Sad Pepe Emojis & Text

Copy & Paste Sad Pepe Emojis & Symbols

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

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

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