⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣟⡻⢛⢷⢥⣂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣢⣼⠾⠟⣉⣱⣿⣿⣿⣶ ⠀⠘⢿⣿⣿⣿⠋⠉⠉⠀⠉⠙⠲⢑⢄⠀⠀⠀⠀⠀⢀⢔⠩⠖⠋⠀⠑⠛⠛⠛⠛⢻⡿⠃ ⠀⠀⠀⢙⣿⣿⣦⡀⡀⠀⠀⠘⠀⡄⡁⢒⠀⠀⠀⠔⠂⡄⠀⠀⠀⠀⠀⢀⣰⢎⠌⠏⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣷⠀⠁⠀⠀⠀⠠⠈⠠⢡⠀⡐⢀⠈⠀⠀⠀⠁⠀⠁⢎⣼⠺⡜⠀⠀⠀ ⠀⠀⠀⠀⠙⠿⣿⣟⣧⡐⡀⠀⠀⠀⠐⠠⠀⠛⠁⠢⠀⠁⠀⠀⠀⣐⡨⢦⢏⠏⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠃⠙⢁⢲⠶⠂⠀⠀⠀⡄⠀⠀⠀⠀⠒⡰⠊⠁⠒⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠏⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠑⣱⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣶⡀⠀⠀⠀⠀⠄⢎⣣⢀⠀⠀⠀⠀⡠⢇⢎⡿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢭⣴⢀⠤⢊⠼⠀⠩⢦⡐⠌⣠⢶⠾⡥⣜⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡷⢾⣿⣈⣜⣭⠆⠀⠀⠶⣉⡞⣯⣎⢶⣹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⠟⠛⠀⠀⠀⠀⠀⠑⠳⠦⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⡤⣤⣀ ⠹⣿⣏⠉⠉⡻⣆⠀⣠⠞⠋⠛⢻⢿⠏ ⠀⠹⣿⣆⡀⠀⠹⠦⠑⠀⠀⡰⣽⠇⠀ ⠀⠀⠈⣩⡟⠂⠀⠀⠀⠀⠺⣍⡁⠀⠀ ⠀⠀⠘⣿⣷⣄⣄⡿⣴⣀⡼⣾⠇⠀⠀ ⠀⠀⠀⠘⠿⠿⠟⠀⠑⠿⠿⠋⠀⠀⠀

⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀ ⠘⢿⣿⡿⠿⢿⣦⡐⠈⡀⢂⡖⠿⠻⢽⣿⣿⠃ ⠀⠈⣿⣿⣮⠂⡝⡻⣆⡰⣻⡣⠜⡧⢾⣞⠁⠀ ⠀⠀⠙⠛⠿⢶⡤⢉⢮⠝⠢⢠⡵⠾⠛⠁⠀⠀ ⠀⠀⠀⣠⣾⣷⡰⠥⣪⡞⡬⡔⡸⣳⡄⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣾⢷⡋⠙⣶⣷⣟⣯⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⠁⢀⣾⣡⡋⠜⡱⢒⣄⠀⠀⠀⠀⢀⡤⢲⡜⡩⢉⡳⣷⠀⢁⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⢿⢣⢟⡞⣲⠅⠊⣿⣋⡾⣞⡍⠚⠉⢴⠫⣟⡽⣿⡀⠀⢾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠂⠀⠀⠀⣼⣋⠮⠜⠁⣚⡡⣿⣽⣻⣝⢦⢌⠀⠣⡑⢢⢟⡟⠁⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠀⠀⠀⣿⣼⣲⣭⣟⣷⡿⠟⠛⠛⠛⢿⣯⣷⢧⣖⡼⣯⣟⠠⠀⠀⠛⣄⠀⠀⠀⠀ ⠀⠀⡀⠉⠀⠀⠀⠀⠀⠘⠻⠻⠛⢙⡁⠀⠀⠀⠀⠀⠀⠀⠙⡻⢿⣿⣿⠏⡐⠀⠀⠀⠈⠓⢂⠀⠀ ⡠⠊⠀⠀⠀⠀⠀⠀⠀⡼⠷⠦⠖⠋⠉⠒⠒⠊⠉⠁⠚⠒⠛⠛⢷⣤⣧⡜⣠⠁⠀⠀⠀⠀⠀⡹⡄ ⣇⡀⠀⢀⣀⣀⣄⣤⡜⠁⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠈⢷⣄⠻⣴⣤⣀⠀⣀⣘⡞ ⠈⠙⠿⠾⠟⢿⣿⢏⠀⠀⢾⣿⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢈⡟⣻⣿⠉⠛⠛⠛⠉⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⢀⠉⣀⠀⠀⠀⠘⣂⠞⠀⠀⠀⠀⢈⢛⢁⣠⣾⣾⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠋⠀⠈⠈⢻⣶⣿⣶⣴⠖⠉⠀⠀⠉⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⠃⠀⠉⠉⣆⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠤⠤⠼⠃⠀⠀⠀⠀⠘⠧⠤⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⢐⣄⠀⠀⠀⠀ ⠀⠀⢠⠁⢰⠶⠮⢴⣠⠂⠁⠴⡇⢸⠀⠀⠀ ⠀⢀⠄⠀⢰⣤⡴⠾⠛⠾⣶⣤⡇⠀⢢⡀⠀ ⢀⠀⠀⠀⡰⠧⠒⠒⠒⠒⠚⠯⡅⠀⠀⠈⡆ ⠈⠓⠛⢿⡀⠿⠀⠀⡀⠀⠸⠇⣸⡿⠛⠚⠁ ⠀⠀⠀⠀⠉⡉⠈⡻⠓⡊⠈⠙⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀