⠉⠆⠀⠀⠀⠀⠀⠉⠈⠐⠠⡄⠀⠆⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣷⣶⣞⠒⣶⣯⣽⣖⣉⣭⡵⡆
⢐⠀⠐⠀⠀⠐⠂⠁⠀⠀⠀⠂⠀⢠⠀⠘⢟⠲⡦⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⠀⠀⠀⠉⠉⠁⠀⠻⣿⣯⢉⣫⣶⠶⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⣠⠀⠈⠀⠐⠷⠔⠲⠤⣄⡀⠀⠀⡀⠀⠀⠀⠀⡠⠄⠉⠀⠀⣀⣠⣰⡞⠛⢂⠀⠀⠀⠀⠀⠀⠀⠿⡅⠂⠰⠚⠁
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣬⠡⠙⠙⢿⢙⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣤⡬⡷⡀⠠⡊⠀⠈⠿⣤⡤⠉⠀⣀⢠⡄⠀⠡⡀⠀⡀⠀⠀⠠⠈
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠓⠬⣅⣀⣉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡚⠛⢋⡙⠠⡌⢣⠀⠀⠀⠀⠀⢀⡠⠅⢲⡤⠀⣄⠠⠄⠑
⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠙⠧⠘⠃⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢉⡀⠀⠁⢤⡄⢳⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⣌⢠⠀⠩⠄⢰⠅⠈⢹⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠐
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⣠⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠁⠀⠈⢆⠰⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠂⠀⠀⢆⡈⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠁⠄⢄⢂⠄⠘⠠⠬⣃⡑⣀⣀⠿⢉⣤⢤⠤⢤⠀⢸⡟⠝⠛⠛⡏⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠦⣞⡦⠔⣂⠴⠚⠩⡦⠀⠀⣀⣤⣀⠀⠀⡾⠉⠈⢄⣠⡄⠀⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⢠⠔⠂⠀⠐⠉⢄⠀⠀⠀⠀⠀⠃⣧⣀⣼⠀⣰⣿⡤⠖⢊⠁⠐⣰⡧⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠘⣿⠠⠓⣀⡥⠖⠋⣿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠲⣦⣅⣀⡀⢰⡇⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠁⠰⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠒⠀⠂⠀⠀⠀⠐⠒⠂⠐⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠂⠐⠂⠀⠀⠀⠀⠀⠀⠒⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⢨⠈⠙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⡀⠀⠀⣀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⡀⠀⡀⡀⠀⠀⠀⠀⠉⢳⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⢠⡀⠀⠦⠀⠠⠀⠁⢖⡏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡈⢉⠱⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⡔⢻⡠⠀⠋⠠⢀⢀
⠀⠀⠀⠀⠀⠰⢠⢾⠀⠀⠈⡙⠈⠊⠙⢁⣹⠀⠀⠀⣠⠀⠀⠔⠀⠵⠔⠛⠃⠀⠀⠰⠆⠀⠀⠦⠉⠁⣀⠄
⠀⠀⠀⠀⠀⠀⠀⣰⠄⠂⣌⠁⠀⢀⡠⡌⠛⡄⠈⠀⠀⡄⠐⠆⠺⠂⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡈⠁⠀⠞⠁⠀⠀⠀⢔⡁⠀⣠⠀⠀⢠⠄⠀⠀⠀⠀⣉⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣑⢶⣦⣬⠀⠀⠀⠀⢨⡀⠀⠉⢧⡐⠦⢄⠀⠀⠀⡤⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⠆⠠⡀⠐⠨⠠⠀⠘⣃⠭⣀⢘⠃⠘⣿⠀⠹⠒⠂⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠔⠃⠀⠀⠀⢹⣤⣤⣥⠀⠁⠀⠀⠀⠈⠀⠈⠀⣀⣀⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠊⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⠿⠆⠀⢀⣴⠶⠶⠶⢶⣤⡀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⡄⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⢠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠐⠐⠒⠀⠂⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂


⡿⠉⠙⡟⢛⠛⠟⠟⠻⣟⠻⠟⠿⠿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣿⣟⣿⣿⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡖⠊⠉⠦⠒⠞⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁⢀⣤⠤⢤⣤⠂⠁⠈⠀⠐⠃⠀⠀⠀⠀⠀⠢⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢨⡏⠀⠀⠀⢹⡆⠀⠀⢀⠀⣎⠀⠀⠀⠀⠀⢢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⢧⣀⠀⢀⣼⠧⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⡖⠚⠛⠹⠉⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠢⠀⠀⠠
⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠢⢄⠀⠀⢀⠴⠒⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠥⠰⡃⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⢀⡰⠉⠉⠱⣄⠀⠀⠀⠀⢀⡜⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠉⠒⠒⠚⠁⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠖⣋⠭⠤⠉⠦⢀⠄⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⢸⠁⠃⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄⠀⠀⠀⠀⠀⣐⣲⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠂⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣨⡀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⢇⡔⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠐⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠘⠁⠇⠀⠄⠀⠀⠀⠸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠀⠐⠒⠒⠀⢹⣤⠁⠀⠠⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡍⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⢠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠤⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠘⠂⠀⠰⠀⠰⠀⣢⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⣀⡂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⡀⠀⠀⠀⠀⠐⢤⠃⠀⣠⠀⠀⢀⡉⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠸⢄⢀⣀⡏⠳⠀⠀⠀⠀⠉⣠⡄⠀⢰⠀⠀⠀⠷⠒⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⠰⣛⡄⠀⠀⠀⠀⠛⢣⠀⢸⡀⠀⠀⠸⡉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⡁⡤⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⠐⠂⠀⠀⠀⢸⡀⠈⠄⠀⠀⠀⠇⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢀⢷⠁⠀⠀⠀⠀⠀⠀⡀⠀⢘⡇⠰⡀⠀⠀⠀⠰⡀⡃⠨⡀⠀⠀⠀⡀⠀⣤⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠈⠁⠀⠀⠀⠑⠀⠀⢁⠀⠀⠧⣠⠇⠀⠀⠀⠀⡍⠇⠀⠂⠀⠀⠀⠇⣠⠃⢣⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠁⢆⠀⠀⠒⠒⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠁⠀⡘⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡰⠁⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢠⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠟⣋⣹⣾⡷⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⢿⣽⠦⣤⡀⢀⠀⠀⠀⠻⣶⡯⣵⡾⠁⠀⠀⠀⠀⠀⠀⠀⣼⡛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣍⢰⠀⠻⣌⡃⠀⠀⠀⠘⡾⠋⠀⣀⣠⢤⡄⠀⠀⠀⢰⡿⢿⣿⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠙⠈⠁⣄⠀⠀⠀⠀⢀⡞⠁⠀⠀⢷⡀⠀⠀⣼⣿⣾⠃⠀⠈⠙⢷⡄⠀⠀⠀⠀⢀⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡄⢠⣿⣦⠀⠀⢀⣸⠁⠠⠄⠆⣶⢿⣟⣞⠻⠷⢯⣀⡀⠀⠀⠀⣿⠀⠀⣠⡴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢀⣿⣯⠷⣾⣱⢿⣤⣠⢠⢠⡀⣘⢷⣸⠳⠂⠀⠀⣷⢤⡀⣀⣬⡶⡛⢭⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡚⠋⢠⡾⢊⢥⣾⠟⠁⠀⠀⠉⠉⠉⠉⠉⠙⠉⠉⠙⠙⠐⣷⣶⡏⠙⣏⣻⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠑⣾⣹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠴⢿⣖⣈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠾⣠⡴⢸⣯⣙⡙⠗⢛⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢾⢿⣿⡟⢲⡤⠤⢄⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⣽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢩⠈⠡⣤⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣽⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣨⠀⠸⣷⣿⣿⡀⠈⣌⣤⠶⠶
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠰⠇⡀⣈⣨⣿⠎⠉
⠀⠀⠀⠈⠒⡄⠀⠀⠀⢀⣁⢰⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⢨⣭⡿⣿⣻⠆
⠀⠀⠀⢀⣙⣛⠐⠀⠙⢛⡃⣀⣀⠠⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁
⠀⠀⠘⠛⢧⣨⡄⠁⠛⠋⠉⢠⣄⣠⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠶⡿⣡⣦⡴⠂
⠀⠀⠀⠀⠀⢙⡇⠀⠀⠀⣀⣻⡿⠟⢋⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⢤⡀⢠⣮⡟⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠛⠉⠀⡠⢞⣷⢾⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢿⠉⠻⢑⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⡴⠋⢠⡿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⢿⡿⣷⣿⣯⡄⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠃⣤⢜⡛⣋⡽⢟⡿⣿⠟⣻⡿⣿⡿⣿⣿⡿⠀⣧⡀⠛⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠀⠀⠀⠀⠀⠀⠸⢳⠵⠶⠋⣠⠊⢹⣏⣣⡈⢿⣯⠿⣛⡋⠽⠉⡁⠈⠹⣯⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠈⡡⡤⠀⠀⠏⠐⣭⡥⣕⢺⡟⠂⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣅⣘⢧⣰⠀⠀⠉⠉⣿⢿⡾⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠀⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⣋⣿⡷⠀⠀⠀⠀⠀⠀⣿⣜⡇⣀⣀⡀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡿⣾⠇⠀⣠⣄⠀⠀⠀⣿⣼⡇⠀⠀⠉⢳⡄⠀⣠⢾⠋
⠀⠀⠑⠦⡀⣴⣲⠤⣄⡀⡀⠀⠀⠙⠇⢠⠋⠀⠈⢣⣤⣤⠿⠿⠧⢤⡀⠀⢀⣷⣞⣍⠃
⠀⠀⠀⠀⠀⠻⢯⣐⠈⢓⠲⢀⠀⠀⠀⢸⠀⠐⠒⠛⢹⢮⣽⡂⢀⣠⢷⣶⣪⣝⡺⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠈⣷⣦⠀⡸⣀⣤⠾⠚⠊⠉⠉⠉⠉⠙⠻⢿⣍⣿⣾⣧⣀⣀⡄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠧⢸⡿⢫⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⡇⡈⠃⠦⣴⣟⠒⢄⣲⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠤⠤⣾⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣈⠀⠻⠛⠟⣶⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⢤⡾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⠃⢖⣿⣿⡗
⠀⠀⠀⠀⠀⠤⣤⣞⣳⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣯⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣰⠦⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⢿⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⣁⡸⠛⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⠓⠘⣿
⠀⠀⠀⠀⠀⠵⢄⠀⢘⣩⡤⠒⠈⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢵⣿⣦⣄⠈
⠀⠀⠀⠀⢰⠮⣹⡤⠈⠁⠀⢸⣿⠟⢩⢙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣧⢐⣄⣉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠈⡽⠀⠀⠘⠟⠁⢠⣻⢟⡟⢹⡿⣿⣷⢶⡶⡶⣶⣺⣟⠻⣿⣻⢗⣯⣒⣤⠀⠀⠈⠙⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢡⠎⠀⠉⠰⢪⣕⣪⡼⢡⢏⠹⠂⠃⠸⠓⣯⣗⣯⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠐⣇⡠⡄⠈⠁⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⢲⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠐⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠚⣷⡂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⠻⡀⣸⣆⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠌⠀⠀⠁⡄⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣒⡀⠀⠀⠈⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠸⠗⢋⠀⣘⠛⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠀⠀⢀⠘⠦⠟⢻⠛⠋⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⣾⠓⣿⢋⣴⣬⡐⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⠤⠀⢡⠀⠀⣐⡀⠀⠀⡶⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣰⣁⠉⠁⡤⠄⠀⠀⠀⠀⠀⠀⠰⠀⠀⢁⡁⠀⠀⢀⠃
⠀⠀⠀⠀⠠⠀⠀⠈⠀⠈⠒⠀⠠⢆⠀⠉⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠋⠉⠙⠂⣼⠀⠀⠀⠀⠀⠀⠀⢀⡔⣆⡀⠛⠁⠀⡠⠊⠠⡤⢤⣀⢀
⡀⡄⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠜⢉⠒⠀⠰⠊⣵⠀⠀⠀⡏⠉⠉⠉⠈⠁⠉⠉⠉⡛⠙⠉⣋⡴⢀⢀⠉⡆
⠇⠠⠄⠇⠀⠀⢀⡀⢤⠴⠄⠀⡐⠀⠀⠀⠀⠀⠀⢀⢠⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇⠀⠀⠁⠐⠄⠀⠀⠀⡇⠈⠀⠀⠉⠉⠉⠁⡇
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⡈⠆⠎⠾⠁⠀⠀⠀⠀⣰⡖⣀⣄⣀⢀⠀⠀⢰⠇⠀⠀⠀⠀⢡⠀⠂⠀⡤⠠⠐⠒⠒⠁⠀⠀⠀⠀⠀⢤⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠆⠀⠀⠀⠀⠀⠀⢈⠀⠀⠄⠀⠀⠀⠀⣈⠣⢄⢀⠀⣄⠀⠀⣰⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⠁⠂⠀⠀⡀⠀⠀⠈⠛⠁⠀⠀⠀⠰⠀⡗⣒⠋⠸⣿⡿⠀⣞⠒⠤⡆⢀⠀⠀⢠⡊⢨⣽⠀⠀⡀⠀⠄⠀⠸⢀⠄⢀⠄⠌⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠀⠀⠀⢈⠂⠀⠃⠀⠂⠀⢤⠃⣍⠭⠀⠈⠀⠀⢲⠀⢐⡞⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠁⠀⠀⠀⠈⠙⠒⠠⠤⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠘⠒⡖⠋⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡄⠠⠼⠒⠒⠒⠒⠒⠲⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠒⠤⢀⣀⠀⠀⠀⠀⣀⠠⢸⠀⠀⡐⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠐⠒⠆⠀⠀⠀⠠⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⡀⠀⢀⣀⣀⡤⠔⠊⠀⠐⠦⣀⡀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⣀⠀⠀⡀⠀⠳⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⡟⠉⢹⠉⠁⠇⠀⠀⠀⠀⠀⠈⠈⢱⠒⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠀⠀⠘⠒⠖⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠸⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⡍⠈⢙⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆⠀⠀⠀⠀⢠⠦⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠃⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡌⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⠃⠀⠀⠀⢰⢀⡇⠀⠀⠀⠀⠤⡀⠈⠀⠁⠀⠀⠀⠀⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠞⠈⡇⠀⡰⠍⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠂⠸⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠠⠆⠼⡀⠀⠀⡀⠄⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣠⡀⠜⠁⠀⠀⠀⠀⠀⡞⢐⡐⡘⡒⡄⠀⠀⠀⠀⠄⡀⠀⠀⠂⡠⡀⢠⠀⠸⠀⠀⠀⢀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠀⠀⠀⠀⢺⠇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⢾⡲⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣢⣰⠄⢀⠎⢠⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠀⠙⠀⢀⠄⠀⠿⠇⠀⣱⣾⠀⠀⠀⠀⠀⣿⠏⠂⠊⡰⠣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠆⠶⢶⡔⠂⠀⠀⠸⣿⣀⠀⠀⡀⠘⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⡁⠀⠀⡄⠀⠀⠀⠀⠀⠈⡉⠀⠶⠁⠂⠠⠚⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠃⠀⠀⣴⣇⡀⡀⠀⢀⠀⢠⠛⠉⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⣷⡶⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠂⠚⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡑⠒⠫⠤⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⢀⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⠠⠭⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⠶⢔⡋⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣥⡂⠀⠀⠀⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠑⠮⣶⣄⠀⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠹⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⡀⠀⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠍⠀⣀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠺⡗⠒⢻⡟⢛⣷⡾⠿⠶⠶⠶⣶⣺⣿⣿⡀⠀⠀⣽⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⡇⠀⢸⣇⡿⠋⠀⠄⡓⠀⣱⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣤⣧⣤⣼⣿⣆⣀⡄⡊⠯⡐⠌⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠏⣀⣞⢡⠏⢰⠁⣼⠁⡞⢡⡿⠻⣷⡌⠀⢀⡈⠙⠋⠀⠀⣀⡀⠀⠀⠘⢋⡟⠛⢛⡟⠻⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠑⠛⠒⠓⠴⡇⣼⠀⠀⠘⡷⠌⣂⠈⠛⠀⠀⠀⠛⠁⠀⠀⡀⡸⠀⠀⣸⠁⠀⡷⢠⡆⠀⣦⠤⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⣿⠛⡟⣹⡧⣠⠄⠠⡄⠐⡒⢾⣄⣇⠀⠀⡟⠀⠀⡇⠈⠉⠉⠉⣀⡠⡇⢸
⠀⠀⠀⠀⠐⣄⠠⣿⠀⣾⠀⠀⠀⣠⡎⠀⠀⠀⢸⠀⠀⠀⢸⣘⣦⣀⣴⠄⣋⡀⠾⣆⠋⢠⠆⠹⠟⠶⡇⠀⠀⡏⠈⠉⠉⠁⠀⢀⠇⢸
⠀⠀⠀⠀⠀⠈⠓⣿⢀⣿⠀⢀⡔⣹⠀⠀⠀⠀⢸⡆⠀⠀⢸⠉⠀⠀⠀⠉⠉⠉⠁⣟⠀⢨⡂⠀⠀⠀⡴⠀⠀⣷⠤⡤⢤⠖⡚⣻⠀⢺⠂⠀⡀
⠀⠀⠀⠀⠀⠉⣷⡟⣷⣿⠀⣾⢷⣏⠄⠀⠀⠀⢸⡇⠀⠀⢸⣆⣀⣤⡤⠤⠤⠶⠶⡟⠃⣀⠓⠛⠛⠻⡆⠀⢸⡇⠚⠐⠒⠘⠉⡯⠀⢀⣀⠼⠁
⠀⠀⠀⠀⠀⣀⣸⡗⣿⠿⠐⢻⡿⠏⠀⠀⠀⠀⢸⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢱⡀⠉⠀⠀⠀⢠⣇⣀⣸⡧⠄⠀⠠⠄⣺
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⣮⣯⣴⣷⣦⣄⡀⠀⢸⡇⠀⠀⢸⣇⠀⣀⣀⣀⣤⡤⠤⢾⡇⣾⠒⠚⠛⠋⠉⡿⢹⠁⠒⠒⠀⠉
⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠳⡾⣷⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⢘⠦⢽⣠⣤⣤⢲⡶⡇⣼⡀
⠀⠀⠀⠀⠐⣎⢙⠛⠛⢻⠛⠋⢩⣠⠏⠉⠓⢶⡇⣿⠀⢀⣀⣀⣀⠤⣤⣶⣒⣿⡟⣾⠀⢘⣶⢿⡺⣿⣛⣷⣿⣽⣦⣄
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠶⠾⠛⠁⠀⠤⡤⣶⣧⣿⣿⣛⣥⣿⣍⡾⡿⡲⣟⢟⣫⣹⠀⢸⡿⢿⠻⡟⣏⣻⡹⢬⣆⠳⣿⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣏⣯⣷⣶⣷⠿⡟⢿⠻⣏⣿⠹⣇⠸⣟⣸⣧⣽⣷⣬⢿⡶⣟⣟⣿⢯⣻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣭⠧⣽⡞⢷⣏⣘⣷⣤⣿⡶⢿⢟⢻⣻⡻⣝⣎⣮⣷⣷⢿⣾⠿⣿⣻⣯⣽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣟⣿⢻⡙⣟⣦⣳⣽⣼⢾⣶⠿⣿⡻⣯⢻⣦⣹⣷⣿⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢿⣝⡻⣮⣿⣶⣿⣷⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠄⠄⢀
⠀⠀⠀⠀⠀⠀⢀⡔⠈⠀⠀⠀⠀⠀⢀⠠⠀⠒⢦⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⢀⡀⠊⠀⠀⠀⠀⠠⠀⠐⠀⠈⠉⠀⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⡰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡄⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠰⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡔⠙⠂⠀⠀⢀⠀⠀⡍⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠙⠀⠠⠀⠀⠀⠀⠰⡆⠀⠑⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠃⠀⠀⠀⢀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠆⠋⢁⠀⢒⠀⢦⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠧⡙⢆⠀⠀⠣⠀⠙⠆⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠦⠠⡀⠠⡀⠰⠒⠀⠳⢌⢳⡀⠀⠀⣴⠦⠀⠀⠀⠀⠀⠀⢠⣾⠿⣲⢶⠯⡖⠈⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠐⢤⠀⠀⠁⠌⠂⡘⣕⠀⠈⠙⠒⢒⣤⠴⠒⠉⠀⠚⠋⠋⠈⠁⠀⣼⡧⢃⠁⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⢀⠀⠀⠀⠜⠐⡬⠗⣋⠥⠚⠉⠀⠢⠗⠄⠀⣠⠶⠶⣄⠀⠠⣿⠀⠀⠡⢦⡼⠇⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⢀⠀⡨⠀⠀⠖⡊⠄⠀⠙⢌⠦⠀⠀⠀⠀⢀⡀⢁⢻⣄⠠⣟⢀⣴⡿⡦⠒⠁⠀⠄⢋⣼⡿⠀⠠⠀⡀
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠉⠀⠀⠀⠀⠘⣿⢀⠗⢀⣀⠴⠞⠊⣽⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢴⣦⣋⠁⠀⡀⢴⡟⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⡹⠀⠚⠉⡛⠙⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠴⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠒⠒⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠉⠁


⣿⢿⠿⡿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⣰⣖⡲⠥⣀⠠⡁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠤⠀⢯⣛⣷⠻⠄⠀⠀⠈⡓⠈⠢⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠥⠀⠀⠀⠀⡄⢛⢰⡈⠐⡠⠘⠁⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠆⠀⠀⠀⠀⠃⢠⠰⠀⠀⠀⠀⠠⣦⠷
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠷⠾⠀⠀⠁
⠀⠀⠀⡠⠰⠬⠀⠀⠘⠄⠠⡄⠈⠀⠤⢤⠀⡀⠀⠀⠀⠀⠀⠀⢄⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜⣈⣠⣀⣀⣠⣤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⢀⣆⠀⠀⠀⣶⠐⠀⠄⠀⠀⠀⠀⠢⠀⠀⣈⠉⠉⠉⠉⠉⠋⠉⠀⠐⡵⠒⢦⠀⠀⠀⠀⠰
⠀⠀⠁⠀⠀⠃⠀⠀⠀⠋⠀⠀⢠⡀⠀⠀⠀⠀⠠⠂⠀⣄⠀⠀⠀⠀⢀⠀⠀⢁⠙⠤⠞⢀⠀⠀⠀⠀⠁
⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠦⡄⠐⠀⠐⠂⢐⠈⡄⠠⠀⠐⠀⠬⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡥
⡇⠈⠀⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠒⠀⠠⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠇⠀⠀⢀⠓⡀⠇⠀⠀⠀⠀⠠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⢀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠰⠄⢙⡟⠲
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣠⣀⢘⣁⣀⡀⠤⠤⠼⠤⠤⠤⠤⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠆⠉⠉⠉⠉⠉⠉⠰⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠚⠛⠛⠛⠛⠛⠒⠀⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠻⠿⣶⣶⣶⣍⡉⠀⠀⠀⢀⣤⣤⣄⠏⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⢀⣤⣼⣿⣿⡟⠛⠓⠀⠛⠉⢀⠉⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⣠⣾⣿⣿⣿⡄⠀⠀⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆⠙⡄⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣤⣾⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢰⣾⡙⢣⡀⠀⠀⠈⣿⣿⢀⡿⠘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢏⣉⣙⡻⢿⡿⠀⠀⠀⠀⠀⠸⣿⡷⢨⡀⠀⠀⠀⠹⣿⣯⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢸⢏⣿⢿⣆⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⣼⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠁⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡤⠚⣓⣶⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⠭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠂⠚⢻⣿⠏⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠖⠈⠉⠉⠁⠀⠀⠀⣿⠀⠀⠀⠉⠲⠦⣄⣀⣀⣀⣀⣠⡀⠶⠋
⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡈⠙⣄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣀⣤⣄⣠⡞⠛⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣈⣳⣀⣤⣤⡀
⠀⠀⣠⠏⠀⠀⠀⠀⢀⣠⠴⣿⣿⣿⣿⣇⡇⠀⠀⠙⣿⣿⣿⣿⣦⣄⣀⡀⢀⣀⡠⢿⣿⣿⠹⣏⠻⣿⣿⣿⣄⡀
⠀⢠⠋⠀⠀⠀⢀⡴⠋⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠈⠻⣿⣿⣿⣧⠉⠉⠀⠉⠀⠀⣿⣿⡀⠘⣦⢹⣿⣿⣿⡙⢦⡀
⢀⡎⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⠀⠀⠀⠀⢹⣿⡇⠀⠈⢎⣿⣿⣿⣷⠀⠹⣄
⠘⠃⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⢿⣿⣿⣿⡆⠀⠘⣄
⡇⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠸⣿⡇⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠈⡆
⡇⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⣿⡇⠀⣠⠞⠁⢸⣿⣿⣇⠀⠀⠀⢰⡄
⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠉⠉⠉⠉⠁⠲⠶⠶⢠⡀⠀⠹⣿⣇⠀⠀⣿⠃⢸⠁⠀⠀⠀⣿⣿⡿⠀⠀⠀⠈⣧
⡇⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣀⣀⠿⢿⣶⢼⣿⣋⣈⣿⣄⠀⠀⣿⣿⡇⠀⠀⠀⠀⠙⡀
⢁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⣁⣠⣤⡔⠚⠛⠃⠉⠀⠀⠀⠘⠃⠀⢹⣿⡇⠀⠀⠀⠀⠀⡇
⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⡅⠀⡾⢿⡿⠿⠓⠀⠀⣀⣀⣀⠀⠀⠀⣧⠀⢸⣿⠇⠀⠀⠀⠀⠀⢣
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⡀⠀⠀⠀⢰⣿⣿⣿⣿⣧⡀⠀⡉⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠸⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠘
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣼⣤⣤⠤⠒⢿⣿⠋⠀⠀⠀⢹⣷⠀⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⢀⣼⡟⢠⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠟⠉⠀⢸⠇
⠈⠓⣶⡦⢀⣀⣀⡠⠴⡶⠚⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠆⢀⣀⣀⡀⢴⠶⠊
⠀⠀⣿⡇⠀⠀⠀⠀⠀⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢸
⠀⠀⢹⡇⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠘⡇⠀⠀⠀⠀⠀⣷⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣟⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⠃
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⢀⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡆⠀⠀⠀⠀⢸
⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⣶
⣿⣿⣿⡟⠋⠉⠛⠋⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣴⣦⣴⣶⣶⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠠⡀
⠀⠀⠀⣧⣤⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠠⠀⠉⡌⠄⠀⠀⠀⠀⢀⡤⢒⡆⢲⡞⡉⠳⣄
⠀⠀⠁⠁⠒⠺⠁⡃⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⢤⣊⣤⢞⣝⣭⠓⢾
⠀⠀⡂⡰⢒⠒⡀⠃⠀⠀⠀⠀⠀⠀⠀⢀⢡⠠⠶⣄⠈⡢⠄⠀⠀⠀⠀⠈⢌⠠⡀⣀⣀⠄⠣⠂⠀⠀⠀⠀⠀⠀⠙⢦⣉⠐⠚⠉⠁
⠀⠀⠐⠶⠞⠶⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠈


⢠⣤⠀⡀⠤⠠⢀⠀⠠⡀⠀⠀⠀⠀⠀⡤⠶⠶⠾⠯⢉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠂⠋⡆
⠈⡙⠊⠀⠐⢆⢶⠂⢠⠁⠀⠀⠀⠀⠀⡇⠀⡤⢤⡀⠀⡇⠀⠀⠀⠀⠀⢰⣛⠉⣡⠶⣄⣛⡻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡃
⠀⡅⢄⠣⣥⢧⠇⡀⢸⠀⠀⠀⠀⠀⠀⠇⠀⣖⣂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⠓⠀⡁
⠀⠃⠀⠑⠒⠂⠈⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠄⠈⠉⠮⠁⠘⠓⠃⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠤⠀⠄⣀⣀⡬⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⡀⠈⠄⡍⠉⢹⢆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣒⣐⡄
⠀⠀⠀⠀⠀⠁⢲⠈⠀⠀⠀⠀⠀⠀⢂⡀⠄⠀⠀⢀⡴⠃⠃⠀⠀⠀⠀⠀⠣⡀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠖⠆⠉⠉⠙⠋⠁
⠠⢀⠀⠀⠀⠀⠄⠀⠤⠀⠀⠀⠀⢀⣬⡄⢰⠉⠉⠉⠒⢀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠢⠤⢀⡀⠠⡄⠈⠁
⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠄⢄
⡀⠠⠤⠤⠜⠶⠖⢁⢐⠄⠀⠀⠀⠀⠀⣀⡐⢢⠀⠊⠱⣵⠀⠀⠀⠀⠀⢀⠔⠲⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⡇⠀⠀⠀⣠⠔⢂⠀⠈⠀⠀⠀⠀⠀⠀⣼⡇⠀⠈⣁⣀⢉⠀⠀⠀⠀⠀⠀⠁⠈⠀⡋⠳⠆⠢⡄⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⡂⡄
⢁⠀⠀⠀⠁⠚⠉⣀⡸⠀⠀⠀⠀⠀⠀⠻⣗⣶⡶⠥⣭⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⢣⣀⠀⣀⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠿⠻⠟⠶⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢤⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠂⢤⡀⠀⠀⠀⠀⢀⡠⠔⠂⢉⠀⠀⠉⠑⢢⡀⠀⠀⠀⠀⠀⢀⠔⠊⠉⡁⠀⠡⡐⢀⠀⠀⢀⡀⠀⠀⢀⠔⠈⠣⠄⠠⠜⠁⠢⡀
⠀⠀⠣⡀⠀⠈⠐⠂⢀⠍⢠⠀⢁⠚⠥⠈⠀⠁⠈⠁⠀⠕⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⠑⢆⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⠜⠂⣈⠕⠀⠈⠀⡡⠐⠒⠢⢄⠀⠀⠀⠀⡀⣀⠜⠁⠀⠀⢸⠠⠈⢈⡈⡀⠀⣠⠀⠔⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠘⠒⠫⠤⠄⠄⡤⠊⢀⠀⢀⡠⠚⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⠀⠀⡆⠁⢀⠀⡘⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠮⠤⠴⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣢⡈⢲⡰⠁⠀⢘⠖⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⣀⡀⡠⠔⠢⢄⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⣀⠀⠀⠀⣀⠀⠀⠈⠒⣄⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠇⢯⡱⢸⠒⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⡤⠴⠎⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠛⠁⠀⣠⠄⠒⠒⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁⣠⡀⡄⠀⢡⣧⠀⠀⠀⢨⠉⠉⡇
⠀⠀⠀⡀⠀⠐⠚⠀⠀⠐⠻⣄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⢰⠃⠀⣙⡷⠃⠀⣿⠇⠀⠀⠀⠈⠳⠞
⠀⠀⢰⠁⠀⠀⠀⠀⠠⡄⢠⠀⠃⠀⠑⠐⠊⠉⠉⠐⠢⠤⠀⠤⠔⠊⠀⠀⢀⠀⠀⠀⠇⠀⠐⠇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⠂⣠⣀⡀⠀⠀⣼⠇⠀⠀⠀⠈⠁⠀⣀
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠲⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠈⠁⢐⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡧⠀⠐⠒⠒⠀⢤⢄⠈⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠚⠉⠢⣄⠀⠀⠀⠀⠀⠙⠶⠶⢥⣤⣤⡾⠁⠀⠀⠀⠀⡚⠓
⠀⠀⣇⠀⠀⠈⠀⠂⠈⣾⠘⠃⡅⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣄⣴⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀⣠⣖⠠⠀⠐⠀⣷
⠀⠀⠉⡄⠀⠀⠀⠀⠀⠙⠐⡀⡇⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠙⠋⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠄⠀⢀⢸⣿⣿⡇⠀⠀⢸⡅
⠀⠀⠀⠲⠶⢤⠤⠤⡾⠡⡾⠐⠁⠀⠀⠀⠀⠀⠀⣀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠈⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⠛⠶⠶⠶⢴⣄⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣉⠀⢀⡂⠀⠀⠀⠁
⠀⠀⡀⠀⣀⠠⠖⠒⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠀⠠⠔⠒⠂⡄⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣤⣀⣀⣀⡀⢈⠀⠀⠀⠀⠀⠀⠀⢀⢄⠤⠄⠀⠀⠄⠀⠀⠰⠂
⠀⠀⢸⡀⠀⠀⠒⠡⡐⠀⠰⡀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⡄⠕⠁⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⡃⠀⠐⠂⠚⠁⠀⠀⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⡈⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⡀⠀⠀⠀⡧⡀
⠀⠀⠀⢣⠀⣤⠴⠖⠚⠀⠀⡁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣄⢣⣤⠇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠂⠀⠒⠊⠁⠈⠒⢄
⠀⠀⠀⠈⠆⡀⠀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠘⠻⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠉⠉⠐⠲⠀⡀⠤⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣤⡎⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠹⠁⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒
⠀⠀⠀⠀⠀⢀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡿⠉⢹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⢿⡇
⠀⠀⠀⠀⠀⣸⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣇
⠀⠀⠀⠀⠀⣿⠃⠀⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⣸⡇⠀⢸⡇⠀⠸⣿⠀⠀⠀⠘⣿⠀⠘⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠃⠀⠸⣷⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢰⡟⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⢿⡄⠀⠀⠀⢹⡆⠀⢻⡆
⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⡏⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⣸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⣇⠀⠈⣇
⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠚⣷⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⠙⢆⣸⠆⣰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⢀⣁⣀⣤⣰⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣄⢀⡀⢀⢀⢂⠀⠀⠀⠀⠀⠀⠙⠁⠂⠈⠉⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠠⠂⠋⠁⠈⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠃⠘⠱⠟⠛⡀⠀⠀⠀⠀⠀⢀⠀⠑⠀⠊⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠐⠁⠺⡄⠀⣄⠀⠛⠀⢀⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢋⠩⠛⠻⠆⣰⠉⠀⠀⠀⠀⠀⠀⠠⡀⠰⠇⠀⢀⠜⣀⢀
⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠓⠂⠒⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠠⠠⠀⣧⠀⠀⢰⠒⠂⠈⠉⠉⠉⠐⠒⠚⠓⣆⠌⠀⠙⡦
⠇⡤⠘⡀⠀⣀⡀⠤⠴⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⡒⠚⠚⠀⠀⠀⠀⣰⠞⠠⠀⡀⠄⠀⠠⠃⠀⠀⠀⠈⡀⠂⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠐⡀⡉⠀⠀⠀⠀⠀⠀⢄⡀⠚⠀⠀⠀⢠⠈⣢⢠⣀⣦⠀⣀⠃⢄⠀⠀⠀⠀⠅⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠤⠤⣠⠀⢠⠀⠀⠰⢼⢠⡆⣈⣛⠏⣸⠦⢽⠃⣴⠀⠀⡗⢒⣻⠀⠐⠀⠀⠀⡜⠐⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠄⢧⡜⠀⠀⠀⠇⠤⣀⣀⡀⠀⠑⠚⠉⠀⠈⠀⠀⠇⡰⠿⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⣆⠀⠀⠀⣀⣀⡀⠤⠤⠤⠤⠤⢤⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠑⠠⠄⣀⡀⠀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣄⣀⣀⣀⣠⣤⠐⠈⠀⠐⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⣀⣀⠀⢸⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠉⠈⠀⠄⣀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⡋⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠠⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⢘⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⢲⠀⠀⢀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡘⠀⠀⠀⢠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⢂⢀⠐⠈⠀⠀⠀⠀⡔⢒⢀⢒⣤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⢀⣤⡾⠛⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣿⡏⠉⢹⣷⡿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢉⣿⣅⢀⠀⠀⠀⠀⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⠀⠀⠀⢀⣘⣁⣀⣠⣴⣿⠿⠿⣿⣿⢸⠀⠀⠀⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⢀⣤⣿⣿⠿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣰⣿⠟⠋⣷⠒⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⢠⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⣤⡄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡄
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡤⠀⠀⠀⢠⠀⠀⠀⠀⠿⠿⠀⠸⠿⠀⠸⠿⠇⠀⠿⠇⠀⠿⠷⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣶⡆⢰⣶
⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠸⠡⢤⠀⢰⣶⠀⢰⡖⠂⠀⣶⡆⠀⣾⣷⢴⡄⢀⠀⠀⢀⠀⢁⡀⠀⠀⠀⠀⠉⠀⠿⠟⠈⠉
⠀⠀⠀⢸⣿⠀⣿⡇⠀⢀⣠⠀⢚⣿⠇⢸⡿⠀⠒⠀⠙⠀⠈⠉⠀⠈⠉⠁⠀⠉⠁⠀⢹⣷⢰⡇⠰⡂⣠⣦⡰⣿⣿⣷⠀⠀⠀⣶⠀⢴⡆⢰⣦
⠀⠀⠀⠤⠤⠤⠤⠥⠄⢈⣿⠁⠸⡏⠀⠈⠀⠀⠰⠀⠀⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢾⡗⢸⠇⠈⠀⠿⣿⣻⣿⣿⠛⠃⠀⠀⠉⠀⠈⠁⠈⠉
⠀⠀⠀⣤⣤⣤⣠⣤⠀⠀⠀⠀⠀⠃⣀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠰⠀⠠⠀⠀⠁⠀⢤⡀⣄⠀⠀⠁⠃⠂⢠⣿⣿⣿⠇⠐⠀⠀⣿⡇⢰⠂⣿⡇
⠀⠀⠀⠿⠿⠿⠿⠿⠠⢤⣧⣤⣀⣠⡹⠿⠆⠀⠀⠀⢀⡀⠀⠂⠚⡤⠀⠀⠀⢀⡀⠾⠇⠀⠀⠀⠒⠀⠀⢺⣿⣿⠿⠂⠀⠀⠀⠛⠃⠘⠃⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠐⣷⣾⣾⣿⣿⠁⠀⠀⠆⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⡇⠀⠀⣿⣿⢹⣿⡟⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣀⠸⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⡀⠄⠀⠘⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⣀⣀⡀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡞⠉⠉⠈⠉⠉⠙⢲⡴⠁
⠀⠀⠀⠀⠀⢀⡠⠤⠤⠶⠽⣛⣹⠗⢛⣦⣼⡿⠛⠓⢶⣿⣷⡖⠒⠲⠶⣶⣶⣾⣷⣶⣶⠺⠥⣤⣼⠿⠷⠒⠒⠶⠲⠴⡒⠢⡀
⠀⠀⠀⠀⠀⢸⡀⡀⢀⡠⠞⢉⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣼⠋⠀⠰⡀⠀⠀⡀⠉⠆⣱⠀⡇
⠀⠀⠀⠀⠀⢸⠈⡔⠁⠀⠀⢨⠄⠀⠸⠆⠀⠀⠐⣀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠻⠀⠀⠀⠈⠢⡐⠜⠀⢠⣯⠠⡇
⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠘⠓⠒⢺⡇⠀⠀⢀⠀⠉⠉⡀⠖⠀⡀⠀⠀⠀⠀⠀⠋⠉⠉⣿⠀⠀⠀⠀⠀⠈⢦⡀⣸⢻⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠠⠀⢀⠼⠁⠀⠀⠀⠁⠀⠀⠀⠂⠀⠠⠀⠀⡀⠀⠘⡄⢀⠔⠋⠀⠀⠀⠀⡁⢎⠓⠆⢰⢸⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠫⠃⡀⢸⢸⠀⢻
⠀⠀⠀⠀⠀⣼⠀⠀⠐⠶⠃⠀⡇⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠓⠁⠁⢸⢸⠀⠈
⠀⠀⠀⠀⠀⢿⠀⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠄⠀⠀⠀⠀⠈⠈⠀⡄
⠀⠀⠀⠀⠀⢸⠀⡂⠂⠀⠢⠀⠁⠀⠀⠀⠐⠀⠠⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢀⢢⣄⠋⠀⡁⠂⣀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠁⠐⡀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠰⢥⠒⢀⡉⠃⡄⡇⠀⡇
⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠑⡀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠲⠀⠀⠀⠀⠐⠠⠀⠀⠀⠈⠀⠀⢈⠈⠂⠀⠀⠈⠐⠇⠀⠁⡁⢠⡁
⠀⠀⠀⠀⠀⢰⠀⠐⢄⠠⠂⠉⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠰⢀⠀⢡⡄⠀⢸⠀⠀⠇⠀⠀⠀⠠⠐⠂⡇⠀⡇
⠀⠀⠀⠀⠀⢸⡀⢘⣀⢑⣄⣀⡃⠀⠀⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠜⠆⠈⠓⠀⠀⠀⡇⠀⢸⠄⠂⠀⠀⠀⠀⠀⠀⠀⣧⣀⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠉⠈⠉⠁⠁⠐⠒⠂⠀⠠⠤⠄⠀⠀⠀⠠⠄⠠⠰⣇⣀⢸⣤⠄⢠⡔⠁⠀⠜⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣾⣳⣄⠀⠀⠀⠀⠀⠀⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⡿⢇⣼⢿⣟⠀⠀⠀⠀⠀⠀⢿⣶⣿⡆⠤⠤⢤⣄⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⢳⡺⠋⠀⢀⣀⠀⠀⠀⢸⣷⣽⡇⠀⠀⠀⠈⢳⡄⢠⣞⣱⠁
⠀⠀⠀⠀⣄⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠉⢻⠁⢀⡔⠋⠙⢦⣀⣀⡸⢿⠾⠧⠤⣄⣀⡀⢀⣿⣏⣬⡍
⠀⠀⠀⠀⠈⠙⠳⠀⢿⣮⡛⠛⢶⣌⣃⠀⠀⠀⠀⠀⠀⢸⠀⠀⣁⡠⡝⢧⣞⢲⠖⠀⢀⣸⣯⡿⢋⡙⢼⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣵⡀⠒⠉⠑⢦⡀⠀⠀⠀⣼⡄⠃⠁⣀⣤⣰⠼⠿⠋⠈⢉⣠⢿⡥⠿⣿⣕⣦⡄⢀⠤⠒⠒⢿⡆⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⣄⣄⠸⣿⡷⢤⢾⣹⠗⠚⠘⠉⠉⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠻⠛⣿⡆⡜⠂⠶⣾⣯⣉⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⣚⡻⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠇⢘⠀⠙⠛⢋⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠹⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⡟⠰⣺⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⣰⢢⣾⠃⠀⠀⠀⠀⢸⣿⢸⠸⣆⠐⢘⡉⠀⢸⣿⠠⠁⠀⠀⠀⠀⠀⢸⣤⡬⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⡨⣿⠀⠀⠀⠀⠀⠘⠋⠘⠀⠈⠀⠘⠓⠀⠈⠛⠀⠐⠀⠀⠀⠀⠀⠸⣯⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⠃⣿⠀⠀⠀⠀⠀⠐⣶⠀⣶⡄⢠⡀⠀⠀⠰⠖⢰⡆⠀⠀⠀⠀⠀⢸⣿⢩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣏⡦⢻⣆⠀⠀⠀⠀⠘⠿⠀⠟⠆⠋⠑⠀⠂⠸⠧⠸⠇⠀⠀⠀⠀⠀⣼⢿⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠏⠀⣀⣤⠠⢬⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣍⠉⠀⡠⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡼⠓⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⠈⢁⢴⢛⢀⡠⠊⠀⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡻⣆⢹⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⡄⠁⢰⠞⠁⠀⣄⣴⡿⠛⡛⢷⣦⣄⣀⣀⡀⠀⢀⣀⣠⣴⣾⣿⡇⣸⢣⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧⣬⣶⠀⠀⠀⢀⣹⡟⠁⢸⣳⠟⠀⠈⠉⠉⣭⡉⠉⠉⠙⢿⠉⣩⠴⣧⡞⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠘⠛⠀⠀⠳⠏⠀⠀⢀⡄⣠⡿⠑⠄⢀⠀⠘⠂⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⡶⡒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⠉⠉⠉⠁⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡠⠤⠄⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠄⢀⣀⡀⠀⢰⣄
⠀⠀⠀⠀⠀⡜⠀⢸⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣬⠀⠳
⠀⠀⠀⠀⠀⢡⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡔
⠀⠀⠀⠀⠀⠀⠟⠋⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣤⢀⣀⡀⢤⠒⠉⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⡇⠀⠀⠀⢸⠉⠉⠲⣄⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡆⠀⠀⠑⣄⠀⣠⠎⠀⠀⠀⡏⢢⠀⢨
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠑⣤
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⡀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⣌⠀⠀⣠⠞⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠈⢦⡀⢀⠱⡄
⠀⠀⠀⠀⠀⡄⠉⡟⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠹⡄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠐⡀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠱⡀⢡
⠀⠤⢀⡀⢠⠂⠘⢢⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⢠⡞⠁⠈⢢
⢰⣄⠀⠘⣷⠀⠀⠀⡿⢶⠚⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣾⣾⣅⠀⢀⣬⡀
⢸⣿⣿⣾⠁⣷⣶⣎⡀⠙⠀⠀⣀⢀⡀⣠⣀⣄⣀⣀⠀⢀⣬⣀⣀⣾⣟⣁⣈⣁⣉⣹⣿⣄⠀⠀⠀⠀⣀⣀⣀
⢈⠀⠉⠓⠸⠿⠿⢿⠇⠀⠀⠀⡧⠤⢤⡬⣷⣤⡤⠤⠤⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠐⣿⣿⣿
⣼⣿⣷⡎⢠⣤⣤⣤⢰⡇⠀⠀⡇⠀⢰⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⣼⠋⠀⠈⠻⣆⠀⠀⠙⢿⣿
⠧⣉⠛⠃⠸⠿⠿⠿⠀⠀⠀⢀⠀⠀⢸⠀⠨⠀⡇⠀⠀⠀⠠⣞⠉⣀⡿⠆⠀⠀⢻⣄⠀⢀⣰⠏
⠀⠀⠉⠁⠒⠒⠒⠒⠚⠒⠂⠙⠀⠀⢸⠀⠀⠀⡇⠀⠀⠇⠀⠙⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢠⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⣸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⢽⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠘⠿⡇⠀⣧⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠚⠂⠚⣄⠀⢠⠓⠐⠛⠐⠒⠠⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣶⣶⣦⣶⣶⣦⣤⣬⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⡀⠀⠀⠀⠠⠆
⠀⠀⠀⢁⢀⠘⠀⠀⠀⠀⣀⠓⢈⡀⢊⣀⠀⠀⠀⠀⡐⠀⠆⠀⠀⠀⠀⠠⠗⢀⠈⠑⠀⠀⠀⡰⠄⠀⠰
⠀⠘⠄⣀⣠⠔⠀⠀⠀⠀⠀⡠⢀⠁⣌⠀⠀⠀⠀⢌⣀⣤⣀⠀⠀⠀⠀⠀⢆⣼⠀⠀⠀⠀⠀⠨⠈⠈⡀
⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢰⠙⠩⠉⠛⣄⠀⠀⠀⠀⢀⡡⠠⠆⠒⠁⠀⠀⠐⡈⠉⠉⠈⠂⠀⠀⠐⠀⡀⢉⠷⠂⠀⠀⠀⡄⠆⠐⢀
⠈⠑⠐⠘⡈⠘⠣⠀⠀⠀⢠⡀⣀⠐⠀⠀⠀⠀⢀⡆⠀⠀⣀⡐⠀⠀⢀⠀⢄⡠⠀⡀⠀⠀⠐⠀⠁⠛
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠚⠂
⠀⠀⠀⡀⡠⡀⠀⠀⠀⠀⠀⠄⠂⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠰⠈⡈⠂⠌⠇⠀⠀⠀⠈⢀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠑⢒⡢⠀⢠⠀⠄⡈⠀⡠⠀⠀⠀⢀⠂⠁⢡
⠀⡆⠄⠡⠀⢠⠎⠀⠀⠀⠀⠑⡦⡖⠁⠀⠀⠀⠼⣒⠶⠂⠁⠀⠀⠀⠀⢨⠁⠥⢈⡂⠀⠀⠀⠌⠄⡀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢄⠀⣀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠄⠠⡀⢠⠄⠀⠀⠀⠄⠀⠠⡀⠀⠀⠀⡀
⠄⠀⢘⢘⡁⠈⠀⠀⢰⠞⠒⠒⠒⠚⡆⠀⠀⠐⠘⠀⠀⠀⡎⠶⠆⠀⠀⠀⠀⣀⡄⠁⠀⠀⠐⠉⠉⠉⠑
⠀⠀⢰⠘⠒⠁⠀⠀⠈⢳⠒⠒⠒⢺⠃⠀⠀⠀⠀⠢⢀⡀⠔⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠐⠀⠀⠀⠘
⠀⠀⠈⠊
⠀⢀⡤⡄⢤⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠂⠀⠒⢄⠀⠀⠀⠀⡠⡖⠐⠂⢄⠀⠀⠀⢠⠊⠉⠑
⠀⣩⡁⣍⢈⣉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠈⢢⠀⠀⡆⠀⠀⠸⠄⠁⠀⠂⠘⠀⠀⠀⠐⡄⠀⢀
⠀⠲⡄⡦⢰⠖⠀⠀⠀⠤⠤⠤⠤⠤⠃⠀⠀⠈⠢⠀⣀⠀⠔⠀⠀⠀⠈⠢⡀⠀⢀⠔⠀⠀⠀⠀⠈⢦⠃
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢏⣾⣿⣿⣎⢿⣷⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣸⣿⣿⣿⣿⣸⡇⣿⣿⢟⡹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠿⠿⠿⠿⠿⠇⢇⣭⣶⣿⣿⣮⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣿⣿⣿⣿⣿⣇⣧⡹⣿⣿⣿⣿⢏⣼⣿⣯⣭⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢸⣿⣿⣿⣿⢸⣿⠷⣙⣓⣚⣋⠾⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⣛⣃⣛⣛⣛⣃⣉⣚⣛⣙⣛⣛⣋⢺⣷⣝⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡞⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣼⢹⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢾⠷⣸⣿⣿⣿⣿⣿⡇⡇⣿⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣿⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣸⢘⢻⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣀⣈⣉⣁⣉⣉⣁⣀




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⢀⠭⠤⠤⡄⠒⠒⠂⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠃⠠⠀⠂⠒⠺⠈⠈⡀⠥⠤⠤⠄⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠔⠂⠒⢲⠀⠀⠀⣀⠀⠀⢘⣉⣙⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠂⠒⠂⠀⠈⠉⠉⠉⠉⠭⢭⣤⡤⢀⠀⣀⠠⠬⣉⣁⡒⠤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠊⠁⢲⢡⠨⠭⠋⠑⠒⠄⠀⠏⠠⢊⠄⠀⠠⣔⠅⠂⠐⡔⠆⢠⡔⠒⠤⠄⠈⠑⡌⢢
⠀⠀⠀⠀⠀⠈⠉⠆⣗⠀⠔⠁⢉⢰⠖⡜⠀⡄⡡⠔⠀⠒⠼⠤⠶⢦⡧⠼⠀⣃⠄⠂⠁⠐⠈⠘⡀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣼⣅⠹⡁⡠⡇⠠⡌⠀⠐⠆⢚⠔⠀⠀⢀⡗⢚⡄⠁⠀⠋⠰⣢⠊⠄⣦⠴⢤⡄
⠀⠀⠀⠀⠀⢀⠸⠀⠒⠸⠡⠤⠤⢎⣌⡇⠀⡏⣲⠊⠀⠈⠐⠦⠀⠀⠈⡄⡇⣈⣀⣔⡊⢐⡖⢒⣩⠐⠀⠓⠒⠀⠈⠁⢢
⠀⠀⡀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠛⡔⠀⠄⠐⠒⠈⠉⠨⢅⠈⠀⠀⠀⠀⠀⢠⢀⡀
⠀⠸⠉⡩⡉⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠑⠒⠊⠀⢠⠀⠀⠀⠀⠀⢀⠠⢖⣒⠠⢄⠀⠀⠀⠀⡇
⠀⠀⢣⣊⣱⠰⠀⠀⠀⠐⡪⠑⣼⠀⠀⠀⠀⠀⡠⣶⠶⠓⠚⠶⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠊⠉⠀⠉⠲⡐⣄⠤⠠⠄⡀
⠀⠀⠈⡀⠁⠐⠀⠀⠀⠀⠁⠝⢸⠀⠀⠀⠀⢎⡞⠁⠀⢀⣀⠀⠀⠱⣵⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠊⠙⡆⠀⢡⡇⠀⠀⠀⠄
⠀⠀⠰⠉⠉⠁⠒⠀⠤⠄⠀⣀⠀⠧⠄⠀⢸⣸⠀⠀⠎⠀⠀⠃⠀⠀⡇⣃⣀⣀⣄⣀⠀⠤⣿⠀⠘⠦⠴⠃⠀⡼⠳⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠐⠒⠈⠀⠀⣰⡟⠀⠀⣀⣀⣀⠀⠠⠴⠓⢄⣀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠒⠒⠃⠠⠤⠄⠒⠈⠁⠑⠤⣄⣀⣀⡠⠔⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠉⠉⠻⣗⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⢠⡠⢤⠀⣿⣠⣂⣀⣀⣿⠀⠀⠀⠀⠻⠛⠛⠻⢿⣿⡇
⠀⠀⠀⠀⠀⢸⠈⠉⡀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠠⠈⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⣠⠀⠄⠀⡆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⠀⠙⠆⣹⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣻⡔⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⢻⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠀⠀⠀⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⠆⠀⢀⠀⠀⢰⠀⠀⠠⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⣀⣀⡀⣠⠂⢀⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣆
⠀⢀⣴⡆⣀⡐⣞⣇⣀⡀⣠⣤⣶⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⢆
⠄⠀⠉⠉⠤⠋⠖⠘⠚⠙⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⣀⡀⡀⣄⠉⠠⠠⠀⢀⣀⣤⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠠⠤⠀⢀⠀⠀⣈⠉⠉⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⣀⡀⠀⠀⢀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡑⠀⠀⠀⠁⠀⠀⠈⠈⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢹⡐⠠⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⡪⡟⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄
⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠄⠤⠂⠂⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠗⠁⠀⠀⢀⣀⡀⠀⠈⠛
⠀⠀⠀⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠉⠁⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠁⠀⠀⢠⡎⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣤⠀⠀⠀⢠⠀⢶⠴⣶⡂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⠂⠀⠀⡇⠠⢤⣄⣀⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠦⠴⠶⠾⠶⠦⠀⠚⠓⠚⠛⠛⠋⠉⠁⠀⠀⠧⠤⣄⣀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣔⣒⣓⡖⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣉⢀⠉⠁⠐⠒⠀⠀⠀⠠⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠂⠱⠟⢰⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠋⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠚⠛⠸⠣⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠸⠄⠠⠀⠚⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⡋⠓⠓⠆⡌⠁⠀⠀⠀⢀⣠⡀⠒⠀⡠⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⢨⠉⠁⠀⠀⠉⠈⠉⠉⠄⠄⠌
⠀⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢠⠄⡀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⠑⣄⣀⡄⢀⠖⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠗⡠⠁⠂⠀⡄⢀⡅⠀⠀⠀⠨⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⡆⠁⠀⠀⠀⠀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠠⠁⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠐⠤⢤⡄⡠⠤⠄⠀⠀⠐⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠰⠁⠀⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠄
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⢸⠋⠙⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢂⠀⠀⠀⠀⠀⠀⠀⡐⡡⠂⠉⡈⠀⠑⠌⠄⠀⠀⠀⠀⠀⢀⣠⡤⣤⠠⣴⠊⡙⢦⡀
⠀⠀⠐⠘⠩⠬⣽⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⠑⠂⢄⠀⠀⠀⠀⠀⠀⢰⠄⠀⣀⠀⠀⠀⢬⢰⠀⠀⠀⠀⠀⢯⣀⠜⢏⣲⠟⢞⣲⢬⣿
⠀⠀⠠⠀⠤⢤⡤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⢠⡄⠀⠤⠀⠀⠀⠀⠀⠀⠐⡌⢆⠀⠀⠀⠀⠀⠔⡸⠀⠀⠀⠀⠀⠀⠉⠻⣍⠷⡋⣩⡧⠤⠛
⠀⠀⢰⡘⣁⣆⡈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⢬⣭⡽⢂⠴⠉⠀⠀⠀⠀⠀⠀⠈⠢⢑⠂⢓⣒⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊
⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀
⢠⣤⡀⣀⠄⠀⠠⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⠍⡁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠩⠉⠸
⠘⡹⠐⠁⠀⠲⡢⣎⠂⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡚⣏⢉⣴⠶⣈⣛⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⢘
⠀⠇⢀⠳⣄⣸⣡⠆⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⠉⠀⡏⠂⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠒⠀⢈
⠀⠛⠀⠓⠬⠥⠅⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⢒⣖⣃⠱⠶⠜⠀⠀⠀⠀⠀⠀⠠⠉⢀⠈⠀⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠾⠿⠆⠠


⠀⠀⠀⠀⠀⡀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣀⡠⢄
⠀⠔⠒⠐⠤⢤⡴⠆⢈⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠞⢀⢄⠀⠀⠀⠀⠀⠀⠠⠀⠐⠐⠀⠀⢰⠱⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣐⣀⣨⣭⣬⡄
⠀⠀⠀⠀⠀⠀⠈⡻⠀⠀⠁⠀⠀⠀⠀⠘⣀⠡⠒⢈⠀⠀⡠⠓⠒⠁⠀⠀⠀⠀⠀⠈⠤⣰⡇⠀⠀⠰⠤⡆⠀⠀⠀⠀⠀⠀⣴⣟⡷⢰⣤⠄⣽⢀⡇
⠸⢄⡀⠀⠀⠀⠀⠄⠀⠴⠀⠀⠀⠀⠀⢠⣥⠄⢰⠉⠈⠉⠑⠂⡄⠀⠀⠀⠀⠀⠀⠱⡀⠸⢄⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠧⢿⣷⣀⣰⣶⡟⠉⠁
⠀⠀⠀⠁⠛⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠒⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⣐⣐⣀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⠀⣈⠁⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠜⠚⠁⡡
⡄⠘⠉⠑⠒⠒⠚⠃⠐⠰⠃⠀⠀⠀⠀⠀⠀⢶⡄⠸⠠⡌⠉⢹⠇⠀⠀⠀⠀⠀⠀⢎⣈⣃⠀⣇⣀⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣤⣄⠐⢆
⡇⠀⠀⠀⢠⠖⢋⡠⠀⢀⠀⠀⠀⠀⠀⠀⠈⣺⡇⠀⠀⠀⢤⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣃⢈⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢨⣀⠂
⠂⣀⣀⣀⣀⣀⣉⢀⠄⠸⠀⠀⠀⠀⠀⠀⡀⢻⣏⣿⣟⠷⢶⣷⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠱⣀⣀⣀⣤⣛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠙⠭⠛⠟⠻⠛⠞⠣⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠓⠚⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⢦⡄⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡤⢄⣀⣤⣀⣄⣠⠠⢴⣿⣧⠘⠁⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⣼⠋⠀⠀⠀⠀⠀⠀⠀⢟⡛⢠⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠀⠀⠀⠠⠈⡠⣶⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⢯⡇⣩⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠦⢰⠸⣾⢦⣾⣴⣽⣾⡶⠦⠶⣶⠟⠙⢈⣭⣴⠤⠤⢤⠤⠤⢴⠗⢿⡷⢻⣀⠀⠀⠒⣼⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣶⣿⣿⣷⡾⠛⠛⠓⠀⣢⣴⣶⣌⢿⣯⡔⠲⡶⠿⠿⠆⠀⠄⠀⠀⠀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠁⠀⠀⠀⢈⣿⣇⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠚⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣴⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠲⣵⣈⣁⡁⣈⣧⣄⠀⠀⠀⡀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢊⣿⠁⠀⠀⠀⠀⡟⣿⣦⢷⡊⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⣿⡶⠒⠚⠋⠋⢰⠄⠼⣷⡈⣀⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡟⠀⠀⠀⢠⢰⢰⠀⠀⢿⣷⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⡇⢠⣿⠀⠀⣀⣀⡤⠼⡼⢤⡀⡄⣹⣄⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠘⡘⣄⣠⡷⣾⠗⢚⣹⣬⠅⠠⠄⠚⢺⡅⠀⠘⢿⡄⠈⡱⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢧⠐⣼⠅⣶⠟⠉⠀⢸⣇⣀⣀⠬⠬⣦⣧⣤⣀⢘⣧⢀⡧⠤⠒⠒⠒⠒⠚⣿⡡⢚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠳⣼⣠⣷⡰⠊⠉⢀⡏⠘⠀⠀⠊⠀⡀⠉⠉⠉⢿⡏⠁⢒⠀⣀⣀⡠⠒⠒⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣫⢩⣽⠛⣷⣤⠤⢸⠀⡆⠀⢸⠀⠀⡇⠀⠄⠀⠈⣶⠘⠌⢀⠇⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⣾⡏⣸⣼⠥⠖⢺⠀⡇⠀⢸⠀⠀⣿⠀⠀⣒⣲⣿⡀⠀⢸⠓⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⢻⡿⠋⢻⠀⠀⠀⠸⠀⣃⣀⣼⡠⠤⠿⠓⠒⠂⠀⢺⣷⠒⠚⠒⠰⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⢿⠁⠀⢸⣲⡄⠤⠚⠋⠉⠁⠋⣀⠤⢤⣤⢖⡒⠒⠚⣿⠒⠒⠒⠠⡌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣿⡧⠔⠒⠉⣀⣤⡤⠶⠶⡆⠀⠀⢱⣈⡍⠀⠀⠐⠢⡀⣿⡏⣉⠉⠒⢷⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡘⣻⣽⣶⠖⡆⢮⢠⣟⡶⠚⡛⣷⠀⠀⠈⡇⠀⠀⡀⠀⣠⠗⢳⣿⠈⠓⠒⡈⣧⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡱⡿⠿⡟⠚⢻⢸⠐⡜⠁⠈⠀⡷⡇⠀⠀⢿⠒⠒⠚⣫⣉⣀⣻⣿⣐⣀⣐⢀⡛⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡠⠰⠀⡇⣀⣓⣀⡼⠘⠦⠶⠒⠒⠒⠋⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠾⠳⠓⠊⠉⠉⠀⠀⣀⡀⠀⠀⠀⢠⠖⡋⢲⣒⣒⡒⢐⡀⠁⣀⣀⣀⣻⣹⣖⣖⣒⣒⣒⡀⠀⠰⣷⠐⠄
⠀⠀⠀⠀⠀⡠⢚⣁⣤⣤⡶⠶⠖⠒⠉⠁⠀⠀⠀⠈⠉⢠⠾⠏⠁⠉⠳⣄⠂⠉⠀⢀⠠⠐⡀⠨⠿⠧⣤⠤⠀⠀⠠⠄⠉⢿⠋⢂
⠀⠀⠀⢀⣼⡟⠛⠉⠉⠉⠑⠢⣤⠤⠄⠀⡀⢀⠀⠀⢴⠏⠀⠀⠀⠀⠀⠘⡆⠀⢌⡀⠀⠒⠭⠾⠶⠁⠉⠀⠐⠚⢛⠈⠉⢹⠀⠘
⠀⠀⢠⣿⠋⠁⠀⡀⣀⠀⠀⠀⠘⣦⠉⠀⠤⠤⠀⢒⡟⠀⢀⣄⠀⠀⠀⠀⢹⣀⠀⠀⢁⡐⠒⠒⠂⠀⠀⠤⠤⠤⣤⡄⠀⢸⠀⢀⡇
⠀⡠⢠⡟⠀⢠⡾⢀⡄⢳⡀⠀⠀⠘⣄⣀⠀⠀⠠⣼⠃⢀⡟⢸⡇⠀⠀⢀⡸⠇⠬⠭⡏⢰⠶⠶⠒⠒⠲⠒⠶⠲⡇⢰⠤⠼⣄⢸
⠀⠇⢀⣇⠀⣾⠣⡇⢹⠀⣧⣀⣀⣀⡿⠀⠀⠠⠤⠾⠤⠸⡇⡏⢸⡄⢀⣫⣄⣀⣀⣀⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⡇⣬⣀⡀⠀⠃
⠀⠀⠀⠀⠀⠸⠀⠳⡟⢀⡅⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠱⡾⠀⡘⠀⠀⡼⠀⠀⠈⠙⠋⠁⠀⢸⠀⠀⠀⡎⠈⠀⣰⠁
⠀⠀⠀⠀⣀⣀⣧⠀⢀⣜⣀⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣄⣀⣰⢁⣀⣰⣧⣤⣤⣤⣤⣤⣤⣤⣬⣄⣀⡼⢁⣀⣰⣃⡀
⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⣾
⠀⠀⢰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠼⠅⠠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗
⠀⢠⣗⠐⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⡾⣶⣤⣀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠚⣷⡿⢽⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠁⡠⢶⡿⠟⠉⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢻⣯⣁⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠘⠣⠀⠀⠀⠀⠉
⠚⠀⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⡄⠀⠠⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠻⠛⠛⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠤⠀⠀⠁
⠀⠀⠀⢁⡀⠄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠺⠃⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠂⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡔⠒⢄⡐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢡⠀⠘⡄⠤⠒⠠⠎⠀⢀⠆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⠰⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠆⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠈⠁⠂⠀⠀⠀⠀⠀⡀⠂⡄⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢁⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⡈⠐⠠⢀⠤⠂⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠈⠐⠊⢦⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠊⠱⠆⠐⠀⠀⠐⢂⠀⣠⠄⠀⡴⠀⠐⠘⠀⠉⠉⠀⠀⠀⠀⠀⡀⣁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠒⠉⠘⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠢⢀⠀⡖⢀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣀⠠⠂⣡⠁⠀⠁⠂⠠⢀⠀⠠⠀⠀⠀⢀⠀⠐⠒⠁⠢⡀⠀⡇⢀⣠⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⢠⡀⠀⠀⠀⠀⠈⠀⡱⠊⠀⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣀⣀⡀⠠⠓⠂⠐⠒⠆⠀⢡⡄⢀⠀⣀⣤⣤⢤⡀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⠀⣰⡀⠀⠀⠀⡇
⠀⠀⠀⡄⠉⠉⠉⠉⠉⠉⢉⢉⠉⠉⢉⠛⠙⢫⢙⡟⡒⠡⢸⢻⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⡇
⠀⠀⠀⡇⢤⠀⠀⠰⣠⠞⠛⠛⠳⣦⢦⠒⠒⠂⠰⣳⠂⢠⢄⣜⡃⠀⠀⠏⠀⠀⠀⠀⠀⠀⢀⠠⠀⠛⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠉⠀⠀⢼⠃⠀⠀⠀⠀⠈⣧⠂⠀⠀⠀⠛⠵⠷⠚⠋⠀⠀⠆⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠉⠁⠀⠀⠈⠐⠀⠀⠀⡃
⠀⠀⠀⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠐⠊⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠘⠪⢳⠶⠶⡞⠋⠂⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠁


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

⠀⠀⠀⠀⠀⡠⠊⠢⡀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢄⠀⠀⠀⠀⢀⣴⣷⣄
⠀⠀⠀⠠⠊⠀⢌⠆⠈⠢⠀⠀⠐⠀⢰⡆⠀⠀⡀⠀⠀⠠⠊⠀⢈⡀⠀⢐⡀⢀⣴⣿⣯⢩⣿⣷⣄
⠀⠀⠀⠀⠀⣸⣀⣺⡀⠀⠀⠀⠀⢰⣏⣹⡆⠀⠀⠀⠀⠀⠁⢰⣂⣸⡀⠈⠀⠀⢸⣿⢱⣶⢹⣿
⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣠⣄
⠀⠀⣸⣿⣛⣻⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⠉⣽⡉⠑⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⢿⡿
⠀⠀⠃⠿⠤⠾⠈⣾⠀⣾⠀⠀⠀⠀⠘⢿⣿⣋⣀⣿⣄⣀⠀⠀⠀⠀⣠⣾⣿⣷⡄⢀⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠼⠿⠗⠿⠶⠀⠀⠠⠾⠿⠿⠿⠏⠉⠉⠉⠁⠀⠸⠇⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣾⣷⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠏⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠛⠛⢋⣿⣿⣿⣿⣿⡿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠃⠀⢀⣾⠃⣠⡀⣿⣿⡏⠡⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⡾⠋⣿⣿⣷⣾⣿⣿⡟⢻⡇⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣴⠃⠀⠀⣀⢠⣿⣿⣿⣿⣿⣿⣷⠀⠀⢀⡀⠀⠠⠤⡄⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⣰⠃⠀⢠⣴⣿⣾⣿⣿⣿⣿⣿⣿⠉⣠⣷⣷⣹⣶⣆⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⣆
⠀⠀⠀⢠⡏⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠙⠛⠉⠉⠁⠠⡀⠀⠀⠙⠛⣿⣧⣤⡀⠀⣿⣧⡀⠘⣿⡀
⠀⠀⠀⣸⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⢀⣴⣿⣿⣿⣿⣄⢹⣿⣇⢸⣿⡇
⠀⠀⠀⣿⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⠈⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠘⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣤⣄⣠⣼⣿⣿⣯⣝⣩⣍⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⣷⣿⣿⣿⠿⠿⢻⣿⣿⣟⡿⢿⣿⣿⣿⣾⣝⡋
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣽⣷⣦⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣯⡟⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⠿⢟⣵⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠙⠛⠛⠿

⣤⡄⣰⣶⠆⠰⠟⠆⣠⣤⣤⣤⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⡶⠂⣀⡀⠀⠀⠀⢀⡀⠀⣠⣤⡄⠀⢀⣠⠶⠀⠀⡀⠀⢀⠀⠀⠀⠀⣠⠀⠀⢀⣄
⠉⠁⠈⠀⠴⠶⡀⣿⢼⡃⠒⠿⠃⠀⠀⠘⢿⠉⢣⠀⣀⡖⠀⠘⠛⢿⢿⣀⢀⠈⣡⣄⠁⠈⡙⠃⣻⠉⢳⣿⣤⣿⡆⠛⣁⡟⠀⢰⠹⡄⠛⠿⠁
⠀⠀⠀⣤⠀⠐⣧⢸⣦⠙⠀⠀⠀⠀⠀⠀⠸⠁⠛⠀⠘⠁⡰⠆⠀⠀⠘⡿⠿⢰⡇⠸⠆⠀⠁⣠⣿⡄⢴⣿⠗⢹⠉⠙⠿⣆⠀⠀⠈⠁⢀⡞
⠀⠀⠀⠋⠀⠀⠈⠘⡏⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢠⠀⣿⣿⣧⢸⣿⡀⢸⠁⠀⠀⠘⠃⠀⠀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⢰⣧⡀⢸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⡿⠷⠀⠀⠀⠀⢀⢰⣿⣿⣿⠸⡿⠁⢸⡆⠀⠀⠀⠀⠀⠐⡈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⣾⡇⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡞⠃⢾⠄⠀⠀⠀⣠⡟⠻⠿⠟⠀⠛⠀⢻⡇⠀⠀⠀⠀⠀⣶⠁⣿⡿⠴
⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠟⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠚⠸⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣶
⠀⠀⠀⠀⡀⠀⠀⠸⡗⠃⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠚⠂⠆⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣀⠀⠀⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠱⠟⢰⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠑⠋⠛⠁⠀⠁⠀⠀⠀⠀⠀⠀⠚⠛⠸⠣⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠸⠄⠠⠀⠚⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⡋⠛⠓⠆⡌⠁⠀⠀⠀⢀⣠⡀⠒⠀⡠⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⢨⠉⠁⠀⠀⠁⠈⠉⠉⠄⠄⠌
⠀⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⢠⠄⡀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠑⣄⣀⡄⢀⠖⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠗⡠⠁⠂⠀⡄⢀⡅⠀⠀⠀⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⡆⠁⠀⠀⠀⠀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠁⠠⠁⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠐⠤⢤⡀⡠⠤⠄⠀⠀⠐⠤⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠔⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠰⠀⠀⢰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠄
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠐⠄⡀⠀⡀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡼⠉⠀⠀⠈⠉⡸⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠑⣀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠑⠦⠄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⡄⠂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡀⢀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠘⠄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠊⠀⠀⠀⠈⠐⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠔⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣆⠀⢦⠤⠤⠀⢀⣀⢀⠐⠒⠀⠒⠒⠒⠒⡆⡠⠊⠀⠀⠀⠀⢀⡔⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⡄⠀⡄⠀⡾⣿⠋⠀⠈⡶⠠⠤⠤⠤⠔⠋⠀⠀⠀⠀⢀⡠⠊⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠀⠸⡄⠉⠁⠀⠀⠐⠦⠄⢀⣀⣀⣀⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⣀⡠⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢠⠛⠉⠉⣩⠛⠁⠒⠒⢦⠤⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢉⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠓⠒⠒⠒⠛⠓⠛⠛⠿⠿⠷⠶⠶⠆⢤⢤⠤⠄⠀⠀⠀⠤⠤⠄⠒⠉⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎⠀⠀⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⣀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⣼⡀⠀⠀⢀⣀⣀⣀⣀⠀⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁




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