⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣶⢶⢶⡦⢤⣀⠀⠀⠀⠀⠀⠀
⠀⠀✧₊⁺⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣾⣿⣶⣶⣿⣦⡀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⣾⣿⣿⣿⠟⠁⢰⣿⣷⣿⣿⣿⣽⣟⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺
⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⢀⣀⣀⣻⡿⠿⣿⣿⣿⣟⣿⣿⣿⣿⢷⣤⣿⡿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢃⡔⢉⣤⣤⣄⠉⠀⠀⠀⠉⢡⣤⣤⡌⠙⣇⢻⣿⣷⡾⠀
⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠹⣻⣿⣿⣄⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠈⡿⠿⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣿⣿⠀⠐⠢⠤⠥⠔⠂⠀⠀⠀⠀⠢⠤⠥⠤⠒⠀⠀⣶⠗⣸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⡵⠃⠀⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺
⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀天才⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣻⠋⣿⢻⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⠿⠛⠉⣇⠀⠀⠀
⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⣿⣿⣼⣿⣾⣿⣿⡿⠋⡇⠀⢀⠏⢻⣿⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺⠀⠀⠀⠀⠀⠀⠀⠀✧₊⁺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠉⡹⠁⠀⠹⣄⡞⠀⠀⢻⠉⠙⠻⠿⣿⣧⣇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⢰⣥⣶⣯⣝⣿⣿⣿⣷⣦⡧⠀⠀⢰⠹⣿⣾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠘⣾⣿⣿⣿⡟⣿⣿⣿⣿⡇⠀⢠⠇⠀⢻⣿⠀⠀