⠀⠀⠀⠀⠀⠈⠀⣀⣀⣀⣀⣳⣤⣤⡀⠤⣴⡾⠋⠛⠛⠛⠻⣾⣿⡖⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⢤⣦⣤⣤⣄⡀⠀⠀⠀⠀⠰⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⢀⣤⣶⣴⣶⣾⣿⣿⣿⣿⠛⠻⣿⠋⠉⠁⠀⠘⣷⠀⠀⣤⠀⠀⠸⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⣷⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⠏⠸⠟⠛⠋⠉⠉⠀⠈⠉⣿⡇⠀⠀⢿⡆⠀⠀⠀⠀⠙⣷⣄⣻⣧⡀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡇⠙⠛⠻⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⠀⡿⢻⣾⣷⡶⣿⣿⣿⠟⢿⣿⣿⣿⣦⣤⣛⣓⠂⣄⡀⠲⢶⣄⠀⠀⠀⠀⠀⠀⠀⣹⣷⡟⠀⠀⠀⢀⣿⣿⡇⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⣾⣿⠁⢀⣤⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣓⣶⣿⣿⣧⣥⣄⣤⣴⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⡀⠀⣀⡀⠀⠀⠀⠀⢿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠉⠉⢻⣿⣿⣿⣟⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠙⠛⠛⠿⠿⠿⠿⢷⣶⣤⣀⣰⣿⡋⠉⢙⣻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠽⢷⣤⣿⣿⣿⣿⡟⣶⣴⣶⣀⠀⢰⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣋⣡⣾⣿⣷⣶⣶⣤⣀⣀⡀⢹⣿⣿⣿⣿⡿⠻⠿⠋⢁⣼⣿⡿⠃⢩⣽⣿⣿⣿⣿⣿⣿⡁⠙⣿⣿⣿⣦⣤⣤⣟⢿⣿⣿⣿⡁⠙⠿⠿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣤⣤⣤⣀⣀⠀⢀⡀⣀⣠⣴⡿⠟⠋⠙⣿⣋⡀⠈⠉⠉⠀⢀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠐⠛⠋⠉⠀⣀⣼⣿⣿⣿⣿⣿⣿⡿⠃⠀⣈⣻⣿⣿⡟⠛⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣍⠉⢿⣿⣿⣿⠏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠉⠻⣿⡿⣿⣿⠛⠛⢁⣀⡀⠀⣼⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⣾⠿⠋⠉⠉⠻⢿⣿⣏⣠⣤⡜⠋⠉⢹⣿⡗⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠀⢻⣬⣿⣦⡄⠈⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣶⣶⠿⠀⡀⠉⠙⢲⣾⣿⠃⢀⣤⠀⠀⠂⠁⠀⠀⠀⠀⠁⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢸⣿⣷⠀⠀⣀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡶⠿⠶⠶⠾⠿⠷⠾⣍⠁⣀⣠⣷⣤⣶⣿⡿⠓⠾⠿⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿⣿⡟⣠⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⠿⣿⣤⣿⣧⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢿⣿⣷⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣋⣴⣿⠿⠛⠁⠀⠀⠀⠠⠾⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢴⣦⣤⣄⣼⣷⣶⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⢠⣤⣴⣶⣶⣶⣿⣿⣦⣤⣴⣦⣤⠿⣦⣛⠁⠀⠀⠀⠙⢿⣿⣿⣷⢦⣄⠀⠀⠀⠀⠀⠀⢀⣠⡀⣺⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣯⠛⠛⠃⠀⡵⠀⠀⠀⠀⠀⠙⠿⣿⣶⣦⣤⣿⣶⣤⣴⣶⣼⣿⢸⡟⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⢠⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠉⠀⠀⠉⠁⠀⠀⠀⠀⠉⠙⠶⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠉⠁⠉⠈⠁⠁⠀⠀⠀⠠⠀⠀⠀⠀⢠⡄⢒⣠⣼⢿⣧⡀⣸⣿⣩⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠀⠀⠀⠀⠀⠀. . ⠀⠀⠀⠀.⠀⠀⠀⠐⠂⠀⣀⣤⡴⢶⡎⠛⠏⣿⢃⠀⢹⡿⠋⠀ .. .. ... . . . . . . ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀