⣞⢽⢪⢣⢣⢣⢫⡺⡵⣝⡮⣗⢷⢽⢽⢽⣮⡷⡽⣜⣜⢮⢺⣜⢷⢽⢝⡽⣝
⠸⡸⠜⠕⠕⠁⢁⢇⢏⢽⢺⣪⡳⡝⣎⣏⢯⢞⡿⣟⣷⣳⢯⡷⣽⢽⢯⣳⣫⠇
⠀⠀⢀⢀⢄⢬⢪⡪⡎⣆⡈⠚⠜⠕⠇⠗⠝⢕⢯⢫⣞⣯⣿⣻⡽⣏⢗⣗⠏⠀
⠀⠪⡪⡪⣪⢪⢺⢸⢢⢓⢆⢤⢀⠀⠀⠀⠀⠈⢊⢞⡾⣿⡯⣏⢮⠷⠁⠀⠀
⠀⠀⠀⠈⠊⠆⡃⠕⢕⢇⢇⢇⢇⢇⢏⢎⢎⢆⢄⠀⢑⣽⣿⢝⠲⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡿⠂⠠⠀⡇⢇⠕⢈⣀⠀⠁⠡⠣⡣⡫⣂⣿⠯⢪⠰⠂⠀⠀⠀⠀
⠀⠀⠀⠀⡦⡙⡂⢀⢤⢣⠣⡈⣾⡃⠠⠄⠀⡄⢱⣌⣶⢏⢊⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢝⡲⣜⡮⡏⢎⢌⢂⠙⠢⠐⢀⢘⢵⣽⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠨⣺⡺⡕⡕⡱⡑⡆⡕⡅⡕⡜⡼⢽⡻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⣳⣫⣾⣵⣗⡵⡱⡡⢣⢑⢕⢜⢕⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣿⣾⣿⣿⣿⡿⡽⡑⢌⠪⡢⡣⣣⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡟⡾⣿⢿⢿⢵⣽⣾⣼⣘⢸⢸⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠇⠡⠩⡫⢿⣝⡻⡮⣒⢽⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⢠⣾⣧⣤⡖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠉⠀⢄⣸⣿⣿⣿⣿⣿⣥⡤⢶⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⣙⣛⣿⣿⣿⣿⡏⠀⠀⣀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣦⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣟⠛⠿⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⣠⣶⣶⣶⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠈⢹⡏⠁⠀⠀
⠀⠀⠀⢀⣿⡏⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠀⢀⣿⡇⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡘⣿⣿⣃⠀⠀⠀
⣴⣷⣀⣸⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠹⣿⣯⣤⣾⠏⠉⠉⠉⠙⠢⠀
⠈⠙⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠛⠉⢩⣷⣴⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣀⡠⠋⠈⢿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀