Japanese food Emojis & Symbols

⣷⠀⠀⠀⢀⣤⠶⣤⡃⡸⠆⠀⠁⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠋⠀⠀⠁⠀⠻⣦⠀⠹⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠄⡀⠰⢿⣿⣷⣿⣾⣆⠀⠀⠀⠀⠀⡀⠄⠰⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣦⣜⠻⠂⠸⠶⠄⠺⠶⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠠
⠀⠁⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠛⠀⢠⣿⣿⣿⣧⣘⠻⢆⣰⣶⣾⠃⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠇⠀⠄
⠀⠀⢤⣤⠀⠑⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡴⢦⠙⡿⡱⢲⡀⠙⠻⢿⣿⣿⣿⣿⣿⣿⠟⠀⠀⡀⠀⠉⠃⠈⠀⠀⠀⠀⠈⠋⠀⠀⠠⡀⠀⠀⠐
⠀⠀⠈⠃⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣿⠀⠀⠀⠙⠻⠿⠟⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠈
⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣤⠀⣠⡤⠀⠀⢀⣀⠀⠐⠋⠁
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠅⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢀⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠰⣿⣿⣿⡿⠋⢠⣦⡘⠿⠆⢀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⣆⡆⠀⠀⠀⠐⠀⠃⡄⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠻⠿⠋⠀⠀⣼⣿⣿⣶⣾⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⡀⠀⠀⠀⠐⠀⠀⢺⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⠄⠀⠀⠀⠈⠀⠰⠂⠠⣄⠀⡉⠀⠀⠀⠀⠀⠀⢻⣿⡷⠄⠀⣠⠀⠀⠀⣸⠆⠀⠀⣀⣀⡈
⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⠀⢸⡂⠀⠀⠀⠀⠀⠀⠉⠀⢀⠐⠁⠀⠀⠀⠉⠀⢰⣇⠀⠠⢉⠄
⣮⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢸⣿⣿⣶⣶⣶
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣦⠀⠀⠀⠀⠀⠀⠀⠦⢠⡤⠙⠻⢿⣿⣿
⠉⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⣧⡀⠀⠀⠀⠇⢄⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠐⠀⠀⠂⠀⠀⠇⠀⢀⡀⠄
⡠⡀⠉⠈⠀⠀⠀⠀⠀⠀⡠⠶⠋⠁⠀⠀⠀⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠨⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠁⠀⠀⠀⠀⠈⠉⠉⣉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠂⠀⣐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇⠀⠀⠀⠆⠀⠦⠈⢅⣀
⠀⠀⠀⠀⠀⠀⠠⠀⢰⡶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠏⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⡉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠡⠈⣿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠠⠀⠄⠄

⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⠆⠐⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⡐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠄⠀⠠⣀⠀⠀⠀⠀⠂⢄
⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠠⠀⠀⠁⠈⠀⠀⠀⠰⠂⠀⡠⠀⠀⡁⢁⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢
⠀⢃⢀⠄⠐⢄⠀⠁⠀⠀⢀⠁⢸
⠀⠈⢀⠀⠀⠀⢀⠀⢀⠌⠀⢀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠠⠂
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠠⠐⠁⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢄⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⡀⠀⠀⠄⠐
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠤⠀⠀⣀⣀⣀⣀⠠⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠂⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠤⠠⢌⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠂⠀⠀⡀⠀⠁⠀⡀
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢀
⢠⠃⠀⠀⠀⠘⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠄

⠴⡁⠀⢀⣀⠘⡀⠠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠋⢀⠠⠀⠊⠀⠀⠀⠀⠀⠀⠘⠦⣤⢀⡀⠴⢊⠠⠒⢉⠀⠠⠒⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠃⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠛⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠁⠀⠐⠀⠀⠀⠀⠀⠀⢀⠔⠀⢠⡬⡐⢄⠀⠀⠀⠀⢀⡠⡔⢑⠎⠏
⠗⢹⠀⠀⠀⠀⠀⣀⠠⠐⠢⢀⠀⠀⠐⢄⡀⢠⣬⡇⠀⠀⠀⠀⠠⢀⠔⠙⠃⠉⠓⢄⠀⣠⠀⠀⠀⠀⠀⠀⠰⠤⢈⣉⠈⠤⠸⠀⠀⠀⠴⠿⠐⡄⡮⢖⣣
⠀⢸⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠉⠢⠀⠀⢰⣦⡡⠂⠀⠀⠀⠀⠁⣏⠀⣨⠙⢢⠀⠈⡄⢠⠀⠐⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠶⠞⠚⠋⠁
⠔⠁⠀⠀⠀⡘⠀⠀⢀⣀⠀⡰⠓⠺⠀⣀⠦⠊⠀⠀⠀⠀⠀⠀⠀⠘⢶⡉⠁⠛⠀⢀⡄⠠⡐⠁⠄⠀⠀⠀⠸
⠀⠀⠀⠀⠐⠛⠛⠑⠪⠈⠉⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢈⠑⠤⠴⣮⡤⠆⠂⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⢀⠠⠤⠀⠠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄
⠠⡈⠓⠂⠄⣠⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⡀⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠠⠊⠀⠀⢠⢂⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⢄
⠀⢠⣀⡄⣂⠔⠀⠀⠀⠀⠀⠀⡠⠂⠠⠄⠀⠀⢀⠠⠀⠒⠶⡦⠤⡧⠀⠀⠀⠀⠀⣔⠨⠐⠀⠁⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠈⠆
⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠄⠈⠀⣀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠣⡤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡀⠠⠤⠒⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⡀⠄⠒⠑⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠂⠀⠀⠀⠀⠀⠀⣔⣀⠤⠚⠃⠀⠀⠀⠒⠉
⠄⠐⠒⠒⠂⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢆⡉⠉⠻⣿⣒⣶⣤⣀⠀⠈⠂⠀⠒⠈⠁⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⡀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⢀⠀⠘⡏⠀⢸⠀⠠⢬⢩⡆⠀⠀⠀⠀⠀⢸⠉⠛⠓⠂⠀⠀⠤⠐⠒⠋⢙⠀⠀⠀⠀⠀⠀⢠⠊
⠈⡁⠠⠀⠀⠐⠒⠖⠁⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⡤⠂⠀⠀⠔⠋⠀⢸⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄⢁⠠
⠀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠧⠖⡁⠀⠀⣄⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠖⠈⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠂⠀⠀⠒⠂⠀⠀⠁⠀⠀⠀⠈⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠺⢥⣀⠉⠙⢻⣶⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⠉⠑⡂⠐⠂⠠⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠤⠀⠄⢀
⠠⡀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⢀⠝⢻⢀⢨⡄⠈⣉⢓⡄⠀⠀⠀⠀⢠⠒⠁⠀⠈⠂⣄⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠈
⠦⠆⠀⠀⠘⠄⠈⠐⠠⠀⡠⠒⠁⠀⠞⠁⣰⠠⠐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡋⠔⠀⠁⢒⠔⠃⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠠⠄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⣀⡀⠐⠈⡠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠄⠈⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⢌⠙⠲⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⠀⠁⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠈⠳⡀⢱⠙⣉⣻⣲⡄⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⢀⠤⠚⡉⠉⠉⢒⣬⣵⣦⠀⠀⠀⠀⠀⠀⠀⣠⣂⠉⠁
⣧⠄⠓⠈⡁⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠣⣄⡀⠀⢀⠤⠂⡁⠐⠈⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⡀⠀⠱⡀
⠀⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠐⠆⠡⠄⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⠀⠀⠵⠂⠋
⠀⠀⠀⢀⡠⠤⠤⠤⠄⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀⠀⠀⠀⠈⠈⠁
⡤⠊⢉⡠⠒⠊⠉⠉⢉⣋⢻⣶⠾⠟⠭⠂⠀⠀⠀⢀⠄⠂⠉⠤⡀⠀⠑⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠁⠀⠀⠀⢀⣀⡁⠐⠠⢄
⠀⣠⠉⠀⠀⠀⠠⠂⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⢀⠀⠠⠄⠠⡤⠬⠂⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⣀⠔⠈⡡⠀⠂⠉⡤⠤⠬⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣀⣂⣠⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⣿⠻⡿⠻⢿⠿⡿⠟⡿⠿⠿⣿⠟⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢴⡀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣥⣿⣴⣇⣠⣶⣦⣷⣶⣶⣼⣿⣶⣮⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⡄⣤⠆⠀⠀⣰⣧⠀⠘⠻⣿⡟⠁⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠆⡀⠀⠈⠙⣿⣿⡾⣄⠀⠙⠡⣾⣿⠇⠉⠐⣷⣶⡞⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⡀⠙⠿⣶⣊⠉⠁⠀⣬⣿⠁⠠⣄⠘⠛⣷⣤⣤⣴⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠲⠶⠄⠀⠠⢀⠴⠯⠽⠦⠄⠀⠠⠿⠷⠤⠽⠾⠇⠸⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠀⠠⠐⣀⡤⠞⠉
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣦⣄⠈⠀⢀⠀⠈⠲⢄⡀⠀⠀⠀⠘⢉⠿⣛⣭⣖⣽⣂⣽⣿⣶⡄
⠀⠀⠂⠀⣉⠜⠂⢀⠀⢦⡴⠋⢐⣿⡷⣄⡀⠁⠀⠄⠀⠉⠂⠀⡀⢠⣴⣾⣿⣿⠍⣩⣭⡭⣭⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣤
⠀⠀⣤⣾⠣⣤⣯⣿⠶⠒⢛⠶⡎⢀⡴⣿⣿⣄⡀⠀⠀⠤⠒⠋⢀⣼⣿⡿⣿⣿⠀⠉⢉⣠⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠩⣿⠀⢀⣿⣣⠐⡋⣹⣧⡴⠿⠟⠋⣁⠄⣽⠆⠀⠀⠀⠀⠉⣺⡿⠃⣾⡇⠀⠀⢰⣇⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣤
⠀⠀⠀⠀⠙⠿⣿⠁⠂⢠⡟⠁⠀⠀⠀⢀⢹⡇⠂⠀⠀⠀⠀⡄⠀⠉⠐⢚⢻⡇⠀⠤⠿⠿⠻⢿⠀⠀⠀⠀⢀⠂⠀⠀⠀⠒⠒⠒⠒⠒⣿⣿⠿⢓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⡾⠇⠈⣀⣰⢷⣘⢿⡛⠂⠀⠀⠀⠀⠁⠀⠀⠀⢉⠈⠃⠀⠈⠈⠁⠀⠌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢤⣤⡴⠾⣋⠥⠚⢋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠡⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⢀⡈⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣤⣤⣄⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠄⠘⠻⠒⢀⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠊⠁
⠀⠀⠀⠀⢀⣠⣶⢿⡿⢛⡋⠻⢏⠉⠛⠛⢻⡛⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⠤⠀⠈
⠀⠀⣀⣴⡿⣯⣥⣹⠔⠚⠷⠀⠲⠆⠀⢀⠈⢅⣹⣧⣿⣿⣷⡄⠀⠀⠀⠀⠀⠘⠋
⠀⢠⣿⣿⡿⠶⠛⠱⠦⣄⠀⠀⠀⠈⢷⣉⠀⠀⠀⡀⢈⡐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⣴⠄⠁
⠀⣼⣿⡏⠁⠄⠀⠀⠀⠀⠀⠛⣆⠀⠈⠹⢆⠀⠀⠁⠀⢶⣾⣿⠀⠀⠀⢀⠀⠀⠀⠠⠘⢀⠁⠀⠀⠀⣿⣮⡟⠁⠀⠀⠀⢰⣀⣤⣤
⠀⢿⣇⣿⠟⠹⡀⠠⠄⡠⡀⠀⢸⣦⣤⠟⠘⢃⠀⣠⠚⢈⢿⣯⠀⠀⠀⠻⠿⣯⢀⣶⣦⣤⡀⠀⠀⠀⠘⣿⣷⣶⠀⠀⠘⣳⡟⢛⣉
⠀⠘⢧⣀⡠⢇⢀⡀⣤⣴⠟⡛⠻⠁⡲⣾⡅⠫⡄⢠⣄⢠⣾⠃⠀⠀⠀⠒⠒⠶⢾⣿⣿⣿⣿⠀⠀⡀⡘⣿⣿⡟⠀⠀⠀⣿⣯⣥⣶⣤⠤
⠀⠀⠈⠻⣿⣿⣥⣩⣴⣾⣦⣀⠀⣀⣈⣹⣤⣛⣠⣴⣾⠟⠁⠀⠀⠀⠀⠈⠛⠲⠯⠿⣿⣿⣿⣤⣤⣬⡷⠖⣛⣛⡳⠾⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠂⠀⠐⠐

⠀⠀⣀⠀⢀⢴⠦⠀⠤⣤⡦⣀⢀
⠔⠛⠛⠘⠛⠒⠚⠓⠃⠀⠒⠑⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣶⠴⠶⣶⡴⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣘⣀⠿⣘⣁⡼⢟⣛⡸⠏⢀⠄⢚⡛⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠤⠴⠖⠒⠂⠒⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠈⠁⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⢠⣤⣄⠄⠩⠕⠒⠒⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣯⣿⣿⣿⣽⣷⢶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣾⣹⣱⣿⣿⣳⣽⣽⣟⣿⣿⣻⣴⣷
⠀⠀⠀⣿⣿⠃⢠⣾⣿⣿⣷⡀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠰⣿⣿⡀⢸⣿⣿⣿⣿⡇⣸⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢛⣋⡩⠤⠐⠂⠉⢁⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠿⠩⠒⠒⠂⠁⠉
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢄⣀⣀⣒⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢚⠉⠠⣈⠉⠙⠛⠉⠉⣵⣦⠀⣠⠔⠒⠋⠡⠴⠶⠐⠠⢐⠀⠀⠀⠀⡀⠤⠄⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢟⡴⠀⠐⡚⠟⠻⣻⣦⣶⣻⣿⡷⠋⠀⠀⢀⣀⡀⣀⠀⢀⡀⠾⣟⡠⠖⠁⠀⠀⠀⠀⠁⠀⠀⠀⣀⡈⠉⠉⠉⠉⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣦⡙⠃⠀⠉⢀⣤⠿⣯⡿⣙⢛⠁⠀⠀⠀⠀⠀⠀⣴⠋⣧⠼⣿⠟⠁⠀⠀⠀⠀⠀⠀⡀⢤⠀⣀⡼⠃⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢙⡿⣿⣿⡷⠶⠞⣃⣤⡾⠋⠀⢿⣭⣱⠤⡀⡀⣠⠄⠈⣨⡶⠋⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡸⠟⠁⠀⠀⠀⠀⠀⣠⠆⢸
⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠈⠃⠀⠉⠛⠻⠿⠋⠁⠀⠀⠀⠲⠉⠛⠷⣮⣭⣤⣶⠟⠋⠀⢀⠈⡿⢶⣤⡀⠀⠀⢀⣠⡴⠟⠁⠀⠜⠀⠀⠀⢀⠖⠁⢠⠖
⠀⠀⠀⣠⠖⠋⠀⠀⢉⣁⠀⠐⠘⠶⠷⠦⠀⠐⠂⠁⠀⠀⠀⠀⢠⣀⣀⡈⠉⢀⡀⠄⠀⠀⠀⠁⠀⠈⠙⠻⠿⠟⠉⠀⠀⠀⠂⠀⠀⢠⠆⠁⢀⠔⠃
⠀⠀⠀⢿⡇⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡶⢶⡀⠀⠐⣈⠄⠀⠀⣠⠊⠀⠀⡰⠃
⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠎⠁⠀⣠⠎
⠀⠀⠀⠀⠈⠉⠁⠘⢢⠆⠠⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠉⣼⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⣀⣀⣤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠒⠒⠒⠒⠒⠒⢒⠲⠶⠤⠤⠤⠤⠤⣤⣤⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢸⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠉⢉⣉⣀⣀⠀⠀⠐⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢄
⠀⠀⠀⠈⠠⠤⠤⠤⢭⣭⣍⣉⣉⣉⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⠋⠀⣠⣤⣶⣶⣶⣾⣿⣿⣷⣶⣄⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠴⠦⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠎⠀⠀⠀⠀⡃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠠⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠂⠄⠀⠀⠀⠻⣤⡀⠙⠻⠿⠿⢿⣿⣿⠿⠿⠿⠛⠁⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠒⠂⠀⠀⠀⣀⣠⣤⠴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⢀⠀⠀⠀⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⣶⣶⡤⢀
⠀⠀⠀⣠⠠⠀⣐⣤⠀⠈⠀⠉⠀⠀⠀⠐⠁⠔⡴⣿⡛⠦⣤⣀⠀⠀⠀⠀⠀⣼⡧⠬⠁⠠⠃⢀⣩⣷⡀⠀⠀⠀⠀⣀⠀⠌
⠀⠀⢻⡂⠙⣏⣄⣀⣦⣽⣖⣳⠂⠀⠀⠀⠐⣺⠀⣬⣽⡉⣍⠯⣠⠀⠀⠀⠀⣝⠳⢶⣿⣦⣴⡯⠾⢃⠁⠀⠀⠀⠀⠀⠐⠀⡨⠃
⠀⠀⠈⠁⠐⠃⠟⠿⠿⠿⠋⠙⠁⠀⠀⠀⠈⠉⠉⠁⠈⠁⢈⠁⠁⠀⠀⠀⠀⠙⠛⢛⠰⠆⠀⢁⠀⠉⠀⠀⠀⠰⢯⡈⠁⢀⢃⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠚⠚⠂⠊⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⢀⣈⠐⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀
⠀⠀⠀⠀⣠⣤⣔⠖⡤⣤⣈⡀⢀⠀⠈⠈⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⣿⣿⣿⣾⣍⡋⢷⡀⠀⠀⠀⠀⡄
⠀⠀⣠⡖⠾⠀⡈⢠⡏⢲⢟⠉⡂⡀⠀⠀⠠⠢⣄⠀⠀⠀⣸⠀⠠⠀⠀⠀⠀⠀⠈⠏⠫⢿⣿⣥⣝⣿⣆
⠀⠀⠘⠢⠤⠀⣠⡲⡏⠱⣺⠲⠟⠀⠀⠀⠠⢠⠀⠈⠀⠈⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠈⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠐⠒⠊⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⡀⣄⠀⠰⡢⠐⠀⠉⢁⣀⠀⠀⠀⠠⢚⠓⠂⠀⠉⠾⠟⠂⠀⠀⠀⠀⢀⠀⠔⣈⠀⠐⠀⣀⠀⠀⢰⣏⣩⣿⠿⣿⣼⣷⡦⣄⡀
⠀⠀⠐⠘⠈⡥⠰⣀⣤⣤⠔⠀⠊⠀⠀⠀⠻⣖⠒⡐⡃⠀⢀⡀⠡⠂⠀⠀⠔⢀⢀⠀⠀⠒⢀⡀⠀⠐⡀⠀⠈⠙⠱⠤⡼⡿⡊⢢⡵⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠅⠐⠉⠀⠀⠀⠈⠙⠶⢤⡀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⡀⠖⠀⡀⠀⠀⣄⣀⣶⣶⣂⣀⡀⠀⠀⠖⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠻⣻⠿⠿⢟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢿
⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⣾⠀⠀⠀⠀⣀⡖
⠀⢠⠞⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢼⣿⣶⣶⠃⠀⢰⠇⠀⠀⠀⡴⠏
⠰⠋⠀⢠⣤⣤⠤⣶⠀⠀⠀⢐⣶⣶⣾⡧⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠼⠁⠀⢠⣤⡤⢴⡇⠀⠀⠀⢲
⠀⠀⠀⠈⠿⣿⠴⠋⠐⣆⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⠾⠃⢰⡄⠀⠈
⠀⠀⠀⢠⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⡦⢤⣬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠳⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⠀⠀⠀⠹⡆
⢀⣂⡀⠀⠀⠘⢧⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⡏⣳⡶⢇⠀⠀⠀⠀⠀⢠⣀⣐⣂⡄⠀⠀⠙⡆⠀⠀⠀⠁
⢸⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⠛⢷⣅⣌⣀⡄⠀⠀⠰⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣻⣿⠇
⠀⡀⢀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠪⡠⠄⠀⠉⠀⠀⠀⠀⠀⠀⣀⠀⡀⠒⢀
⢠⣤⠉⠭⠙⣤⣬⣥⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⡀⢥⠀⠀⠀⠀⡀⠠⠄⢠⣬⡄⠉⠌⢡⣤⣭⣴
⢀⣂⣴⣿⣿⠟⠛⠛⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣰⣧⣀⣀⣀⣼⣿⡿⠛⠛⠃
⢸⣿⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⣽⣷⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣿⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠄⡗⠂⠄⠀⠀⣄⣬⣽⣿⣭⣄⡄⠀⠀⠒⠒⠊⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠠⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡛⢛⣛⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢿
⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠿⠀⠀⠀⠀⢠⠗
⣿⡿⠿⠿⠻⠿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣟⣿⣿⣷⣿⣿⣏⢠⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠏⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠟⠋⠀⢀⠄⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣴⠀⠀⠞⠎⠂⢨⠐⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠈⠋⠀⠀⠀⠀⢰⢊⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣠⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠄⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⣀⠀⡠⠄⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⣰⢽⡬⣦⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡅⢞⡏⢷⠻⡃⣓⠈⠇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡸⢃⠞⠓⢊⡰⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⠄⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⢁⠒⠀⠀⠀⠐⠀⠀⠀⠠⠄⠀⡀⢀⠀⢀⡀
⠀⠀⠀⣶⣦⣤⣉⣙⢉⣀⣨⡆⠀⠀⠢⡀⠐⠰⡀⠐⢤⣄⣀⢂⡀⠀⢀⠀⢁⠀⠀⠀⢲⣦⣬⣙⣀⢁⣀⣨⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠒⠤⣀⡀⠀⠂⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣛⣛⣛⣛⣿

⠀⢀⣀⡄⡤⠄⡤⡤⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⠤⠤⢄⣀⠀⠀⠀⠀⡀⡤⠠⢠
⠀⠋⢁⣴⣶⣷⣔⠢⡐⢄⠀⠁⠀⢠⠐⠶⠶⣖⣶⠶⠐⠀⠀⠋⢡⣾⡿⣻⢿⢳⡌⡁⠀⠀⢀⢴⠤⠷⣦⡄
⠀⠠⣙⠛⠿⠿⠛⢃⡁⠜⠀⠀⠀⡰⣷⣾⣾⣖⣗⢦⠐⠀⠀⣄⠸⠿⠿⠿⠿⠟⠃⡠⢀⠀⠈⡵⠁⡊⣋⡰
⠀⠀⠀⠸⡉⠦⠀⠐⠀⠀⠀⠀⠄⠘⢾⠃⣙⢉⠉⠈⠁⠀⠀⠀⠁⢒⠠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠒⠚⠂
⠀⠀⠀⠰⠖⠒⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣄⠀⠀⠀⡀⠤⠄⠤⡀
⠀⠠⣤⠶⠧⠼⣶⠶⠦⠡⠀⠀⢰⣶⠆⠀⢠⡖⠒⡆⠠⣼⣧⠄⢀⢤⢤⡀⠴⣛⣯⡳⣤⠀⢐⣲⣆⠟⠆
⠀⡈⠙⠄⠠⠀⠀⠴⠢⠀⠖⢀⠀⠭⠀⠀⢸⣏⣉⡇⡰⠻⠏⠦⠜⠚⠘⠀⠀⣟⠫⣗⣀⠀⠀⠉⠈⣁⣀⡀
⠀⠉⠉⢉⣩⣄⣈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠤⠖⣡⣡⡤⠶
⠀⠀⠀⢀⣈⢁⣄⡀⠉⠁⠀⢀⣀⣠⠤⠤⠠⢤⠈⠐⠀⠶⠐⠂⠋⣍⢙⡚⠚⠀⠈⡀⠀⠀⠀⠀⢡
⠀⠐⠛⠁⢲⠤⠶⠨⠙⠀⠀⢈⢀⠀⠀⠀⠀⡀⢀⠀⠠⢰⡂⠁⠉⠀⠈⠙⡀⠗⠄⣤⣆⠀⢀⢠⡼⠂⠂
⠀⢰⠀⠀⠀⠀⠀⠠⢁⠄⠀⢁⠊⠀⠁⠐⠀⡀⢀⠁⢣⠑⢠⠁⠀⠀⠀⢀⠠⠂⠆⢾⡿⠀⠈⡄⠀⠂⢠
⠀⠀⠁⠒⠒⠒⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣤⠀⠤⠤⠀⠠⡀⠀⠀⠀⠀⠀⠠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠂⠐⣀⠀⢀⣠⣤⡀⠀⡦⠀⢄⣀⣀⣀⡼⣇⠄⢁⡸⠓⠂⠀⠀⠂⠒⠎⢉⣹⣋⣉⣉⣴⢼⠀⠀⠀⠄⢆⢆
⠀⢴⡄⠆⣠⡎⠈⡙⢂⡀⠀⠀⠛⠟⣻⡟⠉⠙⠧⠀⢀⡀⢀⠀⠀⢀⢀⡀⠀⠉⠋⠉⠙⠻⣈⡄⠀⠀⠔⠂⠠⠈⠁
⠀⢰⡈⠀⠀⡩⠎⠙⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⣶⢰⣶⣦⣤⡠⡤⢹⡧⠤⣀⡠⠀⠀⠀⠴⠃⡂⠢⢀⣠⣌
⠀⠼⠧⠀⠀⠣⠙⠁⢀⣀⣀⡀⠀⠀⠘⢳⣆⢏⡉⢠⢠⠁⠁⡘⠮⣁⢻⡄⢱⠉⠀⠀⠀⢀⣀⡈⡁⠚⠋⢰⠀⠂
⠀⠀⡰⡊⠀⠀⠀⢨⠻⣿⣿⢿⠀⣀⠀⢸⣷⠀⠤⢉⣌⠉⣤⠀⢰⡌⣇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢂⡴⠛⠦⡀
⠀⠀⣀⡳⠄⠀⠀⢘⠁⠙⠒⠚⢀⡀⢀⣸⠰⣆⣸⣈⣉⡄⣉⣤⣈⡤⠇⠐⠂⠀⠄⠀⠀⠀⠀⠀⢴⡌⠀⢀⠂⠒
⠀⠀⣾⡷⠀⠀⠀⠸⠁⢀⡀⠀⡀⠃⠤⠈⠀⠉⢁⡄⢇⡀⣤⣀⠀⠀⠀⡀⠀⠀⠀⣯⠀⠀⠀⣀⡀⢀⢀⠀⠁⠈
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠄⠀⠀⠀⠀⠈⠟⠓⠉⠛⠻⡿⠃⠀⠀⢀⡿⢰⠒⠚⢐⣎⣻⠌⠐⠀⠑
⠀⠀⠀⢀⣰⠇⢰⣦⠤⣴⣦⣀⣠⣤⡾⢶⠄⠀⠀⠀⠀⠀⠀⢶⠀⠀⡀⠠⠀⠀⠘⢳⣿⣿⣿⣿⣿⢿⠀⠀⠀⢀⡇
⣀⣀⣀⣈⣀⣀⣀⣉⣀⣁⣙⣛⣛⣉⣀⣁⣀⣀⣀⣀⣀⣈⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣈⣃⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡟⡗⠂⠀⠀⠀⠀⢠⣤⣿⣶⣿⣶⣾⣤⡄
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠿⠁⠀⠀⠀⠀⠀⠀⠠⠤⣷⡇⢸⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁


⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠈⢛⣿⣻⣟⣿⡛⠁⠀⠀⠀⠀⠀⠛⠛⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣄⠠⣶⠀⣴⠄
⠀⠀⠀⠈⣿⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠾⢿⣯⠿⠻⠛⠓⠀⠀⠀⠀⠀⢀⣿⣧⣤⣼⣿⡆⠀⠀⠀⠀⣠⣌⡻⣧⣿⣾⣏⣴⠿
⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠛⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣴⡏⢡⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢼⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⣿⣿⡿⠂⠀⠀⠀⠀⠀⢤⣦⠄⠷⣿⣿⡿⠁
⠀⠀⠸⣿⣿⡟⢻⣿⢀⠄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠿⠗⡂⠀⠀⠀⠀⠲⣾⠿⠶⠶⠾⠿⠶⡶⠖
⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⠁


⠀⠀⠀⠀⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⢀⣈⡷⢾⣁⣀⡀⠀⠀⠀⠀⢠⣿⣿⣏⠻⣽⣿⣿⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡤⠀⠀⠀⠀⠀⠀⣀⢠⢰⡂⡆⣲⢠⢀⡀
⠀⠀⠀⠉⢉⡷⠺⣅⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣀⣿⣿⣿⠀⠀⠀⠀⠀⠠⣤⣾⣶⣷⣧⡤⠄⠀⠀⠀⠀⣧⠾⠞⠛⠛⠛⠾⢦⡇
⠀⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠏⠇⠭⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡛⠉⡁⠀⠀⠸⣿⣿⣿⠀⠀⢀⣴⣶⡶⣄⠀⠀⠀⣰⣷⡀⠀⢠⣯⡭⡷⢙⣧
⠀⠀⠀⠀⠀⠀⢀⡃⠀⣃⠀⠀⠀⣿⣿⡟⠀⢀⣾⣤⡀⠀⣹⣆⢀⣸⣿⣿⣿⣀⠈⢯⣫⣾⣯⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠴⠾⠿⠷⠄⠀⠈⠉⠉⠉⠉⠀⠙⠙⠋⠁⠙⠋⠁⠀⠈⠉⠁⡄
⠀⠀⢠⠶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠘⢄⣸⣿⣿⣿⣿⠇⠀⢀⣤⣤⣶⠾⡃⠀⣸⡶⢾⣿⠉⠑⢸⡿⢿⡿⠧⢤⣠⠖⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠭⣽⣿⣿⡯⠍⠂⠾⠻⠯⠿⠛⠀⠀⠁⠃⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠀⢹⣠⠀⡇⠀⠀⣠⠞⠉⢲⡀⠀⢠⣸⣾⣧⢖⡀⢾⡛⠃⠘⠙⣷⠆⣴⣾⣿⣤⡆
⠀⠀⠀⠀⠀⠀⡆⢠⡀⡇⠀⠴⠿⠶⠰⠼⠿⠄⠀⠈⠙⠉⠉⠁⠀⣿⣀⣄⣸⡅⠀⢹⠏⠹⡇⠈
⠀⠀⠀⠀⠀⠀⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠉⠁⠈⠉⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣷⠀⠀⣠⣶⣿⡿⠿⣿⣶⣤⠀⣰⣿⣿⣷⡀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠴⠶⠶⠶⠶⠐⣿⣿⠍⢶⡦⠩⣿⣿⠈⠻⠿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠘⣇⠀⠀⠀⠀⠀⠀⣸⠇⠹⣦
⠀⠀⠀⠀⠀⠀⣸⠋⢻⣄⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠹⣄⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠙⢷⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠹⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠳⣄⢸⠃⠀⠀⣴⡀⠀⠀⠀⢹⡾⠃⠀⠀⢠⣦⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⡇⠘⢦⣀⠀⠈⠀⣀⣠⠔⠃⠈⣆⠀⠀⠀⠀⠈⢷⡀
⣤⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠙⠓⠛⠋⠉⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⣧
⠈⢿⡛⠶⢦⣄⡈⣇⠀⠀⠀⢀⡀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣴⠒⠒⡶⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇
⠀⠀⢳⡀⠀⠈⠙⠻⠆⠀⠀⠀⡏⠳⢄⣸⠁⠀⠀⠀⠀⢰⠃⠀⡼⠁⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠁⢀⡀⠀⠀⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢿⠲⣄⡀⣸⠀⡟⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⠉⣙⣻⣧⣀⡀⠀⠀⠀⠰⠿⠞⣷⠀⠀⠀⠀⢰⠇
⠀⠀⢰⡇⠀⠀⠀⠸⠓⠦⣤⣸⠀⠀⠀⠀⣠⠖⠛⠶⢤⣄⣠⠟⠉⠙⠳⣄⠀⠀⠀⠀⡏⠀⠀⠀⢠⡏
⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡜⠁⢀⣤⣄⠀⣠⠶⠖⠶⣄⠀⠈⢧⠀⠀⠀⡇⠀⠀⠰⢿⣤⠴⠶⠛
⠀⠀⠈⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢰⠁⠀⡏⠠⠎⢻⠁⠀⡶⠀⠈⡇⠀⠘⡆⠀⣾⡁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⡆⠀⠙⠦⠤⠾⣧⡀⠀⢀⣰⠇⠀⠀⣷⠀⠈⣩⠗⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠁⠢⣀⠀⠹⣄⠀⠀⠀⣀⡈⠉⠛⠉⣀⡄⠀⠀⣽⠖⠋⠁⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⠒⠾⠷⢦⡀⠈⠉⣟⠛⡟⠉⠀⠀⠀⡇⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⠹⣄⠀⢸⡖⣇⠀⠀⠀⣼⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠲⠶⠶⠖⢻⡄⠈⣧⢹⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⠿⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠠⠤⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠛⠲⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣶⠓⠟⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢦⣤⣤⣤⣤⡤⠶⠞⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡖⣶⣶⡶⢶⣄⠀⠀⢀⣤⣟⢳⢀⡟⢴⠟⣙⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢀⡀
⠀⠀⠀⠀⢀⣾⣿⣹⣿⠾⢿⣶⣵⡅⠀⣿⡻⣯⣑⠤⢀⣿⣤⣥⣤⠀⠀⠀⠀⠀⢀⠀⢉⠀⠀⠀⠐⠈⠑⢄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠚⠈⠁⠀⠀⢀⠈⠻⡾⡇⠀⠹⢷⣤⣉⣛⣻⣿⣿⠏⠀⠀⠀⠀⣀⠀⢸⣷⣦⣅⡐⠀⠀⣁⣴⣿⠀⠀⢸⡿⢹⠹⢩⡿⢸⠻
⠀⠀⠀⠀⡁⠀⠀⡠⢐⠀⡇⠀⣿⡇⠀⢰⠉⠉⠉⠛⢻⣿⡟⠒⠒⠂⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢼⡯⢮⡄⠺⣿⣿⣸
⠀⠀⠀⠀⢠⠀⠠⠀⠇⠸⠂⠀⣿⠏⠀⠠⠀⠀⠀⠀⠸⣿⣿⡀⠀⠂⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠒⠀⠠⠤⠀⠀⠚⠁⠀⠀⠀⠀⠂⠐⠀⠀⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⡶⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⡤⠀⢠⠤⢤⣤⣄⡀⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠛⠛⠋⠛⢿⣿⣷⠀⠀⠀⡄⠀⠐⠀⠟⢹⣿⣿⠓⠐⡠⠮⠉⠑⢄
⠀⠀⠀⠀⠀⣀⣀⣀⣰⣿⣿⣇⣀⡀⣀⢀⣀⠴⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⣇⣨⠤⢀⠁⣿⣿⣿⠉⠀⠀⠈⠐⢢⠸⣇
⠀⠀⠀⠀⠀⡊⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⡆⣸⡟⠀⠀⠀⠈⡇⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⢸⠃⢆⣧⡀
⠀⠀⠀⠀⠀⠸⢀⠀⠀⢿⣿⣧⡀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠑⠂⠂⠃⠈⠴⠋⠀⠀⠀⠀⠀⠘⠤⡀⣠⠀⢻⣿⣿⡀⠀⠠⠔⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⣤⠖⠒⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡞
⠘⢧⠾⠻⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⠀⠀⠹⣆⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠈⠉⠓⠒⠒⠒⠋⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠤⠀⢀⡴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⡷⣄⣀⣀⣠⣤⠶⠭⣀⡠⠒⠀⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢋⣉⢳⠀⠀⡸⠓⠒⣲⡞⢑⡒⠐⢆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡘⠀⣤⠀⠈⡇⠰⠄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⠋⠈⠉⠀⠀⡇⠀⠀⠉⣇⡈⠀⢀⠞⠀⡀⠸⡇⠠
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠱⡀⠀⠀⣠⠗⡤⡀⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡏⠀⠀⠀⠀⠀⠘⢲⣴⣚⣉⣉⣉⠥⠔⠊⡇⢠⡇⠄
⠀⠀⠀⠄⠀⠀⠀⠻⡄⠐⢷⠬⢥⣉⣁⣀⣀⡀⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢸⡇⠀⠀⠀⢀⠄⠀⠸⣀⢈⠀⠀⢀⣀⠠⢾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⣄⣀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢹⠉⠉⢉⠀⠀⠐⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠳⢤⣀⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢿⡟⠉⠉⠉⢻⠈⠉⢻⠀⠀⢀⡤⠒⠒⠺⣅⠀⣀⣈⣉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠐⠀⠀⠸⠋⠀⢀⠈⠱⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⠀⠀⠀⠀⢸⢀⠀⠘⢄⡀⠀⣀⣧⠀⠀⠀⠀⢠⠃⢠⠏⠀⠑⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠣⣀⠀⠀⠀⡠⠎⠈⠀⠀⠀⠈⣹⡁⠀⠑⠦⠤⠒⣁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⠀⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠉⠉⢉⣀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢿⡿⠿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⢠⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠸⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣅⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠀⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠛⠀⠀⠉⠁⠀⠀⡸⠓⠈⠀⠈⢷⡄⠀⠀⠀⠀⡀⠐⠤⢈⠈⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣖⡓⠀⣤⠀⠸⠆⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠞⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠴⠶⣗⣃⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣦⣦⣦⣤⠶⠤⣄⡀
⠀⠀⠀⢀⣀⠀⢰⣿⣧⡀⠀⠀⠚⣛⡟⠉⠉⢛⣛⣇⡀⠀⢸⣟⣟⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⢠⣾⣿⣆⢿⡇⡈⠃⢀⣄⣶⣯⣍⣲⡆⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠸⠇⠀⠿⠀⠀⠑⠀⠀⠀⠀⠀⠀⡘⣿⡆⠀⠀⠀⠀⠀⠙⠛⠋⠀⣶⣴⣶⣶⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠠⣿⣿⣿⣷⣿⣿⣦⠀⢉⣙⣋⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣽⣿⣽⣽⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠆⠀⡠⠀⠀⠄⠀⢠⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠂⣺⣃⠐⠀⠀⢐⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠤⠋⡭⠀⠀⠈⠀⠀⠀⠀⢢⣀⡴⠀⠀⠀⠀⠀⠀⠀⠲⠴⠏⠀⠀⢀⡈
⠀⢀⡴⠃⣐⡌⠁⡸⠃⠀⢀⠀⢠⡄⡀⠀⠀⠜⠁⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠙⠒⠛⠩⠀⠌⠀⠂
⠀⠁⠀⠀⡈⠀⡀⠀⠀⠈⢣⣕⠄⠈⠚⠁⠀⡀⠀⢀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⡀⠀⣀⡄
⠀⠀⠀⠠⠁⠀⠀⠀⡀⡀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠟⠃⠀⠀⢀⠀⣀⠀⠀⠈⠋⠙⠋⠍⠁⢠⣿⡾⣄
⠀⠀⠀⠔⠀⠀⠀⠈⠁⠉⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠋⠀⠀⠀⠂⠀⠀⠐⠀⡈⣸⢲⢸
⠀⠀⠦⠖⠄⠀⠀⠀⠀⠀⠀⠀⠈⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⠇
⠀⢀⠀⢀⠀⠀⠈⡑⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠽⠇⠀⠀⠀⠀⠀⠀⢠⠖⠊⢥⠉⠓⢦
⠀⠀⠀⠉⠀⠀⠈⠉⠉⠁⠀⠙⠁⠑⠒⠀⠀⠀⠀⢀⢀⠀⡀⠀⡀⠀⠲⠶⠠⠛⣿⡟⠷⠰⠶⢂⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠀⠀⠉⠀⠛⠉⠙⠋⠈⠁⠈⢡
⠀⠀⢤⠀⠀⠀⠀⢤⢶⣀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠘⠀⠀⠀⠐⠀⠀⠠⠀⠀⠳⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⣶⡦⠘⡀⢐
⠀⠀⠤⢀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⠀⠀⣠⢛⣃⣠⣄⠀⠀⠀⠀⢀⠈⠁⢀⠁
⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠚⠁⠀⠈⠑⠒⠀⠀⠐⠈⠀⠑

⠋⠀⠬⠘⠀⠀⠀⠀⠀⠁⠀⠀⢰⠂⡀⠀⠀⠀⠊⠀⠀⠀⠉⠀⠀⠁⠀⠁⠈⠈⠀⢈⠉⠀⠀⢮⣭⡷⠂⠀⠀⠈
⠏⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠨⡀⠆⠀⠀⠀⠀⠤⢀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁
⠀⠀⣀⡔⢒⠙⠛⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣀⠂⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⣠⠂⡸⠂⠀⠰
⠁⠀⠈⢁⡉⠀⢬⠀⡀⠀⠀⠀⡐⠀⢀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠘⠁⠀⠀⠁⠀⠀⠸⠁⠐⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⣑⢶⣄⡀⠀⠀⠀⠀⠘⠁⠀⣀⡀⠀⠀⠀⠀⠘⡅
⠃⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠂⠀⠀⠀⠀⠀⢀⠠⠝⠛⠖⠀⣀⠀⠀⠃⢀⠀⢰⠒⢰⡄⠀⠲
⠁⠠⠂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⠁⠀⠀⠀⠉⣈⠁⠠⡌⠁⠀⠀⠀⠂⠙⠀⠀⠁⠩⠤⠀⠀⠁
⠀⢀⡀⠀⠀⠀⡆⠀⠉⠠⠄⠈⠇⠀⣠⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠓⠀⠀⠀⠀⠠⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰
⠰⠈⠀⠀⠀⠀⣁⠀⠀⠀⠀⢱⠀⠀⠀⣔⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠋⠙⢠⠁⢐⣀⡄⠀⠀⡀
⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢠⠴⣶⣧⠀⠀⠨⠁⠀⠀⠀⠂⠀⠀⠑⠘⠾⡌⠁⠙⠀⠀⠀⠋⠠⡐⠆
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠖⠐⠀⠀⠠⠀⠀⠈⠙⠉⠁⠀⠀⠀⢠⠄⠀⠐⠀⠤⠄⠲⠄⠀⠀⠀⠀⢠⠆⠀⠀⠀⠡
⠲⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣛⡂⡀⠀⠀⠀⣀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠈⡀⠀⠈
⠄⠀⠠⠤⠒⠂⠀⡀⠘⠠⠐⠂⡀⠈⠁⠀⠻⢡⡗⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡅⠀⠀⠈⠀⠀⠀⢃⠀⡅⠀⠀⠀⠀⠶
⣄⠀⠳⠀⠀⠀⠙⠉⠁⠀⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⡁⠀⠀⠢⠀⠀⠀⠀⠖⠆⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⠳⠀⠀⠀⢠⠁⡸⡃⠀⠀⠀⠀⠀⢠⡄⠘⠁⠀⠀⠐⠀⠀⠀⢀⣀
⠷⠃⠀⠀⣀⣤⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢲⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢲⡀⠀⠀⠀⠀⡠⡐⢰
⠀⠀⠀⠯⠽⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠑⢀⠀⠀⢀⠀⠀⠀⠀⠆⠀⣀⠀⠀⠀⠀⠈⢄⠸⠀⠀⢱⠈⠁
⠀⣶⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⠩⠡⢤⠄⡀⠀⠀⠲⠊⠁⠀⠀⠀⠉⠁⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠁
⢠⠋⠠⠂⠀⠀⠸⠸⢰⠋⠁⠀⠄⠀⠀⠰⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⢠⡄⡀⠀⡄
⡮⢄⠢⠀⣤⡴⢒⢉⣢⠖⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠎⠸⠇⠀⠈⠠⠀⡀⠐⠚⢀⣠⠀⠀⠀⠠⡌⠀⠀⠀⠁⠈⠐⠆
⠁⠁⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠂⠛⠠⠁⠀⠈⢃⣘⠆⠀⠦⠄⠀⠀⠀⠁⠀⠀⠄
⢀⠀⠀⠀⠀⢰⠂⣢⡀⠀⠆⠀⠀⠀⠀⠀⡀⠀⡒⡒⡄⢂⠀⠀⠀⠀⠀⠀⠴⡿⠞⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⣀⠁⠀⢀⠀⠀⢈⢉⡅⠁⠀⠁⠀⡇⠀⠀⠟⢋⠄⢁⠪⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⣠⠐⠂⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣠⠶⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣘⡛⠛⠛⢛⣛⣿⣄
⠀⠀⠀⠀⠀⡀⠽⣿⣖⣶⡿⠇⠈⢀⢀⠻⠃⢀⣴⣾⣿⣷⣄⠀⠀⠀⠀⣀⣈⡉⠉⢩⡽⡷⣶⣄⡉⠩
⠀⠀⠀⢠⣬⣽⣳⠮⠿⠿⢥⡉⠀⣀⠋⣢⣶⣿⣿⣿⣿⣿⣿⣷⣤⣜⣛⣯⣭⣽⣥⣀⢀⢀⠆⠉⠋⣗
⠀⠀⠀⠀⠀⠉⢿⠟⠛⠙⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣖⠚⠿⠿⡛⣷⣱⣾⣿⣷⣦
⠀⠀⠀⠘⠛⠒⣄⣠⣶⣿⣿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣤⣼⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋⠀⠙⠛⠿⠿⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⢡⠐⠟⠋⠀⠙⠃⠉⠻⢿⣿⣿⠵⠚⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠙⠟⠋⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢈⢀⡃⠀⠀⠀⠀⠸⢤⡀⠀⠐⡄⢿⠂⠀⠀⠞⠭⠇⠀⠀⢐⢠
⠀⠀⠀⠀⠀⠐⠞⣮⢫⢧⡀⠀⠀⠀⢂⠀⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠢⢀⡀⠀⠠⣄⠠⠤
⠀⠀⠀⠀⠀⠀⢠⡹⣇⣩⣆⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡄⠠⣤⠀⠀⠀⠁⠲⠦⠤⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠶⠇⢠⠀⠀⡀⠀⠀⠀⠀⠉⠰⠬⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠸⠒⠒⠚⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠀⠀⠀⠀⠆⠐⢢⡀⠀⡀⠈⢲⠑⢲⣀⡐⠁
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⡀⣠⠔⠀⠀⢠⠞⠁⠀⠀⠀⣀⠔⠚⠓⢲⣷⡀⡉⠫⢿⣤⡧⠉⣹
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⢠⠟⠘⠁⠀⠀⠆⠀⠀⣰⣦⣆⣿⣿⣿⣠⣴⣿⣤⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⠴⣴⣻⠖⠁⠀⠀⢟⣃⠈⠀⠀⠀⠀⢶⣶⣿⠿⠛⠋⠉⠙⠛⠛⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠠⢀⣈⣥⡴⠶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠚⠻⣦⣀⡀⠀⠀⢀⣄⣹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⠤⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠀⢀⣀⠟⠁⣱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠜⢩⠁⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣫⣷⡏⠀⠀⠐⢻⣭⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠟⠡⠺⠃⣴⠎⠉
⠀⠀⠀⢤⠴⢖⣿⣷⢾⠲⢤⣂⡄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⢀⣀⣙⣿⡽⠾⣛⠀⠀⠘⠉
⠀⠀⠀⠙⠽⡶⡞⣏⣿⠀⠀⠰⠆⠈
⠀⠀⠘⢷⣾⣿⣯⡵⣖⠀⠀⢀⣠⡴⠂
⠀⠀⢤⣤⣬⣧⣷⣷⣫⠀⠀⠀⢁⣀⠄
⠀⠀⠀⠉⢻⢻⢻⡏⡇⠀⠀⠀⠙⠁
⠀⠀⠰⢶⡿⣿⢻⡟⡿⠊⠄⠀⢀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣔⣦⣤⣤⣤⣀⣀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣵⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠋⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⠿⢿⣶⣶⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡇⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢤⣬⣭⠤⠶⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⢠⣤⣀⣤⡄⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣄⣀⣉⣠⣄⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢸⡇⠀⠀⠀⠀⣈⣉⣩⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠟⠀⠀⠀⠀⠈⠉⣉⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠘⠉⠉⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡀⠀⠀⠀⠀⠀⠒⠛⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣼⠃⠀⠀⠀⠀⣘⣋⣉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⠃⠀⠀⠀⢀⣀⣩⣭⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢠⡏⠀⠀⠀⠀⢈⣉⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⡟⠀⠀⠀⠀⠀⢬⠍⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⣠⠏⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡟⠁⠰⠋⠀⠀⠀⠛⠓⠚⢒⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⣀⣘⣛⣛⣓⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠤⣤⣉⡉⣩⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠶⢦⣤⣤⣠⣤⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⢀⣀⣀⠙⠛⠶⠦⣴⣾⡿⠋
⠀⠀⠀⠀⣀⣠⣶⠿⠋⢀⡀⠴⢤⣀⣉⣉⣙⣛⣿⣿⠟⠁
⣀⣤⣾⡿⠟⠋⠁⠠⣤⣀⠙⢻⣶⣤⣽⣿⠿⠛⠋⠁
⠛⠻⠿⣶⣶⣴⣿⣿⣿⣿⡿⠿⠛⠛⠉
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢎⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐
⠀⠀⠀⠀⠃⠀⠂⢀⠀⠐⡆
⠀⠀⠀⠠⠀⠂⣀⡘⠀⢈⣀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⢠
⠀⠀⠀⠤⠐⠂⠑⠀⠠⠈⠋⠀⡀⠈⠉⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠾⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⠿⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣤⡀⠀⠀⣠⣶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠂⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠙⠋⡇⠀⣾⡿⠃⠀⠀⠀⠘⠆⣀⡀⠀⠀⣼⣿⠟⠁⠀⠀⠀⢀⠀⣴⠏⠀⠀⠀⠀⠀⢀⣾⢃⣒⡀⣚
⠀⠀⢰⠁⡸⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⡦⢰⠿⠃⠀⠀⠀⡀⣶⠈⡄⣀⡀⠀⠀⠀⠀⠀⠘⠁⠸⣛⡧⡟
⠀⠀⠈⠦⠄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠃⠀⠀⠀⠀⠀⠙⠲⠬⠥⠴⠒⠁⠀⠀⠠⠟⠀⠀⠸⠿⠇⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄
⡖⠒⠒⠚⠉⠈⠓⠦⠤⡄⠀⠀⠀⡹⠋⠉⢯⠀⠀⠀⠀⠀⠀⢷⣶⠆⠀⡀⠀⠀⠀⠀⠀⣸⣿⣽⣿⣀⣠
⠀⠘⠀⠈⠀⡆⣁⠐⠀⠂⠀⠀⢰⡇⢀⡀⢈⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⢻⣿⠛⠉⠙
⠈⠢⠐⢛⠜⠠⠈⠤⠂⠀⠀⠀⠀⢙⣿⣿⡏⠁⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⢠⠞⠙⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠰⢤⣀⡤⠂
⠀⠐⠀⠀⣶⣆⠀⠐⠀⠀⠀⠀⠙⠳⣶⣏⣲⠞⠀⠀⠀⠈⠙⠦⠍⠉⠉⠁⠀⠀⠀⠀⠀⠋⠁⣤⠉⠉
⠀⠀⢰⣾⣿⣿⣷⠄⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠐⠓⢺⣿⡗⠚
⢀⣤⣼⣿⣿⣿⣿⣤⣄⡀⠀⠀⠀⢨⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⢀⡤⠀⠤⣀⡀⣤⠠⣄⠀⠀⠀⠀⡰⠊⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠖⣒⠲⡄⠀⠀⠀⠀⠹⣿⣿⣿⠃
⢸⡇⠀⠀⢸⠀⠿⠀⣿⠀⠀⠀⠀⢣⠀⠀⡸⠀⠀⠀⠀⢀⡴⢉⡊⠷⡬⠼⠀⠀⠀⠀⠀⠀⢹⣿⡇
⢸⣇⣀⡀⢸⠀⣀⣀⣿⠀⠀⠀⠀⠀⢳⣷⠀⠀⠀⠀⠀⠠⢇⠘⠟⡈⠇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠈⠉⠉⠉⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⠋⠑⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⢛⣛⡛⠲⣶⣤⣶⠶⠶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢠⡾⠋⠉⢹⣿⠿⠶⣍⠻⣦⡀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢸⡇⠛⠛⣿⠛⢦⡄⢹⡇⠀⠹⣆⠀⠀⠈⢿⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠹⣦⠀⣿⠀⢀⣠⡾⠃⠀⠀⢹⡆⠀⠀⢸⡇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣿⠶⠚⠲⢦⣄⠀⠘⣧⣤⠞⠋⠁⠀⠀⠀⠀⠀⡧⠀⠀⢸⡇⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣀⣼⢿⡷⣤⡄⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣠⡟⣠⡞⠁⠀⢀⣠⣤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠚⠛⠉⠀⠀⠻⣦⡀⠀⢸⡇⠀⠀⠀⠀⣠⡴⠟⠛⠳⣦⣿⣡⡾⣫⡾⠋⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠈⢁⣴⠟⠀⠀⠀⣠⣟⠉⢳⡄⠀⠀⠀⠙⢿⣾⣫⡴⣟⣭⠶⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣠⠟⠁⠀⠀⢀⡾⠋⠙⠷⠾⠃⠀⠀⠀⠀⠀⠙⣿⡞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⠃⠀⠀⢀⡴⠋⣰⠞⠳⣄⠀⠀⣴⠶⢦⡀⠀⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠓⠀⠘⢷⣤⡿⠀⠀⢿⣄⣀⣿⠀⢀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢿⣅⠀⢠⡶⠶⣄⠀⠀⢀⣠⣀⠉⠉⢁⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣦⣀⣿⠀⠘⢧⣀⣽⠇⠀⢿⡁⠙⣷⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠉⠀⢀⠀⠀⠉⢁⣤⣀⠈⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢰⡟⠛⣦⠀⢼⡋⠻⣆⠀⣿⡀⠙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠙⠷⠛⠀⠈⠛⠚⠃⢀⣼⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢶⡄⠀⠀⣠⣤⡀⣠⡴⠋⠁
⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢠⡀⠀⠀⢿⣬⡿⠋
⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣁⣠⡴⠟⠉
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣿⣿⣿⣉⢹⢿⣄⡀
⣿⣷⡰⣯⡻⣾⣿⣿⣦
⣿⣿⣿⣮⡷⣿⣿⣿⣿⣿⣦
⣿⠛⠛⡿⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣶⣷⣾⣾⣿⣛⣛⣛⣻⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⣿⣿⡷⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⢀⣺⣄⠀⠀⠀⠀⢠⡤⠏⠻⢤⣄⠀⠀⠀⢠⣶⣷⣦
⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣴⣇⢀⣸⣦⠀⠀⠀⣀⣼⣿⣿⣄⡀⠀⠀⠈⣷⢀⡀⣾⠃⠀⠀⠐⢻⣿⣿⣿⠛
⠀⠀⠐⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠙⠋⠙⠛⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣤⣾⠿⣷⣤⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢀⣠⣋⣉⣃⡀⠀⠀⠈⣿⣇⢛⣸⡿⠀⠀⠀⠐⠿⢿⠿⠟⠀⠀⠀⠸⠿⠻⠿⠶⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠟⠃

⠀⠀⠀⣾⠿⡆⠀⠀⠀⠀⠀⡏⠉⢱⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠀⢀⡶⠿⡛⣶⡄⠀⠀⠀⢀⣤⣤⡄⣄
⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠁⠽⣿⣿⠇⠀⠀⠀⢸⢿⡕⣋⣴⣿⠀⠀⠀⢿⡿⠿⣿⠹
⠀⠀⠰⣥⣤⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠲⠶⠿⠞⠁⠀⠀⠀⠘⠁⠈⠃

⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠠⢴⣦⣦⣶⣦⠀⠀⠀⠀⢔⠉⡂⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣤
⠀⠐⢚⣿⣿⣿⡋⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠀⠸⠋⠓⠀⠀⠀⠀⢀⣾⣿⣿⣾⣤


⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣶⣄⣿⡿⠷⠀⠀⠀⢴⣷⣶⣷⣀⠀⠀⠀⢀⣔⣆⣗⡴⡀⠀⠀⠀⣰⠻⠿⢳⡄
⠀⢰⣿⣿⣿⠗⠀⠀⠀⠀⠛⠃⠛⠃⠀⠀⠀⠀⠙⠉⠉⠉⠙⠁⠀⠀⠀⠈⠙⠋⠋⠁⠀⠀⠐⠻⠷⠤⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠑⣿⠿⣿⠿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠄⢴⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⢺⣟⢿⡆
⠀⠀⣠⠸⠂⠛⢘⡗⠄⠀⠀⠀⢸⣿⣯⣿⡟⢂⠒⠈⠀⠀⠀⠀⠉⠀⣤⡶⣄⢹⣿⠃⠀⠀⠀⢀⣴⣾⡿⠎⠛⠊
⠀⠁⣬⠀⠀⠀⠘⠃⡀⠀⠀⠀⠀⠛⠶⠟⢅⠒⠂⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⢘⠃⠀⠀⠀⡔⠛⠋⠁
⠀⠐⠄⠛⠠⠂⠘⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⡶
⠀⠀⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠐⠻⡿⣿⠗⠀⠄⠀⠀⠀⢠⡶⠶⠿⠶⠶⢶⢶⡄⠀⠀⠀⠀⠄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁
⠀⠀⢠⠓⡾⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⡞⡀⠀⠀⠀⠀⠀⠀⢠⢀⣠⣿⣿⡁⠂⢀⡀
⠀⠀⢘⠁⠘⠀⠀⠂⠀⠀⠀⢸⣇⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀⢀⣸⠇⠙⠲⣌⠀⣄⠀⠀⠈⠂⢕⢠⠀⡀⠔⠈
⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠛⠿⠆⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣀⡀
⠀⠀⣀⢠⡠⠄⠂⠓⠀⠀⠀⠀⣉⠇⠀⢏⡅⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⡇⡤⣀⠀⠀⠀⠀⠀⠀⣹⢺⠗⣯⠤⢠
⠀⢰⣿⣴⣦⣦⣴⣴⠀⠀⠀⠀⡀⠀⢀⣀⣤⣀⣀⣀⠀⠀⠀⢶⡁⢾⡠⢇⣹⢎⡱⠆⠀⠀⠀⢠⡇⢸⠀⢸⡆
⠀⢸⣿⡿⣿⡿⣿⣿⠀⠀⠀⠀⠠⡀⠀⠙⢻⡟⠋⠁⠀⠀⠀⢸⡇⠸⠃⠘⠛⠈⣿⠀⠀⠀⠀⠘⠧⣼⣤⠼⠃
⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠂⠀⠃⠐⠓⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣤⣄⣀⡀⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣠⣤⣶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣲⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠙⠛⠿⣿⣿⣿⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⡟⠛⠿⣿⣿⣿⣿⠟⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⡄⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠶⠂⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢠⠀⠺⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠰⠆⠀⠈⢠⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⡄⠀⠒⠀⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⢀⡠⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁
⠰⠉⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢍⠆
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠐⠤⠐⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠌⠈⢿⣿⣿⣿⣿⣿⣯⡀⠈⢐⠀⠀⠀⠀⠀⠀⡀⢆⢀
⠃⠀⠡⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄

⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠂⢁⠠⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠤⠄⠀⣄⠀⠀⠔⠉⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⡤⠄⠚⠁⠀⠀⠢⠐⠄
⠀⠀⠈⠐⠀⠉⠠⠔⠂⢀⣤⣾⣿⣿⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣄⡀⠀⠀⠀⠐⠀⠀⠀⠄⠈⠀⠂⠐⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡈⠐⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣯⠇
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴
⠀⠀⠀⠀⠀⠀⢤⡿⡷⠚⢻⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠕⠊⠁
⠀⠀⠀⠀⠀⡀⣤⣟⡣⣄⠀⠛⠛⠁⠀⠀⠠⠀⠀⠀⠀⢀⢐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶
⠀⠀⠀⠀⠈⠉⠉⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣛⠐⣀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣼⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠻⠃⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣾⣿⣾⣿⣛⣛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⢫⣵⢤⣤⣤⣤⣤⠀⣠⣬⡙⠿⢀⠙⠿⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠀⣀⠐⠟⠁⠀⢠⠊⠁⠀⠀⠡⣀⣀⣸⡿⠀⢠⣤⠈⠉⠀⠀⠀⠈⠨⢀⢁
⠀⡝⢟⣿⢵⣿⣿⣿⣿⣷⡶⠀⠀⢰⣄⠘⠃⠍⠑⡀⠈⠇⠀⠀⠀⠀⢤⠀⠁⢀⠇⠀⡩⠤⠄⠄⠀⢀⠠⠀⠸⢦⠀⠈⣉⠉⠀⢠⣶⠿
⢦⣀⣀⠈⠙⠇⢻⣷⠈⣿⣿⡦⠀⠀⢑⡙⠄⠸⡀⠀⠀⠀⠀⢀⠀⠀⡈⠃⢠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡐⢒⠉⠀⣀
⠻⠿⠟⠁⠀⣀⠀⠈⠀⠙⢋⠀⠶⠀⠈⢴⣤⠄⣀⣈⠀⠐⣤⡀⠀⡼⢇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢠⠘⢇⣴⡀
⢀⡆⠰⡄⠺⠿⢣⠀⠀⠀⠘⠁⠀⠀⢴⡄⠙⣀⣴⠋⠀⠀⠹⣤⣶⣤⣮⠤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠑⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣡⠆⠚⠛⣦⢾⣿⣿⡛⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⢯⠿⣦⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⣠⣾
⣶⣲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠞⠫⠰⠀⠚⠋⠈⣿⡿⠁⠲⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣽⡿⢷⣿⢋⣠⡤⡠⠀⢤⡶⠄⣀⣴⣿⢋
⡧⣷⣞⡷⠀⠀⠀⠀⠀⠠⠀⣸⣿⡆⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠀⠂⠀⠁⠀⠀⡀⡈⠙⠋⠁⠈⠛⠀⠀⠘⠉⠀⠈⠉⠉⠀⢸
⠛⠚⠋⢀⣀⣠⣤⠶⠆⠁⠀⢈⢉⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣶⣾⡇⠀⣤⡀
⠚⠛⠛⠛⠉⠁⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠉⠀⢠⣽⠗
⠀⠰⠂⣀⡴⠟⠉⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠰⠃⠀⠀⠀⠉⠢⠀⠀⠀⠈⠁
⠀⠒⠛⠉⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⠓⢄⡛⠁⠐⠒
⠰⠵⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⣀⢀⡐⣷⠄⠒⠲⠈⡆⠀⠉⢀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣦⠉⠀⠀⠀⠀⠀⠀⠔⠂⢀⣈⣿⣿⣤⣿⣿⢷⣟⢷⢛⠁⠀⢠⠃⡀
⠀⠀⠒⠰⠟⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠚⠀⡀⠀⣄⠀⣠⣽⣿⢋⣽⡿⢾⠏⠋⠁⠘⣠⢀⠠⠂⠀⠀⠁⠀⠰⠆⠐
⠀⠂⠀⠀⠘⠒⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠃⠀⠀⠀⡈⠆⠙⠻⠟⡘⠋⠁⠀⠀⠐⢾⣶⡷
⠒⠀⠀⠀⠀⠀⠰⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠠⠖⠂⠀⠀⠷⠀⡰⣧⠀⠀⢀⡀⠀⠀⠉⠀⠀⠠
⠀⠀⣉⣀⡀⢀⣤⡄⠈⠁⠀⠀⠀⠲⠶⠤⠰⢂⠀⠀⠠⡤⠀⠀⠠⣤⠆⠀⠀⠀⣤⣀⠀⠀⠀⠐⢶⠶⢤⣇⣤⣔⣨⠟⠀⢆⡀⢧
⣿⣿⢿⣿⣷⣿⣽⣶⡖⠀⠧⡀⠇⢀⡈⠑⠚⠁⠀⠚⠀⠀⠐⠈⠢⡀⠀⠀⠀⠢⠛⠛⠀⡯⢸⡆⢀⠔⠚⣿⣿⣿⣁⣤⣄⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡠
⠚⠙⠽⣟⢿⣷⡌⣿⣿⡗⠀⠀⠀⠈⠘⠐⣶⣄⣠⠞⠀⠀⡄⠈⢢⢑⡄⠀⢠⡄⠐⠂⠀⢤⡍⠐⠛⠓⠈⣿⣟⠏⢿⡌⠁⠐⡦⠀⠀⠀⠐⠦⢤⣤⡴⠶⠚⣁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠉⣉⣽⣶⣲⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡛⠋⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⣿⣿⢿⣿⣿⣿⣿⣍⠓⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⣿⠇⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⡏⠀⠈⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠉⢀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠀⠆⠀⠀⢀⡈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠋⠠⢌⠀⡶⠌⠙⠓⠲⣥⢆⠄⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠤⠤⠀⠀⡀⠀⠠⣀⣀⢤⡤⣀⠁⠺⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠀⠭⢄⡀⠰⠉⠀⠈⠉⠀⠀⠁⠃⢢⡈⠛⣬⡁⠬⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠸⡤⠤⠄⢀⠈⠀⠀⠀⠠⠀⠒⠒⠛⠂⣠⠀⠑⢤⠋⠀⠀⠀⠀⠀⠙⢢⡄
⠀⠀⠀⠀⠀⠀⠠⠔⠳⠀⡀⠀⠀⢀⠀⠀⠰⡄⠀⠀⠀⠀⠸⠇⠀⣈⠴⢦⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⢂⠰⡀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠⡋⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢳⠀⠀⢸⠀⠑⡀⠀⡆⠀⠀⠀⢣⠀⠀⠀⢀⠛⠛⠛⠦⣄⣀⠀⠑⢄⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠸⡀⠀⣜⠀⠀⠐⡀⢀⠀⠀⠀⢀⠁⡀⠀⠈⠉⠓⠆⠤⢄⣉⠙⠓⠦⣙⣄⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣀⠀⠀⠀⠀⠈⠁⠲⢄⡀⠙⡄⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢣⡈⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠒⠀⡀⠀⠀⠀⠀⢇⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠢⠄⡀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠋⡦⡀⠀⠀⡤⢾⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢄⠀⠀⠀⠀⠀⣊⠀⠀⣣⠃⠈⢂⣠⡐⣣⠘⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠀⠀⠀⠈⠀⠀⠀⠐⠁⡀⡐⠻⡄⠀⠀⠀⢱⠈⠆⠈⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠙⢄⣀⠀⠀⠀⠀⠀⠡⠁⠃⠀⡇⠀⠀⠀⠀⠆⠒⡀⢀⠣⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠀⠀⠀⢀⡠⠀⠀⡔⠀⠘⠀⡆⠇⠀⠀⠀⠀⠘⡀⠔⠀⢆⠑⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⡄⠀⡀⠰⠶⠋⡠⠈⠄⢠⠖⠂⢠⠀⡇⠀⠀⠀⠀⠀⢡⠈⠁⠈⢆⠘⠄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠉⠀⡇⠀⠀⡆⠀⢁⣀⠔⠊⡠⠊⡰⠁⡌⠀⡈⠀⡇⠀⠀⠀⠀⠀⠀⢂⠐⣡⠈⢆⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠃⠀⠀⢁⠀⠈⢁⠔⠋⠀⠐⠀⡐⠀⠀⠃⠀⡇⠀⠀⠀⠀⢀⢀⣈⡄⢡⠆⠈⡄⠊
⠀⠀⠀⠀⠀⠀⢀⠴⠋⡄⠀⠀⠀⢸⠀⠀⠈⠶⠞⠁⠀⡀⠀⠀⠰⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⢀⠄⢀⠞⣀⠜
⠀⠀⠀⠀⠀⢰⠀⠀⠠⢃⠀⠀⠀⠸⡀⠀⠀⠀⣀⣠⡞⠀⠀⠠⠁⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢁⠀⢀⡠⠇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⡀⠀⠀⠀⠳⠖⠋⠉⢀⡤⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠄⡀⠴⢚⠠⢂⡡⠔⠉
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠡⠁⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠎⠀⢈⠤⠚⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠎⢴⠎⠁
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⢠⢂⠌⠈
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⡴⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠵⣶⣤⣤⣀⡀⠀⠀⢀⡀⠀⣀⠀⠯⢟⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⣽⠟⠣⠉⠳⣂⡻⣿⡇

⢄⡠⠄⢀⠀⠄⡀⠀⠀⠀⣀⣠⣄⣀⣀⠉⠉⠉⠀⣀⣀⠀⠀⠀⠀⠄⢀⡤⣀⠀⠀⠄⠠⠁⠈⠀⠀⠀⠀⠀⠸⢂⠀⢀
⠀⠀⠀⠛⠀⠄⢠⠀⠀⡞⠁⢘⠛⢻⠗⠷⠀⠀⢰⠉⠉⠙⡄⠀⠀⠀⡸⠉⠈⢣⠀⠀⠀⠀⠀⡀⢈⣁⣀⣀⣠⡠⠀⠐⢣
⠀⠀⠀⠁⠀⠀⠈⠀⢀⠀⠀⠀⢀⠀⠀⡘⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠁⠀⠀⠈⠀⣀⡀⠠⡇⢀⡀⢸⠒⠒⠒⡃⠀⡀⠈
⠀⠀⠀⠀⣄⣠⠀⠀⢨⡀⡀⡅⠀⢺⠀⠀⡀
⠀⢠⠒⠀⠈⠁⠀⠠⡀⢵⡃⠀⠀⠀⠒⠂⠀⠀⠀⠈⠉⠉⠀⣠⡄⢀⠀⠀⠀⠀⢠⠶⠦⡀⠰⠂⡴⢒⣤⡤⠀⡀
⠀⠈⠄⡠⠀⠀⠀⡀⣈⣈⣹⠀⠀⠀⣄⠁⠁⠀⠀⠀⠀⠀⡐⠀⠀⠙⡀⠀⠀⠀⡇⠈⠀⢧⠀⠀⠀⢨⠁⠈⠉⡇
⠀⠄⠀⠁⠀⠀⠠⠡⠠⠄⠈⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠁⠠⠦⠀⠃⠀⠀⠀⣇⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠀⠀⠀⠀⠀⡆⠀⣆⠀⠀⠀⠀⣾⠁⠈⣧⠀⠀⠀⠀⠀⠀⠠
⠶⠶⠾⡖⠷⠀⢢⠀⠀⠀⠀⠰⠆⠀⠀⠀⠁⠀⠀⡤⡐⢄⠀⠀⠀⠀⣴⡀⠀⢢⠀⠀⠀⠀⠀⡠⠀⠀⠈⠉⠀⠠⠆
⠀⠁⠀⠖⠂⠐⠸⠀⠀⠀⡀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡂⠀⠀⠸⠑⠅⠊⠀⠀⠀⠠⢠⠀⠀⠠⠅⠀⠀⢠
⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠀⠀⠀⠃⠐⠀⠀⠀⠺⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠭⢗⡆⠀⠀⠀⡀⣆⠈⠉⠀⠀⠀⠠⠘⠁⠀⠁⠀⠀⠀⠀⠀⠁⣲⠄⠀⠀⠀⢠⡤⠲⣤⠂⠀⠀⠀⡰⠀⠒⡄⠀⠔⠀⣴
⠀⠀⡆⠀⠀⠀⡇⠀⠀⢲⠀⠀⠀⠀⡃⠀⠀⢠⠀⠀⠀⢸⡿⠄⠼⡦⠀⠀⠀⢺⣖⣀⣻⡇⠐⠒⠂⡔⠀⠀⠘⡂⠀⠀⢋
⠐⠀⠀⠀⠀⠀⠡⡀⢂⡄⠁⠀⠀⠀⠓⠈⠠⠎⠀⠀⠀⢨⠠⠀⢠⠂⠀⠀⠀⢧⠀⠄⠀⡄⠀⠀⠀⠘⠐⠓⠈
⠀⠠⠀⠀⠀⠀⠀⠳⠾⠗⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⠁⠀⢀⠀⠪⠄⠀⠀⠂⠀⠀⠀⠀⠄⠀⠄⠀⠀⢀⣀
⡄⠀⠀⠀⠀⠁⠢⠀⠀⠀⢠⠒⠴⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠘⡄⣤⠀⠀⠠⠂⢠⡄⠀⠀⣤⠜⠍⣭⣀
⠀⠀⠀⢱⠀⠀⠀⡆⠀⠘⠧⠀⠀⠀⠠⠀⠀⠀⠀⡄⢀⠀⡞⠀⠀⠀⠁⡀⠀⢀⠃⠀⠀⠀⣿⡆⠨⣦⠀⠀⠙⣷
⠀⠀⠀⠈⢦⢂⣸⡃⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⢀⠉⢨⠀⠀⠀⠀⠀⠐⠈⠈⠀⠀⠀⢠⠁⠀⢀⡌⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠂⠂⠀⣀⠀⢀⠀⠁⠠⡀⠀⢀⣀⠈⠘⠀⠈⠏⠀⠀⠀⠒
⠀⢰⠁⠀⢈⣤⢌⠀⠀⠀⠤⠀⠀⠀⡄⠀⠰⠶⣄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠘⢡⠀⠑⠀⠀⢰⡀⠀⠀⠀⠄
⠀⠀⢀⠘⠀⠀⠁⢇⢠⡀⠖⠀⠀⠀⢄⠀⠀⠀⡟⠀⠀⠀⢉⠀⡀⠀⡇⠀⠀⠈⠅⠀⠀⠘⠁⠀⠀⢰⠀⠀⠀⡞⠁⠀⠰
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠈⠃⠀⠘⠀⠀⠀⠀⢀⠀⠀⡂⠠⠀⠀⠀⢆⠀⢤

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠒⠒⠚⠛⠒⠒⢒⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⠿⠟⠁⡀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣦⣀⣀⠀⠙⡶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠉⠙⠛⠛⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠤⠀⠁⠐⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠹⣶⣶⡄⠀⠀⠀⠀⠀⠰⠅⠨⠴⢥⣀⣼⣴⣦⣥⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣈⣿⡧⢖⣩⠀⠀⠀⠀⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣻⠏⠉⠉⠻⣷⠀⠉⡒⡈⣭⠈⣰⢟⣩⣤⡉⠉⠻⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣿⣧⠀⠈⠻⡏⠙⢶⠀⢠⢶⣦⡀⠀⣁⠈⠰⣿⣻⢿⣿⣾⣧⠀⠀⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠘⣿⣆⠈⠂⠁⠀⣤⠀⠘⠜⠟⢃⠀⣰⡷⠻⢹⠛⣧⠹⠃⢻⣶⡀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⠻⢷⣄⣈⠀⠶⠈⣀⣿⠗⠀⠀⠋⣤⣤⣀⠀⠈⡔⠛⠢⠘⠛⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⢦⣉⠘⠈⣁⢿⡼⣇⣢⣿⠇⠘⡆⣠⡏⠀⠀⠈⠛⠻⣯⣥⡤⠀⠹⠶⠯⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠍⠈⠁⠀⢘⣷⣿⡿⢡⠀⢂⠳⠽⡇⠀⠀⠈⡀⠂⠀⠙⢻⣀⣀⠀⣤⢷⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢸⠀⠀⢰⡦⢄⢉⣗⡬⠃⠀⠀⠀⠀⠀⠙⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⡆⠀⠀⢻⠠⠞⠷⣟⢣⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠆⠻⡄⠀⠹⠰⣶⣤⡜⢯⣝⣧⣒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣄⣂⠀⠀⠀⠀⠙⣯⣿⣶⣿⣯⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⣹⢻⣿⣿⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢂⣟⢺⡏⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣡⠛⢸⡇⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢅⣿⣀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⣀⠀⠠⠀⠀⠰⠃⠀⠀⣀⡀⠤⣤⡴⣁⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⡠⠀⠀⠀⠈⢠⡴⠁⡄⠈⠉⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢤⠈⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢇⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⢆⠀⡅⠀⣿⠀⠠⠀⣼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⢣⡀⠀⠠⠀⠀⠀⠘⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠱⡄⠰⠀⡖⣦⡆⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣴⠄⢳⣄⡿⠻⣿⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢻⡏⣼⣇⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⠃⡿⣣⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣶⢾⣿⣶⡄⣄⡀⠀⠀⠀⠀⠀⣾⡍⠙⠊⠉⠛⢻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡁⣿⡹⢯⡜⠛⡛⢟⣶⡄⠀⠀⠀⣿⣬⡄⠀⠛⠛⢤⡅⠀⠀⠀⠀⠀⠀⠘⣷⣤⡶⠤⠄⠄⠀⠴⠂⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠿⣆⡿⠈⣏⣱⡌⢳⣼⢆⠟⠀⠀⠀⠀⣿⠈⠁⠀⠀⠶⢚⡇⠀⠀⠀⠀⠀⠀⠀⠈⣄⡀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⣯⠠⠾⠷⠖⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⠿⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡆⠀⠿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡯⠀⡠⣼⠍⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣟⣥⢤⣀
⠀⠀⠀⠀⠀⠀⠆⠰⠄⣡⠜⣷⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣶⡿⢻⠀⠀⠀⠀⠀⠀⣀⣿⢛⢉⡱⠞⢋⡟⡸⢿⣷⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠆⣿⡇⠘⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⡏⠀⠀⠀⠀⠀⠀⠹⡷⣽⠿⣤⣧⡾⠀⣧⢾⡿⠁
⠀⠀⠀⣤⠐⠒⠒⠒⠂⢤⠤⠀⠐⠒⠃⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠁⠠⠤⠤⠤⢀⠀⣀⡄⠀⠀⢤⡄⠈⠛⢳⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⠀⠀⠀⢄⠀⠀⠀⠻⢷⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡴⢂⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠀⠋⠀⠰⠦⠀⣸⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⠘⠟⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡷⢀⢠⣀⡞⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠠⠾⠤⣤⠖⠳⡾⣋⡙⠙⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣽⠙⠂⠀⠀⠘⠂⠀⠀⣀⢀⣠⠶⠶⠶⠞⠶⠶⠿⣄⡉⢶⣤⡴⠿⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢐⡀⣀⠀⠀⠀⠀⠉⠉⡁⠀⡀⠀⣂⣀⣤⠀⠈⠉⠁⠈⠛⠲⠶⠂⠰⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠆⠙⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠀⠀⠀⢀⡠⠚⣩⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢋⣡⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠓⢀⢐⡉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠵⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣴⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣒⣼⢦⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠳⠇⠿⠇⠟⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⣐⡤⠤⡂⠀⠀⠀⠀⠀⢀⠀⣀⡀⡀⣀
⠀⠀⠘⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢌⣐⠀⠀⠀⠁⣈⠀⠀⠀⠀⠰⠈⠀⠁⠀⠁⠀⠁⠐⠦⢀
⠀⠀⠀⠀⠢⡀⠀⠀⠀⠱⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠚⣻⠧⡀⠀⠀⣈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⢣⡌⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣯⠏⠁⡀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠁⠨⣯⣆⠹⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⡆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠹⣧⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠙⢿⣾⣆⢄⢀⠀⠠⠖⠂⠈⠀⠀⠀⠀⠰⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠈⠛⠣⣂⣀
⠀⠀⠀⠀⠀⠄⠐⠁⠁⠐⠆⡀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠛⢿⣷⡀⠀⠀⠀⠀⢠⠀⠠⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠤⣀⠀⠈⠉⡁⡀⣀⣹⠀⠀⠀⠰⠇⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠩⠈⡅⠱⠀⠀⠀⠀⠀⠀⠰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠀⠀⠀⠠⠠⠧⠚
⠀⠀⠀⠀⠀⣰⠤⠀⠀⠀⠀⠀⠀⢰⣰⡶⠄⠁
⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡈⠒⠄⢶⣦
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢄⣀⠀⠀⠀⠀⠀⠀⠀⢠⣬⡁⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠒⠾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⡀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢰⣶⣾⣿⣿⣿⣉⣀⠀⠀⠀⠀⠀⠀⢰⢾⣿⣿⠋⡗⠸⣶⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠘⣇⠀⢻⣠⣿⢺⣿⣿⠿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⣰⣿⢫⠞⡐⠓⣿⠉⣽⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣠⢖⠁⡔⢁⠀⢠⣠⣿⣶⣿⣿⠟⠋⠉⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣄⣆⢆⠘⣧⣬⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠰⡁⠠⢏⡉⣴⡀⣺⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⠻⠿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠐⠷⣤⣸⣿⣹⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⡀⠀⠀⠀⢠⠗⠒⠂⡤⠀⠀⠀⠀⠀⠀⠀⡀⣠⣐⠐⠀⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠹⠃
⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⡄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢠⣾⣹⣹⣿⣹⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⣠⡶⠿⢶⣄⡀⠀⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⡀
⠀⠀⣴⣾⣿⡳⣮⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠐⣾⣿⢿⣽⡷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣭⣯⣽⠇
⠀⢈⣯⡶⠻⢾⣏⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⡠⢔⢲⣶⣔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⣀⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠃⠉⠉⠉⠁⠀⠄
⠀⠀⠀⠚⢶⡗⡀⠀⠙⢤⠶⠋⠄⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀
⠀⠀⠈⠁⠤⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠁
⠀⢀⣤⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠔⠀⠀⢠⣾⣿⣹⣏⣿⣳⡆
⠀⠘⠻⠿⠟⠛⠛⠋⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡨⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⣰⣯⣽⣦⠀⠀⠀⠀⣸⡏⠀⣶⣖⣒⣶⣖⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⡀⠀⡠⠤⠤⠄
⠀⢰⡟⠉⠁⢹⡇⠀⠁⠀⣿⠃⠀⠈⢭⠍⣩⠉⡭⡄⢀⡄⢠⡄⡀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠔⠋⠀⢀⠀⠁
⠀⠀⠑⢀⠀⢀⠀⠀⠀⢸⡿⠀⠀⠠⠎⠞⠙⠐⠉⠐⠉⠁⠚⠈⠃⠀⠀⠀⠘⠋⠀⠀⠀⠄⠐⠀⠚⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠛⢀⣀⠘⠀⠀⠀⣿⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠘⡀
⠀⠀⡀⠠⠄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠂
⠀⠀⠰⠂⢀⡀⠀⣼⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣶⡶⣶⣶⣶⢶⢶⣶⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⢄⡁⠠⠴⢋⣁⣠⣴⣾⣿⠀⠒⠒⣒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠠⠶⠿⠿⠿⠻⠟⣷⢀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠁⡄⠂⡀⢘⠃⠌⠁⠀⠀⠀⠉⢻⣿⣶⣶⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡯⠎
⠀⠀⠀⠀⠀⠀⢀⠾⠀⣧⣄⣄⣤⠀⠀⢅⢀⣀⣠⣼⣿⣿⡿⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣟⡧⠀⠀⣰
⠀⠀⠀⠀⠀⠀⣘⣀⣀⣛⣛⣛⣁⣀⣀⣀⣀⣉⣉⣉⣉⠁⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠒⠈⠉⠉⠉⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣃⡀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠁⠀⠀⠀⠀⣀⣴⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠌⡀
⠀⠀⠀⢀⢀⢀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠈⢠⡆⢵⢫⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⣀⠀⠄⠠⠄
⠀⠀⠀⡥⢈⢷⡘⣇⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡇⠁⠀⠀⠀⠠⠈⠀⠀⢀
⠀⠀⠀⠘⢧⣰⣦⣲⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠷⠀⠀⠀⠀⠀⠚⢀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠
⠀⠀⠀⠀⠀⢡⣿⠈⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣌⣨⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠂⠀⡸⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣄⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠓⠒⠓⠺⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣽⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡂⠀⠀⠀⡀⢃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠤⠤⠧⠤⠤⠤⠄⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⢠⠿⣻⠷⠶⠶⠶⠿⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠠⣀⠸⠆⠃⠀⠀⠀⢠⠟⣲⠋⠀⠀⠀⠀⠀⠳⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⠒⠂⠁⠀⠀⠀⠀⠀⣠⣏⣠⡏⠀⠀⠀⠀⠀⠀⢀⣇⣜⣄⠀⠀⠀⠀⠀⠖⢦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⢂
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣩⣤⣾⣟⠃⠂⠀⠀⠀⠀⠀⠀⠀⢠⢠⠄⠤⣶⣿⣿⠇⠀⠀⡀⣷⣿⠀⠀⠀⠀⠀⠀⠠⢰⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠟⡉⠀⠀⠀⠀⡀⢀⣀⣷⡙⠉⡸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⠀⢠⢁⡈⣁⣷⠀⠀⠀⠀⠀⠀⠓⢂⡄
⠀⠀⠀⠀⢀⢀⣄⣄⣀⡔⠐⠁⠀⠀⠀⠀⠀⡠⠋⢙⣥⣤⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢈⣂⠀⠀⠀⠀⡏⠀⠀⢋⣼⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⢠⡟⠃⠁⢠⠟⠹⣧⢱⠠⡤⠀⠀⠊⠀⣰⠟⣧⠀⠁⠈⢳⡄⠀⠀⠀⠈⠀⠀⢉⡍⢉⣈⡛⠀⠀⠀⠀⠃⠀⠆⠛⠛⡃⠀⠀⠀⠈⢀
⠀⠀⠀⡎⠀⠀⣴⣷⣄⣀⣿⠀⣯⣵⠂⠀⠀⢘⡇⠀⠘⢧⡇⠀⠀⡗⠀⠀⠀⠀⠂⠀⢘⣀⣨⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢶⣶⡟
⠀⠀⠀⢧⠀⠀⠨⠀⠀⢠⠅⠀⣙⠉⠀⠀⠀⠀⢧⡀⠀⠈⠑⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠑⠦⠤⠤⠖⠃⠀⠀⠛⠃⠀⠀⠀⠀⠀⠙⠶⠦⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠭⠭⠽⠶⠃⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠠⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢠⠄⠴⠄⢠⠠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠠⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⡏⢉⡀⢀⢀⠀⡀⡀⢀⡀⢀⠀⢀⣀⡀⡀⡀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡄⠀⣀⡷⣏⢸⢸⢸⢧⡁⡆⡄⠀⢾⠐⠛⢣⣼⡇⠛⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⠀⠁⢀⣉⡁⠈⠉⠘⠉⠀⠉⠁⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣧⡀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⠌⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈
⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠉⠀⠘⠀⢀⡀
⠀⠀⠋⠀⠀⠘⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⡠⠤⠄⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡜⠁⠀⣀⠀⠙⣆⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡇⠀⢘⠿⡄⠀⣹⠀⠀⠒
⠀⠠⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠤⠀⠀⠘⣤⣂⢀⣠⡜⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⢠⠃⠈⠈⠀⠹⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠆⠀⠆⠀⠲⠑⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣤⣬⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢈⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠚⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⢸⣿⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠁⣹⡆⠉⠈⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣷⣷⣶⣾⣓⣲⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠒⢀⡀⠀⠀⡿⣿⠷⡇⠀⠀⡀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢠⠖⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⣶⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⡀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣷⡘⢿⡡⠂⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⣆⢸⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣉⣙⡙⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠆⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⡛⣿⣋⣿⣿⣴⣿⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢶⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡐⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠁⠀⠀⡀⠀⡟⡉⠐⢘⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⠆⠀⠀⣦⠦⠿⢀⠁⢨⡉⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠿⠇⠀⠀⠁⠀⡉⠘⠀⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣼⡿⠛⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⣴⣶⣶⣶⣶⣶⣶⣾⣷⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢟⢱⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠠⠀⠀⠀⠂⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙
⠀⠀⠀⠀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡄⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⢆⠀⠄⠀⠀⣀
⠀⠂⡀⡀⠀⠀⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠿⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠑⠲⠒⠂⠉
⠀⠀⠀⠉⠀⠀⠀⠀⠘⠿⠿⠿⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠠⠑
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣀⡀⠐⡀⣰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢚⠭⠉⠑⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠒⠀⢀⡀⠀⠀⠀⡀⠤⠀⠀⠀⢀⠐⠁⠀⡀⠀⠀⠀⠈⠈⠐⠖⠁⠐⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠱⠆⡉⠀⠉⠐⠀⠀⠀⠀⠀⠸⠀⡠⠈⠂⠀⠐⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⣤⠐⠒⠢⠤⣀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠀⠳⣄⠀⠒⢀⡠⢞⠐⠈⠀⠀⠉⠈⠲⡕⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⣦⣄⣀
⠀⠀⠀⠀⠈⠛⠒⠀⠈⠁⠀⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⢀⡘⠇⠤⣬⢉⠋⣩⢀⠀⠀⡠⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠳⣄⠀⠀⡔⣿⣹⢳⣙⣷⢺⡤⡍⢸⡀⠀⠀⠀⠀⠤⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠧⣀⣋⠲⢿⢯⠽⣊⠷⣟⣺⢟⡆⠀⡗⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠡⡆⠙⡝⠲⣶⡉⣷⣿⣉⣟⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢼⡇⢈⡽⠠⠼⠧⣩⠈⠼⠀⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙
⢀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢀⡠⠂⡑⠀⠀⠀⠀⠈⠨⠛⠃⠳⠄⠤⠀⠤⠰⠇⠀⠀⠀⠀⠀⣠⡤⠄
⣅⣀⠀⠀⠻⠿⣿⣶⡤⠀⠙⠲⣄⠀⠀⠀⠠⡀⠀⠀⢄⠀⡈⠁⠀⣅⠀⠀⠀⠀⠀⢰⠈⠄⠀⠰⠠⠀⢀⠎⠀⡠⠀⠀⠀⢨⣀⠀⠀⢴⣦⡄⠳⠆⠀⠉⠳
⣿⣿⣿⣶⣦⣤⣀⣀⣀⣠⣤⣴⡿⠀⠀⠀⠀⠈⠢⣀⠀⠉⠘⣦⠀⠀⠓⠦⠦⠴⠴⠃⠴⠆⠀⠁⠠⠔⠁⡠⠎⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣉⣁⣀⣀⣤⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠁⠀⠉⠁⠒⣂⠁⠂⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠤⣤⣤⡤⠤⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿
⣶⣶⣶⡶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣀⣀⣀⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢈⣙⠻⢦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣶⣟⣉⣈⣭⣿⣿⣿⣿⣯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠟⠉⢭⣽⣿⣿⣿⣿⣿⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠃⠀⠀⠐⣺⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣯⠁⠀⠀⢤⣼⣿⣿⣿⣿⡭⠪⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⢒⠺⢿⣿⣿⡋⠐⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⡀⣸⣿⣿⠿⡉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠈⣙⣿⡿⠓⠚⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣀⣂⣈⡉⠉⠁⠀⠀⢴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣴⣿⡿⠇⣠⠄⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⢀⣤⡾⠃⠀⣠⣴⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣀⣤⣶⡿⠟⣡⣶⣿⣿⠏⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⣾⡿⠛⢉⣐⣿⣿⣿⠿⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠚⠉⠀⠀⢀⣤⠞⠋⠀⣀⣼⣿⣿⣿⣣⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠖⠒⠋⠉⠀⠀⠀⢀⣠⣤⡤⠈⠉⠀⠠⢀⣨⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣤⣾⡿⠋⠉⣀⣠⣤⣶⣶⣾⣿⣿⣿⣟⢛⣋⣀⣤⣶⣾⡿⠟⠋⠁
⠀⠀⠀⠰⣿⣏⠠⠚⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡄⠀⠀⠠⠆⠀⡀⠄⠀⡨⠂⠀⠀⠰⣯⣯⣿⣿⣿⣟⣿⡶⠀⠀⠔⠉⠁⠀⠀⣠⠀⠀⠤⠀⠀⠆⠀⠊⠱
⠀⠀⠁⠀⠀⠀⠀⠀⠀⣨⣤⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅⠀⠀⠄⠀⠤⠀⠈⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣶⢶⣶⣖⣶
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠁⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠀⢬⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠠⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁⠀⠀⠀⠀⢠⣿⠿⠿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠡⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⣠⢶⠶⣶⣶⡄⢱⡀⠀⠀⠀⠀⠀⠻⠇⠆⠀⠰⠀⠿⠂⠠⢠⡄⠀⠀⠀⢀⠀⠂⠈
⠀⠀⠛⠛⠛⠛⠋⠁⢈⣧⣤⢤⡄⠀⢀⠀⠀⢀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⢀⡀⠀⢀⠀⠐⠃⠞⠛⠉⠀⠀⠀⢀⡀⠀⠀⠂⠀⢠⡀⠐⠗⠀⠀⣾⣿⣿⣿⡿⠲⢦⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⡛⠛⠛⠋
⠀⠀⠀⠀⠀⢠⣀⣆⣠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠶⠀⣀⠀⠀⠀⠀⢰⠟⡋⠙⡛⢦⠀⠀⢠⡀⣰⠄
⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⡀⠀⠈⠀⠀⠀⠀⣿⣦⣁⣀⣥⣾⠇⠀⠈⣦⠈
⠀⠀⠠⡄⢀⠄⠀⠁⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⡀⠀⠘⢿⣿⣿⡿⠋
⠀⠒⠀⡀⠁⠀⠈⠀⠀⠀⠀⠀⢼⣿⣢⣏⣈⣿⣴⣯⣌⣿⣬⣼⡇⠀⠂⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⡀⢠⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⡉⠉⠀⠀⠄⠀⠀⠁⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠉⠉⠉⠁⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠛⠷⣶⠆⠈
⠀⠀⣶⣾⣛⣿⣛⣻⣲⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⢛⠓⠀⠀⣤⡤⠀⠀⠀⠀⢀⣀⠀⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⠀⢀⣀⣤⣤⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣒⠚⢛⣿⠋⣠⠶⠛⢻⣿⣿⣿⡟⣿⣿⡿⣿⠛⠻⢯⣝⣲⡜⢧⣀⣀⣤⠴⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣴⠶⠶⠯⣭⣉⣁⣀⣼⣤⣴⠟⣹⣿⢋⡜⠁⢻⣧⠸⠦⢶⣒⡚⠻⢿⠶⠿⢿⣷⡛⠛⢲⡄⢹⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣋⣽⠆⠹⣄⣠⣶⠿⢿⣟⡋⠉⠀⡾⠀⣿⣇⣘⢧⣤⣈⣻⣷⣞⠋⢉⡿⢠⣞⣁⣀⣀⣤⣙⢷⣼⠃⣾⣁⡈⠉⠙⢳⡄
⠀⠀⠀⠀⢠⣶⠛⣿⣩⡤⠤⠤⣤⡾⠋⢁⣹⣄⠀⢬⣭⣟⣋⣁⡼⢻⠏⠉⠉⣻⡮⢉⣿⠙⢷⣿⣀⣤⠽⠿⠿⢷⡆⠉⣧⠙⢷⡒⢭⢙⣧⡴⢿⡇
⠀⠀⠀⠀⢸⡟⠶⣿⣿⣄⣠⠞⢉⡴⢾⣋⠁⠈⠳⣌⠳⣄⢀⡼⢁⡿⠖⠛⠋⠱⣾⣯⣽⣆⠀⠙⢯⡀⠀⣀⡴⢛⡴⠚⠁⠀⣨⡽⠟⠋⣁⠀⣾
⠀⠀⠀⠀⠀⣷⠀⠈⠙⠻⢧⣄⣸⡇⢀⣬⣭⣓⣒⠛⠂⣸⡟⠁⠈⢷⡶⠖⣒⣲⡶⠆⣠⡿⠀⠀⠈⣷⠟⢡⣞⣉⣠⡴⠖⠋⠁⢀⡄⢠⡇⣸⠇
⠀⠀⠀⠀⠀⢸⡆⠀⣤⠀⠀⢬⣍⠛⠿⢧⣀⠀⠉⣩⡿⠋⠀⠀⠀⠘⣿⡋⠁⠀⣶⡛⢹⡇⠀⣀⣀⣿⡷⠾⠛⢋⣡⠄⠀⠀⠀⣼⢃⡾⢠⠏
⠀⠀⠀⠀⠀⠀⢿⡀⠈⢷⡀⠀⠈⠙⠶⣤⣉⠙⠻⠿⢤⣤⣤⣄⣀⣀⣈⣉⣭⣿⠿⠿⠛⠛⠋⣉⣁⣤⠤⠖⠚⠉⠀⠀⠀⣀⡼⣡⠞⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠈⢳⡀⠻⣄⠀⠀⠉⠛⠳⠶⠶⠶⠄⠀⠀⠀⡅⠁⠠⠤⠴⠶⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⡴⠞⣩⡾⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠻⣄⡈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣌⡙⠶⣌⡙⠓⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢮⣝⣛⠶⠶⠦⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠤⣤⣤⣤⣬⣤⡤⠶⠶⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣰⣿⠁⣿⠀⣀⣤⣄⠀⣠⣤⡀⠀⣠⣤⡀⣰⡟⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢻⣿⣰⠇⣼⣏⣸⣿⠸⣿⣾⣁⣾⣁⣿⡇⣿⡑⡿⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠉⠋⠈⠉⠸⠷⠛⠀⠙⠁⠈⠁⠉⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆⠀⠀⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠐⢸⡄⠘⡴⢁⠔⠋⠉⠁⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠄⠘⠲⠀⠀⠀⠀⠀⠀⠀⠠⢀⠊⢀⠔⠁⠀⠀⠀⢠⡀⠀⠀⠃⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢠⠂⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⡇⠇⠀⠀⠀⠀⠀⠀⡃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠒⠐⠎⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠄⠀⠀⠀⠀⠀⠀⠋⠀⠄⠁⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠁⠄⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠠⠀⠒⠀⠤⡀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢳⡈⢀⠘⠀⠀⠀⠀⠀⠀⣧⡇⡆⠀⠀⠀⠀⠀⢠⡘⣿⡀
⠀⠀⡔⠁⠀⠀⠀⠒⠒⠒⣲⣆⠀⠀⠀⠀⠀⠙⢆⠈⠆⠈⣉⡂⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠀⠀⠏⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢀⡯⡑⠤⡀⠀⠀⠀⠘⡆⠸⠄⠀⠙⠀⠀⠀⠐⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠘⡼⡇
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠊⡀⠠⠀⠑⡀⠀⠀⠀⠡⠀⠰⠃⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡼⣆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡖⠀⠀⡼⠁⢠⡇⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⡀
⠀⠀⠀⠀⡜⠀⠀⣼⠁⠀⢸⠁⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠁⠐⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠆⠀⠃⠀⢰⡏⠀⠀⠸⠀⠀⢸⠀⠀⠀⠠⠂⠀⠠⡀⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡆⠀⠀⢸⠀⠀⡰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠇⠀⠀⠀⠀⠀⢀⠺⣍⣼⠢⡀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸⠀⠀⠀⠀⡀⢴⡀⠀⠙⠢⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡆⠈⠁⣢⠀⠀⠀⠀⢆⠿⣟⡷⢿⣄⢣
⠀⠀⠀⠀⠀⠀⠈⢀⠄⣊⣠⠄⠀⠀⣷⡀⠈⠳⣄⠀⠈⢢⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⡧⠀⠄⠝⠀⠀⠀⠀⠀⠀⠙⠁⠘⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠈⠀⡸⠁⠀⠐⠀⠀⣌⢦⡀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣷⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡄⠻⠄⠀⡆⠀⠀⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⡌⠉⠠⣆⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠹⡀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠀⡰⠃⠀⠀⠀⠀⠀⠱⠀⠀⠍⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠐⡀⠀⠀⠃⠀⡀⠈⡀⠀⠀⠀⠀⠀⢐⢛⠀⣰⠀⠀⢆⠀⠀⠀⠀⠀⢰⠈⠁⡆⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠡⠔⠙⠀⠀⠀⠀⠐⠀⠀⠀⠘⡶⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠐⠂⠤⠤⠤⣀⣀⣀⣀⣀⡀⢠⠤⠤⢤⠤⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⠿⠿⢦⡀⠀⠰⠄⠀⠀⠀⣀⣤⣴⣤⣄⡘⠀⠸⠵
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⡟⠿⢣⠀⠀⡬⠿⢣⠀⠂⠀⠤⠶⠿⡿⠿⢿⠿⠿⠿⠷⠦⠄
⠀⠀⠉⠀⠀⢀⡀⣀⣤⣤⣤⣶⣦⣄⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣇⠠⠄⠀⠀⠠⠀⣸⠀⣀⣀⣀⣀⣀⡀⠀⢰
⠀⠀⠀⠀⠀⠸⠍⠿⠿⠿⠿⢿⣿⠒⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⢛⠙⠋⠟⣻⠇⠀⣿⡍⣹⣿⢹⡿⠀⢰⠀⢸⣗⣶⣶⡟
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⠠⠠⠀⣠⣴⠆⠈⠉⠀⢠⣀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣤⠀⠀⠀⠀⠙⢿⣷⣷⡾⠃⠀⠀⣿⡛⢻⣿⢻⣿⠀⢨⠀⢸⡇⠀⢈⡇
⠀⠀⠀⠀⠀⠘⠛⠿⠿⠇⠀⠠⠠⠀⠘⠷⠄⢠⠀⠀⠀⠀⠰⠀⠦⢀⠹⣷⢆⡰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠿⠷⠾⠿⠼⠿⠀⠈⠀⢠⣿⣧⣿⡇
⠀⠀⠀⠀⠀⢀⣀⢠⣤⠀⠠⠀⠀⣠⡴⠀⠀⢨⠀⠉⠀⠀⣀⠀⠀⠋⠀⢉⡈⠃⠀⠀⢠⠶⡆⠀⡟⡻⡇⢠⡟⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠻⠛⠛⡛
⠀⠀⠀⠀⠀⠘⠛⠻⠟⠀⠠⠀⠂⠘⠷⠀⠀⢘⠀⠁⠀⠀⢿⣷⠀⢠⣾⣿⣿⣷⡀⠀⠈⠛⠁⠀⣴⣷⡄⠀⣴⣷⡄⠀⣤⣦⣀⠀⢴⣶⣦⡀⠀⢠⣤⣠⣤⡤
⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⢠⡴⠀⠀⠐⠸⠀⠀⠀⠀⠛⠁⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⢁⡀⠴⠶⢏⠋⠀⠉⢛⣛⠛⠀⠻⠿⠿⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⢻⣿⣖⣂⠔⠑⣷⠿⣿⡉⠁⠀⠀⠀⠀⡤
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠉⠉⣩⡍⠉⠉⣩⡅⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠦⢦⡀⠀⠛⠛⠀⢀⣾⣷⡀
⠀⠀⢰⠏⠉⠙⣷⠀⠀⠀⣤⣤⠿⠋⠀⠀⠀⠘⠃⠁⠀⠀⠀⢠⡄⠀⠀⠙⠃⠀⠀⢤⡄⠀⠀⠀⠀⠀⣠⣄⣠⣤⡄⠀⠀⢀⡀⣾⣆⣀⠀⠀⠀⠽⠿⣿⣯⣄
⠀⠀⠘⣀⠀⢀⡘⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⡇⠀⢠⣤⣾⣾⣿⣿⣿⡿⠃⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠙⠀⠛⠛⠉
⠀⠀⣾⡿⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠸⣨⠆⢸⡇⠀⠀⢀⡄⠀⠀⢸⣇⠀⡈⠙⠛⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⡀
⠀⠀⣿⣧⣾⣦⣿⡄⠀⠀⠀⣠⣼⣿⣿⣿⣿⣾⣿⣷⡄⠀⠀⢸⣇⣴⣿⣿⣿⣾⣧⣾⣟⣿⣿⣦⡀⠀⠑⠀⢸⣿⡶⣀⣀⡀⠀⠀⠀⠀⣀⣤⣶⣄⣀
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⠛⠿⠿⣿⠿⢿⣿⣿⣿⠿⠛⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣡⣔⣭⡁⠀⢠⣤⡘⢷⣮⣵⣭⣯⣷⠀⣤⣄
⠀⠀⠉⠉⠉⠉⢩⣥⣄⣠⣤⣄⣀⣤⣤⡄⠀⠀⡠⠀⠀⠀⠉⠀⠀⢉⣉⣩⣍⣉⠉⠈⠈⢉⣉⠉⠉⢉⣡⠀⠰⠟⢨⣛⠁⠀⠨⠿⢦⣤⠶⠶⠶⠶⢦⣤⠾⠧
⠀⠀⢦⣼⣦⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠻⠿⢴⣤⠀⠒⠀⣠⠞⠉⢠⣾⡦⠈⠙⢦⠀⠘⠼⠃⠀⢺⣿⡀⠀⣠⠔⠉⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠉⣁⣀⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣶⣶⢟⣠⣄⠐⠃⠀⠀⣠⣼⣤⡀⠀⠀⠃⠀⠀⠈⠻⣶⣽⣿⠇⠀⠀⠀⠀⠀⠀⠐⠄⡑⠀⢀⣀⡀
⠀⠀⢠⠾⣿⣿⣿⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⡄⠀⠸⠇⠀⠀⡠⢚⡳⣶⠼⠧⡀
⠀⠀⣄⠛⢲⣤⡖⡟⣤⠀⠀⠀⠛⠟⠿⠋⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⡀⠀⢀⠂⠀⠀⠂⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣦⣤⣤⠄⠀⣷⣶⣶⣾⣶⣶⡆⠐⠿⠂
⠀⠀⠡⠟⣩⣿⣍⠷⠁⠀⠀⠀⢀⣠⣦⣀⠀⠀⠈⠙⠛⠿⠿⠟⠓⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠁⠀⠀⠀⠈⣿⣟⣿⣿⣻⣻⠁⠀⠀⠈⠻⣿⣿⡿⠏⢀
⠀⠀⠀⠺⣿⠿⣿⠗⠀⠀⠀⠀⠈⣿⢿⡏⠀⡶⠆⠀⠶⡄⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣴⣦⠄⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣄⠀⡀⢀⣄⠸⢀⡄
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠖⠂⠀⠀⠀⠀⠀⣷⣾⣿⣶⡇⣻⡇⠀⠀⠀⠀⠂⢀⢀⡄⠀⠀⠀⡉⠙⠀⠠⣤⣿⣷⣿⣿⣾⣿⣤⠄⠀⢤⡙⠄⠇⠰⠞⣿⠛⠦
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠁⢰⠀⠀⠀⢀⡿⢿⡿⠿⣥⣿⡇⠀⠀⠀⠀⠀⠎⠳⠀⠀⠁⠱⠀⠀⠀⠀⠈⣿⣟⣿⣿⣻⣿⠁⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⢸⠠⠀⠀⣼⣷⡄⠁⣠⣿⡏⠀⠀⠂⠹⡂⠈⠀⠀⠀⠀⠀⠀⡤⢤⠀⠘⠻⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⣴⣶⣶⣶⡶⣦⠀⠀⢘⠀⢸⠈⠥⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⡿⢶⡀⠀⠀⠀⢀⡀⠙⠚⠀⢠⣠⣿⣷⣿⣿⣾⣿⣀⡀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠈⢻⣿⣳⡿⠋⠀⠀⢰⠀⢸⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠁⠀⠹⣶⡾⠧⣶⡾⠁⠀⠈⣿⣟⣿⣿⣻⣿⠁⠀⠀⠀⠀⢸⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⠛⠟⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡔⠀⣼⣃⠀⢀⠈⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠛⢅⣺⣤⣴⡿⢿⣿⠭⠭⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⣄⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡏⠀⢠⣤⣤⣄⠀⠑⢆⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠋⠉⠙⠳⣤⡴⠄⣇⠀⠈⣿⣿⣿⣷⣆⠀⠑⠆⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢰⡈⠛⢿⣷⠀⠀⠙⠙⠛⢿⣿⣷⣄⠀⠉⠠⣀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⢘⣇⠸⠁⠀⠀⠀⠀⠀⠀⢻⣿⠿⣳⣤⡀⠈⠙⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡘⠎⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠈⠈⠻⣿⣷⣤⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⣀⣀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣄⡀⠉⠑⠻⣷⠀⠀⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣴⣾⣿⣿⣿⣶⠾⣿⣽⣿⣿⣿⣿⣟⣿⣿⣷⣤⣿⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠛⠿⠿⢿⣿⣦⡀⠀⠀⠸⠙⣿⣿⣿⣾⣽⡿⠏⠀⣴⣿⣇⠀⠀⢀⠆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠄⠀⢀⡀⠉⠙⠷⣦⣴⣄⣫⣿⣿⣿⣿⠀⠀⠞⠁⠉⠉⠉⠀⠁⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠉⠙⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢄⠀⠀⠀⢣⠐⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠀⠀⠈⡆⢁⠰⠀⠀⠀⣀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠙⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢂⠀⠀⠈⠀⠀⡠⠊⠈⢗⡴⠊⠁
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠡⡀⠀⢀⡸⢁⢀⢀⠎⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⣼⢀⢈⠁⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡧⢤⣏⡉⢋⢵⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠘⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⡠⠄⠢⠐
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠠⠀⠀⠊⠐⠂⠀⠈⡡
⠀⠀⠀⠀⣀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠨⣀⠈⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠈⠀⠐⠄⠀⠀⠐⡄⠁⠀⠀⣀⣀⣀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⡈⠀⠰⠁⡠⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡁⠀⠀⠘⡀⠀⠀⠁⠈⠂⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠀⠀⠈⠀⢀⠈⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⢀⠤⠊⠀⠀⢳⡂⠁⠠⢀⠄⣧⠄⠐⣤⠜⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣧⣞⣚⣯⠹⠩⠽⠧⣈⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⣤⠀⠀⠀⠠⣄⣀⡤⠠⠶⢀⡀⠿⠭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠐⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡄⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠉⠐⠀⠠⠀⢳
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣭⣭⣧⣿⣨⣴⣷⣤⣼⣸⣌⣍⣗⣯⣿⣿⠀⠀⠀⠀⠐⠄⣀⣀⠀⠀⠈⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠠
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠄⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣇⣀⣱⡄⠄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠀⠈⠀⠧⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠄⠀⡞⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢈⢿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⠻⠟⠇⢰⡏⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⠀⢨⢁⢹⡘⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠮⡀
⠀⠀⠀⠀⠀⠀⠔⡐⡈⠂⠡⢘⡀⠘⡃⡠⠐⠈⠘⢯⠂⠀⠀⢠⡄⠀⠀⠀⢰⣀⠀⣀⣀⡩⢦⢀⡔
⠀⠀⠀⠀⠀⠀⠸⡷⠋⢀⡀⠀⠆⠈⢽⡄⠂⢁⠀⠎⡀⡸⣗⠠⣌⣴⡁⠑⡦⠈⠈⠍⠽⠓⡄⣩
⠀⠀⠀⠀⢀⣀⣄⠑⠐⣌⠉⡆⠌⢠⠈⠣⠄⠐⠊⠠⢘⠂⠀⠀⠒⠈⣘⣼⢦⠀⠀⠀⢀⠸⡯⠃
⠀⠀⠀⠀⠀⠈⣉⣳⠀⢧⠀⠃⠜⢇⡀⡀⢀⠀⠢⠔⡀⠸⠃⠈⠀⠀⢈⡵⢮⡅⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠈⠱⢟⠉⠀⠙⠈⠀⡠⣦⠅⠀⣍⡀⢴⡁⠡⢋⣄⠀⠚⡁⠀⡗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⠱⢣⠂⠀⢻⠀⢜⡠⢸⡖⠜⡟⣀⣖⡽⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⠌⠀⣰⡴⠠⢰⠆⠠⠀⢛⢴⠠⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠇⠌⢴⢯⠀⠒⠐⠠⠀⡁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡊⠁⠁⣳⣥⠆⠐⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢨⣜⠀⢾⣿⢤⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣐⢉⡶⠜⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡻⠩⠁⡛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣮⣷⣶⣼⣧⣾⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠈⠑⢤⡀⠀⠀⠀⣀⠔⠈⣀⠔⠊
⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠔⠀⠀⠀⠀⠀⣇⡠⠔⠉⣀⠔⠊
⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⡠⠔⠁⡠⠔⠉⠑⠖⠊
⡠⠂⠀⠀⠠⠶⠀⠀⠀⡠⠔⠉⢀⠔⠊
⡇⠑⠤⡀⠀⠀⠀⠐⠉⢀⠤⠊⠁
⠑⣄⠀⠈⡆⠀⢀⠤⠊⠁
⣤⣬⣵⣶⣶⣪⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡊⢤⡀⠀⠃
⠀⠀⠀⠀⢰⠈⠙⠡⠾⠪⣿⡀⠰⣄⣀
⠀⠀⠀⠀⠀⣁⣀⣀⣀⠀⢙⠁⠴⠮⠙⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠠⡊⠉⠀⠀⠀⠉⠉⠀⠀⠀⢀⡄⠈⠚⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣲⡏⠿⣞⢾⠺⣥⣤
⠀⠀⠀⠀⠀⠉⠉⠉⠲⠶⣷⣀⠀⠀⠠⡀⠀⠀⡙⠋⣦⣀⠀⠀⠀⠀⠄⣾⠝⡩⢑⡴⢚⢅⡼⣡⠃⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠈⡀⠀⠚⠒⢴⠛⠙⠳⡄⠀⠀⠐⢭⠮⣷⡯⣴⣧⡾⣁⣻⡼⢳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢓⣠⣰⢼⢬⠀⠀⠀⠋⠀⠀⠀⠐⢄⣀⠀⠀⠀⠀⠀⢀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⣄⢄⡀⠀⠐⠀⠀⠀⠀⠈⠀⠓⠦⠶⠦⠖⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠚

⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠤
⠀⣌⠁⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠁⠀⠀⠀⠀⠀⠈⢧⠈⠈⠠⠄⠀⣶⡘⠉⠀⠀⡀⡄⢀⣀⡤⠤⠾⣿⡶⢶⣦⠤⠄⡀⢆⠀⠀⠀⠀⢀⢀⠀⡄
⠀⠈⠀⠠⠲⠆⠀⢠⠴⣶⣷⠆⠀⠀⠟⠉⠀⣒⣤⣰⣤⣤⣶⣏⣢⡚⠀⠤⠄⠁⠁⠁⠈⠀⠀⠀⠀⠘⠃⠠⢤⣇⣤⣤⣤⣶⣟⡟⣹⠀⡀⠀⠀⠒⠚⠲⠢⠆⣀
⠀⢠⣶⠖⠞⢀⣰⡟⣀⢌⠴⠉⠀⠀⠀⠀⠆⠛⠿⠋⢿⡟⠁⠀⠙⠥⠀⠀⢠⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠉⠉⠓⢧⢈⣄⢀⠀⠀⠔⠒⠀⢰⠄⠈
⠀⠀⡠⠙⠊⠀⠉⠑⢲⡘⠲⠏⠁⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⢸⣅⣀⣒⠒⠀⠐⣂⣓⣻⡄⠂⠀⠀⠀⢀⠀⠀⠀⢀⣹⡇⢬⠠⡄⠀⠀⠀⠰⠈⢁
⠀⠀⢵⠆⠀⠀⠀⠿⢡⣄⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⡠⠤⣤⢤⠚⡻⠜⣿⢻⠟⠛⣓⢻⡛⢉⡿⠩⡍⠑⣦⠊⠁⠀⠀⠀⠀⢉⡠⠾⠀⢩⣤⠖⠛⠓⢆⠈
⠀⠦⠸⠷⢀⠀⠀⠙⠌⠁⣀⣀⣀⣤⣀⣀⠃⠀⠉⠉⠈⠉⣿⡆⠇⡄⠀⣥⢸⡀⢠⠐⡇⠛⠓⣀⣘⣷⠀⢈⠆⠁⠀⠀⠀⠀⠀⡤⣀⡀⢡⠈⠉⠋⠀⡟⠀⠈
⠀⠀⠀⣰⠔⠃⠀⠀⠀⠀⢈⡭⢽⣿⣿⣿⡇⠀⠀⠀⠀⠀⣷⣶⠀⣠⡄⢁⣀⠙⢁⣄⠀⠀⣦⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡉⠀⠐⣠⠞⠳⣄⢀⡀
⠀⠀⠈⠉⢙⠃⠀⠀⠀⠀⣽⠦⠰⢿⣉⣡⡇⠀⠈⠁⠀⠀⡏⢸⠀⢰⡄⠸⠿⠀⠘⠿⠀⠀⠻⠃⣸⠃⢀⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡙⠃⠀⢐⡀⣉⡄
⠀⠀⠀⢔⡄⠉⠀⠀⠀⠀⢤⡀⠀⠄⠈⠁⠈⠠⣤⢄⠤⢚⡗⢈⣤⣤⠗⠤⡤⠞⠢⠶⠺⠶⠖⠚⠁⠤⠉⠀⠀⠀⠋⢠⠄⠀⠁⡀⠀⠀⠈⠻⠇⠀⠐⠤⣀⠀⠁
⠀⠀⢀⣾⣿⡅⠀⠀⠀⠀⠰⠁⠀⢀⡀⠀⠀⠀⠘⢬⠢⠁⠀⠠⠀⠀⡰⠈⠣⡀⠠⣀⣁⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣩⡤⠀⠉⠁⠠⣀⡀⠀⣈⢄⠀⠀⠈⢀⠉
⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀⠊⠈⠉⠒⠦⢇⠀⠀⠀⠁⠀⠉⠀⠐⢏⡿⠧⠛⠿⠷⢶⣶⣿⠇⠀⠀⠀⠀⣿⡇⢂⠠⠶⣇⠙⠌⠹⣿⠈⠃⡀⡀⠸⡄
⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⠀⠉⢠⡀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡀⡀⠀⠀⠙⠁⠀⠀⠀⠀⢰⣿⣁⣴⣤⣤⣤⣴⣿⣷⣯⠋⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣦⡾⠛⠀⢿⣧⠆⢫⡾⣷⣦⣤⣴⣶⣿⠿⢸⡗⠀⠀⠀⠀⠀⠒⠄⠀⠀⢙⡃⠀⢀⠰⠇⠘⠀⠐⠠⠀⠉⢿⣿⣿⣿⣿⣿⣿⠿⡿⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠐⠛⠁⠀⠀⠙⠛⠛⠛⠉⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠈⠂⠒⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠠⠐⠀⠀⢠⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣁⡄⠉⠙⠢⣀⡤⠄⠁⠀⠈⠀⠀⠐⣘⢃⣴⣴⣄⠠⠄⠀⠘⠉⠛⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠜⠛⠲⠁⠈⠳⢌⠀⠀⠀⠂⠂⠐⠁⠘⠛⣿⣿⡇⠆⠀⠠⠄⠘⠁⠀⠀⠠⠁⠀⡀
⠀⠀⠀⠀⠀⠴⠈⠁⠰⠛⠠⢍⠀⠓⠀⢤⠀⠚⠁⠨⠛⠀⠖⠉⠁⣠⣦⣬⣿⡷⠀⠀⠀⠀⠀⣴⣄⠀⠀⠁⠐⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠈⠁⠚⠀⠀⠁⢈⠁⠀⠖⢀⡀⠆⠀⠋⠛⠛⠀⢉⠂⡀⡈⠻⢻⣿⣷⡦⡆⠀⠈
⠀⠀⠀⠀⠀⢣⠰⢄⠠⠒⢄⡠⠤⡄⢂⡀⠤⣶⠀⠀⠄⠚⠁⡌⣠⢄⠀⠀⠀⠇⠈⠀⠓⢾⢤⣼⣿⣿⣷⣯⣀⡈
⠀⠀⠀⠀⠀⠠⡠⠖⢲⡤⠒⢢⠶⠨⣭⠉⠆⢀⠠⠆⣊⡁⠀⣄⠀⠀⣀⠢⠀⢀⠐⠂⠀⠀⢀⡌⠙⠛⠋⢛⡔
⠀⠀⠀⠀⠠⠁⡄⠀⠠⡆⢐⣄⢠⢁⠁⡤⢄⠠⣖⠀⠉⠀⠐⠐⠀⠀⠀⠀⠀⠂⡠⢬⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠂
⠀⠀⠀⠀⠀⠀⢹⠀⠀⡉⣗⠏⢘⠿⠀⣤⡊⠄⠃⠁⢠⠄⠀⠠⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣡⠄
⠀⠀⠀⠀⠀⢰⠸⣶⣤⢿⣿⣃⣤⠀⠀⣿⣀⠀⠀⠀⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠰⡀⠉⢸⣸⣾⣳⡭⡘⠁⢮⠙⠛⠒⡀⠀⠀⠀⢀⠀⠀⢠⡄⣅⠀⠀⠀⠀⠀⠈⠀⠀⠘⠁⢀⡀⠀⢦⢠⡄
⠀⠀⠀⠀⠀⠠⠄⠀⠃⠛⠛⠋⠰⠀⠀⣀⡀⢲⡄⠘⠀⠀⠊⠁⠀⠀⠀⢹⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣦⠹⣆⣋⣇⠁
⠀⠀⠀⠀⠀⠀⠀⡂⢶⠶⣤⠀⠒⡀⠀⢈⠋⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⣀⠀⠂⠀⠀⡠⡀⠘⠋⠉⠐⡎
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠈⣓⣈⡃⣀⡋⣴⢤⠤⢤⣄⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠉⢷⣢⡟⠈⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⢟⡛⢍⡹⠿⠿⠷⣿⡛⠻⠟⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠦⠄⠀⠀⠀⠀⠀⠀⠙⠄⡬⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣋⠁⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠂⠐⢀⠀⠀⠀⠠⣠⠀⠀⠀⠀⠀⠉⢠⡈⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠐
⠀⠀⠀⠀⢰⢄⠀⢀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢁⠀⠑⢤⠀⠈⠃⠐⠄⠀⠀⠀⠀⠀⠑⠠⠐⠐
⠀⠀⠀⠀⣀⠀⠀⠘⣃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠰⢢⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣷⡾⠛⠀⠀⠀⠈
⠀⠀⢰⢔⣽⠄⢀⣼⡿⣶⡄⠀⠹⠛⠿⣷⣦⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠋⠁⠀⠀⠀⠀⠱⠒⠀⠀⠀⠈⢿⡽⠷⠛⠉⠀⠀⠀⠀⠀⠀⢶⣢⠀⠀⠉
⠀⠀⠀⠉⠁⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠁⠀⠘⠀⠢⠄⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⡠⠖⠀⠀⠀⠀⣿⣿⣻⣿⡆⠀⠀⢀⣰⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⡄⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠼⠂
⠀⠀⠀⡀⠻⣄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠬⣤⢁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁
⠤⢄⠀⠀⠀⠐⠀⠀⠀⣠⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠰⠀⠀⠀⠀⡀⡤⢦⡄
⣰⠀⠌⠁⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣆⠰⠂⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀
⠀⠖⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠉⠀⠀⠀⠀⠤⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠊⠂⠀⠠⠀⢀⡀⠑⠕⠢⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⣲⣿⣾⢁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⡴⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠋⠚⠁⣿⣀⣠⠟⢚⡷⠶⢀⡤⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠐⠋⠤⣀⠐⠀⠀⠀⠀⣀⠠⠖⠨
⠀⠀⡄⠀⠀⠀⢀⡀⢀⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠁⠠⠎⠀⣰⠟⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⡁⠀⠂⠀⠀⠀⠀⠐⠆
⠔⠈⠀⠀⠀⠀⢸⣥⡛⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠈⠀⠀⢀
⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣤⣤⣤⣤⡄⠞⠃⠘⠀⠀⠀⠀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣄⡤⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠸⠷⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾
⣿⣿⣯⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣯⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡀⡖⠀⠀⢀⣾⣿⣿
⣿⣿⣿⣿⡿⠁⠀⣀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⣉⣡⠔⠂⠀⠀⠹⣿⣿
⠛⢉⡉⠉⠀⠀⠀⠜⢀⠂⠀⡄⠀⠤⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⡠⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠉⠀⠐⠇⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⡄⠐⠀⠀⠄⠀⠀⠀⣠⠁⠀⠀⠠⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⢠⠀⢒⠀⠀⠀⠀⠐⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈
⠀⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠠⠀⠀⠇⠀⠌⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤
⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠞⢀⠈⡁⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠂⠸⠀⠀⠀⠄⠀⠀⠀⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⢀⡶⣆⣀⠐⠃⠀⢀⢰⣯⡴⢇⡴⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁⠀⠀⠀⠀⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠈⠁⠓⠆⢹⠄⠀⣴⣟⣸⣿⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠠⣤⠀⠀⠀⠈

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠉⢿⢰⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣟⣿⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⢳⢾⣿⡟⠰⠀⠀⠀⡴⠃⠀⠀⠙⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⢰⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⠡⠟⠸⡛⣛⣯⡿⠁
⠀⠀⠀⠀⢀⣸⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⡿⠸⠀⠀⠀⠀⠀⠀⠀⣬⣿⣷⢿⠰⣾⡳⢶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣛⢣⣬⣤⣂⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡹⠟⣼⠁⢹⣆⠙⣯⠘⡿⠇⠀⠀⠀⠀⠀⠀⠈⠈⠙⠽⢿⣿⣿⣿⣿⡿⠿⠋⣀⣀⠔⠁
⠀⠀⠀⠀⠘⢿⡇⡄⠀⠀⢨⣭⣶⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠀⠹⠀⠀⣿⠂⡸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⣠⣴⣶⣾⣭⡏
⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠠⣿⣿⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠘⢀⢙⡝⡃⠀⡈⢹⠀⠀⠠⠤⢴⡗⠀⠀⠀⠀⢠⣾⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠈⠙⠻⠅⢈⡉⠉⠌⠋⠓⠊⠣⡜⠀⠀⠀⠀⠾⠇⠀⠀⠀⣠⣿⣿⠿⢿⣿⣬⣿⠆
⠀⠀⠀⠀⠀⢸⢿⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢸⢹⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠰⠾⠒⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⣶⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣤⢸⠁⠀⠀⠀⢠⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⣀⠀⢿⣿⠷⠶⠶⠀⠀⠀⠐⠺⣷⣿⣿⣄
⠀⠀⠀⠀⢀⣿⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢠⡿⢟⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡧⢼⣿⣢⣾⡁⠈⣿⡃⠀⠀⠀⠀⠀⠠⢶⣯⣿⠁⠀⠉⠁
⠀⠀⠀⠀⠸⠁⣿⠀⠀⢀⣤⣿⣧⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⢹⡇⣶⣯⡘⠛⠟⠛⠻⠏⠁⠀⠀⠀⠾⣴⣿⠃⠀⢰⣦
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠿⠏⣼⡿⠀⠀⠀⠸⠛⣻⡄⠀⠀⠀⠀⠠⠿⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠉⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢁⣾⣿⣷⡀
⠀⠀⠀⠠⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢠⣤⣤⣠⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠈⠉⠀⠉⠀⣤⠀⠀⠀⠀⠀⢸⣿⣯⠏
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⠃⠀⢠⠄⠀⠀⠀⣶⡟⠀⠀⠀⠸⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⢾⣦⣠⣸⣀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠐⢀⠀⢀⣀⣸⣦⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣧⣬⣿⣧⣼⣿⣵⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠶⠦⢄⡓⠚⠻⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢰⣶⣯⣀⣀⣀⣀⠗⠻⠿⣿⠷⣤⡀⠀⠀⢲⣦⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⡼
⠀⠀⠀⠀⠀⠉⠁⠀⠐⣲⢇⡦⣶⡙⡀⡉⠙⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠊⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣄⣀⣀⣸⠀⠴⠁
⠀⠀⠀⠀⠀⠀⢀⠀⡰⠋⠸⠀⢿⠓⠈⢄⣈⠄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁
⠀⠀⠀⠀⠀⡠⣿⠟⠁⠀⢠⣀⣼⠀⠀⠐⠉⠘⠀⠀⠀⠙⠛⠁⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⢀⣀⠀⣾⣻⡆⢠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠷⠂⠀⠀⠀⠀⠀⠠⢄⣀⣄⠀⠀⢠⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⠈⢹⣯⡿⠷⠏⠀⠀⠰⣿⠆⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠶⠶⣄⢀⣀⡽⠉⠁⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣴⠐⠒⠶⡶⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⣀⡀⠃⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠸⠀⣀⣀⢿⡀⢀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢰⡟⡉⡀⠀⠀⠀⠀⠀⠀⡐⢃
⠀⠀⠀⠀⠀⢀⡐⠒⠖⠀⠋⠀⠯⠐⠚⠋⠉⠈⠃⢿⡿⣿⣶⠄⠀⠀⠀⠀⣴⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠘⠀⠀⠀⠀⠀⠈⡧⣬⠁
⠀⠀⠀⢀⡴⢛⣗⣾⣶⡆⡆⠀⠀⠀⠀⠀⠀⠀⢠⣫⣶⣿⠒⣦⠀⠀⠀⠀⠈⠂⣹⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣠⠍⡉⠀⠀⠀⠀⠀⢀⠐⠉⠈⠂⢠
⠀⠀⠀⠀⠀⠈⠸⣷⡾⠇⠉⠉⠉⠉⠉⠀⠈⠉⠉⠿⣦⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⢮⡂⠀⠀⠀⢀⣴⣷⢼⣦⠀⠀⠛⡠⠴⠇⠀⠀⠀⠀⢸⣟⣛⣛⣻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⡀⠀⠀⠉⠀⠘⠁⠀⠀⠀⢀⡀⣰⡄⠀⠀⠀⡆⣿⣿⠿⣟⣦⠂
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠙⡧⠀⠀⠀⣿⣟⣷⣜⣋⣟⡀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⢐⢳⡞⠂⠀⠀⠀⠙⢄⠀⠀⠀⠐⠲⣤⣰⣶⣤⡾⢷⣶⠄⠀⢙⢈⣽⢭⡭⣍
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⣐⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡓⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⣿⣷⣿⣷⣶⠉⠀⠀⢸⣾⣿⢸⣿⣿
⠀⠀⠀⢠⣤⣯⣄⣠⣤⣤⣴⣤⡄⠀⠀⠀⡞⠉⠀⠙⡆⠀⠀⠀⠀⠀⠂⠒⠊⣿⠾⠉⠑⠒⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢨⡿⢣⠼⠭⢥
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠓⢄⣄⠰⠃⠀⠀⠀⠘⣆⠀⠀⢀⡚⣷⠀⢀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣣⣬⢩⣭⡭
⠀⠀⠀⠀⠀⢏⣹⠶⢶⣛⡷⠠⡄⠀⠀⠀⢆⡉⠙⠛⡆⠀⠀⠀⠀⢙⣿⢧⠴⣇⢰⠦⠾⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⠿⡿⢓⣬⣷⣙⠿⡟⡀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⢠⡇⠑⢶⣀⣶⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣦⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠐⠂⠀⠀⠀⠀⠀⢰⢴⣷⢰⣾⠆
⠀⠀⠀⠀⠲⠾⠟⠟⠻⠿⠳⠞⠀⠀⠀⠀⢶⡾⡿⠻⠻⡛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣤⣷⠸⠧⠙⠉⣳⠾⠂⠀⠀⠀⠀⣀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢐⡲⢤⡲⢶⣖⣾⣿⣶⠷⣶⣾⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣴⠾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠸⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣷⣟⣳⣭⣿⣭⡷⣻⣿⣿⡇
⠀⠀⠀⢴⡶⢦⣀⠤⢲⠾⠛⠒⣦⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣩⣍⣹⠿⣿⡿⣏⡻⣭⡛⠇
⠀⠀⢰⣿⡷⡌⢳⢶⡶⠾⢟⣉⠻⠄⠀⠀⠠⠤⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⠤⣶⠀⠠⠀⠀⠀⠒⠉⣍⡤⠀⠀⠀⢀⠉⠴⣫⣿⣇⣿⡗⣿⣿⣮⣙⡇
⠀⠀⢘⡭⣛⢴⠒⠒⠈⣁⣀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⠓⠛⠀⠁⠀⠀⠀⠀⠀⠠⠤⠿⠀⠀⠈⠁⠈⠉⠀⠁⠉⠉⠉⠉⠉⠉
⠀⠀⠈⣇⡈⢸⠀⠀⠘⡁⣯⣠⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⣀⠀⡀⠀⠀⠈⠃⠀⠐⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⠀⡀⠀⣀⢀⣀⡀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⣇⡙⣿⠀⠈⠙⠇⢹⣀⡈⠀⠀⠀⠀⠀⢠⣴⠛⡉⠉⡅⢉⡿⢷⣄⡀⠀⠀⠀⠀⠀⢸⣋⣁⡻⣋⣀⣈⣟⢉⡈⢹⡉⡉⡹⡍⠉⢉⠟⠉⠉⠈⡏⠁
⠀⠀⠀⣏⡙⣿⠀⠈⠈⠈⠸⠀⡆⠀⠀⠀⠀⣀⡎⠀⠲⡜⢼⢃⣞⡤⠞⠙⡇⠀⠀⠀⠀⠀⠹⠀⠀⠀⠐⠖⠒⠀⠈⠐⠂⠉⠀⠃⠘⠛⠛⠓⠛⠋⠉⠘
⠀⠀⠀⡏⠙⣷⠉⠈⠉⠀⠹⠀⡇⠀⠀⠀⠀⣸⠁⣀⡅⢘⣿⣿⡥⢀⠀⠀⢻⠃⠀⠀⠀⠀⠂⠀⣦⡶⠦⣤⣤⣄⡀⣤⠄⣤⣤⠴⣀⣴⣦⣠⡤⣤⣤⣤
⠀⠀⠀⣏⡛⣿⠀⠐⠠⠋⢱⠀⡇⠀⠀⠀⠀⠘⣇⠠⠖⢡⣿⣿⡙⠦⡈⢉⡟⠂⠀⠀⠀⠀⠀⢀⣥⡴⢃⣤⠤⣬⡇⢀⠀⣏⢀⣀⠙⠁⠀⢸⡏⠁⠀⠃
⠀⠀⠀⡏⠙⣿⠀⠰⠀⠋⢹⢉⠇⠀⠀⠀⠀⠈⠙⢧⣄⢰⠇⢿⡇⣀⡴⠛⠂⠀⠀⠀⠀⠀⠶⠿⠿⢟⡛⠠⠤⠤⡷⠴⠤⡷⠶⠦⢶⣤⣦⣼⣇⡀
⠀⠀⠸⣦⣕⣻⠀⠘⠊⡉⣉⣀⡠⠦⠀⠀⠀⠀⠀⠈⠉⡙⠒⠾⡏⠉⠀⠀⠀⠀⠀⠀⠀⠰⢰⡶⣶⣦⡿⠤⠴⠶⡧⢤⡤⣧⠠⣶⠾⣯⡽⣿⣿⣇⡠⢀⡀
⠀⠀⠀⠀⠉⠋⠀⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠻⠏