⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠛⠛⠛⠛⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠒⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣻⣿⣿⣤⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠋⠉⠁⣀⣀⣤⣤⡄⠀⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⣤⣤⣤⣤⣼⣷⡾⠟⣿⡻⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣬⣽⠏⣿⠀⠈⣧⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢹⣆⠀⢹⡄⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣧⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡄⠀⢸⡆⠀⠸⣟⠛⠳⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⣿⣀⡀⣿⣠⣤⡿⠶⠆⠀⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠶⠋⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠀⠀⢀⣴⣶⣦⣆⢄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⡧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠸⣧⠠⡀⠀⠀⠻⣿⣿⣿⣿⣿⠃⠀⢀⣾⣧⡀⠀⠛⠿⠟⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⣴⣎⢁⣬⣿⣏⣉⣷⠙⢷⣌⠠⠀⠀⠈⠛⠛⠛⠁⠀⠀⠸⠟⠛⠋⠀⠀⠀⢀⣴⠟⠁⢀⣠⣀⠀⣀⣀⠀ ⠿⣇⣀⣾⠋⢻⣧⡴⣿⡉⣹⣇⠀⠙⠳⢦⣤⣤⣤⣤⡤⣀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢸⡇⠀⣰⣯⣡⣽⣿⠉⢹⡧ ⠀⢀⡼⠛⠷⣻⣧⣀⣼⣟⣉⣉⣿⠚⠳⣦⠀⠀⠈⠉⢿⣄⡀⣀⣿⣄⣀⣰⡿⣦⣤⡾⠁⢼⡋⣹⣧⣀⡽⠛⠻⣇ ⠀⠸⠧⠴⢚⣯⣼⣏⣀⣸⣿⡉⢉⣿⡛⠛⣷⠀⠀⠀⠀⠉⠛⠋⠀⠙⠙⠋⠁⠉⠻⠇⠀⠈⣹⣏⡀⣈⣿⣤⣴⠏ ⠀⠀⠀⣰⠏⠁⠀⠈⣟⠁⠈⢹⡏⠉⠙⣿⠋⠀⣖⠛⠛⢶⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠛⠒⠒⠒⣻⠛⠳⠶⣿⠛⠶⠾⠋⠀⠀⠙⠶⢥⡥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⣠⣀⢻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⡥⢥⠶⠙⠀⠀⠋⠾⠶⠛⣿⠶⠳⠛⣻⠒⠒⠒⠛⠀⠀⠀ ⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢶⠛⠛⣖⠀⠋⣿⠙⠉⡏⢹⠈⠁⣟⠈⠀⠁⠏⣰⠀⠀⠀ ⠏⣴⣤⣿⣈⡀⣏⣹⠈⠀⠇⠻⠉⠁⠋⠙⠙⠀⠋⠛⠉⠀⠀⠀⠀⣷⠛⡛⣿⢉⡉⣿⣸⣀⣏⣼⣯⢚⠴⠧⠸⠀ ⣇⠻⠛⡽⣀⣧⣹⡋⢼⠁⡾⣤⣦⡿⣰⣀⣄⣿⣀⡀⣄⢿⠉⠈⠀⠀⣦⠳⠚⣿⣉⣉⣟⣼⣀⣧⣻⠷⠛⡼⢀⠀ ⡧⢹⠉⣿⣽⣡⣯⣰⠀⡇⢸⠀⠀⡀⠀⠀⠀⡀⠀⠀⣀⡤⣤⣤⣤⣤⢦⠳⠙⠀⣇⣹⡉⣿⡴⣧⢻⠋⣾⣀⣇⠿ ⠀⣀⣀⠀⣀⣠⢀⠁⠟⣴⢀⠀⠀⠀⠋⠛⠟⠸⠀⠀⠁⠛⠛⠛⠈⠀⠀⠠⣌⢷⠙⣷⣉⣏⣿⣬⢁⣎⣴⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⠁⡾⢀⠁⠟⠿⠛⠀⡀⣧⣾⢀⠀⠃⣿⣿⣿⣿⣿⠻⠀⠀⡀⠠⣧⠸⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢰⠀⡿⣿⣿⣿⢻⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⡀⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⡧⣷⣿⣿⣿⣿⣽⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⣶⣿⣶⢠⠀⠀⠀⠀⠀⠀⢄⣆⣦⣶⣴⢀⠀⠀⠀⠀⡀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠈⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠙⠉⠋⠶⠀⠀⠟⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢷⠛⠉⠀⠀⠆⠶⡿⣤⣠⣿⡀⣀⣿⠉⠟⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⠶⠳⠛⣟⠸⠀⡆⢸⠀⡄⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⣧⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⠀⡄⢹⠀⣆⢹⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⣧⠈⠀⣿⠏⣽⣬⣼⢿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⣿⡻⣿⠟⡾⣷⣼⣤⣤⣤⣤⢁⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣻⠀⡄⣤⣤⣀⣀⠁⠉⠋⠛⠖⠶⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢶⠶⠶⠶⣤⣿⣿⣻⣟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⠒⡟⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠶⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢿⠶⠶⣶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠛⠛⠛⠛⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀