Double Middle Finger ASCII Art

Copy & Paste Double Middle Finger ASCII Art Emojis & Symbols

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠏⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⠆⠀⠀⠀⣿⠛⠉⠉⣩⣯⢉⣿⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⢠⡿⠋⠉⠉⠉⣭⡄⠀⢸⣿⠀⠀⠀⠀⢻⣆⠀⠐⢙⣿⡾⠇⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠀⠀⠀⢸⣧⠀⠀⠀⠀⠟⠋⢀⣼⠟⠀⠀⠀⠀⠀⠉⠛⠟⠛⠉⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡇⠀⠀⠀⠀⠀⠛⠿⣶⣶⣶⡶⠾⠟⠁⠀⠀⠀⠀⣀⣀⣀⣤⣴⣶⡶⠶⠟⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⠶⠶⠿⠟⠛⠛⠋⠉⠉⠀⠘⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣄⠀⠀ ⣿⡅⠀⠀⠀⠀⠠⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢸⣿⠀⠀ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢠⡿⠀⠀⢀⣾⠟⠁⠀⠀⠀⢀⣼⠿⣦⡄ ⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⢀⡿⠁⢀⣴⡿⠋⠀⠀⠀⠀⠀⣸⡇⣄⣾⠃ ⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢿⣿⣠⣴⡿⠋⠀⠀⠀⢀⣠⡴⢟⣭⠶⠛⠁⠀ ⠀⠀⠀⠙⠿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⣠⣿⡿⣿⡏⠀⠀⣀⣤⠞⣋⣵⠿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣿⡿⠷⣶⣶⣶⣶⣶⣶⣶⣶⠟⢫⣽⡾⠛⠁⠀⢻⣧⠴⠚⣉⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢀⣠⣽⠿⠛⣩⣴⠾⠋⠁⠀⠀⠀⠀⢸⣧⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⡿⠀⠀⢠⡶⠟⢉⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡏⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⣀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡟⠉⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣇⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⡇⠀⣀⣀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣀⣀⠀⠹⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⠂⣾⣿⠛⠛⠛⠺⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠗⠛⠛⠛⢿⣧⠀⡟⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣀⣤⠶⠋⣶⣿⣀⣙⣾⣆⠀⠀⣴⠿⠶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠿⢿⣦⠀⠀⢰⣿⣋⣀⣿⣆⠙⠦⣤⣀⣀⣀⠀⠀⠀ ⠀⠀⣼⣟⠈⠀⠀⢰⡟⠛⠋⠉⢻⣿⠃⠀⢸⣿⠛⠉⠙⠋⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠙⠋⠉⠛⣿⡇⠀⠘⣿⡟⠉⠙⠛⢳⣆⠀⠀⠀⣹⣇⠀⠀ ⠀⢸⡿⢛⣧⣤⣒⣿⣧⠀⠀⢀⣾⣿⡆⠀⢸⣿⣦⠀⠀⢠⡿⠷⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠾⣿⡄⠀⢀⣴⣿⡀⠀⢰⣿⣷⡀⠀⠀⣾⣿⣓⣦⣴⡟⠿⡇⠀ ⠀⢸⣄⠀⠉⣻⣿⣿⣯⠀⢀⣿⣿⣿⡇⠀⢸⣿⣿⣻⡀⠀⣿⡟⠛⠋⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⠛⢛⣿⠃⢀⣏⣿⣿⡇⠀⢸⣿⣿⣿⡀⠀⣿⣿⣿⣏⠉⠀⣤⡇⠀ ⠀⢸⣽⠀⠀⣿⣿⣿⠹⠀⣸⣿⣿⣿⠃⠀⠸⣿⣿⣧⠁⠀⢻⣆⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣰⡏⠀⠈⣿⣿⣿⠃⠀⠈⣿⣿⣿⣇⠀⢻⣿⣿⣿⠀⠀⣿⠃⠀ ⠀⠀⣿⠀⢸⣿⣿⣿⠂⠀⢿⣿⣿⣧⡄⠀⠠⣿⣿⣿⡆⠀⠘⣿⡝⡄⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢠⣻⡿⠃⠀⢰⣿⣿⣿⠀⠀⢳⣼⣿⣿⡿⠀⠘⣿⣿⣿⡇⠀⣿⠀⠀ ⠀⠀⣿⠀⠸⣿⣿⠁⠀⠀⠘⣿⡟⠁⠀⠀⠀⠘⣿⠿⠁⠀⠀⠘⣿⠛⠀⠻⣷⡀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠟⣿⠃⠀⠀⠘⣟⣿⡃⠀⠀⠀⠈⢻⣿⠁⠀⠀⠘⣿⣿⠃⠀⣿⠀⠀ ⠀⢸⡟⠀⠀⢿⣷⣼⣓⣶⣦⣿⣿⠶⠿⠿⠿⢾⣿⣦⠴⢶⣒⣲⣹⠇⡶⠀⠈⢻⡄⠀⠀⠀⢠⡟⠁⠀⢶⠀⣏⣰⣲⣶⢦⣽⣿⡿⠿⠿⠿⠷⣿⣿⣤⣶⣺⣷⣾⡿⠀⠀⢻⣆⠀ ⢀⣿⣀⣤⣦⣤⣿⣿⡇⠛⠁⣿⣿⡄⠀⠀⢠⣾⣿⣟⠀⠀⠉⢉⣿⣷⣿⣿⣶⡿⠃⠀⠀⠀⠘⣿⡶⣿⣿⡾⣿⣉⠉⠀⠀⣽⣿⣷⡀⠀⠀⢠⣿⣷⠈⠛⢺⣽⣿⣤⣤⣤⡀⢻⡄ ⠀⢹⣿⡉⠀⢨⣿⣿⡅⠀⢸⣿⣿⡿⠦⡴⣿⣿⣿⠙⠃⢀⣼⣿⡇⠀⠉⠉⣰⣿⠀⠀⠀⠀⠀⣿⣇⠀⠉⠀⢈⣿⣧⡀⠀⠋⣿⣿⣿⠂⠰⢿⣿⣿⡇⠀⢸⣿⣿⡁⠀⢉⣿⠟⢱ ⠀⠀⠙⢷⡀⡈⢻⣿⣿⠀⠀⣿⣿⣷⠀⢸⣿⣿⡿⠀⣠⣿⣿⡇⢀⣤⣴⡾⠟⠁⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⢺⣿⣷⣄⠀⢿⣿⣿⡆⠀⣾⣿⣿⠀⠀⣿⣿⡟⢁⢀⡿⠋⠀⠀ ⠀⠀⠀⠀⠹⣿⡄⠹⣿⡇⠀⠹⣿⡿⠀⢸⡟⠉⠀⣴⣿⡿⠋⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡀⠀⠙⢻⣿⣆⠀⠉⢿⡇⠀⢿⣿⠏⠀⢸⣿⠏⢠⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡇⠀⢸⡇⠀⢠⡟⠁⠀⢸⡇⠀⢸⠟⠛⠁⢀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠈⠛⠻⣇⠀⢸⡇⠀⠈⢻⡄⠀⢸⡇⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⡶⠞⠛⢶⠾⠓⠒⣶⡾⠓⠚⠛⣶⡀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⢠⣶⠛⠓⠚⢷⣶⠒⠚⠧⡶⠛⠳⢦⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣷⡄⣀⣼⠀⠀⠀⠙⣷⣀⣀⣀⣼⣇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⣧⣀⣀⣀⡾⠋⠀⠀⠀⣷⣀⢀⣾⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠈⢙⡶⢶⣶⡏⠉⠉⠓⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠻⠉⠉⢹⣶⡶⢶⡊⠁⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢿⡤⠦⠤⠞⠳⠬⢿⣧⣀⣠⣤⣦⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢤⣤⣄⣀⣼⡿⠥⠞⠳⠶⠶⢤⡿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⡿⠷⠴⢌⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⢃⠏⠁⠀⠀⠀⢳⡹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣾⣄⠀⠀⠀⣠⡾⠃⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣧⠉⠉⠉⠉⠁⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡄⠀⣠⣶⡯⠵⠃⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣧⠀⠉⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣴⣶⣶⣶⣶⣶⠾⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋⠁⠀⠀⠙⢷⡀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣼⠏⣸⠀⢻⡄⠀⢠⠴⣛⣹⠿⡅⠀⠻⡆⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⡴⠋⠀⠘⣿⠀⠘⠚⢉⣡⠤⠞⠁⠀⢻⡄⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀ ⠀⢀⣼⣿⢟⣥⣶⠒⠚⠒⢿⣇⠀⠀⠈⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀ ⢠⣾⡟⢡⠟⠋⠉⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣿⡀⠀ ⣿⡏⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠙⣿⣆ ⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⢻⣿ ⢻⣷⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⣾⡿ ⢸⣿⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃ ⠈⣿⡇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣸⣿⠃⠀ ⠀⣿⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⣿⠃⠀⠀ ⠀⣿⡇⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⠀ ⠀⢿⣷⣄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⢿⣦⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣹⣆⠀⠀⠀⠀⣀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣤⣤⡶⠿⠟⠛⠛⠛⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
AI Story Generator
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⠀⠀⠀⠀⠀⣠⡾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⣼⣦⡻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠇⣿⠘⣷⡙⣷⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣵⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢠⡟⢀⣼⡇⠘⣿⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣦⣤⡿⢋⣴⠋⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠈⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆⠻⣦⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣾⡟⢻⣿⠷⣦⡀⠀⠀⠀⠀⢀⣶⡟⢹⣿⣏⣹⡿⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠙⠻⠾⢿⣶⣾⡷⣀⠀⠀⠐⡾⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⢄⣀⠘⢿⡟⠁⡀⢀⣔⢷⣄⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣭⣤⣾⢷⣤⣛⣈⣥⣼⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠉⠀⠀⢉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠶⠶⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⣠⣶⣦⡀ ⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡾⣿⢿⣾⠟⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢹⣿⠋⠉⢻⣧ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠛⠈⠛⣾⣿⣷⡆⠀⠀⠀⢸⣧⢹⡇⠀⠀⠀⠀⠀⠈⣿⡆⠀⢸⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣘⣿⢸⣧⡀⠀⠀⠀⠀⠀⢻⣧⠀⣼⡏ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢠⣶⣿⣿⢼⣿⣿⣷⡄⠀⠀⠀⢸⣿⠀⣿⡇ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢸⣯⠛⠈⠀⠀⠛⢸⡇⠀⠀⠀⠈⣿⣄⣿⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⣿⣿⠀ ⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣿⣿⠀ ⠀⠘⠂⠀⠀⠀⠀⠀⠀⠠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠀⠀⠀⠀⠸⠿⠂⠀⠀⠀⠺⠿⠿⠀
⠀⢀⣴⡿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣀⠠⠇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢷⠀⢀⣀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣇⠉⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢾⡄⠀⠀⠀⢻⠞⠓⢺⠉⠓⣦⡀⠀⠀⠀ ⠀⣠⡾⢂⣱⠐⠛⠭⠀⢃⠀⠀⠡⡀⠈⠳⣄⠀⠀ ⣴⠫⠛⠀⠈⢇⠀⠀⠀⠀⠆⠀⠀⢡⠀⠀⠘⣆⠀ ⣇⢇⠀⠀⠀⠀⢆⠀⠀⠀⠈⡄⠀⠀⢧⠀⠀⢸⡆ ⢻⠸⡀⠀⠀⠀⢸⡆⠀⠀⠀⠐⠀⠀⠀⠀⢀⡞⠀ ⢸⠀⢳⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⣣⠾⠀⠀ ⠈⠳⣄⢆⠀⠀⠀⠀⠆⠀⠀⠀⣠⡦⠞⠃⠀⠀⠀ ⠀⠀⠈⠛⠷⠤⠤⠖⠚⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢤⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡄⢸⣧⠴⠶⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠶⠤⣼⡇⢠⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⡤⠞⣵⣇⣘⣿⡀⠀⣸⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣇⠀⢀⣾⣃⣸⣎⠳⢤⣀⣀⡀⠀⠀ ⠀⣠⣿⡁⠀⢠⡟⠉⠉⢹⣿⠀⠐⣿⠉⠉⠉⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠉⠉⣿⠂⠈⣿⡏⠉⠉⢳⣄⠀⢀⣿⣄⠀ ⠀⣿⠁⠻⣿⣿⡿⠀⢠⣿⣿⡆⢸⣿⣧⡀⠘⣯⣭⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣭⣽⠇⠀⣼⣿⡄⢰⣿⣷⡄⠀⣿⣿⣿⠟⠋⣻⠀ ⠀⣿⡇⢠⣿⣿⡿⠀⣾⣿⣿⠁⠸⣿⣿⡃⠀⣯⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣽⠀⢘⣿⣿⠃⠘⣿⣿⣷⠀⢿⣿⣿⡄⢰⡟⠀ ⠀⢸⡇⢸⣿⣿⠃⠀⣿⣿⡧⠀⠀⢿⣿⡧⠀⠸⣿⣆⢹⣆⠀⠀⠀⠀⠀⠀⣰⠏⣰⣿⠇⠀⢸⣿⡿⠀⠐⣾⣿⣿⠀⠘⣿⣿⡇⢸⡇⠀ ⠀⣸⠁⢸⣿⣃⣀⡀⢹⣿⣀⣤⣀⣸⣟⠃⣀⣀⢹⡏⠈⠻⣦⠀⠀⠀⠀⣴⠟⠁⢹⠏⣀⣀⠸⣿⣇⣠⣄⣀⣿⡇⢀⣀⣘⣿⡇⠈⣇⠀ ⢠⡏⢀⣀⣹⣿⡿⠿⢻⣿⠉⠉⠉⣽⣿⠋⠙⠛⢻⣿⣷⣤⣼⠇⠀⠀⠸⣧⣤⣾⣿⣗⠛⠋⠙⣿⣯⠉⠉⠉⣿⡟⠿⢿⣿⣏⣀⡀⠹⡄ ⠈⢿⡏⠉⢹⣿⡇⠀⣾⣿⡷⠤⣾⣿⡟⠃⢀⣶⣯⠈⠉⣁⣿⠀⠀⠀⠀⣿⡈⠉⠁⣹⣷⡀⠘⢻⣿⡷⠀⢾⣿⣷⠀⢸⣿⡏⠉⢹⡿⠻ ⠀⠀⠙⢄⡈⢿⣿⡀⢸⣿⣷⠀⣿⡿⠃⣰⣿⡿⠀⢴⡾⠛⠁⠀⠀⠀⠀⠈⠛⢶⡦⠄⢿⣿⣄⠘⢿⣿⠀⣾⣿⠇⢀⣿⡿⢁⣰⠋⠀⠀ ⠀⠀⠀⠈⣿⠈⢻⡇⠀⣿⠃⠀⡏⠀⣰⡿⠏⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠹⢿⣦⠀⢹⠀⠘⣿⠀⢸⡟⠀⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢹⣤⠼⠣⡴⠷⠤⣴⠧⠴⢿⡄⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⢠⡿⠦⠼⣦⠤⠾⢤⠼⠧⣤⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣄⣠⣇⠀⠀⢻⣄⣀⡴⣷⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⢦⣄⣠⡟⠀⠀⣸⢤⣠⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡁⡀⣠⣟⣻⣿⠀⠀⢁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⣿⣟⣻⣄⣀⢈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢁⠇⣳⠻⣤⠤⠴⠶⠶⠦⠤⣤⣀⣰⢞⠕⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠎⠢⠼⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡇⠀⠀⠀⠻⣽⣏⣳⡀⠀⢀⡼⠥⠿⠼⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⡀⢤⣈⠻⡿⠃⢀⢤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠉⠓⠲⠞⠓⠮⠴⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠴⠃⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡽⠁⠀⠀⣀⡀⠀⠀⠀⣷⠞⢷⡀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⠘⠺⢷⠄⠀⠀⡏⡇⠀⠀⠀⢹⡄⢸⠇ ⢻⠀⠀⠀⠀⠀⠰⡄⠀⠀⢀⡼⠁⠀⠀⣠⠏⠀⢠⣴⡇⣿⣦⠀⠀⠸⡇⣸⠀ ⢸⠀⠀⠀⠀⠀⠀⡇⠀⣤⠏⠀⠀⠀⣰⠋⠀⠀⠸⡎⠀⠀⠹⡇⠀⠀⣷⣿⠀ ⠈⡇⠀⠀⠀⠀⢀⡷⠊⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⢻⡟⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠉⠁⠀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣎⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠆⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠰⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⡠⣾⠸⣏⠉⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠉⢹⠇⣕⢄⣀⠀⠀ ⢠⢿⣀⣼⠉⢩⣇⢸⣏⠉⡽⢤⡀⠀⠀⠀⠀⢀⡠⢯⠉⣹⡃⣹⡍⠉⣧⣀⡾⡄ ⠸⡆⣼⣿⢀⣿⡏⠸⣿⡂⢯⡁⡅⠀⠀⠀⠀⢸⢈⡝⢐⣿⠇⢻⣿⡀⣿⣧⢰⠃ ⠀⡇⣿⣋⡈⣿⣃⣈⣿⢇⣈⣗⠸⣄⠀⠀⣠⠇⢺⣁⡸⣿⣀⣙⣿⢁⣙⣿⢸⠀ ⢸⡤⢬⣿⠋⣿⡍⣡⣿⡉⣉⠿⠷⣾⠀⠀⣷⠾⠿⡍⠉⣿⡌⢩⣿⠙⣿⡥⢤⣧ ⠀⠑⣌⢿⡄⢿⡆⡾⠗⣴⠟⢡⠞⠋⠀⠀⠙⠲⡌⠿⣦⠹⣷⢸⡿⢠⡿⣡⠊⠀ ⠀⠀⠸⡀⠇⡼⢀⠇⠼⡉⣠⠋⠀⠀⠀⠀⠀⠀⠙⢆⢉⠧⠸⡀⢇⠸⢀⠇⠀⠀ ⠀⠀⠀⡷⠐⢤⣬⠆⠔⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡞⠒⠰⣥⡤⠓⢾⠁⠀⠀ ⠀⠀⠀⠉⠁⠉⠉⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠉⠉⠉⠉⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠉⣳⣄⠀⠀⠀⠀⠀ ⠀⡼⠁⢠⠤⠖⡒⢲⡆⠀⢏⠉⢿⡝⢳⡀⠀⠀⠀ ⢰⠃⠀⠸⢤⣤⡭⠞⠀⢀⣀⣉⣥⠤⠀⣇⠀⠀⠀ ⢸⠀⠀⠠⠐⠒⠊⠉⠉⠉⠀⠀⢸⠀⢀⡟⠀⠀⡆ ⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⢏⡴⠋⠀⢀⣼⡽ ⠀⠈⠓⢦⣄⣀⣀⣀⣀⢤⣣⠟⣿⡠⢔⠮⠛⠁⠀ ⠀⠀⠀⡜⠁⡠⢜⡫⠖⠉⠀⠀⣿⠞⠁⠀⠀⠀⠀ ⠀⠀⣸⠁⠀⠚⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠶⠶⠶⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣼⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠃⠀⠀⣴⡶⠶⠶⠶⠚⠻⣿⠀⠀⠀⣏⠁⠀⢴⣦⣿⠙⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⣸⠏⠀⠀⠀⣏⠀⠀⠀⠿⠆⣠⡏⠀⠀⠀⠙⠷⠶⠶⠛⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠛⠷⠶⠶⠶⠞⠋⠀⠀⣀⣀⣠⣤⣤⣶⠶⠞⠀⠀⢻⡄⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠛⠛⠋⠉⠉⠁⠀⠀⠘⡇⠀⠀⠀⣸⠇⠀⠀⢠⣦⠀ ⢸⣿⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡇⠀⢀⣴⠟⠀⠀⠀⣸⣿⡀ ⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⡟⢁⣴⡿⠁⠀⠀⠀⢀⡧⣤⡟ ⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⣿⣴⡟⠋⠀⢀⣠⣴⣾⡿⠚⠁⠀ ⠀⠀⠀⠀⠙⠛⣷⣦⣤⣤⣤⣤⣤⣤⣤⠴⣾⣶⠟⠋⢿⣇⡤⠞⣩⠶⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠁⠀⢉⣩⡿⢟⣩⡴⠚⠉⠀⠀⠀⢸⣧⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠀⠀⠔⢋⣥⡶⠛⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⠺⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⣿⣿⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣦⠀⠉⠀⠀⠀⠘⠋⠁⢀⣾⣿⣿⣿⣿⠏⠛⣿⠛⠁⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠁⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠋⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⢉⢰⣤⣿⣧⣰⣧⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢹⣷⠶⠶⢶⣤⡀⠈⢿⡇⠙⠁⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⢿⣆⠈⢷⡄⠀⠀⠀⣦⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣿⣧⠀⠙⢦⡀⠀⢹⣆⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠿⣦⣄⡀⠀⠀⢀⣠⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡆⠀⠈⠷⣤⣨⣿⠀⠙⣷⡄⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠙⢿⣷⣶⣤⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⠏⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠹⣇⠀⠈⠁⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⡇⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣤⣤⣤⣤⣤⣴⠶⠿⠿⠛⠛⢻⣿⣿⡇⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠈⢻⡇⠀⠀⠀⠀⢸⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡏⠀⠀⠉⢿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⠦⣤⣀⠀⠀⠀⠀ ⠀⢀⣾⠟⠁⣸⠁⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⡀⠀⠹⣆⠀⠀⠀ ⣰⡟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢸⣇⠀⠀⠹⣦⠀⠀ ⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢹⡆⠀ ⣿⡄⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀ ⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁ ⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀ ⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠛⠉⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣿⠛⠲⢦⣤⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠹⣧⡀⠀⠀⠀ ⢀⣼⠟⠅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠑⠿⠃⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠹⣧⠀⠀⠀ ⣾⠏⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢽⣧⠀⠀ ⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⣿⣆⠀ ⣿⣆⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀ ⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇ ⠀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀ ⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣶⣦⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣷⠀⠀⣿⣿⣿⠀⠀⠀⢠⣿⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠈⣿⣿⣿⡆⠀⣿⣿⡏⠀⠀⣰⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⢹⣿⣿⣷⣴⣿⣿⣧⣀⣰⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣴⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣉⣩⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⢠⣾⣿⣿⠉⣿⣿⣿⣿⣿⡄⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣿⣿⣧⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⡄⠙⠻⠿⠿⠛⠡⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⣩⣝⢿⠀⠀⣠⣶⣶⣶⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⡝⣿⣦⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣮⢻⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠻⠿⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠀⠀⠀⠀⠘⠘⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣋⣁⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⡥⠀⠀⠀⠀⣠⠴⢀⣠⠤⢦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡞⢸⠁⠀⠀⣠⢚⡥⠚⠉⠀⠀⠘⣗⡄⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⠇⡎⠀⠀⣰⡳⠋⠀⠀⣠⣤⠶⠢⡿⣸⣆⠀⠈⣧⣄⢸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢳⣠⣾⡟⠓⠆⠀⠘⠙⢀⣤⣶⢿⣤⣹⡅⠀⣿⠈⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠸⡇⣾⡛⣶⡦⠀⠀⠀⠛⢱⢼⣷⠸⠋⢣⠀⡇⣹⠛⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠹⣏⠉⢟⣻⣀⠀⠀⠀⠐⠛⠛⠐⠀⠘⣴⡽⣇⠀⢸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢇⠀⠘⡄⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢹⡀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢦⠀⢻⢦⡀⠈⠰⠶⠒⠂⠀⠀⢀⡤⠀⡇⢘⡆⢇⠀⠸⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡼⡀⣟⡶⢄⡀⠀⢀⡠⠖⠁⠀⢀⡇⢸⢻⠸⡀⠀⣿⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⢳⠟⢀⠷⠈⣹⡇⠀⠀⠀⠀⣼⢣⡞⢸⠀⡇⢰⣼⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⣠⠋⢀⡼⠟⠊⠟⠀⠀⠀⠀⠀⣿⠀⠑⢯⣀⣇⣎⢏⡞⠀⠀⠀ ⠀⠀⠀⢀⡠⠾⠔⠓⢞⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡈⠛⠿⠯⣀⠀⠀⠀ ⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠉⠉⠉⠉⠉⣧⡀⠀⠀⠀⠀⠀⠀⠑⡄⠀ ⠀⠀⢻⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⢹⡆ ⠀⠀⢸⠀⠀⡼⠁⠀⠐⢆⡀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡼⠃ ⠀⠀⠘⡤⠊⠀⠀⠀⠀⠀⠈⠣⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢠⠇⠀ ⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡎⠀⠀ ⢠⢇⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡄⠀⠀⡸⠀⠀⠀ ⢸⡀⠛⠆⢀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢓⠷⠀⠀⡇⠀⢀⠇⠀⠀⠀ ⠀⢷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣰⠁⠀⣾⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⠀⠀⢀⣠⠴⠋⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡴⠁⠀⢠⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⡽⠀⠀⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣾⠀⠐⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡄⠀⠀⢠⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢰⠁⠀⠀⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⠁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀

Warning: This item may contain sensitive themes such as nudity.

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

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