Cute Dog ASCII Art

Copy & Paste Cute Dog ASCII Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⣧⣀⡠⠤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠒⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣀⣠⠖⠀⠀⠀⠀⡞⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⡤⠚⠁⣠⠎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡴⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢠⠊⠙⢆⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⣀⣀⠑⠲⠚⠀⠀⠀⠀⠀⠀⢇⣀⣀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠳⡶⠋⠑⠢⡔⠺⢿⣿⣿⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⡜⠀⠀⠀⠀⠘⡆⠀⠙⢻⡗⠈⢱⣶⣶⣭⡍⠓⢦⣠⣾⠿⠛⢛⡏⠉⠉⠉⠉⠉⠫⡑⠲⢄⡈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠀⢠⠉⠓⠦⠤⠴⠚⠁⠀⠀⠀⠙⢄⠀⠙⡟⠋⢀⠴⠊⠁⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⡧⢤⠀⠙⢮⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠘⢧⡔⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠤⠔⡞⠁⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣇⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢠⠇⠀⠀⢠⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⢀⠎⠀⠀⣠⠎⢸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡇⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⢠⡯⠤⠶⠊⠁⡠⢚⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢻⠯⣓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢴⠞⠁⠀⠀⠀⠀⠘⠁⠀⠀⡰⠊⡰⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠈⢱⠢⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠤⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡹⠀⠀⠀⠀⠀⢀⣀⠤⠒⢻⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⡸⠀⣿⢀⠆⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠹⡄⠀⠉⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠇⡼⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡏⢀⣀⡀⠀⠀⢹⣤⠔⠊⠉⠉⠉⠉⠒ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣴⠃⢸⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠒⢿⡖⠓⠒⣤⠄⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠐⣿⠀⠸⣦⠘⡄⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⣼⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠙⢦⠀ ⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠃⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢳⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠖⠛⠉⠉⠉⠉⠉⠙⠒⠦⣿⣏⣀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠀⠀ ⠀⢰⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀ ⠀⠈⣇⢀⢠⠇⠀⣶⡶⠄⠀⠀⠀⢠⣶⡶⠀⠀⣸⣀⣼⠟⠀⠀ ⠀⠀⠙⠛⠾⡆⠀⠙⠛⠃⠀⠀⠀⠀⠙⠋⠀⠀⣹⠟⠁⠀⠀⠀ ⢀⡴⠚⠉⠛⢿⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⢀⣿⠋⠉⠉⢳⡄ ⢾⡀⡄⠀⣄⡼⠻⢧⠤⣤⠤⠤⣤⣠⣦⣾⠶⠞⢿⣤⡄⣠⣀⡷ ⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠶⠖⠶⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⣤⣴⣾⣿⣿⣿⡏⠉⠻⢇⠀⠀⠀⠀⢰⡀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡟⠹⣿⣿⣿⣿⠇⠀⠀⠀⠁⠀⠀⠀⠈⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⢠⡄⠀⠘⠁⠀⠈⠛⢿⡋⠀⠀⠀⠀⣼⡀⠀⠀⠀⣿⢀⣤⣄⣬⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠈⣷⠀⠀⠀⠀⠀⢠⣿⣿⣶⣤⣴⣾⣿⡇⠀⠀⢀⣿⡟⠀⠌⠀⠐⢻⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡄⠀⠸⣶⣶⣿⣿⢿⡟⠉⣽⣿⡿⠃⠀⢠⣿⠉⠁⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣇⠀⠀⠙⠿⣿⠃⢸⠃⢀⡿⠋⠁⠀⠀⠘⢻⡀⠀⠠⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⡷⠾⠷⠿⣤⣀⠀⢠⡏⢠⠟⢀⡼⠁⣀⣠⠴⠂⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢷⡈⠛⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠚⠓⠒⠒⠒⢿⡀⠀⠀⠀⠀⠀⠀⣸⠟⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠒⠒⠒⠒⠒⠛⠒⠒⠒⠚⠻ ⠀⠀⠀⠀⠀⠈⠙⠛⠦⠴⠦⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
completely free, NO signup required (ever), and unlimited!
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠋⢧⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⡤⠞⠓⠉⠉⠉⠀⠉⠉⠉⠛⠉⠉⠙⠒⠶⣤⡀⠀⠀⠀⣠⠶⠋⠁⣴⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠞⠉⠀⠀⠀⠀⠀⣸⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⠋⠁⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠃⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⢀⡴⠒⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⢯⣷⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠁⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣀⣀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⠉⢻⡞⠁⠀⠉⠳⣍⠙⠿⣿⣿⣿⣿⡆⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣴⣶⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡿⠁⢠⠟⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢻⡭⠆⠈⠁⣶⣶⣶⣦⣬⠉⠳⢤⣀⣼⣿⡿⠿⠛⣻⠉⠉⠉⠉⠉⠉⠉⠹⣍⠙⠲⢤⡀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⡞⠲⢦⣀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠙⢦⠀⠀⠻⢿⡿⠟⠃⠀⣀⠴⠋⠁⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠳⣌⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡟⠃⠀⠀⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⣸⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⢹⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣿⡃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠶⠒⠋⣹⠁⠀⡞⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠇⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⢠⠎⠀⠀⠀⢀⡾⠉⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⢠⠏⠐⣀⣠⠾⠋⠀⣠⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⢳⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣿⠛⠫⠉⠁⠀⣠⠞⢡⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⡏⠳⣌⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⢒⡟⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣐⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢠⡇⠀⠀⠙⡶⢤⣈⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣁⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⡇⠀⠀⣸⠃⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠒⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡇⠀⣰⠋⠀⠀⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡠⡴⠚⠋⠁⠀⠘⣧⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢠⠃⢠⡿⠀⡼⠀⠀⠀⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠀⠀⠘⢧⡀⠀⠈⠀⢀⣀⣀⣤⣀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣀⣀⡀⠀⠀⠨⣷⣤⠖⠋⠁⠀⠀⠀⠈⠉⠓ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡀⣸⠃⢸⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠉⠉⠛⠶⢭⣷⡦⠦⠤⢤⣀⡀⠀⠀⠀ ⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⣷⡇⠀⢘⣆⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢷⡀⠀⠈⠓⢯⣄⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡇⠀⠘⣿⣇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢀⣼⢣⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠲⢤⡀⠀⠉⢳⡀ ⡀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠘⣟⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡾⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢹⣆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢷⣦⣤⣀⡹⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡏⣤⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡀⠀⠀⢤⢠⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠈⣇⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⡀⣀⠀⢠⣿⠃⠀⠀⢀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⠀⢠⣠⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⣇⣽⠀⢈⡏⠀⠀⠀⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⠥⠀⠀⠀⠀⣿⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣧⣾⣿⡄⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣼⣿⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⠿⠛⠛⠻⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠉⠉⠛⢿⣦⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣷⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡾⣠⣇⣠⣿⣿⣿⡇⠀⢀⠀⠀⠀⢀⠀⠀⢹⣷⠀ ⣿⣷⡀⠀⣷⠀⠀⠀⣼⣦⣴⣿⠏⠙⠻⠿⣷⡿⠷⣶⣶⡾⠿⠿⠷⢶⣶⣦⣤⣾⣿⣷⣿⣿⠿⠿⠛⠛⠙⠻⣿⣤⣾⣇⠀⢀⣸⣇⣀⣼⣿⠃ ⠘⢿⣿⣾⣿⣷⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠃⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡄⣠⣿⠤⠶⠒⠒⠋⠉⠉⠙⠓⠲⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣋⣠⠤⠤⠤⣤⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⢻⠶⣤⣀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡄⠈⠙⣧⠀⠀⠀ ⡇⠀⠀⠀⣆⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠘⣧⠀⠀ ⢻⡄⠀⠀⢻⣆⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣇⠀ ⠘⣧⡀⠀⠈⣿⣦⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣿⢀⠀⠀⠀⠀⢿⡀ ⠀⠘⣧⡀⠀⠘⢟⢷⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡞⠉⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣸⣷⣴⣿⢸⠀⠀⠀⠀⠸⡇ ⠀⠀⠘⢷⡀⠀⠀⠢⣹⣇⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⣷⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⢹⣿⠈⣇⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠙⢦⣀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⣿⠻⡄⠀⠈⠛⠋⠁⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠁⠀⠈⣿⣧⣘⣦⠀⠀⢠⠇ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠻⣆⠀⠀⠀⠀⢰⣿⣧⡘⢦⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⢶⡀⠀⠀⠀⢀⡾⠀⠉⠛⠻⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠶⠻⣇⠀⠙⢶⣿⣦⣤⡀⠀⡴⠻⡇⠀⠀⠀⠀⠀⠙⠶⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣙⣛⣻⣿⣿⠃⠀⠀⡄⠀⠀⠀⠘⣄⠀⠈⣿⠁⠀⠀⣠⠞⢿⠟⣶⡄ ⠀⠀⠀⠀⠀⠀⣠⣿⣤⣶⡖⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⣟⣩⣥⣿⢤⣤⣼⠀⠀⠀⠰⣄⣼⠳⢼⡿⠀⠀⠀⣿⠖⢾⡷⢻⣿ ⠀⠀⠀⠀⠀⠀⠻⠏⣩⣿⣯⣀⣿⠿⠤⠇⠀⠀⠀⠀⠀⢰⠋⠉⠀⣶⣤⣀⣙⣷⡀⠐⠿⣟⠁⠀⠀⠀⠀⠀⠀⠙⠦⢾⣿⠾⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡀⠀⠀⠢⡁⢈⣿⡾⢧⣀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⢿⠟⠒⠲⠶⠟⠚⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢳⡀⠠⠄⠀⠀⣀⡀⠀⠀⢀⠄⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡔⠁⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢎⡠⠊⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠠⠎⠀⠀⠰⣈⡆⠀⠀⠀⡠⠠⡀⠀⠀⠀⠉⠲⢼⠀⠀⠀⠀⠀ ⠀⠀⢀⡜⡧⠒⠠⡰⢾⣷⠄⠀⠀⣀⠀⠈⣩⣤⡀⣀⣀⡀⡀⠀⢃⠀⠀⠀⠀ ⠀⠀⡜⢠⠡⠀⠠⠔⠀⠘⢅⠘⡿⠃⡨⠚⠉⢡⠃⠀⠀⠀⢡⡉⠢⣃⠀⠀⠀ ⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠆⡳⠀⠀⠀⠀⠀⠑⠂⠐⠺⠁⠆⠀⢸⠀⠀⠀ ⠀⠀⢣⠀⢆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠜⢀⡠⢋⡀⠀⠀ ⠀⠀⠘⠀⠀⠙⠶⡠⢀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠊⠀⠀⠘⠉⢁⢐⠕⠁⠀⠀ ⠀⠀⢀⠃⠀⠐⠀⠸⠑⠂⠀⠀⠀⠀⠀⠤⢰⠁⠀⠀⠀⣀⢤⠒⠁⠀⠀⠀⠀ ⠀⠀⠌⠀⠀⢠⢠⣇⠂⠁⠂⠀⠀⠀⠀⠀⡌⠀⠀⠀⡇⠀⠀⠡⡀⣁⠀⠤⢀ ⠀⡜⠀⠀⠀⢨⠇⡏⡄⠀⠀⠀⠀⠀⡠⢀⠁⠀⠀⠀⠇⠉⠀⠒⠹⡒⠠⡄⠀ ⡘⠀⠀⠀⠀⣸⠀⢹⡜⠀⠀⠀⠀⠊⢀⡾⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠢⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠶⠶⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠃⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠘⡀⠀⣴⣠⣾⣿⣿⣿⣿⣿⡄⠉⠻⢯⡀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⡂⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣾⠁⠀⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⢸⡆⠀⠀⠋⠀⠀⠀⠈⠉⢻⣏⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⢸⡇⣠⣶⣦⣴⠾⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⠀⠀⠀⠀⣸⣧⡏⠀⣆⠀⠆⠐⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢻⡆⠀⠀⢰⣦⣤⣴⣿⣿⣿⣿⡿⠛⢛⣿⣿⣿⡏⠀⠀⠀⣾⠟⠽⠃⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣷⠀⠀⠈⢿⣿⣿⣿⡿⠁⣿⠁⠀⣾⣿⡿⠋⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⠀⢻⡀⠀⠀⠀⠙⠻⣿⠁⢀⡏⠀⢀⣿⠋⠀⠀⠀⠀⠀⠈⠘⣧⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠶⠶⠾⣧⣄⡀⠀⠀⢸⠃⢠⡾⠃⢀⣾⠃⠀⢀⣠⡴⠖⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠀⠀⠀⠈⠻⣷⡀⠸⢷⣤⣤⣴⠿⠷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣄⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣀⣀⣠⣠⣄⣄⣄⣀⣀⣀⣠⣀⣀⣀⣀⣀⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣠⣤⣤ ⠈⠉⠉⠉⠉⠉⠉⢿⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠶⠶⠶⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣇⠤⠤⠐⠒⠠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠓⠒⠀⠐⠚⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀ ⡎⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⠒⢤⡀⠀⠀ ⡇⠀⢠⠀⠀⢀⡴⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠇⠀⢳⡀⠀ ⢸⠀⠈⣧⠀⣸⠁⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢧⠀ ⠀⢣⠀⠘⠷⣽⠀⠀⠀⠀⢸⡀⢀⠊⣷⡀⠀⠀⠀⠀⠀⣎⣷⣼⢠⠀⠀⠸⠀ ⠀⠀⠑⢄⠈⢺⡄⠀⠀⠀⢸⢃⠀⠻⠟⠁⠀⠀⢤⠄⠀⠙⠋⢹⣌⢆⠀⢠⠀ ⠀⠀⠀⠀⠉⠉⠙⢄⡀⢀⡞⠢⡢⡀⠀⠀⣠⠤⠐⠀⢢⡀⢀⡴⠀⠉⠛⠁⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠦⣘⣛⣷⣾⠁⢠⠀⠀⠠⡈⢱⠁⠀⡴⠶⢦⡀ ⠀⠀⠀⠀⣾⢾⡏⢰⣆⡄⠀⠀⠀⡸⠖⣓⠒⢧⡀⣠⡶⠉⠛⠀⠘⣇⣻⣽⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣇⠀⠫⣉⡿⠣⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠎⢀⣠⣴⣶⡖⠲⡂⠀⠀⡄⠈⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠋⠀⡼⠙⢿⣿⠃⠀⠈⡀⠀⢸⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠘⡄⠀⡀⢀⣿⣦⣤⣾⡇⠀⣸⡞⠉⠉⠳⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⢃⠀⢣⠀⠻⣿⠋⡇⢸⠟⠁⠐⢇⠀⠀⠐⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠚⠚⠢⡄⢮⣘⣠⠧⠄⠂⠀⠘⡄⠀⠀⠀⠸⡀⠀⠀⠀ ⠐⠒⠒⠺⣀⠀⠀⢀⡸⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠓⠒⠒⠂ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⣿⣤⣤⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣹⡶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⠯⣟⡷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢯⡛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢁⣀⣀⣀⣀⣄⣈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠷⠛⠉⠉⠉⠀⠀⠈⠉⠉⠙⠻⠿⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠉⠉⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡉⢙⡛⠻⢷⣦⡀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢣⠀⠀⠙⢿⣆⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢸⡆⠀⠀⠀⢻⣧⠀⠀⠀ ⠘⣧⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡌⡇⠀⠀⠀⠀⢻⣇⠀⠀ ⠀⢿⡆⠀⠀⠀⢹⣷⡄⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡇⠀⠀⠀⠀⠘⣿⡀⠀ ⠀⠘⣧⣤⠀⠀⠀⢧⣿⣦⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⢹⣧⠀ ⠀⠀⠸⣧⣀⠀⠀⠈⢳⡹⣷⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡞⠉⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⣷⣤⣿⡇⢧⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠘⢿⣄⠀⠀⠀⠑⣌⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⢸⣷⣤⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣾⣟⣿⢹⣿⡇⢸⡆⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠈⠓⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡀⠀⠀⠻⣿⣿⣾⠟⠀⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⠙⠻⠛⠋⠘⣿⣧⠀⢻⡄⠀⠀⠀⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿⡉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢷⣤⣛⠦⣀⢀⣠⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠻⣆⠀⠀⠀⠀⠀⠀⣼⡿⣧⣀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⡴⣤⣤⠴⣷⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠙⠛⠛⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠤⣤⣤⡼⢿⡁⠀⠙⠶⣬⣛⠦⣄⡀⠀⠀⢠⡾⢻⡏⠉⠀⠀⠀⠀⠀⠘⠻⢦⣄⣀⡴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠒⠲⠯⣟⣾⡿⣶⣴⡿⠁⠀⠳⢀⡀⠀⠀⠀⠀⣦⠀⠆⢉⣻⣶⠛⠀⠀⠀⠀⣠⣴⣶⣶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠦⣤⣤⣤⣾⠟⢿⠇⠠⠀⢠⡞⠀⠀⠀⠀⠀⠈⢷⣄⠈⣼⣿⠀⠀⠀⢀⣾⡁⠈⣭⡁⣼⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢿⣶⣿⣿⡏⠒⢶⣶⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣼⡶⠾⠶⠶⣦⣼⡃⠀⠀⠀⠀⠳⣤⡾⠉⠳⠷⠿⠀⠀⠀⢸⣇⠏⠹⢿⢟⠙⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣏⣉⣽⣿⣇⣀⣸⣿⣷⣤⠿⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠁⠀⣶⣦⡄⣀⣙⢻⣦⠀⠠⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣴⣾⣾⡷⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⡁⠀⠀⠠⣭⠛⠉⠛⢻⣡⣿⡙⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣭⣿⢿⣷⣄⣀⣀⣈⣳⣄⣾⡿⠋⠈⠛⠷⠶⠤⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠺⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡦⡄⠀⠀⠀⠤⣾⣧⣶⡆⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠟⣿⣶⠀⠀⠀⠰⢿⣯⢿⣧⡄⠀⠀⠀⠸⣿⣠⣤⡄⠀⠀⣶⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠁⠀⠀⠀⠻⣿⠇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⣠⣤⣼⣿⠈⡷⣄⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⣍⣉⠉⠉⠉⠉⠙⠒⠚⠉⠀⠀⠀⠀⠈⠁⠀⠛⠊⠳⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⠞⠉⠀⠀⣀⣤⡤⠤⠤⣤⣀⠀⠀⠈⢳⡀⠙⠋⣹⠏⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠙⢶⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡇⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⣿⣦⠀⠀⢳⣄⡾⠥⠖⠒⠲⡆⠀⠀⢾⡉⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⢮⣷⡀⠀⢿⠁⠀⠀⣀⡴⠃⠀⠀⠈⠑⠄⣀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⣠⠏⠀⠀⢀⠀⠀⠀⠀⠀⢰⣽⠁⢀⡟⢀⣠⣤⣤⣄⣤⢤⣦⠒⠚⠛⠋⠙⠋⠀⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡃⢰⡏⠀⠀⢰⣼⣷⣀⡀⡐⣶⣾⠾⠤⣼⠇⠀⠁⠀⠘⠿⢿⣿⠋⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣇⠀⠇⣤⠀⢹⣿⡿⣿⣷⠷⠋⠁⠀⠀⡿⠀⠀⠀⠳⣤⣴⣿⡏⠓⠶⣶⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⣰⡋⠁⢸⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣯⡀⠀⠈⠻⠦⠾⠉⠋⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⣇⠘⠁⣀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⠀⠀⠀⠀⢻⣧⣦⣵⡿⠋⢷⡄⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠙⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠣⣿⢻⠀⠀⠀⠀⢸⣧⣿⣛⠀⣶⠿⠃⠀⠀⠀⠀ ⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡾⠃⣾⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡳⢦⣀⣀⡀⢀⣀⣀⣀⣤⡴⠾⠛⠉⣶⡾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀ ⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙⠳⢦⣭⣭⣉⣉⣉⣠⣠⣠⠴⠶⠋⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣿⣷⣿⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠿⠿⠂ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢙⡶⣦⣀⠀⠀⠘⠄⠀⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠹⡷⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⣠⣠⡿⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠀⡐⠀⠀⢠⠏⠀⠀⠀⠀⠀⡇⠀⠉⠓⢦⣬⣷⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠀⣀⢀⣠⢼⣿⡛⠋⠀⠀⢰⠇⠀⢀⣴⠶⣴⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡿⠀⢸⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⢧⠀⠀⢰⡏⠀⠸⡆⠀⢠⠀⠀⠀⠀⣾⠴⠿⠟⠟⠋⠙⠋⣿⡇⡄⠀⠀⣾⠀⠀⠸⣿⣧⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣧⠀⠈⣄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣤⣷⠀⠀⢻⠀⠘⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢿⡀⠀⠀⠘⢿⣿⣏⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠦⣀⣙⣾⣷⠄⢀⣀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢠⣈⣳⣦⠀⠀⠀⠀⢨⣧⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠈⠉⠉⠁⠀⠀⠹⠟⠛⠛⠒⠒⠿⠀⠀⠀⠀⠀⠘⣿⠀⠃⠀⠀⢷⡀⠀⣀⣀⡀⣀⣀⣀⡀⠄⠈⠛⢶⡿⠟⠋⠀⠺⠗⠃⠘⠯⠿⠟⠛⠀⠂⠓⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣀⣠⡤⣬⡇⠀⠙⠟⠃⠋⠙⠉⠀⠀⠀⠀⠀⠙⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Related Text & Emojis

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠲⢤⡀⢀⠤⢶⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠶⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠙⠋⢰⠀⠈⠢⢤⡀⠀ ⠀⠠⡶⠚⠉⠀⣖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⢆ ⠀⠀⡆⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣧⠀⠀⠀⠀⡾ ⠀⠀⣧⠀⠀⠀⠈⣷⠀⣠⣖⢦⠀⠀⠀⠀⢰⠓⡍⢧⢻⣧⠀⣠⠚⠀ ⠀⠀⠸⣆⠀⠀⠀⢹⠀⣧⣨⡆⡇⠀⠀⠀⠸⣷⡇⡸⠀⡏⠉⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⢀⣧⡀⢻⣿⡡⠁⠀⠀⠀⠀⠙⠒⠣⣜⣀⢀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⡀⠙⣶⡬⠀⠀⢠⣾⡟⠛⢻⠀⠀⢸⠁⠀⠙⠄⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢳⣄⠀⠈⠿⢿⣒⣋⣀⣴⠇⠀⠀⠼⡀⠀ ⠀⠀⠀⠀⢀⠤⠴⣧⣀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⣁⣀⠀⠀⠀⢸⠀ ⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀⢀⣤⡶⡶⢶⠛⠋⠉⠉⠉⠷⣤⡤⠂⠀ ⠸⡄⠀⢸⡆⠀⠀⠀⠹⣷⣾⠟⠃⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡘⢤⣀⣿⡄⠀⠀⢠⡿⠧⣴⠀⠀⣷⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⠤⠭⣥⣤⣤⢽⣤⣶⣸⣤⣰⣌⣼⠾⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠟⠛⠛⠳⣯⡓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡿⠋⠀⠀⠀⠀⠀⠻⣮⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⢴⣿⣭⣭⣟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⡀⠀⠀⠘⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣻⠟⠁⠀⠀⠈⠻⢦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡾⠁⠀⠀⠀⠀⢠⡿⠀⠠⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣳⠏⠀⠀⠀⠀⠀⠀⠈⠹⣦⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣾⠁⠀⠀⠀⠀⢀⣿⠃⢀⠁⠠⡀⠈⣷⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣯⡟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠻⣮⡣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⠃⠀⠀⠀⠀⠀⣼⡟⢀⠠⠐⠀⢡⠀⠘⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⠃⠀⣴⠀⠹⣷⡀⠀⠀⠀⠀⠀⠈⢷⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢰⣿⠀⠄⠂⠐⡈⠀⢃⠀⢹⣎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⣿⠀⠀⠏⠀⡀⠻⣷⡀⠀⠀⠀⠀⠀⠈⢻⣌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡿⠀⠀⠀⠀⠀⠀⣸⡟⠀⠰⠀⠂⠡⢀⠸⡀⠈⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⡏⠀⣠⠂⠐⠀⡀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠙⣧⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⣿⠇⡂⠁⠄⡁⠐⠠⠀⢡⠀⠸⣏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⣟⠀⠠⠁⠀⠄⡈⢿⣆⠐⠀⠀⠀⠀⠀⠈⢿⡜⢦⣀⣤⢴⣖⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⡐⠀⠌⠐⠠⠘⡆⠀⢿⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⡯⠀⢂⠠⠁⠠⠀⠌⢿⣆⠀⠀⠀⠀⠀⠀⣀⣿⣾⡿⠛⠋⠉⠉⢹⡄⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣠⣐⡀⠁⠌⠠⢁⠀⢣⠀⠸⣏⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⢃⠐⠀⠄⠠⠁⡐⠈⡈⣿⡆⠀⠀⢀⣴⠿⠛⠉⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢟⠛⢻⡧⠐⠈⡐⠠⢀⠂⠆⠀⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡇⠀⠀⠂⢈⠀⢂⠐⠀⢂⠐⢸⣧⠀⠀⠀⠀⠀⠐⠀⢸⡁⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣴⣤⡀⠂⢂⠀⡃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⡇⠀⠀⠡⠀⠂⠄⠂⢡⣾⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠉⠉⣿⡇⠀⠡⠀⢸⠀⠈⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡿⣿⠀⠠⠁⠐⠠⠐⠠⡘⢿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢈⠐⠠⠈⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠀⠀⡃⢀⠂⠀⣿⡿⠛⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢀⠈⠄⠐⡀⠀⢼⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⡇⠀⡇⠀⡀⠂⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⡄⠢⠐⠠⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣧⠀⠰⠀⠠⠐⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢿⣄⠂⠐⠀⠀⣼⢧⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣿⠀⠘⠄⠐⠀⠌⢠⡿⠀⠀⠀⠀⣀⣤⣦⣶⣤⣴⠏⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠜⣿⡀⠈⠀⢠⣿⣿⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣇⠀⠻⡀⠈⠀⣿⠃⠀⠀⢠⣾⣿⣿⡿⢿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⢿⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣿⣀⣴⣿⣿⣿⣿⣿⣭⣟⢦⣀⣀⣀⠀⠀ ⠀⠀⠀⢻⣻⣆⠀⠱⣀⢩⣿⠀⠀⠀⠠⠟⠋⠁⠀⣰⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠙⣿⣿⠁⠀⢹⣿⡿⠿⣯⡻⡆ ⠀⠀⠀⠈⢻⣻⣦⠀⠉⢸⡗⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡶⠀⣿⣿⡀⠐⠈⢁⠠⠀⣼⣇⡇ ⠀⠀⠀⠀⠀⠙⢽⡷⣦⣽⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣝⣿⡼⣿⣧⡐⠈⣠⣤⢾⣫⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣧⠀⠀⠀⠀⠀⢀⣾⣧⣄⣀⢀⣀⣠⣾⠋⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⡇⠀⠘⢿⣿⣛⡿⠷⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠳⣶⣤⡴⣾⢿⡹⢮⡝⣯⢻⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣀⣠⣤⠿⢻⡞⣷⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠹⣷⡹⣎⢷⡹⢧⣻⣼⠿⣿⣄⠉⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣽⣧⣤⣀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣯⣞⣭⣻⣟⣷⡀⢀⠛⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⣧⡈⠐⢈⣡⣾⠏⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣓⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠶⠛⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣺⣿⣿⣻⢦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡿⠀⠘⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢿⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠖⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢶⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠖⠶⠦⠤⠤⢤⡤⣤⠤⣤⢤⡤⣤⢤⡤⠤⠤⠤⠴⠶⠒⠒⠒⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
૮・ᴥ・ა
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣠⠒⠈⠉⠐⠲⢤⡀⠀⠀ ⠀⠀⢀⠔⠊⠉⠉⠒⢄⠀⠀⠀⠀⣸⡱⢥⣶⠖⢊⣰⣁⠀⠰⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠘⠀⠀⠀⠀⠀⠀⠳⣀⠤⠊⠁⠀⠀⠀⠀⠀⠉⠙⠒⡼⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣸ ⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠧⡀⠀⠀⢀⡴⠁ ⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠤⠤⠤⠤⠀⠀⠀⠀⢘⡔⠋⠛⢿⣿⡒⠙⡆⠀ ⢇⠀⠀⣠⡤⠤⠤⢤⣤⠴⢃⠴⠚⢿⣿⣷⣦⡀⠀⠀⢸⣧⣀⣀⣼⣿⡇⠀⢱⠀ ⠘⢴⡋⠁⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠻⣿⣿⣿⠿⠁⠀⢸⠀ ⠀⠀⠉⠒⢠⡀⠀⠀⠀⠀⢿⣷⣤⣾⣿⣿⣿⡟⠀⣀⡠⠤⢤⠀⠀⠀⠀⠀⡜⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠛⠿⢿⡿⠿⠋⠀⠀⠳⢄⣀⠜⢀⠀⠀⠀⡴⠁⠀ ⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁⠁⣀⠴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠉⠒⣤⠤⣤⣄⣀⣀⣠⣤⠤⠤⠄⠐⠂⠉⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠋⡃⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⡵⠊⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⣠⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡞⢠⢖⠿⣑⣦⣇⢰⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⣼⣿⣉⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⢺⣹⢲⢽⠊⢿⢸⠀⠀⠀⠀⠀⠀⠣⠀⠀⠰⠽⢞⢙⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣧⠈⠋⠀⠸⠈⣆⠀⠀⠀⠀⠐⢄⠱⠀⠁⠲⡄⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠋⠉⠈⠓⠤⢄⣀⣀⣸⠼⠤⠤⠤⠤⠞⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⣶⠞⠀⠀⠀⢸⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀ ⠀⣠⡞⠋⠉⠉⠙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠀⢠⣾⡥⠤⠶⠶⠶⠾⣤⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀ ⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠛⠢⠤⠤⣤⡿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀ ⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣆⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⢻⣤⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⣈⣧⣄⡀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣠⣶⣿⣿⣿⣿⣷⡒⠚⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠙⣿⠏⢻⣷⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠖⠋⣠⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠸⣿⣧⡀⢀⣰⣿⣶⣿⡿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣴⡿⠿⠿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠹⣿⣿⣿⣥⣤⣿⠟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢸⡆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡤⠟⠁⠀⣾⠏⠀⠀⠀⠈⣿⠋⠉⢻⣷⠀⠀⠀⠀⠀⠘⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣄⡀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢀⣰⣿⣀⣀⣼⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⠛⢿⣿⣿⡿⠃⠀⠀⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣧⣤⣄⣼⣿⠟⠁⠀⠀⠀⠉⠻⢿⣟⠃⠀⣶⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠠⣦⣠⡾⠋⠉⠉⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠖⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠶⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⢋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠂⠀⠀⠐⠒⠒⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⢶⠋⠛⢶⡀ ⠀⠀⠀⠀⠘⣇⠀⢳⡄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⢼⣿⣖⣼⣇ ⠀⠀⠀⠀⠀⢻⡀⠀⠙⣦⣀⡤⠤⠤⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⣮⣭⡿⣿⡏ ⠀⠀⠀⠀⠀⠀⢿⡀⢀⡼⠋⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⠙⠛⠛⣳⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⣀⣤⡤⠤⠤⢬⡝⢦⡀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⠤⣄⢠⡖⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⣾⣏⢠⣴⣆⣶⣦⠹⢮⣧⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣻⣿⡇⣹⣷⣾⣧⠀⠈⣟⡆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⢷⠀⠀⠀⠀⠈⠛⢆⠀⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠈⠻⣍⠁⠻⣿⡿⠃⠀⠀⣿⢁⣠⠾⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⣸⣄⠀⠀⠀⠀⠀⢸⣤⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡙⢦⡀⠀⠀⠀⢀⡼⠟⠉⠀⠀⠀⠈⠙⠓⠢⢤⣤⣤⣤⣤⠤⠿⠾⠃⠈⠛⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠒⠦⠈⠓⠢⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⡶⠋⣿⣟⠆⠀⣀⠔⠀⠀⠀⠘⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠧⠊⢱⠁⣀⡨⠥⠒⠈⡎⠀⠀⠀⠀⡆⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠊⢁⡀⠀⠀⡰⠁⣾⣷⠀⢀⠇⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣧⡀⢹⡿⠆⠀⡇⠀⠈⢁⣴⠏⠀⠀⠀⡕ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠐⢌⣦⣀⣀⣜⠤⠔⢺⡅⠇⠀⣠⠖⠋⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⡜⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠻⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡏⠀⣇⠀⠀⠀⠀⡆⠀⢀⡄⠀⠀⢀⠻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡆⠀⢸⠀⠀⠀⢰⣃⣀⣈⡄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀ ⢠⠴⢒⣚⣉⣳⡀⡜⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸⣰⣁⠀⠀⠀⠀⠀ ⠘⠂⠀⠐⠃⣇⢹⠁⠀⠀⠀⢧⠀⠀⢠⠃⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠣⣀⠀⠀⣸⠓⠒⣏⠀⠀⠀⡰⠓⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠞⠉⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⠠⣄ ⠀⠀⠀⠐⠿⣿⠃⠀⣸⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡰⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠦⣤⣿⡑⠶⠄⢴⠦⠀⠀⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⢰⠂⣠⠔⠉⠉⠉⠈⠉⠑⠺⡤⢽⣀⢀⣀⣴⡟⠁⠀ ⢰⡙⡆⢀⣘⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣩⠙⢻⡍⠀⠀⠀ ⠀⠑⡽⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢾⡵⠛⠀⠛⢄⠀⠀ ⠀⡰⠁⣀⣇⠀⠀⠀⠀⠛⠀⠖⠒⠘⠃⠀⠀⣇⣀⡢⣮⡩⠇⠀ ⠀⠓⠒⠃⠨⠗⠠⠤⠄⠀⠀⠀⠀⠠⠤⠤⠚⠁⠀⠉⠉⠀⠀⠀
⠀⠀⠑⠂⠤⠜⠁⠀⠀⠀⢀⣀⣀⣴⠋⣉⠑⡶⠚⠋⠉⠙⠓⠲⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠯⢤⣤⡉⢿⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀ ⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⡳⣄ ⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠰⡀⢯⡽⠐⣐⠢⠀⠀⠀⣷⢸ ⣠⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡔⠁⡆⠘⡇⢀⡇⠀⠁⠀⡼⠀⣾⣹⠀⢸⠞ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⠏⡜⠀⠀⠀⢸⠇⠈⠀⠀⠀⠺⠇⡰⠀⠀⠀⢸⠀ ⣄⡀⠀⠀⠀⣀⡤⠤⠀⡽⠊⣆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⣾⠀ ⠈⢳⡀⠀⠀⠁⠀⢠⠀⣄⢀⡞⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣰⠏⠀ ⠀⠀⠳⡀⠀⠀⠀⠜⠀⠀⠉⣀⡤⠖⠒⠳⣦⡴⠛⠛⠛⣥⣤⡤⠶⠞⠋⠁⠀⠀ ⠀⠀⠀⠙⢦⣄⣀⣀⣀⡠⠚⠁⠀⠀⠀⣀⡿⢧⣀⣀⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⣩⠇⢠⠤⠴⠒⢚⠋⠉⠀⠀⠉⠉⢹⠀⠹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠇⠀⢻⣤⣀⡴⠋⠀⠀⠀⠀⠀⠀⣸⣄⣀⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⠿⠶⢶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⣠⣤⣶⣷⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠘⠛⠁⠀⣀⣼⣿⣦⠀⠀⠀⠀⠀⠙⣦⣮⣹⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠳⠶⣤⣄⡀⠀⠀ ⠀⠀⠀⠀⢀⣾⡿⠛⢀⡀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣉⣉⣉⣙⣧⠀ ⠀⠀⠀⠀⣼⠏⠀⠀⠀⣷⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⣿⠀⢿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣯⣤⡾⠃⠀⠀⠀⠈⠻⠶⣾⣿⣿⣿⣿⠄ ⠀⠀⠀⣸⡇⠀⠀⠀⢰⣿⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀ ⠀⠀⣰⡿⠀⠀⠀⠀⠈⢹⣿⡼⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁⠀ ⠀⣰⡿⢡⠂⠀⠀⠀⠀⠀⣿⣇⣰⣂⣠⠀⠀⠀⣟⣀⣀⠀⠀⠀⠀⠀⣠⣤⠶⠿⠿⠿⠛⠿⣧⠀⠀⠀ ⣰⡿⢠⣏⡔⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⢠⡀⠀⢿⣿⣿⣿⣍⣙⠛⢻⣏⣤⠾⣦⡀⠀⠀⠀⢹⡇⠀⠀ ⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣧⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⡿⣶⣾⣿⣶⣦⣴⡟⠁⠀⠀ ⠹⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠉⠉⠉⠙⠿⠟⠁⠈⠙⠛⢻⡿⠀⠀⠀⠀ ⠀⠀⠙⠻⣧⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⡴⣾⣿⣷⣶⣤⣤⣤⣤⣤⣶⠤⠶⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣴⣿⣿⣿⣿⠃⠀⠀⠀⢰⡟⢿⣿⣿⡿⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠙⢿⣿⠀⢠⠄⠀⡼⠀⢸⣿⢹⡇⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⡟⣸⠁⠃⠀⣿⣿⡀⠧⠀⣸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣴⣿⠀⠀⠀⣿⠹⡇⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣻⡿⢿⣆⢠⣿⠀⠁⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠋⠁⢈⣿⣿⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⢿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠜⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⣠⡶⢟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⣀⣴⠞⠋⡰⠋⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠾⠋⠁⢀⡞⠁⠀⠀⠀⠀⢠⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⡶⠛⠉⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠖⠒⠚⠛⠉⠉⠙⠛⠒⠲⢤⣄⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠤⠶⠶⠶⠦⠤⣤⣄⣀⣀⣀⣀⣾⠉⣡⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡎⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣡⡤⠟⠛⠳⢤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣰⠇⣠⡴⠀⠀⠀⠀⡸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣄⣠⣖⣲⣦⡤⠇⠀⠀⠀⠀⠀⠀⢀⣤⠤⠭⣵⣒⢶⣺⣷⢊⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⠶⠾⠛⠻⠿⣮⣁⠀⠀⠰⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣢⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣵⠾⠋⢳⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⢿⡉⢿⣾⠟⢯⣙⣲⣶⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠾⣟⡉⠀⠀⠀⠀⠈⠿⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡞⠉⢻⣿⢀⠞⣇⢿⣩⣟⢻⡛⣿⢿⢿⣿⣷⣦⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠙⢦⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⣴⡗⠀⠀ ⢻⡇⠀⠀⢿⣸⠀⠈⠀⠁⠈⠛⠿⠻⣏⢦⠶⢧⣙⢙⣧⡀⢀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⣿⣆⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣠⠞⣽⢀⣰⠀ ⠀⠁⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢉⣿⠾⡇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠹⡍⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⢻⣦⡷⠋⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⢀⣠⡇⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⣀⣙⣷⡦⡷⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⡾⠋⠀⣾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣰⣟⡾⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⡤⠶⠾⠟⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣻⡄⠀⣼⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣤⣼⣹⠟⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⣠⡾⠏⠀⢀⡤⠛⢹⠋⠋⢁⣿⠋⠉ ⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣤⣯⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⡾⠋⠁⠀⠐⣏⠀⢠⡏⠀⢀⡾⠋⠀⠀ ⠀⠀⠀⠀⣿⡇⢸⣆⠀⠀⣰⣿⣄⢸⢦⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⡾⠋⠀⠀⢰⠋⠉⣿⠛⠋⢀⣴⢟⣁⢤⡤⠀ ⠀⠀⠀⠀⢹⣽⣾⡜⢶⣾⠳⣿⣨⠿⠋⠀⠀⢀⣀⡤⠤⢶⣄⠀⠀⠀⠀⠀⠀⣸⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣀⡴⣟⠿⠀⠀⠀⠀⠸⠦⠼⠁⢀⣴⠟⠻⠽⠾⠭⠤⠤ ⠀⠀⠀⠀⠀⢿⡿⣧⣈⠽⠞⠋⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠈⢹⡟⠛⠻⠆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣥⣴⠟⠫⠛⠁⢠⠴⠲⡄⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠷⣄⣀⣀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⠾⠛⠉⠀⣀⣀⠀⠀⢺⣀⣀⡏⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣻⣄⠀⠀⠀⢀⣠⠾⢿⣿⣶⣦⣀⠀⡞⠉⢹⠃⠀⠀⢈⣡⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠉⠉⠉⠛⠛⠋⢁⣀⣀⠀⠉⠻⢻⡄⠻⠤⠏⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⡿⣟⣆⠀⢰⢦⠀⠀⠈⠧⣸⠆⠀⢀⣼⣁⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣽⣿⡀⠈⠛⠀⠀⠀⠀⣀⣤⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠿⠒⠋⠉⠀⠘⡻⢦⡤⠴⠶⠶⡛⡛⢉⣡⣞⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠛⠛⠛⠛⠓⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⠛⠛⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⡞⠀⠠⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢰⠃⢀⣶⣦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡟⠀⢰⠃⢀⣴⣶⣶⣦⡀⠀⠀⠀⠈⣷⠀⠀⠀⢸⠀⢸⠛⢿⣿⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⡇⠀⠘⢀⡟⠉⢻⣿⣿⣿⣦⠀⠀⠀⢸⡆⠀⠀⢸⡆⢸⣄⣸⣿⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⢹⣧⠀⠀⠘⡇⠀⠀⠈⣇⢸⣿⣿⣿⣿⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⢻⣿⠀⠀⠀⣇⠀⠀⠀⢹⡀⣿⣿⣻⢿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⣸⢉⡇⠀⠀⣿⡤⠤⠶⠚⠛⠛⠛⠛⠛⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡞⠛⠛⠻⠶⣦⣿⠀⠈⣇⠀⠀⠀⠘⣿⡭⣍⣡⠔⠁⣸⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡇⠀⠉⠓⠲⢤⣍⠻⢦⣌⠳⣄⠀⠀⠈⠛⠶⠤⠤⠞⠁⡞⢰⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠉⠻⣦⠙⢿⡮⣕⠦⢄⣀⡀⠀⢀⣀⣠⡇⠀⣿⣿⣶⣶⣤⣤⣴⣶⠏⣡⠞⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⣄⠑⢦⡈⠉⠉⠉⠉⠉⢳⠀⠸⡿⠿⢿⣿⣿⣿⡿⢠⣇⡴⢿⣀⣤⡴⠶⠒⠚⠛⠋⠉⠙ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⡆⠀⠉⠓⢤⣄⣀⡀⢈⣇⠀⠱⡄⠀⠙⣿⣿⠃⡼⠁⠀⢸⡋⠁⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⢣⡀⠙⠦⣄⡿⠃⣰⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⠀⠀⢠⣤⡤⢤⣽⣧⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⣀⡼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡎⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⣄⠀⠀⢀⣠⠞⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡞⠀⠀ ⠀⠀⠀⠀⠀⢧⡼⢦⡀⠀⠀⠈⠉⠉⠉⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠏⠀⠀⠀ ⠀⢀⡶⢶⣤⣸⠃⠀⠻⣄⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡾⠃⠀⠀⠀⠀ ⠀⢸⡇⠀⠈⢻⠀⠀⠀⠹⣆⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡴⠾⠋⠀⠀⠀⠀⠀⠀ ⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⠶⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣀⣀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠛⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣽⡛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⢷⡆⠀⠀⠉⠉⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠⣴⠟⣅⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢀⣠⣾⠟⠁⢸⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢀⣴⠟⣿⠃⠀⠀⠸⣿⣿⣷⡾⠃⠀⠀⢀⣠⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡾⠛⠁⣸⡇⠀⠀⠀⠀⠈⠉⠉⢀⣠⡴⠚⠋⣡⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠘⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠛⠋⠀⠀⢀⡿⠀⠀⣀⣠⣤⠖⠛⠛⠉⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢀⣾⢁⣴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⣶⣶⣦⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢻⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣿⣿⣿⠟⡇⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢸⣧⠀⠀⠀⠸⢿⣿⣿⣦⡀⠀⠀⠀⡟⠀⠀⠀⠙⠿⠿⠚⠁⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠘⣿⣤⣀⠀⠈⣿⣿⢿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢹⡍⠛⢷⣄⠉⠉⠁⠉⠀⠀⠀⣼⠃⠀⠀⠀⣀⣤⣶⠿⢻⣿⠁⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠻⣆⡀⢻⣆⠀⠀⠀⠀⢀⣼⣁⣀⣤⡶⠿⠛⣿⡤⠀⣼⠇⠀⠀⠀⢀⣤⡶⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⠶⠾⠟⠛⠉⠉⠁⠀⠀⠀⠛⣷⠀⣿⠀⠀⠀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⣿⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢹⣇⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣿⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⣀⡀⠀⣀⣹⣇⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣀⣤⣴⠾⣿⡀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣸⡏⠀⠉⠙⠛⠛⠋⠉⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣴⠾⠟⢋⣏⡉⠁⠀⠀⠹⣷⡀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡀⣰⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡁⠀⠀⠻⠟⠛⢻⣿⠛⣿⠛⢿⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⢸⣿⠟⠙⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠷⠶⠶⠶⠶⠶⠿⠋⠘⣿⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⣀⣴⡿⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣎⡉⠉⠉⠉⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠢⡀⠀⠀⢀⠃⠹⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡎⣀⣤⣄⠀⠀⠹⡄⠀⢸⢀⢿⣧⢃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⡆⠀⢰⠋⢻⣿⣷⡀⠀⣇⠀⢸⠸⣤⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⡇⠀⢸⣦⣾⣿⣿⣇⠀⢸⠀⠀⣇⣿⡿⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠤⢤⣸⡀⢃⠀⠈⢿⣻⣛⠝⡘⡠⠘⠊⠉⠉⠀⠀⠈⢉⠆⠀⠀⠀⠀ ⠀⠀⠀⡆⠈⠐⠮⣕⠮⣢⢄⠈⠑⠂⠚⢹⢱⣄⣀⡀⢀⣀⠄⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡀⠀⠀⠈⠣⡙⠅⠫⡑⠒⠒⠻⠀⢿⠿⣿⣿⡏⣮⢾⣀⠤⠄⠒⠒⠒ ⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⠀⠈⠑⠒⠀⠳⡈⢂⣘⡿⡰⠁⢸⠀⠀⠀⠀⠀⠰ ⠀⠀⠀⡶⠲⠷⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠈⠢⠤⠔⠁⠀⠀⡄⠀⠀⠀⣠⠁ ⠀⠀⠀⣧⢦⠀⠉⠒⠒⠉⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀ ⠀⡞⠓⠄⠀⠳⡀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠞⠁⠀⠀ ⡤⡇⠀⠀⠀⠀⠱⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⢣⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⢣⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠦⣀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡦⠤⠤⠤⠤⠖⠋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⢲⠚⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⣀⣰⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡏⢢⠀⠀⠀⠀⠀⠀⢠⢾⠽⣀⠀⠀⠀⠀ ⠸⡉⠙⠭⡐⠢⣀⡠⠜⠒⠂⠤⣇⠀⠀⠀⠀⠀⠀⠉⠑⡌⡭⠃⠀⠀ ⠀⠑⡄⠀⠈⣢⠈⢠⣶⡄⠀⡰⡿⢆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠈⢦⡰⠁⠀⠀⠉⠁⠀⠀⢻⣏⡇⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠒⡡⠔⢢⠤⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⠤⣀⠀⠀⠀⠉⠀⠀⠀⢣⠀⠀⠀⠀⠑⣄⡀⠀⢀⡀ ⠀⠀⡔⠁⢢⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⢱⠒⠚⠋⠁ ⠀⠀⠑⠒⠊⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⡜⠀⠀⡌⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠑⠤⣀⣀⠀⣇⠀⠀⣧⠒⠉⠈⢆⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⡔⠁⠀⠀⢸⠀⠀⡏⠀⠀⠀⢎⣀⠜⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠅⣀⡼⠀⠀⠀⠀⡎⠀⣀⠃⠀⠀⠀⠀⠀⢰⣒⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣴⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡀⠀⠀ ⠀⠀⢰⣿⠿⠏⠉⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⣹⣿⣿⡆⠀ ⠀⠀⣴⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠰⠋⣿⡿⣷⡄ ⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠘⠁⢠⡿⠁ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⢀⣿⠷⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⢠⡾⠁⠀⢀⠀⠀⠀⣠⣞⠋⠁⠀⠀⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⣈⣉⣳⣄⣀⡀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀ ⠀⣿⠃⢀⣴⣁⣴⠾⠛⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠛⠷⣦⣀⢢⡀⠈⣿⡀⠀ ⠀⣿⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⣿⡇⠀ ⠀⢹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀ ⢠⣿⡏⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀ ⣸⡟⠀⠀⠀⠀⠀⢠⣶⠟⠁⠀⠀⣰⣾⣟⠉⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠉⣿⣷⣄⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⡀⠀⠈⣿⡇⠀ ⣿⡇⠀⢀⠄⠀⣴⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣆⠀⠀⢹⣦⡀⢹⡇⠀ ⣿⡇⣠⡏⢀⣾⠏⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟⠋⠉⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠉⠙⠻⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⣿⣷⣼⡇⠀ ⣿⣿⣿⣁⣾⠃⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣿⣿⠿⠃⠀ ⠈⠉⣿⣿⠃⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀ ⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⣿⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠀⢸⣿⠀⠀⠀ ⠀⠀⣿⡀⢸⣷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠒⠶⠞⠛⠉⠉⠛⠳⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⣧⣸⡟⠀⠀⠀ ⠀⠀⠸⣧⣸⣿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠀⠀⠀⣾⠿⠿⠃⠀⠀⠀ ⠀⠀⠀⠙⠛⢿⣇⣰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⡄⠘⣿⡆⠀⠀⣧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡼⠀⠀⣼⣿⡇⢠⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣿⡿⣦⣀⣹⣷⡀⠀⢷⠀⠠⠶⠖⠚⠛⠒⠒⠂⢀⡾⠀⣠⠞⢁⣠⣾⠿⣿⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠈⠙⢻⡏⠉⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠁⠀⠀⣿⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⠟⠋⠉⢉⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠘⣿⠶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠹⣦⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠀⠈⠇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⢈⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡄⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣼⣷⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⢿⣇⠀⢠⠀⣠⠀⣀⢀⣾⡟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠾⢶⣦⣼⣾⠏⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣷⣿⣷⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢋⣃⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⢡⠏⠹⡄⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⡞⠀⠀⣧⣀⣠⣬⣧⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠙⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠘⣷⣧⡴⠞⠉⠁⢀⠜⠀⡠⠀⠈⠉⠙⠓⠦⠖⠋⠁⣀⡤⠶⣦⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⡰⠋⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠀⠀⡏⠀⢸⠇⠀⠀ ⠀⠀⠀⢀⡴⣫⣴⣦⠀⠀⡜⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠃⠀⡾⠀⠀⠀ ⠀⠀⣴⠟⢸⣿⣿⠏⣠⠞⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠀⣼⠃⠀⠀⠀ ⠀⣼⠃⠀⣸⣿⣯⣬⣁⠀⠀⡇⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀ ⢰⡏⠉⠉⠁⠸⣿⣿⠟⠀⠀⢳⠀⠀⠀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⢠⡀⠀⣠⠀⠀⠈⡆⠀⠀⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠈⢷⡄⠀⠀⠀⠛⠛⠉⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⣠⡤⠤⠤⢤⣤⣀⣀⣸⠁⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⢈⠉⠙⠓⢦⣄⠀⠀⠀ ⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⣠⡶⠛⢉⣤⠶⠚⠛⢶⣄⡀⠀⢀⣠⠾⠗⠲⢶⣄⠙⢧⡀⠀ ⠀⠀⠀⠀⢰⡟⠉⢉⠛⠳⣾⠋⠀⢰⠏⠁⠀⠀⠀⠀⠈⢹⣿⣟⠁⠀⠀⠀⠀⠙⢷⠈⢷⠀ ⠀⠀⠀⠀⠈⠳⣦⣧⠀⢰⠇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆ ⠀⠀⠀⠀⠀⠀⠈⠹⡆⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠀⠀⢀⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢉⣻⠶⢤⣤⣤⡶⢟⣁⣦⣍⡓⠦⡼⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⠔⠋⢀⣤⡄⢸⣿⢷⡘⣧⣈⣿⢁⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣞⠁⠀⠀⠛⢻⣥⢾⣇⡾⢧⣽⡦⠿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠬⠿⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡏⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⣗⠺⢧⣀⠀⠀⠀⠀⠀⠀ ⢺⡉⠛⠿⣍⡑⠲⠤⣄⠀⠀⠀⢀⣠⣧⣴⣧⣀⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⣄⣙⣏⣹⠀⠀⠀⠀ ⠈⢧⠀⠀⠀⠉⠲⣄⠈⠙⢶⠞⠉⠀⠀⠀⠀⠀⠈⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡿⠁⠀⠀⠀⠀ ⠀⠈⢧⡀⠀⠀⠀⠈⢷⠀⠀⠀⣴⣶⣦⠀⠀⠀⣰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⠀⠀⢠⠏⠀⠀⠀⠻⠿⠿⠀⠀⠈⠁⣼⣾⣶⠻⣆⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣯⣠⡏⠀⠀⠀⠀⠀⢸⣭⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠤⠚⠁⣠⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠘⣯⠉⠉⠉⠉⠉⠙⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⣠ ⠀⠀⠀⢀⡤⢤⡀⠀⠀⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣙⣒⣒⣶⡾⠟ ⠀⠀⢰⡏⠀⠀⢘⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀ ⠀⠀⠈⠳⠤⠤⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⡼⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢠⠇⠀⠀⣠⠾⣅⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠳⢤⣀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⢦⠖⠋⠁⠀⠈⢧⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡼⠋⠉⠓⠒⠚⣧⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣄⣀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠸⢦⣀⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠤⢤⡀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠒⠦⢄⣠⢖⣒⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣴⣿⣷⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⣹⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⡄⡀⠀⠀⣾⣷⠄⢀⠀⢸⠀⠀⠀ ⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⡉⠉⠀⠀⢐⠏⡇⠀⠀⠈⠉⡐⠁⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠄⠀⢀⡠⢼⣰⠀⠀⠀⢠⠤⣇⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⣀⠤⠧⢿⡢⢴⣤⠐⠊⠀⠞⠁⠀⠈⢻⡤⢯⢹⣋⣧⣟⢹⠊⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⢀⡴⠋⣧⡼⠊⠁⠀⢠⠟⠢⡀⠀⠀⠀ ⠀⠀⢹⠉⠉⠩⡉⠉⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⢸⠀⠀⠀⢸⡀⣰⠃⠀⠀⠀ ⣀⣀⣸⠀⠀⠀⠁⢰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣼⣤⣤⣤⣴⣋⣀⣀⣀⣀⣀ ⠀⠀⠀⣇⣀⣀⣀⣸⠀⠀⠀⠀⠀⢀⣀⠤⠒⠒⠒⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠈⠙⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⡴⡋⠀⠀⠀⡨⠓⣄⠀⢳⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡼⠀ ⠀⠀⠀⢀⡞⠀⢸⠓⠒⢺⡀⠀⠈⢣⠈⡇⠀⠀⠀⠀⠀⢠⡤⠴⠋⠀⠀ ⠀⠀⠀⡼⠒⠒⢏⠀⠀⠀⠙⣦⠖⠉⢧⡿⠀⠈⠙⡖⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⡖⢧⡀⠀⠈⣦⡤⠤⠊⡏⣀⡴⠊⡹⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀ ⢶⡞⡟⠦⣌⡓⠾⠥⠤⠴⠒⠋⣁⠴⢊⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⢉⣙⣒⣒⣒⣚⣉⠁⠀⢣⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠒⠒⠚⠒⠋⠉⠉⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣤⣴⡶⠿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠛⢦⡀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⠶⠚⠁⠀⠀⢰⠇⠸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⢡⣥⠀⠈⠻⠶⣤⣄⣀⠀⠀⠀ ⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠻⣧⠀⠀⠀⠀⠀⣼⣿⠁⣠⡾⠟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⢀⣼⣿⡟⢀⡿⠁⡜⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⡾⢋⣽⢿⣆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠛⢻⡏⠀⢸⡇⠀⣷⣴⣿⠇⠀⠀⠀⠀⠀⠀⢸⠁⣼⠃⢀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢿⡀⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣷⣾⣿⠀⠀⢹⡀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⣤⣀⢳⡶⠊⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⢻⣿⠏⠀⣀⣼⣧⠀⢀⡴⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⠀⠀⢹⡏⠀⠀⠀⢀⣾⣿⣿⣿⣷⣶⣤⠀⠀⠀⠀⠉⡋⢁⣤⡾⠟⠉⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠀⠀⣷⡀⠀⠀⢸⣯⡀⠀⢀⣹⣿⣿⠀⠀⠀⠀⠀⢹⡿⠟⠒⠒⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣈⡷⠄⠀⠀⠀⠸⣿⣦⣀⠀⠙⠛⠻⠿⠿⠿⠟⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠛⠛⠳⠶⠤⠤⠤⠤⠶⠾⠛⠁⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⠿⠛⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢦⣀⣀⣠⣴⡿⠋⠉⠙⠛⠛⠛⠻⠿⣷⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⣹⠋⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⡏⠉⠛⢻⣷⣤⣀⣀⣠⣴⡟⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡇⠀⠀⠘⡟⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⡜⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⠀⢸⣿⠀⠀⠀⡇⠀⣙⣿⣷⡄⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⢀⡜⠁⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⡄⢠⠞⡛⠋⠀⠀⠀⣷⠟⣍⠙⠻⢿⡆⠀⠀⠀⠀⣾⣿⣧⠴⠞⠋⢀⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠷⣿⣰⣁⣸⣆⣀⣤⣯⣠⣿⣄⣤⣶⣦⣤⣤⣤⣤⣶⣤⠤⠶⠶⠚⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠁⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣘⠭⡉⠉⠉⠇⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢜⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣧⠟⣶⣲⠒⠐⢤⡤⡤⢸⡇⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣹⠀⠻⢇⣀⡀⢸⡷⠀⢘⣷⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⠙⢧⣀⠀⠛⠄⠀⠀⡠⠂⠹⡀⠀⠀⠀⠀⠘⠀⠀⢠⡀⠀⠀⠀ ⠀⠑⠒⠉⣹⣶⣦⣤⣴⣦⣶⣶⣾⣉⠢⢄⣀⣀⠜⠀⠀⠀⡃⠱⡀⠀ ⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠣⡄⠀⠀⠀⠀⠀⢀⠃⠀⣱⡆ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠎⠀⢀⣾⠇ ⠀⠀⠀⣞⡇⠀⢐⠀⡄⠀⠀⠀⢰⡯⠈⠀⠀⠑⣦⡉⠠⠤⠴⣿⠷⠀ ⠀⠀⠨⠿⠇⠀⢸⠀⡇⠀⠀⢺⢿⣄⡀⠀⠀⠀⢰⠈⠉⠉⠉⠁⠀⠀ ⠀⠀⣧⣷⢠⠀⣸⢠⠗⡀⠀⣼⣼⣿⣅⢀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠁⠀⠁⠉⠉⠁⠈⠁⠈⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠒⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⢇⣶⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⣄⠀⠀⠳⣌⠑⢄⠀⠀⠀⠀ ⠀⣀⡠⠔⢃⢴⣇⠃⢀⣾⣿⣿⠔⠀⠀⠀⠀⢾⣿⣿⡦⠀⣟⣧⡌⠹⣄⡀⠀ ⢠⠏⢀⠀⠁⢸⡼⠀⠀⠉⢉⠋⠀⠀⠀⠀⠀⠈⢂⠉⠀⠀⠹⣿⠠⡐⢌⢻⠤ ⣺⡀⠐⠡⠃⢸⡇⠀⡀⠄⠁⠀⣴⣿⣿⣿⣷⡄⠀⠃⢀⡀⠀⣿⡆⡨⡑⢽⠃ ⠸⣗⡀⠈⡔⢹⡇⠈⣤⠀⠀⠀⠸⢿⣿⣿⠿⠁⠀⠀⣀⡘⢸⣿⠁⢐⢔⢼⡇ ⠀⠻⣤⠚⢁⣸⡗⡄⠻⣧⡀⠀⠀⣀⣾⣕⡀⠀⠀⣴⣿⠃⣼⡿⡠⣓⡴⠛⠁ ⠀⠀⠙⣭⣝⣿⣧⠆⠘⣹⡌⢽⠉⠁⠘⠀⠉⣿⠋⢰⠃⠀⣿⡇⢅⠏⠃⠀⠀ ⠀⠀⠀⠀⣷⡇⢹⢢⠀⠸⡳⡘⡆⠀⠀⠀⢰⠏⣠⠏⢰⡷⠀⢛⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡀⠈⣞⣄⠀⠑⡑⣝⢤⣀⠠⣪⣾⠋⣀⡌⠃⢀⣮⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠹⡟⡇⡀⠈⠊⢷⣶⡾⠏⠈⢈⣿⠇⠀⡘⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢫⡃⠀⠘⠋⡧⠄⣄⢦⡀⣄⢀⡴⠰⠏⠀⠰⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠁⠀⠉⢸⠏⠻⢂⠔⠁⠀⠀⠕⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀ ⢀⡤⠔⠦⣄⠤⠒⠋⠉⠀⠀⠀⠀⠀⠈⠉⠓⠿⣿⡎⡆⠀⠀⠀⠀ ⡎⣼⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡇⠀⠀⠀⠀ ⠙⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠃⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣀⣀⡀⠀⣾⣿⠴⠀⠀⠀⠀⠁ ⢧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠀⠀⠀⠀⢀⣬⡢⢀⣀⠀⠀ ⠘⣆⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠟⡷⠉⣦⠏⠀⠀ ⠀⠈⠲⣄⡀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⢀⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀ ⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⠀⠀⠈⠓⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢤⢀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢰⠁⠀⢸⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠦⠮⠀⠀⡜⠀⠀ ⠀⠀⠀⠀⡇⠀⠈⢆⠀⠱⡄⠀⠀⠀⠀⢀⠼⣴⢀⠀⡄⡀⢺⠀⠀⠀ ⠀⠀⠀⢀⠨⠦⠀⠈⠦⠄⠧⡀⠀⠀⠀⢸⠐⠉⠋⠁⠉⠊⢀⠇⠀⠀ ⢀⡠⡜⠁⠀⠀⠀⠀⡤⢄⠠⠜⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⠸⡀⠁⠀⢠⣀⠀⠠⢅⡉⠉⠈⣼⡀⠀⢘⡄⡄⢠⠀⣄⡄⠀⠘⠙⡄ ⠀⠈⠉⠒⠒⠚⠒⠒⠒⠓⠒⠚⠊⠀⠀⠈⠒⠓⠚⠒⠙⠒⠒⠒⠊⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠠⠄⠠⠀⠀⠀⠄⠦⠀⠠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡶⠶⠶⠶⠿⠛⠛⠛⠻⠿⠷⠶⢶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢿⣷⡄⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠉⠉⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⣿⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⣸⣿⠇⠀⣿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠘⣦⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣄⣀⣠⣼⠋⡿⠀⣼⡟⠘⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⣧⠀⣄⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⣿⣿⣿⡾⣃⣾⡿⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⠀⠹⡄⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠸⣿⡄⠀ ⠀⠀⠀⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⠛⢻⣻⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⢆⠀⠀⠀⠀⠀⢹⣷⡄ ⠀⣀⣀⣠⠞⠋⠀⠉⠛⠓⠢⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠷⠖⢺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢀⣼⣿⣇ ⡟⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⣠⣤⠴⠒⣶⠒⠒⠀⠀⠀⠀⠀⠀⢠⠇⠀⡟⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣤⡴⠛⠛⠛⠛ ⢣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⠟⢱⣄⣠⠇⠻⠀⠀⠀⠀⠀⠀⠀⡞⢀⡼⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀ ⠈⠻⡖⠲⠶⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠸⠴⠟⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢁⣀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠟⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠙⢆⢀⡴⡀⠀⠉⡉⠙⠲⠶⢤⣄⣀⡀⠀⠀⠀⢀⣀⣠⠴⠞⠉⠀⠀⢸⡟⠾⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠙⢦⡀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠹⣄⠞⠙⢦⣀⠀⡰⣌⠉⠉⢻⣋⠉⠉⣉⡀⠀⢠⡟⠲⣤⡎⠀⠀⠀⠀⠀⢀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠹⣄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠈⠳⠤⠻⠿⣦⣴⠁⠙⠦⠞⠀⠀⠀⠀⢀⣀⣀⡴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⠀⠀⢹⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⣿⡓⠒⠶⠶⠶⠖⠚⢛⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠚⠉⠁⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⣰⠟⠉⠛⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⢶⣤⡾⠃⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠏⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢠⣶⠖⠒⠲⠾⡆⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣀⣴⡶⠟⠋⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣴⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡼⠁⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⣇⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⢶⣦⣤⣀⠀⠀⢀⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣤⠶⠖⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠐⠢⡀⠀ ⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡤⠀⢰⠁⠀⡄⠀⠀⠀⢰⠀ ⡎⠀⠀⠉⠐⠢⡀⠀⢠⠔⠁⠀⠈⠉⠉⠙⠃⠤⡔⠀⠀⠀⡘⠀ ⢡⢀⡀⠀⠀⠀⠈⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡔⠀⠀ ⢀⠏⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢈⡴⢿⡷⡖⢊⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢸⠀⣪⣴⣶⣤⡀⠀⢻⣦⡔⣷⠇⠈⠀⠀⠀ ⠸⡀⠀⠠⠄⠀⠐⠊⢰⠁⠀⣝⢉⡇⠀⠀⠙⠋⠁⠀⠀⠆⠀⠀ ⠀⠈⠂⢤⠀⠀⠀⠀⠈⢿⣋⣹⡿⠁⠰⢿⡇⢀⠀⠀⡰⠀⠀⠀ ⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⢀⡔⠁⠀⠀⠀ ⠀⠀⢀⡀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠈⢢⠀⠀⠀ ⠀⠀⠋⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀ ⠀⠀⡆⢆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⣯⢷⣽ ⠀⠀⠱⣀⠏⠉⠁⠢⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡌⠙⢛⠏ ⠀⠀⠀⡆⢠⣎⢤⣴⠻⡆⡇⠀⠀⠀⠀⠈⠢⠀⠀⢀⡁⢘⠁⠀ ⠀⠀⠀⠱⣈⢋⠙⠋⢀⡧⠘⠠⢀⡀⠀⢉⣤⠧⢀⠀⠥⠊⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠑⠢⢤⣀⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠉⠛⠳⣦⣤⣶⠾⠛⠛⠛⠛⠳⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠿⣿⣄⣠⠶⢶⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠶⠾⢿⣶⣤⣶⣄⠈⢻⣧⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣄⠀ ⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢶⣄⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠻⣧ ⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠈⣧⠀⢻⣅⣨⡇⠀⢈⡉⠢⡀⠀⠀⠀⠀⠈⣿⡄⢹ ⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠖⠂⢢⠀⠘⣿⠀⠀⢹⡆⠀⠉⡹⠁⠀⠈⣿⠓⠁⣴⠶⣦⠀⠀⢹⣇⣼ ⣠⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⠏⠀⠀⢸⠀⠀⣿⠀⠀⣾⠃⠀⢰⠃⠀⠀⣰⠏⠀⢰⢿⣤⣾⠇⠀⢸⡿⠋ ⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣼⠇⢰⠃⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⡀⠠⠾⣿⠀⢀⡞⠀⠀⠀⠀⠀⢸⡇⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣟⣰⣇⠀⠸⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠳⣄⣀⣉⡴⠋⠀⠀⠀⠀⠀⠀⣸⡇⠀ ⣧⡀⡄⠀⠀⠀⠀⠀⢀⣤⣶⠶⠦⠀⢠⣤⠿⠁⠸⡆⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀ ⠈⠻⣷⠀⠀⠀⠀⠀⠉⠁⠀⠀⡀⠀⢸⣆⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢦⣤⠾⠁⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⣀⣀⣀⣀⣀⡤⠖⠃⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁⠀⠀ ⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠛⠻⠿⣦⣴⣿⠋⠉⠉⠙⠻⣧⣤⣤⣴⣶⡶⠿⠿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣤⣤⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠙⢿⣧⣤⣀⣠⣴⡿⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⡿⠀⠀⣀⣤⣤⡴⠶⠾⢿⡟⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⣿⡀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢰⣟⠁⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠈⢿⣶⣦⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣄⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⡷⠂⠀⢸⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠿⣧⡼⠁⠀⠀⠈⡦⠾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⡍⠢⣄⡀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣀⡇⠀⢰⡄⠀⠁⢀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠉⢙⠧⠤⣼⡏⢀⣿⠟⠑⣶⣉⠉⠉⠉⠛⠂⠤⠈⠉⢻⣿⣿⣿⠟⠁⠀⠀⠈⠓⠀⠠⢿⢀⡏⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣶⢷⠀⠀⠀⠈⠑⢄⠀⣰⣿⣿⠽⠓⡧⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣴⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡃⢘⣆⠀⢾⣄⡀⠈⢻⢉⡞⠁⢀⠜⠀⡀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⠈⠳⣌⣻⡥⠀⠀⠸⣄⠴⠛⠖⠊⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠘⠛⠿⠿⠿⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠳⣤⣴⡏⠉⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⠉⣉⣉⣀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⡇⠀⠀⣠⠾⠿⠻⠿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠞⠋⢀⣴⣾⠿⠟⠛⠛⠓⠦⣤⣴⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⣠⣶⣶⣶⣦⣄⡈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⣀⣤⣴⣶⣶⣶⣦⣆⠈⠙⠛⠛⠛⠋⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣼⠋⢀⣀⣀⣀⡉⠙⠢⡀⠀⠀⠀⠀⠀⠔⠁⢀⣾⣿⠟⠛⢻⣿⣿⢿⣿⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⡿⠿⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡁⠀⠀⣼⡿⠁⠈⣿⡀⢤⣶⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣘⣿⣿⣯⡀⠀⢀⣿⠙⢿⣄⠀⠀⠀⠀⠀⢸⡏⢻⣷⣶⣿⣿⣷⡀⠀⣿⠃⠀⠀⠀⠀⣀⣠⣽⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢏⠹⡇⢻⣿⣿⣿⣿⠀⢸⣿⠀⠀⠀⠀⠀⠈⠳⠀⠻⣿⣿⣿⣿⣿⣾⡟⠀⠐⠲⠿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣀⡹⣄⠙⢿⣿⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢌⣉⣻⡭⠿⠋⠀⠀⠀⠀⠀⠀⡈⠻⡟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠈⠓⠦⠤⠤⠤⠒⠂⠀⣠⡄⡰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡈⢢⠤⠜⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠗⠚⠓⠺⠿⣶⠀⠀⠀⠀⠀⠰⢶⣏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣤⣠⣤⠄⣀⡠⠧⢶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡾⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡀⢀⣴⣿⣿⡿⢆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢷⡆⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣈⡉⠉⠉⢀⣼⡀⠀⠰⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠆⠳⡀⠙⢦⠀⠀⠀⠀⠀⡀⢸⣿⠟⠁⠠⣾⣿⣿⣁⣀⡴⠿⠿⠂⡽⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⢢⡜⡩⠀⡄⠀⢀⣇⠞⡏⢁⠀⠀⠀⢀⣞⣿⡀⣿⠶⠖⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠓⠷⠤⠧⠤⠚⠉⠛⠦⠧⣤⣤⣶⣋⣀⣀⣀⢀⣀⢀⠀⠀⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠶⠦⠤⠤⠤⠬⠼⠬⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠶⠚⠋⠛⠲⢶⣄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠲⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⢀⣠⣤⣴⡾⠿⠟⠛⠛⠛⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⢀⣤⠶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠴⠋⠀⢠⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣍⡛⠻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠟⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠫⣉⣿⡶⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢀⣴⠖⠀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⢹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢸⠏⣰⣿⠛⢉⣽⣷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠘⢿⣧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠘⢸⣿⣧⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠈⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠙⣻⣧⠀⠀⠀⢹⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠉⠀⠈⢾⣿⡿⠀⠀⢀⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣀⣤⣤⣤⣶⣤⣿⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣀⠀⣶⡆⣰⣶⡟⠁⠀⣠⣾⡏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⡾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⠛⠛⠛⢛⣿⠟⠻⠶⠿⠛⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣀⠀⠀⠀⢀⣤⣴⠿⠋⠀⠀⠀⠀⣠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⠿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠋⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡟⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠿⠶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣠⣤⣶⡾⠿⢻⣿⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⠉⣿⠟⠛⠛⠙⠛⠛⠛⢛⣿⠟⠉⢻⣯⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⣅⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢲⣄⡀⠘⢶⡄⠈⢿⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀ ⣼⠁⠀⢠⣄⠀⠀⢳⣄⠀⠹⣷⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⢸⡇⠀⢸⣷⣀⣾⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣄⣈⠙⠛⢿⣦⡀⠀ ⣿⡄⠀⠀⣹⡆⠀⠀⣿⡄⣠⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠾⠿⠿⠟⠋⠉⠁⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢶⣄⠀⠈⠛⣿⡆⠀⠹⣧⠀ ⠘⠿⣶⡶⠿⠿⠶⠾⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣄⠀⠀⠈⢣⠈⠙⢻⣦⠀⠀⠀⠀⣿⡆⠀⠀⠀⢻⡇⠀⠀⣿⡇⢀⣼⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⣷⡀⠀⠘⢷⡄⠀⣿⡇⠀⠀⠀⠹⣿⣦⣄⣤⣿⣷⣴⣾⡿⠋⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⢀⣿⣇⠀⠀⣼⣷⣾⠟⠃⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⡟⠋⠛⠛⢛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣥⣤⣬⣤⣽⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣯⣭⣭⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⢤⣄⣀⣀⣀⣤⡴⠶⠶⠶⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠿⢧⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠉⠛⠲⣦ ⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⣴⡿ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡏⠀⠀⠀⠀⣠⣿⡉⠀⡄⠀⢷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢁⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⣉⠁⠐⠈⠁⣿⣿⡷⠄⢠⡀⣀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣼⣶⢦⣤⣭⣯⠀⠈⠛⢿⣿⣦⡀⢸⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⣤⣼⣿⠿⣿⣯⣦⣤⡀⠐⢆⡀⠀⠼⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠦⢤⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣧⣦⣖⣀⣛⠋⠰⠀⠀⠀⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀ ⠀⢀⣰⣆⠀⠀⠀⠀⠀⣿⡀⣷⣐⣶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⡉⢹⣿⣶⣄⣀⣶⣶⣟⣻⡿⠟⠁⠀⠀⠀⠀ ⢀⣿⠋⢿⣆⠀⠀⠀⠀⢿⣇⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⡇⢈⠉⠉⠽⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⡇⠸⣟⠀⢀⣤⠤⢶⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣧⡀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠐⠻⣦⣙⣷⠟⠁⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⣾⣿⠃⠀⠈⠿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠋⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠙⢿⡶⠚⠟⠀⠀⠀⡄⠀⠈⠻⣆⠀⠀⠀⠀ ⠀⠀⠀⣴⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠆⠀⣤⢠⣄⣤⡀⠰⣿⣿⡇⠀⠀⠀⠀⢻⣦⠀⠀⣠⣀⠃⣤⡶⠟⠛⢻⡇⠀⠀ ⠀⢀⣴⠟⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠉⠉⠙⠁⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⡸⠆⢻⣴⣠⣴⠟⠃⠀⠀ ⠀⢻⣟⣀⣀⣠⣿⠉⠉⠹⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠉⠉⠉⠻⠶⢾⠟⠋⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠉⠛⠓⠶⠶⠾⠿⠲⠶⣦⣬⣤⣄⣀⣀⣐⣀⣂⣀⣀⣀⣐⣀⣐⣠⣤⣤⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣞⠉⢡⠐⠒⠈⠀⠒⠒⢎⠐⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈⡄⠀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠥⠃⠀⣟⠊⠀⠸⠀⠀⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠀⡄⡆⠀⠀ ⠀⢰⠸⠀⠀⠀⠀⠠⠤⠤⢄⠀⠀⠀⠀⠀⢀⠃⠧⡀⠀ ⠀⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠄⡀⢨⠁⠀⠀⠈⡄ ⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⢀⠇ ⠸⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡎⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠀⠒⠂⠉⠀⠃⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀ ⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀ ⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⢸⢸⠀⠀⠀⠀⠀⢲⠤⠤⡔⠒⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⣰⢠⠀⡀⠀⠀⠀⡦⠀⠀⢇⠀⠀⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠈⠉⠉⠈⠈⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣾⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⣶⣤⣤⡀⢸⡇⢸⡇⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣡⡤⢞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠢⣍⠛⠻⣿⣯⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣧⡀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠈⠛⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡄⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⠋⠀⢀⣿⠁⠀⣀⣀⣠⡄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠟⠁⠀⠀⣼⡏⡔⠛⣿⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡾⠋⠀⠀⠀⠀⣿⣇⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢀⣿⡉⠉⠁⠀⠀⠀⠀⠀⠀⠐⠶⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡿⠃⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠈⠻⣶⣤⣤⣤⣴⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⢷⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣠⣴⡿⠋⠀⠀⠀⠉⠳⠀⠀⣸⠇⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠙⣷⣶⣄⡀⠀⠀⠀⠀⠀ ⠘⢿⣄⠀⠀⠀⠀⢀⣀⣤⡾⠻⢷⣆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠈⢿⡉⠻⣶⣄⠀⠀⠀ ⠀⠈⠉⠻⠿⠿⠿⠛⠋⠁⠀⠀⠈⠙⢷⣦⣄⠀⠙⣿⣉⠀⠀⠉⠉⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣀⣤⣾⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⣿⡀⠈⠻⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⣷⣦⡈⠛⠷⠦⠤⠤⠶⠞⠋⠀⣀⣖⣀⣤⣶⠾⣿⣿⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢹⣇⠀⠀⠹⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡶⢤⣀⣀⣀⣀⣀⣴⣾⡟⠙⣿⣿⣿⣀⣸⡿⠟⠚⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢹⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣀⣿⣿⣅⣠⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⠟⠋⠉⠁⠀⠀⠀⠈⠹⢦⣄⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠈⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢶⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⢀⣠⣤⣤⣀⡀⣠⡾⠋⠀⠀⠀⠀⢸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⠉⠉⠙⠛⠿⣿⣅⠀⠀⠀⢀⣴⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠛⣷⣄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡶⠛⠛⠛⠛⠳⠤⢤⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⣸⡇⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣼⣇⣠⣤⠒⠀⠀⠀⠀⠀⠀⠠⠖⠚⠛⠛⠛⠛⠻⠶⣤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣶⣤⣿⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠈⢷⡄⠀ ⠀⠀⠀⠀⠀⠀⣿⡀⠀⣴⠋⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠘⡇⠀⠀⠀⣿⡆⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣰⡇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣄⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⡿⠀⠀⢀⣠⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⣀⣸⠀⠀⠀⠀⣀⣀⣤⡶⠟⠁⠀⠀⠀⠈⠻⢷⣀⡀⠀⠀⠀⢠⡟⠀⠀⠀⣸⡏⣀⣤⡾⠋⠛⠶⠶⠶⢦⣾⣧⣤⣤⣴⣾⠶⠶⠿⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠾⠷⠶⠶⠾⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠒⠂⠄⡀⠀⠀ ⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠱⡀ ⠀⡠⠂⠁⠀⠀⠈⠁⠂⢄⢀⡤⡰⠊⡅⠀⢴⠁⠀⠀⠀⢀⠠⠐⠒⠠⡀⢡ ⠰⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠁⠀⠉⠀⠀⠛⠀⡔⠁⠀⠀⠀⠀⠈⠘ ⡇⠠⠒⠈⠀⠒⠠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠀⠀⠀⣀⠼⠃ ⠡⡇⠀⠀⠀⠈⡫⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⢦⣄⡀⢖⠒⠬⠂⠁⠀ ⠀⠙⢦⣄⡀⠀⣈⡏⣴⠋⠉⢳⠀⠀⠀⠀⢰⡅⠀⠀⣯⢷⠈⠆⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠈⢿⡸⣦⣤⣾⠀⠀⠀⠀⠈⠿⣖⣚⣥⠟⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠳⠶⠖⠋⠀⣀⢒⣀⡰⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠑⠤⠂⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡂⡤⠄⠀⠀⠀⡀⠠⠄⠐⠈⠉⠠⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣁⡰⠁⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⢰⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠁⠑⡀⠀⠀⠑⠂⡴⠖⢥⠀⠀⠀⠀⢸⠀⡰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠧⠄⠀⠀⢀⢡⠀⠀⡆⠀⢀⡠⠓⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠖⠒⠒⠦⢤⣀⡤⠤⠤⠖⠒⠒⠲⠤⠤⣄⣀⡤⠖⠒⢢⡀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠙⠲⣄⠀⣧⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢔⠀⢙⡟⢡⢄⡀⠀⠈⠳⣼⠀⠀ ⠀⣠⠻⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠓⠒⠒⠋⠙⠒⠚⠳⢤⡀⠀⠘⣆⠀ ⢠⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠸⡄ ⡞⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣧ ⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸ ⡇⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠾⠏⠉⠱⠀⣀⢀⢀⠐⠾⠉⠩⢆⢿⠀⢸ ⢧⠀⠀⠀⠀⢷⠀⠀⠣⣀⡠⠃⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠢⢸⠀⣸ ⠈⢦⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢠⠏ ⠀⠀⢓⢤⣀⠀⠀⠙⠲⠤⣄⣀⣀⣀⣠⠤⠤⠤⠤⠤⠤⠶⠚⣁⠴⠋⠀ ⠀⢠⠋⣇⠈⣩⠖⠒⠶⠤⠤⠤⠤⠤⠿⠦⠤⠤⠴⠖⠒⢿⠉⠁⠀⠀⠀ ⠀⠸⡇⢸⣰⠟⠠⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⢳⣠⠃⠀⠀⠳⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠴⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⠿⢒⠯⠭⠟⠛⠓⠶⢤⣄⠀⠀⢀⣠⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⠟⠉⠉⠙⣷⡄ ⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢦⣜⢷⣀⠄⠀⢸⡇ ⠀⠀⣀⣄⣰⡟⢀⡴⠒⠛⠓⠲⣄⢠⠞⠁⠀⠀⣀⣀⠀⠈⢿⣿⠀⠀⣼⡇ ⢠⡞⠉⠈⣿⣷⠋⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢸⣀⡸⡷⠀⠀⢻⣷⡾⠋⠀ ⣿⠀⠀⡠⢽⡏⠀⢠⠊⢹⣦⠀⠀⠀⢀⣀⡀⠈⠛⠛⠁⠀⠀⢸⡇⠀⠀⠀ ⣿⠀⠈⠀⠘⣿⡀⠘⠷⠿⠋⠀⠀⢎⠀⠀⠊⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀ ⠘⢷⣤⣠⣴⠿⣷⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⡀⠀⠀⠀⠉⣁⣠⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠉⠉⠈⢷⣄⣠⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠞⢻⡿⠁⠀⠀⡄⠀⠅⠀⠀⠀⠈⢿⡅⠀⠈⠻⡆⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⢀⣾⠁⠀⠀⠀⢷⠀⢀⡇⠀⠀⠀⠈⣿⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠘⣷⣄⢸⣇⠀⠀⠀⠀⢸⡆⣼⠇⠀⠀⠀⢀⣿⠀⣠⡾⠁⠀⠀ ⠀⠀⠀⣔⣋⠭⡛⣻⠿⢷⠶⠶⢶⠾⠿⡿⢦⣤⣴⠶⢿⣟⠛⡉⢉⣓⣦⠀ ⠀⠀⠀⠙⠗⣿⠜⠛⢻⣡⢴⣃⡼⠛⠋⠓⠚⠲⣕⡮⠽⠏⠳⠼⠒⠾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⢶⡤⢄⡀⢸⣆⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢋⠒⠲⠶⢦⣭⠗⠊⠙⠫⡻⣦⢀⣀⡤⠤⢲⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢆⢠⢾⠟⡻⠋⠀⠀⠀⠀⠈⠓⢄⠀⠠⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⠃⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠏⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣇⣀⡀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠈⡇⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢸⢙⣆⠀⠀⠀⣾⣇⣀⣽⣿⡆⠀⢸⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⡿⠿⠀⠀⠀⠘⣟⠻⡿⠋⡇⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠀⠀⠘⠃⠀⡤⠀⠀⠈⠂⠤⠜⠁⠀⠀⣻⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣤⣤⣀⡀⠀⠉⠀⠀⠀⢀⣀⢤⣤⣲⡤⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⡇⠈⠉⠀⠀⠀⠈⠁⠀⠀⡹⣗⡁⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢾⡷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⠀⠀⠉⠛⠦⡀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠠⠀⠈⠑⢄⠀⠀⠀⢀⠏⢸⠀⠀⠀ ⠀⠀⠀⣄⣲⣴⣸⠁⠀⠀⠀⠀⠰⣶⠁⠀⠀⠀⠀⢁⡠⠞⡃⢀⡏⠀⠀⠀ ⠀⠀⣲⠟⠉⠁⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⡾⠁⡼⠀⠀⠀⠀ ⠀⣾⡅⠀⠀⠠⢇⠀⠀⠀⠀⠀⠀⢸⢳⡀⠀⠀⢸⣴⠉⠀⣸⠁⠀⠀⠀⠀ ⢐⠏⠀⠀⠀⠀⠀⠉⠐⠲⢯⣄⡠⣃⣀⣳⡀⠀⠘⣿⡀⠀⢯⣼⣧⠀⠀⠀ ⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢢⣴⣜⡿⠶⢌⡮⠟⠀⠛⠋⠀⠀⠀⠀ ⠈⠙⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠁⠓⠺⠾⠶⠴⠤⢐⣤⡌⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⢤⣀⡀⣠⠔⠒⠲⢤⡀⠀ ⢀⠖⠉⠉⠑⣄⠴⠚⠉⠀⠀⠀⠀⡠⠊⠒⠠⡤⠉⣓⣦⣀⠀⠀⠹⡄ ⠏⠀⠀⠀⠀⢹⡀⠀⠀⠀⣀⠔⠈⠢⠀⠀⢀⢁⣀⣀⣀⣈⣳⣀⣴⣷ ⠀⠀⠀⠀⠀⠀⣇⣠⣔⣬⣤⣶⠒⠒⢃⠀⠈⡅⠈⣿⣿⣧⣀⣻⠿⡿ ⠀⠀⠀⠀⠀⠀⡏⠀⢸⣿⣿⣿⣷⣶⡏⠀⠀⠘⢄⠈⢻⣿⣿⣿⠀⡇ ⠀⠀⠀⠀⠀⠀⡇⢄⠀⠙⠿⠿⠿⡻⠁⠀⢂⣀⠔⠉⠀⠀⠠⠍⠺⡁ ⡄⠀⠀⠀⠀⠀⡧⠄⠁⠒⠠⠐⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⠀⢡ ⢣⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢣⠀⠀⠀⠀⠀⠁⠀⡜ ⠈⣆⠀⠀⠀⠀⡇⠈⠙⠒⣲⣤⢤⠤⢤⠤⠖⠒⠓⠤⡀⣀⠀⡤⠊⠀ ⠀⠸⡄⠀⠀⠀⡇⠀⠀⣸⠁⢀⡛⠂⠈⢏⢳⠀⠀⠀⡇⠀⠀⡇⠀⠀ ⠀⠀⢁⠀⠀⢸⠀⠀⠀⡇⠀⢢⠃⠸⣉⠇⣹⠀⠀⠀⢃⠀⠀⡇⠀⠀ ⡀⢀⡜⠀⢠⠇⠀⠀⠀⡇⠀⢺⠄⠀⠀⡞⡇⠀⠀⠀⠸⡀⠀⣇⠀⠀ ⠛⠂⠤⠐⠁⠀⠀⠀⠀⡇⠀⠈⡆⠀⢀⠇⡇⠀⠀⠀⠀⠙⠦⠈⠱⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢱⠀⠆⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠙⠃⠀⠀⠀⠉⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⢟⣥⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣠⣾⠟⠁⢸⣿⣿⣹⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⡴⠟⢩⡏⠀⠀⠈⠛⠛⠁⣀⡤⠖⢻⠏⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠋⠀⠀⡾⠀⣀⣤⡴⠒⠊⠉⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⢷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⣾⣿⣷⠀⠀⠀⣼⠁⠀⠀⠘⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⠁⠀⠀⣶⣶⣦⡀⠀⠀⢸⠃⠀⠘⠿⠿⠼⠀⠀⣼⠏⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢹⣦⣄⠀⣿⣿⢿⡗⠀⠀⣸⠀⠀⠀⠀⠀⣀⣴⡾⠃⠀⠀⠀⠀⠀⣠⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢧⠉⢷⡄⠀⠀⠀⠀⣠⠇⠀⣀⣤⣶⠟⠋⣿⠁⠀⠀⠀⣀⣤⠞⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠓⠶⠿⢦⣤⣤⡶⠷⠒⠛⠉⠁⠹⣯⢸⡇⠀⠀⣴⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡇⠀⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷⣰⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣤⠼⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⠋⠉⠛⠛⠛⠙⣧⠀⠀⠀⠀⢸⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠛⢩⣥⣄⣀⣀⣽⣧⡀⣸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⣆⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣦⣀⣈⣁⣨⡿⠠⡏⠈⢻⡟⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣼⣇⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣿⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⡿⠛⠛⠋⣿⠁⠀⠀⠀⠀⠀⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠤⠴⠟⠁⠀⠀⠀⠘⠷⢤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠔⠒⠒⠒⠤⣀⠀⠀⠀⢀⡀⣀⣴⣇⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣾⠿⠋⠋⠉⠉⠁⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢄⡀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⣀⠤⠐⠒⠒⣦⣤⡔⠉⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⢚⡿⠁ ⢣⢀⡞⠁⠀⠀⠀⠘⠻⡿⠂⠀⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣘⣄⠀⠀⠀⠀⠀⠀⠀⣀⢴⡚⣉⠀⠀⡠⠋⠀⠀ ⠈⢾⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⢼⡇⠀⠈⣿⢿⣘⣆⠀⠀⠀⣀⠔⢊⠤⠊⣁⣏⣠⠎⠀⠀⠀⠀ ⠀⠀⠑⠤⣀⣀⣀⣠⡆⠀⠀⠀⢀⣴⣿⠶⠶⣄⠀⠀⠀⠀⠀⠉⢷⣤⣴⣿⡤⠀⣸⣿⠽⢋⡠⠊⢁⡤⢊⡤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⡇⠀⠀⠀⣾⣿⠁⠀⠀⢹⠀⠀⠀⠀⣀⡀⠀⠈⠉⠉⣀⠼⢋⡡⠒⢁⡠⢒⡡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠛⣦⣤⣴⡿⠀⠀⠀⠘⠋⠁⠀⠀⡴⠊⠠⠖⢉⣀⡀⣩⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⠓⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⠤⠴⠃⠀⠀⡼⠉⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠚⡍⠉⠉⠉⣑⠄⠀⠀⠀⠀⢰⡤⠤⠖⠁⠀⠀⠀⣀⠴⠛⢒⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠻⠐⡞⠁⢒⡤⠒⠁⠀⠀⣀⠔⢂⠤⠊⠁⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⢘⣄⣠⢚⠔⠊⢀⠤⢊⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣶⣷⡏⠀⢀⡠⠒⢁⠤⠋⢁⡠⠂⡡⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⣱⠶⢯⠤⠊⠁⡠⠚⣡⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡼⣋⡿⠛⠁⡠⠔⣉⡴⠮⠤⠤⠤⠖⠒⠒⠒⠒⠒⠀⠀⠀⠒⠀⠤⠀⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡠⠖⢛⡼⠋⠁⣀⠔⢉⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠟⣓⠲⡁⢀⠔⢊⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣄⠿⠆⣟⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡜⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⣃⡔⠁⡇⠀⣀⣀⣀⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠱⡀ ⠀⠀⠀⠀⠀⢸⠏⠁⡠⠛⠙⢦⠀⠀⠈⠉⠙⢤⡀⠀⠀⠀⠀⢰⠁⠀⣠⡇ ⠀⠀⠀⠀⠀⢸⢀⠎⣰⡞⢢⢸⣠⣤⣄⡀⠀⡠⠛⢦⠀⠀⢀⡆⠀⠀⠛⡇ ⠀⠀⠀⠀⠀⢸⣿⠀⢿⣿⡿⣻⣿⣿⣿⣿⢎⣴⠒⡌⡆⣠⣿⠀⠀⠀⢰⠇ ⠀⢀⠔⢉⠉⠑⣟⢷⡀⢠⠠⣬⢿⣿⡟⠋⢾⣿⣿⢃⣗⣹⢻⣀⢠⢄⠟⠀ ⠀⣧⡶⠤⠤⡀⢸⠦⡻⡻⢇⠙⡿⠶⢏⣙⠦⡬⠋⠀⠈⠉⢸⣿⣿⣡⠄⠀ ⢠⣿⠯⠁⢺⠿⠯⠔⠋⢪⠙⠛⠶⠶⢳⣾⠟⠀⠀⠀⠀⢰⠬⣿⣏⠀⠀⠀ ⠀⡟⠀⡰⢏⣀⣀⣀⣴⠃⠀⠀⠀⠀⡏⠀⢀⡠⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠧⠔⠁⠀⠉⠉⢁⡏⠀⠀⠀⠀⠀⣇⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠷⢧⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠞⠳⢄⠀⠀⠀⠀⣠⣋⣀⢨⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⡹⡃⠒⠉⠉⠀⠘⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠖⠒⠲⠶⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣀⣠⢴⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⣈⠉⠉⠀⠘⠛⠿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠶⣖⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⣠⠞⠋⠉⠛⠚⠛⠦⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣿⡳⠻⣄⣀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠁⠀⠀⠀⢾⣷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣷⠀⠀⠀⠀⠀⠙⢟⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⢀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⣿⠓⠶⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠸⣟⣠⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠹⣄⠀⠀ ⠀⢀⡞⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀ ⢠⡾⠀⠀⣧⠀⠀⢀⣠⠴⠒⠚⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀ ⢸⡟⠀⠀⠘⣦⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣗⡀⠀⠀⠀⠀⠀⣀⣤⡖⠛⠀⠀⠀⢸⡇ ⠸⡟⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠲⠤⣴⣶⠛⢁⡞⠁⠀⠀⠀⠀⣸⠀ ⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠛⠀⠀⣿⡆⠀⣶⠀⣴⠋⠀ ⠀⠀⠈⡟⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡾⠉⠙⠛⠉⠀⠀⠀ ⠀⠀⠀⣇⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠳⠀⠀⢀⣀⣠⠤⠒⠁⠻⣄⣹⣤⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠾⠒⠗⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⢀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣷⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣠⠜⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⣲⣛⣿⡿⢿⣛⠛⠓⠒⠲⢶⣤⣤⣀⠀⠀ ⠀⣇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠿⣦⣀⣤⡴⠋⠁⠀⠀⠀⠀⠈⠛⠓⠲⠒⢚⣛⣦⣨⣿⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠹⣆⠉⠉⣩⣭⣉⣛⣛⣛⣛⣉⣉⣉⣉⣩⠉⢁⡞⠁⠀ ⠀⠀⠙⠲⠤⠤⠤⠤⠴⠋⠳⢄⡀⠀⠀⠀⠀⠀⠀⢸⣧⡿⠀⠀⠀⠀⠀⠙⢦⣀⣛⡻⠗⠿⢛⠛⠿⠶⠟⠀⠃⠀⣠⠞⠀⠀⠀ ⠀⠀⡀⠀⠰⠠⠤⠠⠀⠀⠀⠀⠉⡛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡿⣛⡿⠛⠉⠉⠉⠉⣻⡿⠉⠁⠈⠉⠙⠛⢯⣝⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣶⠿⠟⢻⣿⠟⠽⠋⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⢿⣷⠈⠙⠻⢿⣶⣄⡀⠀⠀⠀ ⠀⣰⡿⠛⠁⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠈⠛⢿⣶⣄⠀ ⢀⣿⠁⠀⢀⣀⣀⣿⣯⣤⣤⣤⣤⣤⣤⣀⡀⠀⠸⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣘⣿⣧⠀⠀⠀⠀⠀⠙⣿⡇ ⠀⣿⡄⠀⠘⣿⣿⠟⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠇ ⠀⢹⣷⠀⠀⠘⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡇⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⢻⣷⡀⠀⢿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⣠⣾⠟⠀⠀ ⠀⠀⠀⠙⢿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⡇⢠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠿⣿⠛⠛⠛⢻⡟⠋⠀⣀⣀⣀⣀⣀⡀⠈⠙⠛⣿⡛⠛⠋⠁⠀⠀⠀⣿⠹⣷⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠀⢻⣧⠀⠀⣸⡇⢰⣿⣋⣛⣛⣹⣽⣿⣷⡀⠀⠘⢿⣄⠀⠀⠀⠀⢰⣿⠀⠹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⠀⠘⣿⠈⣿⣿⡏⠉⢿⣿⠇⠀⠀⠸⣿⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠙⢿⣿⣸⣿⣿⠟⠃⠀⠀⠀⢠⣿⣶⣶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠀⠀⠈⣻⣅⠀⠀⠀⠀⠀⢠⣾⢋⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢿⣿⣿⣿⣿⣿⣷⣶⣶⢾⡿⣯⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣸⠋⠉⠉⡏⠉⠉⠉⢻⠈⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣶⣶⣶⣾⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣴⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣄⣀⣀⣀⡀⣀⢀⣀⢀⣀⣀⣀⣀⠀⠀⡀⣀⢀⣀⡀⠀⠀⢤⠀⡄⡤⢀⡀⣀⢠⣄⣀⠠⡄⠀⢠⢄⠀⠀ ⠀⠀⠀⠂⠋⡛⠛⡓⢃⠓⠚⠘⡛⠛⢛⠛⠛⠓⠘⠒⠓⠛⠃⠃⠀⠀⠒⠒⠃⠚⠛⠚⠓⠛⠚⠓⠛⠀⠐⠘⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠒⠀⠐⠒⢆⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣮⡁⠈⠙⠛⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠄⠀⠀⠀⠑⡄⠀⠀⠀⠀⠼⢖⠎⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠸⠀⠀⠀⠀⠀⠐⢄⠀⢀⠔⠒⠂⠣⠕⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠰⡾⠉⠒⣲⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠳⡂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⡀⠀⠀⢀⡔⠀⠀⠀⠀⠀⣡⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠒⠊⠀⠀⠀⠀⠢⠀⠼⠐⠂⢄⠀ ⠀⡐⢸⠁⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⢰⠅⠘⣄⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢀⡤⠄⠀⢸ ⠘⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⣲⡎⢱⡁⢀⠀⡸ ⠀⠈⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢨⠓⠚⠊⠀ ⠀⠀⢇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⢀⡠⠪⡠⣀⡠⠃⠀⠀⠀⠀ ⠀⠔⠚⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡿⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⡎⠁⠀⠀⠀⣀⣀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠃⠀⠀⠰⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢤⠒⣂⡩⠋⠛⠛⠭⠉⠁⠶⡂⣤ ⠀⢇⠀⠀⠀⢐⡄⠀⠀⠀⠉⠁⡰⡀⠀⠀⢫⠉⣠⣤⣶⣖⡦⡤⡤⠍⡩⠁ ⠀⠀⠉⠉⠉⠁⠈⠂⠀⠀⠀⠀⠛⠁⠀⠀⠀⠑⠒⠁⠁⠂⠉⠁⠀⠒⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⢉⠀⠈⠉⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠰⠚⢙⣰⣄⠀⠀⠀⢌⡗⡄⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠉⡙⠶⠤⡀ ⠀⠀⠀⡾⠁⠀⣆⣴⠋⠀⠀⠀⠀⠀⡄⢀⠄⠀⣎⠲⣿⣿⣿ ⠀⠀⢠⠇⠀⢀⣿⠃⠀⠀⠀⠀⠒⠻⠟⠁⠀⠀⠀⠉⢿⣿⡟ ⠀⢀⡞⠀⠀⠀⢸⡎⡀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠁ ⢀⡞⣜⠄⠀⠀⠸⣿⣿⣃⡄⠸⣿⣷⣔⣒⣯⡕⢄⡀⠀⣳⠀ ⠘⢿⣿⡄⠀⠀⠀⢻⣿⣿⡇⠀⠈⠛⠛⠛⠿⠝⠛⠿⣿⠁⠀ ⠀⠀⠙⢧⣀⠀⢀⣼⣿⣿⠋⠀⢺⣿⣷⣶⣶⣶⠗⠚⠁⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠉⠻⡇⢠⡀⡎⢸⡿⡁⢹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣣⡇⠀⣸⠇⠁⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡽⠛⣆⣿⠈⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⣶⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣰⣿⣿⡻⠟⠋⠉⠉⣻⠟⠉⠉⠉⠛⢯⡛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⣠⣴⠾⠛⢋⣿⠟⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠂⣹⣿⡈⠙⠻⢶⣄⡀⠀ ⣸⠏⠀⠀⠀⣾⣋⣀⣀⡀⠀⠀⠀⢸⠁⠀⠀⢀⣀⣀⣀⡀⠀⠈⠻⣧⠀⠀⠀⠉⠻⣦ ⢿⡀⠀⣿⣿⠟⣫⣽⣿⣿⣿⣿⣶⣶⣶⡶⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿ ⠸⣧⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⠁⢹⡇⣼⣿⣿⣿⣿⣿⣿⣿⠁⣼⡇⠀⠀⠀⣼⠇ ⠀⠹⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡇⠀⣠⡾⠋⠀ ⠀⠀⠈⢿⣿⢿⡿⠿⠿⣿⠟⠉⠀⠀⠀⠀⠙⠛⢿⡿⠿⠛⠉⠀⠀⡿⣷⣾⠏⠀⠀⠀ ⠀⠀⠀⠈⠋⠘⣷⠀⢀⡿⢰⣾⣟⣛⣿⣿⣷⡄⠀⢻⣆⠀⠀⠀⢰⡇⠘⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣼⠃⠈⣧⣼⣿⣇⣈⣿⠃⠀⠀⣿⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⠙⢿⡛⠉⠁⠀⠀⣠⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢶⣶⣾⣿⣶⣤⣤⣶⢿⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡼⠁⠉⠏⠁⠈⢹⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣾⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⡀⠀ ⠀⠈⠘⠛⠚⠛⠻⠛⠓⠃⠟⠻⠓⠐⠒⠒⠛⠁⠀⠀⠠⠇⠗⠟⠛⠚⠛⠒⠁⠐⠟⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠛⠓⢦⣠⠞⠉⠁⠈⠉⠙⠲⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⢀⠴⠛⠁⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠜⢛⠉⠳⢄⣀⠀⠀ ⣏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⡇⠀ ⠙⢄⠀⠀⢠⣿⢠⠞⡳⡄⠀⠀⠀⠀⢀⣠⡀⠀⢰⡏⠀⠀⠀⢀⡇⠀ ⠀⠀⠑⠰⢿⠃⣾⢸⣠⡇⠀⠀⠀⠀⠏⡞⢹⡄⢸⠁⠀⠀⠀⣼⠁⠀ ⠀⠀⠀⠀⠘⢄⡘⢌⠿⠁⠀⠀⠀⠀⡄⢷⣿⠃⢸⡀⠀⣠⠞⠁⠀⠀ ⠀⢀⠞⠉⠙⡎⠀⠀⣴⠶⢶⣦⡄⠀⠈⢛⣡⡴⠋⠑⠊⠀⠀⠀⠀⠀ ⠀⠀⣦⠀⠀⠹⣄⡀⠳⠤⠶⡿⠇⠀⠀⣸⠉⠁⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⡎⠀⠀⠀⠀⠉⠛⠉⠉⠛⠒⠒⠒⠋⠁⠀⠀⢠⣧⣄⡀⠀⠀⠀⠀ ⠀⠑⣄⣠⡴⠛⠛⠛⠓⠲⡶⢶⣦⣤⡀⠀⠀⢈⡟⠀⠀⠈⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠈⡿⣷⣶⠟⠀⠀⠀⠀⡞⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⢃⢼⠇⠀⢃⡬⢿⣦⠀⠀⠀⣼⣇⣠⠔⡸ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⣦⣇⣦⣤⢮⣼⣤⡼⢤⣤⣤⡭⠥⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠉⠉⠉⠀⠀⠀⠀⠈⠉⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠛⠛⠿⢶⣦⣄⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣨⣿⢷⣦⡀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⣦⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠙⢿⣆⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠙⣿⠶⣤⣤⣤⣴⣿⠃⠀⠀⠀⠀⠈⢻⣦⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣠⣴⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣼⡏⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣀⣀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⢀⣤⡶⠟⢻⣧⠀⢸⣇⠀⠀⠀⠐⠺⣶⣶⣤⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡟⠉⠀⠀⠀⢻⣆⢸⡏⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣴⣏⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣠⡾⢛⡿⠀⠀⠀⠀⢀⣼⡿⢿⣧⠀⠀⠀⠀⢀⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠉⠻⣦⡄⠀⠀⠀⠀⠀⢹⣦⣤⣤⣴⣶⠿⠋⠀⢸⡇⠀⢀⣠⣾⠟⠉⠀⣰⡿⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡀⠀⣀⣼⣿⣄⡀⠈⠻⣷⣤⣀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⣀⣼⣧⡾⠟⠋⠀⢀⣠⡾⠋⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣛⠿⠉⣿⠟⠿⣶⣄⡀⠉⠛⠿⠿⠷⣤⣤⣴⠶⠶⠿⠛⠛⠉⠀⠀⢀⣠⣴⠟⠋⢀⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠷⠾⣿⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠾⠟⠋⠀⠀⣶⠟⠋⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⣍⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢻⣄⣰⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢰⡿⠻⣶⣶⣶⣶⣶⣶⣶⡶⠶⠷⣶⣄⠀⠀⠀⣀⣼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣶⣶⡾⠿⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡇⠈⠐⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡒⠁⠀⠀⠀⠀⢀⠜⡀⠀⠀⠀⢡⠀⠀⠀⠀ ⠀⠀⠀⡐⡙⢁⢼⡆⠀⠀⢀⣧⣤⣀⠑⣧⠀⠈⡄⠀⠀⠀ ⠀⢠⠊⠀⢣⣼⣿⡿⠀⠀⢸⣿⣿⡿⡆⠘⠡⠀⠐⡄⠀⠀ ⠀⡆⠀⠀⢰⠵⠟⡧⣄⣀⡈⠿⣛⡫⠃⠀⡇⡇⠀⠈⢂⠀ ⠀⠱⡀⠀⠘⣶⣯⠻⢿⠟⠑⢆⡀⠀⠑⡤⡝⠀⠀⠀⢈⠆ ⠀⠀⠈⠒⢠⠤⠫⠋⠑⠀⠙⠒⡖⠒⠪⡁⠃⡀⢀⠠⠊⠀ ⠀⢀⠤⠊⣁⡰⠁⠀⠀⠀⠀⠀⢘⢀⠀⠘⡉⠀⠀⠀⠀⠀ ⠘⡀⠰⡁⠀⠀⠑⡀⡔⠈⠉⠐⡎⠀⢣⠀⠐⢄⠀⠀⠀⠀ ⠀⠀⠉⠑⡀⠀⠀⣠⡇⠀⠀⢀⠃⠀⢸⠠⠔⠊⡱⡀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠁⠘⠠⠄⠂⠀⠀⠓⠒⠀⠤⠧⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⢥⣄⡀⠀⢀⣀⡛⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠚⠉⢣⠚⠁⠀⠈⠚⢁⣀⠀⠑⡤⠇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠊⠀⠄⡇⠀⣰⣯⣷⡄⣼⣿⣷⡄⠸⣄⠢⠀⠈⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡏⠀⠀⠰⡟⢇⠀⢻⣿⣿⠇⠿⣿⡿⠁⢠⠋⡆⠁⠀⢀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡀⠀⠀⢸⡈⠒⢤⠤⢒⡺⠿⣒⠤⢴⢃⡾⠀⢠⠖⠁⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⣄⠀⢾⠘⡄⠀⠈⠻⣶⣾⠋⠀⠀⡸⢠⢇⡇⠀⢠⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⡷⣌⠒⠤⢀⠤⠥⠤⢴⡪⠔⢇⠈⠁⢠⠃⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⡄⠉⠑⠦⢄⡀⠴⠋⠀⣠⣎⣀⠔⠁⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢊⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢌⠢⡀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡎⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠘⡦⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⡄⠀⠀⠀⢀⡬⣦⠘⡃⠀⠀⠀⠀⠀⠰⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⡀⠀⠀⢱⢀⠀⠀⠀⣯⠙⠈⣇⠀⠀⠀⠀⢀⠇⡘⠀⠀⡇⠀⠀⠀⠀ ⠀⢀⠤⠒⠉⡠⢦⠊⠈⠀⠀⠀⢸⠄⠤⡞⠀⠀⠀⠀⣞⠀⠀⠀⠀⠧⢀⡀⠀⠀ ⡼⠋⠁⠀⠀⠀⡃⠆⠀⠠⠀⠀⢸⠀⢠⡁⢀⠀⠀⠠⡈⢇⠀⠀⠀⠉⠑⠪⡑⠄ ⠳⣀⠀⣀⡤⠖⠓⠦⠤⠴⠤⠤⠊⠀⠈⠣⣄⣇⣀⣠⡯⠞⠢⣄⡀⠀⠀⢀⣱⠜ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡨⠟⠾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠁⠘⠦⣀⣠⠞⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡀⡄⠀⢀⡆⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣧⣱⡄⡄⠇⠀⢀⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠉⢳⣿⣟⣟⠉⠘⠁⠀⠀⠞⠋⠑⡄⠀⠀ ⠀⠀⠀⢀⣴⣶⣷⣶⣶⣦⣵⣤⣄⡀⠀⠑⠂⠋⣠⣄⡀ ⠀⠀⢠⣾⣿⣿⢯⣷⣷⣮⣿⣿⣿⣿⡄⠀⠀⠀⠙⠋⠀ ⠀⢀⣿⣿⣿⣿⣞⡯⠯⣏⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢹⡠⠔⠂⠉⠉⠉⠉⣲⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡬⠂⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠔⠒⠒⠒⠤⣀⣀⡠⠖⠉⣉⠲⣵⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠓⡆⡜⠰⢁⣀⣀⠀⠀⠀⠀⠀⢀⣤⡬⡆⠘⡧⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⡇⡇⠀⣯⣼⣷⢃⠀⠀⡀⠀⣼⣼⡇⠁⢀⠃⡘ ⠀⢠⠖⠉⠉⠙⢆⠀⠀⠣⡀⠸⣧⠀⠻⣟⣋⠆⠀⠐⢤⠃⣞⠿⠕⢁⡬⠔⠀ ⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠓⢄⡀⠀⠈⢣⠶⡈⠍⣜⡠⠴⠓⠒⠂⡄ ⡇⠀⠀⠀⡠⠊⠁⠀⠀⠀⢎⡁⠀⠉⢣⠈⠉⠉⠑⠪⠅⠊⢄⠀⢠⡀⠠⠨⡆ ⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⡐⢠⠞⠂⡏⠁⢀⠊⠁⠙⡌⠀⠀⠈⠢⡁⠇ ⠘⡄⠀⠀⠘⠦⣀⠀⠀⠀⠀⠑⢓⡃⠄⢺⠀⠀⠸⣀⣀⠠⡓⠀⠀⠀⠀⠀⠀ ⠀⠈⠢⢄⡀⠀⠀⠉⠉⠉⠉⠉⢀⢤⠒⡓⠒⠤⡉⠯⠤⠚⡠⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠂⠀⠱⢁⣊⠠⠔⠀⠋⠢⠴⠠⠬⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠑⠢⠤⢤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠤⡴⠚⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⠈⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠉⠀⠀⠻⣦⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⢁⠀⠀⠀⠀⠀⠀⠀⠠⣬⢷⠀⠀⠀ ⠀⠀⢰⠋⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢸⠀⡤⣀⣠⠀⠀⠀⢾⣽⡏⣇⠀⠀ ⠀⠀⠘⡆⠀⠀⠳⡀⠀⠀⠀⢎⠀⠀⠀⠀⡞⠘⢸⣧⡾⠀⠀⠀⠀⢀⣀⠙⢦⡀ ⠀⠀⠀⠙⡄⠀⠀⠙⡄⠀⠀⠈⠳⡄⠀⢠⡇⠀⠀⠉⠀⠀⠀⡴⢒⢁⣾⠀⣠⠇ ⠀⠀⠀⠀⠈⣢⠀⠀⠘⠊⠉⠉⠉⠙⢦⡼⠀⠀⠀⠀⠰⡀⠀⠙⢚⡿⠓⠚⣹⠀ ⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⣀⡤⠞⠁⠀ ⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡆⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢾⠀⠀⠀ ⠀⡞⠀⠀⠑⢲⠤⣄⣀⡀⠀⠀⠀⢀⣰⠃⠀⠀⢰⣀⣀⣀⠴⡇⠀⠀⢸⠀⠀⠀ ⢰⠁⠀⠀⢠⠃⠀⠀⢸⠏⠉⠉⠩⡏⢹⠀⠀⠀⢸⠉⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀ ⡆⠀⡀⢠⠙⡄⠀⠀⠸⣄⠐⣆⣣⡸⢸⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢘⡓⢤⡀ ⠳⠶⠳⠜⠛⠁⠀⠀⠀⠈⠉⠈⠀⠀⢸⡄⠀⢄⠈⣏⠲⡀⠀⣧⠀⢱⠀⣹⡠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣼⣄⣼⠚⠃⠀⠈⠙⠉⠉⠁⠀⠀ ⣿⣏⣉⣍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⡤⣴⣶⣿⢿⣿⣿⣿⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀ ⠀⠀⡇⣿⠟⢁⣴⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⢄⠀⠀ ⠀⠀⢃⢻⣶⣿⣿⡟⠉⠁⠀⣀⣀⡀⠀⢀⡤⠤⢷⡀ ⠀⠀⢸⢸⣿⣿⣿⡇⠐⠊⠉⠉⠉⠉⠀⡌⠀⠀⠀⣧ ⠀⠀⢸⠸⣿⣿⣿⣷⢀⣀⣀⣀⣀⡤⠀⡇⠤⠔⠚⢹ ⠀⠀⠀⡆⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠏⠀⢀⠇ ⠀⠀⠀⡇⣿⣿⣿⣿⡆⠀⢯⣒⣒⣲⡶⠊⠀⢀⡞⠀ ⠀⠀⠀⡇⣿⣿⣿⣿⡇⠀⠀⠙⠭⠒⠓⠂⣠⠎⠀⠀ ⠀⠀⢠⠃⣿⣿⣿⣿⣿⠀⠀⢐⠒⠠⠤⠞⠁⠀⠀⠀ ⠀⢀⡞⢠⣿⡏⠉⢻⡿⢍⢩⢟⣦⣀⡀⠀⠀⠀⠀⠀ ⢠⠎⣰⣿⣿⡇⠀⠈⠷⡀⠼⠿⠘⢦⣱⠀⠀⠀⠀⠀ ⡎⢰⣿⣿⣿⣧⠀⢠⠽⠕⠀⠒⠒⠊⠙⢢⠀⠀⠀⠀ ⠳⡘⢿⣿⣿⣿⠀⠸⡄⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀ ⠀⠈⠑⡝⣿⣿⠐⠒⣿⣆⠀⠀⠀⠀⠹⣳⠀⠀⠀⠀ ⠀⠀⢀⢇⡿⠿⠀⠀⡿⠿⣧⠀⠀⠀⠀⢹⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⢤⣄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⣿⣿⣿⣿⣭⢻⣻⣿⣿⣿⣇⣤⡷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⠋⠁⠑⡄⠀⠉⠙⠻⣿⣵⡀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⡀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣤⡘⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠽⠿⣿⠿⢷⡄⠀⠀⠀⠾⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠊⢁⣶⣿⣿⣦⠀⢠⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⠂⠸⡟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⢀⣸⣿⣿⣿⣗⡧⡘⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣈⠉⠉⠉⠉⢁⠌⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡼⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣂⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀ ⠀⢐⣯⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠹⣿⣄ ⠀⠘⣇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢠⠃ ⠀⠀⣿⠀⠀⠀⠀⠀⠙⠦⣄⣠⣤⣤⣤⣀⣠⠟⠀⠀⠀⠀⠀⠀⣼⠀ ⠀⢠⠋⠀⠀⣀⠄⠒⠂⠄⠀⠀⠀⠀⠀⠠⠐⠒⣠⣄⣀⠀⠀⠀⣏⠀ ⠀⣧⣴⠖⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣦⣸⠀ ⠀⡿⠁⠀⠀⢀⠤⠂⢉⡁⠀⠀⠀⠀⠀⢀⡁⠐⠠⢄⠀⠀⠀⠈⢿⠀ ⢸⡇⠀⢠⡞⠁⠀⣾⣧⣿⣆⠀⠀⢀⣸⣿⣼⣷⠀⠀⠑⢄⠀⣄⠸⡀ ⢸⣵⢡⠋⠀⠀⢀⡿⠋⠉⠀⣉⣉⣉⠁⠉⠙⠿⠀⠀⠀⠀⠣⣸⣿⠃ ⠀⢹⠏⠀⠀⠀⠉⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠀⠂⠀⠀⠀⢹⡇⠀ ⠀⢸⠀⡄⠀⠀⠀⠀⠀⠠⠀⠤⠶⠤⠀⠤⠀⠀⠀⠀⠆⠀⠀⣨⡇⠀ ⠀⠈⠷⣇⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⡼⠛⠁⠀ ⠀⠀⠀⠈⢳⣸⣆⡸⡄⢠⠀⠤⠤⠤⠀⡆⠠⢃⡼⣿⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠀⢩⠉⠀⠂⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠶⠲⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⡿⠀⠀⠀ ⠀⠀⠀⠀⢠⡞⡇⠀⠀⠑⢄⡐⢄⠀⢀⠊⠀⠀⠀⢸⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⠀⢸⢃⣁⠀⠀⠀⠀⢁⠀⠀⡘⠀⠀⠀⠀⢸⢀⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⡄⠀⠀⢀⡼⠟⠛⢇⠀⢀⠀⢠⠧⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠓⠓⠓⠋⠀⠀⠀⠈⠓⠛⠚⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣜⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡌⠘⣀⣈⣆⣀⡀⠀⠀⠀⢀⡠⠤⠠⡄⠀ ⠀⠀⠀⢱⠗⠋⠁⠔⡡⠂⠈⠉⠐⠊⡡⠔⢲⠀⡇⠀ ⠀⢀⣴⣯⡄⢀⠊⡐⠁⠀⠀⠀⠀⠀⠱⡀⡘⢀⠇⠀ ⢠⠋⢸⣿⣕⠁⢰⠀⠀⢀⣀⠀⠀⠀⠀⠑⢁⠎⠀⠀ ⡎⠉⠀⡛⠛⠀⠘⡀⢠⣿⡿⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⢱⡀⠀⠑⠊⠀⠀⢡⠀⠉⢀⡠⠤⠤⠤⣀⣞⠀⠀⠀ ⠀⠙⠦⣀⠀⠀⢀⡤⢓⡫⠵⢄⡀⠀⣀⠦⠤⣙⢦⠀ ⠀⠀⠸⡉⡍⢹⠋⢠⠋⠀⠀⠀⠈⡿⠁⠀⠀⠈⡆⢇ ⠀⠀⠀⠈⢳⡜⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸ ⠀⠀⠀⠀⠀⢣⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⡏ ⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⡨⠙⡒⢶⣞⢥⢶⠅⡾⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⣊⠀⠚⣯⢿⡼⠼⠽⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠙⠳⡄⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⡿⠃⠀⠈⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠁⠀⠀⠀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠤⢤⡿⠀⠀⠀⠀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠛⠙⠳⢾⡁⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠳⡄⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⣾⡤⢀⠀⢠⣤⡀⠀⠉⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢹⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⠯⠉⠱⠟⠶⠌⠹⠭⠇⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠖⠒⠛⠓⠀⠀⠈⠉⠉⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣄⡼⣆⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀ ⣰⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⣰⠆⢀⡼⢦⠀⢀⡘⡇⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀ ⢻⡄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⢸⡆⢠⡄⠀⣤⠀⢠⠀⣠⡄⠀⠀⠀⠃⠘⡇ ⠀⠙⠒⠲⣄⣀⣀⣀⣹⣄⣀⣀⣀⣀⣹⣀⣀⣠⣴⣋⡼⠁⠀⠀⠀⢸⣅⣸⣇⣀⣿⣀⣸⢾⣍⣀⣀⣠⣄⣠⠾⠃ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⠒⠀⠀⠐⠒⠂⠐⠒⠂⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⡴⠃⠈⠀⠀⠀⠤⢀⠀⠀⠀⢸⠦⢄⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡠⠊⠀⠀⠀⠀⠀⠀⠈⠁⠐⠚⠁⠢⡉⠢ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⡠⠄⠒⠒⠒⠒⠀⠈⠘⡀⠀⠀⠀ ⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡤⠂⠁⠀⠀⠀⠔⢒⣀⡀⠐⠂⠈⢄⠀⠀ ⠀⠀⠀⠀⠀⠉⡛⠿⣿⣿⡇⠀⢠⠊⠣⣀⠔⠓⡀⠀⠀⣼⢶⣶⣦⠖⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⢸⠙⡄⠀⠙⣧⣀⠈⠒⠀⠑⢤⢶⣿⡦⡀⠀⠉⠉⠁⠀⠀⠀⡗⠀ ⠀⠀⠀⠀⠀⢘⠀⣇⠀⠀⣘⣹⣿⣿⠉⢂⠀⠏⠉⠉⡇⢀⡀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⢰⠞⠀⠋⠛⢿⣿⣿⣿⡏⠀⠀⠃⠐⡀⠀⠈⣈⡠⠔⡟⠀⠀⡘⠀⠀ ⡀⣠⣄⣰⡟⡆⡇⠀⠀⠳⣿⣿⣿⠃⠀⠀⡆⠀⠈⠢⢄⡉⠒⠚⠁⢀⠜⠀⠀⠀ ⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠙⢉⠀⠐⠒⠂⠀⠀⠂⢄⠀⠁⢒⡖⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠟⠐⠂⢄⡀⠤⢆⠀⠀⠀⠀⠔⡠⠐⠒⠈⠁⠁⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠐⠣⠀⠀⠸⠀⠀⠀⠐⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡐⡄⠀⠀⠡⠀⠀⠀⠑⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠗⢄⡀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠶⠶⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠦⠤⠤⠶⠞⢹⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⠀⠀⠀⠀⠈⠉⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡟⠻⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡄⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠶⢤⣤⠾⣆⣀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣤⡀⣰⡟⠀⠀⢀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣛⣝⠙⠻⣤⣤⢼⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠋⠁⠀⠀⠀⠀⢾⣳⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡇⠀⠀⠀⠀⠀⠀⠨⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⢹⡾⡷⢦⣀⣀⣀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡠⠿⠒⠋⠉⠙⢶⡄⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀ ⠀⠀⢀⡴⠋⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀ ⠀⢀⣼⠁⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆ ⢀⣾⣿⠀⠀⠀⢿⡀⠀⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠀⠀⠀⠀⢸⡇ ⠀⣿⣏⠀⠀⠀⠈⠳⣞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣿⣆⠀⠀⠀⠀⠀⠀⢀⣤⠶⣿⠋⠉⠀⠀⠀⠀⢸⡇ ⠀⢻⡟⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠓⠶⠤⣴⣶⡞⠋⠀⣼⠋⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢷⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠇⠀⠀⢹⣦⠀⠀⣤⠀⠀⣠⡾⠁ ⠀⠀⠀⠛⠷⣤⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠀⠀⠀⠀⢈⡟⠦⢤⣼⣦⠴⠛⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠟⣦⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠹⣤⠀⢻⣄⢀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⣘⣇⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⢀⣤⠴⠒⠛⠋⠁⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠛⠀⠀⠉⠀⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠛⠉⠁⣠⡴⠦⠖⠒⠛⠛⠳⣄⣀⣀⠀⠀⠉⢙⣻⡿⠲⢤⣄⠀ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣀⣴⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠎⠉⢉⣉⣹⣦⣠⣾⠇ ⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣷⡀⠀⠀⠀⠀⠀⠈⢷⡀⠉⠉⠉⢉⣉⡙⠓⠛⠟⠛⠛⠛⠉⠉⠉⠉⠉⢉⠉⠉⢁⡶⠁⠀ ⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⢀⣰⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣷⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠸⣟⣿⣿⡙⣿⢭⢽⣶⣟⣩⣿⡏⢹⡏⠉⠀⢀⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠳⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠷⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⠤⣌⣉⣀⣋⣠⣄⣈⣉⣉⣉⣀⣈⣀⣀⡴⠟⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⠀⠒⡀⡖⠒⠐⠂⠀⠀⠀⠀⠀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠑⡄⡜⠉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡆⡎⢣⢸⠰⠑⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣡⢸⡟⣼⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠠⠥⠾⠧⠼⠿⠥⠄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀ ⠀⠀⢠⠊⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠑⡄⠀⠀ ⠀⢠⠃⢀⣈⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡄⠘⡄⠀ ⠀⡌⠀⢰⣿⣭⣿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⣻⡏⠀⢡⠀ ⠀⢇⠀⠘⢿⡿⡿⣿⠏⠀⢀⠈⢛⣁⠀⠸⣿⣿⡿⣿⠇⠀⡘⠀ ⠀⠈⢦⠠⣐⠢⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠱⠀⠆⡰⠁⠀ ⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⢱⠒⡒⠒⣒⣿⣯⡽⡉⠀⠀⠀⠀⠀⠀⠀ ⢀⣦⡄⠀⠀⠀⠀⢀⡆⢀⠈⣸⡏⠸⣏⢀⢱⠀⠀⠀⠀⠀⠀⠀ ⠈⠋⢢⡸⠒⢰⣿⡳⣓⡀⠈⢗⠀⢩⠃⠀⠞⠿⣭⡆⠀⠀⠀⠀ ⠀⠀⠸⠇⠖⠛⠣⠔⠯⠧⠀⣀⣉⣁⡀⠀⠮⠚⠴⠷⠶⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠒⠲⠶⠶⣦⣶⣛⠛⠛⠛⢒⣺⣟⣀⣀⡀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠈⣩⠿⠋⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⠾⠛⠉⠉⠉⠉⠉⠉⠉⣿ ⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⣠⡤⠔⠃⢰⡟ ⠀⠀⠀⠀⠀⢸⠃⢠⡾⠁⡀⠄⢆⠀⣆⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣠⡿⠁ ⠀⠀⠀⠀⠀⢸⣠⣿⣧⡞⠀⠰⣌⣳⣾⠟⠛⣛⣶⣄⠀⠀⠀⠀⠀⣠⡾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢻⣿⠀⠀⢀⡾⢡⠃⡴⠋⠉⠈⠙⣷⡀⠀⢰⡟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⡇⢸⡇⠀⠀⠀⣠⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣠⠤⣀⣴⡿⡄⠀⠘⣇⢧⠘⣿⣶⠖⠚⢻⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀ ⣀⠀⣈⣳⡍⢧⢸⡇⠀⠈⠑⠤⣈⠊⠳⣜⣻⣦⣴⠟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠙⠒⣤⣌⡙⠎⡧⣿⢦⣴⢖⣷⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢼⡇⠀⠀⠀⠀⠀ ⠀⠛⢦⡤⢴⠒⠷⠌⠳⡤⠟⠒⠲⢄⠀⠀⡄⠀⠀⢠⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠒⠒⠩⠏⣡⠔⠀⠀⠀⢆⡆⠀⠀⢸⡴⠞⠋⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢀⣾⠀⠀⠀⢸⡇⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⢯⣋⣀⣿⡀⠀⠀⠈⣙⡻⢹⠀⢸⡇⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⠦⠤⠬⠿⣦⣄⣀⣰⣱⣃⣄⣢⣵⠤⠤⠥⠟⠀⠀⠀⠀⡀⢀⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣆⠭⠭⡁⠒⠂⠤⣀⠀⠀⠀⡰⠁⡠⠆⢒⡲⠖⠀⢀⡠⠔⠒⠂⡩⠭⢄⡄ ⣇⠐⠉⠉⢆⠀⠀⠈⡳⠔⠉⠀⠈⠠⢬⠤⣉⡐⣴⡉⠀⠀⢀⠎⠉⠑⢀⠇ ⠘⣆⠸⠁⠈⢆⠀⠀⢀⠠⡀⠀⠀⠉⠢⣱⠀⡨⢅⠀⠀⢀⠊⠀⠱⢀⡜⠀ ⠀⠈⠢⡀⠘⠿⠅⠈⣀⣄⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠐⠽⠇⠀⡠⠊⠀⠀ ⠀⠀⠀⣜⡢⣰⠀⣼⣇⠀⢈⣧⠀⠀⠀⢠⡏⠀⢀⣷⡄⢠⡰⣛⡀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⠀⣿⣿⠿⣿⣿⠆⠀⠀⣿⣿⡿⢿⣿⡇⡘⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠹⢕⡤⣼⠟⠀⡤⡄⠘⢿⠄⣔⠝⠁⢣⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⡔⠒⠒⠠⠄⣀⡀⠀⠈⠐⠯⠓⠈⠀⠀⣀⡀⠤⠐⠒⠂⣤⣄⡀⠀ ⠈⠀⠀⠀⠉⠢⡀⡔⠀⠀⠨⠉⠈⠉⠉⠈⠡⠀⠀⠘⡀⡴⠊⠁⠀⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠐⢂⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠑⠤⣀⡠⠔⠁⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠠⠐⠉⠀⠈⠑⠤⠰⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣽⠃⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⣤⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣷⡀⠉⠻⣦⣤⣤⣄⠀⠀⠀⠀⠀ ⠘⣇⠀⠉⠛⠶⣄⡉⠉⠳⢶⣄⡀⠀⠀⠀⣀⣠⣿⠤⠾⠧⢤⣄⣀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⢷⣤⣘⣇⣠⡿⠀⠀⠀⠀⠀ ⠀⢹⣆⠀⠀⠀⠀⠙⠷⣄⠀⠈⠛⢦⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⢳⣄⠀⠘⠁⠀⣤⣤⣤⡀⠀⠀⠀⠀⢰⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⢀⡿⡄⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⣶⠶⢻⣛⣛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢷⡄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠠⣾⣿⣿⡿⠙⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣦⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣁⣠⡿⠀⠀⠀⠀⠀⠀⠀⢿⣔⣢⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡴⠟⠁⢀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠉⠉⠀⣠⡶⠋⠉⠻⣦⣤⣤⣤⣤⠤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡇⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠳⠦⠤⣤⢤⢴⣾⠿ ⠀⠀⠀⠀⣴⠟⠋⠙⢳⣄⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⡟⠓⠲⠶⠶⠚⠛⠁⠀ ⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⢦⣤⣤⡾⠋⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣼⡋⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⠀⣀⣠⠶⠋⠁⠻⣦⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠉⠛⠶⣤⣀⣀⣀⠀⠀⢀⣷⠀⠀⠀⠀⠀⡟⣻⠋⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠉⠉⢹⡄⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠛⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⠤⠐⠒⠒⠢⠤⣄⡀⢠⠋⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠈⠑⢤⡀⠀⠀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡀⢉⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀ ⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⢷⡀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢳⡀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣶⣴⣾⡟⢦⣀⠀⣠⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⣦⠀⠀⠀⠀⣠⣿⣤⣤⣾⣿⡿⣇⠀⠀⠀⠀⠀⠀⠈⢹⠉⠻⣿⣿⣿⠃⣸⠈⠉⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢤⣀⠴⢏⠸⣿⣿⣿⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠿⠟⢋⡴⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⢆⡈⠻⠿⢷⡾⠃⠀⠀⢾⣻⣿⡇⠀⢢⠀⠈⠑⠚⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠒⠒⠋⠁⠀⠸⢄⣠⣽⣛⣦⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠉⡴⣿⠆⠀⠀⠀⠀⠀⢀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⣀⠠⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣇⠀⣠⠛⠋⠉⠉⠉⠙⢯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢰⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⡽⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⡞⠀⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⠲⣄⠀⡇⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡴⠋⠁⠀⠈⠙⢦⡻⡇⠀⠀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣄⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠙⢿⣀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡱⠂⠀⠀⠘⣄⠀⣠⠔⠒⠋⠐⠒⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢰⠁⠀⠀⠀⠀⠈⣟⠁⡔⠁⠀⠀⠀⠀⠀⣸⣶⠒⣲⢄⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣆⣀⣀⣀⣀⠤⢿⣇⣧⠀⠀⠀⠀⠀⢠⡏⡇⢠⡇⠀⠉⠢⡀⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠉⠉⠙⠓⠒⠓⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠒⠲⠤⣄⣠⡜⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠾⠚⠋⠀⠀⠀⠀⠀⠑⢷⡈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠠⠾⠀⠀⠀⠀⣤⡄⠀⠙⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⢊⠀⠀⠀⣰⣶⣶⣶⣄⡀⠉⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⢀⡏⢤⠒⠀⠘⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⠃⠀⠘⡇⠈⠣⣄⣀⣼⣆⠀⠀⠀⠈⡹⠢⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠀⠘⣄⠀⠘⣿⣿⣿⣷⣶⣶⡟⠀⠀⠀⣠⠃⠀⠀⠈⣇⠀⠐⣤⣀⠀⠀ ⠈⠒⠒⠒⠉⠈⠳⣤⡹⣏⡉⠉⡡⠋⠀⢀⣠⣾⠁⠀⠀⠀⠀⢸⠀⠀⠘⡌⠳⡀ ⠀⠀⠀⠀⠀⠀⠸⡿⢿⡆⣤⣤⣤⣞⣻⠯⠝⠒⢧⡀⠀⠀⢀⡾⠀⠀⠀⡇⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠒⢾⡉⠀⣀⠀⣰⠃⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢃⠀⠀⠀⠟⠉⠉⠙⢣⣀⠴⠃ ⠀⠀⠀⠀⠀⠀⢀⠏⢳⡀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⠀⠀⠳⡀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⡠⠒⠒⠣⠄⠀⠀⠙⣆⠀⡇⠀⠀⠠⠤⠼⢥⣄⠀⠀⠀⠐⠒⠒⠧⢄⠀ ⠀⠀⠀⡇⡔⠁⠠⠂⠀⠀⢀⡇⢹⠁⠀⠀⠠⠀⠀⡀⠘⡆⠀⠈⡆⠀⠃⠀⢀⠇ ⠀⠀⠀⠉⠳⠤⠧⠤⠤⠔⠋⠉⠉⠓⠤⣀⣸⣀⣸⠥⠞⠑⠒⠒⠃⠐⠓⠒⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⡀⠂⠄⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠄⠂⠄⡁⠂⣿⣿⣿⣿⡀⠀⠀⠀⢀⣀⣠⣀⣤⣴⣶⢶⣿⣿⠿⠿⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⢠⣌⣐⣶⣶⣷⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣯⣽⣩⣽⣾⡟⠁⡀⠂⠄⡙⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠠⠘⢿⣿⣯⣿⣽⣍⣯⡹⣍⢯⡹⣍⢯⡹⡹⢟⡻⢟⣿⡿⠋⡀⠂⠄⡁⠂⠄⡉⣿⣿⣿⣿⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⢂⠐⣠⣼⣿⣿⣿⣿⣿⣷⣼⣄⢧⡘⣄⢣⡓⣜⢣⢾⡿⢃⠠⢀⠂⠄⡀⠂⠄⡀⢸⣿⣿⣿⡤⣜⠻⢿⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢐⣶⣾⣿⣿⢛⡭⣋⡝⣹⢛⡟⣻⢿⣿⣶⢣⡝⡬⣳⣿⠃⠄⠂⠄⡈⠐⠠⢁⠂⡐⠸⣿⣿⣿⣿⣾⣿⣶⣶⣽⣿⣿⣿⣿⣿⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣬⣷⣾⣿⣿⣿⣷⣾⣿⣿⣯⣽⣶⣧⣳⣿⠍⠀⠌⡐⠠⢀⠁⠂⠄⢂⠐⠠⢸⣿⣿⣿⣿⣯⢹⣙⡛⢿⣿⣿⡍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣾⣿⡿⠿⡿⠿⠿⠿⢿⠻⣟⠻⣍⢯⡹⣍⢏⠿⡻⣍⢯⣹⣿⠇⠠⢈⠐⠠⢁⠂⠌⡐⠈⠄⡈⠄⣹⣿⣿⣿⣿⣿⣇⢮⡙⢦⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⢿⡟⢯⣙⣦⣳⣼⣘⢧⡹⢍⣏⡙⢢⡙⣤⠛⣬⢲⡱⢎⣎⢳⡱⣮⣖⣿⠟⠀⠂⠄⡈⠐⠠⢈⠐⠠⢁⠂⡐⠠⠀⣿⣿⣿⣿⣿⣿⣦⣝⣎⣎⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣾⣿⣿⣿⡿⢿⢿⣷⣿⣾⣶⣿⣷⣿⣶⣿⣦⣧⣷⣽⣦⣧⣷⣿⣿⣿⣤⡁⠌⡐⠠⢁⠂⠄⡈⠐⡀⠂⠄⡁⠂⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣯⣿⣿⣿⠟⣧⣿⡿⢫⡜⣣⠞⣜⢫⣏⣛⢻⢻⣿⠟⡿⢿⠿⡿⣛⢻⡛⢯⡹⢿⠻⣿⣷⣦⠀⡁⠂⠌⡐⠠⠁⠄⡁⠂⠄⡁⢻⣿⣿⣿⣿⣿⣿⡳⠼⣿⡏⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢏⢧⣿⡿⣛⡜⣣⠞⣡⠞⣬⢓⢦⡙⣎⠳⣎⠽⣘⠧⡛⢴⡩⢖⡹⢦⡙⣎⠳⡜⢿⣿⣷⣦⠁⠂⠄⠡⢈⠐⠠⢁⠂⡐⢨⣿⣿⣿⣿⣿⣿⣏⡳⣿⣷⠹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⢟⡣⣾⣿⢯⣵⣣⣾⣿⢿⣿⣿⣦⢋⠶⣙⢬⠳⣌⢇⢣⢎⡱⣊⠵⣋⣼⣇⠳⡌⢣⠙⣦⡙⢿⣿⣿⣦⣌⠐⠠⢈⠐⡀⢂⠐⢨⣿⣿⣿⣿⣿⣿⣿⡱⢿⣿⡱⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣍⠮⣽⣿⡿⣟⢻⢫⣽⣷⣾⣿⣿⣿⢎⡳⣹⣎⡳⡜⡬⣒⢎⠶⣩⠞⣡⠾⣿⣷⡘⢆⡹⣰⡙⢦⡛⢿⣿⣿⣷⣄⠂⡐⢀⠂⠌⢰⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣮⡙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⡱⢚⣌⠳⣍⠳⣜⣬⣷⣿⡿⣻⣹⡜⣿⣿⡎⣵⣻⡿⣱⠣⡕⣎⣾⣿⢔⡫⢖⡹⣜⢻⣿⣾⣵⣶⣙⣦⣙⣮⣹⣿⡭⢿⣿⣦⠀⠌⡐⢨⣿⣿⣿⣿⣿⣿⣿⣿⢊⢿⣧⡙⡖⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⢣⢎⣕⣣⣾⣿⣾⣿⠿⡻⣍⠶⣱⣿⡿⡍⢿⣿⣿⣴⣿⡷⣡⢛⡜⢦⣿⣿⣪⣿⢌⡳⣌⠯⣙⢿⣿⣯⢝⡻⣿⣿⣿⠿⣛⢬⡹⢿⣷⣦⡐⢨⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡧⣙⠾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⡿⢳⣌⢳⣱⣮⣽⣿⡟⡴⣙⠮⣿⣿⣿⣿⣇⠧⣫⢜⣹⣿⣿⣷⣿⣮⣕⢮⡱⣍⢮⣹⣿⣿⣼⣹⢿⣿⣿⣧⣮⣕⣣⢏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣷⡍⣞⡹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠿⠛⠉⣹⣿⡧⢣⡝⢣⡜⣣⢾⣿⣿⢏⡼⢱⣩⢾⣷⣿⣿⣿⣿⣮⠱⣎⡜⣿⣿⡰⣹⣿⣿⣷⣷⣮⣶⣱⣞⡿⣿⣿⣯⣟⣿⣿⣛⠿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢣⡛⣿⣾⣔⡣⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⡗⣣⠜⣡⠞⣡⣾⡿⢆⠯⣜⢣⣾⣿⣿⣿⣿⣿⣿⣿⣷⡜⡼⣸⣿⡵⡩⢿⣷⣹⢯⡟⣟⠻⣿⣿⣿⣿⣿⢞⡜⣻⣿⣾⣴⣋⠟⡞⡴⣩⠞⣛⠻⢿⠿⣿⣿⣿⣷⣭⣿⣿⣿⣷⣧⣿⣿⣿⡂⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⡓⢮⡱⣮⣽⣿⣋⢎⡳⣌⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣇⢇⢫⣿⣿⣶⡹⣌⢳⣬⣛⠶⣰⠌⠌⡸⡑⡞⢿⣿⣿⣾⣵⢃⢧⡹⣬⣟⡾⢷⣾⣿⣿⣿⣿⣿⣿⣯⢛⡿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣤⣶⣴⣶⣾⣿⣿⡧⣙⢦⡓⣿⣿⢻⡕⣎⡱⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⣏⢎⠦⢹⣿⣿⣶⣍⠿⣾⢿⣾⣷⣾⣷⣵⣹⣜⢣⢞⣻⣿⣿⠿⣢⠳⣾⣿⣧⢫⡜⣭⠹⡭⣍⢻⢻⣿⣷⣾⣭⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣷⣶⣶⣶⣿⣿⣿⡿⠛⠛⠛⠛⠛⠋⠁⢈⣿⣷⡍⣶⣭⢿⣿⣧⢚⡤⠳⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡜⣪⠜⣡⢎⣿⣿⣿⣼⢡⢏⡼⢫⢭⣹⣿⣿⣿⣿⣿⣷⣿⣿⡇⢧⢛⡬⢛⣿⣷⣾⣶⣽⣶⣿⣾⣿⣿⣿⣿⡛⢧⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡹⣿⣿⣿⢿⣎⠶⣙⢦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⢿⣿⣧⣛⠴⣪⠼⣿⣿⣿⣷⡎⡖⣉⠦⢣⢽⣿⣛⠿⣿⣿⣿⣿⣿⢣⢏⡜⣣⢎⠟⣿⣿⣿⣿⣿⣿⢋⡟⡻⣅⠻⣌⢏⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⡧⢸⣿⣿⠸⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣁⠫⢿⣿⣿⣿⣦⣿⣼⣿⣿⣿⣿⣜⢦⡹⣘⢎⣿⣿⡜⣼⣿⣿⠿⣿⣿⣾⣼⣡⣎⣝⡦⣍⢏⠿⣿⣿⣣⣞⠱⣎⠳⡜⠮⣔⣻⣷⡄⠀⠀⠀⠀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⡇⠀⢻⣿⣿⣜⡹⣿⣿⡿⠿⠿⠿⣿⠿⠻⢟⡱⢂⡑⢂⠩⡙⢿⣿⣿⣿⣿⡿⢈⣿⣿⣧⣗⡩⢎⣿⣿⣯⣿⠗⣿⣿⠰⣎⠽⡹⠿⢿⣿⣿⣷⣮⣝⣭⣻⣿⣿⣿⣦⣛⡜⡳⡜⣢⠟⣿⡄⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠸⢿⣿⣷⣿⣿⣇⠢⡑⢢⠐⡌⢡⠂⡔⢡⠘⡄⢃⠌⡩⢏⡍⡙⢩⠑⡌⢞⡋⠿⢿⣿⣯⣽⣿⣿⣿⠭⣿⣿⠱⣎⠳⢭⡙⢦⢣⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣣⣧⢫⠽⣿⣆⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢂⠻⣿⣿⣿⣿⡰⢁⠢⡁⢆⠡⡘⢠⠂⡅⢒⠨⢄⡑⢊⠤⠑⡂⠥⡘⠤⡑⢂⠍⡟⠻⣿⣿⣿⡿⡱⢻⣿⡳⣌⡛⢦⡙⣎⢿⣿⣿⢸⣹⣿⣇⠶⣌⣻⣿⣏⡟⢿⡿⣿⣧⣟⡼⣿⣄⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⠈⡔⡁⢢⠡⡘⠿⠿⢿⠣⢆⠡⢒⡈⠔⢡⢂⠱⢈⠢⡁⢆⡘⢄⢊⡑⢌⠰⣀⠣⡐⢡⠊⡔⢡⠂⣽⣿⢣⡝⡻⢿⡷⢬⡙⢦⡹⠜⡦⣿⣿⢦⡙⣿⣿⡞⡴⢻⣿⠞⣜⢣⠞⣿⣿⡿⠿⠿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡎⡀⠎⠰⡈⣀⠱⢀⠇⡉⠆⢱⠈⡆⢁⠆⡉⠆⢆⠱⡈⢰⠁⢆⠰⡈⡀⠶⢈⠰⣀⠱⠈⡆⠸⠰⢆⢹⣿⡇⢷⡸⢹⣿⣿⣇⠹⣆⢹⠹⡶⣿⣿⣆⢹⡈⣿⣿⡎⡹⣿⣿⡈⣇⠿⣸⣿⣷⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢂⠅⡒⠨⠌⡑⠰⢠⠑⡌⠰⡁⠎⡄⢃⠌⢢⠘⡐⢌⠂⢆⡑⠢⡘⠄⡃⠔⡡⢊⠄⢣⠐⡌⠡⢌⠡⢃⠌⢢⣿⡟⢦⡹⣹⣿⣿⣌⠳⣌⢧⢛⡴⢻⣿⣎⢧⡹⢾⣿⣿⡕⣿⣿⣞⡴⢋⡼⢿⣿⡄⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⢁⠊⠔⢡⠊⠔⡡⢂⠥⡈⢅⠢⡑⡈⢆⡘⠄⡃⢌⠂⡍⢄⠢⡑⠄⣃⠘⠤⠑⡄⢊⠄⡃⢌⡑⠢⢑⠨⡘⢰⣿⡙⢦⡓⡭⢿⣯⠜⡳⣜⣊⢧⢚⡽⣿⣏⠶⣩⠖⣻⣿⣿⣿⣿⣿⣷⣭⢚⣽⣿⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠔⡈⠜⡈⠔⡈⢆⠑⡂⢆⠡⠊⡔⢠⠑⡂⢌⠢⢑⡈⠒⡄⢊⠔⢠⠃⡰⠈⢆⠱⢈⠆⡘⡐⢢⠐⡡⠊⡔⠡⣾⣿⡙⢦⡹⡜⣽⣿⣍⠳⠦⣍⠶⣩⠞⣻⣿⡇⢧⢛⡴⣿⣿⣟⡻⢜⣿⣿⣮⣽⣿⡧⠀⠀⠀⠀ ⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⠐⠌⡰⠁⢎⠰⡈⠆⠱⣀⠣⢑⠨⠄⡃⠜⡠⠑⡂⢌⠡⢂⠅⡊⢄⠊⡄⢩⠐⡌⢢⠘⢄⡑⢂⠱⣀⠣⡐⠡⣿⣿⡘⢧⡱⣚⡜⣿⣮⣙⠳⣌⢳⡱⢎⡽⣿⣿⢎⡣⢎⡽⣿⣿⣷⢩⡜⣿⣿⣿⣿⣿⡀⠀⠀⠀ ⠠⣿⣿⠛⠛⠛⠛⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡘⢠⠑⡌⠢⡁⢆⡉⠒⠤⡘⠄⢣⠘⢄⠣⡐⢡⠘⡄⠣⠌⣂⠱⢈⠔⡈⠆⡡⢂⠅⡊⠤⡘⢠⠃⡐⢢⢁⠃⣿⣿⡙⢦⢳⡑⣎⢿⣿⣌⡳⣌⠳⣜⢣⠞⣹⣿⣧⡙⣎⠶⡹⣿⣿⣷⣎⡭⢻⣿⡟⠛⠀⠀⠀⠀ ⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⡐⠡⢒⠈⡅⠒⠤⣈⣱⣦⡕⡈⢆⠡⢊⠤⠑⡂⢅⠢⡑⢌⠰⢈⠆⡘⠤⠑⡄⢃⡘⠤⠑⡄⢃⠜⡠⢁⠆⡡⣿⣷⡙⢮⡱⣚⡜⣺⣿⣧⡳⣍⠳⣌⠧⣛⠼⣿⣿⡗⣬⠳⣱⣹⣿⣿⣿⣷⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠹⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⡑⠌⢒⡈⢑⢢⣰⣿⠟⡠⢑⡈⢆⠡⢂⠱⣈⠢⢁⠒⠌⢢⠡⡘⡐⢌⠡⡘⠄⡒⠌⡡⠘⡄⢢⠑⡨⢐⠡⣿⣷⣝⢦⡓⡵⢊⢷⣿⣿⡷⣌⠳⣌⠳⣍⢞⣿⣿⣿⣶⡙⢦⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠈⠻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠰⣈⣤⣼⣶⣿⠿⢋⠆⡑⢂⠌⡄⠣⠌⢒⠠⡑⢌⡘⠌⡂⢅⠢⡁⠎⡐⢡⢊⠰⢁⠆⡱⢈⠔⡨⢐⠡⢂⣿⣿⣿⣷⣿⣮⣽⣾⣿⣿⣷⣬⣷⣎⣷⣼⣾⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣧⡈⠹⢿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⡿⠿⢛⠩⡁⢎⠰⡈⠔⡡⢊⡐⢡⠊⡄⠣⢌⠰⣀⠣⢘⠠⡑⢄⠣⠘⡄⠢⡑⠌⡰⢀⠣⢌⠰⠁⠎⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⢿⣿⡉⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⢈⠡⣁⠒⢌⢂⠱⡈⠔⣂⠱⡈⠔⡂⢜⣤⡑⢌⠒⡨⠐⡄⢊⠄⠣⢌⠢⢌⡑⠄⢣⠘⠤⢑⡈⠆⡌⢢⢉⠒⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢠⠉⡄⢊⣴⣈⣶⣤⣦⣱⣼⣶⣾⣿⣿⣿⣶⣷⣷⣾⣶⣿⠿⡿⠟⡠⢂⠍⡰⢈⠆⡡⠒⡨⢐⠢⠌⢒⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⢿⣿⣿⣷⣿⡾⣿⠾⡷⠷⠿⠿⢿⣛⣻⣿⠿⣿⠿⠿⠛⠛⣻⡟⠛⣿⡍⣉⢉⡉⠩⢄⠃⡔⢡⠂⡅⢊⠄⠣⡐⢡⠘⠤⡁⢆⡉⢆⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣩⣍⣤⣴⣦⣴⣤⣸⡟⠁⠀⣻⣿⣶⠠⢌⡑⠂⠥⡘⢠⢊⠰⢁⠊⡅⡘⠄⡃⢆⠱⢠⠘⢤⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣿⢛⣛⣛⣿⣿⣿⣿⡏⠀⢀⣤⣿⣿⢿⣷⡆⠰⡉⠔⡈⢆⠢⠑⡌⠒⠤⠑⡌⠰⣈⠢⢁⠎⣜⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠛⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣷⣾⣿⣿⠏⢠⣼⣋⣴⣾⣾⡟⠉⢿⣦⡙⣿⡴⢈⠆⡑⠢⠌⡑⠤⢉⠢⡑⢨⠡⡐⢌⠢⡘⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣾⡟⣽⣯⢀⣾⣿⣿⢿⣿⠇⢠⣄⠈⣿⣷⣿⣿⣦⡘⠄⢣⠘⢄⠣⠌⣂⠑⡂⠥⢘⠠⡑⠌⢢⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢀⣿⣿⣿⣿⣷⢿⣿⠏⠀⣠⣿⣷⠿⢿⡿⣿⣿⣶⢉⠰⡈⠆⢢⠑⡠⠃⠜⡠⢃⠢⠑⡌⢢⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⣰⣾⡿⠟⣿⠀⢀⣿⢧⣶⣿⠟⠉⠈⠀⢸⣷⡈⣿⣿⠠⡁⢆⠩⡐⢌⠰⢉⠂⡅⢢⢁⠣⡐⢡⠊⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢛⣿⡃⢸⣿⠠⠿⠿⢟⣿⡏⠀⠀⠀⣠⡿⣿⡗⠈⣿⡆⠡⢌⠂⡅⢊⠄⢣⠘⡠⢁⠆⡑⠌⣂⠱⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⠆⢸⡿⠀⢀⣴⣿⣿⠀⠀⣠⣾⠟⢡⣿⣿⣇⣿⣿⠇⡌⢒⡈⢆⡘⠄⢣⠐⡡⢊⠄⢣⠐⣂⠑⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⣾⣧⣼⣿⣿⣿⡟⣠⣾⡿⠋⠀⣋⣿⣿⣿⣿⣿⣿⡐⠢⡐⢂⠌⡘⠄⢣⠐⡡⢊⠄⢣⠠⡉⢆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⢹⣿⡿⠏⠹⣿⢿⣿⡀⢀⣼⣏⣹⣿⡟⢿⣿⣿⡇⠱⢈⠆⡘⠤⢉⢂⠱⣀⠣⢘⠠⡑⠰⡈⢆⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⣠⣿⣿⡇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠈⢿⣆⠰⢁⠎⡠⠑⡌⠢⠌⢒⠠⡘⠄⡃⢌⠡⠒⠤⡘⢄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠁⠀⣴⣿⣿⣿⠏⠁⣿⣿⣿⣿⣿⣦⣿⣿⠀⠣⠐⢡⠑⡄⢣⠘⡄⠃⠜⠠⠑⡌⢢⠉⡔⠰⠈⠆⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠛⠿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠉⢿⣿⣠⣾⡿⣿⣿⠏⠀⢀⣿⣿⡿⢻⣿⣿⣿⣍⣌⣂⣱⣈⣔⣡⣌⣂⣱⣈⣄⣃⣆⣡⣊⣴⣵⣦⣵⣬⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠻⠛⠛⠉⠻⣿⠿⠙⢿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣠⣿⣿⣿⣿⣱⣿⠁⠀⣰⣿⡉⠉⢠⣿⠏⠙⢿⠟⠻⠻⠟⠿⠛⠟⠻⠛⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠙⢿⣿⣿⣿⢠⣶⠟⣿⡄⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠻⠿⠟⠁⠀⠸⣿⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣡⣥⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⠏⠸⣆⠀⠀⠨⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⢀⡟⠀⠀⢻⡀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠶⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⢸⡇⠀⢀⣬⣷⠶⠾⠛⡻⠛⠛⠳⠶⠶⣤⣄⣀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⢸⣷⠾⠋⠁⠀⠀⢀⡼⠁⢀⡴⠃⠀⠀⠀⠀⠉⠙⠷⠛⠉⠀⢀⣠⠶⠞⠛⣷⠀⠀⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠀⣠⠏⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⡟⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡟⣋⣒⡂⠀⠀⢀⡼⠁⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⢸⡇⠀⢰⡟⠀⠀⠀ ⠀⠀⠀⣠⡾⢫⣾⣿⣿⡿⠀⢠⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⢀⡟⠀⢀⣼⠁⠀⠀⠀ ⠀⠀⣼⢟⠀⣿⣿⣿⡿⢁⡴⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡾⠁⠀⣼⠇⠀⠀⠀⠀ ⠀⣾⠃⠀⠀⣛⢿⣯⣤⣏⡀⠀⠀⠰⡇⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⠋⠀⠀⠀⠀⠀ ⢸⡏⠲⠒⠛⠋⢹⣿⣿⣿⣿⠀⠀⠀⣧⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡅⠀⠀⠀⠀⠀⠀ ⣼⠁⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⢹⡀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⢹⣦⡀⣠⣶⠀⠀⠀⠀⢧⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠘⣷⡂⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢀⣀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢦⣤⡀⠀⠀⠀⠀ ⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⡛⢋⣁⣢⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣇⣀⣀⡀⠈⠻⣦⡀⠀⠀ ⠀⠀⠀⠀⠈⠙⢻⣶⣤⣄⡀⠀⠀⢀⣴⠟⠉⠀⣠⡿⠛⠋⠉⠉⠛⢷⣦⣤⣀⣀⣤⡾⠛⠉⠉⠙⠻⢶⡄⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⡏⠉⠉⢉⠙⠛⢿⡿⠁⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣿⠍⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⢿⡄ ⠀⠀⠀⠀⠀⠙⢷⣄⢸⡇⠀⢀⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡸⡇ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⠀⢸⡏⠀⠀⢰⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠂⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣾⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢰⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣦⣄⣀⠀⠀⠀⠀⣀⣴⡿⢛⠛⠷⣄⣀⠀⣸⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠛⠻⠿⣿⣿⡟⢫⣤⠼⣿⣶⡤⠉⣳⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⢀⡴⠚⠁⠀⣠⣶⡆⢴⣿⡿⣷⠈⣿⣦⣭⣿⢁⣴⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡶⠏⠀⠀⠀⠻⠿⢟⣃⣶⣶⢀⣾⣤⣈⣷⣤⣿⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣀⡀⠀⢻⣟⣠⣷⠿⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡖⠒⠒⠒⠒⠚⠿⣧⡀⠈⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠬⠗⡤⠄⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣴⣫⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠀⣤⣤⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⡇⠀⣿⣇⡍⠉⠁⠈⠛⣶⡖⢻⠓⠀⢿⣿⠀⠀⠀⠀⠀⠀⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡿⠉⣹⠃⠀⣿⣿⠇⠀⠀⠀⠀⣿⣿⡾⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣜⠀⢰⣷⡀⠀⠈⠉⠰⣶⡶⠄⠀⠙⠛⠁⠀⠀⠸⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢇⠀⠈⠙⣧⣄⣀⡀⠴⠛⠢⣄⠀⠀⠀⠀⢀⡔⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀ ⠘⢧⣀⣠⡼⠛⢿⣅⣀⡀⠀⠀⠀⠀⠀⠈⠁⣀⣀⣠⣼⠿⣄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠙⡟⠢⡀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠑⠦⣄⣀⣀⣠⠟⠁⠀⠀⠀⠀⠀⡇⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⢀⡾⡯⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠹⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢹⡴⡆ ⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠞⣿⣿ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⣾⣿⠇ ⠀⠀⠀⢀⣤⣼⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⡒⠒⠀⠀⠈⠢⢤⡀⠤⠔⠒⠁⠀⠀⢀⣴⣿⡽⠃⠀ ⠀⠀⠀⢀⡾⣽⡇⠀⠀⠀⡁⠀⢸⠃⠀⠀⠀⠀⡆⢠⣿⠿⠂⠀⠀⠀⠀⠀⠀⢷⣦⡀⠀⠐⠶⠾⠿⢿⣿⠟⠃⠀ ⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⠠⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠉⠉⠓⠒⠒⠊⠉⠀⠀⠀⠀ ⠀⠀⢠⠞⡉⢸⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣿⠘⣿⣶⣤⠄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣤⣷⡇⢰⠄⠀⠀⣿⣠⣾⢫⠀⠀⡀⢰⣿⣠⣿⣿⣇⢀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠙⠓⠼⠧⠜⠛⠃⠈⠳⣼⣷⣦⣼⣬⠋⠹⣿⣍⣉⣽⡤⠽⠭⠤⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠒⠒⠤⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⢣⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢞⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢃⣮⠤⣄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠒⠤⣀⢠⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠁⡎⠀⣠⣾⣷⡀⠀⠀⠀⠀⢀⣧⣶⣦⣄⠀⠈⢣⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⢸⡁⢠⣿⣼⣿⡇⠀⠀⠀⠀⣸⣟⣿⣿⣿⣿⡄⠀⢻⡣⡀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⡰⠁⠀⠀⠈⢧⣼⣿⠿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⣿⠀⠀⡇⠱⡄⠀⠈⠳⡀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⢰⣙⣮⣿⡿⢀⠀⠀⠀⠀⠘⣿⠯⠿⠭⠊⡼⠀⠀⢸⠀⢱⠀⠀⠀⠙⢄⠀ ⠀⢸⡄⠀⠀⠀⠀⢘⠁⠀⣀⣾⣟⣻⣳⣶⣦⠀⠈⠙⠲⠴⢮⣀⠀⠀⢸⢀⠏⠀⠀⠀⠀⠈⣆ ⠀⠀⢳⡀⠀⠀⠀⠸⡿⢿⣿⡉⠿⣿⡿⠟⠃⠸⠵⣀⡀⠀⠀⠈⢳⢀⢇⠎⠀⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠑⢄⣀⠀⠀⠈⢛⡿⢷⡤⢼⡁⠀⠐⢶⣀⣛⡃⠀⢀⣠⠾⠋⢸⠀⠀⠀⠀⠀⠀⢠⠏ ⠀⠀⠀⠀⠀⠈⠉⡳⠒⠋⣠⠊⠀⠀⠉⠉⠉⠉⠀⠀⡏⠉⡁⠈⢦⡀⠈⢣⣀⣀⣀⡠⠖⠉⠀ ⠀⠀⠀⢀⣠⠔⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⡁⠀⠀⢹⡉⠉⠉⠉⠀⠀⠀⠀⠀ ⢀⡤⠚⢹⠁⡠⠖⠒⠲⢅⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⠇⠳⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⡇⠀⠈⢿⠁⠀⠀⠀⠀⠙⢆⠀⣠⠚⠉⠀⠀⠈⢳⡏⠀⠀⠙⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⠢⠞⢇⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⢀⣠⠵⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢀⡧⢧⠀⠀⠀⠀⠀⡼⠀⠀⠀⢠⠧⠔⠒⠉⠀⠀⡌⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠉⠀⠈⢦⣀⣀⣠⣞⣀⣀⣀⣀⡸⠦⠤⢀⣀⣀⣀⣇⣨⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣣⠞⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⡿⠟⠒⠂ ⠀⠉⠙⠻⢿⣟⠛⠛⠿⠯⢭⣍⣉⠉⠙⠛⠒⠦⢤⣀⡀⣠⣿⣽⣟⣁⣼⣁⣀⠀⠀⠀⣀⣀⣤⠶⠞⠛⣩⡽⠟⠉⢁⡴⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠈⠉⠓⠦⣄⡀⣠⣾⣿⣿⣿⣏⠁⠀⢹⣿⣿⣿⣿⣿⣯⣀⠀⢀⡴⠛⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⢲⡀⠀⠀⠀⢈⡿⣫⣿⣿⠿⠛⠁⠀⠀⠀⠉⠛⠿⣿⣯⡁⠙⣶⠏⠀⠀⡖⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠙⠲⠤⣴⠋⢰⡿⢋⣥⢶⡖⠀⠀⠀⠀⢠⣤⣄⠈⠻⣧⠀⠈⣧⠀⣰⠇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣤⣀⣠⡏⠀⠉⢠⠟⠁⠀⢳⠀⠀⠀⠀⡾⠁⠈⠳⡄⠙⠀⠀⢸⣛⣡⣴⠋⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠟⠃⠀⠀⠀⠀⠙⠛⢶⣶⣶⣾⣷⠀⠀⢼⣷⣶⡶⠖⣿⠶⠚⠛⠉⠉⢉⣹⡿⣿⡖⠒⠊⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠲⢦⣄⣀⡀⠀⠀⠀⠀⠙⢧⡀⣿⢀⣀⣸⡇⠀⣠⠞⠁⣀⣤⠴⠚⣋⣩⣥⣤⣤⡿⢷⡤⠶⠒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣼⣧⣤⣶⡶⠊⣹⣯⣉⣛⠒⠶⠤⣄⣀⣻⢿⣯⣽⡿⢿⣾⣵⣾⡯⠿⠒⠛⢉⣩⠴⠲⡟⠻⡛⣿⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⢻⠏⢸⠀⡼⠁⠀⣹⠛⠿⠭⠽⠷⠿⡿⠀⠉⡏⠀⠀⠹⡯⠤⠤⠤⠒⠛⠉⠿⢄⠀⢸⠀⡇⢸⠻⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠣⠸⣤⣬⣷⣧⣀⣀⣉⣧⠤⠄⠀⠀⢸⡁⠀⠀⢧⠀⠀⢸⠁⠠⣀⣀⢀⣀⣀⡤⠤⣶⣿⣤⠧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡄⠈⠁⠀⢹⣠⣄⠀⠀⠀⢧⠀⢖⠚⠒⠀⣏⡴⡄⠀⠀⠀⡟⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢸⠇⠸⣾⠛⣶⠾⣦⣀⣉⣀⣠⡟⠀⢹⡶⣦⣼⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⠀⠀⠿⠀⠛⠀⠹⣮⣉⡭⢿⡇⠀⠘⠃⢿⢻⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣸⠃⠀⠀⠀⠀⠘⣷⣄⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠇⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠹⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡇⠠⠤⠤⠤⠤⢤⠤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡾⠀⠀⢀⡠⠖⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉⠈⠉⠓⠒⠒⠒⠒⠒⠒⠚⠋⢉⠄⠒⠁⠀⣀⠀⡄⠂⠀⠁⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠛⠛⠓⠲⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡾⠛⠉⠉⠛⢷⣄⠀ ⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢠⠶⢦⠀⢹⡆ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⠀⣸⠇⢸⡇ ⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⢀⣾⠃ ⠀⣸⠿⠖⠀⠀⠀⠀⠀⠰⠿⠿⠷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠟⠁⠀ ⠀⣿⢦⡀⠀⠀⠀⠀⢀⡴⠶⣒⣲⢶⣄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢸⣿⡏⣇⠀⠀⠀⢰⣏⣴⣿⣿⣿⣷⣜⣷⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⢸⣿⡇⣿⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⢸⠆⠀⠙⠿⣦⣄⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⢸⣿⣷⣿⢿⣿⡿⠿⣦⡻⣿⣿⣿⡿⢏⡾⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⣯⡿⣹⣦⡏⠀⠀⠈⠻⣶⡶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⣿⠃⢀⣿⣿⡀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀ ⠀⢿⣤⣼⣧⣼⣧⡀⠀⠀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠈⢿⡙⢿⣄⣘⣿⡶⠶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢻⣶⣤⣄⣀⡀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⢿⡄⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡿⠉⠛⠛⠻⠿⣧⠀⢠⣿⠤⠤⠴⠶⠶⠿⣿⣿⠃⠘⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡼⠁⠀⠀⠀⠀⠀⠠⠖⠂⠀⠀⠘⠷⠟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⠿⠟⠛⠉⠉⠙⠛⠻⠿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⣀⣤⣤⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠠⣾⠟⠋⠁⠋⠀⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⢶⡄⢨⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⢿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁⡀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠈⢉⣻⣆⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢻⡆⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡟⠀⣶⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⣿⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⢀⣴⠋⠀⠀⠀⠘⣧⣄⣙⢛⣻⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣶⠟⠁⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠇⢻⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⣰⣿⠃⣠⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⣰⣿⠃⣼⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣿⣀⣴⠆⠀⠀⠀⣿⣤⣤⣄⣄⣀⣀⣀⣀⠀⣠⣴⡶⢛⠛⠛⠛⠛⠋⠉⠻⣷⡄⠀⠀⠀ ⠀⣰⣿⠃⣸⡇⡼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⣆⠀⠀⢻⣿⣿⣿⣿⣯⣉⠙⠛⠙⠿⣁⣠⡾⢷⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⢰⣿⣏⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⠽⢿⣦⣤⣀⣀⣾⠏⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⣿⣿⣯⠴⠚⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⠉⢉⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠉⠀⠀⢠⣾⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣴⣷⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⢸⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⠿⠟⠻⣿⣿⣿⠇⠀⠀⡀⠀⠀⡿⠁⢸⣿⡟⢿⡏⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣼⠁⡄⢀⡇⠀⢸⣿⡇⢸⣇⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠏⣰⡇⠈⠀⠀⢸⣿⣧⡀⢿⠀⠀⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⠇⣠⣿⡇⠀⠀⠀⣼⡏⣿⠃⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣷⣄⡀⠀⣿⡇⠸⡇⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣠⣿⠿⠙⣿⣇⢰⣿⣇⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⣿⣿⣿⣿⣿⡀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠛⢹⣧⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠊⠉⠉⠑⠒⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡤⠚⠉⠀⠑⢌⠀⠀⠀⠀⠀⠀⢇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠊⢀⣴⣿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢠⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠇⢸⣿⣿⣇⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢨ ⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠱⡄⠀⠀⠈⠦⣻⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡸ ⠀⠀⢀⣔⢋⢵⠋⠉⢺⢝⣆⠈⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁ ⠀⠀⡞⠐⡎⡠⠵⠒⢭⡆⠙⡄⠈⡆⠀⠁⢲⠦⠤⠡⣄⣀⣀⣀⡤⠴⠚⠁⠀⠀ ⠀⡴⣧⡤⠃⢇⡀⢀⡨⠘⡲⢏⡹⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⢛⡶⢍⣋⡒⢲⡒⣎⣙⠶⠊⢀⠴⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡸⠁⠀⢸⠿⡿⠿⢼⠀⠀⠀⢾⠐⣞⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⣦⣤⣺⣴⠇⠀⠸⣀⣠⣤⣾⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⣀⠀⠀⠀⠀⢀⣴⡾⠿⠟⠛⠉⠛⠛⠿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠉⠀⠀⠙⣷⡀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣤⡴⠞⠉⠀⠀⠀⢠⡟⠀⢸⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡄⠀⢀⣤⣾⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣤⣿⠛⠉⡋⠉⠉⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠺⣿⠀⠀⠀⠈⠉⠛⠿⣷⣶⡄⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⣠⣶⣿⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀ ⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣾⣿⣿⠀⣰⡿⠋⢠⡾⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⣦⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⠀⣠⣾⣿⣿⠇⢠⣿⠁⢀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⡾⠿⣿⡄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⠁⠀⢸⣿⠀⢸⣿⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⣿⠁⠀⣼⣷⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠈⢿⡄⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣤⣴⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⣘⢿⣦⣈⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⢿⣿⣿⣿⠏⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣤⠴⢶⣦⣄⣹⠟⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣌⣹⣿⠟⠀⠀⣠⣾⣿⣧⡀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠈⠉⠉⢁⣀⣴⡿⠟⠉⠀⠸⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠙⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣾⣿⣫⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠘⢿⣷⣤⣤⣴⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⠓⠂⠀⠀⠀⠀⠘⣿⣿⣶⣤⣀⠀⠈⢉⣽⡛⠛⠛⠛⠋⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠛⠛⠉⠛⠻⠿⠶⣶⣤⣤⣤⣶⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⠿⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⣿⣿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠳⣦⣤⣤⣶⣿⠿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⢻⡿⠿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡏⠉⠉⠉⢿⣿⣶⣤⣀⣀⣀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢲⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⠀⠀⠀⠸⡟⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⡿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⢸⣿⠀⠀⠀⠀⡇⠀⠙⢿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⢀⡼⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠃⠀⣠⣾⣿⠀⠀⠀⠀⣧⠀⣠⣬⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⢀⣤⠞⠁⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢀⡟⢠⡾⢉⡉⠁⠀⠀⠀⠀⢸⡿⠹⣆⠉⠙⠻⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠴⠞⠋⠁⢀⣤⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣼⣧⣾⡃⡎⠀⢠⣇⠀⠀⣠⣿⡁⢸⣿⠀⢀⣠⣴⣍⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⠶⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⠟⠻⠿⠿⠿⠿⠿⠟⠛⠿⠟⠻⠿⠿⠿⠛⠉⠛⠿⢿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⡿⠛⠻⡉⠉⠛⠻⢷⣠⡀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⣀⣀⣉⠙⢿⡆⠀⠀⠀⠀ ⣿⠀⠀⠈⠢⠀⠀⠀⠈⠛⣦⣀⣀⣀⡤⠞⠛⠋⠉⢁⣤⣛⡁⠀⠀⢻⡄⠀⠀⠀ ⣿⠀⠀⠀⠀⢡⣀⠄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢉⣉⣓⣾⣷⡀⠀⠀ ⢿⡄⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⠤⡀⠙⣷⡀⠀ ⠈⣷⡀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⠀⠀⠀⠀⠸⣷⠀ ⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⢿⡆ ⡆⣿⠁⠀⠀⠀⢀⣠⣶⣯⣍⣽⣋⣉⣉⠀⠀⠀⠀⠀⠀⣠⣥⣤⡶⣶⠟⢻⣿⣇ ⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⡿⣹⠏⠙⣿⣷⣄⣠⣤⣾⣿⣿⡿⢰⠇⠀⣾⣿⡇ ⠹⣯⠈⠉⠉⠛⢻⣿⣿⣿⡿⢡⡟⠀⣰⣿⣿⠛⠛⠋⠹⣿⣿⠃⡿⠀⢸⣿⣿⣇ ⠀⣿⠀⠀⠀⠀⠘⣿⣿⣿⢣⡿⠁⢠⣿⣿⣇⠀⢀⣀⣤⣹⣿⣼⡇⣀⣿⡿⠈⣇ ⣼⠏⠀⡠⠔⠒⠊⠈⠛⠿⣿⣧⣤⣿⠿⢿⡄⠀⠘⣿⠿⠃⠈⠙⠛⠉⠁⠀⠀⢸ ⣷⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠔⠛⠒⠂⠀⠀⠀⠀⠀⠀⢀⣽ ⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉ ⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⢛⡿⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⠛⠛⠛⠿⣦⣀⣠⣴⣶⡿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣾⣟⠁⠀⣀⣤⣄⠀⠈⢿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣿⠟⠉⠀⢀⠈⠙⠻⣷⣶⠋⠁⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡾⠿⠟⠛⠛⠛⠛⠛⠿⠿⢿⣿⣷⣄⡀⠙⣿⡷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠙⢿⣆ ⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣦⠀⠀⠘⣦⡀⠀⣾⡟⠉⢻⣇⢀⠠⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠈⣿ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠘⣿⡆⠀⠀⢹⣧⠀⠹⢷⣶⣿⠇⠀⠀⢶⣤⣈⠳⡀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢸ ⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢀⣴⠋⠁⠈⣷⠀⠀⣿⣇⠀⠀⢸⣿⠀⠀⠀⢠⠏⠀⠀⠀⠀⣿⠉⠀⢠⡿⠛⢻⣦⠀⠀⢸⣿⣠⣿ ⣠⡶⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢀⡾⠁⠀⠀⠀⡿⠀⠀⢸⣿⠀⠀⣸⡿⠀⠀⠀⡟⠀⠀⠀⢀⣾⠇⠀⠀⡾⣿⣤⣴⡿⠀⠀⢸⣿⡟⠁ ⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢀⡾⠁⠀⠀⠀⠀⠁⠀⠀⣾⡿⠀⠀⠉⠁⠀⠀⠀⡇⠀⢀⣴⣿⡇⠀⠀⢰⠃⠈⠉⠁⠀⠀⠀⢸⣿⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⣾⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⠇⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣷⣴⠿⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀ ⣿⣄⣰⡆⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠿⠿⠗⠀⢰⣶⠾⠟⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠀⠀ ⠈⠛⢿⣧⠀⠀⠀⠀⠀⠀⠈⢋⠁⠀⠀⢀⠀⠀⠘⣷⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀ ⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠙⢷⣄⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣤⣄⠀⢀⣴⣶⠾⠿⠿⣷⣶⣿⡉⠀⠀⠀⣀⣀⣠⣤⣤⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠁⠀⠀⠘⠛⢿⣿⣿⠟⠒⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣧⣀⣀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣤⣀⣀⣀⣤⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠻⣿⣯⣤⣀⣀⣀⣤⣾⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢛⣿⠋⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣶⣿⠿⠿⠛⠉⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⡇⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⢰⣿⠟⠛⠛⠉⠉⠉⠁⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣿⣧⡄⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠘⣿⣷⣿⣤⣶⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣤⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠉⠉⠓⢦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀ ⠀⢀⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⣹⠟⢁⣀⣀⣇⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⡴⠁⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠐⠋⠉⠀⠀⠀⠾⠥⢀⣀⣸⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀ ⠈⢆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀ ⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⣩⣶⣿⣶⣤⠤⢴⡋⠀⠀⠀⠀⠀ ⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⢻⡟⢻⡆⠀⢳⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⢚⣥⣶⣶⣶⣦⣄⠀⠀⠀⠸⣿⣦⣠⠾⢷⣿⠇⠀⠀⡇⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⣰⠟⠉⠉⠹⣿⠿⢿⡇⠀⠀⠀⠙⢿⣿⠿⠟⠁⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠳⣄⠀⠀⠐⠊⠉⠉⠉⠉⠁⠀⠀⣿⡀⠀⢀⣰⣇⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⣿⣿⡟⠀⠀⢶⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠋⠀⠀⠀⡀⢉⣽⠤⠤⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠊⠁⠈⢢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⡼⢸⠁⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⣇⠸⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⠶⣎⠑⣆ ⠀⠀⠀⢹⡀⠱⣄⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠋⠀⠀⠀⠀⠀⠀⢰⣿⣃⠿⣷⣿ ⠀⠀⠀⠈⢧⠀⢈⠗⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠿⠿⢯⠏ ⠀⠀⠀⠀⠈⢳⠏⠀⢀⣀⠤⠤⠤⣝⢦⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣼⠤⠤⣄⡴⠋⠀ ⠀⠀⠀⠀⠀⣾⠀⢠⣾⣅⢴⡶⣾⠎⠻⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⡀⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⡀⠈⢿⠟⢹⣿⡿⠀⠀⡿⠀⣹⣄⠀⠀⠀⠀⠀⠀⠐⢦⠀⢱⠀⠀⠀⠀⠘⣄⡰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⣄⣳⡄⠈⠀⢀⡴⠟⠈⠀⠀⠙⠒⠠⠤⠤⠤⠤⠼⠶⠋⠑⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠐⠒⠠⠤⣠⠂⠀⠀⠈⠂⠄⡀⠀⠀ ⠀⠀⡠⠃⠀⢈⢢⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢸⠀⠀ ⡔⠊⠀⠀⠀⠀⠑⢄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠌⠀⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠆⠀⠀⠀⠀⠔⠁⠀⠀⠀ ⠀⠑⠠⡀⠀⠀⠀⠀⡘⠉⢳⡄⠀⠀⠀⠀⣼⣿⣤⣼⢢⡀⢀⢾⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢱⣀⠀⣠⢳⣶⣿⢻⠀⠀⠀⠀⠹⣈⣿⡿⢠⠀⠁⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠆⠁⠘⢌⡻⢷⠞⠀⠰⣶⡆⢠⠈⠒⠒⠁⠀⠀⢀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠰⠓⣻⡇⠀⠀⠀⢀⡀⠄⠊⠀⠀⢀⣀⡀ ⠀⠀⠀⠀⠀⠈⠂⠤⠄⠀⠠⠤⠄⠲⠤⠋⠉⠉⠉⢋⠀⠀⠀⠀⠀⡰⠁⡘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⢀⠃⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠨⣺⠀⢠⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡓⠌⡄⠀⣀⡸⢀⡀⢸⠀⠀⠀⠀⠈⡧⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡎⠀⠀⠈⣎⠐⠀⠀⠀⠸⡖⡢⢄⠀⠀⡁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠈⠙⠲⠤⠤⠐⠣⠦⠧⠤⠵⠐⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠙⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠶⠶⠖⠒⠚⠉⠉⠉⠉⠉⠛⠲⠦⣄⣠⠎⠀⢀⡄⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠙⠲⣀⠀⠀⠀⢀⣠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠳⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠑⢤⣚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀ ⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡖⠚⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀ ⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⣷⣄⠀⠀⢨⣿⣄⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⠈⢳⢦⣀⣠⡾⠃⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⢀⣾⣷⣦⣤⣶⣿⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⢿⣿⣿⣿⡿⠀⣸⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡷⣤⡀⠀⣠⣿⠁⢹⣿⣿⣿⣿⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣼⣿⣿⠟⠁⣴⠏⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠉⠉⠁⠘⣆⠈⠻⣿⣿⣿⣦⣠⡾⠀⠀⠀⢠⡤⣦⣤⣤⠀⠀⡀⠈⠙⠯⢭⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠳⣤⣈⡉⢉⣩⡟⠁⠀⡄⠀⠘⠶⣿⣷⠏⠀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠙⠦⣤⢶⣏⣉⣽⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠋⣴⡴⣳⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡷⠾⠷⠶⠶⠶⠶⠶⣖⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣀⣀⣀⣠⡤⠴⠶⡶⠚⠋⠙⠦⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣸⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⡀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠓⠶⣌⠳⣼⡇⠀⠀⠀⣼⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠈⠳⣜⣧⠀⠀⣰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠷⣄⠀⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣴⠆⠀⠀⠀⠘⢦⠀⠀⣠⡶⠖⠚⠉⠉⠑⠆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡼⠁⠀⠀⠀⠀⠀⠈⢳⡞⠁⢠⡞⠀⠀⠀⠀⠀⠀⠀⠈⣷⣴⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣧⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⠋⠀⡞⠉⠙⢦⣀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠤⠤⠤⠤⠴⠚⠋⢳⣷⣸⣆⡀⠀⠀⢀⣀⣀⣤⣇⣸⠀⠐⡇⠀⠀⠀⠙⢷⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠈⠉⣉⡉⢉⠉⠉⠉⠁⠀⠈⠉⠛⠚⠛⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⠛⠛⠛⠓⢶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠞⣰⣃⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠙⠛⠦⢤⡀⠀⣤⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠋⢰⠋⠁⠀⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⡀⠀⠀⠙⢦⡸⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠋⢠⡏⠀⢀⣾⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣄⠀⠀⠻⡽⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠞⠁⠀⢸⡇⠀⣸⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣧⣿⣿⣿⣿⣯⣦⠀⠀⢱⡙⣆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⣴⠃⠀⠀⠀⠀⢿⣀⡿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡏⣿⡄⠀⠈⣧⠘⢦⠀⠀⠀⠙⣦⠀⠀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⡽⢻⡙⢦⣾⡟⠀⠀⠀⠀⠀⠀⠘⣿⣽⣻⠿⢿⣫⠞⣱⠇⠀⠀⢹⠀⠘⡆⠀⠀⠀⠈⢳⡀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⢰⡷⠚⠛⠚⠛⣤⣶⣤⣄⣀⣀⡀⠀⠘⢷⣭⡉⠉⢁⡠⠋⠀⠀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⠙⡄⠀ ⠀⢿⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⣤⣸⣿⣦⣭⣭⣿⣿⣿⠂⠀⠀⠈⠉⠙⠛⠲⢤⡀⠀⠀⣼⢀⡼⠀⠀⠀⠀⠀⠀⠀⠹⡆ ⠀⠈⢧⡀⠀⠀⠀⠀⠈⢿⡧⢿⣽⡀⠙⢿⣿⣿⡿⠟⠁⠰⣯⠇⣀⡀⠀⠀⠀⠀⠙⣦⢀⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠻⠮⣷⣿⣄⣀⡘⡏⠀⠀⠀⣴⡦⠸⡯⠇⠀⠀⠀⠀⣠⣿⠏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⠀⠀⠀⠀⠈⠛⠶⠤⣄⣀⣀⡴⠋⢁⡽⠋⠙⠷⠤⠤⠤⠥⠗⠓⠒⡶⠤⠤⠖⠻⡍⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⡆⠀⠙⠶⣄⡀⢙⣲⣤⣤⣤⠴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⠖⠉⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢸⠀⠀⠀⠀⢱⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⠴⢻⠏⠀⢀⡠⠤⠤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠁⠀⠈⣧⡼⠋⠀⠀⠀⠀⠙⠣⡀⠀⠀⠀⢀⡤⠖⠛⠛⠓⠦⣄⣰⠏⠀⠈⢷⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡴⠋⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢻⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠓⠒⠒⠻⣆⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⠟⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⢸⣄⣧⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣸⣀⡤⠴⠞⠁⠀⠀⢈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣀⣀⣠⠞⠁⠘⣇⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠤⠤⠤⠾⠥⠤⠤⠤⠤⠤⠒⠋⠛⠓⠒⠦⠤⠤⠤⣿⠤⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠙⢿⣿⣿⣿⣄⠈⢻⣶⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⣿⠋⠉⠙⢧⡀⢿⡄⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⢸⡇⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣉⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠿⠒⠻⣧⢸⡇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡀⠻⡄⠀⣶⣿⣷⠀⠀⠀⣀⡀⠀⠈⠻⣧⢻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣷⣄⣹⣆⣿⠋⠁⠀⠠⣿⣿⣟⠀⠀⢀⡿⠿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠈⠉⠛⢷⢰⠆⠀⠀⠀⠛⣿⠗⣺⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣶⣄⣸⠦⠤⠤⠤⠾⠥⠚⠹⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀ ⠀⣠⢖⣢⠀⢀⠀⠀⢀⣴⣿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀ ⣾⣿⠋⣠⣾⠛⠀⣴⡿⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠈⠁⣰⡿⠁⢀⣾⠟⠁⠀⢻⣷⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡘⢿⡆⠀⠀⠀ ⠀⠀⣿⡇⠀⣼⠃⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⣠⣧⠈⢷⠀⠀⠀ ⠀⠀⣿⣇⢰⣿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⡟⠀⠀⠀⣠⣴⣿⠃⠀⠘⡆⠀⠀ ⠀⠀⢹⣿⣾⣧⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⢹⣦⣴⣾⣿⢿⡿⠀⠀⠀⣧⠀⠀ ⠀⠀⠈⢻⣿⣿⣄⣼⣿⣶⣿⣿⣿⣿⣷⠀⠀⢀⣸⣿⡿⠟⠁⢸⠇⠀⢤⡾⠿⣦⡀ ⠀⠀⠀⠀⠙⢿⡟⠉⠉⠉⠁⠈⠻⡏⠀⠰⠶⠛⠋⢹⡄⠀⠀⠸⡄⢀⠀⢸⡔⣆⢳ ⠀⠀⠀⠀⠀⠀⠹⠤⠼⠤⠼⠷⠞⢷⣀⡀⠀⢰⠀⣦⣷⠀⠀⠀⠉⠙⠒⠚⠳⠞⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⡇⢰⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣻⠛⠉⠉⠉⠉⠉⠉⠛⡛⣻⢶⣤⣿⡾⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⠾⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣷⡄⠙⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠰⣿⠏⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠈⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⣃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⣰⠋⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠀⢰⡏⣠⣴⠶⠖⠀⠀⢻⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⡟⠁⠀⠀⣿⡏⠀⠹⣆⠀⠀⠀⠀⠉⣿⠛⠛⠋⠁⠀⠀⠀⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡟⠀⠀⠀⠀⢹⣧⠀⠀⠙⠷⣤⣤⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⢦⡀⠀⠀⣠⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⡿⠁⠀⠀⠀⠉⠀⣰⠏⠀⠀⠀⠀⠘⣿⡄⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀ ⠻⣆⠀⠀⠀⠀⢀⣠⡿⣧⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠹⣟⠷⣤⡀⠀⠀ ⠀⠉⠛⠿⠿⠟⠛⠉⠀⠈⠛⢶⣤⡀⠻⣏⡉⠉⠋⠉⢀⣴⠋⠀⠀⠀⢀⣠⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⣆⠈⢻⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣯⣿⣦⣌⠛⠓⠒⠚⠋⢀⣤⣯⣶⣾⠛⢿⣯⣨⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⣿⠀⠀⢻⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠙⣿⣟⢙⣷⣶⣶⣾⣿⣧⣤⣿⠿⠟⠛⠉⠀⠙⣦⡀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⠟⠋⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠳⣦⣠⣴⣶⣦⣤⣴⠟⠀⠀⠀⣰⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠉⠛⢷⣄⣀⡴⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢻⣆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠙⣷⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠞⠋⠉⠙⠓⠒⠆⠀⠀⠀⠀⠈⢻⣆⡀⢸⡟⠀⠀⠀⡤⠤⠶⠶⠶⠿⢤⣶⡃⠀⠀⠀⠀⠐⠛⠋⠉⠙⠛⠛⠶⢤⡀⠀ ⠀⠀⠀⠀⢰⡏⠀⣠⠞⠀⠀⢠⠄⠀⠀⠀⠀⠀⣾⠏⠛⣿⠃⠀⠀⠀⠀⢠⠀⠀⠀⢤⠀⠈⢻⣆⠀⠀⠀⠰⡄⠀⠀⢳⡄⠀⠀⠈⣿⠀ ⠀⠀⠀⠀⠈⣷⣰⡇⠀⠀⣰⠋⠀⠀⠀⠀⠀⣰⣿⣄⣀⣿⡀⠀⠀⠀⠀⠈⡇⠀⠀⣸⡆⠀⢸⡏⠀⠀⠀⠀⣿⠀⠀⢠⡗⠀⢀⣠⠟⠀ ⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣿⣀⣀⣀⣤⣴⠾⠋⠀⠀⠀⠈⠳⢤⣄⣀⡀⣸⠇⠀⣀⣿⣠⡴⠟⠙⠛⠷⠶⠾⠷⠶⠶⠾⠶⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⠊⠉⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀ ⡇⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘ ⢇⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⠀ ⠘⡄⠀⠀⠀⠀⠀⣟⡦⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡴⢹⠀⠀⠀⠀⠀⠸ ⠀⢷⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡀⠀⠀⠀⢀⠃ ⠀⢸⣆⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣼⠀ ⠀⠀⢧⣙⢺⢀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠠⠀⢇⣀⢞⡇⠀ ⠀⠀⠀⠈⢁⡇⢀⣄⣴⣶⡇⠀⣀⠤⠤⠤⠤⢄⣀⢰⣷⣧⣀⡄⠈⣾⠔⠋⠀⠀ ⠀⠀⠀⠀⠸⡧⡀⠻⢿⡿⠃⠀⠀⢠⣔⢒⣶⡄⠈⠈⢿⡿⠿⠃⡠⡻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢱⡈⠉⠉⠀⠀⠀⡀⠘⠿⣿⠿⠁⢀⡀⠀⠈⠉⠁⢠⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣙⢀⡄⠒⠀⣸⠀⠰⠂⡄⢉⡀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠁⠀⢀⡴⠾⠿⠷⠦⡀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠲⢄⣀⡠⠔⠳⢄⣀⣀⣀⣀⠬⠦⢄⣀⣀⠔⠁⢠⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠂⠺⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠊⠀⢠⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⢡⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢆⠀⢃⠀⠀⠸⠀⠀⠀⠀⠀⡇⠀⢀⠎⠀⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠒⠳⢀⣣⠀⢸⣀⣀⣀⣀⣠⠇⢀⣎⡀⠚⢲⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠣⣔⢡⡱⠰⣫⠓⡤⠂⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⠤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⠒⠚⠋⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⣶⠀⠀⠀⠀⠀⢰⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠞⠁⠀⠀⠀⠀⠀⢘⡿⢿⠓⠚⠿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠁⠀⠀⠀⠀⣴⢄⣴⣿⣷⡿⣿⣤⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⠴⠶⠞⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⢻⡿⠿⠻⣿⣷⣬⣿⣆⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⠾⠟⠿⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠒⠿⣭⣉⣁⣿⣦⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣷⣦⣨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣷⣄⡀⠀⠀⠀⣰⣿⣿⣷⣦⣀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⣿⣿⢛⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣿⣿⡏⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⢡⣤⠄⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢫⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠇⢠⣿⡏⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣼⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣤⣿⣿⣿⣿⣶⣤⣀⣀⣀⣤⣾⣿⣿⣿⣿⡿⠣⡞⠋⠉⣿⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⠉⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠓⢦⣀⡈⠙⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢸⣿⣶⣷⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠛⢶⣤⣈⠛⠿⠟⠛⠛⠛⠛⠛⠛⠛⠁⠀⢀⡤⠀⣰⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣸⣿⡇⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠶⢾⣿⣶⣄⡀⠀⢠⡶⠿⠿⢿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⡟⠁⠉⠉⣼⡇⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡿⢿⣷⣄⠀⠀⠻⡏⠛⠿⠟⠛⠉⠉⠉⠉⣿⣿⠀⢸⣷⡀⠀⢸⣿⠁⠀⠀⠀⣴⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⡿⠃⠀⢀⣿⣧⣀⣼⠏⠀⠀⢀⣧⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣽⠏⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠘⡏⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⠏⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⣇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡏⠀⠀⠀⢰⣿⣿⡇⢸⠙⣍⠻⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣰⣿⣿⣿⣿⣿⣿⡇⢸⠀⠈⣇⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠿⣿⡏⠀⠀⠀⢠⣿⣿⣿⠀⠈⠀⣿⠀⢻⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣇⡼⠀⠀⢿⠀⠀⠀⠀⠀⢠⠟⠁⠀⢀⣴⠏⠀⠀⠀⢠⣾⠇⣾⢿⠀⠀⠀⣿⠀⠘⠎⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠘⠃⠀⠀⠀⢀⣸⣀⣠⡴⠟⠁⠀⠀⢀⡴⠛⠁⢠⡟⣿⠀⠀⠀⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣶⡴⠖⠀⠀⠀⡞⠀⠀⢠⣿⡇⢻⠀⠀⠀⠘⣆⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⡤⠖⠀⠀⠀⠀⠀⠀⢠⣿⢿⡇⢸⠀⠀⠀⠀⠹⡀⠳⡀⢻⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣤⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢸⡇⣼⠀⠀⡄⠀⠀⢻⡄⠙⣆⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠵⠖⣀⣀⣤⣤⠀⠀⠀⠀⣸⡏⢀⣾⢳⡏⠀⠀⣧⠀⠀⠀⢿⡄⠘⣦⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⡿⢋⣿⡿⠃⠀⠀⠀⢀⣿⠀⢸⡟⢸⠁⠀⠀⢿⠰⡄⠀⠈⣿⠀⢸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣼⡷⢋⣿⠃⠀⠀⠀⠀⠸⢿⠀⣼⡇⠀⠀⢀⡄⢸⡆⡇⠀⠀⢹⡇⠀⡏⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⠀⣼⣳⢇⡆⠀⣼⡇⢀⣇⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⡤⠀⣀⠀⠀⠀⠀⢹⣧⡆⢰⠋⣰⢣⡟⡾⢰⠀⣿⠁⣾⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣇⠀⡇⠀⠀⠀⡆⠘⣿⠁⣿⠀⣿⣾⣁⡇⣾⢺⣿⢠⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢿⣦⣿⡀⢦⠀⠸⣦⡙⣧⠹⣧⣿⣿⣿⣷⣿⣾⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⣿⣷⣼⣧⣳⣬⣽⣿⣶⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠶⠷⠀⠙⢿⣿⣿⣿⣿⣿⣷⠈⠓⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠧⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀ ⢠⢏⡠⠤⠤⣀⠉⠉⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡠⠇⠐⠒⢉⣩⠷⠂⠀⠀⠀⣀⣤⠴⠒⠚⠉⠉⣀⠤⠤⢤⣀⠀ ⢸⡈⠀⣠⠔⠚⠷⣄⠀⠀⠀⠀⠉⠻⣦⡀⠀⡠⠞⠁⠀⠀⠊⠀⠠⠔⠚⠓⠢⢄⡀⢀⣴⠟⠉⠀⠀⠀⠀⢠⠾⠓⠲⣄⠀⢻⡇ ⠈⣧⠀⠇⠀⠀⣀⣘⣆⠀⠀⠀⠀⠀⡨⠟⠉⠀⠀⠀⠀⠀⢀⠒⠒⢶⠒⠶⢤⣄⣙⡿⢅⠀⠀⠀⠀⠀⣰⣃⣀⠀⠀⠸⠀⣼⠁ ⠀⠹⣧⠀⠀⡟⠁⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠱⡀⠀⠀⣉⠁⠀⠁⠀⠀⠀⣰⠋⠀⠈⢳⠀⠀⣸⠇⠀ ⠀⠀⠙⢧⡀⠑⠄⠀⢠⡬⣦⡀⠀⢀⠔⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠚⠉⠙⠢⡀⠀⢀⣴⢥⡄⠀⠀⠎⢀⣴⠋⠀⠀ ⠀⠀⠀⠈⠳⣦⡀⠀⠘⠻⠶⠏⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠩⠶⠟⠃⠀⢀⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢙⣦⡄⠀⡄⠀⠀⣴⣿⠁⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠈⣿⣦⠀⠀⢀⠀⢠⣴⡋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠿⢲⡏⡠⡇⠀⣸⣿⣿⣄⠀⠀⣠⣿⣇⠀⠀⠀⠀⠀⣼⣿⣄⠀⠀⣠⣿⣿⣧⠀⢸⢠⡙⡗⠿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡿⣿⠉⠉⠙⢿⣿⡿⠀⠀⠀⠀⠀⢿⣿⣿⠋⠉⠉⣿⣫⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠙⢮⣓⡤⢤⣾⠟⠁⠀⢤⠤⡤⠀⠈⠿⣿⡤⢤⣾⡵⠟⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣥⠀⠀⠀⠀⠈⠉⠉⠁⠀⠳⢤⣴⠛⣧⡤⠞⠀⠈⠉⠉⠁⠀⠀⠀⠀⣬⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡴⠾⠭⢥⣀⡀⠀⠈⠉⠑⠒⠢⠤⠤⠀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⡀⠤⠤⠔⠒⠈⠉⠁⠀⢀⣀⡤⠭⠵⢶⣄⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠎⠀⠀⠀⠀⢰⠛⠁⠀⠀⠀⠀⠀⠈⠋⢇⠀⠀⠀⠀⠙⡄⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣎⣀⣀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⣀⣀⣰⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠹⣀⠀⠀⠀⠀⠀⣀⠟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢈⣉⡵⠶⢦⣉⡁⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣀⣠⠔⠋⠀⠀⠀⠀⠀⠉⠢⣄⣀⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⡆⢀⣠⠤⠖⠒⠛⠉⠉⠉⠙⠒⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠥⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢳⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠖⠒⠒⠒⠲⢤⣄⠀⠀⠀⠀⢀⣤⠖⠛⠉⠉⠛⢦⡘⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⢀⠀⢀⡞⢡⡶⠒⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠉⠀⠀⠀⠈⠲⡄⠀⠻⣾⠉⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⡏⢀⡏⠀⠏⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⣽⠀⠀⢻⠳⡄⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠒⡇⢸⠁⠀⠀⣼⠋⢹⣿⣮⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣷⠈⡇⠀⢸⠀⠁⡌ ⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⡀⠀⠀⠀⠀⢸⡀⠣⠀⢻⣸⡄⠀⢸⣿⣿⣿⣿⣿⢸⠆⠀⠀⠀⠤⢄⠀⢸⣿⣿⣿⡟⢠⠇⠀⡞⠀⡰⠁ ⠀⠀⠀⣠⡴⠋⠁⠀⠀⠈⠙⣆⠀⠀⠀⠀⢳⣄⠀⠈⢿⣧⠀⠀⠻⣿⠿⠟⢁⡜⠀⠀⠀⠸⢦⡼⠁⠳⡝⠯⠭⠴⠋⠀⣼⣡⠞⠁⠀ ⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠉⠓⠲⠬⠿⢷⡀⠀⠀⠉⠉⠁⠀⠾⣤⢄⣀⡸⠥⠴⠋⡿⠀⠀⢀⣠⢞⣉⣀⡀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣳⣦⣄⡀⠀⢀⡀⠙⣆⠒⣄⡠⠃⣴⡧⠴⠚⡹⠋⠁⠀⠀⠈⢙⡄ ⢀⡏⠀⠀⠀⠀⠀⠀⣤⠖⠋⠁⠀⠀⠀⠀⠀⢠⡞⢉⠄⠀⠈⠉⠣⡀⠈⠉⠉⠛⠛⠒⠤⣍⣉⡤⠞⢡⡀⠀⠀⢧⠀⠀⠀⡀⢨⣣⠀ ⢸⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠋⡀⠀⠀⠀⢀⠇⢀⣀⡠⠄⠀⠀⠀⣀⠤⠤⢄⠀⢻⠉⠉⠉⠳⣄⠀⠱⡀⢻⠀ ⠈⣇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠀⡜⠁⣰⠛⠋⠁⣸⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳⠀⡆⠀⠀⠀⠈⠳⢄⣧⡜⠀ ⠀⢹⡄⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣀⡴⠁⠀⣀⠴⡏⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣄⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠒⠉⠀⣰⠁⠀⠀⣀⣈⣳⣤⡤⠴⠚⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢀⡠⠔⠒⠛⠒⠲⢄⣸⠁⣾⣁⣀⠤⠚⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡜⡽⠋⣠⠔⠂⠀⣀⠀⠙⣦⡇⠀⠀⣄⠀⠐⠲⣍⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⢤⣧⠤⠴⠚⠉⠁⠒⠁⠘⠒⠐⠋⠑⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠈⡖⠒⢄⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀ ⠀⢀⠆⠙⠀⠀⠀⡀⠀⠀⠀⠀⣼⣀⣀⡴⠛⢧⠤⢀⠀⠀ ⠀⢸⠀⠀⠀⢀⡴⢓⣒⡒⠂⠁⠀⠀⣼⠛⣿⠻⡒⠠⡑⡄ ⠀⠀⡠⠜⠉⠠⢠⣾⣏⣎⢷⡀⠀⠀⢿⢇⡿⠀⡏⠑⠋⠁ ⢀⠊⢀⡀⡆⡀⠉⢿⣿⠟⡈⡇⠀⢀⣈⢭⠀⡸⠀⠀⡠⢤ ⡎⠀⡊⢔⣷⡑⠄⡀⠈⠈⠉⠰⣢⣭⠖⡊⡜⠁⠉⠀⠗⠱ ⠑⠂⠂⠁⠀⡱⠀⠀⠁⠐⠒⠒⠬⠼⠎⠀⠀⠑⠄⢀⠜⠁ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀ ⠀⠀⢀⠤⣴⣁⡀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⣨⠀⠣⣆⠨⠊⠀⠀⠑⡀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀ ⠀⠀⠣⢀⡀⠘⡀⠀⠀⠀⠀⢰⠀⠀⣀⠄⢐⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠘⠀⠀⠀⢠⠻⡉⠉⠀⠲⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠠⢵⡑⠤⣠⣐⣾⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⠖⠢⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⡀⠀⣀⠇⠀⠀⠀⢦⡄⣀⠀⠀⣀⡀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠎⠀⢀⠤⡀⠀⠈⢒⢥⡫⡳⢄⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀ ⠀⠀⠀⠀⠢⠈⠀⡇⠀⡰⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠈⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⣩⣿⡿⠁⠀⠀⠀⠸⣿⣿⣗⠒⡄⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⡺⠀⣦⠀⢀⡆⠸⡹⣿⣿⡸⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠈⠀⠀⠈⠉⠉⠀⠀⠁⠚⠛⠁⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠦⡠⠊⠉⠉⠒⠄⠀⠀⠀⠄⠀⠀⠐⠢⡌⠀ ⠀⠀⠀⠀⠀⠀⡄⢈⡉⠁⠀⢱⡄⠀⠀⠀⢸⠀⠀⠀⠈⠢⡀⠀⠀⠘⠄ ⠀⠀⠀⠀⠀⠀⢠⠀⠈⠢⡀⡀⡅⠀⠀⢀⠌⠀⠀⠀⠀⢀⠜⠁⠒⠊⠁ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠧⠤⠒⠁⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠨⡊⠀⠀⠀⠀⡀⠤⠄⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠋⠉⠉⠉⠓⠢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠊⢹⠂⠀⠀⠀⠀⠀⡠⠞⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀ ⠀⠀⡘⠀⠀⠸⡀⠀⠀⠀⡠⢊⠄⠊⠁⠀⠀⠀⠀⠉⠒⠄⡀⠀⠀⠀⢻⠀⠀⠀ ⡰⠉⣧⠀⠀⠀⠈⠉⠀⣎⠔⠁⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠑⡄⡔⠉⠙⠢⡀⠀ ⡇⠀⠘⠢⣀⣀⡀⠀⠀⠀⠀⢠⠀⣾⣿⣿⠓⡝⣦⡀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠄ ⠹⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢄⣹⣿⣿⣿⣿⣷⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠈⠲⡤⠤⠐⠊⣠⠀⢠⠀⠀⠬⢿⡿⢿⡿⠟⡸⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⢒⠜⠁⡠⢻⠌⠀⠀⠀⠙⠭⠤⠭⠐⢀⡠⠧⡔⠁⠀⡀⠤⠄⠀⡸ ⠀⠀⠀⠀⠀⠀⠁⠉⠀⣎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠑⠊⠀⡠⠊⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠑⠦⠤⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠚⡱⠀⠀⠀⠑⢄⡀⢀⠀⠀⠀⠀⠀⢰⡸⠀⠀ ⠀⡞⠁⠘⡄⠀⠀⠀⠀⢀⣔⠉⠺⡀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢠⠀⡸⠁⠀⠀ ⠸⡄⠀⠀⠈⠒⠤⠄⠤⢏⠈⠁⠒⠓⠂⠀⠀⣠⠞⠀⠀⠀⢀⡰⠋⠊⠁⠀⠀⠀ ⠀⢱⠤⣀⡀⢀⣀⡀⠤⠀⠈⠉⣇⠀⠉⠉⢡⣀⣀⡠⠤⢲⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⢄⣀⣀⣀⠄⢂⠤⢄⡤⢚⡖⢤⢒⡁⠠⢌⣱⠒⢍⣀⠔⣉⡁⠢⡄⠀⠀ ⠀⠀⠀⠀⠁⠒⠒⢲⢁⠔⠒⠉⠉⠀⠈⠁⣸⢠⡀⢀⣀⣀⠀⠀⠀⠀⢠⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⡠⠔⠊⠉⠉⠁⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠚⠉⠉⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⢯⢱⡀⠀⠀⠀⠀⠈⠻⣗⠒⠠⢀⠀⠀⠀⠀ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣸⠋⡇⠀⠀⢀⠀⡀⠀⠙⢧⡀⠀⠑⢄⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣤⣴⡙⣼⡁⠀⠀⠈⢢⠘⡠⡀⠀⠑⡀⠀⠈⢷⠀ ⠀⢀⠿⠤⠀⣀⠀⠀⠀⠀⣧⡙⡿⠋⠀⠀⠀⠀⠀⠀⡆⡇⡇⠀⠀⠐⠄⠀⢈⣧ ⡇⠁⠀⠀⠀⠀⢐⡒⡄⠀⠀⠈⠠⡴⣆⡶⠀⠀⠀⠰⠐⢠⠁⠀⠀⠀⠘⡖⠉⠉ ⠈⢍⣡⠐⡂⠤⢀⣁⠁⣀⡀⠔⠈⡦⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡇⠀⠀ ⠀⠀⠀⠉⠈⠒⠓⠤⠷⣔⡢⠌⠁⣀⡠⠔⠊⠀⠀⠀⠀⠀⢀⡆⠈⡆⠀⢃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⢀⠔⠒⢄⠀⠀⠀⠀⠔⠊⠁⠀⠀⡇⠀⠘⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠉⠀⠀⣀⣱⠀⠀⠸⠀⠀⠀⣠⠔⠁⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣠⠚⢧⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⢀⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣⠀⠀⠘⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣤⣴⠖⠒⠶⠶⠤⠤⣀⣀⡴⠁⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄⡀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠠⠐⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣄⠶⠬⢦⣠⠄⠀⠀⠀ ⠀⠀⠀⠀⠸⡷⠂⠀⠈⠀⠘⣿⠀⠀⠀ ⠀⠀⡠⢄⠜⣖⣇⣀⣶⡆⢀⡐⡀⠀⠀ ⠀⠈⡄⢡⣧⣌⠻⠃⠹⡝⠁⠀⢸⠀⠀ ⠀⡠⠂⠘⠈⢸⢰⡦⢀⠃⠀⣦⣚⣄⠀ ⢘⠀⠀⠀⣼⣿⠓⠦⠳⠇⠀⠀⠀⠈⡄ ⠘⠤⠤⠾⠳⣡⣴⣦⣠⣼⣦⣀⣀⡰⠃ ⠀⠀⠀⠁⠁⢿⣿⢯⣻⣿⣿⠈⡀⢡⠀ ⠀⠀⠀⠁⡄⠈⣳⠊⠙⣆⠀⠀⠇⠸⠀ ⠀⠀⠀⠡⡘⢄⡀⠀⠀⢀⡠⠊⢠⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠔⠒⠈⠁⠀⠀⢀⡀⠈⠉⠐⠂⢄⠀⠀⠀ ⠀⠀⡠⠊⠀⢀⣀⠀⠀⠀⠀⠀⢄⣀⡈⠁⡆⠀⡘⠀⠀⠀ ⠀⡐⣠⠔⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⢳⡤⠇⠀⠀⠀ ⣸⠜⠁⠀⠀⠀⠀⢀⣴⣿⢿⣿⣷⣦⣀⠀⢸⠇⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠉⠻⢿⣷⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⣀⡀⢹⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⠁⢀⣤⢤⣀⡞⢹⣧⢀⣿⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣇⠈⢻⣦⣽⢈⡺⠏⢼⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⠍⡉⢚⣉⡤⢰⡗⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣏⠉⠹⠖⠊⣿⣿⣇⣸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠲⣼⠟⠀⠀⢀⣿⣿⣿⣽⣼⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣰⠆⡤⣼⣿⣿⣇⠙⡇⢠⣦⡰⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠯⣿⣷⣾⣿⣿⣿⣷⣿⣤⣼⣾⠼⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠤⠴⠤⠤⠤⠴⠤⠤⠄⠀⠆⠶⠶⠖⠶⠒⠶⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢂⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢤⣤⣤⣤⣤⠤⠤⠤⣀⣀⠀⠀⡠⣿⠕⡝⠁⠀⠀⠀⣀⡤⢤⡶⠖⡻⠟⠋⠁ ⠀⠀⠈⠑⠢⡀⠈⠉⠒⠤⣀⣭⣿⣿⠉⠉⣷⣷⣶⡯⡉⡠⠚⠁⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡀⠣⢄⡰⢣⠿⣫⡥⠀⠀⢀⣈⠻⡆⠘⡄⢠⠁⡜⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣩⡦⠤⠃⠤⣎⣀⣱⡀⢀⣎⣀⣱⣈⡠⠭⠵⣮⣀⣀⠠⠤⠀⠀ ⠀⠀⠀⠀⢈⠝⠓⢤⡄⣀⡀⠈⠙⣍⣇⣀⡏⡩⢊⡡⢤⣒⡪⢭⣽⣦⡄⠂⠀⠀ ⠀⠀⠀⠀⡿⡶⡝⡰⠛⡶⠾⢉⡶⡾⠓⡟⠙⢟⠃⠩⠤⠲⠉⠱⢰⠱⢷⠀⠀⠀ ⠀⠀⠀⠀⠑⠓⢺⡳⠤⠼⣒⠀⠀⡇⢀⣃⠀⢇⠂⠤⢤⠔⠒⢺⠚⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⠀⢀⠏⢳⢢⠺⡌⣀⣰⠃⢣⢦⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⣸⠀⠈⠀⠀⢹⠒⢹⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠃⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠈⢻⢦⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠂⠀⠒⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⡇⠀⠀⢀⠤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠤⠄⠚⠂⠤⠤⠤⠤⠤⠒⠡⠐⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⢀⣀⣤⡤⠶⠖⠛⠛⠋⠉⠉⠙⠛⠛⠓⠶⢦⣤⣀⣀⡴⠞⠛⠳⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠟⣡⣤⣤⣤⡙⢷⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣾⣿⣿⣶⡈⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⣿⣿⣿⣿⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⢮⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢐⣾⣿⣿⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⡿⠏⠀⠀⠀⠀⣿⠷⣾⠀⠀⠀⠀⠙⠿⠟⠃⠀⠐⠉⠀⠀⢹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⢀⡟⠀⡟⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⣸⠃⢸⠇⠀⠀⠀⠀⠀⢀⣀⣸⠄⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⣠⡶⠛⠛⠛⢶⣼⠀⢀⣤⣠⣀⣀⣿⡉⢹⣴⣤⡀⢀⡼⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣾⣧⣾⣷⠦⣤⣶⣤⣤⠰⠊⠀⠀⢠⡾⠋⠀⠀⠀⠀⠘⣿⣤⡼⣧⠀⢻⡏⣙⣷⣿⡏⠈⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠉⠻⣶⡟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⠀⢸⣆⡼⠟⠉⠉⠉⠙⣶⣇⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⢸⣦⡾⠋⠀⠀⠀⠀⠀⣼⠋⠉⠙⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⣏⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠀⠻⣦⡤⠾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠄⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⣁⣠⣤⣤⠴⢶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛ ⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠉⠁⠤⠄⠈⠉⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡿⠛⠛⠛⠻⠶⢦⣤⣀⠀⣀⣠⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣄⣀⠀⢀⣤⡶⠞⠛⠛⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣄⡀⠀⠀⠈⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠻⣶⣄⠀⢸⣇⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⣤⠀⡀⠸⣿⣿⠟⡀⠀⠀⠀⠀⠀⠈⠙⢷⣄⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣇⠉⠁⠄⠁⣀⣾⣧⡀⠾⢉⣶⠂⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀ ⠀⠀⠀⣾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠉⠀⠀⠙⠛⠲⠒⠛⠋⠁⠈⠛⠛⠛⠙⠻⣦⣄⠀⠀⠀⠀⠹⣧⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠹⣇⠀ ⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⢻⡆ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠸⣷ ⢸⠇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠤⠤⢤⡀⢸⡇⠀⠀⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⠿⠧⠤⠤⠜⠃⠀⣤⡄⣀⣀⣤⠀⠙⠿⠧⠤⠤⠾⢃⡘⣷⠀⠀⢸ ⢸⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠰⣄⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⣎⠀⣿⠀⠀⣸ ⠈⢿⡀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⣿ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣰⡏ ⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠃⢀⣼⠏⠀ ⠀⠀⠀⠀⣈⡻⢶⣄⣀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠋⠉⣀⣤⡶⠛⠁⠀⠀ ⠀⠀⠀⣸⠋⢿⡄⠈⠙⠛⣷⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣤⣀⣀⣀⣀⣀⣤⣤⣤⡶⢶⡟⠛⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠸⣇⠀⢀⣾⡟⠁⠀⠀⠀⠈⠉⠉⡉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⢿⣠⡿⠟⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⢈⡿⠁⠂⠀⠸⣷⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣦⣼⡇⠀⠀⠀⠀⠙⠷⣦⣤⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠟⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⢶⡶⠟⠉⠁⠉⠙⠛⠳⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣫⡶⠋⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡠⠞⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣠⠤⠤⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣞⡵⠋⠀⢀⣴⣾⡿⠛⢆⠀⢸⡇⠀⢀⣠⠤⠶⠶⠦⢽⣷⠀⠀⠀⢠⠿⣆⠀⢶⡄⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠁⠀⣴⣿⣿⣿⣇⠀⣸⡀⢸⠁⠀⣀⣤⣶⣶⣶⣶⣤⣌⠳⣄⠀⡏⠀⠹⣇⠀⠉⠉⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⢰⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⢸⢀⡾⠋⠘⣿⣿⣿⣿⣿⣿⣷⡀⢰⠇⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⢸⢻⣧⣄⠀⠉⠛⠻⣿⣿⣿⡿⣿⡾⠀⡔⠻⣦⢸⡈⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠘⣆⠀⠀⠹⣿⣿⣿⣿⠿⠋⣠⠏⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣹⠇⣸⣀⣰⣿⡄⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⢠⡀⠀⠈⢦⣀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠙⢿⣇⠀⠀⠀⢀⣴⣿⡿⢠⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⢸⡇⠀⢀⣠⡬⠽⠶⠶⠿⠽⠯⠤⠤⠤⠤⠤⠤⣄⣉⣻⠶⠞⠛⠉⠀⡇⠸⣿⣿⣿⣿⠁⡇⠀⠀⠀⠀ ⠀⠀⠀⣴⠃⠀⠀⣸⢳⣜⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠓⠦⣄⠀⢷⡀⠙⠿⠟⠁⢰⠃⠀⠀⠀⠀ ⠀⠀⢠⡇⠀⠀⢠⡏⠀⠻⣿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠤⠤⠀⠀⠈⠙⠾⣿⣦⣀⣀⣴⡏⠀⠀⠀⠀⠀ ⠀⠀⣼⠀⠀⢠⡟⠁⠀⠀⠙⢦⠙⣟⡷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⡿⠀⠀⡞⠀⠀⠀⠀⠀⠈⠳⣿⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠞⠛⡄⠀⠀⠀⠀⠀ ⠀⠀⡇⢀⡼⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣻⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣩⣿⡿⠛⠉⠀⠀⢳⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⣠⡶⠛⠁⢀⣿⡟⠀⠀⢶⣎⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⢷⢸⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⡼⣿⡇⠀⠀⢾⣧⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠈⣧⠀⠀⠀ ⠀⠀⠸⣿⠀⠀⠀⠀⡞⠀⠀⠀⠀⠛⠛⠺⢧⡀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢻⡄⠀⠀ ⠀⠀⠀⢻⡄⠀⠀⣸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠙⢦⡘⣇⠀⠀ ⠀⠀⠀⠈⢿⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢻⣙⣦⣀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢻⣿⡀⠀ ⠀⠀⠀⠀⠈⢦⠀⠹⣧⠀⠀⠀⠀⠀⠀⠰⠚⢢⣀⣽⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⡄⠀ ⠀⠀⠀⠀⠀⠈⠳⡀⠹⣄⠀⠀⠀⠀⠀⠀⣀⣿⣿⣇⢠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠷⣦⡀⢠⡀⢀⣽⡟⢨⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀⢀⣤⠶⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣤⣄⣀⠀⢀⣠⣴⠶⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣿⣿⣶⡘⣷⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⢋⣩⣤⣬⡙⢷⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⣽⠆⠀⠀⠀⠀⠀⠀ ⣾⠁⣿⣿⣿⣿⣿⠎⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀ ⢹⣆⢻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀ ⠀⢹⡷⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⢀⠎⠀⠀⠀⠀⠀⠀⠂ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⠀⠀⢠⣀⣤⣠⡄⠀⠀⠸⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠸⡧⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⢿⣌⠑⠒⣶⠂⠀⠀ ⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢻⣿⡆⠙⣷⣴⠏⠀⠀⠀ ⠀⠀⠻⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡏⠀⠈⠉⠀⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠶⣤⣀⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠟⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢷⣄⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣨⡽⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠙⠒⠦⣤⡀ ⠀⠀⠀⠀⠀⣠⣤⣼⣿⡆⠀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣠⡇ ⠀⠀⠀⠀⠀⠙⠿⠿⠿⠁⠀⠀⢠⣿⡈⡠⠀⣳⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣠⣅⠀⠿⡟⠡⣴⣶⣂⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣉⣩⣿⠿⣷⣦⣀⡈⢭⣉⠈⠿⣈⡁⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢶⠒⠲⠤⢤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢷⣦⣆⣘⣋⠂⠀⠀⢀⣠⣾⣿⠏⠀⠀⠀ ⣴⣾⣆⠀⠀⠀⢸⡄⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢸⡟⠷⠦⢿⣿⡟⠛⠁⠀⠀⠀⠀ ⢿⡈⣟⡀⢀⣀⠬⣧⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣶⡀⠀⠹⣷⡄⠀⠀⠀⠀⠀ ⠘⠳⢌⣷⠋⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢨⡿⠃⠀⠹⢿⡀⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠛⣿⠉⠁⠀⠀⠀⣀⣽⣦⡄⠀⠀ ⠀⣰⠇⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠈⠿⠋⠀⠻⠟⠾⠆⠘⠛⠉⠀⠀⠀⢸⣏⣀⣈⢦⢸⣯⢀⣴⠏⠀⠀ ⢺⣅⣀⣠⣟⠋⠙⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠉⠉⠙⠷⠬⠟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠒⠚⠋⠓⠒⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⠒⠒⠒⠠⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠙⠲⣤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠉⠉⠒⠢⢄⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠳⠶⠤⠤⣀⡀⢸⠀⠀⠀⡎⠀⠀⠀⠀ ⠀⠀⢀⠞⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⣰⠇⠀⠀⠀⠀ ⠀⢀⠎⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⢀⠀⠀⠀⣴⠿⣿⣷⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣇⠀⠠⣶⣿⡟⠛⢳⡴⢧⡀⣿⣿⡇⢀⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠘⢿⣿⣦⣸⡇⠀⠻⠿⠿⠡⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⣄⡈⠻⢿⡿⠃⣸⡿⠆⢀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⠀⣠⣤⣴⣾⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠋⠉⠈⠙⣧⠴⠚⠙⣿⣿⣿⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡛⣷⣦⡄⠈⠀⠀⠀⢠⣿⣿⣿⣿⣟⠿⡟⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣼⣳⣿⡦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣛⣻⣿⣇⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡇⣠⣶⡄⣿⣿⣿⣿⣿⡀⠈⣿⡇⢀⣴⣶⣀⣶⣶⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣻⣶⣿⣮⣱⣿⣿⣿⣿⣿⣿⣦⣿⣇⠘⠁⣹⣇⣽⢛⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠾⠿⠿⠿⠛⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⣀⣀⡀⢀⠀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠞⠛⠿⠛⠛⠛⠟⠻⠛⠐⠛⠛⠛⠃⠀⠐⠈⠳⠟⠛⠛⠛⠛⠒⠉⠛⠛⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⣿⣠⣤⠴⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⡄⠀ ⠀⠀⢠⡟⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣀⣠⣼⠇⠀⠉⠁⠀⢠⣾⣋⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠘⣷⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⢹⣦⣤⠶⠞⠛⠉⢩⡟⠀⠀⠀⠀⢀⣈⣹⣿⠛⠛⠶⢦⣤⡾⠋⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿ ⠀⢸⠇⠀⠀⣿⠀⠀⠀⠀⠀⣴⠟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣴⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⢰⡏⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⢰⡿ ⠘⢷⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠇ ⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠴⠾⠋⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠛⠉⠀⠙⠻⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
If you'd like to report a bug or suggest a feature, you can provide feedback here. Here's our privacy policy. Thanks!
AI Story Generator - AI Chat - AI Image Generator Free