⠀⣇⠈⣧⣼⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⣀⣀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠶⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢦⣨⠦⣈⠛⠿⢿⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⣲⣶⣌⠓⠥⠝⣆⠉⠒⠒⠀⠀⢠⠀⠢⡀⠈⣮⢣⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⢠⡼⢛⣭⣤⠀⠀⠀⠀⢀⣀⡠⢶⠆⠀⠀⣰⣿⡿⠛⠛⠉⠉⢹⡆⠀⡌⡾⠄⠀⠀⣼⣠⠃⠁⠀⠘⡄⠘⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⣀⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⣸⡁⠃⠀⠔⢂⡠⠤⠲⠴⠁⣦⠀⠀⢏⠀⠀⠀⠀⠠⣤⣟⣀⣰⣿⠃⠀⢔⣿⠃⣡⠏⠀⠀⠀⡇⢀⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡘⣀⡜⡁⠳⣀⣠⠖⠁⠀⠀⡄⠀⠀⢻⣇⠀⢈⡻⠶⠶⣤⢾⡋⢠⡾⠩⠷⠚⠋⠛⠓⣺⡧⠀⢀⣠⠞⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡙⡸⠁⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣀⣻⣽⠿⠳⠶⢦⣿⣚⣽⠏⠀⠠⣶⣦⣤⣤⣒⣶⣫⠉⢹⣏⣦⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⡇⠀⠀⠀⠀⠘⣄⠀⠀⠀⣫⣟⠛⢉⣠⠤⠄⠀⠀⠀⠈⠁⠀⠀⠘⡟⠀⠹⣿⡍⠻⡃⠂⣸⡘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⢸⠀⠠⡀⠈⠓⢶⡞⠚⢁⣼⡿⠛⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⣿⢻⠀⡇⠀⡿⣱⡋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡸⡀⢶⣕⠤⢀⣤⣽⣓⣺⡏⣧⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⣰⠁⠀⣷⡿⠁⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠙⠳⣌⡪⢹⡽⠷⡠⠭⠾⡄⢻⣷⣾⣧⡅⠀⠀⠀⠀⠀⣄⠀⠀⠀⠂⢉⠁⢘⠀⢰⣿⣦⣄⣠⣄⣀⣀⣶⣇⣀⣬⣵⣷⣤⣦⣦⣤⣤⣄⣼⣄⣤⣤⣠⣤⣤⣤⣤ ⣇⣀⣠⣤⣤⣤⣿⣴⣿⣿⣿⣦⡀⢏⣦⡀⠑⢄⣩⠽⠟⠟⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠈⠀⠀⠂⣜⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣛⣛⣛⣛⣋⣻⣿⣯⠩⡷⣶⣾⣿⣦⣤⣱⣄⠀⠀⠰⠀⠃⠀⠀⠀⢀⣀⣀⠴⠂⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣾⣭⣟⡻⢷⣿⢿⣿⡿⢿⣿⣛⣿⣿⣿⣛⣻⣿⣿⡛⠛⣻⣿⣿ ⠃⠀⠀⠀⠀⠀⠀⠉⢷⡙⣽⣷⢫⠉⠉⣹⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠓⠪⠽⣿⣟⣿⣿⣿⣿⢿⣏⢝⣵⣮⣴⠿⣭⣯⡍ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⣧⣧⠀⠙⠻⠋⠀⠙⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⡶⠖⠋⠀⠀⠀⠀⠀⣠⣾⣷⢿⣵⣿⡿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠉⣷⡶⠦⠤⠤⠤⠤⠚⠁⣀⣠⣶⣿⡿⠿⠿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡤⣪⣞⢟⡵⢋⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣿⣻⢳⡀⠀⠀⠀⠀⠀⠀⡰⠋⢹⣤⡤⠲⠒⣶⣾⣿⣿⡿⠿⠛⠁⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⢗⡵⢋⡴⠋⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡸⣷⣧⢧⠀⠀⠀⠀⠀⡸⠁⠐⠚⠿⠷⢤⠴⠛⠋⠉⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⢀⡤⣺⣵⢿⣫⠞⣡⠔⠉⠓⢤⠀⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢻⣿⣎⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⢴⣺⣵⢿⣫⠔⣋⡴⠋⠀⠀⠀⢀⣠⠇⠀⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠞⡈⢧⣻⣿⣌⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣀⣤⣶⣽⡿⣟⣩⠖⢉⣠⡞⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀