⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠈⠉⠛⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠛⠛⠛⠛⠒⢀⡀⠀⠀⠀⠀⠙⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠁⢀⣠⣤⡶⠀⣠⣴⡟⠁⠀⠀⠀⣄⢠⠀⠈⠉⠛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣄⣀⣀⣀⣀⣤⣴⠿⠛⢉⡤⠀⣠⡴⠋⣠⠏⢀⣾⣿⠟⠀⠀⠀⠀⠀⠘⡄⠳⡄⠀⠀⠀⢠⡈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠻⢿⣿⣛⣋⣩⣤⢤⡶⠋⢀⡼⠃⢀⣴⡏⠀⡞⣿⠏⠀⠀⠀⠠⡀⠀⠀⡇⢸⢹⡀⠀⠀⠀⠙⣆⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠁⡼⠁⢠⠟⠀⣰⠏⣾⠀⢠⢿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠀⣷⠀⠀⠀⠀⠘⣆⠀⢻⣻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢠⠇⢠⠏⠀⡴⠃⠀⣧⠀⠸⣾⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⠀⣿⠀⢰⠀⠀⠀⠸⡆⠀⢧⠹⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣯⠀⠀⢸⢠⠏⢀⡼⠁⠀⣠⣿⡀⠀⣿⠀⠀⠀⠀⠀⡀⠀⣸⠃⢀⡟⢰⣏⡀⠘⣇⠀⠀⠀⢧⠀⠸⡆⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢸⡞⢀⣾⠃⠀⣰⣯⡿⣧⠀⣿⠀⠀⠀⠀⣸⢁⣴⠋⢀⡼⣡⡏⢻⡷⠀⢿⠀⠀⠀⠸⡇⠀⣷⠀⢹⡆⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢸⢁⣾⡏⠀⣰⣿⠏⠀⢸⣦⡿⣇⠀⠀⣠⠇⡾⠁⣠⣾⠟⣿⡃⠀⢻⡄⠘⡇⠀⠀⠀⡇⠀⣿⡇⢸⣇⠀⠀ ⠀⠀⠀⠀⢀⡿⠀⢀⠀⠀⠈⣼⢹⠇⢠⣿⠏⠀⠀⠈⡇⠙⠿⡄⢀⡏⡼⠁⢴⡟⠉⣼⡿⠃⠀⠀⢿⡀⣿⠀⠀⢰⠇⢰⡟⡇⢸⣿⠀⠀ ⠀⠀⠀⠀⣼⠇⠀⣸⠀⠀⠀⣧⣿⠀⣸⠟⠶⣄⡀⠀⣇⠀⠀⠈⡿⠀⠀⢀⡞⠀⡼⢁⣀⠴⠂⠀⠈⣧⣿⠀⠀⡟⢠⡟⢷⠀⠘⣿⠀⠀ ⠀⠀⢀⣾⠏⠀⣠⡏⢠⠀⠀⣿⠙⡇⡟⠀⠀⠀⠭⣷⣿⠀⠀⣰⠃⠀⣠⡿⣠⣾⠗⠋⠀⠀⠀⠀⠀⠸⣿⠀⣼⣵⣿⠃⠸⡆⢀⣿⠀⠀ ⢠⣴⡿⣃⡴⢞⣿⠀⢸⡀⠀⡏⠀⢿⣧⣤⣶⣶⣶⣦⡬⣇⠀⡇⢀⣴⣿⠟⠉⣨⣵⣷⣶⣶⣤⣄⠀⠀⣿⢼⣿⣿⠁⠀⠀⢹⣼⡏⠀⠀ ⠈⠛⠛⠻⢶⣾⠃⠀⣸⣇⠀⣇⣴⡿⠛⡿⢯⣿⣿⣿⡟⠸⣆⢠⠞⠉⠁⠀⠀⠟⡽⢿⣿⣿⣽⠟⢿⣶⡟⠈⡼⣩⣷⣄⡀⠀⢿⡇⠀⠀ ⠀⠀⠀⣠⡿⢣⣠⣾⠿⣿⡀⢿⠈⠃⠀⢶⣾⠛⢻⣿⠇⠀⠙⠏⠀⠀⠀⠀⠀⠀⢻⣞⡻⢿⣿⠀⢠⢿⠃⣼⣵⠏⠙⢻⣿⣦⡈⢿⣄⠀ ⠀⠀⠀⠟⠛⢻⣧⠸⣇⠈⠳⣜⣆⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣟⣠⠟⠁⠀⠀⣾⣠⡿⠻⠿⢿⡷ ⠀⠀⠀⠀⠀⠀⢻⣧⣿⣦⣠⣾⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣟⣥⣤⡤⣤⣼⣳⡟⠁⠀⠀⠀⠀ ⢀⣤⡀⠀⠀⠀⠀⠙⢿⠎⠛⢿⣆⠀⠀⠀⠀⠀⠀⠰⡖⠚⠛⠛⠋⠉⠙⠓⠒⠒⡶⠀⠀⠀⠀⠀⠀⢀⣭⡿⣿⣜⣷⣿⠁⠀⠀⠀⠀⠀ ⠛⠧⢽⣲⣄⠀⠀⠀⠀⠀⠀⠀⢙⣷⢤⣀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⣴⣿⣿⣴⠟⠉⠻⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠓⠦⠀⠀⠀⠀⣴⣿⡧⢴⣯⢿⣶⠦⣤⣤⣈⣙⣒⡒⣒⣒⣋⣁⣀⣀⣤⡤⢶⣿⣯⣜⣿⡛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⢸⡟⣠⠔⢛⣆⣿⢶⡿⠋⢀⠹⣟⠉⠉⠉⣹⠏⠁⠈⢻⣿⠾⠏⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠟⠛⠉⠉⠉⠉⠁⠀⠀⠀⢸⣧⠀⠘⠁⠹⣿⣾⣿⣤⣈⣦⣈⣳⣴⢞⣁⣀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣠⣠⠴⠂⠀⠀⠀⢻⣷⣌⣁⡴⢿⣧⣹⣿⣿⣿⣿⡅⠉⢹⡏⣿⠉⣿⣿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⣾⠥⠴⣻⣟⣿⣿⣿⣿⣻⠀⠀⢸⣧⢻⣯⣟⣿⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀