Chikawa Emojis & Text

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠙⢷⣄⠀⠀⠀⠀⠀⣀⣤⠶⢤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠈⠛⠛⠻⠶⡴⠟⠉⠀⠀⠀⠹⣧⠀⠀⠀ ⠀⠀⠀⢀⣤⠖⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀ ⠀⢀⣼⠟⠙⠳⠶⣦⣤⣤⣤⠶⠞⠋⠛⢷⣄⣀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⣈⡙⠻⠶⠶⣤⣤⡴⠿⣷⡄⠀ ⣿⠁⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⣿⠀⠠⣢⢉⡁⠢⢿⣿⣾⡟⠀⠀⠀⠀⢰⣿⣍⣷⠀⠀⠀⠀⠀⠀⠀⢹⣧ ⣿⡀⠠⡋⠛⠽⣧⠀⠉⠉⠀⣀⢠⡄⢀⠈⠛⠿⡫⣠⣩⣑⣄⠀⠀⠀⢸⡿ ⠸⣷⡀⠈⠉⠉⠀⠀⠀⠀⠀⠈⣿⣿⠏⠀⠀⠀⠃⡉⠉⣙⠝⣀⠀⢀⣿⠇ ⠀⣘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠨⡥⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⣷⣼⠏⠀ ⠘⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⡿⠃⠀⠀ ⠀⠀⠀⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⡶⢶⣄⠀ ⠀⠀⠀⠀⠀⢻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⣀⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⢾⣇⣀⣴⢦⣤⣀⣀⣀⣀⡀⠀⣠⣤⠾⠛⠁⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⢿⣄⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⡔⣹⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⡈⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⡄⠠⣇⠻⣄⡤⠤⠦⠶⠤⣄⣼⣠⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣬⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣴⣏⣴⠀⢲⠂⢤⣄⠀ ⠀⠀⢀⡞⠁⠀⠀⣀⡀⠄⠀⠀⢀⢀⣀⠀⠀⠈⠳⡈⠆⠉⠀⠋⠘⡄ ⠀⡶⠚⠀⠀⠀⢼⣥⣬⡆⠀⠀⢰⣧⣤⣷⠀⠀⠀⠣⠤⠄⠀⠀⠀⢹ ⢸⢋⠀⠀⡰⡢⡼⡍⠉⠠⠄⢆⡄⠉⠉⡵⣤⣶⠄⠀⡒⠄⠀⠀⡉⢻ ⠈⢧⡆⠀⠁⠂⠋⠀⠀⠀⠈⠃⠀⠀⠀⠉⠑⠈⠀⠰⡜⠀⠀⣀⢉⠏ ⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⢀⠈⡟⠀ ⠀⠀⠀⢿⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠀⠀⢠⢠⠟⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣴⣀⡧⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⢰⡤⢤⣤⣤⣤⢤⡤⢤⣤⢸⡏⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣿⣇⣠⣤⣴⣶⣶⣶⣶⡶⢶⣶⣶⣶⣤⣼⣿⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⢸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⣶⡆⠁⠳⣤⣠⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⢠⣴⣤⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀ ⠀⠈⢻⣤⡾⠋⠁⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠿⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢶⣦⡄⠀⠀⠀⠀⠀⠀⢀⣠⣶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣿⣿⠆⠀⠀⠀⠀⠀⢸⣿⣅⣲⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⣤⣝⣿⣿⣯⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣯⣿⣿⠿⢀⡤⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⣿⣿⣯⣿⣻⣿⠀⠀⠀⠀⢠⣆⣰⣷⡀⣶⡀⠀⠀⠀⣴⣟⣾⣿⣿⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⣙⠻⠿⠧⠟⠉⠀⠀⠀⠀⠈⠛⣿⢻⣿⠛⠁⠀⠀⠀⠙⠾⠯⠿⠿⠁⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⢠⣾⠟⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⠻⣷⣄⢻⣯⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⢻⣦⠛⣻⣿⡿⠶⢶⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣶⠀⠀⠈⢿⡜⠿⠃⣿⠋⠀⠀⠀⣶⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⣤⠾⠙⢧⣄⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀ ⠙⢧⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡬⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣠⠄⠀ ⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣧⠀⣿⠀⣸⡟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣿⣦⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡞⠹⣦⠰⡞⠙⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⠀⠀⣿⠐⡇⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡸⣄⠀⣿⣨⡇⠀⣟⡀⠀⠀⠀⠀⠀ ⠀⠀⢠⡶⠚⠉⢁⡀⠀⠀⠀⠀⠀⡈⠉⠙⠲⣤⡀⠀ ⢀⡶⠋⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠈⠻⡄ ⣾⠁⠀⠀⠈⠀⣠⣂⡄⠀⠀⠀⣔⣢⠀⠈⠀⠀⠀⢹ ⡇⠀⠀⢠⣠⣠⡌⠓⠁⠀⡀⠀⠙⠊⡄⢀⣀⠀⠀⢸ ⢷⡀⠀⠈⠁⠁⠀⠀⠈⠓⡓⠂⠀⠀⠉⠈⠁⠀⠀⡼ ⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁ ⠀⠀⢾⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⠀⠀ ⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠊⠁⠀ ⠀⠀⠀⠘⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠀⠀⠀ ⠀⠀⠀⠀⢿⣼⠉⠉⠙⠛⠛⠛⠛⠉⢹⣁⠟⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣉⠘⠒⡇⢹⠈⡇⠲⢎⣠⠿⡄⢶⠦⢃⠿⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⡤⡴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢣⡱⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⢀⠤⠆⠃⢃⠀⢤⡀⠀⠀⠀⡋⠒⠒⠒⠊⢙⡀⠀⠀⠀⡀⠃⠈⠂⠀⠊⢳⠀ ⡰⢁⠊⠁⠀⠀⡈⢦⠹⡄⢰⠁⠀⠀⠀⠐⠂⠀⠈⡆⢠⠎⠙⠒⠊⠙⠆⠤⠴⡄ ⡇⢠⣤⠛⢀⣨⠛⡒⠆⡇⠆⢠⠶⡍⢠⠄⠐⣛⠆⡐⢸⢰⢴⠛⢃⡐⢿⣀⡀⢸ ⠘⢄⠀⠀⠀⠀⠀⠀⠰⠁⢘⠦⠀⠀⠀⠃⠀⠀⠐⡃⠀⡆⠀⠀⠈⠁⠀⠀⢶⠆ ⠀⠠⣦⠀⠀⠀⠀⢀⠟⠁⠀⠉⣆⠀⠀⠀⠀⢀⠆⠀⠀⠀⣄⠀⠀⠀⠀⢀⠧⡄ ⠀⠀⠢⠑⠢⣤⠲⠈⠀⠀⠀⠀⠈⠑⠒⢣⡄⠁⠀⠀⠀⠀⠚⠒⠦⠤⡴⠊⠉⠁

⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡏⠂⠂⠂⠂⢙⠛⠙⠛⠻⢿⠟⠁⠂⠂⠸⣿⣿⣿ ⣿⣿⣿⡿⠟⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⠂⣿⣿⣿ ⣿⡿⢋⣴⣤⣀⣀⣀⣀⣠⣤⣾⣷⣤⣀⠂⠂⠂⠂⠂⠂⢿⣿⣿ ⣿⢁⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣟⣿⣶⣦⣤⣤⣤⣦⠹⣿ ⡇⣼⣿⣿⣿⣿⣿⢋⣭⠹⣿⣿⣿⣿⠟⡛⢿⣿⣿⣿⣿⣿⣇⢸ ⠁⣿⣿⡟⡛⠛⢿⣄⣂⣴⣿⣿⣿⣿⡀⠉⢠⣿⣿⣿⣿⣿⣿⠂ ⡇⢻⣿⣷⣿⣿⣾⣿⣿⣿⣙⠁⠛⣻⣿⣿⣣⣃⢉⢹⣿⣿⡟⢸ ⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣾ ⣿⡘⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⣦⣄⠀⣀⣤⣤⣶⣶⠶⠶⠶⠶⠶⣶⣦⣤⣤⣀⡀⢀⣤⡾⠷⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠈⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⠏⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣦⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⣤⣤⣀⣼⣟⠙⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⠉⠙⠻⣾⣟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢰⣆⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢶⣤⠀⠀⠀⠀⠀⠀⠀⢠⣴⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⠠⡄⢤⠤⣸⣿⡶⣞⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⢶⢾⣿⠄⣀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢀⡵⣻⡾⣶⢯⡮⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠡⣸⣖⣬⣵⢦⡭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠑⠦⠱⠌⠿⠉⠀⠀⠀⠀⠀⣶⣄⣿⣆⣠⡄⠀⠀⠀⠀⠘⢗⣺⠣⠟⣿⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠰⢿⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣷⣆⣀⣀⣀⣤⡿⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣀⣤⣤⣤⣤⣤⣤⣴⠾⠋⠀⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⣀⡔⡖⠄⠀⠀⠀⢠⠐⢢⣄⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠁⠗⠎⡘⠀⠀⠀⢸⡈⢰⠯⠌⢆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣤⢄⠀⠈⠲⢀⣀⠝⠁⠀⠀⠀⠀⠳⣢⣄⠴⠊⠀⢀⡠⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡣⠁⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢁⡀⠀⠈⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣤⣦⣴⣴⣶⣾⣷⣄⣠⠄⢤⠄⠤⡤⢀⣀⣾⣵⣶⣾⣿⣷⢧⠃⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣨⣿⣿⠿⠛⠉⢅⠤⣟⠏⠏⣄⠉⠬⡄⡈⠄⢀⠉⠛⠻⢿⣿⣥⣼⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠅⣄⢰⠆⡟⡬⡟⣶⣃⡿⠓⠴⣡⡀⡂⠐⡌⠀⠀⠀⠉⠙⠿⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⡨⡐⡶⠴⠞⢛⣅⣐⠿⠋⠁⠀⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⢀⠀⠉⠱⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠯⠤⠮⠾⠿⠷⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠴⠦⠤⠦⠤⠴⠾⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣄⡀⠀⠀⠀⠀ ⠀ ⠀⠀⢸ ⠀⠀⠀⠀⡠⠐⠠⡇⠀⠀⠀⢀⠀⠀⠀⠀⣾⢷⣥⣾⣿⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⣽⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈ ⡎⠀⠈⠉⠀⠀⠐⡇⠀⠀⠀⠀⢁⣴⣶⣶⣾⣿⣷⡾⠏⠀⠀⠀⡀⠀⠀⠀⠻⣦⣿⡾⣧⣴⣶⣤⡀⠀⠀⠀⢰ ⠱⣄⠅⠀⠀⠀⣰⠵⣄⠀⠀⠀⣶⣿⣿⣿⣿⡇⠀⠀⠀⢰⣄⣘⣿⣀⣠⡀⠀⠀⠀⣨⣾⣿⣾⣿⡇⠀⠀⠀⡘ ⠀⠈⡱⠶⢤⠘⡁⠀⢨⡆⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠉⢉⣍⣍⠉⠀⠀⠀⠀⠘⠻⠷⠿⠛⠀⠀⠀⢠⠃ ⠀⠘⢄⣀⠀⣳⡑⢔⠁⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀ ⠀⠀⠀⠀⠉⠀⠑⡌⡖⠒⠨⢦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡌⢦⠀⢸⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⢃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⣁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⢀⠜⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢲⠂⠒⠒⠒⢤⠐⠒⠒⠒⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠔⠛⠢⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

(՞⸝⸝ o̴̶̷̥᷅  ̫  o̴̶̷̥᷅ ⸝⸝՞⁠)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣿⣳⣄⠀⠀⢠⣖⣿⣾⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⡟⠀⠈⢿⣯⣧⠀⣾⣿⡇⠀⠙⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢸⣿⣿⢀⣽⣿⡇⠀⠀⢸⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠰⠀⠈⣿⣿⢸⣙⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⡇⠀⠨⠀⢠⣿⣿⢨⣿⣿⠀⠀⠀⠀⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⡆⠀⢸⣿⣿⢻⣽⣿⠀⠀⠀⠀⣿⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⢀⠀⢸⣿⣿⠸⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠸⠀⢸⣿⣿⣼⣿⣿⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣧⠀⠁⠘⣿⣿⣽⣿⡏⠀⠀⠀⣾⣿⢧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣭⡿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⠻⠿⣯⣿⣂⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣺⣽⡿⠋⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠛⢷⣯⡢⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣮⣾⠟⠁⠀⠀⠀⠀⢀⣠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣦⣄⠀⠀⠀⠀⠀⠙⢿⣮⣢⠀⠀⠀ ⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀ ⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠹⣷⣷⠀ ⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⡛⣷⡄⠀⠀⠀⠀⠀⠀⠀⣴⡟⠛⢳⣄⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢻⡏⡇ ⢸⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⠚⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣀⣄⢀⡆⡄⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⡀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⡇⠀⠀⠀⠀⠀⢸⡟⣼⠏⣾⢿⡿⠀⠀⠀⠀⠀⣀⠀⢰⣾⠃⠀⡀⠀⠀⠀⠀⣾⡟⣾⢧⣿⣾⡗⠀⠀⠀⠀⠀⢰⣿⣿ ⢹⣻⣧⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⠀⠙⠳⠞⠛⠷⠞⠋⠀⠀⠀⠀⠉⠀⠛⠘⠁⠛⠁⠀⠀⠀⠀⠀⣼⣿⠏ ⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡟⠀ ⠀⠀⠻⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⠋⠀⠀ ⠀⠀⠀⠘⢪⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠿⣿⡂⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⣿⣗⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⢿⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⣾⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠇⠸⣿⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⡦⠌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢸⣿⡗⠛⠃⠙⠃⠘⠛⠟⠿⠭⠽⠿⠿⠛⠟⠃⠓⠚⢻⣿⡇⢀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡿⣾⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢷⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠙⣿⠀⢀⣴⠟⠋⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⢰⡟⣠⡾⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣿⢣⡟⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣸⠇⣾⠀⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢠⡿⣸⡇⠀⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡇⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⣿⠀⣿⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⣿⠉⣿⠀⠀⠀⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⡹⠷⠀⠀⠻⠟⠛⠀⠀⠀⠛⠿⠷⠶⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣼⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⡠⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣾⠟⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⡄⠀⠀⠀ ⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠷⣆⠀⠀⠀⠀⠀⠀⢠⡾⠛⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠶⢶⣿⠀⠀⠀⠀⠀⠀⠸⣿⣶⣺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣳⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠔⢒⡆⢀⠂⢌⠉⠉⠁⢀⠀⢰⣆⠀⢠⡀⠈⠉⠉⠀⣤⠀⣼⢩⡏⢵⡆⠀⠀⠀⠀⠀⠀⠀⡘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡀⠀⠀⠸⠻⡿⠁⠏⠸⢯⠇⠀⠀⠘⠳⣾⣿⣶⡞⠃⠀⠀⠀⠈⡇⠸⠋⠸⢃⢛⠀⠀⠀⠀⠀⠀⠀⠰⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠐⠒⠒⠂⠁⠀⠀⠀⠀⠀⢻⡿⡟⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣴⣟⣫⡿⠞⠛⠋⣛⣷⡦⠤⠶⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⣦⣀⣄⡀⠈⠉⠁⣀⣠⣴⠟⠋⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀

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⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣤⣀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⢏⡾⣸⢧⣳⠀⠀⢀⠀⡀⠰⠄⠀⠆⠀⠀⠃⠀⠀⠀⡴⣏⢿⡹⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⣜⢧⡻⣜⢧⢫⣽⣃⠄⠂⠀⠀⠀⠀⠀⠠⠐⠀⠉⢠⢀⢠⣿⣹⢲⣝⡳⣎⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡳⣝⢮⡳⣏⢮⣛⡶⣇⠀⠀⠀⠀⣁⣀⣀⣀⡀⠐⠈⠀⢀⡾⣧⠳⣭⢞⣵⢫⡶⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡳⣝⢮⡳⣝⣮⡝⣷⣻⡴⣶⢶⡶⣯⣻⡽⣭⣗⣖⣶⣲⣼⣳⡟⢦⡿⣜⣟⡾⣳⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⣳⢻⡼⢶⣻⢷⣯⢿⡽⣯⣟⡷⣯⣟⣷⣻⣞⣷⣻⣞⣷⣻⢯⣞⡽⢮⢷⡻⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣯⣛⣯⢷⣟⡾⣯⣟⣷⢯⣟⣷⣻⣾⢷⣻⣞⣷⣻⢾⣽⣻⣞⣽⣻⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣄⢰⠖⡑⢖⡤⣄⣀⡴⣝⣳⣟⣾⣻⣞⣿⣳⢯⡿⣯⣟⣾⣽⢯⣟⡿⣾⡽⣯⢿⣞⣷⣻⢾⣵⡳⡄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠄⣀⠸⠴⡂⢏⡕⡊⢽⣳⡟⣼⣏⣷⣻⣞⣷⣻⢾⣽⣻⣽⢷⣻⣞⣯⡿⣽⣻⢷⣻⡽⣟⣾⣳⣯⣟⡾⣽⣳⣾⣛⡾⣝⡯⡤⠀⠀⠀⠀ ⠊⣱⡍⣣⠙⢎⡜⠱⢢⢱⣻⢳⣞⣧⣟⣾⠳⠋⣋⣓⠫⢬⢿⣽⠋⣇⣹⣽⣡⠾⠙⠛⠹⢷⣻⢾⣽⣻⢷⣫⣷⢿⣹⠾⣵⢧⡀⠀⠀⠀ ⢀⣹⣎⡵⢂⠦⣒⠼⠌⡡⢏⡿⣎⣷⣻⢮⠀⡘⠓⠚⠁⠈⣟⢶⣻⠽⣳⢯⡇⢀⠫⠵⠛⠀⢯⣟⡾⣽⢯⡷⣯⢿⣽⣻⢮⡟⣵⡀⠀⠀ ⠠⢑⢚⠘⢃⣎⠠⡜⢠⠃⠉⠘⠹⠞⢽⢲⠥⡄⣌⣉⣤⢾⣽⣳⡝⢿⣳⢯⡶⣄⣁⣉⣡⣀⣿⣽⣻⡽⣯⢿⣽⣻⣞⡷⣛⣾⢳⣟⡄⠀ ⠀⠘⠊⠀⠈⠉⡀⠁⢈⠀⠀⠀⣤⣀⡈⡌⣐⣁⣯⣟⡿⣾⡽⡉⠇⠘⠋⣞⣷⣻⢿⡽⢋⠉⡉⡙⢩⣷⡻⣾⡽⣯⣟⣷⡻⣽⡺⣽⣷⠂ ⠁⠀⠀⠓⠝⣖⡤⡐⠤⠠⣩⢻⡵⢯⣷⣻⢾⡽⣾⣽⣻⢷⣻⣽⣘⡃⣿⡽⣾⡽⣯⢷⣯⢿⡽⣽⣻⣼⢳⣯⣽⣳⢟⡾⣝⣳⢽⠣⠟⠀ ⠀⠀⠀⠀⠠⣖⡳⡵⢀⠣⢀⠻⡜⣟⢶⢯⡟⣽⢳⢯⣟⣯⢷⣯⢦⣝⣷⣻⢷⣻⣽⣻⣞⣯⣟⢷⡳⣞⢯⠶⣳⢽⡺⣵⠯⠃⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠁⠀⢁⠈⡌⠀⠈⠘⠩⠞⠉⠀⢡⠈⠈⠘⠳⢞⡻⢞⡳⠏⠏⠓⠊⠑⠘⢳⢎⠯⠓⠉⡠⡰⢍⠘⠹⠎⠛⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⣔⣆⠐⡈⠢⠀⢁⠂⠀⢀⠀⠌⠀⠁⠀⣨⡐⢍⠀⠀⠀⠀⠒⠈⠀⠠⣀⠂⠠⢈⢶⣛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡞⡀⠠⠐⠀⠀⠀⢂⠀⠀⠠⢀⠀⠸⡱⠆⠹⢘⢬⠃⠀⢀⠂⠐⡀⠀⠔⡀⠂⠁⠀⠀⢨⣒⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢓⡼⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⠱⢊⠆⠀⠀⠠⠀⠁⠀⢈⠐⠀⠀⠀⠀⠀⠀⢱⡓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡼⣭⢳⡽⡇⠀⠀⠀⠀⠀⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡝⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢧⢏⡾⣵⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠈⠐⠀⠀⠀⠀⣤⡠⣄⢤⣠⡐⣮⠵⠃⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠈⠚⡶⣩⢞⣳⢢⡔⡤⣖⣦⣀⠀⢀⡄⣾⢯⡝⣄⠀⢀⣀⢀⣀⣤⣞⡷⡽⣎⠷⣣⡛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⠱⣧⢚⡵⣛⠼⢦⣝⣣⢞⣭⢳⢻⡼⢯⣷⣞⡧⣟⠯⢟⣩⣑⠎⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠁⠉⠓⠚⠒⢫⢞⠭⠓⠞⡽⠚⠊⠁⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

꒰՞o̴̶̷̤ᾥo̴̶̷̤՞꒱

ᥥ ᥥ (◜o̴̶̷̤⩊o̴̶̷̤◝) ́( ) ̀ usagi :3 ̀ ́ ̀ ́

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣁⢈⣭⣿⣷⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣖⣦⣤⣲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⡿⠟⠋⠉⠻⡟⢟⡽⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⢞⢝⣍⢿⣹⡿⠳⣛⣋⣓⣩⣲⡤⡀⠀⠀⠀⠀⠀⣰⡿⣣⠟⠁⠀⠀⠀⠀⠀⠘⢑⡻⣟⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣿⣽⡿⣿⣟⡁⠀⠀⠀⠉⠉⢻⣟⠋⠝⢓⢤⣠⡴⣶⡿⣟⣭⣓⠖⠢⣤⣀⣀⣀⣬⡶⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣫⢿⡇⣃⠴⡀⣀⡠⠤⠶⠒⣺⠿⣟⢸⣯⣃⣳⡾⡲⠷⣮⣥⣼⣮⣤⣥⣾⣿⣿⣻⡿⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⠣⣿⣿⣶⣾⣿⣷⣶⡂⢩⡭⢊⣽⣿⡿⠿⠿⢿⣦⣴⣙⠈⠙⠏⠉⠋⠉⠀⠩⠀⠂⠀⢀⣤⢤⣤⣤⣂⣅⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠙⠟⡟⢛⠋⡵⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⠖⣫⠵⢏⣽⣿⣿⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣩⢅⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣢⣴⣿⣿⣿⠟⠁⠈⢿⢿⡿⠄⠀ ⠀⠀⣰⣾⣏⣩⣉⠰⣄⠀⠀⠀⠀⣠⢖⣴⢟⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠣⠂⢀ ⠀⣰⡇⠈⠙⠤⣽⣿⣹⣷⣤⣈⣴⣩⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⡫⠁⠀⠀⠀⣀⣴⣾⡿⠃⠁⠀⠘ ⢰⣿⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡀⣤⡶⠁⢼⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⡆⠡⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⢂⠣⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⣿⣿⡶⡤⣕⡤⠀⠂⠀ ⠀⢀⠀⣤⠔⠆⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⠀⠀ ⠁⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⋆౨ৎ˚⟡˖ ࣪⋆୨୧⋆⋆ ˚｡⋆୨♡୧⋆ ˚｡⋆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣄⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠘⢷⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣾⣿⡟⠀⠈⠉⢹⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠷⣾⣿⠁⢸⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⣤⣤⣴⣿⣿⡅⠀⠀⠀⠀⠀⢹⣿⣿⡟⠻⠿⠿⣿⣿⣿⣿⣿⣿⡄⣀⡄⠀⣾⠛⡆ ⠀⠀⠀⠀⠈⣿⠀⢸⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⡷⣦⡟⠉⠁ ⠀⠀⠀⠀⠸⣿⠀⠀⢧⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⠿⠛⢡⠃⠀⠀⠀⠀⢸⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣖⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⠳⣄⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⢾⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠟⠁⢠⡏⠀⢿⡞⢻⠀⠀ ⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⣀⣠⠴⢚⡟⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣼⠇⠀⣼⢣⣼⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠲⢤⣀⣀⣀⣀⣀⠤⠚⣹⡟⠀⡠⠃⣼⠋⠀⠀ ⢀⡀⠀⠀⠀⣿⣿⣿⣷⡄⠉⠐⠒⠂⠤⠀⠒⠊⠁⠀⠀⣀⣤⣶⡒⢢⣄⠀⠀⠀⠑⢄⡀⠀⠈⠉⠁⠀⠀⣰⣿⠀⠾⢧⡾⠃⠀⠀⠀ ⠈⢿⣦⡀⠀⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠈⠑⠒⠀⠄⣶⣾⠟⠛⠁⣴⡟⠁⠀⠀⠀⠀ ⠀⠘⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠛⠶⣶⣛⣛⢛⢿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣤⣶⡾⢋⣯⣴⣶⡿⠑⢲⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⠛⠛⠛⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⡟⢽⣟⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⠒⠂⠤⠼⢿⡙⠛⡿⢿⣿⣿⣿⣿⣿⡿⠋⠙⠋⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⣿⠀⠀⠀⢀⣄⡳⣾⠁⠀⠀⠉⢹⣿⣿⠇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠉⠉⠉⠉⣿⠀⠸⠛⢩⡿⠃⠈⣿⡀⠀⠀⠈⠯⢿⣿⣦⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠀⠀⠀⠀⣿⠀⠀⣠⡿⠃⠀⣼⣿⣿⡷⠶⠦⠤⠬⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⠀⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⡆⢸⣟⠁⢠⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⠖⠻⣷⡀⠀ ⠀⠀⠀⠀⣧⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⠴⠖⠛⠛⠛⠻⠿⠷⠀⠀⠘⠋⠀⠀⠀⠀⠘⣷⠀ ⠀⠀⠀⠀⢿⠀⢿⣿⣿⣿⣿⣿⣿⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⢠⣿⣆ ⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣇⣀⣀⣠⣤⠴⠟⢹⡇ ⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣧⠀⠴⠿⠶⠶⠶⠶⠶⠟⠋⠀⠀⢁⣀⣀⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢠⡟⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣶⠤⣄⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⢀⡿⠀⠀ ⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠘⢦⣤⣄⣩⣩⣩⡭⠏⠁⠀⠀⠀⢀⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠈⠻⣍⣛⣶⣾⣽⣤⡄⠀⠀⣰⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⣠⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡓⠒⠶⠤⠤⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⢰⣿⣿⣿⠿⢿⣿⣿⣿⣿⠶⢤⠤⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⣼⣿⣿⣿⠀⠀⠸⡟⡟⠻⣦⡠⠷⠿⣼⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠃⢠⣾⣿⣿⣿⡏⠀⠀⠀⢹⡿⡄⠈⡅⢿⣷⡇⠘⢧⡀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⢳⣹⡀⠈⠓⠛⠁⠀⠈⠻⣦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣄⡷⠷⠤⠤⠤⠖⠒⠒⠋⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠘⣧⡀⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠲⣤⡙⢿⣿⣿⣿⡧⠤⣀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡈⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢡⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀

▲_▲ ( ́o̴̶̷̤ ̫ o̴̶̷̤ˋ) 𝓗𝓪𝓬𝓱𝓲𝔀𝓪𝓻𝓮 :3 (⊃ ⊂） ̀ ́ ̀ ́

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⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀ ⠀⡐⠁⠀⠀⠐⠄⠈⠉⠀⣤⣶⣒⡂⢠⣍⡪⡢⡀ ⠀⠃⠀⠀⠀⠀⠀⠁⠀⣠⣓⢢⡀⠉⠁⢀⣖⣸⡄ ⢀⡜⠒⠒⠠⣀⠀⠄⠜⠀⣠⠤⣌⠂⠀⠶⠶⡼⠆ ⠈⢇⢈⠉⠐⠠⠑⠅⠀⢸⢀⣀⢖⠆⠀⠡⣐⡶⡃ ⠀⠀⠑⢕⡢⠤⠆⠀⠀⠊⠀⠀⡽⠂⠀⠀⠀⠁⠇ ⠀⠀⠀⠀⠀⠉⠙⢅⠀⠈⠀⠨⢏⠀⠈⣂⠤⡤⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⢀⠔⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣣⣰⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⣠⠊⢸⢯⠀⠡⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣦⡾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠀⠉⠀⠻⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⡶⣶⠀⠀⠀⠀⢯⣷⣽⡇⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠛⠞⠏⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢤⣿⣿⡆⠀⠈⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠲⣶⠞⠛⠻⣶⡴⠖⠶⣄⠈⠃⠉⠁⠀⠀⠀⠈⠻⣄⠀⠀⠀ ⠀⠀⢀⡾⠃⠀⢠⡶⣤⣀⣶⠟⠉⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠟⠒⢿⣄⠀⢀⣀⠀⠀⠹⣧⠀⠀ ⠀⢀⡿⣡⢾⡆⢸⡇⢾⣝⠿⣦⣀⣀⣤⠴⠶⠖⢻⡟⣿⠛⠶⠶⢦⣤⣀⢀⣠⣿⣿⡛⣿⠀⢀⣄⠘⣧⠀ ⠀⣾⠁⠻⣾⡷⢾⣇⣼⡿⠃⠈⠉⠉⠀⠀⠀⠀⣸⠉⣿⠀⠀⠀⠀⠈⠉⠋⠽⢿⣿⢡⣿⣀⠘⢿⠇⢹⡆ ⢸⡇⠀⣸⡏⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⠃⠈⢳⡄⠀⠀⢿ ⣾⠁⢀⡿⠗⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢹⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠻⣦⠀⠸⣧⡀⠀⢸ ⢻⡀⣿⠀⠀⡿⠀⠀⠀⠀⠰⣶⣶⠆⠀⢀⣼⠃⠀⠀⠀⢿⣤⠁⠀⣾⣶⡦⠐⠀⠀⠀⠹⣇⠀⠀⣻⠀⣼ ⠸⣧⣼⠗⢸⡇⠀⣠⣤⣤⣤⣤⣤⣤⣤⡞⠁⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⠸⣿⣠⡏ ⠀⠹⣇⠀⢸⣇⣸⡟⢹⣿⣿⣿⣿⣿⠏⣿⠀⠀⠀⠀⠀⠀⡟⢹⣿⣿⣿⣿⣿⠏⣿⣀⣀⣿⠀⠀⢸⠏⠀ ⠀⠀⠙⣷⠺⡏⠉⠻⢮⣝⣛⣟⣛⣥⠾⠃⠀⠀⢠⣶⠀⠀⠻⢮⣝⣛⣻⣛⣭⠞⠉⠀⠀⡟⠀⢴⡛⠀⠀ ⠀⠀⠀⢿⣄⣻⡀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣸⠃⠀⢨⠇⠀⠀ ⠀⠀⠀⠀⠉⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠶⠒⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣉⠓⠶⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠖⠋⣡⣾⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠻⢿⣶⣤⣤⣀⣨⣭⠟⣿⠛⢯⣭⣁⣀⣀⣤⣴⠞⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⢏⣴⣦⡄⠀⠀⠈⠁⠀⣼⠃⣰⠟⢧⡈⢿⡈⠉⠉⠀⠀⣠⣶⡄⢹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠸⠿⠛⠁⠀⠀⠀⠀⠀⠛⠟⠉⣀⠈⠛⠛⠁⠀⠀⠀⠀⢳⡿⠇⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⢸⣻⡇⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡇⢠⣤⠀⢸⣄⣀⣀⣀⣀⣀⣠⣿⠈⠫⠼⣿⢀⣀⣀⣀⣀⣀⠀⣟⢀⣄⠀⢻⡄⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠛⠋⠁⠀⠉⠉⠛⠻⠷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣴⠟⠋⠉⠉⠉⠛⠛⠒⠒⠓⠲⠶⢦⣤⣤⣄⣙⣷⣤⡄⠀⠀⠀⠀ ⠀⠀⣸⡏⠀⡆⠀⠀⠀⠀⣠⡶⡶⠶⠛⠉⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠻⠿⢷⣆⠀ ⠀⠀⣿⠇⠀⣳⡄⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠀ ⠀⢠⣿⠀⠀⢈⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄ ⠀⢸⣿⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡶⣦⣄⣤⡶⠶⠶⠦⣤⣤⣦⠴⢶⣶⠶⠶⠶⠤⢤⣤⣤⣀⣠⣤⣀⣠⣿⠇ ⠀⢸⣿⢀⡿⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⡉⠛⠛⠛⢁⣾⠋⠀⠀⠀⠀⠀⠀⠹⢷⡞⠁⠀⠀⠀⠀⠀⠀⠙⢿⡁⠀⠉⢿⡅⠀ ⠀⠘⣿⠈⣿⡀⠀⠀⢀⣀⣴⡿⠋⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢠⣾⣿⣿⣧⠘⣿⣠⢯⣿⣿⡆⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀ ⠀⠀⣿⡀⠙⢿⢶⣶⡿⠋⣩⢤⡀⠀⢠⡏⠀⠀⠀⠘⣷⣀⣀⡀⠘⢯⣟⡿⠟⣠⡇⠙⣾⣻⠽⠃⠀⠀⢠⡾⠁⠀⠀⣸⡟⠀ ⠀⠀⣿⡇⠀⠀⠀⢸⡗⣼⠃⠀⢹⠀⢾⡀⠀⠀⠀⢶⠛⢻⣯⠿⠷⣆⢀⣠⡾⠋⠻⣦⣀⣀⣀⡤⠴⠚⠛⢻⡦⠀⣴⡟⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⢸⡇⠸⣄⢀⡾⠀⠀⢷⠀⠀⠀⠈⠳⠚⣿⣦⠤⠟⠛⠉⠀⠀⠀⢿⣍⣉⣁⣀⣀⣤⡴⠛⠀⠀⣿⡄⠀⠀ ⠀⢠⣽⣧⣦⣴⣶⣾⣿⣄⠈⠉⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡏⠉⠛⠶⣤⣤⣄⣀⣀⣀⣀⣀⣽⣷⣬⣥⠀⠀⠀⠀⣸⡇⠀⠀ ⣠⣿⠉⠀⠀⠀⠀⠙⣷⣿⡆⠀⠀⣴⠶⢬⣧⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡁⢈⡏⠹⡇⢈⣿⠁⠀⢀⡴⠶⢦⣴⡿⠁⠀⠀ ⣸⡧⠀⠀⠀⠀⠀⠀⢿⡝⣷⡀⠀⣧⠀⠀⢹⡇⠀⠀⠀⢸⡅⠀⠀⠀⠀⠈⠉⠉⠁⠀⣏⠉⠁⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀ ⠻⣷⡄⠀⠀⠀⠀⢠⣾⠛⠙⣿⣀⠈⠳⠴⢻⡅⢀⡠⢄⡘⣿⠛⠛⠿⣟⠛⠶⣄⡀⢀⡟⠀⠀⠀⠀⠘⢆⡀⢀⠟⣿⠇⠀⠀ ⠀⠈⠛⠛⠻⣶⡶⠟⠃⠀⢠⡟⠙⣷⠀⠀⠈⡇⡏⠀⠈⢧⣌⠳⢶⣤⣌⣀⣀⣨⣷⠟⢡⡄⠀⠀⣠⠤⣄⡙⠁⢰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠹⣧⠀⠀⡇⠙⣦⡴⠋⠀⠓⢦⣤⠴⠿⠛⠻⠶⣶⣞⣁⣀⡀⠙⢦⡾⠁⢀⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⣴⣶⣿⡻⣾⣿⡛⠿⢶⣶⠿⠿⣿⣷⣶⣤⣤⡴⠶⣿⢋⣉⣿⣙⣻⣿⣿⣿⣻⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸⣟⠻⠿⠿⣿⠛⠛⠿⠿⠿⠿⠿⠯⠿⠯⣿⣉⣈⣿⠭⠍⠉⠉⠭⠭⠯⠤⣿⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠬⠽⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣷⣦⣄⣸⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣽⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠑⡈⠷⣄⢹⣏⠛⠋⠉⠉⣹⡏⠉⠉⠉⠉⠉⠙⣯⣉⠉⢉⣩⡿⠈⢈⣿⡰⣍⠙⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇⢻⡷⠟⠀⠉⢻⡗⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⠁⠀⠀⣿⣿⢹⠙⣶⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠾⠃⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠛⠛⠾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠻⠛⢦⣄⣀⡀⠀⠀⠀⠀⢠⡏⠀⠀⠙⠓⠛⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣄⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠘⢿⣒⣤⣤⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⠻⠶⣶⣖⡶⠟⠀⠀⠀⠀⠀⢀⠀⢀⣀⣈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠟⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⢶⡶⠟⠉⠁⠉⠙⠛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⡶⠋⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡠⠞⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣠⠤⠤⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣞⡵⠋⠀⢀⣴⣾⡿⠛⢆⠀⢸⡇⠀⢀⣠⠤⠶⠶⠦⢽⣷⠀⠀⠀⢠⠿⣆⠀⢶⡄⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠁⠀⣴⣿⣿⣿⣇⠀⣸⡀⢸⠁⠀⣀⣤⣶⣶⣶⣶⣤⣌⠳⣄⠀⡏⠀⠹⣇⠀⠉⠉⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢸⢀⡾⠋⠘⣿⣿⣿⣿⣿⣿⣷⡀⢰⠇⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⢸⢻⣧⣄⠀⠉⠛⠻⣿⣿⣿⡿⣿⡾⠀⡔⠻⣦⢸⡈⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠘⣆⠀⠀⠹⣿⣿⣿⣿⠿⠋⣠⠏⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣹⠇⣸⣀⣰⣿⡄⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⢠⡀⠀⠈⢦⣀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠙⢿⣇⠀⠀⠀⢀⣴⣿⡿⢠⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⢸⡇⠀⢀⣠⡬⠽⠶⠶⠿⠽⠯⠤⠤⠤⠤⠤⠤⣄⣉⣻⠶⠞⠛⠉⠀⡇⠸⣿⣿⣿⣿⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⣴⠃⠀⠀⣸⢳⣜⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠓⠦⣄⠀⢷⡀⠙⠿⠟⠁⢰⠃⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⢠⡏⠀⠻⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⠀⠀⠈⠙⠾⣿⣦⣀⣀⣴⡏⠀⠀⠀⠀⠀ ⠀⠀⣼⠀⠀⢠⡟⠁⠀⠀⠙⢦⠙⣟⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⡞⠀⠀⠀⠀⠀⠈⠳⣿⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠞⠛⡄⠀⠀⠀⠀⠀ ⠀⠀⡇⢀⡼⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣻⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣩⣿⡿⠛⠉⠀⠀⢳⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⣠⡶⠛⠁⢀⣿⡟⠀⠀⢶⣎⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⢷⢸⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⡼⣿⡇⠀⠀⢾⣧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⡞⠀⠀⠀⠀⠛⠛⠺⢧⡀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢻⡄⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠙⢦⡘⣇⠀⠀ ⠀⠀⠀⠈⢿⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢻⣙⣦⣀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢻⣿⡀⠀ ⠀⠀⠀⠀⠈⢦⠀⠹⣧⠀⠀⠀⠀⠀⠀⠰⠚⢢⣀⣽⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡄⠀ ⠀⠀⠀⠀⠀⠈⠳⡀⠹⣄⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⢠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠷⣦⡀⢠⡀⢀⣽⡟⢨⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⠳⡦⢄⡀⠐⠤⡀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⢷⣶⣶⡿⠯⠁⣹⢿⠀⠀⠈⢂⠈⠱⢄⠈⠑⣜⠐⡄⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠉⠉⠏⠀⣸⠀⢀⣀⣬⠦⠤⠤⢵⣄⡋⣧⣰⠀⢀⣠⣴⡶⠟⠛⠉ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⣴⢿⠋⠋⠀⢰⠺⣿⡏⠈⠹⠿⡪⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡀⠉⢸⠀⠀⣞⡵⢉⠆⣀⠔⠻⡀⠙⠁⠀⢀⠎⠀⠀⢀⠄⠀⠀⢀⠜ ⠀⢀⣀⠀⠀⠈⢹⣰⣾⣯⣿⢽⣤⣾⠶⣪⠧⠤⠀⠀⢈⡗⠒⠉⠀⠀⣠⡾⠑⠈ ⠀⠀⠀⠈⠁⠂⢌⡄⠙⢭⡹⡾⠤⠜⢻⠿⠭⠭⣉⣉⣾⠷⠶⠒⠚⠯⢓⡄⠀⠀ ⣀⣀⣀⣀⣀⡀⠤⠝⠒⠒⠚⠛⠓⠺⠥⠤⢤⡔⠚⠉⠉⣒⠢⣤⣤⠔⠛⠂⠀⠀ ⠀⠀⠠⠤⠄⠒⠂⠉⠉⠉⠉⠀⠐⠒⠂⠤⢀⣀⠈⠉⠚⠛⠁⠤⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠅⣒⠂⠠⠤⠤⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠑⠢⢄⡀⠈⠁⠒⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠈⢆⠀⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀ ⠀⠈⠛⠉⠉⠉⠉⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡁⠀⠀⠀⠀⠀⠙⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢳⡄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⣠⡞⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⣠⡿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢸⣟⣁⠀⢾⣿⣿⠻⣿⣿⣿⠏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣇⠀⠀⠀⠀⠀ ⢸⡟⠛⠀⣾⣿⢿⣷⣌⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀ ⠘⠀⠀⢠⣿⣿⣆⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡘⣿⣿⣿⡂⢻⣿⣬⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣿⢻⣿⣇⠈⢿⣿⣷⠉⢻⣧⠀⠻⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢳⡄⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⣀⣀⡀⠀⡇⢿⡇⢻⣿⣵⡀⠻⣷⠀⣀⣿⡤⣀⣹⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⡿⠂⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠴⠛⠉⠀⠀⠀⣧⢸⡇⠀⠹⣿⠳⠀⢸⣿⣫⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠹⣿⡏⣇⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣭⣼⡇⠀⠀⠘⠇⠀⠈⠛⠋⣽⡾⠟⠛⠛⠉⠉⣿⣿⣿⣿⣿⣦⢹⣿⢹⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⡿⠃⠀⠀⢀⣤⡆⠀⠀⣠⠔⠁⠀⠀⢀⣠⠄⠸⣹⣿⣿⣿⣼⢸⣿⡼⠀⠀⠀⠀⠀⠀ ⢸⠒⠲⢾⣿⣿⣿⣿⣿⠀⣠⣾⡿⣟⣿⣷⣿⠿⠛⠀⠀⠠⠶⣯⣅⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⣿⣿⠏⣸⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⡿⠿⣷⠟⢁⣼⠟⠋⠁⠀⠀⠐⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⢳⡶⣿⣧⣨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⣒⣿⣭⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣤⡗⣿⢻⢷⡄⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⣾⣭⠵⠚⠛⠉⠁⢹⣿⣿⠃⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣧⡙⠿⣽⣷⡄⠀⠀⠀⠀⠀⠘⣿⠙⣿⡀⠀⠀⠀⠀⣀⣴⢾⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣅⣹⣦⠀⠀⠀⠀⠀⠈⠳⢬⣻⣶⣶⣞⡯⠽⠚⠉⠀⠀⢀⣴⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⡆⣻⣿⣿⣿⣿⣿⣿⠟⠿⣽⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⢃⣿⣿⣿⣿⣿⣏⣀⣼⢺⣝⣙⣷⣶⠤⢤⣀⣀⣀⡀⠀⠀⣀⣴⠟⠉⢰⣿⣿⣧⠀⣿⣿⣿⣿⡏⣿⡄⠀⠈⢳⡍⢳⡶ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⣿⠁⠀⡎⢸⠈⠻⡏⠙⣧⡀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣼⢹⣧⣿⠀⣿⣿⣿⣿⣿⠈⣧⠀⠀⠀⢿⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣿⠀⣿⡇⠀⡇⢸⡄⢰⡇⠀⠈⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢻⣿⠀⣿⣿⣿⣿⣿⡄⣿⠀⠀⢠⣾⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⣸⠁⠈⡇⣸⣧⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⡼⠁⠀⣀⣾⡏⠀⣿⣿⣿⣿⣿⣇⣿⠀⢠⡞⣹⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣧⣿⠀⠀⢳⣿⡟⢦⣄⡀⠀⠙⣦⠀⠀⠀⢀⣼⣁⣤⠞⠉⢸⠇⠀⣿⣿⣿⣿⣿⣿⣿⢀⡞⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣇⢸⣿⣿⣿⣿⣿⠃⠀⣀⣘⣿⣇⣈⣉⣙⣷⣶⣶⣤⣀⣀⣸⣛⣉⣀⣀⣀⣸⢀⡀⣿⣿⡇⣿⣿⣿⣿⡾⣁⣸⣁⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣟⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠢⡆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀ ⣿⣿⣿⣿⣿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠇⠀⠀ ⣿⣿⡿⠍⡀⠆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⣿⣿⣷⠀⠡⣠⠘⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣤⡀⠀⠀⢸⢰⡂⠀⠀ ⣿⣿⣿⣇⠀⠹⡀⠱⠀⠀⠀⠀⣻⠿⠂⠁⠁⠪⠿⣥⡤⠀⠈⣆⠃⠀⠀ ⣿⣿⣿⣿⡆⠀⢃⠰⡀⠀⠉⢉⠖⠾⠪⢋⠁⠁⠁⠀⠀⠀⠀⢼⡄⠀⠀ ⣿⣿⣿⣿⣿⠀⠈⠀⢸⢂⠔⣽⢢⡀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢬⠇⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⡇⡆⡏⣘⠇⡾⡁⠀⠀⠀⠀⠀⠀⠀⡷⡆⢃⢋⡄⠀ ⣿⣿⣿⣿⣿⡇⠀⢠⠃⠁⠋⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠠⠙⡀⠂⢸⡄ ⣿⣿⣿⣿⣿⣇⠀⠘⠈⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡌⠀ ⣿⣿⣿⣿⣿⣿⠀⢸⠀⠐⡀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣤⡜⠀⠀⡸⡀⠀ ⣿⣿⣿⣿⠟⠁⠀⠈⢫⠉⡇⠀⠀⡈⣽⣿⡿⣿⣷⣌⡟⢁⠀⠀⠃⠈⡆ ⣿⣿⣿⣿⠀⠀⠀⠀⠈⡦⠁⠀⢀⣻⣿⣿⡇⣿⡿⠛⡱⢸⠀⠀⢠⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠛⠓⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⣀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣄⣀⣼⠿⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢙⡿⠞⠋⠁⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⡀⠀⠀⠀⠀⠀ ⢰⡏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⣉⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⠙⠳⣄⠀⠀⠀ ⢸⣇⠀⠀⠀⣼⠁⠀⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣄⠈⢳⡄⠀ ⠀⢿⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠹⠿⠟⠋⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣰⠋⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⡆⠀⢷⠀ ⠀⠘⣷⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠁⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⡄⢸⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠹⣦⡀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⣼⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⠦⠀⠀⠀⢠⡿⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⠀⢹⡄ ⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣰⡿⢻⡁⣰⣋⣀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣇⠀⠀⢿ ⠀⠀⠀⠀⠸⣇⠀⠀⠀⢰⡟⠀⠘⠛⠉⠉⠉⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠁⠀⠀⠀⠀⠀⢿⡄⠀⠀⠹⣆⣿⣿ ⠀⠀⠀⠀⠀⢿⡄⠀⠲⢾⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⢿⡇ ⠀⠀⠀⠀⠀⠘⣧⠀⢀⣀⣿⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠉⠉⠛⣿⠇⠀⠀⠀⠀⠀⠛⠻⣶⡶⠶⠖⠚⠋⠉⠸⣇⠀⠘⢷⣄⡀⣀⣀⡤⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣌⣿⣄⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣷⡍⠛⠋⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠈⠻⣷⡀⠀⠀⠀⢀⣿⠒⢲⠀⠀⠀⢸⡆⠠⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣤⠶⠶⠟⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⢘⣷⣤⠈⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⣼⠗⢶⡤⣄⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣾⣥⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠛⢷⣼⣀⣸⣠⣿⠶⣤⡴⢤⡀⠀⠀⠀⢠⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⡻⠋⠲⡄⠀⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⣦⣼⣧⣤⡷⠴⠶⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠚⠳⠶⢻⣯⣀⢸⠋⠉⢷⠀⠀⠀⣀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠟⠙⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⡲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⠋⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠢⣈⠛⢦⣄⠀⣀⣤⣤⡤⠤⠤⢴⣏⣀⡼⠁⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠘⢲⡤⠞⠋⠁⠀⢸⡇⠀⠀⠀⠀⠈⠉⠲⣄⡀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⠹⡀⠀⠀⠀⠀⣀⠀⠀⠙⣄⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⠏⠀⣀⡠⠤⣄⡀⠀⡏⠀⠳⣄⣴⣾⣍⡉⠉⠓⣄⠈⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⢀⡞⠁⢠⣾⡷⠿⣿⡀⠀⠀⣿⣯⣩⣿⣿⣦⠀⢸⡄⢹⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢸⡄⠀⢿⢿⣿⡾⡿⢻⠀⠀⣏⠻⣏⣛⣡⠏⢀⡞⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠳⣄⡈⠓⠶⣛⣡⠞⠠⡷⠈⠓⠚⠛⠒⠚⠙⠒⠦⢼⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡤⢞⡋⠉⠉⢡⡀⢀⣠⠟⠦⣄⡼⠃⠀⠀⢨⣍⣩⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣞⢉⡥⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢲⣴⡏⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢛⣴⣃⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⢹⠁⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠋⢀⡏⠉⠉⠑⠒⠒⠉⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠀⠤⢤⡤⠤⠀⠀⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡟⠀⠀⣀⡤⠞⠁⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⢀⣴⠞⠋⢠⡟⠒⠋⠁⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀ ⢠⡾⠁⠀⢠⡼⣇⠀⠀⠀⠀⣀⡤⠤⢤⣘⣇⣀⠤⠤⢤⣸⣄⡤⠤⠤⣀⡿⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠻⠤⠼⠧⠤⠤⠼⢧⣠⡀⡄⠈⡟⠀⣤⢠⡄⢸⡁⣠⠀⣆⡈⣳⠀⠀⠀⠀⠀ ⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡗⠛⠒⠛⠒⠛⠛⠓⠛⠓⠛⠚⠛⠛⠋⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠒⠶⠶⠶⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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‸ ‸ ( | \_/ | ) ‘ .” = o̴̶̷̤ ̀⩊ ́o̴̶̷̤ =‘ , “ ́( ) ̀ “_. ‘ ̀ ́ ̀ ́ Momonga :3

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⢯⠓⠦⣄⡀⠀⠉⠲⢤⡀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⣿⣋⠋⠈⢻⣿⡇⠀⠀⠀⠈⠻⡄⠈⠙⢳⣄⡀⠀⠈⠳⣄⣰⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⠛⠿⠿⠿⣿⣛⣋⣭⣤⠴⠟⢹⡇⠀⠀⠀⠀⠀⠹⡄⠀⠀⠙⠛⢦⠀⠀⢨⣿⣆⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⢀⣀⣠⣿⡦⠤⠤⠤⣤⣷⣄⣸⠀⢻⣧⢸⡇⠀⠀⢀⣀⣤⢶⣾⣿⠿⠛⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢺⡇⢀⣴⣾⣿⣿⡿⠇⠀⠀⣀⣤⣴⣾⡿⠟⠲⢬⣿⣿⣇⡤⣶⣿⣭⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡇⠀⠀⠀⠘⣷⣿⠟⣯⠁⠀⠀⠀⠀⢸⠏⠉⢿⣹⣷⠀⠀⠀⠿⠛⢃⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢺⡇⠀⠀⠀⣼⡏⣡⠞⢻⡇⠀⠀⢀⣤⠿⣆⠀⠈⠷⠙⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼ ⠀⠀⠀⠀⠐⠀⠀⠠⠤⣀⣸⣇⠀⠀⣈⣿⣴⣯⣄⣼⠇⠀⣲⡟⠁⢀⣽⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣀⡤⠞⠀⠀⠀⠀⣀⡴⠋⣀ ⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⣘⣏⣩⣿⣿⣿⣼⣿⣩⣿⣤⣼⣿⣿⠿⠶⣼⣧⣤⡄⠀⠀⠀⠀⢀⡽⠛⠋⠉⠀⠀⠀⠀⠀⣠⣾⡯⠖⠉⠀ ⠀⠀⠀⠙⠛⠒⠤⢤⣀⠀⠀⢿⠈⠻⣿⡯⠿⢿⣇⢻⠛⠋⠹⣷⣴⣾⡿⠴⠦⠴⠶⠤⠤⢤⣾⣧⣀⣀⣀⣀⣠⣴⡶⢿⣋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⡆⠀⠈⠻⣦⡀⢿⡙⠒⠚⠉⢁⣽⠛⠿⠿⠓⠶⢤⣄⣀⣴⣿⠿⠿⠛⠋⠉⠉⠉⠛⠀⣨⡷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⡤⠦⠤⠤⠿⠿⠿⠶⣶⣶⣋⣀⡀⠀⢀⣀⣠⡴⠞⠋⠙⠓⠶⠤⣄⣀⠀⢀⣀⣤⠾⠯⠤⠂⠀⠀⠀ ⠶⠦⠤⠤⠤⠤⠤⠤⠖⠊⠉⢁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠳⠦⢤⣄⣀⠀⢀⣴⣂⡤⠼⠛⠛⠧⠄⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⣀⣀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠤⠤⣀⣀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠤⠤⠤⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠒⠦⢄⣈⡉⠉⠙⠓⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⡀⠀⠀⠀⠉⠙⠒⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣴⣶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠀⢸⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣀⠀⠀⠀⠀⡎⠘⣿⡏⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣅⣀⣽⣿⡄⠀⠉⠻⣿⣦⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⢀⣴⡿⢋⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠀⠀⠀⠀⠈⠻⣿⣍⠉⠉⠉ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀ ⠀⢠⣿⣿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷ ⠀⣼⡟⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢀⣿⠇⢀⣦⡉⠳⢦⣄⡀⠀⠀⠀⠈⠻⢷⡦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢰⣿ ⢸⣿⠀⣼⣿⣿⣷⣤⡈⠙⠳⠦⣤⣀⡀⠀⠙⠲⣄⡈⠉⠙⠓⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠛⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿ ⠸⣿⠀⠛⡇⠈⠙⠻⣿⣷⣦⣀⠀⠈⠉⠙⠓⠒⠒⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⡟ ⠀⣿⡆⠀⣇⠀⠀⠀⠀⣿⣿⣿⣷⣦⣀⠀⢠⠀⠀⡄⠀⠀⠀⢀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣾⡟⠀ ⠀⢻⣷⠀⠘⢦⡀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣾⡄⢸⣧⣶⣾⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋⠉⠉⣹⠛⠷⠀⣿⣿⠟⠚⠲⣄⠀⠀⣼⣿⠁⠀ ⠀⠈⣿⣧⡀⠈⠛⢦⣀⠀⠀⠈⠉⢉⣠⠞⠛⠃⠛⠻⣏⠉⠙⠻⠿⠿⠟⠋⠀⠀⠀⠀⢀⣴⠋⠀⠀⢰⡿⠁⠀⠀⢀⡟⠀⣼⣿⠃⠀⠀ ⠀⠀⠘⢿⣧⡀⠀⠀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁⠀⠀⠀⠈⠁⠀⢀⣠⠟⢁⣼⣿⠃⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⣀⣀⠀⠀⠀⠀⠀⠠⣖⠋⠁⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠉⠙⢦⡀⠀⠀⠀⣈⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠶⣤⣀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⣁⣤⣶⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⢸⠟⠋⠉⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣠⣴⠚⠉⢹⡍⢿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣄⣀⣀⣀⠄⠀⠀⠀⠀⢠⡞⢹⠋⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⡼⠁⠀⠀⠀⣷⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⡇⠀⠀⠀⠀⠀⣾⠀⢸⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⡀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠇⠀⣾⠀⠀⠀⢐⣞⣛⣂⣀⠈⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡞⠀⣠⣇⡴⠞⠛⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢈⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠈⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⡽⠿⡍⠉⠙⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⡏⢀⣀⠀⢹⡀⢰⠃⣀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⡿⠟⠋⣰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⡇⢼⣿⠀⠀⡇⢸⢸⣿⠆⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠘⣇⠈⠉⠀⢀⣇⠸⡀⠉⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡏⠀⢴⣶⣄⠀⠙⣄⠀⢀⡼⠀⠀⠳⡀⠀⢀⡾⣿⣿⠀⠀⣤⣤⣀⠀⠀⠀⠀⣾⣿⠋⢻⣿⣿⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⢈⣿⣿⣷⡀⣸⢈⣧⠀⠀⠛⠛⠋⠀⠀⠀⣀⣈⣛⣟⣂⣀⠙⣧⠀⠘⢦⠈⠙⠲⣤⡀⠛⠁⠀⢸⣿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⠏⣿⠃⣻⢯⡈⣱⢦⡀⠀⠀⢰⣾⣉⠉⢠⣤⣤⣤⣭⣭⣿⣧⣀⠈⣧⠀⠀⠀⠙⢦⠀⣰⠟⠁⠀⠀⠀ ⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠘⠏⣠⡟⠀⢸⣾⣿⣧⣴⡁⠀⡍⢀⡻⢿⣿⣷⣶⣿⣿⣿⡿⠋⠀⠉⢷⣿⡄⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀ ⠀⠸⣿⡟⠀⠀⠀⠀⢀⣤⣴⢞⣩⠄⠀⠀⢻⣿⣿⠿⠓⣦⣀⣀⣀⣀⠽⢿⣿⡿⠿⢯⣀⣀⣀⣠⠾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⣿⣍⣻⡿⣿⠀⠀⠀⠀⠙⠿⢷⡤⠀⠀⠀⠀⠀⠀⣞⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤ ⠀⠀⢀⠀⠀⢀⡴⣆⠉⠛⢿⠀⢹⣷⡀⠀⠀⠀⠠⣀⣀⣀⠆⠀⠀⠀⢸⣯⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠳⢤⣾⠀⠘⣦⣀⣾⣤⣿⣿⡷⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⣿⣿⣋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣷⣤⣄⣀⣤⣤⣶⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢩⣽⣿⣿⣿⣿⣿⣿⣷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⡟⢫⠉⠋⠭⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⣿⣿⣿⡧⠃⠀⠠⠐⠴⠹⢤⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⡇⠈⠀⠈⠀⠆⢐⡉⠀⣠⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣴⡆⣀⣄⣈⣿⡿⠛⠀⠀⠀⠀⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠉⠉⠀⠆⠁⣆⠀⠀⠀⠀ ⠀⠀⠀⠛⢿⠟⣟⠉⣉⠙⠻⣿⡀⠀⠀⠀⠀⠀⠈⡆⠀⢀⣤ ⠘⡏⠲⣠⢴⠤⠉⠉⠁⠀⠀⠈⣧⢀⣀⠤⠒⣻⠒⠋⠢⣎⡸ ⠀⠈⠢⡴⡪⠓⢳⠀⠀⠀⠀⠀⢸⣿⡀⠀⠰⡉⠬⡣⢳⠊⠀ ⠀⠀⠀⢣⡘⢀⡋⠀⠀⠀⠀⢠⣿⣿⢷⣄⠀⠙⣤⣥⡊⠀⠀ ⠀⠀⠀⢀⣼⣻⣿⣦⣀⣀⣴⣿⢸⣿⠈⢻⣷⣄⣿⣿⣿⣦⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠂⠀⠐⠒⠒⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠔⠋⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉⠙⠓⢶⣄⡀⠀⠱⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⠇⠀⣇⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⣀⣀⣀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⢹⠀⢀⠘⢦⡀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢹⡀⠀⠀ ⠀⠀⠀⢀⠞⠀⠀⠘⣆⣺⣄⡀⠉⡳⠏⠀⠀⢀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⣇⠀⠀ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⠁⠀⡾⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⣦⣠⣤⣾⠿⠃⠀⡆⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠃⠀⠀⠀⠀⡇⠉⠛⠛⠛⠉⠉⡆⠀⠀⠀⠀⢹⠩⠁⠀⠀⠀⠀⢧⣀⣠⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠀⢸⠀⠀⠀⠀⢸⠉⠓⠲⠤⠤⠤⠖⢧⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠋⠀⠉⣿⠈⠣⣀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡸⠀⠀⢀⠀⠀⠀⠀⠰⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠁⠀⠀⢰⠉⠀⢠⡟⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠚⠁⠀⢀⡞⠁⠀⢀⣀⣠⠞⠒⢦⡀ ⠀⠀⠀⠀⢀⠇⠀⠀⢀⡇⠀⠀⣸⠉⠉⠉⠉⠉⠒⠒⠒⠦⠤⠤⣄⣀⣀⣀⠀⠀⣰⠋⠀⠀⢠⢞⡟⠁⠀⠀⠀⢧ ⠀⠀⠀⠀⣸⠀⠀⠀⣸⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠁⠀⠀⣠⢿⡞⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⡇⠀⠀⠀⣧⣤⣀⣸⠄⠒⠒⠒⠒⠒⠒⠠⠤⢄⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⢸⠀⠀⠀⢀⡿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⢠⠇⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⡇⠀⠀⣠⠋⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⢠⠇⠀⢀⠃⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠘⠿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀ ⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀ ⠀⠀⠇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⠀⢰⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀ ⢀⠗⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠐⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⠀⠀⢀⣀⣀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⠝⢾⠉⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢀⠖⠁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⣉⣉⡉⠙⠻⢦⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁ ⠀⠀⠀⠀⠀⣠⠴⠛⠥⠐⣉⠤⠤⣌⡀⠀⠀⠙⢷⡄⠀⠀⠀⠀⡇⠀⠀⠀⣠⠔⠉⠀⣇⣀⣀⠤⠤⠤⠴⠶⠦⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⣠⠔⠋⠉⠉⢲⠞⠁⠀⠀⠀⠙⢦⠀⠀⠀⠹⣆⠀⠀⠀⠁⠀⣠⢞⡡⠴⠒⠉⠉⢀⣀⡠⠤⠤⠀⠒⢲⣶⣿⠤⣄⡀⠀ ⠀⢀⡾⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢻⡄⠀⠀⣠⡾⢟⣩⣖⡥⠖⠊⢉⡀⠤⠔⠂⢀⡤⠚⠁⠀⢸⠀⠀⣹⠀ ⠀⡜⠀⠀⣴⣶⣦⣸⠀⠀⢠⣶⣶⣤⠀⠀⠘⡇⠀⠀⠀⣧⣠⣾⣫⣶⠟⢋⡠⠔⠊⣉⡀⠤⠄⣠⠞⠁⠀⢀⡔⠀⣿⠴⠚⠁⠀ ⠀⡇⠀⠀⠻⠿⠿⢻⡀⠀⠸⣝⣻⡽⠀⠀⠀⡿⠀⠀⠀⢹⠁⠉⠙⠳⣮⡥⠔⠊⠁⠀⢀⡴⠊⠁⠀⢀⡴⡟⠀⣸⠛⠲⣄⠀⠀ ⠀⢳⡀⠀⠀⠀⣀⡾⢧⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢸⠀⠀⠀⠀⠈⢷⠤⠤⢴⡶⠋⠀⠀⣠⣴⠋⣸⠁⢀⠏⡇⠀⠘⣧⠀ ⢠⡏⠙⠓⠒⠛⠁⠀⠈⠳⣤⣀⣀⣀⣠⠴⠃⣀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠘⡇⣠⠏⠀⠀⣠⣾⠟⠈⣧⠇⠀⡼⠀⢸⠀⠀⣿⠀ ⢸⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⠀⠙⠂⠀⢠⡏⠀⠀⠀⠀⠀⢀⡿⠃⢀⣠⣾⠟⠁⠀⠀⡿⠀⢰⠃⢀⠏⢀⡼⠃⠀ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠃⠀⠀⢀⣾⠁⠀⠀⠀⠀⣀⣼⣧⠿⠛⠋⡸⠀⠀⠀⣰⡷⢀⠇⣠⣮⡴⠛⠁⠀⠀ ⠈⢷⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⡠⣿⠀⠀⢀⣾⣷⣛⡲⣄⢀⣰⣿⣤⣌⠳⣄⡴⠁⢀⣀⣴⣿⠇⡼⠞⠋⠁⠀⠀⠀⠀⠀ ⠀⠈⠳⣤⡀⠀⠀⠀⠙⠒⠒⠒⠚⠭⠚⠁⣀⣴⢿⠛⠛⣻⣿⢸⣿⣇⠀⠉⠉⡇⣿⠉⠉⠉⠉⠉⣸⢰⠧⠤⣄⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣤⡤⢶⠚⠉⠙⠚⢳⠀⣷⠺⠞⠉⠙⠳⣄⡴⠣⠋⠉⠓⢦⠀⣞⣉⣀⣀⣀⡀⠀⠉⠓⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠙⠦⢤⣤⣤⠤⠋⠙⠲⠤⠤⠤⠚⠀⠉⠀⠀⠀⠉⠉⠉⠉⠛⠚⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣁⡼⠃⠈⠀⠀⠀⠤⢀⠀⠀⠀⢸⠦⢄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡠⠊⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠁⠢⡉⠢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⡠⠄⠒⠒⠒⠒⠀⠈⠘⡀⠀⠀⠀ ⠉⠙⠻⡿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡤⠂⠁⠀⠀⠀⠔⢒⣀⣀⡐⠂⠈⢄⠀⠀ ⠀⠀⠀⠀⠀⠙⡛⢿⣿⣿⡇⠀⢠⠊⠣⣀⠔⠃⠀⠀⠀⣼⢶⣶⣦⠖⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⢸⠙⡄⠈⠙⣧⣀⠈⠒⠀⠑⢤⢶⣿⡦⡀⠀⠉⠉⠁⠀⠀⠀⡗⠀ ⠀⠀⠀⠀⠀⢨⠀⣇⠀⢀⣸⣿⣿⣿⠉⢂⠀⠏⠉⠉⡇⢀⡀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⢰⠞⠀⠋⠛⢿⣿⣿⣿⡏⠀⠀⠃⠐⡀⠀⠈⣈⡠⠔⡟⠀⠀⡘⠀⠀ ⣀⣴⣄⣼⡟⡆⡇⠀⠀⠻⣿⣿⣿⠃⠀⠀⡆⠀⠈⠢⢄⡉⠒⠚⠁⢀⠜⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠙⢉⠀⠐⠒⠓⠀⠀⠂⢄⠀⠁⢒⡖⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠐⠂⢄⠀⠤⢆⠀⠀⠀⠀⠔⡠⠐⠒⠈⠁⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠣⠀⠀⠸⠀⠀⠀⠐⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡐⡄⠀⠀⠡⠀⠀⠀⠑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠗⢄⡀⠀⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶ ⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠿⠋⠁⣰⠃ ⠀⢸⠉⢿⡒⠒⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣡⠚⠁⠀⠀⣰⠇⠀ ⠀⠘⣇⠀⠙⠢⢄⣀⠀⠀⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⢠⠞⠀⠀⠀⢀⣴⠃⠀⠀ ⠀⠀⠘⣄⠀⠀⠀⠀⠉⠑⢦⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡰⠃⠀⢀⡠⢶⡟⠁⠀⠀⠀ ⠀⠀⠀⠘⢦⣄⣀⠀⠀⠀⠀⢳⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠞⣀⠤⠚⢁⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠲⢬⣉⡉⠉⠙⠳⣄⡀⣧⠴⠒⠊⠙⠛⠉⠧⢤⡎⢀⣴⠟⠋⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠙⡆⠀⠀⠀⣠⠖⠋⠑⠢⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣴⣻⣦⠀⢹⠀⠀⡴⢁⣾⣿⣆⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⣿⣿⣿⠀⢸⠀⠀⡇⢸⣿⣿⣿⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠙⠿⠋⠀⣾⣖⣲⡇⠀⠛⠿⠃⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠐⣇⠀⠈⢻⠋⠁⢀⡷⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⣦⡀⠀⠀⠀⠈⠑⡎⢹⠑⡶⠋⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠚⠋⠈⠋⢩⠟⠁⠈⠙⠒⢢⣤⣆⠈⠙⠋⠀⣠⣤⠤⠖⠒⢺⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠞⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢸⠀⠈⠑⠒⠒⠋⢹⡄⠀⠀⠀⠀⢧⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠷⠒⠒⠦⢄⡞⠀⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠒⠋⠉⠀⠈⠹⡆⠀⠀⠀⠀⠀ ⢰⠋⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⢷⡀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢧⠀⠀⠀⢀⡞⠀⠀⠀⣰⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠑⠦⢄⣀⡀⠀⠀⣀⣙⣦⠀⠀⠘⣦⡀⠀⡼⠀⠀⠀⢸⡅⢀⣀⡤⠶⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠈⡇⠀⠀⢀⠹⣾⠁⡄⢀⠀⣸⠏⠉⠀⠀⠀⢄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣰⠃⣠⠆⠀⡰⠷⣀⣹⣨⡶⠛⠶⠧⠼⠞⠧⣄⣀⠀⠙⣆⣸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⠤⠚⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢠⣿⠀⠙⣦⣤⠀⠀⠠⠀⡄⠀⠀⣸⣧⠀⢤⡀⠀⠸⠳⡤⡀⠀⡀⣄⠈⠀⠀⠒⠀⠀⠀⡟⠀⠀⠀ ⠀⠀⠀⢘⣿⡤⠔⢠⠀⠀⠠⠀⠤⣄⠀⡴⡉⠉⠱⠼⠀⡆⣠⠀⠀⠀⠠⠐⠿⠰⡶⠤⠆⢰⠶⠘⢤⠄⠀⢀

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⣿⢿⡇⠀⠀⠀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣽⣿⣿⣤⣄⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠶⢶⣤⣀⣀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠸⡆⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡍⠙⠒⢶⡤⠀⢻⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⡇⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠘⢧⠀⠸⡄⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⣼⢆⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⢧⡀⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⡀⠀⠀⠀⠀⠀⠘⡇⠀⡇⢸⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⣠⠴⠟⠛⠳⣤⡘⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢻⢰⡇⣾⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⢻⡅⠁⠀⠀⠀⠀⠀⠙⠶⠮⠭⠤⠖⣶⡶⠂⠀⠀⠀⠸⣾⡃⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢳⠀⠀⢀⡇⠀⠀⠀⠀⣤⣤⣶⣖⠉⠋⠀⢠⣀⣀⣤⣖⣶⣤⣠⣤⣤⡤⠶⠚⠻⠉⠀⠀⠀⠀⠀⠀⢹⡇⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⡄⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⣻⢋⡽⢋⣰⠏⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣷⠀⠀⠻⣆⠀⠀⠀⠀⠀⣠⣎⠀⡠⠀⠊⠀⠋⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⠀⠀⠀⠘⣶⢶⠀⣠⠞⢡⣧⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣸⣿⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣀⠀⠀⣰⠃⣼⡾⠁⢠⣯⠏⢀⡏⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢻⠉⢿⠉⢫⡙⣆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣹⠀⢰⠇⢸⣿⠀⢠⠟⡼⠀⣸⣻⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡄⠈⣧⠀⢳⠙⣇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡆⢸⠀⢺⡇⠀⣸⣠⠃⠀⣧⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⣳⡀⠈⢆⠀⣇⠹⡄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⡇⢸⡄⠸⠁⠀⡿⠃⠀⢸⣻⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣧⠀⠸⣄⠈⠀⢳⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣷⠘⣇⠀⠀⠀⠀⠀⠀⠈⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⡀⠀⠁⠀⠀⢸⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠙⠀⠀⠀⠀⡼⠙⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢰⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠁⠀⠀⠀⠀⢀⣞⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⢤⣤⣽⣀⣀⣀⣀⣬⡆⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣄⣤⣤⣤⣤⣤⣶⡒⠚⢿⣿⣥⣿⡇⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠹⣿⠉⠀⠈⢻⠀⠀⠀⠀⠀⢀⡏⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⡿⠃⢧⠀⠀⠀⠀⠀⢸⠀⠀⠈⢳⡀ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⡿⠀⠀⠀⠀⠀⢸⣇⣾⣿⣿⣿⣿⣿⢹⡿⣿⣿⣿⣿⣾⣿⡀⠀⣸⡆⠀⠀⠀⠀⠀⡇⠀⠀⢀⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⡼⠁⠀⠀⠀⠀⠀⣾⢻⣿⣿⣿⣿⣿⡇⢸⡇⣿⣿⣿⣿⡿⠛⢻⡄⡏⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⢠⢫⣿⡿⣿⣿⣿⣿⡇⢸⡇⢹⣿⠛⢁⣀⢰⡟⠀⠇⣇⠀⠀⠀⠀⠀⢣⠀⠀⢸⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢇⠀⠳⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠘⣧⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢘⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⣷⣶⣤⡀⣿⡇⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣿⣿⣿⣿⣿⣯⣦⣼⠋⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠛⠋⠉⠉⠙⠛⠛⠛⠉⢉⣁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣰⠋⠀⣠⣶⠟⠙⢿⣿⣿⠿⠛⠛⠛⠛⠛⣉⣀⣀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠁⠀⣰⡏⠁⠀⠀⠈⠉⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⢸⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣼⡟⢘⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⠅⠀⠀⠀⢀⡾⠋⠀⣼⣧⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠸⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⡁⣱⠀⠀⢀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⡆⠀⠀ ⠀⠀⢀⡟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠈⠙⢿⡋⠉⠉⠀⠀⢸⣿⢟⠃⠀⠀⠀⠀⣶⠛⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣇⠀⠀ ⠀⠀⡸⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⠙⠓⠒⠒⠶⠞⠛⠃⠀⠀⠀⠀⠀⠙⠷⠖⠒⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢸⡄⠀ ⠀⢠⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⢻⣄⡴⠂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢧⠀ ⠀⣾⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⣸⠇ ⢀⠇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣄ ⢸⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣶⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠛⠋⠉⠉ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠙⣆⠀⠀⠀⠀⠀⣴⢟⢭⢛⡅⠀⣆⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⠶⣤⣘⢧⡀⠀⠀⠀⠙⠚⠛⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣀⣀⣀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠓⠷⣤⡀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠉⠉ ⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠳⠶⠤⣤⣤⣤⠤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⠀⠀⠀⣾⠁⠀⢹⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠉⠙⠓⠒⠒⠼⠲⠴⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢩⡟⠉⠉⢩⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠙⠛⢻⡟⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠁⡾⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠰⠖⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⢳⠀⠀⠀⠀⠙⢿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⢠⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠿⣿⣿⣿⣿⠃⠀⠀⢸⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜ ⠀⠀⠀⠈⠛⢿⡇⠀⠀⠀⢸⡀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠸⡇⠀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⣠⠇⠀⠉⠳⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠀⠉⠛⠒⠦⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠶⠒⠋⠉⠘⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠒⠈⣉⠨⠮⠭⠄⡀⠒⠉⠐⢄⡀⠀ ⠀⠀⠔⠁⡠⠊⠀⠀⠀⠀⠀⡇⠀⠀⡀⢀⢇⠀ ⠀⡜⠐⢠⠁⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠸⠀ ⠀⣇⠀⣴⣶⣲⡄⠰⣶⣶⣦⠀⢇⠀⠀⠐⠤⠇ ⢰⠁⠀⡟⠻⢿⠁⠀⠿⠟⠁⠀⢸⠤⠂⠀⠀⡇ ⠀⡀⢄⡇⠀⡦⡠⠬⠦⡀⠀⠀⡄⠀⢀⠤⠊⠀ ⠀⠑⠄⢃⠀⠂⣚⡆⠰⠁⠀⠀⡸⡢⠋⡄⠀⠀ ⠀⠀⠀⣈⠦⣀⠐⠂⠀⡀⠤⡰⠋⠀⠀⢃⠀⠀ ⠀⠀⢀⠁⠀⣫⣮⡭⠥⢲⡎⠀⠀⠀⠀⠈⢄⠀ ⠀⠀⡏⠉⠉⠉⣭⢉⣹⡉⣉⣭⣉⣭⠉⠉⠉⢹ ⠀⠀⠇⠀⠀⠸⠉⠋⠟⠙⠏⠉⠜⠛⠀⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠿⠛⠛⠛⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⠶⠿⠛⠛⠉⠉⠀⠀⠀⠉⠉⠛⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣠⣴⠿⣧⣀⣨⣧⣤⣴⣶⣶⣿⣭⣭⣍⣉⣁⡀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⢀⣴⣿⡣⠹⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⡿⣋⣥⣶⠟⠛⠉⠉⠀⠀⠀⠀⠉⠙⠻⢿⣶⡲⢬⡉⠀⠀⢸⡇⠀⠀⠀⠀⣴⡟⠹⠟⠁⠀⠈⢿⣦⠀ ⠀⠀⠀⠀⣠⣴⠞⡏⠀⠀⢀⣴⡟⣣⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⢿⣦⠉⠀⣠⡿⠁⠀⠀⠀⠀⠙⢿⣆⣠⡶⢠⠀⣀⣽⡗ ⠀⠀⢠⣾⠟⠁⠀⡇⠀⣠⣾⣥⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠹⣧⡾⠟⠁⠀⠀⠀⠀⠀⠀⣠⡿⣋⣴⠋⣠⡿⠃⠀ ⠀⣰⡟⠁⠀⠀⠀⠙⣰⣟⣽⡟⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⣠⡾⢋⡼⠋⠙⠿⠋⠀⠀⠀ ⢠⡿⠀⠀⠀⠀⠀⢰⡟⣽⡟⠀⣰⠏⣠⠶⠛⠛⠛⠻⠷⢦⣤⡀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠘⣿⡀⢀⣠⣤⡤⠴⣿⣶⣿⣥⣤⣀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⣿⢱⡿⠀⢀⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⣻⣶⣦⡀⠀⢹⡿⠛⠁⠀⠀⠀⠀⠙⣷⡀⠉⠙⢷⣦⡀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⣿⣿⠇⠀⠸⣝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⡏⠛⠋⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠙⢿⡄⠀ ⠀⠀⠙⢷⣦⣀⠀⢻⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠉⠙⠓⠚⠉⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠈⠙⠛⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠙⢲⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢦⠀⠀⠀⢻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣚⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠈⢧⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠓⠀⠀⠀⠀⢰⣏⢠⠟⠉⠀⠉⠙⠛⠓⠦⠤⠤⠤⠤⠞⢷⣄⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠸⣇⣼⠏⠀ ⠀⠀⠀⠀⠀⢸⡏⠀⠳⡖⠶⢤⡀⠀⠀⣈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⡀⠀⠘⠒⠦⠽⠆⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠶⠛⠁⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⢶⣶⣶⣶⣶⡶⠶⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠈⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⢁⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠖⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⡤⠞⠋⣠⠴⠒⠋⠉⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢿⡇⠀⠀⠀⠈⣇⠀⠀⣷⠀⠀⠀⠀⠀⠀⣧⢀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠁⢺⠥⢦⠀⠀⠀⢹⡄⠀⢸⣆⣀⣤⣶⣶⣾⣯⣭⠭⠭⠭⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢸⠠⠀⠀⠀⠀⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⢈⣻⣿⡟⣁⠀⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠘⣿⠋⠣⣟⡰⠳⢤⠀⢀⣀⣀⣤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠀⢀⡴⠚⠉⠀⠈⠉⠒⠊⢡⡆⠀⠀⠉⠱⠞⠋⣁⠤⠔⣠⠾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠹⣄⠰⠊⠛⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⣏⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠳⣤⣀⠀⠈⠙⠒⠒⣲⣶⣖⠋⠉⠢⡄⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⡾⣿⣿⣿⡞⠋⠉⠉⠉⠈⠓⠲⠖⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⢀⣀⣀⣠⡃⠈⢙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣾⣿⣿⣿⣿⣷⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣤⠤⠶⠛⠛⠋⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠚⠋⠉⣁⠀⠐⠂⠀⠀⠀⢤⠞⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢿⠿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠛⠛⠛⠿⠿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⡆⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⠻⡆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⣅⣀⠀⢱⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡆⠀⠸⡅⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣡⡄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⠘⢆⣣⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣀⠀⠀⣴⣶⣦⡄⠀⠀⠀⠀⢸⡁⠋⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⠀⠀⠈⢿⡀⠀⢣⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡧⠖⠉⠉⠑⢦⣙⠿⠟⢁⣀⣀⠀⠀⠈⣷⡇⡗⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⠇⠀⠀⡇⠀⠀⠀⣀⣠⣤⠰⠋⠁⠀⢀⣀⣀⣀⣀⡈⣉⠭⠽⠛⠁⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⠀⠰⡁⠀⠀⠀⠀⠀⢉⡽⢒⢟⠝⣩⠟⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠈⠇⠀⠙⢆⣀⠀⠀⡠⣾⣀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⡸⢹⣠⠊⣰⡟⢙⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠶⡖⢾⢷⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⢠⠃⣾⠁⢠⢻⠁⣸⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡀⠱⡀⢊⢳⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⡇⢸⠀⡏⠀⣶⠎⢀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⣷⠀⢱⠈⠌⢧⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠸⡄⠀⠀⠋⠀⠘⠟⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⡇⠀⠃⠀⠘⣦⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠘⠂⠀⠀⢰⠋⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠈⢆⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢀⡎⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⢀⢸⣄⣀⣀⣸⡄⠀⠀⠀⠀⢸⣤⣀⣀⣀⣀⣀⣤⣤⠔⢶⣾⣹⣿⠀⠀⠀⠀⢸⠙⢦⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⣧⠀⠈⡇⠀⠀⠀⠀⡜⢨⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⠏⢸⠀⠀⠀⠀⢸⠀⠀⢱⡀ ⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⣆⢸⡇⠀⠀⠀⢸⠀⠀⢸⠁ ⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⣿⢸⡿⠛⣉⢠⠏⠘⣇⠀⠀⠀⠀⡇⠀⢸⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣨⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⡆⠻⣿⡿⢿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢄⠀⠈⢧⢀⠀⠸⡄⠈⠁⠀⣆⠀⠀⠀⢧⠹⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⠀⠀⠀⢸⢷⡀⠀⠀⢸⡦⠀⠚⢿⡖⠒⢳⠀⠀⠀⢸⡀⠀⠀⠸⡆⠙⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢃⠀⠀⠀⡎⠀⠀⠀⢠⠀⠀⡇⠀⠀⢸⠀⢧⢰⡀⠀⢳⠀⠀⠘⣷⡀⠈⢷⡀⠀⠀⣇⠀⠀⠀⣷⠀⠸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⡇⣼⠀⠀⠘⡆⢀⣷⠒⠁⢸⡀⠈⢧⣷⡀⢠⣿⣉⣩⣽⣷⣤⣴⣧⡀⠀⢹⠈⠱⣤⣿⠀⠀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢿⡇⡀⠀⠀⣷⡏⠀⠀⢀⡷⠋⢸⡴⢒⣉⡇⠀⠈⢿⣷⡀⢳⠘⠋⣿⣿⣿⣿⣯⠀⠀⢸⠀⠀⢹⡇⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠈⣷⠃⡀⠀⢸⣧⠀⠀⠈⢹⣰⣿⣿⣿⣿⣿⡅⠀⠈⠟⠉⠉⠀⠀⢙⣿⣿⣿⢻⡆⠀⠸⡀⢠⣿⡇⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠸⣾⠀⠀⣀⣿⠀⠀⠀⠸⣿⠏⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣏⣟⣿⡇⠀⠀⢿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢻⣧⡜⠁⢸⡇⠀⠀⠀⢿⡆⣀⡈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢁⣷⠀⡆⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣧⡀⠀⢷⠀⠀⠀⢸⣿⡟⣷⣾⣿⠛⠁⠀⠀⢀⣀⠤⠀⠀⠀⠀⢀⣾⣿⠀⡇⢸⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣶⣼⡄⠀⠀⠈⣿⡉⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴⣿⣿⣿⡀⡇⠈⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢀⠀⠀⢻⣿⣦⣤⣄⣀⣀⡀⢀⣀⣤⣴⣾⠋⢩⣿⣿⣿⣿⡇⣿⣠⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠈⡇⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⠿⠟⠋⠀⠀⠀⢉⣿⣿⣿⣿⣯⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢻⡀⢸⡿⠿⢿⣿⣛⣯⣿⡏⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣿⣿⣛⢿⣿⠀⠀⠀⠀⠸⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⢷⡀⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⢧⣿⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢹⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿ ⣿⣿⣿⣿⡇⢧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⠿⠟⠿⠿⠿⠛⠿⠿⢿⣿⣿⣿⣷⣽⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣿⣿⢷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣭⣽⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣶⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡆⠈⠙⠛⢿⡿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣯⣉⣉⣹⢿⢿⣯⣼⣧⠀⠻⣿⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⣸⡎⢿⣿⣿⣆⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡡⢴⣿⣿⣿⡆⠀⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣿⣿⣿⣿⣿⣿⣿⣴⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀ ⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀ ⠈⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢲⠓⢶⢶⣶⠒⢲⠰⠶⠶⠖⠠⢶⠶⣶⠂⠀⢸⢹⣸⠿⢟⣷⡿⠇⡿⠟⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⢀⡶⠲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠠⡇⡀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀ ⠀⣧⢹⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⣿⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⣿⢸⢳⡀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡞⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀ ⠀⠸⡞⡄⢳⡄⠀⠙⢷⡀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣸⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠀⠀⣧⢳⠀⠙⣦⠀⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⢀⡇⠀⢸⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠸⡎⣇⠀⠈⠳⣄⠀⠈⢳⡄⠀⠀⣿⠀⠀⣸⠁⠀⡾⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠹⣌⠳⣀⠀⠙⢦⡀⠀⠹⡄⠀⢸⠀⠀⡟⢀⡼⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣌⡳⣄⡀⠻⣄⠀⢹⣄⣸⣤⡶⡧⢟⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠶⣍⡓⠾⠆⣸⣿⣿⣿⣧⣠⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣾⣟⠉⠛⠀⠟⡻⣯⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢟⡟⣿⣄⠀⠀⣸⣿⢾⡀⠈⢳⡄⠀⡤⣤⢤⣄⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢰⣿⡟⢧⠀⢾⠛⠁⢳⠀⠀⢙⣦⣧⣹⡀⡬⢷⡄⠀⠀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣟⠁⠈⣇⠸⣆⠀⢸⡶⠞⠉⠀⠀⠙⠻⣧⡀⠹⡄⢰⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠶⠶⠼⢦⣀⣼⣤⣼⣷⢋⠤⠔⠚⠉⠉⠀⠀⣿⠱⠀⢻⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠢⠤⠐⠒⣂⣀⣴⡯⠛⣋⣹⣷⣒⠒⠒⠉⠉⠉⣱⠛⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡤⠴⠚⠉⣡⣴⣿⣯⠉⢣⠠⣿⠋⠁⠀⠀⣠⠾⡇⢠⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢦⡀⠀⠈⠁⠉⣿⣿⣧⣼⣦⠏⠀⣠⡴⠛⠁⠐⣇⢸⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢮⣝⣛⣩⠥⠔⠋⣼⡗⠶⣄⠀⢹⣾⣀⡤⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠧⡀⠀⠀⡏⠻⣆⠘⢧⡈⢳⠒⠚⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢣⠀⠀⠀⠀⠈⢧⡀⢻⣼⡆⠀⠈⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄⠙⣧⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢹⠀⠸⡆⠀⠀⢹⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⠀⣀⠀⢿⡆⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠸⠀⣱⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⢸⣆⠀⠸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⢸⣿⣷⣤⣿⣄⢠⠿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⣋⣠⣴⣾⣿⣿⣿⣿⣿⣇⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⡰⠃⢀⡴⠋⠙⣿⠿⠛⠋⠉⢛⣉⣠⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢈⡞⠁⢠⣿⣤⣤⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⣰⡟⣿⠿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠯⠀⠀⠀⠼⠋⢠⡧⠄⠺⢿⣿⣿⣿⣿⣿⣿⣦⠘⡆⠀⠀ ⠀⠀⢀⠎⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⢣⠀⠀ ⠀⢀⡞⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠓⢾⡖⠒⠂⠙⣿⣷⠆⠀⠀⠀⣤⠴⠒⢲⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠀⠀ ⠀⡜⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠑⠒⠒⠒⠛⠛⠀⠀⠀⠀⠙⠶⠒⠚⢿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢇⠀ ⢰⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣙⡴⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⡄ ⡎⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢘⡁ ⠃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢳⡀⠀⠀⠀⠀⢀⣴⠶⡤⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒⠒⠛⠉ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠲⣄⡀⠳⡄⠀⠀⠀⢾⣯⡩⠁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠓⠿⣆⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠒⠒⠒ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠉⣳⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠒⡶⠶⣶⡾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠓⠲⠤⠄⢀⣧⣠⠞⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢻⠟⠉⢉⣁⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣉⠛⠛⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⠟⠁⡎⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠉⠉⠉⠀⠀⠀⠀⠈⡆⠀⠀⠈⢻⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠋⠀⢰⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⡋⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠈⠛⢿⡏⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠈⡇⢰⠧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠀⠀⠀⠀⣇⠀⠀⠀⠀⡔⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⢳⠋⠀⠀⠉⠓⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢺⡀⠀⠀⠀⠀⢸⠀⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⢻⣿⣿⣖⣲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀⣠⡴⠚⠉⠁⠈⠻⣄⠉⠉⠛⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠛⠓⣶⢶⣏⡁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣿⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⡾⠁⠀⠀⠉⠳⢦⡀⠀⠀⠀⣠⠾⡷⢦⣄⢸⡇⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⡟⣴⡄⠀⠀⠀⠀⠀⠙⣦⣶⠛⠁⠀⢿⡀⠈⢹⣧⣴⡾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢿⢶⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣆⠀⣀⣼⣷⣤⣼⣿⠋⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⢈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡋⠀⣿⣀⣿⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⡏⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣾⣯⢿⣿⣶⣤⣤⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠷⣾⠻⣿⣦⣄⡀⠀⢀⣠⣴⡾⠿⢧⣿⡤⠶⠿⣏⠈⢻⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⡷⣄⠉⠙⠻⠻⣿⣿⡉⠀⠀⢰⠇⠀⠀⠀⠹⣦⡞⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⢷⡀⣠⡼⠋⠀⠉⠳⢶⣿⣤⠴⠶⠒⠒⢻⡅⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡟⠿⢤⣀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠙⠳⣤⣉⠳⣄⣰⣇⣀⣤⡤⠤⠶⠒⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠓⣷⠼⠿⢿⣿⣯⣁⣀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⣿⠀⠀⠀⢸⠁⠀⢹⡏⢙⣿⣿⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⣏⠻⣿⠦⠤⣤⣼⡦⠤⠶⡟⠉⣸⢧⡀⠀⠀⠀⣈⣽⠶⠦⢤⣀⣀⣀⣀⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣏⠁⠀⣠⡾⠋⠀⡇⠀⠀⠀⡿⠀⠀⠀⣿⠀⠏⠈⠳⣄⣤⠞⠉⠀⢀⣠⠴⠛⠁⠀⠀⠀⣈⣉ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢶⣋⡁⠀⠈⣳⣾⡋⠀⠀⢠⡇⠀⠀⢰⡇⠀⠀⠀⢻⠀⣀⣤⣾⣻⣷⣤⡖⠚⠉⠀⠀⠀⣀⣤⠖⠛⠉⠀ ⠀⠀⣀⡤⠖⠛⠛⠷⣄⡀⠀⠀⠉⠙⣻⠟⠿⠶⠿⠷⣦⣾⣥⣤⡀⣼⢁⣠⣶⣶⢿⡟⠉⠉⠉⠀⠀⠈⠳⣄⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠈⠈⠙⢦⣄⣴⠞⠁⠀⠀⠀⠀⣸⠋⠈⠙⢦⣝⣿⡿⠛⠉⠀⠈⣧⠀⠀⠀⠀⣀⣠⡤⠾⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠙⠓⠶⢤⣀⣴⠇⠀⢀⣤⢄⢸⡏⠠⣄⠀⠀⠀⢻⣀⣠⠶⠛⠉⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⣿⠤⣤⣀⡀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢈⡟⠛⢻⡿⣷⣿⣼⣅⣴⡾⣷⡖⠚⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡀⠠⠀⠐⠂ ⢹⡀⠀⠈⠉⠳⢦⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⣿⣱⣿⣼⣿⣿⣼⣿⡾⠷⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⢻⡅⠀⠀⠀⠀ ⠈⠇⠀⠀⠀⠀⠀⣹⠟⠓⠶⢤⣀⡀⠀⠀⠀⣿⠀⢈⣧⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⢸⡆⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢹⣦⣤⣶⣶ ⠀⠈⠀⣀⣤⣶⣿⣿⣷⣤⣀⠀⠀⠉⠓⢦⣄⣿⠀⠘⡇⢹⠁⣿⣿⣿⢀⡟⠀⣿⠃⣀⣨⣷⠶⠋⠁⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣆⡀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣼⣿⣿⣿⣿⡟⠛⠳⡆⣦⣼⠿⠟⢋⣩⡽⠏⠀⠀⠀⠀⠿⠿⢿⣿⣿⣿⣿⠟⠋⠉⠛⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⠙⣷⣶⣶⠟⠉⠀⠀⠈⠉⠉⠛⠶⣶⣶⠶⣶⣆⡀⠀⠈⢹⣿⠃⠀⠀⠀⠀⠘⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⠛⠟⠛⠶⠺⣴⡿⢋⠞⠁⠀⠀⠀⠠⣄⠙⣏⠉⠉⠃⠈⠱⣌⠙⢷⣤⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⡾⠋⢠⠋⠀⠀⠀⠀⣠⡾⠀⠑⠾⠆⡷⢦⣀⠀⠈⢧⠀⠻⣷⠄⠈⠛⡿⣶⣦⣤⣤⣴⣿⣿ ⣿⣿⣿⣿⣿⠏⠠⠤⠤⠤⠀⠀⠀⠀⣰⠏⠀⢀⠏⠀⠀⣠⠴⠚⠙⢦⠀⠀⠀⣸⠁⠀⠉⠓⢦⣀⣳⡀⠹⣷⡀⠀⠁⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡜⠀⢀⡞⠁⠀⠀⠀⠈⡆⠀⢀⡇⠀⠀⠀⠀⠀⢇⠀⢣⠀⢹⣧⣆⣀⢹⣿⣿⣿⣿⡿⠋ ⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠁⠀⡼⠀⠀⠀⠀⠀⠀⢳⠀⠘⡇⠀⠀⠀⠀⠀⢸⣠⠜⠓⠉⠉⠉⠉⠛⣿⣿⣿⣿⡀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠤⠒⠒⠛⠒⠲⣧⣤⣀⣀⣠⣤⣶⣾⠃⠀⣿⣶⣶⣶⣶⠿⠛⠳⠦⠄⠀⠀⠀⠀⠀⢨⣻⣿⣿⣷⣆ ⣿⣿⠇⠀⠀⠀⠀⠀⠀⣴⣫⠁⠀⠀⠀⠀⠀⠀⠈⠒⠛⠉⠙⠳⢞⣋⡏⣀⣠⣼⢦⡽⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠃⠙⠋⠁ ⠹⡟⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢽⠋⠉⠁⡹⢀⣀⣀⣀⡠⠤⠒⠈⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀ ⣰⠁⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠐⠀⠒⠒⠒⠒⠒⠒⠈⠹⡃⠀⠉⢰⣎⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠋⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠤⠔⠋⠀⢀⣠⣀⣠⡤⠒⠉⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⢲⠦⠤⣤⢤⣄⣀⣀⡤⠤⠤⠤⠤⣤⡖⠒⠉⡏⠀⢰⠁⠀⠀⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣧⠞⠉⠉⠙⣷⡀⠀⠀⠰⣯⠙⡆⠀⠁⠀⡇⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡾⠀⢰⡇⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⡷⢿⣼⠀⣸⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⢸⡃⠀⠀⠀⢇⠀⠀⠈⠑⠦⠤⠇⠈⢻⣀⠇⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⣸⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡴⠃⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣠⣶⣶⣄⠤⢤⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⠀⢸⠀⠈⢻⣿⣿⣿⠀⠀⠩⣵⣦⠀⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠉⠑⠢⠤⣤⣼⡄⠀⡎⠀⢻⣇⣧⠀⠀⠈⣦⣽⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⢀⠔⠉⡠⠒⠒⠒⠀⠙⢦⡀⣀⣀⣿⣿⣿⢻⠀⠀⠈⢻⠋⡇⣠⣼⣿⣿⡇⢀⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣉⠤⡍⠉⠁⠀⠈⠙⡄⠀⠀⠀⠀⣠⠟⠃⠀⠠⣤⣀⠙⢆⠀⠀⣠⣷⣿⡟⠉⢨⣿⠴⠿⠓⢿⣅⡉⠑⠒⠒⠚⠛⠻⡄⠀⠀⠀⠀⠀ ⠁⢀⣼⠇⡠⠋⠉⠙⠦⣈⣢⠀⢀⠜⠁⠀⠀⠀⣴⣿⠾⠷⠺⡶⠖⠛⠛⠻⣅⡴⢏⣡⣶⡦⠀⠈⠉⢣⣀⡠⠖⢢⣀⠀⢇⠀⠀⠀⠀⠀ ⠀⢾⠯⠚⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⢠⠟⣇⠀⠀⠀⢧⡀⠀⢀⡠⠏⠀⠈⠹⣿⣗⠀⠀⠀⢤⡏⠀⠀⡞⠀⠁⠸⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡾⠀⠸⠓⢢⣤⡤⠘⠛⠣⣄⣀⣀⣠⢴⠃⢸⠀⠀⠀⠈⠇⢀⠜⣠⠖⠀⢆⠀⢉⠲⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢿⠀⠀⢧⡞⠳⠃⠀⠀⠀⠀⣧⢧⢠⠃⠀⢸⡆⠀⠀⠀⢸⠈⠉⠁⠀⠀⠈⣄⠈⢦⡙⢧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⢀⡠⠤⠒⠢⠤⣀⠁⠈⠁⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠢⠄⠻⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡇⠀⡰⠋⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢸⠀⠀⠀⢀⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠸⣴⢁⣀⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡎⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢀⠔⠋⠁⠀⢈⣳⣄⡀⠀⠀⠀⠀⡇⠀⢰⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠔⠉⠀⠀⠈⢳⡀⠀⣰⣅⠀⣦⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡴⢂⠀⣇⡰⡇⠈⢧⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠉⢳⡏⢳⣇⣀⡼⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⠇⠉⠉⠉⠁⠀⣀⡠⠔⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠤⢤⣀⣠⡴⣮⣉⣉⣭⣟⣛⡉⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣰⡏⠀⠀⢸⣍⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⢓⡆⠀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡹⠁⠀⠀⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⢀⣀⣛⡓⠤⠖⠒⠪⣉⠒⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⣀⣿⣽⡯⠤⠀⠂⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠟⠛⠛⠛⠋⠙⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠃⠀⠀⢰⡶⠾⠿⠿⠛⠛⠻⣿⠋⠀⠀⢸⡟⠉⠉⣭⣍⢹⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⠀⣿⡀⠀⠀⠰⠿⠆⣠⡿⠀⠀⠀⠈⢷⣤⣀⣼⡿⠟⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠘⠿⣶⣤⣤⣶⠾⠟⠁⠀⠀⠀⠀⠀⠈⠉⣁⣀⣀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⡶⠶⠶⠶⠶⠖⠛⠛⠛⠛⣿⠋⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⣺⡇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⡇⠀⠀⠀⣤⡄⠀ ⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢠⡿⠁⠀⣠⣾⠏⠀⠀⠀⢀⣿⣇⠀ ⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠟⠁⣠⣾⠟⠁⠀⠀⠀⠀⣿⠉⣽⠂ ⠀⠀⠈⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣹⣿⣴⡿⠋⠀⠀⢀⣠⣤⣶⣿⡽⠞⠁⠀ ⠀⠀⠀⠀⠀⣸⡿⠻⠿⢶⣶⣶⣶⣶⣶⠶⣛⣷⡾⠛⠉⣿⣁⣠⠴⢞⣫⡵⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡟⠀⠀⢀⣤⡴⠟⣋⣥⡶⠚⠋⠁⠀⠀⠀⣿⣋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⠀⠀⠐⣋⣤⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⣤⡀⠀⠀⠀⠀ ⠀⠀⣠⠖⠚⠙⠁⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣤⠤⠤⠖⠛⢦⡸⢷⡀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢴⡶⣶⣦⣤⣤⣤⣀⣠⠤⣴⣖⣿⣍⣿⣧⡙⢦⡀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⠛⢛⣉⡉⠉⠉⠛⠓⠒⠶⠟⠛⠋⠁⠀⣠⣤⣽⣆⢻⡀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣠⣏⠉⠉⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣘⣀⣿⣼⠃ ⠀⠀⢳⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣰⠞⠁⠈⠉⠙⠚⠃⠙⢦⡀⠀⠀⠀⠀⡼⠁⠈⠀⢠⣷⠃⠀ ⢀⡴⠚⠉⠀⠉⠙⠓⠦⣄⡀⠀⠀⢰⠃⠀⠠⡏⠀⠀⢀⣠⢶⣶⣦⣄⠀⢳⡀⠀⠀⢸⣟⡭⠿⠷⣼⠉⣷⠀ ⢸⡇⠀⠀⣤⠤⢤⣀⠀⠈⠙⠦⣄⢸⡀⠀⠀⠀⠀⢰⠟⠋⠉⠉⠈⠋⣧⡀⢻⡀⠀⢸⡆⠀⠀⠀⢹⠀⡿⠀ ⠀⢻⡄⠘⣇⠀⠀⠀⠉⠓⠤⣀⡈⢦⣷⡄⠀⠀⠀⢿⡀⠀⠀⠀⢸⡗⢺⡆⠀⠁⠀⠀⠻⡄⢰⣻⣾⣿⠃⠀ ⠀⠀⠙⢦⠘⢦⣀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⢈⡷⠞⠋⠙⠳⣽⡏⠀⠀⠀⠀⠀⠀⠙⠳⢿⣏⡘⣦⠀ ⠀⠀⠀⠀⠱⢦⡈⠓⠦⣄⣀⣈⡷⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣹⡖⠒⠦⠄⠀⠀⠀⠀⠀⠀⠀⠙⣾⡆ ⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⣿⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣱⣬⠉⠉⠉⠉⠀⠙⠲⣄⣀⢀⣠⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠋⠙⠲⠤⠤⠤⠤⠤⠖⠋⣉⠽⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⣧⠀⠀⣿⠖⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⢠⣿⡦⣴⢿⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⣠⡶⠋⢸⣷⡏⣿⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣤⢞⡋⠀⠀⢸⡇⣹⣿⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀

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⣿⣿⣿⣿⣿⠏⠉⠉⠉⢀⣿⣿⣿⣿⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⢿⣿⠛⢍⡭⠿⣛⡿⠋⠉⠉⠿⠿⣿⣿⠟⠛⠻⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⡿⠿⡣⣀⡽⡻⠋⠀⢀⢤⠬⠽⠋⡛⢧⡀⠘⣇⠀⠀⠀⠙⣿ ⣿⣿⣿⡿⠟⠀⠀⠀⠀⡰⠋⠌⠀⠀⣠⠃⠑⢃⠓⢄⡈⢂⠹⣆⠘⠓⣶⣤⣶⣿ ⣿⣿⡏⠀⠉⠉⠀⠀⡜⠀⡘⠀⡔⠁⠀⢡⠀⡘⠀⠀⠈⡆⢃⢹⣦⣀⣿⣿⣿⠟ ⣿⡏⠀⠀⠀⠀⠀⣼⣀⠠⢁⣘⠀⠀⢀⣈⡄⢡⣀⣀⣠⣤⣎⠁⠀⠈⢹⣿⣿⡀ ⣿⠇⠀⠀⠀⢠⠎⠁⠀⠀⠀⠙⠛⠛⠹⣻⣠⣬⡭⠋⠀⠀⠀⡀⠀⠀⠀⡟⠙⠋ ⡘⠀⠀⠀⠀⣏⠀⠀⠀⠄⠀⠀⠀⠠⠤⠅⠣⡤⢣⠒⠒⠀⠁⠀⠀⢀⡼⠃⠀⠀ ⠁⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⡄⠀⠀⠀⣀⠤⡶⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠈⠐⠂⡤⢤⢄⣀⡠⠤⠭⢥⡄⢒⠃⡙⠀⢰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⡰⠁⠀⠙⣄⠀⠳⣼⣸⢠⠁⢀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⡄⠈⠑⠠⠃⢻⡈⠀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡠⠁⠀⠀⢡⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿⢀⣀⡤⠶⠖⠛⠉⠉⠉⠉⠉⠉⠛⠶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⠴⠏⠀⢀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠞⠉⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢥⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣾⣡⠴⠖⠒⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠉⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠋⠋⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠅⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⢻⣄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡀⣀⣀⠌⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣿⣿⠿⣿⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣿⣻⣿⠟⠀⠀⣰⡶⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠿⠋⠙⠛⠶⠦⣠⡟⠀⠈⢷⡀⠀⠀⢀⣀⣤⣀⡀ ⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⣀⣠⠶⠟⠀⠀⣦⣀⠙⠷⢦⣼⠁⠀⠉⢷ ⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠗⠆⢠⡾ ⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁ ⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠖⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠓⠒⠒⠒⠛⠋⢉⣍⠉⠉⠉⠉⠙⠒⠾⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣾⠃⠈⠳⣄⡀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠉⣳⡶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⣾⣇⠀⠀⠐⣾⠉⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣆⠀⠀⠹⢶⣄⣀⣀⣤⠴⠞⠉⠀⠀⠀⠀⢀⣠⠾⠉⠀⠀⠀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⢿⠳⣤⣀⠀⠀⠉⠉⣧⣀⠀⣀⣀⣀⢴⣶⠉⠀⠀⠀⠀⣀⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠷⠤⠤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⣤⣀⢀⣤⢴⢄⣀⣀⡀⡀⣤⣀⣀⣀⣤⣄⠀⣀⢀⣀⣀⣀⣀⠀⢀⠀⢴⢤⣖⣦⣖⠀⢢⠠⡆⠐⣶⡖⣄⢠⠀⠄⠀⡆⠀ ⢿⡟⠻⢛⠚⡛⣜⣘⢿⡛⢀⢋⠛⡙⠚⣛⠚⡛⠀⢙⠚⡓⣟⠃⠚⠀⠈⠀⢺⠂⠚⠁⠲⠑⠂⠀⠓⠘⠀⢓⢋⠙⠁⠀⠀⠃⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀⠀⠑⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢞⠀⡠⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⢹⠠⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⢡⠃⠀⡁⠀⠀⠀⢲⢄⠀⠀⣫⢆⢔⣿⢇⡇⡆⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠈⠚⣷⣄⣱⢄⠀⠰⠁⡰⠕⠞⢊⣱⣼⡗⢸⢀⠁⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣢⣄⠉⠁⠀⢀⠎⢊⡿⠟⣾⠁⡸⠘⠀⠀⣴⢯⠀⠀ ⠀⠀⠀⠀⣠⣤⡀⣰⠈⡗⠚⠚⠃⡀⠀⠀⠀⠀⠀⢰⢹⠊⠀⡆⠀⣸⢏⠃⠀⠀ ⣅⠁⠀⠀⠹⢿⣿⠃⢀⢓⢄⠀⠈⢃⣀⢤⡎⠀⢀⣼⢰⠀⠀⡇⠀⡿⡀⠀⠀⠐ ⠿⠇⠀⠀⠀⢀⡧⠄⡜⡬⢀⡉⠢⠄⡉⠉⡀⢴⠁⣸⠘⣶⠤⠓⠚⢇⠀⠀⠀⠐ ⠀⠀⠀⠀⣠⠋⠀⡐⡐⢀⠀⠀⠉⠁⠁⠀⠀⢘⣶⣿⠀⡿⠀⠀⠀⠀⠡⠀⠀⠀ ⠀⠀⢠⠊⡌⠀⡰⣐⠄⠀⠁⠂⢀⣀⣤⣶⣾⣿⣿⣿⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⡴⠁⠀⠃⠤⠿⠧⠤⠶⢊⡏⢿⣿⣿⣿⣿⣿⣿⣿⠀⣣⠁⠀⠀⠀⣆⣀⠀⠀ ⢼⢣⡀⠀⠀⠀⡐⠘⣿⣿⣿⣿⣦⣬⣍⠉⠉⠉⠉⠉⠉⠣⠀⠀⠀⡜⠘⡌⠑⠒ ⠘⠀⠈⡍⢏⣀⣧⣤⣿⣿⣿⣿⣿⣟⡡⢂⠄⠀⠀⣀⠴⢀⠃⠀⢰⠁⠀⠘⡀⠀ ⠀⠀⠀⢧⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣷⣧⣮⣽⡿⠁⠀⢸⠀⢀⠳⠀⠀⠀⠰⠀ ⠀⠀⠀⠈⡄⢸⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠀⡌⠀⡆⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠙⠲⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠌⠻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠎⠀⡘⠈⣁⠤⠒⠒⢲⡤⢄⠀⠀⠀⠀⠱⡀ ⠀⠀⠀⠀⠀⢸⠀⡾⠁⢩⠒⣆⠁⠙⠿⠷⠂⢠⡧⣿⡶⠵⣆⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⢨⡾⠁⡐⠘⢄⠈⠀⠈⠀⠀⠁⠘⣕⠠⠐⢠⠙⠃⠀⠀⢸ ⠀⠀⠀⠀⢰⠃⢐⠊⠀⠀⠀⠱⡀⠀⠀⠀⣠⡬⣄⠀⠀⡜⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠀⠀⠑⣄⠀⠞⠓⡈⡻⢀⠜⠀⠀⠀⠀⣸⠇ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⡇⠁⠒⠒⠒⠊⠁⠀⠀⠀⢀⣴⠮⠄ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡊⠀⢼⣀⣠⡴⠒⠉⠉⠆⠀⢀⣴⠟⢹⠀⠀ ⠀⠀⠀⠀⢠⠀⠀⠀⡐⠁⢀⠏⠀⠀⠀⠀⡠⠄⠀⡇⢼⠛⠓⠀⢸⠉⠀ ⠀⠀⣽⣧⣀⡧⡀⡜⠀⠠⡃⠀⠀⠀⠀⢰⠀⠀⢠⡷⢾⡿⡷⠀⢸⠀⠀ ⠀⠀⠷⢝⢮⣻⢞⠀⠀⠈⠉⠒⠤⢀⣀⡆⢀⠔⡕⠑⣫⠊⠉⠉⢹⠀⠀ ⠀⠀⠘⢖⣃⡀⢃⠑⠖⠠⠤⠀⠀⢀⠀⠈⠠⡬⠠⠜⢲⠃⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⢚⡛⠛⠒⣒⣠⣤⡤⠤⠤⢤⣴⠗⡒⠒⠚⠒⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⡟⢿⣿⣿⣿⣿⣿⡿⡿⠿⠟⠛⠛⢻⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠋⠉⣠⠞⡽⢟⠦⣍⡙⠛⠛⠻⣷⠀⠀⠀⠀⠀⢼⣿ ⣿⣿⣿⣿⣿⣿⣿⠥⠖⠒⢋⢉⡤⠞⠁⠈⠙⠦⣍⣙⠒⠢⣼⡆⠀⠀⢀⣠⣿⣿ ⣿⣿⣿⣿⣿⣿⡏⣠⢴⡞⠋⠉⠉⠓⠦⠀⠀⠠⠖⠛⠙⠲⣄⣷⠀⢰⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠋⡷⠼⠗⢶⣤⠤⣄⣣⡀⠀⢀⣀⣀⣬⣦⣽⠻⡆⢾⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡇⠀⢳⣀⡄⠀⠉⣒⠒⠈⠀⠤⡍⠛⠒⠊⠁⣿⠀⢷⠈⠻⢿⣿⣿ ⣿⣿⣿⣿⣿⠀⢀⣿⣿⣇⠀⠀⢗⢯⣟⣡⠶⠖⠀⠀⠀⣠⠇⠀⢸⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡆⠈⠑⠉⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇⠀⠘⣶⣤⣴⣾⣿⣿⣏⡿⠀⠀⣸⠇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠇⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇⠀⢰⡟⠀⠀⠀⠀⠀ ⣿⣿⣽⣿⣿⡄⣸⠋⠀⠘⡜⣄⠀⠀⠀⠱⡱⡄⠉⠻⡟⠀⢠⡟⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⣷⠈⠉⠉⠉⠉⠁⠉⠑⢦⠹⣴⣿⡀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⢹⣿⣿⣿⣿⣷⣶⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣇⢀⣀⣀⣰⡒⠲⡶⠯⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢘⡭⠵⠚⠉⠙⣄⠟⠉⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠉⠉⠙⠛⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⠉⣿⣿⣿⣿⣿⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⣠⣾⣿⣿⣿⢿⣿⣿⠃⡀⠀⠘⣿⡝⣿⣿⣿⣿⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢟⣻⣿⡟⠀⣷⡀⠀⠸⣿⡼⣿⡻⣿⣦⣙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣩⠟⠋⣿⡟⠉⣿⣿⣷⡀⢹⣿⠀⠀⣿⣇⣿⡗⠸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⣴⣧⣿⢣⡶⢿⣿⣏⣿⠈⣿⡆⠀⣛⣿⣾⡇⣿⡄⠈⢹⣿⣿⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣾⣃⢸⣿⣿⡏⠿⣿⣷⠀⢿⣿⣿⠃⠉⣿⣄⣀⢸⣿⠀⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣙⣿⣿⡿⢻⣿⡆⣿⣿⡇⢀⣿⣿⡆⢸⣿⡟⠀⡀⣿⡇⠨⢸⣿⠀⣼⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣿⣿⣿⡷⣿⣿⣷⣼⣿⣇⣿⣿⢿⣿⡸⣿⡇⠀⠁⢹⣧⠠⢼⡿⢀⣼⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⡿⠀⠼⣿⡼⣿⣿⣿⣼⣿⠀⠻⣿⣿⣿⠀⡀⣸⣿⣧⣼⣧⣾⣿⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⡇⢀⣀⠻⣇⠹⣿⣿⣿⣿⢀⣀⣹⣿⣿⣦⣄⣿⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣻⣿⡿⣿⣿⣿⡿⠛⠉⠉⠛⠀⠘⢿⡿⣿⡏⠁⠀⠈⣿⣿⣿⣿⡟⢻⣿⣿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠛⠀⢧⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⠎⠃⠀⠀⢠⣿⣿⡿⣿⠇⠛⣿⢻⣿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡞⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠸⣼⡟⠀⣿⣷⡿⠃⠘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⢿⣄⠀⠀⠀⠘⣿⣯⣼⠇⠀⠀⠀⠀⠛⣡⠞⠛⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⢤⣀⣀⡤⠴⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⡠⢀⡆⠀⣇⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠲⣤⠞⢡⠒⠊⠀⣼⣡⠶⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⢢⠀⠈⠑⠮⣄⣠⡴⠛⠁⠀⢀⡤⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠈⠳⢍⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣡⣾⣿ ⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⢤⡀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣙⣦⠀⠀⠀⠀⠀⢀⣼⣿⣿⣵⣿⣿⣿ ⠀⠀⠀⠀⠀⣰⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢧⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⡇⠀⢰⡏⣿⣯⣾⣿⣿⡟⣿⢹ ⠀⠀⠀⠀⢰⣧⠀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⡞⠁⠀⠀⠀⡀⠀⢧⠀⢸⣿⣿⣿⣿⣿⡟⢸⡇⣾ ⠀⠀⠀⠀⣸⢹⠀⠃⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢰⡿⠀⠀⠀⠀⢠⠇⠀⠸⣆⣸⣿⣿⣿⢿⡿⠷⣜⠃⣏ ⠀⠀⠀⢰⠇⢸⢰⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡟⠁⠀⠀⠀⠀⣾⠀⠀⠀⢹⣿⣿⣿⣿⡘⠇⠀⠀⠀⠘ ⠀⠀⢀⡏⠀⢸⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⢰⠃⠀⠀⡇⠸⣿⣿⡿⣟⠓⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⢸⣼⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⢠⡏⠀⠀⢠⡇⠀⠹⣿⡀⢻⡀⠀⠀⢠⣤⣀ ⠀⢰⠃⠀⠀⢸⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡇⠀⠀⢀⡞⠀⠀⠀⠸⡇⠀⠀⢳⡁⠈⢻⡀⠀⠸⠏⠁ ⠀⡏⠀⠀⠀⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡇⠀⢀⡾⠀⠀⠀⠈⠀⠇⠀⠀⠀⢧⠀⣀⡽⣄⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⣓⣦⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠝⠁⠈⣛⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⢻⡛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⠀⡖⠀⠀⠈⠉⠉⠠⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠜⠀⠀⠀⢀⠀⠑⠤⡧⢸⣆⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠤⠤⣀⡼⠂⠀⣆⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⠋⠀⠸⣄⡀⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣆⢀⠀⠀⡀⠀⠉⣭⣽⣿⡷⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠙⠶⣾⣾⣿⠿⢟⠙⢆⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⠀⠘⠆⠈⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⠟⠋⠉⠉⠛⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡆⠀⠀⠀⠀⠀⠀ ⢀⣄⡀⠀⠀⠈⢻⡇⢠⣿⣦⣤⡤⠆⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⣧⡀⠀⢀⡼⢻⡆ ⠺⣇⠙⢶⣄⡤⣼⡧⢼⡏⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢀⣀⣤⠶⠟⢩⣿⠉⢹⠏⠙⣦⡞⢁⡼⠁ ⠀⠙⣦⡌⠙⣀⡜⢧⡠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠋⠁⠀⠀⢠⡟⢯⡑⠂⣴⢒⣇⣼⠟⠁⠀ ⠀⠀⠀⠛⣿⢧⣝⣁⡴⢋⡷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠈⢷⠒⠋⠙⡗⠋⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠸⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠳⣤⣀⣁⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢲⣴⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣿⡟⣿⣿⡇⢻⣿⣦⡀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⣀⣀⣠⣾⣿⡟⠁⣿⣿⣇⠀⠹⣿⣿⣦⣼⣿⣿⣿⣿⣿⣷⡄⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⣷⣾⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠟⠛⠛⠛⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⢿⣿⣿⣿⡇⠀⠀⠉⠉⢻⣿⠛⠋⢹⣿⣧⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣿⣿⣿⠟⠀⠀⠀⠀⠀⣸⣿⠀⠀⠘⢿⣧⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾ ⠀⠀⠀⠀⢀⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠀⢀⣴⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣄⣀⣀⣤⣤⡶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢠⣿⠟⠉⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣤⣤⣤⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀ ⢠⡟⠁⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠻⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠉⠛⢿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠘⣏⠛⠻⠿⣿⣶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣶⣶⡿⠿⠛⠋⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⠉⢻⡟⠛⠛⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠛⠛⠛⣿⠉⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠶⠦⣽⣦⣤⣀⣀⣀⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣸⣇⣀⣠⣤⣤⠴⠾⠷⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⣿⠉⠉⠉⠉⠉⠙⢻⣿⠛⠛⠛⠛⠛⠛⠛⢻⡟⠛⠋⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣠⣼⣿⣾⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣀⣀⣀⣀⡀⢸⣇⢀⣀⣀⣀⣀⣠⣤⣾⣶⣾⣿⠿⠿⠛⠋⠉⠁⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⢹⠛⡛⠦⡆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⢠⣴⣷⣆⣀⣠⡤⠤⣤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠿⠿⣿⣿⣾⣏⠀⠈⠛⠻⣧⡀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠓⠤⣀⡀⠀⠀⠀⠀⢷⠀⠀⠀⡼⠋⢻⣿⠹⡄⠀⠀⠘⢯⡛⢦⣴⠏⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⣀⠀⠀⠉⠙⠓⢲⣶⣾⣧⡀⢸⠁⠀⠈⣿⣇⣷⡀⠀⠀⠀⢳⣶⣏⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⢀⡖⠉⢀⡴⠒⠒⠒⠋⠉⠉⢳⡀⠀⢀⣀⣸⣿⣙⣿⡙⣿⠀⠀⠀⠘⣿⠉⣳⢀⣤⣾⣿⣿⣿⠀⢀⣾⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠋⣉⣙⠒⠚⠋⠀⠀⠛⢷⠀⠀⠀⠀⠀⠀⠀⣻⠿⠍⠉⠉⢀⣀⠈⠙⢿⡀⠀⠀⠀⣘⣧⣷⢿⡿⠋⠉⣻⣏⣠⣿⣿⣽⣿⠉⠙⠒⠦⠤⠤⠔⠺⠟⠶⡄⠀⠀⠀⠀⠀⠀⠀ ⠋⠒⠋⣰⡳⠀⣠⠴⠒⠦⣄⠀⢷⡄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⢉⣾⣛⣦⠀⢱⡀⠀⣺⣿⣿⣿⡿⠀⢀⣴⠟⠋⣀⣄⠀⠀⠺⠿⣖⠀⠀⠀⢀⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⡷⢁⡴⠋⠀⠀⠀⠈⠑⠦⠼⠆⠀⣰⢋⠀⠀⠀⠀⠀⢮⣿⡛⠋⠙⠋⢉⡟⠉⠁⠁⠉⠉⢳⡞⠋⠳⣶⣯⣿⡞⠁⠀⠀⠀⠘⢦⡤⠚⠁⠈⣳⠤⣄⢹⡀⠀⠀⠀⠀⠀⠀ ⠀⠸⠿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡏⠀⠀⠀⠀⢀⡾⠸⡄⠀⠀⠀⠘⢧⣀⡀⠀⣀⣠⠞⠁⠀⠀⠙⢾⡿⢿⠉⠀⠀⠀⢲⣾⡆⠀⠀⡼⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡼⠀⠀⠀⠀⠀⢸⡇⠀⢹⠒⠤⣤⣤⣤⠬⠟⠻⢤⣀⠀⠀⠀⢀⣠⡾⠁⠘⡆⠀⠀⠀⠀⢱⡀⢀⡴⠁⣠⠖⠒⢦⠀⠈⠉⠲⡶⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡄⠀⠸⡆⢠⠿⣬⠇⠀⠀⠀⠀⠈⣿⢹⡏⠉⣸⠁⠀⠀⡇⠀⠀⠀⠀⠀⣇⠾⠴⠚⠁⠀⠀⠈⢇⠀⠹⣄⠙⢿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠚⠀⠉⠀⠀⠀⠀⠀⠀⠿⠟⣽⡴⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⢷⢤⣹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣠⠔⠚⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠬⠷⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⣇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⣸⡾⠔⠛⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢠⠃⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠞⠁⠀⠀⠀⢀⡤⠞⠓⠦⣄⡀⠀⠀⠀⢀⡇⠀⠀⡞⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠹⡄⠀⢀⡾⢤⡀⢰⣇⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡄⠈⣇⢀⣼⡇⠀⢹⣸⠹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡴⠛⣆⡽⠻⣼⠇⠀⢈⡿⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⠤⠼⠧⠤⠿⠤⠖⠛⠁⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣀⣀⣀⣀⣀⣀⡠⠴⠚⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠲⠤⢄⣀⣀⡤⠴⣯⣉⣉⣉⠭⠿⢛⢋⠁⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢾⡉⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⢦⡀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠍⠉⠓⠚⠁⠀⣀⡤⠜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⣤⣤⡚⠁⢀⣀⣀⡤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡏⠀⠀⣀⡠⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠲⠶⠤⠤⣌⣉⠉⠀⠐⠒⠢⣄⣙⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣸⣷⣼⡧⡤⠄⠐⠛⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣴⣷⡖⠲⢆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠠⠊⠁⡑⠂⠤⣬⡀⡌⠹⣵⡀⠘⡵⡋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⣒⠀⠈⠀⠎⠉⠀⢐⠤⠒⣓⠣⠇⠀⣡⣧⠞⢻⣃⡾⣗⠀⠤⠤⠤⠄⠀⠀⠀ ⢉⡼⡠⠉⠑⠨⠆⠠⠀⠀⢠⡾⠚⢚⠒⠛⠻⡔⢯⣶⡂⠈⠣⠄⠒⠤⢠⠀⠀⠀ ⠈⠉⠀⠀⠀⠀⠀⠛⠀⠀⠸⠰⠠⣄⠱⠶⢈⣀⡀⠏⡇⠀⠘⢀⢌⠄⢀⠑⢠⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠀⠛⠙⣀⣀⠘⠺⠌⠀⡇⠀⠀⠇⠁⠀⠀⠂⠱⡽ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠘⡀⡔⠁⠀⠀⠈⠄⠀⠀⡇⠀⢠⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠵⠐⠂⣄⠀⠀⠈⡀⢠⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠐⠁⠀⡈⡄⡰⢄⣤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⢲⡗⣅⡨⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣀⡮⢤⡤⠤⠐⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠤⠸⠀⣐⠍⠉⠉⠉⠉⠉⢐⠆⢀⡨⠀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠚⠥⣀⣰⣵⡀⠠⠀⠀

⣴⣦⣤⣄⣀⣠⣄⠀⣰⡆⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠹⠛⠛⢽⠟⠁⠸⠛⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⠚⠛⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣸⣶⣇⠀⢰⣿⣿⣷⣤⠤⠴⠖⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣴⣇⠀⢰⣾⣿⣄⣼⡿⠿⢿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠖⠚⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢾⣿⠽⢼⡛⠋⠉⠉⠁⢸⠀⠀⠈⢻⣄⣀⣠⠤⠤⣶⠒⠚⠋⢉⣉⣠⣤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠟⠋⠉⠉⠀⠀⣾⠃⠀⠈⢻⣀⣠⠤⢤⣿⠀⠀⠀⠀⢿⡇⠀⢀⣤⡿⠗⠒⢚⣏⠉⠱⡄⠀⠀⠀⢸⠈⠙⠲⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣤⣀⣀⡤⠤⠶⡿⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠀⠀⠀⠘⣇⣴⠃⠀⠻⢤⡸⣿⡿⠏⢀⡿⠀⠀⢠⣏⡀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⡆⠀⠀⢸⡁⠀⠀⠀⠀⢹⡏⠀⠀⠀⣰⣿⣗⠓⠒⠛⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢳⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢳⠒⠒⢙⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⢿⣧⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠛⠛⠀⣠⠞⡉⠉⠳⣄⠀⠀⠀⠀⠀⢳⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢠⠇⣴⣿⣷⠀⠸⡆⠀⠀⠀⠀⢸⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢸⡄⠉⠋⠉⠀⠀⢷⠀⠀⠀⠀⣸⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠃⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⠇⠀⠀⠀⠀⠀⠀⣸⠀⣠⠞⠁⠀⡼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣄⣀⡀⢀⣀⣀⡠⠷⠚⠁⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⠞⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠤⠤⠤⠤⠤⠦⠶⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠐⠶⣿⣿⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⡿⠟⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣆⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀