⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢶⣦⠶⠖⠓⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⣀⣉⣳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣱⠟⠀⣠⡾⠋⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠉⠻⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣾⠋⢀⣴⠋⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠁⢠⡾⠁⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣀⣀⣀⣀⣀⣈⣳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣴⠟⠀⠀⠀⢀⣾⣫⣤⣤⡴⠶⢦⣤⡀⠀⣠⠶⢻⣿⢛⣿⠿⣿⣍⠙⠛⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡾⠃⠀⠀⠀⢠⣿⣿⢛⣿⠿⢿⣦⠀⠈⣷⠛⠁⠀⣿⣿⡿⣿⣤⣿⣿⣤⣶⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣾⠃⠀⠀⠀⢠⡟⣿⣿⣿⣿⣦⣾⣿⣧⡼⠷⣤⣤⣤⣽⡿⠷⠿⠟⠛⢩⡿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⡏⠀⠀⠀⠀⣼⣷⣾⣿⡿⠾⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢻⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⢉⣿⣛⡻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⢿⡆⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⣿⣮⣿⣿⣟⣿⣷⣶⣿⣿⣭⣭⣭⣽⣿⣿⣭⣭⣅⠀⣿⡋⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢿⡈⠛⢾⣝⡻⣿⣟⣛⠿⣶⣬⣉⣉⣹⡷⠀⢀⣹⡷⢘⣷⠀⣸⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⢷⣄⠀⠉⠛⠷⣮⣝⣛⡳⠿⠿⠿⠿⠛⠛⠛⣉⣤⡾⠃⣰⠏⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠈⠛⢦⣄⡀⠀⠈⠉⠛⠛⠻⠿⣶⣶⣶⠞⠋⠁⢀⡾⠋⠀⣸⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢀⣴⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡳⣦⡀⠀⠀⠀⠀⠉⠛⠿⣥⡀⠀⠀⢀⣴⠟⠁⠀⠀⠀⡾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣤⡀⠀⠀⠀⠀⠈⠙⢦⡴⠛⠁⠀⠀⠀⠀⣸⠃⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⣰⣯⠭⠭⣝⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⣸⣧⠀⡇⣯⢠⣖⡚⠿⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀ ⠀⣠⠞⠁⣿⠀⠹⣌⠧⣭⠿⣸⠇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣦⠀ ⢠⡟⠀⠀⢹⣇⠀⠈⠙⠒⠒⣶⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⢸⣇ ⠈⣷⠀⠀⠐⠙⢷⣄⠀⠀⠰⣇⡳⠶⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣰⣏⣀⣀⣤⣤⡶⠾⠛⠋⠁⠀⠀⣸⠏ ⠀⠈⢷⣄⠀⠀⠀⠙⠳⢶⣤⣈⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠛⠁⢀⣴⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀ ⠀⠀⠀⠉⠳⢦⣤⣀⣀⠀⠀⠉⠙⠛⠛⠿⠿⠶⠶⠶⠶⠶⠟⠛⠛⠛⠋⠉⠁⢀⣀⡤⠞⠛⠷⠶⠶⠶⠶⣤⣤⠴⠶⠶⠞⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢒⡶⠒⠈⠐⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⡟⢁⠔⠁⠀⣀⠔⠊⠉⠉⠺⡦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠋⡰⠃⠀⢀⠜⠁⠀⠀⠀⠀⠀⣉⣉⡙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡞⠁⠀⣠⣯⣶⣖⠒⢢⡠⠒⣽⣭⡟⣷⠉⡡⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡎⠀⠀⡞⠀⠀⢰⢻⣿⢷⣼⣧⠼⠤⠤⠽⠷⠛⢋⡿⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠀⠀⢰⠃⠀⠀⡟⣿⡯⢭⣁⣀⡀⠀⠀⠀⣀⣀⠼⡄⡇⠀⠀⠀ ⠀⠀⠀⠀⣰⠁⠀⠀⠘⡆⠀⠀⡗⢿⣯⣿⡶⣿⡛⠿⠿⡟⠛⣄⢯⠀⡇⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⣄⠀⠘⢄⡉⠛⠯⣓⣛⣛⡛⠓⢚⡡⠞⡰⠉⡆⠀⠀ ⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠲⢤⣤⣤⣬⠽⠟⠁⣠⠞⠀⢸⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⣦⡀⠀⠈⠙⠣⡄⣠⠖⠁⠀⢠⢻⠀⠀⠀ ⠀⠀⡞⢀⡦⠭⢔⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠈⢧⠀⠀⠀⠎⠈⢣⠀⠀ ⠀⡴⢻⠘⡑⢐⠎⡝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢸⡄⠀⠀⠀⠀⠈⡦⡀ ⢸⠀⠘⢦⠈⠁⢰⣜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⢀⣀⡤⠞⠁⡧ ⠈⠢⡀⠀⠙⠦⢌⣁⣀⣀⠀⠀⠀⢀⣀⣀⣀⠤⠖⢉⡠⠋⠉⠉⠉⠀⠀⣀⠔⠁ ⠀⠀⠈⠙⠒⠢⠤⠤⠤⠭⠭⠭⠭⠥⠤⠤⠤⠔⠚⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀