⣿⣿⣿⡿⠁⠀⠀⠀⢀⡾⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢰⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⠟⠀⠀⠀⠔⢠⠾⢣⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢹⠀⠀⣿⠁⣿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⡟⠀⠀⠀⠀⢠⠃⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠃⠀⢸⠀⢻⠇⢰⡤⣤⣀⣀⠀⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠁⠀⠀⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡏⠀⠀⢸⡆⢸⠆⠀⠀⠀⠀⠉⠉⠃⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⣧⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣘⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⣿⣿⣧⡀⣄⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢷⣿⣿⠀⠀⠀⠙⢿⣿⣿⣮⡛⢶⣦⣼⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣦⣛⠃⠀⠀⠀⠀⢦⣌⠉⠙⠻⢾⣿⣿⣿⣿⣏⣡⣴⣦⣤⣀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣌⡛⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⢘⢿⣿⣿⣿⣿⣿⡿⠟⡛⠛⠉⠉⠃⣃⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀
⣿⡇⠀⠀⠀⠀⠀⠀⢈⢿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣷⣤⣶⠀⠀⣿⣿⣿⣿⣿⣿⣿⠆⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡇
⣿⠅⠀⠀⠀⠀⠀⠀⠀⣶⣙⣛⣛⡟⢻⣿⣿⣿⣿⣿⣯⡙⢿⣾⣿⣿⣿⣿⡿⢟⣡⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡾⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣛⣛⣛⣭⣾⡾⠿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡸⢁⣰
⣯⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠰⠾⢓⠨⢍⣚⣭
⣿⠀⠄⢀⣀⣠⡄⠀⢐⠃⣈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣏⣻⡿⢻⣿⡄⠀⠀⠀⠀⠀⠀⢰⣤⣚⣛⣛⠛⠻
⣦⣀⣬⣉⡙⠋⣀⣀⠀⡢⣝⢶⠎⠻⣿⣟⠿⣿⣿⣿⡿⠟⣛⣭⣴⣿⣿⣿⣿⣿⣿⠟⡫⢾⣿⣿⡇⡀⠀⠀⠀⠀⠀⢤⡭⢛⣛⠛⠛⠿
⡻⠿⠟⣛⣥⣄⠉⢻⣿⣄⠸⣦⢱⣶⣮⡻⣿⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣴⣶⣿⣿⡿⠁⠅⠀⠀⠀⠀⠀⢐⣦⣵⣶⣿⣿⣿
⠄⠸⣿⣿⠿⠋⠀⠀⢻⢿⠀⢹⠚⠟⣛⣋⣒⡙⠻⣿⣿⣿⣿⠿⠛⡋⣡⢀⣼⣿⡿⠿⠛⠋⠁⢰⢐⣋⣥⡄⢠⠀⠀⢸⣿⣿⠿⢛⠋⢉
⣭⣶⠿⠋⠀⠀⠀⠘⠐⡝⠁⢀⣼⣿⣿⡿⠛⢉⣤⣤⣤⣤⠀⢠⣶⡀⠀⠈⠁⠀⠀⠀⠀⢀⣠⣴⠈⣛⢿⣿⠎⠇⠀⠈⠉⠀⣀⣤⣤⣶
⠁⠀⠀⠀⠀⠀⣀⣐⠉⢁⣴⣿⣿⣿⡟⢀⣶⣿⣿⣿⡿⠃⣶⣮⣭⣂⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⡆⠈⢠⡀⢀⣠⡄⢰⣿⣿⣿⣿⡿⢿
⢀⣠⡴⣶⣷⣾⣿⠿⣛⣼⣿⣿⣿⣿⠁⢼⣿⣿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠀⣻⣮⡙⠷⠸⠟⠛⠉⡀⣬⣿
⣿⣿⣷⡿⢛⣭⣶⣿⣿⣿⣿⣿⣿⣿⢀⣌⢻⣿⣿⣧⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣶⣾⣿⣶⣀⠀⠴⣿⡭⣿⣿