⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠛⠉⣉⠉⡙⠛⠻⢿⣿⣷⣤⣤⣴⣾⡿⠿⠛⠛⠛⠉⠛⠛⠛⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣶⣤⣈⠙⢿⡿⠛⣁⣤⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄⡉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡟⢁⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠉⠻⣿⣷⣄⣴⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⡈⠻⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠏⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠹⣿⡇ ⠀⠀⠀⠀⢸⡟⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⢹⣿⣇ ⠀⠀⠀⠀⣿⠇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⣉⢾⡋⢖⣡⢚⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠈⣿ ⠀⠀⠀⢸⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⢳⣷⢢⡙⢆⠦⣉⢳⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿ ⠀⠀⠀⢸⣿⡆⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⣾⣿⢡⠚⣌⠖⣩⠒⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿ ⠀⠀⠀⠀⣿⡇⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣿⣆⠹⣀⠏⣰⠉⡾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢰⣿⠟ ⠀⠀⠀⠀⢹⣿⡀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⢻⣷⣗⢌⡚⢤⢋⢖⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⡜⠀ ⠀⠀⠀⠀⠀⣿⣧⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣾⡇⠈⠐⠀⡉⠻⣷⣯⣦⣉⠶⣐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⣰⣿⠃⠀ ⠀⠀⠀⠀⠀⠘⢿⣷⡈⠻⣿⣦⡀⠀⠀⠀⠀⢸⣿⠀⠀⡁⠐⠀⡐⠀⠉⠛⠻⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⣴⣿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠙⢿⣿⣄⠀⠀⠀⢸⡟⠀⠠⠀⠐⢀⠀⠌⠐⠠⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢀⠞⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠛⣿⣷⣤⡀⣾⡇⠈⡀⠄⠁⡀⠠⠀⠂⠁⠄⣿⡇⠀⠀⠀⣠⣴⣿⠟⢁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠛⢿⣿⣿⣧⠐⠀⢀⠂⠀⡐⠀⢈⠐⡀⢸⣷⠀⣠⣾⣿⠟⢁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠙⠿⣿⣷⣬⡀⠄⠂⢀⠐⡀⠄⡀⣼⣿⣿⡿⠋⣁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣈⠛⢿⣿⣶⣥⡀⣠⣴⣶⣿⡿⠟⢁⣤⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣆⠈⠹⣿⣿⣿⣿⠿⠉⣀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡙⠋⣁⣴⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⣾⣴⣁⠋⡙⣄⣦⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⣾⣀⠉⠿⣿⣿⣿⣿⠹⠈⣆⣷⢿⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⣤⢁⠟⡿⣿⣶⣴⣠⡀⣥⣶⣿⢿⠛⣈⣦⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⣁⠋⡿⣿⣿⣼⡀⠄⡀⠐⢀⠂⠄⡀⣬⣷⣿⠿⠙⣄⣷⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⢁⠟⣿⣾⣠⠀⣷⢸⡀⠐⢈⠀⡐⠀⠂⢀⠀⠐⣧⣿⣿⢿⠛⣄⣦⢿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣴⢁⠟⣿⣴⣠⠀⠀⠀⡇⣿⠄⠁⠂⠀⠠⡀⠁⠄⡀⠈⡇⣾⡀⣤⣷⣿⠛⡄⣷⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠞⢀⠟⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠠⠐⠌⠀⢀⠐⠀⠠⠀⡟⢸⠀⠀⠀⣄⣿⢿⠙⣄⣿⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⣿⣴⠃⡿⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⣿⠻⠛⠉⠀⡐⠀⠐⡁⠀⠀⣿⢸⠀⠀⠀⠀⡀⣦⣿⠻⡈⣷⢿⠘⠀⠀⠀⠀⠀ ⠀⠃⣿⣰⠃⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣐⠶⣉⣦⣯⣷⠻⡉⠀⠐⠈⡇⣾⠀⠀⠀⠀⠀⠀⠀⣄⣿⢿⠈⣧⣿⠀⠀⠀⠀⠀ ⠀⡜⠃⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣻⢖⢋⢤⡚⢌⣗⣷⢻⠈⠃⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⢿⡀⣿⢹⠀⠀⠀⠀ ⠟⣿⢰⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡾⠉⣰⠏⣀⠹⣆⣿⢿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⢸⡇⣿⠀⠀⠀⠀ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠒⣩⠖⣌⠚⢡⣿⣾⢣⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⡆⣿⢸⠀⠀⠀ ⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣹⢳⣉⠦⢆⡙⢢⣷⢳⢣⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⣿⢸⠀⠀⠀ ⣿⠈⣷⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠻⢚⣡⢖⡋⢾⣉⠻⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣸⠇⣿⠀⠀⠀⠀ ⣇⣿⢹⡆⣿⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣶⣶⣾⣶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⢠⡟⢸⠀⠀⠀⠀ ⡇⣿⠹⣄⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⢠⠏⣾⢀⠀⠀⠀⠀ ⠀⠀⠀⣦⣿⠻⡈⣶⣿⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠋⠟⣿⣾⣴⣄⣷⣿⠻⠉⠈⠀⠀⠀⠀⠀⠉⠛⡿⣿⣴⢁⡟⣾⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣄⣷⣿⠻⡉⣄⣦⣶⣿⣿⣿⣿⣿⣾⣶⣤⣁⠛⡿⢿⠙⣈⣤⣶⣿⣿⣿⣿⣿⣿⣾⣴⣠⢉⠟⣴⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⣷⣿⠿⠛⠛⠛⠉⠛⠛⠛⠿⡿⣾⣴⣤⣤⣷⣿⢿⠻⠛⡙⠉⣉⠉⠛⠛⠿⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣤⣤⣤⣤⣀⣠⢀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣤⣶⣶⣶⣶⣶⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀