Naruto run Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢠⣵⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠉⠉⢉⣉⣛⣿⣿⣿⣿⣦⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠢⢤⣤⠀⢾⡿⠿⡿⣿⣿⣿⣿⣿⣷⣶⣧⠀⠀⠀⠀⠀⢀⠀⣠⣤⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠀⠠⡆⠀⠈⠀⠀⠀⢰⡇⠁⠀⠉⠙⠻⠿⠟⢛⣻⣶⣤⡸⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⢀⠀⠙⠶⣄⣐⡮⡗⢯⠹⣶⣶⣶⣶⣶⣦⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣇⠀⠀⣠⣿⣶⣦⣤⣤⣤⣼⣿⢣⣿⣿⣏⣽⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡧⠬⠿⣿⣿⠉⠉⢹⠛⠻⣿⣿⣧⣾⣿⣇⣿⣿⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠖⠋⠀⠀⣰⣿⣿⣧⣾⣾⡒⠀⣸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠸⣷⡄⠸⣧⡞⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣠⠈⢻⣿⣿⣿⡇⢉⣉⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠛⠚⠛⠛⠉⠉⠼⠇⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠋⢑⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠈⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣦⡀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣹⣯⠳⣿⡶⢶⣓⡶⣭⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣏⣄⠰⢷⣭⡿⠋⠉⠙⢻⣿⣳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠶⠿⢿⠁⠢⠀⠀⢀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢸⡄⠀⣘⣶⣤⡀⠀⢰⡞⣿⣳⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠃⠀⢟⣫⣿⠁⢰⣄⠀⠙⠛⢛⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠋⡙⠑⢠⠟⣻⣷⣦⡀⠌⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡼⢀⡏⢹⣶⣝⢦⡟⢤⣹⣷⣿⢻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⣧⡞⠀⢸⢻⣿⣴⡄⠪⢽⣿⣾⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠹⣇⠀⠉⣸⠟⢻⣿⣷⣿⢨⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⢖⢆⠙⠄⠈⣿⠿⣟⠈⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢮⣽⡗⠁⠀⢹⣭⣿⠀⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⠀⠀⠈⠉⠁⠀⢻⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⡶⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄⠀⠀⡀⠀⠄⠀⠠⢦⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠐⡇⢠⠅⠀⢠⠀⠀⠈⠇⠀⠡⠀⢘⠉⠀⠈⢁⣴⡀⠀⠂⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠙⠋⠀⠀⠈⠉⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠠⠀⠐⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠉⠀⠐⠂⠠⠤⢤⣤⠓⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠔⠈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡖⠐⠒⢲⠒⣶⣶⠒⠈⢹⡀⠐⠂⠙⠲⠤⠤⠴⠿⠢⠵⠶⠋⠉⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠀⠀⠀⠍⠶⠣⠏⡀⡀⠸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠐⠀⠀⡠⠉⠀⠀⠀⡻⠂⠤⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⠀⠤⢀⡰⠁⠀⠀⢀⠊⠀⠀⠀⡠⡖⡃⢢⡑⠂⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠰⠁⠀⠀⠀⢐⡣⢈⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠒⠒⠒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⢠⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣉⠁⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⠀⠀⠀⠀⠠⢤⡶⠒⠂⠁⠀⠀⠸⡏⠀⢈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢲⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡅⠀⠀⠐⠠⢄⢀⡉⠀⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⠜⠑⠢⢀⠀⠐⣜⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡑⢄⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⠔⠉⢄⣀⠔⠀⠑⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠑⢄⠀⠀⠀⢀⡞⠀⡰⠀⠀⡰⠑⡡⠛⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣂⢄⡞⠠⠊⠀⢀⠨⠐⠁⠀⠀⠡⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠑⠣⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠠⢄⠀⠈⣳⠎⠀⠀⠀⡘⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⣰⡄⠑⢅⣤⠟⠀⠀⠀⠰⠁⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣴⣿⣏⣤⣤⣤⣶⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀⣀⣠⣤⣶⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣙⡛⠳⡀⢠⣄⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠄⢲⣌⣿⣿⣿⣿⣿⣿⡿⢿⠁⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠶⢿⣿⡿⠟⡛⠛⠋⠀⢼⣅⢀⢀⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠫⣧⠄⠐⣿⠀⠀⠀⠘⢁⢀⣾⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⣾⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣀⣀⠄⠈⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣐⣠⣶⣯⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⡟⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⠀⠀⠐⠀⠀⣤⣤⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠀⠹⢿⣿⣿⣿⣿⣿⣿⣷⠀⡀⠀⠀⣀⠀⣰⣿⣿⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠹⡏⠈⠛⠻⣿⣿⣧⠁⣸⣶⣶⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣄⡀⠀⠀⠀⠀⠁⢀⡀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠋⢰⣤⣀⠀⠀⠀⢀⣾⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡙⢻⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴⣶⣶⣤⡘⢋⡄⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⡟⠃⠘⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⡦⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⠀⢰⠀⠀⠙⢷⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠⠂⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⠀⠀⠀⠘⠿⢿⣿⡟⠈⠛⠿⠿⠻⣿⢋⠶⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠁⠐⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠁⠈⢀⠁⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⣀⡠⢴⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣹⠆⢹⢇⣠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠃⠀⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡠⣿⣦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣸⠟⠃⠀⠀⠀⠀⠠⠈⠛⢛⡿⢛⣛⠒⠒⠒⠒⠶⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎⣼⡏⠠⢰⣶⣾⠛⠉⠉⠈⠀⠀⠁⠀⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣈⠀⠀⠀⠀⠀⠙⠈⠢⡄⢸⣿⣿⣿⣶⣶⡀⠀⠀⢀⣀⣤⠄⠀⣠⠾⡛⠃⠈⠀⠀⠀⠈⣿⣋⠀⠀⢠⠄
⠀⠀⠀⢡⡂⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣶⣿⡛⠻⣿⣠⠞⢁⣴⡗⠁⠀⠀⠀⠀⠀⠙⡓⠊
⠀⠀⢠⢷⡶⠒⠀⠐⣋⠉⠉⠉⠙⠉⢿⣍⢿⣧⠈⠀⠀⠀⠙⠟⢻⣧⠶⠚⠋
⠀⠀⠁⢸⢳⠌⠓⠂⠀⠁⠀⠀⠐⠃⢸⠇⣾⠃⢀⡴⢆⠀⣀⠀⣤⣤⣤⠶⠒⠒⠒⠒⣖⠀⠀⣀⣮⢳⣶⠞⣷⣴⣤⠖⢶⣶⣶⣶⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣨⣾⣤⣤⣀⣻⣾⣯⣽⣿⡟⠝⠁⠀⠀⠀⠀⠀⠠⠈⢿⡨⣿⣼⡿⢠⣿⠟⠁⣀⣾⠿⠛⢉⣀⣤
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠀⠀⠀⣠⠏⢨⡟⠿⢿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⢁⣂⣐⣺⣿⡟⣡⣾⣥⣶⡿⠟⢁⣠⣾⣿⣿⡷
⠀⠀⠀⠀⠀⠀⢡⡤⠀⠀⠀⣠⣾⣟⡔⠉⢻⡑⢬⡙⡿⢛⡿⠛⠁⠀⢀⠀⠀⠀⠀⢀⢄⡿⣹⠿⢋⣴⣿⣿⡿⠋⢀⣴⣿⣿⣿⡿⢿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣶⣿⠿⣻⠙⢇⡀⠀⠹⣾⣷⠇⠈⠀⠀⠀⠀⢈⡁⣀⣀⣀⣭⣉⣤⣤⡶⣻⣿⣿⣿⣶⣤⣿⣿⣿⣿⣷⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡅⠠⡀⠻⣦⣴⠿⠧⠀⠂⠀⠀⠀⠀⠀⠀⢶⡂⠀⠀⣀⣠⣤⣼⣿⠟⣫⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⣛⠛⣿⣫⣥⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣾⣿⣿⣿⡿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡟⣿⣿⡏⠀⠀⠀⠀⠀⠀⡀⠠⢤⣶⣿⣿⣿⣿⣿⣿⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣼⣿⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⣘⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡝⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣄⣄
⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠉
⠀⠀⠀⢿⠄⢰⣷⠀⠛⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⣄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠻⢿⠀⠀⠀⠀⠀⠀⠀⢿⢀⠀⠀⠀⠐⠀⠉⠀⢠⡟⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣶⡏⠀⠀⠀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣀⣀⣈⣉⣀⡀⠀⠀⢀⡕⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠰⣾⣧⠀⠹⣿⡃⠀⠀⠀⠀⠀⢀⣠⣷⣤⣶⡶⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣶⣿⣤⣀⡀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠐⢿⣿⣶⣿⣿⣷⡀⠘⠇⢀⣠⠰⣲⢾⣿⣿⡟⠉⠁⠀⢀⣴⡄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠉⠉⠛⠛⠷⢦⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠋⢉⣟⠛⢿⣿⣶⣾⣿⠋⢀⠁⣠⣿⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠤⡀⠀⠀⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢻⣿⡿⠿⣿⣿⠿⠇⠸⠟⠹⠟⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⡴⠋⠀⠀⠀⠀⢠⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⢀⣶⣤⡀⠛⠛⠟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⢠⣾⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠲⠆⠀⠀⠀⣀⠴⠛⠀⣦⠰
⠀⠀⠀⠀⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠸⣿⣿⣿⣿⣿⠆⠀⣸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⠶⠶⠎⠀⠙⠀⣟⠂
⠀⠀⠀⠀⣿⠋⢁⡀⠙⠛⠧⠀⠀⠐⣀⠀⣈⡉⠀⠀⢻⣿⣿⡿⠁⠀⠀⠛⠿⣿⣿⡿⠁⠀⠀⣤⠀⠀⠠⠂⠘⠀⠀⣹⣤⣦
⠀⠀⠀⠀⣿⣿⣿⡇⢻⣶⣄⡙⠓⢠⠤⠄⣹⡯⠁⠱⠜⡍⢿⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⡐⡏⠀⠰⠖⠊⠁⢈⣴⡆
⠀⠀⠀⠒⠉⣻⣿⣿⠀⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠄⠀⠸⡇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠾⠛⠃⠀⠀⠐⠋⠉
⢠⡀⠀⠀⠀⣿⣿⣟⠚⣽⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⠀⠈⠐⠀⠀⠂
⠈⠀⠀⠀⠻⠛⠙⣿⡷⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠀⣠⡀⠀⠀⠀⠄
⠀⠀⠀⢰⠐⣶⣾⣿⣿⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⡿⠃⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠙⠛⠋⠁⠀⠂
⠀⠀⠀⠀⠀⠉⠛⠁⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠭⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣎⢻⡇⠀⠀⠀⠀⠀⠀⠐⠿⣶⣤⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡐⠿⠛⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⢰⣤⡀⠀⠀⠀⠀⠙⠛⣻⡿⠃⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿
⠀⠀⠀⠈⡼⢢⡀⠀⠀⠀⢀⡔⢶⠂⠀⠀⢀⣄⣠⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣤⣄⣀⠀⠀⢐⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠋⠉⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⣴⡿⠛⠁⠀⣉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠥⠔⠂
⠀⠀⠀⠀⠀⣿⡟⠙⠻⣦⡘⠐⠠⠈⠀⠀⠀⢀⣿⡁⠀⠚⠁⠀⠀⠀⢸⠛⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠋⠈⠀⡁⠒⠁⠀⠀⠁
⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣰⣤⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠘⠀⣿⣿⠀⠀⠀⢹⣿⠶⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⢶⠀⠠
⠾⣿⠀⠀⣿⣿⣿⣷⡆⠀⠀⠀⢿⡿⠟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠘⠃⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣿⠋⠙⢿⣿⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠀⣾⡇⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡇⠀⢿⢧⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠷⠾⣿⣾⣄⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⣀⣀⡥⡎⡇⠀⠀⠀⠛⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠟⠋⠟⠉⣷⣧⠀⠀⣠⠤⣴⡆⢱⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡞⠀⠀⠀⢠⣎⡏⠀⠀⠀⠀⠁⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠞⠀⠀⠀⣠⡿⠟⠀⢀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠠⣄⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠄⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠞⡛⠀⢀⠁⠒⠒⠖⠀⠀⠀⠶⠀⠠⡎⠀⠀⠉⠲⢄⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⣀⣀⡨⣮⠀⠀⢰⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠣⢄⡀⣀⠴⠊⠀⠀⠀⠀⣈⠄
⠂⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡄⠀⠐⠂⠁
⠈⠠⠠⠈⠁⠀⠀⠀⠈⠁⠒⠰⠬⢔⡀⠤⢙⣦⣤⣀⣀⣀⣀⣠⠴⠊⠀⠀⠀⢀⡢⠴⠊⠘⠦⠄⣠⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠌⠑⠐⠊⡤⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡲⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⣤⣀⣀⡀⠀⢀⣀⡤⠞⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠉⠁⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣀⠄
⣿⣿⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡤⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⣠⣾⣻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⣀⣿⡿⠋⢀⣠⣴⣾⠃⣠⣾⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡔⠛⢳⣤⣴⣾⣿⣿⣿⠏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣭⣿⣿⣿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⣤⣀⠀⠀⠀⠀⢀⣤⣿⣷⣦⣤⣾⣿⣿⣿⠄⠀⠀⢻⣿⣿⣿⣿⣧⢻⣿⡿⠋⠁⠉⠛⠿⣿⣿⣿⣤⣀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠁⢀⣲⣾⣤⡈⣿⣿⣿⣶⣀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⢛⣿⣿⣿⠟⠃⠛⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣸⣿⡿⠋⣠⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠃⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⠛⠿⠃
⠀⠀⠀⠀⠔⢛⣿⠟⠁⣴⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⡀⣤⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠚⠛⠛⠁⠀⢺⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠀⠀⠀⠂⣈⣯⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠰⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⡀⠀⠛⠉⠀⠀⠀⣠⣾⠃
⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣴⣾⡿⠃
⠀⠀⡀⠀⠀⠀⠀⠂⣀⣀⡤⣶⢿⣿⣿⣿⠿⠇⠀⠀⠈⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡏⠀⢀
⠀⠘⠿⢆⣄⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⢀⣀⣀⣀⣀⣹⡿⢿⡿⠃⠀⣠⡞
⠀⠀⣿⣛⣷⣶⣤⣠⣴⣾⣿⡿⠿⢿⣿⣷⣶⠶⡶⢂⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠀⣠⣾⠋
⠀⠀⢿⠯⠿⠟⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⡟⠀⠙⠻⠋⠁⠀⠀⠀⠀⢀⠀⠤⠄⠠⠤⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋⠉⠀⢀⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠹⠁⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⣀⣠⡤⠶⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⡐⣤⣤⠀⠀⠀⠀⠀⣰⡟⠀⠀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣶⠛⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡋⠀⠀⠀⠀⢰⣿⣷⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⠿⠿⠛⠛⠿⠿⠿⣿⣿⣿⠁⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⣴⣾⣿⣿⡿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⢦⣤⣀⣀⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠱⠶⣤⣬⣉⣿⡿⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢹⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠠⡄⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠺⠳⢾⡆⠰⠛⡠
⠀⠀⠀⠀⠲⡀⠘⡀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠠⣴⣀⢀⡀⠀⠰⠈
⠀⢰⠀⠀⡀⠑⠄⠀⠄⣀⠀⠀⠀⢀⠄⢀⠔⠀⠀⠈⠑⠒⠀⡀⠉⠉⠉⠆⠀⡀
⠀⠀⠑⢄⠈⠢⣈⡄⠘⠋⠀⢰⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠙⠶⠈⠀⢠⠄⠉⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⢦⡀⠂⡀
⠀⠀⠘⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠙⠦⡄⢀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢙⡷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠖⠉⠀⠀⠊⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢂⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠶⠀⠉⠉⠉⠛⠻⠶⣿⡄⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢠⠀⠀⢀⡠⠆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢦⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⡄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠔⠋⠀⣼⣷⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⠘⢷⠒⠂⠐⠒⠒⠊⠉⠁⠀⢀⣤⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢻⠀⠀⠀⢧⣤⣄⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⡷⠀⣀⡀⠀⠀⣀⡀⠐⠈⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⡀⠠⠿⢻⡟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⠓⠴⠂⣀⣀⣀⠴⠋⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠐⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠷⣤⣤⣀⣀⣠⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⣤⣤⣤⣠⣤⣤⠴⡾⠋⣀⠀⠷⠈⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢻⡅⠀⠀⡇⠀⠈⠁⠶⠂⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⢀⣀⠴⠛⠁⠀⠘⠀⢆⣤⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠈⠁⠀⠀⠀⠀⠀⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⢛⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡀⠀⠀⠀⠀⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣄⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣉⣤⡞⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⠳⠶⠞⠁⡇⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⠴⠞⠉⠀⠻⣆⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡴⢾⠁⢠⣼⣁⣀⣀⣀⣀⠀⡴⢶⡞⠉⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢇⠀⠁⠀⠀⠀⠀⠀⠀⠄⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠡⣀⠀⠀⠀⠀⠀⢠⠂⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢦⣤⣤⡴⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⠁⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠤⠐⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣶⡿⠃⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠀⠉⠁⠈⠀⠑⢋
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠜⢻⡄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠠⠀⠄
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠁⠘⠓⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣤⣴⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣈
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠁⠀⢤⣤⣠⣤⣤⣤⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣙⣿⣿⣿⡿⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⠏⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣣⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣆⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢻⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢦⣠⡄⠀⢼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⠣⡾⠀⣿⣿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⣶⣶⠏⠀⠀⠀⣠⠤⠀⠀⠘⣷⣤⡀⠀⠀⠿⢿⣄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠷⢙⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠈⠛⠉⠉⠀⠀⠀⣈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣼⡿⠁⠀⠠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡎⡰⣾⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢃⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠈⠛⠀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢡⣌⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠀⠠⡀⠐⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣿⣿⡇⠀⠀⠙⡄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢹⣿⣆⠀⠀⠀⢱⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢁⣴⡿⠇⠀⠀⠀⣰⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡏⣿⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣷⣿⣿⣤⠆⠀⠀⠀⣻⠃⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣷⣿⣧⠀⠈⠻⣷⡀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣶⣮⣤⡼⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⣿⣿⠀⠀⠀⠈⢷⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠀⠀⠀⠀⠈⠁⢰⡿⠿⣿⣿⢿⡏⣿⡟⢉⣤⠔⠀⠛⠚⠀⠠⠆⠐⠋⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⣷⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⢰⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⡇⢀⣿⠀⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠛⠀⠀⠀⢀⡀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⣴⣿⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡆⠀⠀⠀⠀⢹⣿⣾⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⢸⣿⡿⠛⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣿⣿⡄⠀⠀⠀⠀⢨⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡅⠙⢻⣿⡄⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠘⣿⢷⠀⠀⠀⠀⢹⡟⠉⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣀⠀⣀⡀
⠀⢴⣴⣿⣿⣿⡇
⠀⠀⠀⢹⣿⣿⣿⣦⣄⢰⣶⢸⣷⡆⢠⣶⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⠀⢀⣆⣿⣷⣀⡀
⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣭⣿⣿⡇⢸⣿⣷⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠛⢛⣿⣿⡟⠀⢹⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⣦⣶⣶⣶⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢈⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣴⣴⠂⠀⢠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠘⣿⠃⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠆⠀⢀⣻⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⠀⠀⠘⠿⠿⠛⢛⣛⣛⠋⠀⣼⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⠛
⠀⠀⠈⠑⠒⠒⠀⢹⣿⠻⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠉⠁⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠻⣶⣤⣄⠀⠀⢋⠉⠉⠉⠉⠙⠛⠛⠛⠃⠈⠁⠀⠀⢀⠜⣿⢛⣿⣿⠿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡠⠀⣀⡞⠀⠈⠛⠛⠀⠀⠀⡏⡏⠁⠓⠢⠔⣠⢤⣤⣤⡤⢀⠤⣠⠞⠁⠸⠋
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⡀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠈⠉⢙⣷⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⢔⡾
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣠⠴⣪⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠗⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠂⡠⠶⠭⠭⠭⣉⡵⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡇⠂⡆⢀⠔⢤⡇⠀⣇⠀⠀⠀⠀⠀⡞⠿⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡉⠀⠀⠁⠁⡇⠀⢸⠀⠀⠀⠀⠀⣧⡘⠒⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠬⣖⣊⡯⠇⡧⠄⢸⠀⠀⠀⠀⣰⡑⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣶⢲⠶⠶⠷⠊⠁⠀⠀⢀⡼⣑⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠒⠻⠶⠓⠒⠒⠦⣤⣄⣠⠮⣱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡅⠈⠉⠉⠉⠉⠒⠒⡎⢹⡗⣉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠲⡇⠀⡩⢩⠉⠉⢱⡀⡇⠸⠭⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢲⣷⠀⡍⣉⠀⠀⢸⡃⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢺⢸⠀⢟⣒⣁⣀⣸⠇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠸⡄⠀⠀⠀⠀⠀⠀⣇⡠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣈⡷⡀⠧⠤⣤⠭⠭⠭⢭⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠁⢂⣱⢠⣉⡇⠀⠀⠀⠀⡦⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠈⠉⢸⠒⡇⠀⠀⠀⠀⣏⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢬⠃⠀⠀⠀⠀⡗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢼⣺⢦⠀⠀⠀⡐⠫⡼⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡡⢼⠀⠀⠀⠹⣒⠠⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠊⠁⠀⠀⠀⠀⠀⠉⠉⠉

⢠⢀⡲⠒⠄⠒⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⢐⠐⠀⠰⠄⠢⠀⢒⡄⣤⡄⠀⠀⠐⠀⠀⢦⢀
⡨⢞⡀⠀⠀⠀⢡⠁⠈⡆⠀⠀⠀⣆⠐⢂⡀⠩⠀⠠⡘⠆⢉⡈⠁⢠⠆⢈⠣⠈⠉⠀⢀⠃⣆
⠐⠘⣇⠑⠦⠄⢀⠀⠐⠅⠀⣀⢀⠈⠓⠔⡀⠤⠰⡠⠒⢡⠀⠀⠀⢈⠀⢢⢕⠁⠀⠀⠀⢢⠡
⠸⡀⠈⠻⡀⠤⣾⢶⠈⠷⠶⣿⣟⠋⡀⠀⠢⢉⡅⠀⠡⠀⠀⠀⢈⢠⡏⠸⠛⢈⠀⠈⠉⠁⠠⣀
⠀⠈⠢⡀⠴⣦⡻⡘⡂⠘⠁⢀⠳⢧⡑⡤⠁⣆⣠⠒⠄⠀⠈⠕⢖⠒⠀⠀⠀⠩⢭⠠⠄⠀⡀⣀⡀
⠀⠀⠀⠈⠐⢄⠙⢄⡇⠂⠀⣼⠗⠂⠐⠯⠇⠀⠀⠹⠀⠒⠀⠀⠨⣄⠀⠀⠀⠀⠀⠃⡀⣢⠘⡦⠧⡤⣄
⠀⠀⠀⠀⠀⠀⢆⠀⢹⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⡂⢀⡤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠧⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄
⠀⠀⠀⠀⠀⠀⠀⢨⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢠⣎⡀⠀⢀⣄⠐⡀
⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠁⠉⠉⠁

⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡠⡊⢫⠭⡉⠶⡄⠀⠀⣤⠴⠋⣳⠀⠀⠀⠀⣀⠤⠶⠤⢄⡀⠀⠀⢠⠊⡭⢍⠉⠒⡄⠀⠀⠀⠀⣠⠊⠀⢸
⠀⢰⢁⠀⡇⠀⢹⠀⢸⠀⠀⠉⢹⠀⡇⠀⠀⠀⡞⠁⢾⠵⣆⠀⢱⠀⠀⠣⣤⠇⡠⠃⠀⡏⠀⠀⣠⢞⣴⣇⠀⢸
⠀⢸⠀⠀⡇⠀⣸⠈⢸⠀⠀⠀⢸⠀⣧⠀⠀⠀⠘⠢⢚⡴⠃⣀⠜⠀⠀⣠⢤⡈⠣⡄⠘⢆⠀⠀⣄⡨⠩⡁⠀⢈⡵
⠀⠈⢧⡠⠱⠤⢃⣀⠆⠀⠀⣠⠼⠀⠸⢄⠀⠀⢀⠔⣡⣖⣉⣁⠖⡆⠀⢇⠠⣇⣀⠆⠀⡸⠀⠀⠀⠀⣠⠜⡀⠘⣤
⠀⠀⠀⠉⠒⠖⠊⠁⠀⠀⠀⠉⠙⠻⠋⠉⠀⠀⢾⡤⣤⣤⣀⣤⠴⠁⠀⠈⠙⠺⠄⠒⠉⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣶⡒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⡕⠒⢫⠙⡄⠀⠀⢀⡠⠴⠤⣀
⠀⠀⠀⠀⡇⠈⠛⢒⣢⠇⠀⢀⡞⠀⡌⠀⠧⠠⠇⠀⢰⠲⠖⠚⠓⠲⠒⡆⠀⣇⠀⠉⠒⠚⢴⠃⠀⣸⠁⡴⠉⢱⠈⢣
⠀⠀⠀⢠⠃⠿⠟⠯⢤⡀⠀⢸⠀⠀⢋⣉⠉⠑⡄⠀⢸⣰⠋⠙⡶⢂⡞⠀⢠⠏⡠⠶⠤⡀⠀⢳⠀⢹⡀⠳⠄⠌⠀⢸⡆
⠀⠀⠀⢈⠧⡈⠳⣦⠀⠹⡀⠈⢆⠀⢿⣿⠃⠀⡇⠀⠈⠁⢀⡞⢑⡞⠀⠀⠘⣀⠑⣄⣀⠜⣀⡜⠀⢀⡭⢕⠒⡾⠀⢸⠁
⠀⠀⠀⢧⠀⣼⣰⠟⠀⣸⠁⠀⠈⠳⢤⣥⠴⠊⠀⠀⠀⠀⣸⠀⢸⠀⠀⠀⠀⠀⠉⠳⠞⠋⠁⠀⠀⠸⣄⣘⢒⣁⡠⠋
⠀⠀⠀⠀⠙⠒⠶⠖⠊⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⢶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⢬⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣢⣶⣧⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⡠⢀⣀⣠⣬⡿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣦⡀⡠⢔⣠⣾⣿⣿⣿⣿⣿⣯⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣟⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣾⣯⣿⣿⡷⡀
⠀⠀⠸⢻⢿⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣷⠴⠍⠛⡿⢻⡉⠳⢄⢻⠉⠙⣿⣿⣿⣿⣿⣿⡿⢰⣿⣯⣿⠠
⠀⠀⠀⠀⠈⠛⠿⠿⠿⢻⣿⡟⣠⣄⡔⠜⠁⠀⠉⠀⠒⠩⠷⢦⣤⣯⠿⠟⣺⣿⢇⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡾⠫⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠄⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠉⠀⣀⡀⠀⠀⠀⠘⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⢦⣤⡄⠀⠀⠀⠀⠛⠋⢡⠴⣿⣿⡻⠋⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣹⣿⠗⠀⠀⠀⠀⠀⠈⠐⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡀⠉⢠⣾⣿⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣟⢁⣴⣄⣹⣿⣤⣤⣀⣠⣾⠛⠿⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⣉⠔⡀⢀⠀⡦⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⢺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⢁⢄⠀⠂⠠⣴⠆⣤⠀⠐⡀⠀⠀⠀⢰⢟⡟⠛⠛⠛⠛⠿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⢠⢐⢸⠈⠀⡄⠉⢁⡞⠈⢄⣀⠴⡄⠀⠀⢸⠋⠀⠀⢀⠃⠐⡀⢰⠇⠀⡴⠦
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢠⣷⠀⠖⠀⠉⣀⡴⠋⠀⠀⢸⣅⣤⣼⣀⠀⠈⣆⠀⠀⠀⠀⠈⠉⠙⢻⣦⡗⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢿⣇⠀⡀⣸⠃⠀⠀⠀⠀⠀⠈⣿⣿⡏⣻⠖⢏⡀⠀⣠⠆⠐⠇⠤⠚⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣍⡤⠋⠁⠀⠀⠀⢠⠄⠒⠲⠿⣿⡃⣿⢠⠊⢰⣆⠀⢄⠀⠀⠀⢀⡦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣿⣧⢹⠀⢰⣯⡼⠦⢄⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⢀⡄⠂⠉⠑⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠘⢻⣿⣿⣧⣯⣷⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢈⠕⠶⠀⠀⠀⠈⠳⣇⠂⠀⠀⢁⡹⣿⣷⣿⣿⣿⣿⣿⠁
⠀⢀⡤⢀⣤⠤⠄⠠⠤⠄⠠⠗⠀⠀⠀⠀⠀⠀⠀⣹⡌⠁⠀⠀⠐⢻⣾⣿⣟⠛⣿⠏
⢀⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣴⣿⣷⡄⠢⠀⠀⠘⠋⠀⣠⡧⠋
⠘⠥⠄⣀⠐⠂⠀⠀⠀⠀⢀⡴⠋⠙⢽⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣴⣶⣿⠏⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠒⠀⠻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢰⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠛⢀⡎⠻⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣦⠀⠀⢹⣿⣿⠿⢿⣿⣿⡇⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡟⠰⠆⠀⠈⢌⣿⣿⣿⣿⣿⠿⠋⢰⣿⣿⣿⣧⠀⠀⣿⣿⡄⢀⣿⡟⢰⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠷⣦⠀⠸⠂⠀⠛⣉⠛⠯⣄⠀⠀⠀⢹⣿⣿⣿⣆⠀⢸⣿⣿⣿⣏⡀⢾⣿⢻⣿⣿⢿⣿⣿⠃
⠀⠀⢀⡴⣶⣋⠙⣯⠝⢯⡐⠋⣿⣤⡘⠗⠀⠙⠀⠀⠙⠓⠦⣄⢸⣿⡏⢿⣿⡄⠀⣿⣿⠉⠻⣿⡆⠀⢸⣿⡏⠈⠛⠃
⠀⢀⣏⠀⡟⠂⡇⣿⠆⢠⠌⢁⢰⡟⠁⢴⣶⠄⡛⠀⠺⠃⣠⡏⠈⣿⣿⣿⣿⣷⠀⢸⣿⡆⠀⢻⡇⠀⣸⣿⡇
⠀⢸⠃⢺⠁⠀⡇⣿⠘⠀⣤⢉⡾⠀⠀⡝⠰⡆⠁⠘⠃⣀⣙⡇⠀⢿⣿⡁⠹⣿⡇⠀⣿⡇⠀⢸⡇⠀⣿⣿⠁
⠀⢸⠀⣼⠂⠰⠟⣧⠿⠒⠈⠊⠁⠀⠈⣷⠐⢲⠿⣤⠼⣟⣻⠦⡄⣸⣿⣧⠀⣿⣷⡄⣽⣷⣄⣸⣇⢀⣿⣿⡀
⠀⣸⣦⣽⣷⣠⣾⣷⣶⣶⣶⣶⣶⣶⣾⣇⠀⠉⠓⠒⠒⠛⣿⣴⣧⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣧
⠈⠛⠛⠛⠻⠿⠿⠛⠛⠛⠛⠛⠛⢿⣿⣿⣾⣷⣤⣦⣤⣤⠽⣾⠿⠛⠛⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠋⠽⠏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠩⣕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣶⣶⣒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣶⠢⣄⣤⣀⠀⠀⡆⠸⡁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⣠⡀⠀⠈⣉⣉⣉⡒⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣲⡄⠀⠐⢬⣓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⣤⡉⠛⠋⠉⣧⡬⣍⣛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢄⠨⣟⠈⠙⠒⠃⠈⠑⠋⢑⣒⣖⣛⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⠖⠚⠛⠛⢲⡄⣀⣀⡙⢥⣬⡄⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⠉⠁⠈⢽⠧⢷⣤⣄⡇⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣴⣿⣷⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⡛⠛⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣆⠀⠀⠀⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠐⠶⡎⠉⠑⠒⠃⠀⠈⣹⠟⣿⢿⣿⣿⣿⡇⢻⠀⠀⠀⣼⣿⣿⠿⠉
⠀⠀⢀⠐⠒⣖⠲⠤⣀⣹⠆⠉⠋⠁⠀⠀⠀⠀⠀⢠⠏⡸⠃⠀⣼⠟⠙⡇⢸⠀⠀⢠⠟⠋
⠘⠛⠳⠯⣍⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠤⡴⠋⠀⢀⣠⠞⢁⣀⣺⠃⢸⠀⠀⡞
⠀⠀⠀⠀⠀⠉⠀⠀⣤⠟⣀⡤⠚⢙⣇⠞⢠⠞⠁⢀⡴⠫⢤⡄⠞⠁⠀⠀⠘⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢿⠐⢀⠏⠠⣤⣤⣟⣠⡀⢀⠀⡀⠰⠇⠒⠒⠉⢉⣉⣉⣀⣁⣈⠁⠒⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠈⠁⠒⠛⢹⣀⣁⡠⠴⠒⠚⠉⠉⠀⠀⠀⠀⠈⠓⠬⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡚⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣉⣥⣤⣿⡿⠟⠀⢀⡾⣠⡶⠀⣴⡾⠿⣿⣟⢋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⣿⠟⣼⢋⣿⠽⢿⣀⣀⣤⣿⣷⣿⡇⣼⠏⣴⢟⡭⠖⠋⠁⠀⣰⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢩⣶⠟⢁⡼⢃⣏⣴⣾⣿⣿⡿⢟⣿⣿⣩⣾⡏⣸⡿⣢⠷⠂⣠⣶⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢣⣿⣘⠻⣒⡋⣴⣿⣿⡿⠛⠋⣉⣴⡈⠿⠿⠟⢋⣰⡏⢸⣧⣤⣾⡿⣿⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢃⣿⣿⣿⣿⣏⣼⣿⣿⣋⣰⣾⣿⣿⣿⣿⣶⣶⣶⣿⣿⠷⢀⣭⣽⣛⠅⣿⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡟⢉⡉⠉⠛⠛⠛⠛⠿⠿⠛⠛⠻⢿⡿⠿⠿⠿⢷⣾⣿⣿⣿⣱⡿⠋⣸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⣾⣿⡿⢸⣿⣿⠇⢠⣴⣾⣿⣶⣄⢀⣶⣦⣤⣤⣤⡄⢘⣿⣯⠷⠶⣋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⡏⢀⣿⣿⡇⣼⣿⣿⠀⣿⣿⡏⣹⣿⣿⠘⠛⣿⣿⡿⠛⠃⣸⡟⣱⠿⣛⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⡇⢸⣿⣿⠁⣿⣿⡇⠀⢰⣿⣿⡇⢰⣿⣿⡿⢁⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⣿⣿⡟⢻⣿⣿⠁⣿⣿⡿⢸⣿⣿⠃⠀⣼⣿⣿⠀⣾⡟⠉⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⡇⣿⣿⡟⢠⣿⣿⡇⣾⣿⡿⠀⠀⣿⣿⡏⢀⣿⣤⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣼⣿⣿⢰⣿⣿⠇⠈⠿⣿⣿⡿⠟⢁⡀⠸⠿⠿⠃⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣶⠿⢷⣶⣶⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣹⣷⡍⠙⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡿⠗⠂⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠛⠁⠀⠀⠀⢀⣠⡴⠖⠶⣦⡀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠙⢦⣄⠀⣰⠟⠁⢀⣀⣠⡈⢻⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣡⡿⠛⠳⣦⠙⣾⠃⢀⡴⠋⠉⠉⠻⣆⢻⡄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡏⠀⠀⠀⠘⣧⠀⠀⣾⠁⢀⣀⡀⠀⢻⡌⣧⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⠀⢠⣾⢷⣆⢸⡄⢸⡇⢠⣿⠉⢳⠀⢸⡇⢹⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣾⣿⠀⢹⡜⡇⣸⠁⣿⣿⠀⢸⠀⢸⡇⢸⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⣿⣿⡀⢸⡇⡇⣿⠀⣿⣿⣤⣿⠀⣼⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⡄⢸⣿⣿⣿⡇⡇⢸⡆⣿⣿⣿⠇⣰⠇⢠⠇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠹⣆⡹⣿⣿⠟⠻⠋⣛⣛⢿⣏⡼⠋⣰⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠳⣬⢙⡿⠁⠀⢀⣠⢿⣏⣁⡽⠰⣞⠁⠀⠀⠘⢿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡟⠸⠷⠶⠺⡟⣧⡾⣸⠉⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⣤⣤⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⡇⠀⠀⠀⠀⠻⣭⠴⠃⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠙⣷⠶⣦⣤⣤⣤⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡶⣶⡛⠉⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣿⠶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠙⠶⣍⣓⣂⣀⣤⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣭⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠛⠻⠶⠶⣶⠶⢾⡟⠋⠁⠀⠐⠲⠤⣭⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡴⠋⢁⡤⠀⣠⡟⠀⠀⠙⢦⣄⠈⠙⠶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣴⣏⣀⣴⠟⠀⠀⠀⠀⠀⠙⠻⠶⠶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢂⣾⣿⣿⡿⢆⡄⠉⠹⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠉⠉⠉⠀⠀⠠⢤⢤⠤⠂⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣾⣶⣷⡀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⣀⠀⠀⠀⠀⠋⠉⠙⡄⠀⠀⠀⠀⠰⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣠⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣀⡀⢀⡀⠀⠀⠀⢙⣥⡀⠀⠀⠀⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⣧⠈⠉⠉⠁⠀⠀⠴⣀⣿⠇⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠂⠀⠀⠀⠀⢅⣻⡁⠀⠀⠀⠀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡏⠀⠠⠀⠐⣾⣿⠧⠀⠠⠀⠸⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢦⠀⡀⠀⠈⣷⣆⡀⠄⠀⣹⣿⡇⠀⠀⠀⡐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢛⠙⢦⢀⠻⣻⣿⣿⡄⠀⠀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⡓⣻⠿⣿⣿⣟⠃⣠⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⣠⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣀⡀⣀⣀⢀⣠⠄⣠⡀
⣀⣀⣀⣄⣠⣤⣤⣤⣤⣤⣤⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣭⣅⣽⣏⣭⣮⣹⣿⣿⣶
⣉⣭⣯⣍⣩⣭⣉⣩⣭⣭⣥⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿
⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣠⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣻⣿⣿⣿⣿⠀⠀⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠛⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⢹⣿⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢿⣿⠟⠛⠻⠟⠋⠁⠻⠟⠩⣽⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠀⠀⠒⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⠀⢀⣠⣤⣀⠀⠀⣠⡤⣤⣄⠀⠈⢙⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣯⣾⣿⣿⣦⣼⣷⣿⣿⣶⡇⣷⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠻⡁⠻⢿⡿⠽⠃⠈⠳⠯⠵⠞⠁⢈⡟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡟⠦⣤⡤⢤⣶⣦⠤⠤⠤⣤⣖⠋⠙⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢰⡑⡐⠀⠩⢀⡔⡆⠂⠀⠈⣧⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣢⣿⣿⣷⣴⣾⣷⣶⠚⠋⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢿⣷⣜⣿⣿⣧⣼⣿⠀⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡠⢽⣿⣿⣿⣿⣿⣿⠀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⣸⣿⣿⣿⣿⣿⣿⠀⢡⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠿⠿⠿⠿⠿⠿⠿⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣤⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢠⣿⡇⠀⢸⠃⠀⠀⢸⣷⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣾⣿⣇⠀⣾⡄⠀⠀⢸⣿⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣾⡇⠀⠀⣿⣿⣿⡀⢸⣷⣀⣠⣿⡿⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣸⡿⠀⠀⠀⣿⣿⣿⣧⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⣿⡇⣰⠀⢠⣿⠃⠀⢂⠀⢻⣿⣿⣿⡄⠀⣿⡟⢠⡌⠀⠀⠀⠀⢿⣿⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⢀⣿⣿⠀⠀⢸⡄⠈⢿⣿⣿⡇⠀⡻⢀⣿⠁⠀⡶⠀⠀⢸⣿⣇⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⠀⠀⣼⡇⠀⠸⣿⣿⡇⠀⠁⣼⣿⠀⢸⡇⠀⠀⠘⣿⣿⠀⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣾⣿⣿⣦⣴⣿⠀⠀⠀⣿⣿⠀⠀⢀⣿⣿⠀⢸⣿⠀⠀⢠⣿⣿⡇⠀⠀⢸⣿⣷
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⠇⠀⠀⢸⣿⣿⣇⠀⢿⣧⣤⣾⣿⣿⣷⠀⠀⠘⣿⣿⡆
⠀⠀⠀⢠⣿⣿⠏⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⡼⠃⣼⠀⠀⠀⣿⣿⣿⣄⠀⠻⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣼⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣷⠀⠀⠀⢻⣿⣿⣿⣦⠀⠹⣿⣿⣿⣿⣤⣤⣾⣿⣿⡇
⠀⠀⠀⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⡄⠀⢲⡈⢿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⡀⠀⢰⣿⣿⡍⠻⣿⣿⣿⣷⡄⠀⠈⣿⡄⢸⡇⠈⢿⣿⣿⣿⣿⡿⠁⢹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⢻⣿⣿⣿⣶⣿⣿⣿⠃⠀⠙⣿⣿⣿⣿⣦⠀⢸⡇⣾⡇⠀⢸⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⡟⢀
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⡇⠘⠁⣿⡇⠀⠈⣿⣿⣿⣿⣿⣾⣿⡿⣿⣿⣿⣧⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⣿⣦⣴⣿⣿⣿⣿⣿⣿⠟⠀⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⡀⠀⠀⠀⣿⠟⠻⣿⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⣿⣿⣿⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⡀⠀⣿⠀⠀⢹⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⣴⣿⣿⣿⠀⢠⡇
⠀⠀⠀⠀⠀⣦⠀⢿⣿⣿⡿⠛⠻⣷⠀⠈⠁⠀⢸⣿⣷⣄⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣇
⠀⠀⠀⠀⠀⢹⡆⢸⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣆
⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⣇⠀⠀⣿⠀⠀⠀⣼⡿⠋⠙⢿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⡉⠀⢸⣿⣿⣿⡆⢰⡟⠀⠀⢠⣿⠀⠀⠀⣾⣿⠿⢿⣆⠀⣸⡿⢿⣿⡟⠁⢀⣼⣿⠿⠿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⡇⠀⢸⣿⡿⠋⠀⠸⡇⠀⠀⠘⠃⠀⠀⠀⣿⡇⠀⠀⢻⡆⠙⠀⢸⡿⠀⠐⠛⠋⠁⠀⠀⣈⢻⣿⡿
⠀⠀⠀⠀⣿⡇⠀⣼⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠈⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⣧
⠀⠀⠀⠀⣿⣧⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣹⡇
⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃
⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆
⠀⠀⠀⠀⣿⡏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⣿⡇⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣿
⠀⠀⠀⠀⠸⣧⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣴⠀⢸⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢹⡄⠀⠀⢀⣾⠃⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⣰⣿⡇⠀⠀⠀⢀⣾⡇⠀⠀⠀⢀⣿⡇⠀⣰⡿⠃⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⣼⣿⣇⠀⠀⣠⣾⣿⠁⠀⣿⣷⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣶⣶⠟⠻⠿⠿⠿⠿⠋⠁⠀⠀⠈⠛⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡿⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡄⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣵⡅⠀⢠⡀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢀⣿⣧⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣮⣻⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡠⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⣿⣿⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣷⢿⡿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣽⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣷⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠁⠀⢀⡙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣝⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣴⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠋⢺⣯⣿⡉⠀⠀⠀⠀⠀⢁
⠀⠀⠀⣠⠊⣠⢈⣵⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢾⣿⣿⣷⡄⢢⡀⠀⠀⠘⡄
⠀⢀⡜⠁⠀⠀⠜⠁⢀⠈⠉⠙⠓⠒⠲⠒⠒⠒⠦⣀⠀⠀⢨⠀⠀⠈⢻⣿⡿⠹⣦⡙⣦⣄⣀⣿
⢠⠋⠀⣤⣸⣶⠾⠿⠿⠿⠿⢿⣷⣶⣶⣤⣀⣤⣀⠈⠹⠶⠌⠀⠄⠀⣸⡿⠁⠀⠘⢷⣌⠛⠻⣿⣇
⣆⡼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⡶⠟⠃⢀⣴⣿⠃⠀⠀⠀⠘⣟⢦⠀⠘⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣶⣿⡿⠃⠀⠀⠀⠀⠀⢸⡆⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠦⠤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣶⠞⠇⠙⠳⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠶⢦⣄⣀⠀⢀⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⣬⣭⣭⣄⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠉⠉⠙⠛⠓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣯⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⠞⠁⢠⠎⢠⠃⠀⠀⠀⠀⠀⠀⡆⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⡴⢚⡋⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⢠⠏⠀⠀⡏⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠘⣏⠳⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠛⠉⠀⣀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣟⣀⣀⣀⣇⣸⣀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⣦⣄⠈⠑⠲⠤⣄⣀⣀⣸⡏⠙⣧⣞⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠉⠉⠁⣏⠹⣿⣿⣍⣿⡟⢻⠛⠛⢻⣿⣿⣟⣹⡏⣣⠀⠀⠀⠀⠈⠉⡙⠋⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢘⠦⣈⣉⡩⡞⠁⠘⢦⡀⠘⠿⣿⣿⢟⡵⠁⠀⠀⠀⠀⠀⠀⢷⡴⠞⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢠⡤⠀⠀⠀⠝⠲⢦⡤⠶⡋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢁⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠠⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡼⠀⡜⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⢀⣀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⠇⢠⠃⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠭⠝⠛⣛⠏⠙⠃⠤⠤⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡌⢀⠎⢀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢦⡄⡀⢀⠤⣀⡠⠢⠴⣅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⡀⠆⠀⡄⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣍⠀⡼⠀⠈⠁⠀⠀⠀⠸⡆⠈⢙⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⣧⠀⢡⡈⢆
⢀⠀⠴⠀⠠⡀⠄⣐⠭⠒⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⢿⠛⠙⣕⠦⣀⠀⠀⠀⢀⠒⡀⢀⡀⠀⠀⠀⠀⠀⠙⠿⢦⣄⣉⣒⣿⡶
⢁⣚⢀⠀⠠⠂⠁⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⠪⢍⣒⡖⠁⠌⠰⣪⠄
⠀⠉⠀⠂⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⠢⠤⣐⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣸⢸⠇⠄⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⡘⠓⠀⠌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠅⠀⣠⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢤⣀⣈⣉⣋⡩⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⣸⣿⡟⠉⠀⠼⣷⡄⠀⡔⠒⠰⢄
⠀⠀⠀⠀⢀⣤⢀⡀⠀⢸⣿⠀⣿⣿⣼⣧⣼⣿⣿⣿⡇⠀⠀⠻⠿⢁⠀⠀⢐⣂⠸⣇
⠀⠀⢀⣶⣾⣿⣿⣇⣠⣼⣿⠀⣿⣿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠊⠀⠀⠈⠀⠀⡈
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⢿⡿⢄⠀⠈⠷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠀⠀⠀⠀⣠⡴⢊⠥⠄⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣤⣤⣦⣴⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣦⣤⣀⣉⡔⣶⣾⡄⠱⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣶⠇⠀⠀⠀⠀⠀⠀⣀⡤⠠⢰⣾⣿⣿⡿⠛⣯⣵⡟⠋⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢿⣀⢀⣠⣤⡶⠊⢉⣡⣴⣶⣿⣿⣿⣿⡾⣿⣿⣿⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠖⠋⠹⣿⣿⣿⣿⠟⠛⠋⠀⠀⠀⠀⠉⠋⠀⠀⠀⠈⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⣞⣵⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⡴⡇⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣟⡵⢚⣛⣿⠋⠁⢀⣾⣵⡟⢠⡾⠋⢉⣉⠥⠞⠁⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢋⣽⠚⣡⠞⣵⣭⣶⣿⣿⠿⢻⣿⣏⣵⡟⠀⢀⡸⠗⣀⣴⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠈⠉⠉⣡⣾⣿⠟⠉⠉⠀⠀⠈⠛⠋⠉⠀⠀⠸⠶⣾⠟⢹⠀⢀⣠
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⢛⣉⣙⡓⢿⠟⣛⣛⣛⡳⠞⣛⣛⡳⡴⢛⣛⣛⣛⠻⣀⣴⠟⢱⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠁⣾⣿⠛⣿⣿⠀⣰⣿⣿⣿⡇⢠⣿⣿⠁⠀⣿⣿⠿⠟⢠⡿⠙⠖⠋⡸
⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⣿⣷⣤⠀⢠⣿⡟⣿⣿⠀⣼⣿⡏⠀⢰⣿⣿⣶⠄⣯⠀⣠⡶⠋
⠀⠀⠀⠀⠀⢠⣿⠃⣴⣶⠎⣿⣿⢇⣿⣿⣷⣿⣿⢠⣿⣿⠁⠁⣿⣿⡏⠀⢴⠋⣠⡿
⠀⠀⠀⠀⠀⠸⣿⡀⠻⠿⠿⠿⠋⠾⠿⠏⠸⠿⠿⠸⠿⠿⠿⠱⠿⠿⠿⠟⣸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠖⠻⠶⠶⠚⠷⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠞⠋

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⢿⣿⣤⣀⣄⣀⠀⠀⠀⠀⢙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣄
⢠⣄⠀⣿⣿⣿⡉⠙⢳⣀⠘⢧⣸⣿⣿⡿⡇⠀⠀⠀⠀⠙⢇⣿⣿⣿⡇⠹⡆⠀⠀⠀⠀⠰⢦⣀⣿⣿⣿⢻⡄
⠀⠈⠛⠋⠙⣿⣷⡀⠀⠙⠁⠀⠛⣻⣿⣷⠇⠀⠀⠀⠀⠀⠈⢛⣹⣿⣷⠀⠙⠃⠀⠀⠀⠀⠀⠙⠋⣻⣿⡇⠻
⠀⠀⢀⣤⣶⣿⣿⡇⠀⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠃⡀
⠀⠀⠙⠿⠿⢦⣿⣧⡀⠀⠀⠈⠛⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⠻⣇
⠀⠀⠀⠀⠀⠀⠹⠋⠻⣄⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡁
⠀⠀⠀⠀⠀⣤⣄⠀⠀⣽⠟⠀⠀⠀⠀⠀⠀⢸⡿⠂⠀⣾⣷⠀⠀⠀⠀⢨⣿⠆⠀⠀⣶⣶⠀⠀⠀⠀⠀⢈⣷
⠀⠀⠀⢰⡄⣿⣿⣤⣴⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣽⣿⣿⠶⣄⠀⠀⠀⢀⣄⠀⣽⣿⣶⣶⣤⡄⠀⠉⠉
⠀⠀⠀⠘⣷⢿⣿⣿⡇⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠀⠘⠓⠀⠀⠀⠹⣴⢿⣿⣿⠀⠈⢳⡀
⠀⠀⠀⠀⠉⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣥⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣻⣿⡇⠀⠈⠛
⠀⠀⠀⢰⣾⠿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠛⠛⣿⣿⡀⠀⠀⠀⠀⢺⣿⠛⠿⣿⣇
⠀⠀⠀⠀⢿⡀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⢧⣀⠙⢿⣄
⠀⠀⠀⢀⣼⣧⠀⣠⣤⡀⠉⠳⣶⠄⠀⠀⠀⠀⠀⠰⠾⠛⠀⠀⠀⠈⠙⢷⣄⣀⠀⠠⡿⢋⣀⡀⠙⢷⣄⡀
⠀⠀⠀⠈⠉⠀⠀⠸⣿⣆⠀⠀⠙⠁⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢿⣿⣁⡀⠸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠰⡆⣾⣿⣿⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠁⠀⠀⠀⠀⠀⠈⠻⠾⣿⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠐⠷⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⣿⣇⢀⣀⣴⣷⢦⠀⣴⣿⠿⢿⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⡏⠉⠉⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠹⠿⠟⠋⠀⠀⠀⢠⡿⠀⠀⠀⠻⠟⠛⠛⠛⢷⠀⠀⢀⣿⠀⠀⠀⠀⠙⠿⣦⣄
⠀⠀⠀⠀⢀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣄⣤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⣀⡠⠔⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠡⠀⠒⠒⠒⠊⠉⠀⠀⠀⠀⢀⣤⣤⣤⣀⣄⣀⠀⠀⠀⣀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⣤⣶⠶⠲⠶⢄⠐⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠘⡀⠀⠈⢀
⠀⠀⠀⠀⢀⡼⠀⢀⣠⣶⣧⣽⣿⣗⣿⣶⡄⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢦⡄⠈⢂
⠀⠀⠀⢀⡞⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⣦⡈⢆
⠀⠀⠀⡌⣰⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⢿⣿⣷⠀⢀⡀⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢻⡛⠛⠈⢣
⠀⠀⠠⢱⣿⣿⣿⣿⠿⠿⠏⢶⣀⣸⣿⣾⣿⣿⡇⠰⣿⣧⣴⣦⣌⣂⣄⣲⣦⣤⣤⡀⠀⠀⠛⣶⣄⠀⢣
⠀⠀⠀⢨⠿⠋⠁⣀⣤⠀⠀⢿⡿⠿⠿⠿⠛⠉⠀⠘⠛⠛⣉⣝⣿⠿⠛⠛⠛⠻⠶⢮⣄⠀⠣⡈⢿⣿⡄⠃
⠀⠀⠄⠁⠀⠐⢛⣻⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢁⣴⣶⣶⣶⣶⣶⣤⣤⣤⣁⡀⠳⡀⢿⣿⢸
⠀⠀⠀⠀⠀⣀⡾⠿⢀⠄⢀⠠⢘⣃⠐⣄⡀⣤⡀⠤⡞⠂⢟⢻⣿⢟⣷⣿⣿⣿⣿⣻⣿⣿⣿⡆⠱⠈⣿⢸
⠀⠸⢠⢎⣡⣵⣾⣿⣿⡆⢰⠀⠀⠏⠀⢿⠁⠸⠇⠀⣿⢲⣌⢸⣿⢸⣿⣿⣿⣿⣿⠃⣠⣿⣿⠻⠿⣠⣿⢸
⠀⢀⢡⠞⢿⢿⣿⣿⠁⣅⣈⣤⣴⣶⣶⣾⣷⣶⣿⣶⣦⣤⠛⣯⡻⣮⣻⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⡀⡀
⠀⠘⡸⣷⣌⡤⢿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⣀⠗⢸⣿⣿⣷⣶⣿⢿⠻⣿⣭⣿⣿⣿⠃⠇
⠀⠀⠑⢌⣿⣿⣿⣿⣷⠾⢼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⣿⣿⣧⣿⣶⣿⣿⣿⣿⣿⡜
⠀⠀⠀⠀⠉⣽⠋⣀⣿⣏⣹⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠃
⠀⠀⠀⠀⠀⠑⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢰⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣛⣿⣿⣿⡿⠿⠿⠿⠿⡿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠈⢆⠘⣿⣿⣟⠉⠁⠈⠉⠛⠛⠿⠿⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣱⣿⡿⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣄⣾⣿⡿⢱⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⣿⣿⡗⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠐⢶⣽⣿⣿⠇⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣥⣀⣹⡆⠀⠀⠀⠀⣀⠄⡤⠾⡁⠰⡄⣸⣯⣿⡟⣼⢟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⡄⢰⠙⡓⢲⠀⢸⠁⢁⠀⣶⠀⣸⣶⣯⣿⣿⣏⣰⡏⣽⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⣾⣄⠷⡈⣄⢸⣂⣸⡧⣿⣝⠙⠋⠻⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠋⠈⠸⠟⢹⡇⢹⡍⢰⣿⠉⠓⣠⢜⣡⣮⣿⣿⣿⣯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠐⠆⢠⣈⣷⣈⢳⣘⣿⣾⣿⣿⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠉⠿⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⣿⣟⡭⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡤⠤⠴⠦⠄⠀⠈⠅⠒⠁

⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠒⠀⠉⠉⠉⠉⠄⠂⠈⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⡀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⠈⠀⠰
⠀⠀⠀⠀⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢢
⠀⠀⠀⠀⠀⢀⠞⠀⢀⡒⢉⡁⠀⠀⠀⠀⠀⠀⠐⠋⢑⠂⠀⠀⠀⢀⠀⠀⢃
⠀⠀⠀⠀⠀⢸⠀⢠⠋⣁⣈⣙⣄⠀⠀⠀⣠⣊⣁⠀⠈⠑⠀⠀⠀⢨⠀⠀⠸
⠀⠀⠀⠀⠀⡇⠀⠻⠋⠿⣿⢬⠃⠀⠀⠀⢋⠀⣿⣿⣋⣿⠃⠀⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠁⠐⡇⠀⠀⠘⠶⣬⣭⠟⠃⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣤⣀⣀⣀⣀⣀⢤⣤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠄⡠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠂⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⠀⠀⠀⠀⠣⣄⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⡼⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⣠⠃⢠⡤⠀⠋
⠀⠀⠀⠀⠀⠀⡼⠁⢠⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠰⣄⠀⡄⠛⢦⠋
⠀⠀⠀⠀⠀⡸⠀⠀⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⠀⠀⠘⠞⠀⠀⢀⠇
⠀⠀⠀⠀⠀⡇⠀⠀⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢳⡀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠣⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⢦⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⠒⠂⠀⠀⠀⠀⠀⢤⣤⣀⡀⣤⠤⠐⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠟⠉⢳⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⣺⠤⣤⠤⠤⠤⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠀⠉⠃⡀
⠀⠀⣠⠄⠛⢄⠲⠀⠆⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⠀⠠⠈
⠠⠊⠀⠈⠠⡀⠈⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠉⢀⠀⠀⠉⠑⢄
⡆⠀⠀⠀⠀⢰⣠⠼⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡐⠂⠀⠀⠀⠀⢀⡄
⣉⣫⣤⣌⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣠⣤⣤⣤⣬⣁⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀
⠀⠀⠀⡀⠹⣿⣿⣄⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⡟⠀⣶⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡏
⠀⠀⠀⢻⡀⣾⣿⣿⣿⣿⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣦⣹⡄⠀⠀⠀⠀⠀⢸⣶⠉⣿⣿⣦⣀
⠀⠀⠀⠘⣿⡟⠹⣿⣿⣿⡇⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⠙⠿⡷⠀⠀⠀⠀⠀⠀⢹⣦⣿⣿⡿⠻⣷⡀
⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢹⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣦⠘⠃
⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠻⣿⡿⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⢰⣿⠁⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⠈⠛⢿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠿⣆⣀⠀⠀⠀⢀⣀⣠⣾⠿⠛⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⢷⣶⣦⡀
⠀⠀⠀⠀⠀⠰⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠘⠋




⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⡀⢘⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣷⣄⢹⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣿⣿⣶⣦⣄⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠛⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠋⠹⣿⣿⣿⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⠘⢷⠀⣾⣿⣿⣿⡏⠙⠛⣷⡀
⠀⠀⠀⠐⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⣿⣿⣿⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠙⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⠙⠁⠀⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷
⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡛⠻⣿⣿⣆
⠀⠀⠀⠻⣿⣿⣧⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣼⡿⣿⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣧⡀⠙⠿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠛⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⢰⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢢⣿⣿⣷⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠏⠘⣿⡉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢋⠁⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⡀⠴⣤⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⠛⠉⠀⠀⠹⡧⠀⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣷⡀⠀⠀⢀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣧⣄⡀⠀⠀⠘⠦⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢘⡠⠀⣼⣿⣯⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠰⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢰⠐⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠈⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣧⣀⣀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣯⣴⣤⣽⣥⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⡼⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⠇⠀⢠⠟⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡆⠀⢰⠃⣸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⣀⣤⡄⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡏⠀⠸⣄⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡸⢃⡎⠀⡴⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡇⠀⠀⠈⢧⠈⡇⠀⠀⣆⠀⠀⠀⠀⢸⠇⠇⠈⣧⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣄⠀⠀⡇⠀⠀⠀⠈⠷⠃⠀⠀⡿⣇⠀⠀⠀⡾⠀⠀⠀⠘⣇⠀⡠⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡆⠀⣧⠀⠀⠀⠀⠀⠀⠀⡰⠃⡟⠀⠀⢰⣇⡔⠀⠀⠀⣿⡼⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⣸⠀⠀⠀⢰⣦⡀⢰⠁⠀⣇⢰⣿⠀⠉⠀⠀⠀⢰⢫⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⣠⠏⠀⠀⠀⢠⠟⢇⡼⠀⠀⢹⣼⠈⢣⡀⠀⠀⠀⠃⣸⠇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠉⠀⠀⠀⢀⡞⠀⠋⠁⠀⠀⠈⠁⠀⠀⢧⠀⠀⠀⠙⠉⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠓⢦⢄⠀⢰⠆⡄⠒⠒⢧⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⢀⠔⢂⣾⠀⠀⠘⣦⣿⠀⠀⠀⢿⠉⢴⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣩⠜⠁⠀⢸⡇⠀⠀⢸⣼⡇⠀⠀⠀⢸⣆⠀⠉⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠰⠞⠁⠀⠀⠴⣻⠁⠀⡤⢂⠇⣷⠀⠀⠀⠘⣟⡄⠀⠀⠪⡻⣇⠀⠨⠉⠛⠓⠒⠠⢄⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠁⠀⢀⣠⠞⠀⠀⠀⠀⣠⢊⡟⠀⠀⡆⢸⠀⢸⠠⠀⠀⢀⢿⢢⡠⠀⠀⠀⠙⢦⣀⠀⠀⠀⠈⠀⠀⠀⠉⠱
⠀⠀⠀⠀⡤⠊⠁⠀⠀⠀⢀⡾⠋⠀⠀⠀⢀⣤⡞⠁⢸⡇⠀⠀⣠⡇⠀⠈⡇⠆⠀⠸⡸⠀⠑⢄⠀⠀⠀⠀⢽⣍⠑⠒⠀⠀⣀⣀⣄⡳⠂
⠀⠀⠀⠘⢆⢂⡀⠄⢒⡾⠋⠀⠀⠀⠀⠔⢩⠞⠀⢀⡼⠀⠀⠠⣿⠁⠀⠀⢃⠀⠀⠀⢧⡆⠀⠈⡂⢀⠀⠀⠀⠪⡳⣄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠉⢀⡔⠁⠀⠀⠀⡠⠂⠀⡴⠃⠀⠀⢫⠇⠀⠀⠀⢻⠀⠀⠀⠸⠀⠀⠀⠸⢲⠀⠀⠸⡌⡳⢄⡀⠀⠈⠪⠳⡀
⠀⠀⠀⠀⠀⠀⠹⡠⡀⢈⡡⠊⠀⢀⡾⠁⠀⠀⠔⠹⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠡⠀⠀⠀⠇⠀⠀⠈⠀⠀⠩⡉⠀⡀⠠⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠑⠡⠘⠋⠀⣷⠂⠀⠀⢤⠇⠀⠀⠀⠀⣧⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⠺⣔⡢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠷⠊⠀⠀⠀⠀⠀⠸⣤⢂⠅⡄⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠭⠵⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣤⣶⣿⣿⢿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢄⣀⠀⠀⠤⢤⡵⣫⣿⣿⣿⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⢀⣤⠴⠖⠒⠚⠋⣑⠉⠛⣒⣶⣶⣾⣧⣤⣤⣬⡩⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⢟⣋⠁⠀⠀⠀⠉⠉⠛⠛⠉⠙⠓⠦⠀⠠⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡩⠛⠁⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣟⠁⠛⠿⠃⠀⠀⢠⣶⣿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢸⡟⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠾⠼⣧⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠛⠉⢉⡴⠶⡿⣤⣿⣿⣿⣿⣿⠛⠟⠋⠘⣿⣿⣿⡄⢠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⣠⣧⡈⠀⢾⣶⣿⡟⠋⠁⠉⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢀⢸⣿⣿⣿⣾⣶⣬⣕⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣴⡾⠟⠃⢸⡌⢿⣿⡋⠛⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠁⣀⣀⣤⣾⣟⡲⠭⠛⠓⠦⠙⢿⣟⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⣫⠞⠡⠖⠛⠛⣻⣿⡿⠋⠁⠀⠀⠀⠈⠉⠑⢈⣩⠤⠽⠿⢟⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠶⠛⣛⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⣚⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢞⣀⣠⣤⡶⠟⠋⠀⠀⠀⢀⣀⣀⠤⢀⣠⡤⠶⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡓⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠤⢤⡶⠋⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠠⣤⣶⡖⠒⣠⠴⠋
⠀⠀⠀⡈⠀⡴⠋
⠀⠀⢰⠃⣞⠁
⣀⣀⣙⣦⣨⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣯⣭⣭⣽⣿⣭⣭⣭⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⠉⠙⠋⠉⠀⠘⡸⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⢿⣿⣿⡿⠁⠀⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠈⠻⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣧⡀⠀⠀⠀⠀⠀⢀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣷⡄⢸⣿⣿⣿⣿⣿⣿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⡹⣿⣿⡿⠟⠁⣾⣿⣿⣿⣿⣷⠈⠻⢿⣿⣿⢏⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⡇⠿⠋⠀⠀⠀⢟⣭⣷⣾⣭⡻⠀⠀⠀⠙⠿⢸⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿



⠀⠀⣀⠀⡀⢀
⣿⣏⢹⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⠋⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⢀⡿⠃⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⣄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣿⣔⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⡻⣿⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⣿⣷⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⣿⡟⠿⣆⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣭⣿⠿⠽⠿⠿⠾⠿⠷⠤⠤⠤⠠⣤⣤⣤⣤⣤⣬⣿⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⡤⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣒⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠛⠉⠀⠀⠀⠀⢀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠛⠓⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠏⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠈
⠀⢀⡟⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠒⠈⠉⠉⠉⠙⠒⠢⣄
⢠⠟⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠈⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠈⢳⡆⠀⠀⠐⠒⠉⠉⠉⠀⠀⠀⠀⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠄⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠀⠀⠉⠒⢲⡶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⡀⠀⠀⠉⠉⠒⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠐⠻⣍⠉
⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠄⠀⠀⢀⡴⠒⠲⣌⠢⠀⠀⠑⠲⢄⡀⠀⠀⠀⠉⠁⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢄⣀⡼⠀⠀⠀⠀⠀⢀⣈⠑⠄⠀⠀⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⣹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢠⠀⢠⠀⠀⡆⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠇⠀⠜⠀⠘⠀⠈⠁⠐⠁⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠹⠀⠀⠀⠀⡀⢀⡇⠀⡴⠋⠀⢀⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⡴⠁⢸⠃⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⡎⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠱⠀⠀⠀⢀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠣⠀⠀⠀⠀⢘⠄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡠⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠙⡆⠀⠀⡜⠀⠈⠀⠀⠀⠀⠒⠉⠀⠀⠀⠉⠉⠁⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠱⠀⠈⡇⠀⠀⣠⠞⠀⠀⠀⠀⠐⠢⠤⠀⠀⠀⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⠤⠤⠄⠀⠀⠀⠀⠀⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢸⡆⠀⠠⠒⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠋⢀⣀⠀⠀⠐⠁⠀⠀⠐⡄⠀⠘⠉⠉⠃
⠀⠀⠀⠀⠀⠀⢠⠒⢦⡽⠀⠔⠁⢈⠇⠀⣠⠞⠛⠒⠋⠁⠀⠔⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⣁⣄⣀⡬⠇
⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠈⢁⡀⠀⣠⠞⠉⠛⠉⠁
⠀⠀⠀⠀⡠⠊⢀⠞⠁

⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⡆⠀⡆⢰⠠⠀⡆⡐⡆⢠⠐⠀⠀⣄⠀⠀⢌⠀⡆⢰⣐⢠⠀⠂⣠⡂⢠
⣤⣤⣤⣤⣤⣤⣶⣦⣷⣮⣴⣤⣧⣧⣤⣶⣾⣴⣶⣶⣦⣴⣶⣤⣧⣼⣤⣮⣶⣦⣦⣴⣶⣶⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣧⠀⠀⢠⡀⠤⢠⣤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⡟⢉⣉⣁⣼⣦⠀⠀⠀⠀⡀⠀⠀⠈⢯⣿⣿⣿⠇⠀⠀⢿⣷⠀⢸⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠉⠀⠘⠿⢡⣿⣿⡿⠿⠟⡀⠀⠀⠀⠁⠀⢀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠀⠀⠈⠂⠀⠀⠀⠘⢿⡿⢋⣴⣾⢿⠃⠀⠀⡀⠀⠀⠀⢂⠀⠄⠀⠀⠀⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠛⠓⠂⢠⠀⢰⠀⢀⡀⠀⢸⡄⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠲⡄⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠀⠀⣑⠀⣠⣂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠈⠁⠁⠁⠙⠐
⠀⠀⠓⠀⠀⠠⠀⠀⠐⠀⢀⠐⠂⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡹⠀⡏⠉⣳⣤⣤⣤⣤⣤⣤⣴⣇⠀⠀⠀⢀⣤⢀⠀⠀⠀⢀⣠⢤⡀
⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⡈⢠⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠆⠀⠸⠿⠟⠁⠻⠛⠘⠻⠿⠃
⠀⣠⡄⢠⣶⣄⠤⠀⣠⡇⠀⠀⠀⡀⠀⡴⠒⠀⠀⠀⠀⢠⣄⠀⠁⠀⣦⣾⣿⢯⣿⣝⣿⣿⣽⣯⣿⣿⣿
⠀⢿⣧⣸⢏⣴⣶⠀⠸⣿⠀⠀⠀⠀⠀⠁⠀⣶⡄⢶⡶⠈⠋⠀⠀⠀⠀⣿⣿⣮⣿⣽⣏⣿⣽⣿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⣤⣭⣥⠀⠙⠉⠀⠀⢻⣇⠀⣠⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣀⣔⠂⣄⠀⠀⠀⡀⠀⠀⠀⠸⣶⣾⣧
⠀⢠⣍⣉⡀⠀⢀⠠⠀⠊⠀⠙⠦⡀⠀⠈⢃⡀⠀⣀⠀⠉⢀⠄⠈⠑⣄⡀⠄⠩⢿⡿⠋⠈⢿⣿⣯⡑⠊⠀⠀⢠⢙⠆⠀⠀⠀⠀⠀⠀⠠⠾⢿⣿⡿⠟
⠀⠀⢉⠛⢻⠔⠃⠀⠀⠀⢀⠀⠀⠈⢆⠀⠀⢡⢰⠙⢏⢆⠘⢀⡔⠋⠀⠀⠀⠀⠀⠈⠱⡄⢸⣿⣿⡐⠂⠈⠁⠀⠂⠀⢸⠑⠠⠄⠒⠂⠠⢄⡈⠻
⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⢔⠀⢩⠈⡆⡊⠀⢀⡀⠀⠀⠀⢀⡀⠀⠐⡾⠛⠛⠣⠄⡠⠊⠙⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠄
⠀⠀⠘⠄⠀⢀⡠⠀⠚⢧⡄⠀⠀⠀⣀⣡⣤⣰⣿⠣⡀⢎⡟⠀⠀⠙⠚⢀⣲⡂⠘⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⣂⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣃⣠⣾⣿⣿⡿⠛⢿⣷⡌⠉⢃⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⡠⠀⠐⠿⠂⠀⠀⢀⠹⡀⠀⠈⠀⠀⠸⠂⠀⠠⡦⠀⠈
⠀⠀⠀⠈⠦⡈⠀⠀⠀⠀⠀⢹⣿⢁⡙⣿⡇⠴⠀⣿⣿⠀⠄⢵⠀⡀⠀⠀⠀⠀⠀⢀⣤⠊⠻⠃⠀⠀⠀⠀⢰⣿⣷⣟⢄⡀⠀⠀⠈⠀⠀⠀⠀⠀⡈
⠈⠿⣌⡐⢴⠁⠉⠂⠁⠀⠀⠙⣿⡈⠁⠎⠉⢂⢀⣿⣿⢘⡄⠀⠱⠁⠉⠁⠀⡀⣈⢹⣄⣀⠀⠦⠀⠀⠀⠀⠨⣿⠟⠋⠥⠀⠈⠁⠢⣤⣤⣤⡤⠊
⠀⠀⠀⢑⠀⡲⠉⣰⣤⣶⣶⣶⣼⡿⠚⠄⠀⠀⠛⠋⠛⠀⠀⠀⢠⠦⡤⠊⠁⠀⢈⠀⠀⠀⠈⠐⢆⠉⠉⠲⠊⠀⠀⠀⠀⠀⠀⠈⠑⠸⣿⣿⠃
⠀⠀⠀⠀⠈⣣⣾⣿⣿⣿⡿⠟⠿⣿⣄⠄⠀⠀⠀⠀⠀⠑⠂⠈⠈⠐⡃⠀⠐⡆⠁⠀⠀⠀⠀⠀⠀⢡⢀⡟⠀⠀⠀⢀⢸⡶⠀⠀⠀⠀⣟⠉
⠀⠀⠀⢠⣶⠛⠟⡿⠋⢹⠁⠀⣠⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠇⠀⠀⠀⠀⠀⠈⠂⠀⠓⡀⠀⠀⠀⠈⠛⠗⠀⠀⠀⠀⠈⣕⢀⢄
⠀⠀⠀⣼⣿⣷⣾⡇⠀⠈⠀⠀⣿⡟⠛⣿⡧⠀⠀⠷⠀⣀⡀⠿⠃⠀⠀⢀⠀⢰⡄⠀⠀⠀⣶⠀⠀⠐⢀⣼⠦⠼⡆⠀⠀⠀⠀⠀⡠⠄⣀⠏⠉⠀⠇⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣶⣿⠧⣀⠀⠀⠀⠈⠀⠀⠀⠀⣤⠁⠀⠀⠁⠀⠀⠀⠀⠀⡠⢳⣶⣅⠀⢀⢐⠟⢦⣾⣗⠊⠄⠀⡨⢦⠈⠁⠀⠑⡀
⠀⣄⢣⡙⡖⠉⠻⠿⢿⣿⣿⣿⠿⠿⠋⢁⣤⣄⣉⠖⠀⠀⠀⠲⡂⠁⠀⠑⠂⢤⡄⡀⡀⣤⠄⢚⠀⠈⣿⣿⠀⣿⠿⢄⡸⠿⢇⢩⣷⡾⠀⡎⠀⠁⠘⠀⠓
⠀⠰⠤⠼⠦⣄⣴⣆⠀⠀⠀⠀⠠⣶⡀⠈⠁⣹⡟⠀⠀⠀⠀⠀⢱⠀⠀⠀⣠⠎⠀⠀⠀⠈⡄⠀⠁⡄⣿⣿⢰⠁⠀⠀⠁⠀⠀⣿⣿⡇⠸⠀⠀⠀⠀⡰⠉
⠀⠀⠚⠀⠤⠚⠛⢿⣿⣷⣤⣽⣿⣿⠷⠶⢾⡟⣃⠀⠀⠀⠁⠀⡈⠒⠀⢴⠡⠀⢰⠀⡄⠀⢷⡜⠀⣀⢻⣿⠀⢢⣀⠀⠀⢀⠔⣿⣿⢀⡗⠤⠄⠀⠈
⠀⠀⠀⠈⢄⠀⠀⣸⠟⠛⣿⠟⠻⣟⠀⠀⣸⠁⠝⠁⢳⡔⠃⢶⠉⠙⣴⠉⡐⠃⠰⡴⠓⢺⠉⢒⠆⠈⢺⣿⡀⢸⣿⠁⢲⣿⢀⣿⡏⠘⠀⠀⠶⡞⢀
⠀⠀⠀⠀⠀⠉⠀⠑⠒⠒⠛⠒⠒⠙⠲⠚⠁⠀⠙⠀⠈⠉⠐⠘⠲⠖⠛⠀⠚⠦⠜⠓⠴⠚⠃⠘⠀⠀⠀⠀⠉⠉⠉⠁⠛⠛⠘⠛⠃⠃⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣀⣠⣤⡴⠞⠛⠉⠛⠛⠶⣤⡀⠀⠀⠀⠀⢀⡀⠤⠋⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⡄⠀⠀⠀⠀⠈⠛⠒⠀⠀⣠⡁⠀⠀⣸
⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⡿⠷⠾⠿⣭⣭⣽⣿⠿⠿⠿⣿⠋
⠀⠀⠀⠀⠈⠛⠶⠶⣦⣤⣤⡶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⣠⣼⠟⠀⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡶⠋⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⢿⠟⠙⠣⢄⣠⣄⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⡰⠃⠀⠀⠀⠀⠀⠈⠙⣷⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢖⣒⣋⣀⣈⣀⣉⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⣿⣿⣶⢿⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣰⣟⢩⣭⢿⣷⠋⣶⣾⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠞⣁⣴⣿⡿⠛⡯⢚⣿⣿⣿⣟⣻⣻⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣰⣿⣿⣿⣿⣿⣶⣿⡿⣬⡟⠛⠛⠟⠛⠦⠐
⠀⠀⠀⡀⠀⠻⢱⠜⣿⣿⣿⣿⣿⡿⢿⠋⣽⠛⠓⠃
⠀⠀⠀⠸⠷⢸⣿⣼⣿⣿⣿⣿⡿⢶⠖⢛⡇
⠀⠀⠀⠀⠀⠹⠿⣿⡿⢿⡛⢿⡷⣬⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠈⠁⠀⠀⠈⢻⣷⡠⢀⣀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠤⠄⠀⠀⠚⠛⠚⠻⠿⠶⠿⠿⠿⠷⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⢲⠶⠞⠛⠉⠉⠻⣏⡉⠉⠉⠛⠛⠷⢶⣼⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠛⠶⣤⣄⣤⣴⡾⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⠁⣇⠀⠀⢠⠏⣾⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠾⢿⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣱⣿⡟⠀⠀⢸⠀⠀⡞⢸⡏⠀⠀⠀⠀⠀⠈⠙⠻⣶⢦⣀⠈⠑⠒⠺⡟⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⣼⣿⣿⠁⠀⠀⠘⡇⢰⠃⣸⡇⠀⠀⢰⡀⠀⠀⣀⣀⣈⣦⣿⣷⣦⣠⠴⠧⢴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢸⣿⣿⡿⢄⠀⠀⠀⠘⢾⠤⢾⣄⠀⠀⠈⣿⡿⣿⠏⠁⠀⠀⠀⠀⢨⠃⣾⣿⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣿⣿⣿⣇⠀⠙⠢⣄⡀⡆⠀⢸⡿⠀⢀⣾⠋⣼⠃⠀⠀⠀⠀⠀⠀⣼⢠⡈⠁⣻⣁⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢰⡿⠿⢻⣿⠀⠀⠀⠀⠈⡟⠒⠺⣧⡀⣾⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⣿⡼⢻⡾⠟⣛⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⡾⣰⡏⢹⡆⠀⠀⠀⣀⣧⠀⠀⠈⢻⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣸⡷⢟⣉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⡾⢱⡿⠀⠀⢻⡄⠀⡜⠁⢸⡉⠢⡀⣾⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢋⠴⠋⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⣿⣧⣶⣶⣾⠿⣶⠁⠀⠀⢧⠀⠈⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⡰⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⠿⠛⢉⣿⡟⠀⠈⠳⣄⡀⠈⢆⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⢠⣮⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡴⢾⢃⣾⣿⣡⣤⣶⣶⡎⠛⠶⣬⣧⡀⠻⣦⣀⠀⢀⣀⣴⠾⠋⣀⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⡟⣼⣿⣿⡿⠟⡋⣽⣇⣤⡤⠤⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⠟⣡⡶⢻⠃⠟⢋⣥⢞⡿⢁⣾⡿⠿⠿⠛⢛⣫⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢃⡾⠋⠀⢸⢀⡴⠋⠀⣼⢁⣤⡴⠶⠶⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⡼⠋⠀⠀⠀⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣭⣥⣤⣷⡾⠿⠃⠀⣠⡖⣠⡶⠂⣠⣶⡾⠿⣿⣿⠛⣡⡟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠾⢿⣿⠟⣱⠟⣽⠿⠾⣿⣂⣠⣤⣴⣿⣾⣿⡇⣰⡿⣡⣾⢫⡽⠚⠋⠉⠀⢀⡖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⡉⣴⣾⠋⣁⡼⢋⣼⣵⣾⣿⣿⣿⡿⠟⣩⣿⣟⣥⣾⡟⢠⡿⢛⡬⠛⠁⣠⣶⣶⡿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢡⣾⣦⡿⠿⠿⠿⠿⠿⣿⣿⠿⠿⢿⣦⣾⣷⣿⣿⣿⣿⣉⣴⣿⠀⠿⣤⣴⣾⡿⢹⡇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢁⣿⣿⡟⢠⣶⣶⢠⣶⣶⠈⣠⣶⣶⣦⡌⢡⣤⣤⣤⣤⡌⢻⣿⠟⣣⣴⣶⣾⡭⣂⣼⠇⢰⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢸⣿⣿⠃⣼⣿⡏⣼⣿⡏⣸⣿⡟⢹⣿⡇⠘⢻⣿⣿⠛⢃⣼⠇⠘⠿⢟⣱⡏⣾⢻⣁⣠⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠈⣿⡿⢀⣿⣿⣿⣿⣿⠃⣿⣿⠇⣿⣿⡇⠀⣾⣿⡇⢸⣿⣷⣤⣤⣶⡿⠋⣱⢟⣼⣻⡭⣢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⣼⡇⣸⣿⡟⣹⣿⡟⢰⣿⣿⢰⣿⣿⠀⢠⣿⣿⠁⣾⣿⣿⣿⣿⣿⡁⢈⣡⠞⣩⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⢀⣿⣿⠇⣿⣿⠇⢸⣿⣷⣾⣿⠇⠀⢸⣿⡟⠠⣿⣿⠿⠿⠿⠿⣿⡿⠋⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣌⣉⣉⠀⣩⣽⣶⣦⡍⠉⢩⣴⣶⣶⠈⢩⣷⣶⠈⠁⣶⣶⣶⣶⠈⣿⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡇⢸⣿⡟⢹⣿⠇⢀⣿⣿⣿⣿⠀⢸⣿⡿⠀⢠⣿⣿⠉⠉⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡇⠻⣿⣿⣦⣄⠀⣼⣿⠏⣿⣿⠀⣿⣿⡇⠀⢸⣿⣿⣿⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢡⣤⣌⢻⣿⣿⢰⣿⣿⣴⣿⣿⢰⣿⣿⠀⠀⣿⣿⣇⣀⠰⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢼⣿⣧⣼⣿⢏⣿⣿⡏⢹⣿⣿⣸⣿⣿⣿⠣⠿⠿⠿⠿⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⣙⠛⣋⣡⣌⣉⣉⣤⣤⣤⣤⣤⣤⣤⣶⡶⡶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠙⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣝⣴⠶⠀⠐⠻⢷⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠺⠀⠀⠀⢈⡔⢢⠀⡴⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡤⠤⠼⣦⢸⠀⣧⡀⣨⠷⠒⠒⠀⠐⠂⠄⠀⠀⠠⠒⠋⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠉⢹⠀⠀⠀⠈⠧⠤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⡳⢤⣀⡐⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠐⠒⠀⠐⠀⠀⠸⠤⠄⠀⠠⢏⠉⠉⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢶⣚⣠⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠉⠀⠀⠀⠂⠈⠁⢈⢧⡀⠀⠀⠉⠀⠈⠙⠒⠦⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡶⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠓⡤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⠞⠳⢄⣀⠀⣀⣠⠴⠋⠳⣄⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⣀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠿⠇⠀⠀⠀⠉⠉⠱⠾⠛⠙⠶⠶⠶⠶⠶⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢷⠟⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡄⢠⡞⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠘⠳⣶⠟⠓⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⣿⠀⠀⠀⠀⠘⠋⠈⠉⠛⠛⠀⠀⠀⠀⠀⢀⣤⣄⣀⠙⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⣀⡀⢰⡏⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠦⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⢀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⣿⣿⣷⣶⡶⠿⠋⠉⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢇⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠙⣿⠏⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣠⣶⠿⠛⠛⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⢸⠂⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⣤⣄⠀⠀⠀⠀⠀⣿⡇⠀⣸⡿⠁⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠿⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⠀⢀⣷⡀⠛⠋⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⣴⣄⠀⠀⠀⢰⣿⣿⣿⣿⣶⣶⣾⣷⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠂⠀⠀⠐⠀⠀⠉⠁⠐⠒⢠⣤⠾⠟⠉⠀⠈⠉⢻⣷⡀⠛⠃⠀⠀⣠⡾⠋⠙⠛⠛⠛⠛⠋⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠠⡄⠀⠀⠙⠿⢷⣶⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⢀⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣶⣤⣤⣄⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠈⠛⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢶⠀⠀⠀⠀⢰⣶⣦⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⣤⣀⡈⠀⠀⠀⠀⢠⡄⠛⣦⣤⠤⣤⣤⣤⡤⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠶⠄⠛⠻⣿⡏⠙⠉⠀⠀⠀⠾⣧⠤⢀⣀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢠⠆⢰⠀⠁⠀⠀⠀⠀⠈⠀⢈⠄⠈⡟⠀⠀⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠀⠘⢣⡈⠓⠀⠠⣤⣤⢀⡤⠴⠛⠀⣴⠃⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⣤⡤⠤⠤⣤⣤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣤⠞⠉⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢘⠀⠘⠓⢤⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⣸⠏
⠀⠀⡀⠴⠾⠳⠶⠀⠀⢣⡄⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠟
⠀⠈⡁⠀⠀⠀⠀⣠⣄⠈⢳⣄⡀⠀⣀⣀⡴⠾⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿
⠀⠘⢳⣄⠀⠀⠀⠀⣽⡆⢀⠙⠃⠀⠀⠀⠀⠀⠀⠀⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠹⣿⣟⠉⠀⢠⡾⢿⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠛⠢⠤⠤⢀⣀⣀⣀⣀⡀⠀⣠⡟⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠈⠙⠻⠟⢀⡀⠸⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⢸⠁⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠛⠓⠒⠐⠶⠖⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⡄⠀⠠⠀⠀⠀⠀⠀⠙⠂⣤⡄⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠀⠀⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠘⠷⣤⣼⣦⠀⢙⣦
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⣷⡶⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠉⠉⠁⠈⠉⠉⠻⢿⡄⠾⢷⣀⠀⠀⠀⢀⣠⣿
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⠛⢠⡶⠟⠃⠀⠉⣦
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⣁⡴⠶⠆⠠⠾⠉⠙⠁⠀⠀⠀⠀⠀⠀⡟
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣠⣤⣤⣀⣀⣀⣤⡤⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣾⣿⣿⡄⠀⠀⢠⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⣷⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠸⣧⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⣼⠁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢠⣿⣿⠃⠀⠀⣼⡟⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⢀⣾⣿⣿⠀⠀⣼⣿⠇⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣴⣾⣿⡟⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⣿⣿⣿⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢀⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠟⠀⠀⢀⡇⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠛⠉⠀⢀⣾⣿⣿⣿⠟⠁⠘⣿⣿⣿⣿⠏⠀⠀⠀⠀⣸⡇⠀⠀⢿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⠀⠈⣦⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣿⣦⠘⢷⡀
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢿⣧⡀⠻⠆
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⡆
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⣿⣿⣿⡀
⢻⣿⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⢰⣿⣿⣿⣷
⠘⣿⣿⣿⣿⣦⡀⣤⣴⣾⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠘⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣆⢠⣤⣶⣾⣿⣿⣿⣿⣦⣲⣤⣤⣴⣾⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⡿⠟⠋⠁⣾⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡆⢹⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢻⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⡏⣿⣷⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠇⠘⣿⣿⣿⣿⣿⣿⠂⣤⣉⡛⢛⣉⣡⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⠛⠛⠋⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⣙⢻⡋⢩⡛⢛⣟⠋⣿⡟⣻⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠢⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠢⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠏⢀⠀⣀⠤⢐⡾⠋⠉⠉⠉⠉⠁⠀⠒⠒⠀⠤⢈⡇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⡘⠀⡾⠋⠀⠀⢀⠔⣀⡍⠑⠂⠀⠀⠀⢀⠆⣭⡌⡑⢦⠉⠒⢤⡀⠀⠀⡇
⠀⢰⠊⠉⣺⠃⠀⠀⢀⣃⠼⠿⠷⠿⠦⠇⠀⠀⠘⠚⠛⠛⠛⠒⠃⠀⠀⣯⠀⠀⡇
⠀⠘⣤⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⡇
⠀⠀⢸⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⡟⠉⠳⡄
⠀⠀⠀⢣⡀⠘⢆⠀⠀⠀⠀⠀⠀⢻⡒⠠⠤⠤⠄⠒⣩⠁⠀⠀⠀⠀⡸⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠙⢦⣈⠳⣄⡀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠚⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢐⠀⠲⡀⢀⠔⢀⡠⢊⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠤⣀⣀⠀⠀⠀⠒⠀⠀⢀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠤⠆⡀⠈⠓⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⠙⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠓⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⢲⡒⠁⠀⠀⠑⣲⠒⠒⠂⠤⠤⢀⡀⢀⣀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠰⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⠴⠦⠤⠜
⠀⠀⠀⠀⠀⠀⠀⢰⡥⠤⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⣧⢤⡤⠤⠤⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡘⠀⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠁⠀⠀⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⡌⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠠⠃⠀⠀⢂⢀⣇⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⢤⠤⣤⠇
⠀⠀⠀⢠⠁⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠈⠀⢀⠀⠀⠀⡀⢡⠀⠀⠀⠀⢀⠖⢆⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠘⠦⣌⢀⡇⢀⡵⠦⠂⠀⠀⠀⡆⠀⠘⡀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠉⢸⠁⠀⣀⡀⠀⠀⢰⠀⠀⠀⢇⠀⠀⣀⣀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⣀⠤⠤⠘⠤⠤⠤⠤⠤⢤⣤⡋⠀⠀⠀⠀⠸⡤⠤⠤⠤⠤⠄⠀⢧
⢀⠔⠉⠀⠉⠒⢄⠀⠀⠀⠀⠀⢇⣀⢷⠀⠀⠀⠀⠀⣇⠤⠒⠒⠉⠉⠁⠐⠳⢄
⡇⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢤⠊⢙⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⣉⣉⣉⣉⣉⣉⣉⣙⣓⣒⣒⣒⣓⣒⣊⣀⣀⣀⣀⣀⣈⣓⣶⣤⣤⣤⣤⣤⣶⣖⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣾⣿⣶⡀⠀⠀⢀⣤⣶⣦⣄
⣶⣦⡀⠀⢻⣿⣿⣿⣷⣦⣾⣿⣿⠋⠛⠿⣷⡄
⠘⢿⣷⡀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣧⣄⠀⠈⢿⣿⣶⡆
⠀⠀⠙⢿⣶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⠉⠁
⠀⠀⠀⠀⠙⠿⠿⠋⠁⠙⠻⢿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⠙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⣿⣿⣾⣿⣷⣄⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⢀⣴⣶⣶⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⣀⣠⣤⣤⣭⣍⠉⠀⠀⠀⠘⠛⢻⡇⢨⣿⣿⡿⠟⠰⣄⠀⢸⣿⣿⣿⡿⠀⠀⠀⢿⣿⠷⠶⢶⣤⣤⣌⡻⠿⣿⡃
⠀⠀⣿⠉⠀⣿⣿⠻⣧⣠⣤⠴⠿⠃⢸⡇⠀⠀⠀⣶⡆⢀⣼⠆⠀⠙⠛⣿⣿⣄⠀⠀⠀⠀⠀⠀⣶⣦⡀⡀⢁⣾⣿⣧
⠀⠀⣯⠀⣸⣿⠏⠀⠈⠁⠀⠀⢠⠀⢸⡇⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠈⢻⣿⣷⡦⣤⣤⣦⠀⠀⠀⠉⠛⠻⠟⣿⣿⡆
⠀⠈⠛⠀⣿⡿⠿⠿⠿⣿⡆⠰⠋⠄⢸⡇⠀⣠⡾⣿⡇⠀⠀⠀⢀⣤⣶⣦⡄⠹⣿⣿⣤⣶⢿⣤⣀⠀⢀⡤⠀⠀⣹⣿⣧
⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⣸⣷⡾⠋⠰⣿⡇⠀⠀⠐⢿⣿⣿⣿⣿⠀⠈⢿⡄⠀⠀⠀⠉⠙⠻⠃⢀⣼⠟⠁⢿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢉⠉⢁⣴⣿⡿⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠛⣛⣥⡀⠀⠘⣿⡄⠀⠀⡆⠀⠀⢰⡿⠁⠀⠀⠸⣿
⠀⠀⠀⠀⣿⡁⠀⢠⣾⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⢸⡇⠀⢠⣾⣿⣦⡀⢹⣿⣧⠀⠀⠘⢷⡀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠛⠛⠂⠸⣿⣿⣿⡏⠈⢻⣦⣤⣄⡀⠠⠾⠇⠀⠈⠛⠟⠋⠙⠛⣿⣿⡄⠀⠀⠘⡷⠾⠃⢀⣀⣼⡇⠀⠀⠀⢀⣈⣯
⠀⣠⣶⣶⣤⠀⠀⠀⠀⠙⣧⡁⠀⠀⠀⠀⠉⡽⠄⠀⠀⣿⣀⣠⣤⡴⣶⣤⣽⣿⣧⠀⣠⣶⣶⣄⠀⠀⠉⠉⠁⢀⣀⡀⠈⠉⠉
⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⣌⡗⢀⣠⣾⣿⣿⣆⠀⠀⠀⠈⠉⠁⣀⣀⠀⠀⠉⢹⣿⠀⣿⣿⣿⣿⠷⠀⢀⣀⣤⣿⣿⣿
⠀⠈⢛⣻⡅⠀⠀⢀⣀⠀⠈⠀⠈⠹⣿⣿⣿⠟⠀⢸⣄⠀⠀⣾⣿⣿⣷⣤⠀⢸⣿⠀⠈⣿⡟⣡⡶⠾⠛⠉⠀⠈⢉⣥⣤⡀
⠀⠀⣿⣿⣿⣆⢰⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⡄⠀⠈⠈⠁⠀⠻⣿⣿⠟⠁⠀⢸⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⡆
⠀⠀⣿⠈⢿⣿⣧⠙⢋⣡⣤⡀⠀⠀⠀⢸⣿⣷⡀⠀⠀⣶⠶⠶⢶⣶⡀⠀⠀⢘⣟⠀⠀⣿⡇⢀⣠⣤⣶⡀⠀⠀⠙⢿⣿⠋
⠀⠀⣿⠀⠀⠻⣿⡷⠟⠋⠉⠻⣦⠀⢀⡤⢻⣿⣧⠀⠀⣿⠀⠀⢸⣿⡇⠀⠤⠼⠿⠀⠀⣿⡿⠛⠋⠁⠈⢿⣄⠀⠀⢸⣿⡇
⠀⠀⠿⠀⠀⠀⢻⣇⠀⢰⠀⠀⠀⠻⠿⢁⣨⣿⣿⡆⠀⠹⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣿⡆⠀⠰⣄⠀⠀⠻⡶⠛⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⡆⠘⠀⠀⠀⣀⣴⠟⠋⠀⠸⣷⠀⠀⠀⠀⢸⡿⠛⠛⣿⡇⠀⢀⣠⣿⠄⠀⠀⠈⠀⠀⠀⠀⢀⡸⢿⡇
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⢸⡟⢁⣤⣤⣤⡀⢿⣄⠀⠀⠀⢸⡇⠀⠀⣿⡇⠀⣬⣯⡶⠀⣦⣠⢠⣤⡶⠾⠛⠋⠁⣸⡄
⠀⠀⠀⠀⠀⣰⣾⣀⠀⠀⠀⠀⢾⡇⠠⣿⣿⣿⣿⠀⠻⣦⡀⠀⢸⡇⠀⠀⠛⠛⠂⠈⠁⣠⡶⠘⠉⠁⠀⠀⠀⢀⠀⠀⣿⡇
⠀⠀⠀⡀⠀⠈⣉⡉⠀⠀⠠⠴⠿⠇⠀⠙⠻⠟⠋⠀⠤⠼⠿⠄⢸⣇⠀⠀⠀⠀⠀⠀⣰⡟⠀⣀⣤⠾⠀⠀⠀⢸⠀⠀⢿⡇
⠀⠀⣄⠹⣦⣰⡿⠻⣶⣤⣀⠀⠀⢠⣿⣿⠟⢻⡇⠀⠀⡀⠀⠀⠈⢉⣷⣤⣄⠀⠀⣼⢏⣤⡾⠛⠁⠀⠀⠀⠀⠀⢀⣤⣾⠆
⠀⠀⣿⣄⣥⣤⣤⣤⣤⣭⣿⣷⣿⣿⣿⠃⠀⢸⡇⠀⠀⠇⠀⠀⢠⣿⣿⣿⣿⠆⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⢼⣿
⠀⠀⠉⠀⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡧⠀⢠⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣾⣿⣿⣿⠇⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠆⠁⠀⠀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠀⠀⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⢠⠤⡀⢠⠙⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣬⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢩⠀⣠⠚⣣
⡇⠘⡁⠀⢷⠄⠘⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣈⠷⠁⡰⠉
⠃⡀⠀⠀⠠⠠⣤⣄⣡⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣴⡇⠀⠛⠀⠼⠁⠀⢀
⠀⢡⠀⠀⠀⠀⠀⠈⠁⢠⠄⠼⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠈⠡⠀⢀⣀⣠⡀⣠⡀⠀⠀⠀⠀⠀⠙⠶⣀⠈⠃⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠳⣀⠀⠀⠀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠛⠀⠀⠋⠀⠀⠠⠟⠀⢹⠀⠀⠀⠀⠀⠀⠀⣹⠀⠘⠳⠄⠀⢀⡔⠦⢀
⠀⠀⠀⠈⠛⡦⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠤⣄⡀⠀⠀⠘⢦⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⢰⡄⠸⣧⠀⠀⠀⠀⠀⠀⠀⢴⣆⢀⣀⠠⡤⣤⢤⡄⣀⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⢀⠌⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠘⡇⠀⢹⡆⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠻⣄⠀⠀⠀⣰⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⢀⡤⠊⠁⠀⢀⣄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠙⠀⠀⣴⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣦⠀⣀⣧⣠⠛⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⡆⠀⠀⣄⢠⡜⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⢨⡏⠀⠀⠀⠀⠀⠀⠐⠀⠈⠃⠀⠀⣀⡤⠞⣋⠀⠀⠀⢰⠀⠀⣿⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡘⠁⠀⠀⠀⣤⣄⠤⡤⢤⣤⡤⠚⠛⠉⢀⣴⡿⠀⠀⠀⠘⠓⣤⣿⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣀⣤⡴⠾⢿⣿⠃⠀⠀⢠⣄⢀⡼⠋⠙⢶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢠⡄⠀⠀⠀⢹⣿⣿⣿⣿⣿⢋⣀⣀⣀⣼⠃⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢣⠀⠀⠀⠀⠙⢿⣟⠉⠀⠀⣀⡤⠏⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠷⣀⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠛⠉⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠻⡏⠉⠉⠉⠉⠉⠀⠲⠶⠒⠦⢤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠶⡶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⠉⠠⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⢀⣀⣀⣀⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠉⠉⠉⢛⠉⠉⠀⠘⠒⠒⣶⠶⠤⣤⣤⣤⡤⠔⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⠃⠀⠀⠀⠀⠀⠘⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡆⠀⠀⠀⠀⠀⠀⢀⡦⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠉⠉⡷⠀⠀⠀⠀⣀⡤⠋⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠀⠀⢿⡀⢠⡄⠒⠉⠀⠀⠀⢀⢼⡇
⠀⠐⠋⣀⠀⠁⠙⣀⠀⠀⠀⠀⢀⡼⠶⠊⠙⠂⡀⠀⠀⠀⠀⡰⠃⢠⠃
⠀⠈⠲⠄⣀⣉⣉⣉⣉⣉⠉⣰⠛⠤⢀⡀⠀⠀⢡⡄⢀⣀⠐⠷⢀⡙⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣠⣤⣤⣤⣬⣥⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠻⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⣀⣠⣴⡶⠛⠋⠉⠉⠉⠙⢿⡳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣶⣶⣤⣄⡀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠙⠛⠳⠶⣤⣄⣹⣆⣉⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣀⣤⣴⠶⠶⠛⠛⠛⠉⢿⡉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠶⠛⠋⠉⠀⠀⠀⠀⠀⢀⣤⠶⢿⡟⢦⣸⡇
⠀⠀⠀⠑⢦⣤⣤⣤⣶⣿⣿⣿⣿⣿⠟⠉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢸⠇⠈⣿⠃
⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠿⠋⠁⠀⣼⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⡿⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⣛⣿⣿⣿⣿⣦⣀⣀⣤⠶⠛⠁⠀⠀⠀⢀⡼⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠲⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⣷⣦⣤⣀⣀⣀⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠟⠛⠛⠛⠉⢁⣴⣿⣿⣿⠿⠟⠛⠉⠁

⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⡠⣤⣠⣾⣷⣶⣿⣿⡀⣹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄
⡿⢩⡇⠀⠀⠠⣤⣶⣴⣾⡛⢻⣿⡟⠁⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠁⢸⣿⠀⠀⠀⠀⠀⠉⣉⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠿⠟⠉⠉⣿⣶⣤⣤⡤
⠀⣼⡏⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣛⣿⡟⠁⠀⠀⠈⢻⣿⣿⣾⣿⣷⣾⣿⣿⣿⡉
⣿⣿⣄⠀⠀⠀⠀⠀⢸⠿⣿⡿⢻⣿⠿⢿⣿⣿⣇⠀⣠⣦⣀⣸⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⡀
⡏⠈⠙⠀⠀⠀⠀⠀⢸⠿⣿⣧⣄⣹⣆⣴⢿⡟⣻⣿⣬⣿⡽⢏⣿⣿⣿⣯⡀⣬⣝⡮⣿⠃⠀⠀⠀⠰⣷⡀
⣂⠀⣠⠀⠀⠀⠀⠀⠈⣠⣤⣽⣿⣿⠵⠟⠻⢾⣿⣧⣈⣽⣿⣿⡿⠛⣹⣽⡿⠛⣿⠷⢿⠀⠀⠀⠀⠀⠙⣿⣄
⠇⢀⣹⠀⠀⠀⠀⠀⠀⢹⣿⣻⡚⡯⠙⢶⣤⣼⣿⣿⣿⣿⣻⣿⣴⣿⣟⢃⣷⣞⣿⣫⣹⣄⠀⠀⠀⠀⠀⠘⣿
⠀⣾⣿⠀⠀⠀⠀⠀⣤⣨⣧⣴⣶⣿⡿⢛⣋⡍⢹⣿⣿⣷⣶⠋⠉⠛⠿⢿⣿⣶⣿⣶⣸⣏⡀⠀⠀⠀⠀⠀⠙
⢸⣿⡏⣴⣿⠀⠀⠀⠸⢿⣧⣤⣼⣿⣀⣈⠟⣠⣤⣴⣿⣿⣿⣿⣷⠐⠦⡼⠿⠛⣟⣿⣿⠿⠁
⣿⣿⣷⣿⡟⠀⠀⠀⠀⠀⠈⠓⢿⣿⣯⣿⣴⣿⣿⣿⣿⠟⠉⠉⣀⣀⣉⣴⣶⡶⠻⣋⡀⠀⠀⠀⠀⠀⠀⢰⡀
⣿⣿⣿⣿⠃⠀⠀⠀⠰⡿⢀⠀⠀⣿⢿⣹⣿⣿⣿⠿⣷⣶⣶⣾⢟⢻⣏⣷⣿⠋⢀⡙⠋⠀⠀⠀⠀⠀⠀⣼⣧
⣿⣿⣿⡏⠀⠀⠀⠀⠀⣄⠈⠁⠀⣿⠀⢹⣯⣼⣯⣴⢹⠛⢸⣷⣿⣿⣼⠿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⡠⠀⠻⢼⣿⣿⣿⣿⣿⣾⠀⣾⣿⣿⣿⠄⠨⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡇⢀⡀⠀⠀⠀⠀⠈⠀⢼⣿⠄⢸⣿⣿⡟⢿⣿⣀⣿⡿⠋⠉⠀⢠⣿⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠸⣽
⣿⣿⣿⣡⣾⣿⡆⠀⠀⠀⠀⠀⠈⢉⡄⠀⣿⣿⡇⢸⣿⣿⢿⣤⣤⠔⠀⢸⠏⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠸⡅⠀⢿⣿⡇⠸⡇⠁⠘⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠛⢣⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⣿⠀⢸⡏⠉⣶
⠀⠀⠀⠀⠀⣀⡰⠶⠏⠉⣀⣠⣎⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⣿⠗⢶⡄
⠀⠀⣶⠖⠞⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢱⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣿⠛⠛⠛⠃⠀⠀⠀⠀⠀⣀⣀⡀⢸⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠱⢿⠀⠀⠉⠀⠈⠁⠀⠻⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠛⠛⠳⣤⣤⡄⠀⠀⠀⠀⠀⢠⡝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠛⢦⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢆⡀⠉⠶⣀
⠀⠀⣤⣤⣤⣤⣤⣤⢀⣴⠃⠀⠀⠀⠛⠛⠛⠛⠛⢣⡄⠀⣾⠛⠛⠛⠛⠛⠃⠀⠀⠙⢣⡄⣠⣤⣤⣤⣤⣤⡄
⠀⠀⣿⠀⠀⠀⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡇⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢠⠄⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣤⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡇⠤⠀⠀⢸⡇
⠀⠀⠿⠶⠶⠶⠶⠿⠉⠉⠱⠶⠶⠶⠶⠶⠶⠶⠶⠎⠁⠀⠉⠶⠶⠶⠶⠶⠶⠶⠶⠾⠉⠉⠻⠷⠶⠶⠶⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣾⣿⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⣿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡏⠘⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠙⠀⠉⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡛⠿⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠈⢿⣇⠁⠀⠀⠀⠁⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠇⠀⠀⠀⢞⣁⡀⠀⠀⠀⠀⠀⠀⠀⣙⡂⠀⠀⠀⢘⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣟⣳⣴⣶⡿⢿⡛⠋⠀⠀⠀⠀⢠⣴⣿⣿⠗⣴⣷⡆⢿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠛⠛⠉⠁⠛⠛⠟⠶⠀⠀⠀⠀⠀⠉⠋⠁⠀⠿⠿⠇⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⣿⣧⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⡇⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⠉⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠉⠀⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⡷⣠⣶⡤⣿⣷⣦⡀⠀⠀⠀⠀⠰⠿⠶⢦⣠⣤⣶⣾⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⣿⣿⡇⠈⠛⠛⠋⠀⠀⠀⠀⠀⣶⠿⠿⠛⠋⠱⠾⡷⣶




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠠⢄⠀⠀⠀⣀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠀⠒⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡼⠁
⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⡿⠉⠓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀
⠘⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠈⢿⣅⡀⠀⠠⠀⠀⠅⠀⠒⠠⠄⠀⠀⠀⢀⡀⠀⡐⠁⠀⠀⠈⠑⠀⠀⠀⠐⠢⣀
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⢌⠐⠀⢈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠢⡈⠂⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠑⢄⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠁⠒⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⣀⡀⠀⠀⠀⠀⢀⠔⠂⠉⢁⣀⣀⣀⠤⢄⣀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⢀⠤⠒⠂⠐⠊⠉⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⣠⠐⠃⢠⠤⠖⠁⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠉⠳⡀
⠀⠀⠀⢠⠚⠁⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡇
⠀⠀⡰⠁⣠⠖⠉⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢠⠃⡐⠀⣀⣠⡤⠤⢤⣄⣀⠸⡄⠀⠀⠀⠇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠐⠇
⠀⠀⣥⠎⠀⠀⠀⠀⠀⠀⠧⠀⢤⣀⡀⠀⠀⠀⠀⢸⢀⠃⠀⠃⠉⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠌
⠀⠀⠲⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠈⠑⠢⣄⠀⡸⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⡡⢋
⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢰⠳⡀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⣠⠓⠐⠁
⠀⡀⠀⠈⢢⡀⠀⠠⣀⠀⠀⠀⢀⠄⠀⠀⢀⠜⠁⠀⠘⡀⠀⠘⡄⠀⢀⠀⢀⡄⢀⡴⠃⠀⠀⠀⠀⠀⠀⣹⠛⠦⣄⠀⠀⠀⠨⠄⠀⣀⡤⠞⠁
⠘⠛⠢⣄⣀⣈⠢⢄⣀⣉⠒⠚⣁⣀⡠⠖⠁⣀⠼⠚⠃⠑⠤⠤⠞⠢⣄⡀⠀⠀⠈⠓⣦⣤⣄⣀⣀⣀⠴⠁⠀⠀⠀⠉⣙⠶⠒⠚⠫⣁⣀⣀
⠀⠀⠀⠀⢅⣀⣩⠋⠀⠫⠉⠩⠋⠙⣖⠊⠙⠁⠀⢀⣤⠤⠤⢤⠔⠀⡞⠉⡉⢉⠟⢻⠅⠢⣄⣀⡤⠤⠾⣂⣠⢴⠁⠠⠃⠘⠤⠔⠀⠘⢆⢹⠶⠶⠤⢄⣤
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠀⠀⠈⠉⠀⠀⠈⠢⡰⠀⠀⠀⠀⠀⠀⣦⠤⠊⠀⠀⢷⠊⠁⠀⠀⢦⠁⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⣠⠤⠦⠄⣈⠉⠐⠒⣤⠤⠤⠤⠀⠒⢾⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠼⣀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠖⣮⣀⡀
⠀⠀⠘⣦⠀⠀⠀⠈⠑⠊⠈⠢⢠⠄⠀⠒⠚⠀⠀⠀⠀⠰⠥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⡇⠀⣀⡀⠀⠰⣀⡠⠤⠖⠋⢁⡞
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⣤⠤⠤⠤⠴⠒⠙⢄⠀⠀⣠⠀⠀⠀⢩⠏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠾⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠑⡾⠃⠐⠦⣄⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣰⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠈⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢠⠃⢡⠀⠀⠀⠀⠀⢀⠊⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⡀⠀⠀⠀⡰⠃⠀⡌⠀⠀⠀⠀⡠⠃⡸
⠀⠀⠀⠀⠀⠀⠐⢦⡒⠢⢄⠀⠀⠀⠀⠀⢱⠀⠈⢦⡀⢰⠁⠀⠸⡀⠀⠀⢀⡔⠁⢀⠃⠀⠀⠀⠀⠀⡠⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠳⣄⠀⠀⠀⠈⡆⠀⠀⠙⣬⠀⠀⠀⠳⡀⢠⠞⠀⠀⡌⠀⣀⣀⣀⡠⠞⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠙⠒⠢⣄⢹⠀⠀⣀⡨⠦⠴⠒⠒⠓⠯⢄⡀⢰⡴⠊⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣀⠀⠀⠈⣧⠗⠋⠁⠒⠶⠶⠖⠀⠀⠀⠀⠉⠛⢦⡀⢀⠴⠒⠒⠚⠉⠀⠀⢀⣀⡀
⠀⠀⠠⣤⡤⠤⠤⠤⠤⠤⠤⢄⣀⣈⣱⣄⡼⠁⠀⠀⠀⠉⠉⠓⠒⠂⠉⠀⠀⠀⠀⠀⠙⣿⠶⠒⠒⠒⠋⢉⣩⠥⠒⠉
⠀⠀⠀⠀⠈⠙⠒⠦⢄⣀⠀⠀⠀⠀⠀⣸⠀⢀⠤⠤⢤⡀⠀⢰⠀⣀⡠⠤⠶⢤⡀⠀⠀⡻⡄⢀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣒⣤⣄⣀⡇⠀⠤⢶⡶⠢⡄⠀⢸⠀⠀⢚⠿⠛⡒⠀⠀⢐⡪⡿⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠉⠀⠁⠀⠈⣇⠀⠐⠒⠒⠊⠀⠀⠈⠀⠀⠀⡉⠀⠀⠀⠀⠦⡈⣿⠀⠀⠀⠀⠈⠓⠶⠖⠒⢢
⠀⣀⠤⠒⠉⠉⠉⠁⠀⠀⣀⡤⢖⡶⠦⢹⡦⠄⠀⠀⠀⠀⢸⣀⣄⣠⠴⠃⠀⠀⠀⠀⡳⣌⡿⠾⣉⠉⠓⠢⠤⠤⠖⠉⠉
⠉⠉⠑⠒⠒⠋⠉⠉⠉⢉⡡⠐⠉⠀⠀⣀⢻⡵⣀⡀⠀⠀⢀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠹⣾⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⢀⡠⠔⣲⠋⠁⠀⠙⢯⣥⠄⠀⠀⠠⣤⣤⠤⠀⠁⠀⠀⣠⠞⠉⠻⡓⠶⢤⣈⡓⢤⡀
⠀⠀⠀⠀⠀⣴⠭⠴⠒⠋⠁⢀⡰⠁⠀⡠⠒⠉⡟⠙⠻⢥⣄⣀⣀⣀⣀⣀⣤⢴⡞⠧⣄⠀⠀⢹⠀⠀⠀⠉⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⢀⣀⠔⠁⠀⡼⠀⠀⢠⢾⠀⠈⠉⢹⣯⠀⠀⢸⡇⠀⠘⡆⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⡤⠊⠉⠀⠀⠀⣰⠁⠀⣠⢃⡞⠀⠀⠀⡼⠈⣇⠀⠈⡇⠀⠀⠹⣄⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠇⠀⡴⠁⡞⠀⠀⣰⠊⠀⠀⠸⡄⠀⡇⠀⠀⠀⠈⠓⠲⠤⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣠⠎⠀⠀⢳⠀⠠⡇⠀⠀⠀⠀⢳⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠜⠁⠀⠀⠀⠘⡆⠀⡇⠀⠀⠀⠀⠈⣆⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡇⣰⠃⠀⠀⠀⠀⠀⠸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢪⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠣⡀⠀⠀⠉⠀⡰⡆⠀⠀⠀⢀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠃⠀⠱⡀⠀⢀⡜⠀⠘⡄⠀⠀⠸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢵⠀⡜⠀⠀⠀⢱⢀⠎⠀⠀⠀⠈⢆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣄⠀⠀⠋⠀⡀⠁⠀⠀⠘⡄⠀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⡎⠀⠀⠋⢂⠀⢀⠔⠀⠀⠱⡀⠀⢡⠜⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⠇⠀⠌⠀⠀⠢⠀⠀⠀⠀⠀⠑⡀⠀⢀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠁⢂⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡣⠜⠀⠀⠀⡌⠁⠄⠀⠤⠀⡰⠒⡄⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠂⢄⠀⠀⢰⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠔⠀⠀⠀⠀⢀⠤⠐⠀⠀⡔⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠤⡄⡄⢠⠊⠑⡒⠧⡂⠑⠀⢀⡀⠄⠢⣠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠤⠂⠀⢴⠘⡉⠛⠀⠀⠐⡀⢀⠴⠀⠁⠀⠀⠀⠈⠀⡀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢸⠀⢀⠃⠀⡰⢄⠀⠀⠀⠱⠀⡖⠠⠄⢀⠀⠄⢔⠀⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠨⠭⠦⠘⠒⠊⠉⠉⠒⠒⠒⠚⠑⠠⠤⠤⠤⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠲⠀⠀⠀⢀⢄⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠕⠀⠀⢀⡃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡾⠃⠀⠀⠐⠈⠛⠲⠶⠂⢺⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠹⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠂⠄⢦⠀⠀⠀⠀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠉⠁⠂⠀⠐⠃⠀⠀⠁⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠡⠴⠤⠌⡠⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⠀⠠⠂⠀⢢⠔⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆⠀⢠⠛⠇⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠄⠀⡀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢩⣭⢽⡾⠀⠰⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁
⠀⠀⠀⠦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢄⣁⣀⢈⣀⠀⠈
⠀⢀⠴⡻⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠣⠀⡁⢈⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⠂
⠀⢈⠘⠁⠀⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⡦⡈⠁⠀⠀⠀⠀⠀⢀⠔⠁⠨⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⠀⠀⡆⡄
⠀⠊⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡹⠀⠀⠀⠀⠀⠀⠢⡈⠢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⣿⡇
⠀⢤⠤⢃⡈⢟⣘⢆⡠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠡⠒⠀⢀⣎⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣶⣶⣷⣿
⠀⡦⠀⠢⠄⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⣿
⠀⢳⢠⠄⠀⠈⠀⠀⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⡇
⠀⠘⡀⡀⠀⠀⠀⢠⡿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠘⢷⣦⣤⣀⣼⣿⣦⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠇
⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⠯⠍⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠛⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠄⡀⠱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡆⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠠⠦⠠⠀⠈⠚⠀⠮⢗⠀⠀⠀⠀⠀⠐⢋⠄⠪⡇⠀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⡠⡈⠈⠀⣠⡀⠀⠀⠀⢔⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⠇
⠀⠀⠀⠀⠀⠈⠁⠙⠑⠊⠀⠀⠀⠀⡀⡀⠀⠙⠓⠁⠀⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠇⠰⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠨⠆⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠗⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠧⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠄⠀⠆⠀⠀⠀⠐⣅⠹⠍⡆
⠀⠀⠐⣃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⠐⠓⠔⡄
⠀⠈⢂⠘⢁⡂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢀⠉⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠪⠂⠟⠆⠉
⠀⠐⠑⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠔⠁