⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠉⠀⠀⠀⠀⣀⣀⠈⠉⠉⠉⠉⠹⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠁⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣿⣁⣠⣤⣤⣤⣤⣤⣤⣀⣀⣹⣷⣀⢠⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠞⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣦⣄⣬⣥⣶⣶⠾⠟⠛⠿⢿⣿⣿⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣰⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣆⠀⣴⣿⠿⠿⠻⠿⠷⠾⠃⠀⢀⣶⣫⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠏⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⣰⡿⠿⠛⠿⠿⠶⠆⠀⣿⠀⠀⠀⠀⠻⡆⠉⠁⠀⣀⣀⣀⣀⣠⣤⣶⣯⠭⠥⠶⠀⣀⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀ ⠀⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⣋⣂⠀⠀⢀⣀⣀⡀⠀⠉⢳⡀⠀⠀⠀⠀⣠⣰⣿⣭⠿⣟⣹⠟⠁⠀⠀⠀⠀⠀⠉⢉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⢿⡿⠯⢾⡟⡇⠀⠈⢷⡄⠀⠀⣰⠏⢡⣛⣟⣛⣉⣠⡤⠶⠖⠛⠒⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⠟⠋⠁⠻⣦⠀⣸⠇⠀⣴⠟⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⣷⠏⢀⣸⣟⡰⠞⠋⠙⣿⠶⢦⣄⡀⠀⢀⣀⡴⠾⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⠀⢸⢸⣯⣇⠀⠀⣰⡿⣾⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⢸⣄⣠⣾⠟⠋⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣤⣼⡷⢷⠿⡏⢹⡛⢿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠙⠿⣶⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⢀⣤⡞⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⡏⠀⡇⢸⣄⣿⡴⢟⢻⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣧⡀⠀⠀⠀⢡⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢾⡁⠙⠷⠷⠴⠟⠛⢋⣀⣤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠁⠙⣿⣆⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣦⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⠶⠿⠿⢭⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣆⠀⠀⠀⠀⢈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠁⠀⠀⠈⢿⣦⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠷⠦⣤⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⣁⡴⠇⢀⣀⣀⣤⡴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣦⣾⠁⢤⡀⢈⣷⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣥⣾⣿⣟⡛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠈⠛⠀⠈⢿⣿⠛⢳⡈⠻⢦⣤⣀⣀⣀⣀⣠⣤⣤⡴⠞⠛⠛⠉⠉⣿⠋⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢺⡟⠛⠓⠂⠶⢤⡀⠉⢀⣼⠏⠙⠋⠉⣹⡿⠋⠉⠀⠀⣹⣀⣀⣀⣀⣠⣤⣿⡦⣀⠀⠀⠀⠀⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⣤⣦⠀⠈⠃⢰⣿⣯⡀⠀⢀⣼⠏⠀⠀⠀⢀⣼⣿⠉⠉⠉⠁⠀⠀⠀⠀⣿⠳⢦⣄⡀⠀⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣾⣿⡻⣿⣿⣦⠟⠁⠀⠀⢀⣴⣟⣁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⢙⣳⣶⣶⣀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣤⣀⠀⠀⢀⣀⡤⠴⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⢈⡽⠛⠉⠁⣀⣤⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⠗⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⠁⠀⠀⢀⠖⠒⠒⠒⠒⢲⣶⣶⣶⠒⠒⠒⠒⢦⡀⢀⡤⠤⠤⠤⠤⣤⣤⣤⣤⠤⠤⠤⢄⡀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⠿⠿⠋⠀⠀⠀⠀⢠⠇⠘⡀⠀⠀⠀⠀⠻⣿⡿⠇⠀⠀⠀⠀⡇⠀⢽⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠉⠳⣄⠀⠀ ⠀⠀⠀⠀⠚⠀⢸⡀⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⢀⣀⡠⠶⣯⠤⠤⠤⢤⣭⣶⣄⣀⡀⠀⠀⠀⣀⡴⠚⠀⠀⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣠⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢰⣩⠟⠒⠤⢤⣉⣙⣶⠋⠉⠙⣫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⠀⠀⢤⡀⠀⢹⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⠀⠀⠀⠀⠈⠉⠉⠉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀⢀⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠓⠦⣀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠞⠁⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⢳⡀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⣷⠃ ⣀⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⣀⣀⣀⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡴⠋⠀ ⠉⠛⠻⠿⢯⣀⡀⠀⠀⠈⠀⠀⠀⠈⠙⠒⢤⣄⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢙⣧⣤⣤⣤⣤⣤⣤⣤⣤⣥⣬⣭⡿⠛⠉⣹⣧⠀⣀⣀⣀⣀⣠⣤⣤⠤⢤⡤⠤⠴⢲⠒⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠉⠉⠉⠉⠉⠉⠩⣭⡿⠋⠀⢀⣴⣿⠛⣦⣠⣾⣇⣾⡟⣹⠟⠒⠾⢤⡤⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣯⠤⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⡴⠛⢹⣷⣀⡟⡼⣿⣸⣿⣷⡇⢠⠖⢻⠋⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⢀⡴⠋⠀⠀⣾⣈⣿⡿⠁⣿⣿⣿⠙⣷⡿⠤⠬⢧⣀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⡴⣿⡅⠀⣀⡴⠋⠀⠀⠀⢸⣿⣿⣿⣇⣼⣿⡟⣿⢰⡿⢿⣦⠤⠄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⠲⠖⠛⢦⣈⡷⠞⠉⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠀⠉⠀⢸⡏⠁⠀⢉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡚⠉⣀⣀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢻⣿⡿⠋⠉⠁⠀⠀⠀⠀⢀⣤⣾⣷⣿⣿⠟⢃⢀⣤⠶⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠖⠀⠀⠈⠉⠛⠛⠉⠀⡀⣬⠟⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁ ⠀⠀⠀⣀⣠⠤⠤⣄⣐⣁⠀⠀⢀⠀⢀⣀⣠⡤⠴⠾⠓⠒⠒⡒⠒⡒⠒⠒⠦⠽⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⢠⡞⠁⠀⠀⠀⠀⠀⠈⢙⣳⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⢀⡀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣀⡀⠀⣠⣾⡿⠟⠀⠛⢻⣿⣄⠀⠀⢀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠙⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣤⣀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⢠⠇⠀⠀⠀⠀⢀⣤⣾⡿⠟⠛⠉⠉⠉⠙⠛⠿⣿⣦⡀⠀⠀⢀⣴⣿⠿⠛⠉⠉⠉⠉⠛⢿⣿⣦⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⠰⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀ ⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠋⠉⠀⣸⠉⠙⠓⠦⢤⣄⣉⣛⣛⣻⣟⢋⣀⣠⣼⠋⠉⢹⠶⣤⡀⠀⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⠀⠀⢹⠀⠀⣀⠀⠀⠀⠀⠀⣠⠏⠀⠈⠳⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠳⠶⠋⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠸⡟⠉⠉⠀⠀⠀⠀⠀⡏⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⢻⡀⠀⢀⡀⠀⠀⠀⣧⠶⠛⠉⠉⠉⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠲⣦⣼⠇ ⠀⠀⠀⠀⠀⠻⡶⠟⠋⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡽⠀ ⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣠⣦⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢠⣦⡀⠀⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣏⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠀⠉⣻⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣄⣀⡀⠈⠙⠓⠒⠤⠤⠤⠤⣼⣤⡤⠤⠤⠤⠤⠖⠒⠚⠉⠀⠀⠀⢀⣀⣤⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣹⣷⣶⣀⡀⠀⠀⠀⠀⣤⡤⠤⠤⠤⠤⠤⠴⣶⣶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⡀⢈⣿⡉⠙⠛⠲⠦⣤⣿⡀⠀⠀⠀⣀⣠⡞⠁⣼⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⢀⠄⣾⢷⡏⠉⠉⠓⠶⣤⣀⡾⠈⢷⡀⠀⠰⡇⣀⣙⣟⣩⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣤⣊⡴⠛⠁⡞⠀⠀⠀⠀⠀⠀⢩⡇⠀⠈⢷⣀⣴⣷⡈⢹⣏⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⣾⣿⣦⡀⢸⠃⠀⠀⠀⠀⠀⠀⡼⢻⡀⠀⠾⣿⣿⣿⡷⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⡏⠀⠀⠀⠀⠀⠀⢰⠃⠀⢷⡀⠀⣹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡟⠛⠋⠉⠁⠀⠀⢠⣶⡶⠶⠶⠶⠶⣶⡆⠀⢀⣅⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢀⣀⣠⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣽⠶⠤⠴⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⢀⣀⠤⠴⠒⠚⠉⢉⡉⠉⠙⠒⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠃⣰⠏⠀⠀⠀⢀⡤⠞⠉⠀⠀⢀⣠⣴⠚⠉⠀⠀⠀⠀⠀⠀⠻⠿⢿⣷⣦⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⣰⠇⠀⠀⣠⠶⠋⠀⠀⣀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢰⢧⡄⡟⠀⣠⡞⠁⠀⢀⡴⠚⣁⠤⠤⠲⠤⢄⡀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠉⠉⠙⠒⢤⡀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣈ ⠀⠀⠀⠀⠀⢸⠀⢷⣧⡴⠋⠀⢀⡴⠋⡴⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣀⣙⣆⠀⢸⡆⠀⠀⠀⠀⣄⡈⠀ ⠀⠀⠀⠀⠀⢸⠀⣠⡟⠁⠀⣰⠋⠀⡜⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⡄⠀⡏⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⣧⠀⠀⠀⠐⣈⠁⠀ ⠀⠀⠀⠀⠀⢸⢀⡏⠀⢀⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⢷⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⠀⠀⠈⠉⠳⣄⠀⠙⢀⡀ ⠀⠀⠀⠀⠀⢸⠀⠷⣄⣯⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠈⢳⡀⠀⠁ ⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⣠⢾⣧⠄⠐⠲⣶⣾⣷⣦⠤⢤⡔⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⡇⠀⠀⢀⠀⠀⠀⠈⠉⠒⠒⠊⠉⠀⠀⠈⠉⠒⠒⠠⠤⠽⠤⠤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⣿⢹⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡼⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠀⣿⠀⢻⡄⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⣨⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⢰⡇⠀⠀⠙⢦⣾⠋⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⠿⠼⣧⡀⠀⠀⠀⣟⠓⠦⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣺⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⣆⠀⠀⠘⣆⠀⠀⠉⠉⠓⠒⠲⣤⣤⣤⠀⠀⢀⣀⣀⣤⣤⠶⠶⠒⠒⠚⠋⣉⣡⠴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣴⡷⠋⣿⠋⠉⡉⠀⣿⠀⠸⣇⠤⠤⠖⠚⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣶⣶⣶⣾⣷⣄⣀⢀⣀⣼⣷⣶⣶⣶⣦⣴⣿⡶⠖⢾⣿⠟⠁⢰⣿⣤⡞⢳⡴⢿⡀⠀⢻⣤⣤⣤⣤⡆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⢿⡇⣠⠟⠁⠀⣴⣿⡇⢸⠁⢸⠀⢈⣧⠀⠈⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⡿⣿⣿⠁⠀⠈⠉⠋⠠⠀⠈⣿⡇⠈⠀⡿⣿⠗⠲⠾⣯⣸⡇⣼⣤⡾⠒⠺⢿⠓⢦⣸⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠃⠛⠋⠀⠀⠀⠀⠀⠐⠀⠀⠛⠓⠐⠚⢧⣇⣀⣘⣦⣽⠿⠛⢿⣉⣟⣀⣀⣨⣇⣤⠿⠿⠿⠿⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣯⣤⣤⣤⣤⣤⣤⣀⣀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠷⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⣠⣴⣾⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣦⣄⡙⠳⣦⣶⠛⠋⠉⠁⠀⠉⠉⠛⢦⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⣿⣿⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠃⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣴⠖⠒⠓⠒⠲⠦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⡼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣼⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣰⠟⠁⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⡇⣰⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⢿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣠⡼⠋⠀⠈⢿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⡽⣭⣽⠿⣿⣥⣤⡤⠤⣤⣈⣛⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠈⣹⠟⠛⠛⠉⣁⣀⣀⣠⡭⠽⠛⠉⠙⠛⠒⠒⠲⠶⠶⠶⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⠀⢀⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣷⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣿⣦⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣦⠀⢀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⢈⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣶⡶⠚⠲⠦⣌⡻⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⢻⣷⡀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣼⣄⣀⣀⡀⠀⠻⣎⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⣹⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠻⠟⠉⠉⣉⡿⠀⣠⣿⡆⠀⠀⠉⠙⠒⠶⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⡋⢀⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⠤⠤⠤⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠓⠛⣿⣿⣽⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⢻⡷⠶⠶⠖⠛⠛⣻⣿⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠟⠁⠈⠓⠒⠶⠒⠒⠒⠚⠉⠉⠀⠀⠀⣿⠀⣀⣠⣤⣤⣾⣿⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⢾⡟⠉⠉⠉⠀⠀⠀⠉⣦⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠛⠛⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⡾⢳⣄⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⢦⡀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣀⣬⣿⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣾⣿⣿⣿⣿⣶⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⠀⠀⠚⠉⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⣀⡠⠀⠙⣇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠿⠒⠒⠒⠒⠒⠒⠒⠶⠤⠤⠬⣷⣄⣀⠈⠀⠀⠀⠹⣆⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⡿⠀⡴⠣⠔⠛⠗⠶⠀⢀⣀⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⢀⣤⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⣄⡀⠀⠀⠈⠙⠳⣧⣤⠴⠒⠚⠋⠉⠉⠉⠙⠳⢶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠺⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡄⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢀⠀⢠⡄⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⣾⠇⠀⢣⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢰⠇ ⠀⠀⣼⠟⠀⢀⢸⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠹⣿⣿⡟⠻⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⡟⠀ ⠀⢰⠃⢀⠈⠀⡾⡇⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⣿⣿⣿⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⡟⠀⠀ ⠀⣼⠀⠀⢀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀ ⢠⡏⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠲⠶⢶⣶⣒⣒⠒⠲⢶⣒⢒⣶⡶⢤⣄⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠈⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠛⠛⠓⠒⠒⠒⠛⠛⠛⠒⠒⠒⠚⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠘ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢦⣀⡀⠀⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣄ ⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⢀⡿⠀⠀⠠⠄⠀ ⢸⡄⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠿⣦⣀⣸⠁⠀⠀⠀⠀⢠ ⢸⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠈⣻⠇⠀⠀⠀⠀⠀⠀ ⠘⠿⣆⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣦⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠘⢧⡀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠙⣷⣤⠟⠁⠀⠀⠀⢠⡄⠀⣠⡟ ⠀⠀⠀⠀⠙⢾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⣠⡴⢛⣥⡀⠀⠀⠀⣀⣸⣯⢄⣥⣶ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡿⠖⠛⠉⠀⠀⣀⣤⣀⣙⠙⠉⠉⠉⠉⠉⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠶⠦⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠺⣆⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠷⠖⠚⠛⠋⣩⣽⣿⣿⣷⣦⡀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠒⠦⢤⣍⣅⡂⠀⠠⠀⠈⠩⠿⠶⠶⠆ ⠀⠀⠀⠀⠀⠈⢀⣈⣃⣀⡞⠁⢈⡇⠲⠛⠋⠉⠉⢰⠟⠁⣟⢀⣀⣀⣤⣴⣿⢽⠟⠛⠻⣿⠇⠀⠉⠳⠦⣴⡟⠙⢷⣄⡀⠀⠀⠀⠀⣀⣀⡈⠛⣂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡴⠋⠋⠉⢉⣿⡀⢿⣁⠈⠁⠢⠀⣴⠋⠀⢠⡟⠛⠛⠶⠶⣾⡟⢸⣆⠀⠀⠘⣧⠀⠀⠀⠀⠈⣷⣄⣸⠛⠛⠓⢦⣍⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡰⣿⡵⢛⣦⡄⠈⠉⠁⠀⠙⢷⣄⣠⡼⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠘⣦⡀⣀⡴⠟⠉⠘⠛⠃⣠⡠⣴⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠳⠿⠥⠤⢾⡏⠀⠀⠀⠀⠈⠙⡇⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⢰⡿⢹⣆⠀⠀⣼⠋⠉⠀⠀⠀⠀⣷⣄⣈⣹⣶⡿⠇⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠻⡄⠀⠀⠀⠀⢠⠇⢀⡴⢹⡇⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠹⡄⠀⢿⡀⠀⠀⠀⠀⣠⡟⠌⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠙⢦⣤⣀⣴⠿⠴⠞⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠒⠄⠻⣦⣈⣷⣄⠀⣠⡾⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠛⢿⣿⡿⠿⠀⠀⠀⠀⣀⣠⣭⠁⢄⣀⣀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⢀⠄⠀⠛⠛⠋⢁⡴⠋⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆ ⡀⡠⠒⠀⠒⠒⠤⡴⠤⠒⠊⠉⠉⠀⡀⡌⠉⠉⠑⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⢀⠔⠉⠀⠀⠀⣤⣀⣴⠗⠃⠙⢷⣄⣠⡀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⡇⡸⠀⠀⠀⣀⣤⡶⠶⠶⢶⣤⡀⠀⠀⢀⣴⠶⠾⠶⢶⣄⠀⠈⡄⠀⠀⠀⠀ ⠀⠸⠇⠀⠀⠾⠛⠁⠀⠀⠀⠀⠈⠻⠆⠰⠟⠁⠀⠀⠀⠀⠙⠷⠀⠑⠢⣀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⢀⡄⠒⢲⠒⠦⢀⣒⣲⣶⡶⢒⣲⠒⢢⢄⠀⠀⠀⠈⢣⠀ ⠀⠀⣧⠤⠀⠀⠀⡐⠁⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠱⠀⠀⠀⠀⡇ ⠀⠀⠸⡀⣀⡀⠀⡧⠔⠊⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢤⡇ ⠀⠀⠀⠙⡍⠀⣀⠘⣄⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣀⠀⢰⠁ ⠀⠀⠀⠀⠈⠛⢍⣀⠀⠑⠢⢄⣀⠀⠀⠈⠀⠀⠀⠀⣀⡀⠴⠊⠀⠀⣈⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⣲⣦⣈⠉⠉⠉⡭⠉⠩⠤⢤⣤⠔⠒⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢉⣄⡼⠦⣉⡉⡲⢧⠀⢠⠒⢧⢞⣲⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡋⣤⡦⠊⡹⠀⠀⠀⠉⡇⠈⢧⣼⣎⣹⣽⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠃⠀⠀⠀⡸⠘⡄⠙⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣶⣶⣶⣿⣿⣿⣏⡀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠚⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⢻⡄⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣤⡴⠶⠶⠖⠚⠛⠛⠛⠛⠛⠛⠋⠛⠿⠿⣿⣿⠿⠿⠛⠁⠈⢿⡄⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⢸⠃⠀⠀⠸⢷⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⣼⡇⠀⢀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⣾⠀⠀⠀⠀⠀⠈⠉⠻⣦⣄⡀⠀⠀ ⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⢀⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀ ⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄ ⠀⠀⠀⠈⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣭⡽⠟⠁⠀⠀⣴⠶⠞⠛⠛⠛⢿⣟⣛⣛⣛⣛⣻⣿⠿⠿⣿⣛⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⢰⢏⣸⣧⣤⣀⣀⠀⠉⠉⠉⠙⣿⠉⠉⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠉⠉⠙⠛⠓⠒⠒⠾⠷⠶⠶⠶⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⣠⣾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀ ⣾⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄ ⣿⠀⠀⠀⠀⠀⠠⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠈⣻ ⢻⣆⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⣰⠏ ⠀⠙⣷⣄⣰⣿⠏⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⣠⡾⠋⠀ ⢶⣶⣾⣿⣿⣅⡀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣶⣶⣶ ⠀⠀⠀⠀⢿⡈⠛⠷⣤⣀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣷⠀⠀⠈⠙⠛⠿⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠴⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠶⠶⣶⣤⣤⣤⣤⡿⠁⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠰⣶⡶⠶⣶⡖⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣶⣦⣤⣤⣤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣶⣴⣿⡇⠀⠀⠀⠀⣿⠻⠿⠿⠶⠶⠶⠶⢿⣆⠀⠈⢿⣶⣶⣦⣿⣧⣶⣿⣶⣦⣦⣴⣤⣤⣤⣤⣤⣤⣀⣀⣤⣤ ⠉⠉⠀⠀⠁⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠈⣿⠀⠀⠀⠀⢰⡟⠚⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣀⣀⣀⣀⣤⠾⠋⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⡸⠛⠛⠛⠿⠷⠶⠶⠶⠤⢤⣿⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠒⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡆⠀⢀⣿⠀⠀⠀⠀⢺⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⠿⠿⠿⣿⠀⠀⠀⢘⣿⣿⣿⠷⢶⣶⠶⠶⣤⡀⠀⠀⠀⠀⠈⢿⣿⣿⠿⡿⢿⣿⠿⠛⠿⣿⡿⠶⠶⠶⠒⠖⠲⠾⠿⠿ ⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⣛⣛⣛⣛⣿⠃⠀⠀⠈⢻⡆⠀⠀⠀⠀⠘⣿⡿⢿⠟⣻⠏⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⣦⣤⣿⣿⣿⣟⣛⣷⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠘⣿⣟⣛⣻⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠋⠉⠉⠉⠉⠉⠙⠓⠒⠲⠼⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢀⣤⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣶⣤⣙⠶⣏⠉⠀⠀⠀⠈⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡇⠈⢳⣄⠀⠀⠀⠀⠀⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠞⠋⠉⠉⠙⠒⠒⠦⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⣠⠖⠋⠉⠛⠒⠒⠲⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⣇⣰⠃⠀ ⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⠀⠀⠀⠀⡿⠃⠀⠀ ⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⢤⣤⣤⠴⠊⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡇⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠚⠻⣿⡿⠿⠿⠓⠒⠒⢻⡷⠦⠤⣤⣀⣀⣀⣀⣀⣀⣠⠴⠋⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠿⠶⠒⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠘⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⢸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⡄⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠈⠻⣷⠇⠀⠀⠀⠀⠀ ⠀⣀⣤⠤⢤⣙⢦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠻⣦⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀ ⣼⣿⣇⣀⡀⠈⠳⡝⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢙⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠛⠉⣉⡽⠃⣰⣿⠀⠀⠈⠙⠒⠢⠤⠤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡧⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣤⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣃⣀⣀⣤⣤⣤⣴⠒⠒⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠟⠓⠤⠤⠤⠤⠤⠖⠚⠉⠁⣸⠉⢀⣀⣀⣴⡏⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⠀⠀⠀⠀⢀⣀⠤⠶⡟⠋⠉⠉⠁⠈⢳⡀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⢸⠙⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡏⠀⠈⣳⡀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢠⣧⣴⣿⣿⣷⣦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣀⣀⣀⠈⠀⢀⡀⣀⣀⣀⣀⣈⣁⠀⣀⠀⡇⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠻⢦⡀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣁⣀⣀⣀⣀⡈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⢤⣄⡀⠀⠀⢀⣿⣀⣀⣀⣀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣠⣴⣶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣬⣙⠻⣿⡋⠉⠀⠀⠀⠉⠙⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣷⠀⠙⢦⡀⠀⠀⠀⠀⠘⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢠⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣴⠛⠉⠙⢛⣿⣿⣿⣿⠛⠛⠒⠲⡄⠀⣴⠖⠒⠒⢲⣶⣶⣶⡖⠒⠒⠒⠲⢦⠀⠀⠀⣷⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠃⠀⣿⡀⠀⠀⠘⢿⣿⣿⡿⠀⠀⠀⢀⡇⠀⢷⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠉⠉⠀⠀⠀⣠⠟⠁⠀⠘⣦⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⣴⠏⠀⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⢤⣤⣤⣤⣶⣿⣥⣤⠤⠤⢤⡈⠓⠦⣄⣀⡀⢀⣀⣠⠴⠛⠁⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡋⠁⠉⣻⣛⣉⣥⠤⠖⢯⣧⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣀⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⢀⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⣆⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠘⢿⣤⠟⠁⠀⠀⠀⠀⠀ ⣀⣀⣄⣀⣴⣿⣿⣿⣷⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⣀⣴⣾⣿⣶⡀⠀⠀⠀⠀⠀ ⡌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⣄⣀⣀⣤⠴⠾⠛⠛⠛⠛⠛⠛⣇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⣻⠟⠛⢛⣷⡶⠤⠶⠖⢿⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⡾⠉⣿⠲⠤⠶⠚⡃⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣾⡁⠀⠸⡆⠀⠀⠀⢱⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⣤⣼⣿⡷⢦⡴⠷⣤⣤⣤⣬⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣹⣿⠀⠀⣿⣿⣿⣿⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡏⠻⣦⠀⢿⡏⣿⣿⣿⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣶⠶⠾⠿⠇⠀⠈⠛⠾⠛⠛⠻⠿⠷⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣾⣿⡿⢟⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣤⡤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣶⣤⡀⢠⡇⢰⡏⠀⣠⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡶⠒⠒⠒⠲⣶⣶⣶⣶⣶⣿⠛⠿⣿⣿⣿⣧⢸⣷⣿⣿⡿⠛⠛⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⢶ ⠀⠀⠀⠀⠀⠀⢀⣠⠇⢰⢺⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠉⢻⡏⠈⢻⡟⠁⠀⠀⠀⠹⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣠⠖⠉⠀⠀⢸⡄⢷⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣤⣾⢧⣤⣈⣷⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣠⡟ ⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠻⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠷⣤⡴⠾⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡼ ⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡙⠳⠦⠤⠤⡤⢤⡾⠋⠀⠀⢀⣼⣧⡀⠀⠀⠹⣮⠙⠲⠤⣤⣤⣤⣤⠤⠖⠛⣡⡴⠋⠁ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⣀⡴⢟⠁⠈⠻⣦⡀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⣾⠀⣴⠀⠈⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⢻⡄⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⠀⣿⡀⢿⡇⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣄⠀⠀ ⢹⡘⣷⡿⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⣄⠀⠀⠀⠈⠻⣦⡀ ⢸⡇⠟⣧⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⣠⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢰⠀⠈⢻⣦⡀⠀⠀⠀⣹⣿ ⣿⡀⠀⠈⠳⣄⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠻⣤⣋⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⣥⠟⠀⠀⠀⠹⣷⣤⡴⠟⢉⣿ ⠃⣷⠀⠀⠀⠈⠛⠷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠞⠋⠁⠀⠀⣾⣿ ⣀⣿⣇⣀⣀⣀⣀⠀⢀⣀⣉⡙⠛⠒⠶⠶⠶⠶⠤⠤⢴⣤⠤⢦⡄⠀⠀⠀⣰⠞⠉⠉⠻⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿ ⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⢸⠇⠀⠀⢿⣶⣿⣿⡏⠀⠀⠀⠀⠹⣯⠻⣦⣀⠀⠀⠀⠀⣀⣼⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⡿⠛⠻⡇⠀⠀⠀⠀⢲⢹⣆⣨⣿⣿⠶⣶⠞⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣿⠀⢰⣦⣤⣤⣤⣤⣾⡄⢿⣿⣿⣿⣇⣿⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⠿⡿⠿⠃⠸⡿⠿⠿⠟⠻⠷⠿⠿⠿⣿⣿

⠏⠉⠁⠀⢰⡖⠒⠒⢲⣦⠼⠤⠐⠒⠒⠂⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣷⡶⠋⠁⠀⠀⠀⣀⠤⠔⠒⠉⠉⣀⣀⣈⠑⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⢋⠆⠀⠀⡠⠔⠉⢀⣠⠔⠂⠉⠀⠰⢶⣤⡈⠓⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠁⡎⢀⠔⠋⢀⠔⢊⣉⠀⠀⠀⠀⠀⢀⠠⠤⢅⡀⠈⢂⠀⠀⠀⠀⠸ ⠀⠀⠀⡇⠳⡤⠋⢀⢖⠕⠉⠀⠀⠈⠐⡀⠀⡔⠁⠀⠀⠀⣨⣢⠈⡆⠀⠀⣄⠈ ⠀⠀⠀⡇⡜⢀⠔⠁⠈⠀⠀⠀⠀⢸⣿⣷⠀⡄⠀⠀⠀⠘⢿⢿⠀⠓⠢⡀⠣⠀ ⠀⠀⠀⡇⠑⢼⠀⠀⠘⢄⠀⠀⠀⠀⢉⣏⣀⣐⣤⣀⣀⣀⠤⠊⠀⠀⠀⠈⠆⠀ ⠀⠀⠀⢸⠀⢸⡄⢀⡀⠀⠁⠒⠒⠊⠉⠑⠒⠈⠭⠯⠬⠃⠀⠀⠀⠀⢀⠀⢸⠀ ⠀⠀⠀⠘⡆⢸⠱⡋⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢙⡆⠀ ⠀⠀⠀⠀⣇⡆⠀⠈⢾⣁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠊⠀⠀ ⠀⠀⢠⠊⠀⠈⢣⠀⠘⡄⠉⠐⠒⢀⢤⣄⣀⡀⡤⢄⠀⠒⢒⣂⡭⠂⠁⠀⠀⠀ ⢠⣤⣼⣄⠀⢀⣼⣤⣤⣌⣦⠤⣴⡿⢁⣇⡰⡤⣇⠈⣆⣉⣀⠋⢇⠀⠀⠀⠀⠀ ⢸⣿⣿⡿⠛⠿⠟⠛⢿⠟⠻⣤⣋⣠⢾⡇⣇⣇⣸⣄⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠘⠛⠘⠃⠀⠀⠀⠀⠘⠃⠘⠬⠀⠮⠟⠻⠯⠂⠀⠧⠵⠿⠿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⠛⠛⠋⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠋⠉⠉⣿⣿⣷⣤⣴⣶⣿⣿⣿⡟⠙⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣋⣉⣉⡉⣿⣿⣿ ⣿⣿⣿⣿⣿⠙⢛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⢟⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⣙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⣉⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⡏⢻⣿⣿⢣⣿⣿⣿ ⣿⣿⣿⣿⣿⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠫⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠉⠉⢸⣿⣿⣿ ⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣼⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠓⠒⠒⠦⢤⣄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⣶⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣟⣛⣛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⢿⣿⣯⣍⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣶⣌⠻⣟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠇⠙⢧⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡾⠋⠓⠒⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢉⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⢸⠋⠉⠙⠓⠲⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣰⣿⡿⣿⡿⠿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⢶⣶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⣛⣻⠟⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣶⡄⠀⠀⢸⢃⣼⣿⣿⣷⡶⠶⣶⣾⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠁⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣬⠟⠛⠶⣶⣿⣿⣥⢤⣤⣀⡘⣧⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⣿⣧⡴⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡋⣀⣾⢿⡿⣿⣿⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠶⠒⠒⠶⠶⢿⣹⡏⠛⢦⣀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⢁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠸⠇⢻⣿⣇⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠈⠉⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡇⣼⠛⠾⣿⣿⣧⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿ ⣿⣿⣿⣿⣿⣿⣿⣿⣜⡃⠀⢻⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠻⣦⣰⠟⠁⠉⠙⣛⠿⠿⠿⠋⠉⠉⠉⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠈⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠘⣷⡀⠀⣠⣾⣯⣤⣤⣤⣤⣿⡀⢠⣶⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣧⣤⣀⠀⠈⠉⠙⠲⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣸⣷⡾⡿⠿⠿⠿⠿⠿⠛⠿⠇⠘⠻⠛⠛⠛⠛⠛⠛⠛ ⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠷⢦⣄⣀⠀⠀⣷⣴⠶⢶⠶⣶⣶⣶⣶⣤⣤⣤⣴⣶⣾⣿⡾⠿⣿⣷⣾⣶⣿⠶⠶⠶⠶⠶⠶⠷⠤⠤⠶⠒⠆⠤⠤⠤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢿⣄⣠⡤⠶⢿⡀⠀⠉⠛⠓⠦⢤⣀⣀⠀⠀⠀⢠⡟⡟⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠈⠉⢶⠦⢤⣄⣀⠀⠘⣿⣿⣶⣦⢼⣅⣃⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⣧⠀⠀⠉⠙⠓⠺⠿⣿⣿⣆⣠⡿⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⠀⠀⠀⢀⣀⣀⣭⣷⣄⣠⡤⠴⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠤⣶⣻⣿⣿⣋⣁⣠⣾⣿⣤⣄⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢿⣿⣶⡶⠟⠛⠛⠉⠛⢿⣏⠉⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡗⠒⠻⣇⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡶⠛⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢶⠤⠼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⡛⢉⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣥⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣁⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⢀⣠⠴⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣯⡝⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣦⡄⠀⠀⠀⠀⣀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠻⣷⡀⢀⣼⢿⡞⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⠟⠛⡟⠀⠀⠀⣀⡤⠿⣿⣷⣦⣴⣾⣿⠇⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠐⠒⠶⣄⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣐⣋⠀⣸⠁⠀⢠⠞⠁⠀⠀⠈⠉⠉⢉⣽⣿⣷⡄⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡿⢀⡇⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢿⡄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠉⣇⠀⠀⠀⠀⠘⡇⠀⠀⠐ ⠿⢿⣿⣿⣿⡿⠃⣸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⢿⣿⣯⡿⠛⠉⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⢈⣽⠋⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣄⣀⣤⣤⣶⣟⣒⡶⠒⠒⠒⢶⠈⠳⣄⣀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⣤⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⣀⣹⣩⡤⠤⠔⠒⠉⠻⣧⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢰⣄⡀⠀⣾⠀⠀⠀⢀ ⣿⠛⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣶⡟⠄⠀⠀⠨ ⠿⠈⢿⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⣰⢻⡇⠀⠀⠀⠀ ⠀⠀⠸⣯⡀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠹⣧⡼⠁⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⡤⠞⠉⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠛⠉⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣨⣇⠀⢀⡀⡉⠉⠛⣶⣶⣶⠶⣤⣤⠤⠤⣦⠀⠀⠀⠀⣀⣠⠞⠋⠙⠿⣏⠉⠓⢦⣀⡀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⣧⡴⠖⠛⢋⣉⣼⡄⠀⠀⠀⠈⠳⣄⠀⠈⠙⢳⣶⣶⣶⣾⣿⣿⣿⣿⠀⢀⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠑⢦⡀⠀⡷⠔⠒⠉⠉⠀⠀⢱⣄⠀⢀⣠⠞⢻⣷⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠋⠀⠈⣳⣄⣹⢿⠇⠀⠀⠀⠀⠀⠀⠀⡟⢶⣋⣠⡞⠉⠘⢿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠻⣅⣈⣡⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣛⠁⣹⠇⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⣬⡙⢦⣄⡀⠀⠉⣀⣼⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⠋⠁⠀⣀⣴⠊⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢒⡠⠄⠒⠂⠉⠉⠉⠉⠁⠐⣒⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡀⠀⠀⢀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠂⠑⠢⡀⠀⠀⠀⠀ ⠀⠀⠙⠧⣠⣯⠃⠀⢀⣤⣄⣀⣠⡄⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠘⢆⠀⠀⠀ ⣀⣀⣀⣘⠁⠆⢀⠔⠁⠈⠙⠛⣿⣧⡀⠀⢠⠊⠁⠀⠀⢰⣿⣦⠀⠀⠈⢆⠀⠀ ⢿⣿⣿⡿⢸⠀⠈⠀⠀⠀⠀⠀⠛⠛⠁⠀⠇⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⢸⠀⠀ ⠀⠸⡿⠋⠁⠀⠰⡀⠀⠀⠀⠀⠀⢀⠇⠀⢇⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢸⠀⠀ ⠀⠸⠁⠀⠀⠀⠀⠈⠢⠤⡠⠤⣶⠳⠖⢒⣢⠓⠄⣀⣀⡠⠔⠁⠀⠀⠀⠸⠀⠀ ⡶⡇⠀⢀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠈⠉⠀⠈⠃⠀⠀⠀⠀⠀⡀⠀⠳⢤⠇⠀⠐ ⠃⢳⡞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣆⢠⠊⡇⠀⠀ ⠀⠀⠱⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡠⠚⠁⠀⡇⠀⠀ ⠀⠀⠀⣹⠉⡒⠂⢤⡤⠤⢄⡀⢠⠀⠀⠀⣀⠄⠤⣖⠲⣍⠁⠀⠀⠀⡸⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⠀⢸⣒⠨⠍⠚⡀⠀⢈⣦⡄⣉⣷⣶⣿⣿⣿⣄⣼ ⠉⠉⠉⠉⠉⠙⠛⢛⠟⢉⡢⣵⠾⠀⠀⠀⠀⠙⢖⡩⡊⠙⢟⠛⠛⠛⠉⠉⠉⠉ ⠀⠀⠀⠀⢀⢀⣀⣘⢄⡈⠑⢂⡅⠀⠀⠀⠀⠖⠐⠒⠊⣀⠜⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡄⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣠⡴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⡛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣬⡛⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⡿⠟⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠠⣴⣧⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⣼⡿⣱⡟⠀⠀⠀⠀⠀⠀⣰⣤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠻⢳⡟⠀⠀⠀⠀⢀⣠⡼⢿⣿⣿⣦⣤⣴⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠛⠛⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⡾⠀⠀⠀⢀⡴⠛⠁⠀⠀⠙⠛⠿⠿⠿⢛⣿⣻⣦⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⡤⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣶⣶⣶⣾⣶⠆⣸⡇⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⡇⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈ ⢿⣿⢿⣿⣿⣿⣿⣿⠇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠ ⠀⠀⠘⣿⣿⣿⣛⣶⡾⠛⠋⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⢤⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣄⣀⣀⣀⣤⣴⡶⠿⠗⣒⣾⠗⠛⠓⠒⢶⡆⠙⠷⣤⣀⠀⠀⠀⠀⠀⢀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠉⢻⡟⠋⢉⣀⣀⡤⠴⠚⢦⣿⡄⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠒⠒⠒⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⣸⣧⠀⠀⠀⠀⢲ ⣿⡇⣸⡇⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠉⢻⣿⠀⠃⠀⠀⠐⠐ ⠿⠀⠹⣿⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⣰⠏⣿⠀⠀⠀⠀⠃⠀ ⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠈⠻⣧⣀⡾⠋⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⣧⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⣀⡼⠛⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⡴⠞⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⡀⠀⠀⢿⡝⠓⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⠁⠀⠀⢹⡇⠀⠀⠀⠉⠙⠛⠲⠶⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢿⣿⠛⠉⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀ ⣤⣤⣴⣶⣿⣶⣶⣿⣿⣶⣶⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣦⣶⠿⠁⠀⠀⢸⠀⠀⣀⣠⣴⠶⠞⢻⡏⠀⠀⠀⠀⠙⢿⣦⠀⠀⠉⠻⢶⣤⣄⣀⡀⣀⣀⣴⣿⣧⣶⣶⣦⠀⡀⠀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣅⠀⠀⠀⠀⢸⠟⠛⠉⣀⣠⡤⠶⠞⢻⡀⠀⠀⠀⠀⠀⢙⣷⣤⡀⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣀⣴⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠳⣄⡀⠀⣸⠶⠚⠋⠉⠀⠀⠀⠀⠀⢷⣄⠀⠀⣠⣴⠟⢁⣿⣿⣀⡶⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⢻⡿⠋⠀⠙⢷⣄⠈⢻⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⡞⠉⢀⣴⠛⠉⠹⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠈⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣶⠏⠙⠻⠟⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢿⡾⠋⠳⣦⠀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠙⠳⣦⡴⠞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠒⠶⣤⣠⡶⠛⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⢀⠀⣀⠀⠀⠀⠀⠀⣆⣀⣠⣤⣀⣴⣤⣉⠳⣦⣆⡀⠀⠀⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠈⢁⡀⠀⢀⣤⣾⡋⡠⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⢀⡀⠀⡀⠀

⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⠇⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦⣤⣤⣾⣿⣿⡀⠀⠀⢀⣠⡤⠤⠤⠤⠶⠶⠶⠒⠒⠒⠒⠒⠒⠀⠙⢲⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⠀⢠⡴⠖⠒⠒⠒⠒⠈⠉⠉⠉⠛⠿⠿⠿⠟⠋⠉⢻⡄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣄⠀⢸⠃⠀⠘⠷⣤⣀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡀⣸⠃⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⡞⠀⠀⠀⠀⠀⠈⠳⢦⡄⠀ ⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠏⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄ ⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⢀⣀⣀⣉⣳⣤⣄⣀⣀⣀⣀⣀⣤⠽⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⣀⣠⣤⠴⠚⠋⠀⠀⡼⢫⡉⠉⠉⠻⠯⠭⣭⡭⠿⠛⠛⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠋⠙⠓⠒⠶⠤⠤⢬⣧⣤⣤⣤⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡀⠀ ⡿⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶ ⣧⡀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠀⠀⢀⡾ ⠈⠳⣄⣠⡿⠃⠀⠀⠀⠀⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⣠⠞⠀ ⠓⠿⠻⣿⢦⣀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠿⠿⠾⠶ ⠀⠀⠀⢹⡄⠉⠛⠶⢾⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠦⢤⣤⣤⣤⡟⠁⠀⠹⣆⠀⠀⠀⠀⠀⣶⠶⣶⡖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠶⠶⠶⠶⠾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠷⠶⣿⠃⠀⠀⢠⡟⠛⠛⠛⠛⠓⢻⡄⠀⢻⡶⠶⠿⠶⠾⠶⠶⠶⠶⠶⠶⠶⠶⠤⠴⠦ ⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⣿⠀⠀⠀⢸⠧⣤⣤⣄⣀⣀⣀⣻⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣤⣀⣀⣀⣆⣀⣼⠁⠀⠀⣸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣀⣀⣀⣀⣀⣂⣀⣀⣀⠀⠀⠀⠀⣀⣀ ⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠋⠉⠉⢻⡀⠀⢠⣿⣿⣿⣿⡟⠉⠙⢦⡀⠀⠀⠀⢻⣿⣿⣿⣿⠋⠉⠙⢿⠉⠉⠉⠉⠉⠉⠉ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣸⣿⣿⣿⣿⡀⠀⠀⠈⡇⠀⠀⠀⠀⢿⣿⣾⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢿⡀⠀⠘⣿⣿⠃⠀⢨⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⡇⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠦⣰⡟⢿⣆⠀⢸⣿⣟⢿⣿⣿⣿⡇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⣿⡇⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⠀⠘⠻⣦⣀⡹⣷⣼⣿⣿⣿⣁⣀⣀⣬⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⡛⠛⠛⠛⠿⠀⠀⠀⠈⠙⠛⠋⠉⠉⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡷⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣶⣿⣿⣿⠿⣻⣿⣿⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣴⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣷⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⣶⠀⢀⣾⠀⠀⠀⠀⣠⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣄⡀⢰⡟⠀⢸⡇⠀⣠⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⣴⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣾⡿⠻⢿⣿⣿⣿⣾⣷⠀⢸⣶⣾⣿⣿⡿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠻⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡇⡏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⠿⣿⣿⠃⢸⣿⡿⠛⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠀⣿⠀⣿⡀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢹⣧⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠷⣶⣄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⡄⠀⠀⠀ ⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣶⣶⡶⠿⠛⢷⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⢁⣾⠃⠀⠀⠀ ⠀⠀⢠⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠛⠶⣤⣄⣀⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠹⣧⡙⠻⢦⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠋⣠⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠈⠉⠉⠉⠉⠉⣿⠁⠀⠀⠀⣠⡾⠋⠙⢿⣄⠀⠀⠀⠈⣿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠰⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣴⠾⠋⣆⠀⠀⠀⠙⢷⣤⣀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢰⣏⠀⢸⡇⠀⠀⠀⠁⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠸⣧⠀⠀⢀⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⢰⡟⠀⢿⡿⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⢻⡆⣿⣄⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⡟⠀⠀⠀⠀⠀⠘⠛⠃⠸⣿⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠝⣿⣧⡀⠀⠀⠀⠀⠀ ⢸⣧⠸⣿⠛⠁⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣀⠀⠀⣾⣧⡀⠀⠀⠀⠀⠈⠻⣿⣤⡄⠀⠀⠀ ⢸⣿⠰⠘⣷⡄⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣴⡄⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢻⡇⠀⠈⠿⣷⣄⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀ ⣾⢃⠘⠀⠈⠻⣦⡀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣚⣁⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⣈⣥⡿⠁⠀⠀⠀⠹⣿⣦⣠⣴⠿⠋⢰⣿⠇⠀⠀⠀ ⠏⣸⡀⠀⠀⠀⠈⠛⢿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⣀⣤⣴⠾⠟⠉⠁⠀⣠⣿⣿⡇⠀⠀⠀ ⠀⣿⣧⡄⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⣦⣠⣠⣤⣶⡶⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⢠⣽⣿⣿⡇⠀⠀⠀ ⣤⣿⣿⣧⣤⣤⣤⣤⣤⣀⣀⣠⣤⣄⣤⣀⣈⣉⣛⣛⣛⣛⡛⠛⠛⠛⠻⣿⠟⠛⠻⣷⠀⠀⠀⣀⣰⡿⠉⠀⠀⠈⠻⣿⡻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠘⣷⡝⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢿⡿⠿⠿⣿⠀⠀⠀⠀⠀⠀⢦⠹⣷⡀⠈⣿⣿⣶⣦⣤⣴⠾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡇⠀⠀⣏⠀⠀⠀⠀⠀⠀⢸⡄⢻⣷⣾⣿⣿⣷⢀⣸⡆⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣾⣷⠀⠀⣿⣿⣷⣶⣶⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣰⣿⡇⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⠀⠀⢿⡿⠿⠿⠿⢿⡿⠛⠋⠀⢹⡟⠛⠛⠛⠛⠛⠛⠚⠛⠛⠻⢿⣿⣿⡇⠀⠀⠀

⣿⠟⠋⠋⠉⠁⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⡟⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⢸⣿⣤⡶⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⣶⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣠⣦⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠋⠉⠉⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠁⠀⠀⠀⠀⣀⣀⡤⠤⠖⠚⠛⢛⠛⠛⠛⠛⠓⠶⢼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⢀⡾⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⢸⣿⣶⣶⣦⣄⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⢠⡟⠁⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⣠⣴⣾⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⣿⡷⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢠⡿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⣸⢇⡄⢸⡇⠀⢀⣴⠟⠁⠀⠀⢀⡴⠞⢁⣠⡤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠉⠉⠉⠛⠲⢤⡀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉ ⠀⠀⠀⠀⠀⠀⠀⣿⠈⣷⣺⡄⣠⡟⠁⠀⠀⢠⡴⠋⣠⠞⠋⠁⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡐⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⢿⣷⠋⠀⠀⢀⣴⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣷⠀⠀⢹⡄⠀⠀⠀⠀⢠⠟⣴⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡿⠁⠀⠀⣰⠟⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣧⣀⠀⠀⠀⠘⣤⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⢀⡾⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⣿⠀⠀⠀⠀⠉⠻⢦⡀⠀⠙⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⢷⡀⠠⡟⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣹⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⠃ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠒⣿⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⣠⡴⠚⢷⣞⠋⠉⠉⠙⠿⢿⣭⣽⡿⠛⠺⢿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠈⠉⠙⠒⠶⠶⠦⠬⣷⣤⣄⣤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⣿⢻⡀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⢰⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⡯⠀⢿⡟⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢸⡿⠀⠊⢿⣄⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⢀⣼⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣸⡇⠀⠀⠀⠙⢷⣼⠟⠁⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣿⡀⠀⠀⠀⠀⠈⣿⠳⢶⣄⡀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠈⠙⢷⣀⠀⠀⠀⠸⣆⠀⠈⠙⠛⠦⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠞⠛⣉⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠉⢉⣿⢟⣿⣿⢀⣀⣀⣤⠤⣴⠶⠿⣯⠉⠉⠉⠉⠁⠀⣀⣀⣤⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⣴⣞⣵⠟⢡⡟⠉⠉⢀⠀⠀⣿⠀⠀⢹⣧⠤⠤⠖⠒⠋⠉⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣶⣶⣶⣶⣿⣄⠀⠀⠀⠀⢀⣰⣿⣶⣶⣤⣤⣤⣄⣬⣿⣶⢦⡴⢶⣟⣵⡿⠁⠀⣾⣧⣀⣰⠿⣤⣤⢿⡇⠀⠀⢿⣆⣀⢀⣀⣀⣤⠉⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⡿⠋⠀⠀⣰⣿⡏⢹⡇⠀⣿⠀⠈⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡿⣿⣿⣿⠿⠟⢻⣿⣿⣿⡿⠟⠛⢛⣿⣿⠛⢿⠏⣿⢠⣾⡋⠀⠀⣠⣾⠿⣿⠀⢸⡇⠀⡟⠀⢀⣿⣇⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⡇⣿⣿⡿⠀⠀⠀⠉⠉⠉⠠⠆⠀⠀⣿⣿⠀⠀⠀⣼⠟⣿⠟⠛⠛⢻⣷⡄⣿⢀⣾⣶⣶⠛⠛⠛⠻⣍⠛⢶⡌⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠛⠛⠃⠛⠛⠃⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠾⠿⠷⠐⠲⢿⣸⡃⠀⠀⢷⡈⢻⣿⡿⢾⣽⠋⢹⠖⠀⠀⠀⣹⠂⢀⣿⣿⣿⣿⣿⣿⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠁⠀⠀⠉⠉⠉⠈⠀⠀⢹⠀⠀⠀⠀⠈⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⠶⠿⢶⣦⣀⠘⠋⠘⠓⠚⠛⠒⠛⠛⠛⠃⠐⠓⠀⢻⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⠈⠻⣦⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠿⠷⣤⣤⣀⠀⠀⠀⠀⠄⠸⠇⠀⢀⣀⡀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣀⣤⣤⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⠻⢶⣦⣶⠿⠛⠛⠛⠛⠛⠛⠛⢶⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⢰⣿⣿⡿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⡈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⢀⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⣾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣰⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣼⠋⠉⠉⠉⠉⣽⣿⣿⣿⣿⣏⠉⠉⠉⠛⠳⡆⠀⢠⡾⠛⠛⠛⠛⣻⣿⣿⣿⣾⡒⠒⠒⠒⠒⠒⢶⣆⠀⠀⠀⢸⣷⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠀⠀⢿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⡇⠀⢸⡇⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠛⣷⡀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢠⡾⠁⠀⠈⢷⡀⠀⠀⠀⠙⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠤⣤⣤⣴⣶⠿⠯⣶⣶⡶⠶⠶⠶⣦⠀⠉⠻⢦⣤⣀⣀⣀⣀⣀⣤⡴⢟⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⠁⠈⠛⣿⠛⢋⣉⣀⣤⠶⢾⣜⣇⠀⠀⠀⠀⠀⠉⠉⠉⠁⠂⠀⠀⠀⠀⢀⡀⠀⠀⢀⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⣸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣠⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠙⢻⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠘⢿⣦⣼⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣷⣄⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⣠⣶⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀ ⠷⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠙⢿⣤⣤⣴⡶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢙⣿⠏⠉⠉⢹⣿⡷⠶⠶⠶⠞⠻⣧⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⢠⡿⠉⢿⣶⣤⣤⣤⣶⠿⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣾⠃⠀⠸⣷⠀⠀⠀⠀⠀⣇⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢀⣾⣷⠀⠀⠀⣿⡀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢤⣤⣾⣿⣿⠶⢶⡶⠿⢳⣶⣶⣦⣤⣬⣧⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠾⠿⠖⠒⠒⠒⠒⠒⠶⠶⠤⢤⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠉⠉⠛⠶⠶⣄⣀⣠⣴⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠛⠁⠀⢀⣠⣴⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣦⣤⣀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⣿⣿⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⡇⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣆⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣴⡇⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⢻⠀⢠⡏⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⡏⠉⠉⠉⠉⠙⣆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠠⠄⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⢠⡇⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⣿⣿⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⠏⠀⢻⡆⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣁⣀⣀⣀⣀⣈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⠶⠒⠚⠉⢸⡿⣭⣉⠉⠉⠙⠿⢭⣭⣛⣳⡶⠦⣤⣤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⡏⠉⠉⠓⠲⠦⣤⣤⣻⣀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠤⣀⠀⠀⠘⣷⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣆⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠛⠳⠦⣄⡀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠹⣦⠀⢀⣾⠟⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⠁⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠹⣄⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠈⣿⠁⠀ ⡀⣾⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⣻⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⡾⠃⠀⠀ ⠛⠿⢿⣿⣷⣖⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠛⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠛⠛⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢟⠛⠳⠦⢤⣤⡾⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⣿⣷⣾⣶⣶⣶⣶⣾⣾⣾⣶⣶⣶⠟⠁⠀⠀⣾⣿⡖⠲⠶⢶⣴⠤⢤⣼⣿⣿⣿⠛⢻⡟⠛⠛⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠉⠉⠉⠉⠀⠀⠉⠀⠩⢭⣿⠟⠁⠀⠀⣀⣼⣿⠉⢻⣄⣠⣾⣿⣤⣾⣿⢠⡿⠛⠓⠚⠷⣦⣤⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⣠⡾⠟⢹⣿⡄⣸⡏⣸⢿⡏⣿⣿⢣⡟⠀⢀⡴⠖⡿⠋⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣠⡾⠋⠀⢀⣿⠙⣿⣿⣸⠋⣸⣷⣿⡿⣿⣷⣤⡞⠁⠀⢷⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⣠⡾⠋⠀⠀⠀⣸⡏⣴⣿⣿⠇⢀⣿⣿⣿⣷⠀⣿⣿⡏⠛⠓⠚⠳⠦⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⢀⣴⠻⣿⠆⠀⠀⣤⡾⠋⠀⠀⠀⠀⢀⣿⣳⣿⣿⣿⣀⣿⣿⣿⠇⣿⢠⡿⠻⣿⣷⠦⠶⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⡴⠛⢷⡀⢘⣷⣶⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢹⡞⠃⠀⠈⠙⢳⡖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣟⣫⡷⠆⠀⠀⠀⢿⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣀⣰⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠿⠿⣤⣤⡤⠴⢦⣄⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣜⡀⠀⠀⠘⠁⠈⠳⡄⠀⠀⠀⠀⢸⠃⠀⠀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⢿⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠥⠤⠤⠤⠤⠤⠤⣄⣱⣄⠀⠈⠀⠀⢳⡀⠀⠸⠁⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠒⠦⢼⣃⠴⠲⠊⢛⣂⣀⣤⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⣴⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣦⡀⠀⠀⠉⠓⢾⡉⠉⠀⠀⠀⠀⠉⢳⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢸ ⠀⠀⢀⡄⢰⡀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡾ ⠀⢀⡾⠁⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠴⠻⣿⣿⠶⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣸⠃ ⠀⡼⠁⠀⠀⣻⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣿⠿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⠃⠀ ⠀⡇⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⠘⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠉⠉⠛⠓⠨⠿⠷⠿⠭⠭⠶⠶⠤⠤⠤⠤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠠ ⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶ ⢸⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⡞⠀⠀⠀⠀ ⢸⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠙⡿⠀⠀⠀⠀⠀ ⠈⠻⣄⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠹⣦⡀⢀⠞⠁⠀⠀⠀⠀⣠ ⠀⠀⠈⠢⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⣨⢿⡋⠀⠀⠀⢸⡇⢐⣧ ⠀⠀⠀⠀⠈⠑⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠷⠖⠋⠁⠈⣁⣀⡒⠛⠛⠉⠙⠛ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠲⠦⣤⣀⣀⣀⣀⢠⣤⣤⡤⠤⠴⠒⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀ ⠀⠀⠀⠐⠂⠙⠦⢀⠔⠓⡄⡠⠤⠄⠀⣠⠞⡟⠉⠀⠀⣰⣿⡿⠿⣿⡆⠐⠤⣀⣀⡴⢤⠀⠀⠀⠀⠉⠘⠒⠤⠀⠀⠀⠉⠉⠁ ⠀⠀⠀⢀⡴⠛⠉⢙⣇⢰⡃⠐⠠⠀⡴⠃⢠⡷⠾⠯⠭⣽⢻⣇⠀⠈⢧⠀⠀⠀⠙⣦⣸⠟⠲⠦⣐⠒⠈⠁⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠤⢿⣟⡽⠆⢀⡀⠀⠉⠲⢤⡞⠁⠀⣸⠃⠀⠀⠀⠀⠘⣿⡄⠀⠈⢧⣤⠴⠋⠈⢉⠁⢤⣰⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠹⡄⠀⠀⠀⠀⡇⠀⣼⡏⠀⠀⠀⠀⠀⢀⡏⠸⡄⠀⣾⠀⠀⠀⠀⣸⡷⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⣼⡥⠞⢡⠇⠀⠀⠀⠀⠀⢸⠃⠠⠙⣤⣸⣄⠀⣠⡾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠠⠤⠤⠤⠤⠤⠼⠀⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣋⣀⣀⣈⣫⣀⠀⠀⠀⠀⢀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣥⣤⠀⠀⠀⠀⠀⠈⢉⣑⡢⣤⠞⠒⠒⠢⡄ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠆⠑⢄⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡸ ⠀⠀⠀⠀⠀⠀⢸⠀⡤⠤⢤⣤⣤⠤⠤⢄⠀⡠⠤⢤⣀⣀⠀⠀⢀⠀⠈⣦⠃ ⠀⠀⠀⠀⢀⠴⠊⠀⢇⠀⠘⠿⠿⠁⠀⡸⠀⡆⠀⠸⣿⠟⠀⠀⢠⠃⠀⡇⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠤⢀⣠⣤⣮⡤⠤⡌⠢⣀⣀⣀⣀⠔⠃⠀⠀⡇⠀ ⠀⠀⠀⣾⠀⢀⠀⠀⠀⠀⠀⠣⠤⠝⠑⠒⠉⠺⠀⠀⠀⠀⠀⠀⠰⢤⣰⠀⠀ ⠀⠀⠀⣸⡴⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⣠⠃⠀⠀ ⡀⣀⣠⣽⣷⣄⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⣽⣥⠀⠀⠀ ⡆⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⢤⡤⢤⣀⣀⣠⡖⠐⡤⠒⠊⠉⠉⠉⠙⡆⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡜⢹⠂⠐⢃⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣀⣼⡦⣬⢇⣀⣘⡄⠘⡄⠀⠀⠀⠀⠀⢻⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣒⠉⠀⠐⠒⠒⠵⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠾⠛⠛⠁⠀⠀⠀⠀⠀⠀⣤⣭⡢⢤⠒⠒⠒⠢⡀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠑⡄⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⡘⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡘ ⠀⠀⠀⠀⡠⠔⠃⣧⣄⠀⠀⠉⠉⠐⠢⡀⢀⠄⠠⠤⠤⠀⢀⣀⠀⠀⠀⢸⠰⠁ ⠀⠀⢀⠎⠀⠀⠀⠙⠥⢀⣀⠀⠀⠀⡠⠃⣷⡶⠀⠀⠀⠀⠀⠀⠙⡄⠀⢸⠁⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⣤⠒⢺⠿⠶⠒⣚⡶⠤⠤⠄⠀⠀⠠⠔⠁⠀⡸⠀⠀ ⠀⠀⢧⠔⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⠃⠀⠀ ⠀⠀⠘⢄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡄⠀⢙⠎⠀⠀⠀ ⣼⣏⣈⠑⡗⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣸⠖⠁⠀⠀⠀⠀ ⠀⢰⣎⣴⣷⡀⠀⠀⠉⠁⠒⣒⣀⣀⣀⣀⡤⠤⠤⠄⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢟⠉⠒⠒⠒⠈⢉⣸⠥⠤⠴⡁⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⡄⠀⠀⠀⡜⢆⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⣃⣴⣧⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠡⡀⠈⠈⢱⡀⠀⢠⠃⠀⠈⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⠁⠀⠀⠤⠼⠄⣐⠀⢣⠀⠈⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠒⢁⣴⡶⠖⠀⠀⠀⠀⠀⣶⣤⡈⠙⠪⣌⠒⠒⠚⠢⣄ ⠀⠀⠀⠀⢀⠜⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠑⡀⠀⠀⢸ ⠀⣠⠠⠀⡌⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡸ ⢰⠃⠠⣆⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠴⣶⠦⠀⠀⠀⠀⠀⠀⠸⢠⠁ ⡄⡠⠊⠁⠀⠀⠀⡠⠤⠤⢤⣤⣄⡤⠄⣀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢸⠀⠀ ⡇⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⡄⠀⠈ ⢷⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⡝⠀⠀⠀ ⠀⠑⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠽⡊⠀⣀⣆⣪ ⠀⠀⠀⠈⠑⠒⠀⠤⠤⠤⡀⢀⣀⣀⣀⠀⠠⠤⠄⠒⠉⠁⠀⠐⠒⢄⡀⠀ ⠀⠀⢀⠵⢔⢱⠐⠒⢂⠊⣇⣤⣴⣿⠛⠇⠐⠢⡔⢢⣀⡀⠉⠐⠂⠀⠉⠉ ⠀⠔⣷⣆⡨⠈⠂⢤⠃⣰⠃⠀⠈⢸⢆⠈⡦⠔⠊⣓⠠⣾⠄⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢄⣀⣜⠐⡹⠀⠀⠀⠸⠈⢆⢇⠀⡠⠛⠉⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⣉⠙⢉⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠋⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠛⢿⣿⣿⣿⣿⠿⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⣿⣿⣿⡆⠈⠑⣂⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⣿⣿⣿⠿⠟⠁⠰⣢⣼⠟⠋⠁⠀⡈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠘⠀⠈⠁⠉⠂⠀⠀⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⣚⠁⠀⠀⠀⢀⡀⠀⠀⢀⣠⣤⣤⡶⠿⠗⠒⠒⠒⠓⠒⠒⠒⠒⠲⠶⠦⣽⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⣡⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢻⡀⢸⡇⣼⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣤⣾⣿⠟⠉⠁⠀⠁⠹⣿⣷⣤⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⡇⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⢠⡟⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣼⠃⠀⠀⠀⠀⠀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠘⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⢶⣶⣶⡶⠶⠶⠶⠶⢶⣶⣶⡶⢶⡶⠶⣶⡶⠶⠦⠤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣏⠁⠀⠀⠀⣾⠀⠈⠙⠛⠳⠦⠤⣤⣄⣉⣉⣉⣻⣏⣉⣀⣀⣠⢴⡏⠀⠀⢈⡿⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠙⢧⣀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠻⢦⣴⠞⠃⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⣷⡶⠶⠿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀ ⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⣠⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣤⡀⠀⠀⠀⢸⡴⠞⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠛⢷⣦⣾⠀ ⠀⠀⠀⠀⠀⠀⠈⣷⣾⠿⠛⠁⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣠⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⣀⠀⠀⠀⢠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣤⣾⠟⠃⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⣷⣤⣠⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⣄⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⣨⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⡀⠀⠀⠈⠉⠛⠲⠶⠶⢤⣤⣄⣀⣾⣀⣀⣀⣠⣤⣤⠴⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⢶⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⠴⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠙⣿⡟⠶⣶⣤⣄⣀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⢉⣼⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⢀⡆⢀⣾⣧⣄⡀⠀⠉⠉⠛⢷⡿⣷⡀⠀⠀⠀⢀⣴⠶⢿⣅⢠⣾⡷⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⢀⡤⢒⣿⢾⡏⠀⠀⠉⠛⠿⢦⣤⣀⣾⠃⠈⣷⡀⠀⠀⢸⡇⣀⣀⣹⣟⣡⣴⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⣀⡤⢂⣥⡾⠋⠁⡟⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⠀⠀⠘⣿⡀⢀⣴⣯⡀⠙⣿⠋⣙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢰⣯⣷⣿⡁⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⢸⣿⣿⣿⣿⣷⣠⣽⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣆⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⢷⠀⠘⠋⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣾⣿⡟⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⣧⡀⠀⢈⣿⠟⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⡯⣭⣿⣿⣿⣿⣯⣩⣿⣷⣾⣿⡯⣭⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⡯⣿⢽⣿ ⣿⣿⣧⣬⣿⣿⣿⣿⣧⣬⣿⣿⣿⣿⣯⣬⡿⠿⣿⣿⣧⣤⣽⣿⣿⣿⣧⣤⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣛⡛⠒⠠⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠉⠁⠀⠀⠀⠀⣭⣻⣯⠿⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢢⠀⠀⢻⣿⣿⣿ ⣿⣿⣿⠿⣿⣿⠟⠁⠀⠸⡀⠀⠀⢰⣿⡖⠠⠀⠤⠀⣀⠀⠀⠀⡆⢠⡿⠿⢿⣿ ⣿⣿⡿⢽⣿⡏⣀⠀⠀⠀⠈⢶⠠⡴⠯⠄⣰⡀⠀⠀⠰⣿⡗⠀⣷⣿⡿⠽⣿⣿ ⣿⣿⣷⡟⣛⣯⠁⣠⠄⠀⠀⠀⠀⠀⠀⠉⠋⠈⠐⠒⠒⠉⠀⢠⣿⣿⣷⣶⣿⣿ ⣿⣿⣿⣿⣆⣿⣿⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣆⠈⣢⠋⢙⡟⣛⣉⣉⣀ ⣿⢿⣿⣿⣿⣿⣿⣷⣤⣌⡁⠒⣄⣀⢀⣀⣀⣀⣸⣤⣼⣞⣟⡛⠋⣇⣉⣉⣉⡉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⠒⠑⢤⢉⡐⢢⣤⣸⡻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⢆⡀⠉⠙⠓⠋⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣮⣶⡶⣨⡿⢭⠥⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⣫⠀⠀⠀⠑⠶⣋⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⢒⠀⠀⠀⠀⠀⠈⢹⣛⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣀⡀⠴⠥⠤⠤⠄⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⠈⡩⠖⢈⣡⣤⡦⠀⠀⠀⠀⠀⢤⣤⣍⡐⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⡠⠊⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠀⠀⠀ ⠀⠀⠘⡄⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠱⠃⠀⠠⠒⠒⠒⣶⣶⠀⠀⠠⡀⡤⠀⠀⣤⣤⡤⠤⠤⡀⠃⠀⠀⠀ ⠀⠀⠀⣴⠀⠀⠘⢄⠀⠀⠉⠁⠀⠀⡰⠁⢣⠀⠀⠈⠉⠀⠀⢠⠁⠘⠢⡀⠀ ⠀⠀⠈⠀⡇⠀⠀⠀⠑⠂⠤⠤⠄⢺⢗⣒⠲⠷⡢⠤⢤⠤⠒⠁⠀⠀⠀⠈⡄ ⠀⠀⠠⠀⠰⠖⠁⠀⠀⠀⠀⠀⠀⢸⢁⣀⠈⠉⠁⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠂⠱⣠⠊⠀⢀⠄⠀⠀⠀⢆⠀⠉⢢⠀⡰⠀⠀⠀⠀⣀⠀⠙⢢⠆ ⢼⣦⡀⠀⠀⠀⠈⠒⠴⣋⠀⠀⠀⠀⠈⠒⠤⠤⠓⠁⠀⠀⠀⠀⠈⢦⡠⠊⠀ ⠀⠀⠈⠉⢰⣤⣤⣤⣤⣤⣭⣥⠖⠉⣦⠤⢄⢀⣤⣤⢤⠤⠀⡖⠂⠉⠀⠀⠀ ⠀⠀⠀⠀⣘⠁⠀⠀⠀⡠⠟⠁⡠⢺⣇⣗⢿⣾⣷⢉⠭⠋⠐⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠁⠀⢀⣠⠊⢀⡤⠊⠀⣮⣽⠏⣾⣿⢹⣗⡒⠂⡴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⢤⡐⠻⡸⠖⠋⠀⠀⠀⠉⠉⠉⠉⠸⡏⢈⡳⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠓⠒⠒⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡤⠤⠤⣉⠉⠙⠙⠿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠋⠤⠤⠄⠈⣧⣀⠀⠀⠘⠿⢿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣤⠤⠛⠛⠻⢿ ⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠑⠀⠀⢰⠀⢀⣀⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡆⡼ ⠀⢀⠔⠊⠁⢠⠖⠒⠄⢰⠀⠈⠆⢋⣁⣩⡥⠴⠯⢁⠤⠀⠀⠀⠀⠀⠘⠀ ⢠⠃⠀⠀⠀⠈⢲⣶⡵⣆⢱⠀⡰⠹⠿⠯⠄⠒⠒⠒⠁⠀⠀⠀⠀⠀⡇⠀ ⢸⠀⢀⡀⠀⠀⠀⠀⠠⣬⡎⣼⡔⠉⣖⠦⠤⠤⠒⠀⠀⠀⠀⢀⡀⢠⠃⠀ ⠸⡖⠉⠀⢀⠆⠀⠀⠀⣸⠳⠋⣟⡽⢽⠂⠀⠀⠀⠀⠀⢠⡀⠀⢙⠏⠀⠀ ⠀⠑⢄⡴⠋⠀⠀⠀⠈⠪⡭⠭⠴⠎⠁⠀⠀⠀⡀⠸⡄⠀⢙⡶⠋⠀⠀⠀ ⠀⠀⢀⡉⡲⠠⡤⡄⠀⠀⠀⠀⠀⠀⢀⣤⣺⣅⡀⠤⠜⠊⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⠌⢃⡑⠗⡞⠦⢤⠤⠤⡔⠚⠉⣏⠉⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠒⠦⣡⣾⣄⡰⠁⢀⡜⡏⠉⠀⠀⡇⠂⣄⣄⠉⣢⠀⠀⠀⠀⠀⠀

⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⣀⣀⣀⡀⠠⠴⢷⣶⣶⡿⢧⠀⢠⠒⠒⠒⠒⠂⠀⢀⣉⡉⢹⠀⢸⡀⠀⠀⠀ ⠀⡅⠀⠀⠀⠀⠀⢀⣴⣶⣤⢰⠀⠸⡀⠀⠀⠀⠀⢰⣿⣿⣿⡼⠀⠀⠈⠑⢦⠀ ⠀⠙⢄⠀⠀⠀⠀⠘⢿⣿⡿⠋⠀⠀⠈⠢⣄⣀⠀⠀⣙⡿⠛⠁⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠉⠒⠂⠄⠐⠒⠈⠀⣸⡭⢍⣙⡛⢻⡛⠉⢓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀ ⣇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⣹ ⣈⣦⣞⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣔⣁ ⠀⠀⢏⠑⠢⠯⣀⡀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠊⠁⠀⠀ ⣤⠤⠼⣆⠀⠀⠀⠀⠉⣹⡿⣿⠃⠀⡱⠤⠤⠤⢏⠙⡤⠤⠤⠤⠤⠤⠤⠤⠀⠤ ⠀⠀⠀⠈⠲⠤⠀⠤⠚⠁⠀⢸⠀⠀⡓⠒⠂⠤⠬⢆⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⣠⣠⣀⣀⣀⣤⣤⣴⣀⡇⠀⣸⣧⣀⣀⡀⠀⠈⢾⣀⣄⣀⣀⣀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣯⣭⣟⠀⠘⡄⠀⠘⣿⣿⡃⠀⢹⠀⠀⠀⠀