⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠢⠤⠤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡠⠴⠤⣄⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡏⠀⠀⠀⢸⠂⠀⢸⠀⠀⡦⠀⠀⠹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⠀⠀⠀⠀⡇⠀⠘⣆⠠⠤⠤⠤⠤⠄⠀⠀⠀⣰⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠸⡆⠀⠀⢀⠟⠀⠀⠀⠙⠲⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣹⡄⠀⠘⠦⣄⠀⠀⠀⠀⣀⡴⠓⠀⠉⠉⠓⢦⡀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣴⣋⣀⣀⡀⠀⠀⠈⠉⠑⠊⠉⠁⠀⣠⠞⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⢧⠀⢀⡠⠤⠤⠤⣄⣀⠀⠀⠀
⢠⠎⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⢀⠖⠊⠉⠑⢲⣇⢀⠀⡀⠀⠀⢰⡼⢉⠀⠀⠀⠀⠀⠀⡇⠀⠀
⡇⠀⠀⠀⠶⠋⠹⡆⠀⠀⠀⡤⠖⠁⠀⠀⠀⠘⠦⢄⣀⣀⡺⠞⠚⠙⢳⣠⠤⠬⢧⡬⣄⠀⠀⣀⣠⢴⠁⠀⠀
⣇⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣰⠙⠈⠙⣦⠤⠤⢲⠓⡧⣄⣀⣀⣼⠉⠉⠉⠁⠀⠘⡆⠀⠀
⢸⡀⠀⠀⠀⣠⠔⢣⢱⠀⠀⡜⠃⠀⠀⠀⠀⣴⠍⠀⠀⢠⠟⠀⠀⢸⠜⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡀⠀
⠀⢳⡀⠀⠀⠀⠀⢈⣉⠤⠞⠁⠀⠀⠀⠀⣼⠁⠀⠀⢀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣇⠀
⠀⠀⠑⠲⠤⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠘⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠢⠤⠤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠴⠤⣄⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠀⢸⠂⠀⢸⠀⠀⡦⠀⠀⠹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠀⠀⠀⠀⡇⠀⠘⣆⠠⠤⠤⠤⠤⠄⠀⠀⠀⣰⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⡆⠀⠀⢀⠟⠀⠀⠀⠙⠲⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣹⡄⠀⠘⠦⣄⠀⠀⠀⠀⣀⡴⠓⠀⠉⠉⠓⢦⡀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣋⣀⣀⡀⠀⠀⠈⠉⠑⠊⠉⠁⠀⣠⠞⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⢧⠀⢀⡠⠤⠤⠤⣄⣀⠀⠀⠀ ⢠⠎⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⢀⠖⠊⠉⠑⢲⣇⢀⠀⡀⠀⠀⢰⡼⢉⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⡇⠀⠀⠀⠶⠋⠹⡆⠀⠀⠀⡤⠖⠁⠀⠀⠀⠘⠦⢄⣀⣀⡺⠞⠚⠙⢳⣠⠤⠬⢧⡬⣄⠀⠀⣀⣠⢴⠁⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⣳⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣰⠙⠈⠙⣦⠤⠤⢲⠓⡧⣄⣀⣀⣼⠉⠉⠉⠁⠀⠘⡆⠀⠀ ⢸⡀⠀⠀⠀⣠⠔⢣⢱⠀⠀⡜⠃⠀⠀⠀⠀⣴⠍⠀⠀⢠⠟⠀⠀⢸⠜⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⢳⡀⠀⠀⠀⠀⢈⣉⠤⠞⠁⠀⠀⠀⠀⣼⠁⠀⠀⢀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠑⠲⠤⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠘⠆