⠀⠀⠀⠀⠀⣀⡾⣫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠙⣿⡇⠀⣰⣿⣿⣿⣶⣄⠉⠛⢦⣈⠛⢷⣤⡀⠀⠈
⣶⣄⠀⣀⡾⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠸⠀⣰⠿⢫⣤⣀⠀⠀⠀⠀⠀⠀⠻⣄⠈⢿⣶⡀
⣀⣬⢿⣿⡀⢀⣴⠿⠉⢙⡭⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣠⡿⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢻⡀⠙⣿
⠃⠀⠀⠀⣿⡟⠁⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣿⣿⣿⣦⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠛⢰⡿
⠀⠀⣠⣿⠋⣠⠟⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⢸⣿⣿⣿⣿⣧⣿⣿⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢾⡇
⠀⣰⡿⠁⣾⠁⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣦⡀⠀⠀⠀⣰⡿⠁
⣰⡿⢀⡿⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠉⠟⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢿⡀⠀⠀⣿⡇
⣿⠀⡟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣷⠀⠀⠘⣿⣤⡀⠀⢀
⡏⣼⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠉⠛⠛
⠀⡇⠀⠀⠀⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⠁⠀⠀⠀⠀⣀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⣀
⠀⠃⠀⠀⣰⡿⠀⠀⠀⣟⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠉⠛⠆⠘⣷⠀⠀⠀⠀⠀⠘⣷⣿⣿⣄
⡀⡇⠀⣰⣿⠀⠀⠀⣾⠛⠉⠻⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠹⣿⣿⣿⣧
⣧⠙⢀⣿⠁⠀⠀⣾⠁⠀⢀⣀⣈⣿⣀⠀⠀⠀⢿⡀⠀⠀⣿⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠙⣿⣿⣿⡇
⢿⣄⡿⠁⠀⠀⣾⠁⠚⣡⣴⣶⣶⣶⣿⣷⣄⠀⠀⣿⣦⣀⣈⣿⡄⠀⠀⠈⠔⣾⣿⣿⠿⠿⣷⣾⣤⡀⠀⠈⠻⣷⣤⡀⠀⢀⠛⢿⣿
⣾⣟⠀⠀⣠⠟⣡⣾⣿⠟⣿⣿⡿⠁⠀⠈⣿⠻⠟⠁⠀⠈⠉⠉⠁⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⣿⣟⠿⣷⣄⠀⠀⠈⠙⠛⠻⠶⢾⡟
⣿⣿⣿⠙⣿⣰⣿⡿⠀⢰⣿⣿⣧⣀⣀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠶⣤⣾⣿⣿⠀⠘⣿⣧⠀⠀⣠⠴⣾⠋⠀⣿⢸
⣿⣿⣿⠀⣿⢻⣿⠀⠀⢸⣿⣿⣿⣯⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣴⣿⣿⣿⣿⠀⠀⠘⣿⡄⠈⠁⣤⠿⠀⣰⡟⣿
⣿⣿⣿⣷⡿⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⡿⠋⠀⠀⠀⠉⠀⠀⠀⢀⣠⣾⣩⣿⣿
⣧⠻⣿⣿⡃⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⣿⠟⠉⠀⠀⠀⠉⠛⠶⡀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠤⠶⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣴⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠛⠶⠋⠀⠀⠀⠀⠀⣷⣤⣾⣿⠋⣸⠇⠀⠀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢉⣿⣦⣤⣄⣤⣤⡶⠂⠀⢿⣿⣷⠶⠶⣶⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⡿⠁⢠⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⢣⠿⣶⣿⠀⠠⣤⣀⣀⣀⣀⣤⣶⠿⠛⣠⡿⠋⠀⣠⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣿⠛⣁⣿⣿⣿⣿⠀⠀⠀⠛⢿⣷⣷⣿⡀⣀⣾⠏⢀⣤⡿⠋⠀⢦⠀⠀⣠⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣻⣟⣀⣿⣀⣀⣀⣀⣀⣀⣀⣻⣟⣁⣝⣿⣾⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣛⣛⣛⣿⣿⣷⣀⣀⣸⣿⣿⣿⣿⣿⣿