⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣶⢾⠿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠇⠛⠿⠿⠛⠛⠛⣿⠷⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠟⠼⠦⠷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢹⠋⡝⣿⣿⠿⣿⣿⣿⣿⢿⠸⠀⡄⣤⣄⣤⣤⣁⣄⣤⣄⣤⢠⠀⠿⣿⣿⣿⣿⠿⡿⣿⣿⢚⡩⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣶⣠⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠷⣿⣿⣿⣿⣿⣿⣿⣸⣀⣦⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠨⠈⡦⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⢿⡿⣿⣿⢿⠿⠹⠠⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣄⣧⢿⣻⡋⣿⣿⣿⣿⣿⣿⣿⣺⣴⣿⣖⣶⣷⣿⣿⠿⣿⣿⣿⣛⣛⣟⣿⣿⢰⣿⡏⢻⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠀⠀⣀⣇⣿⣿⣿⣿⣿⣿⣿⣾⢽⣿⣿⢽⠉⠋⣗⣿⣿⣿⣿⣿⣿⣿⣾⣡⣹⠁⣿⣟⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⣿⡏⢰⠀⡅⣿⣿⣿⣿⣾⣵⣯⣿⣵⣿⣾⣻⣿⣽⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣶⣿⢻⠟⣿⣥⣬⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠗⣿⣿⣿⣿⠀⠀⡀⣿⣿⣿⣿⣿⢿⡿⣸⣆⣧⢿⣿⢻⡽⢏⠺⣷⣿⣷⣿⣿⣿⣿⣿⣽⣯⣻⡟⣿⡏⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⣿⣿⠼⠀⠁⣿⣯⡟⠿⣟⣿⣿⣾⡷⣿⣿⣿⣿⣿⣿⠹⡿⢟⠿⡤⣆⢧⣝⣿⡿⣿⠙⠋⣿⣿⣿⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡃⣿⢥⠓⡏⡺⣓⣿⣻⢛⡟⣿⢿⡝⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠈⠀⡀⣆⣹⢀⣿⠀⣿⣿⣿⣿⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡏⣾⣀⣀⣦⣖⣵⣯⠶⣿⣿⣯⣿⣼⣦⣿⣿⣿⣿⣿⣥⣿⣶⣿⢿⠈⠀⠀⣄⣀⣀⣀⣇⡏⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠀⠀⠀⠀⠀⠁⣟⣿⣺⣩⣾⣿⠿⣿⣿⣿⣿⣿⣾⢀⠀⡄⣿⢿⠙⠀⠀⠀⠀⠀⠀⣿⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣷⠻⠉⠉⠓⠟⣿⣿⣾⠟⠿⣽⢤⡷⣻⣿⣿⣿⣿⠿⠧⠿⠻⡟⣿⣿⢿⠙⠉⠈⠉⡟⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⣀⣀⣀⣋⠛⢀⠛⡘⣦⣯⣿⣿⣴⣤⣷⣿⣿⣾⣠⠀⡀⡀⣋⣜⣤⡤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛ ⣿⢹⠉⠉⠉⠁⠉⠀⠋⠘⠀⡏⠭⠭⠬⠥⠯⡿⣿⣿⡧⣿⢽⠥⡭⣥⣽⠘⠋⡿⣵⢭⠭⠤⠥⠬⡧⣿⢽⠭⠭⠭⠥⠭⠤⠁⠈⠀⠉⠉⠁⠉⠀⠋⡿⣿⣿ ⣴⣸⣷⣧⣾⣼⣷⡷⣴⢿⣿⣷⣿⣾⢿⣿⣿⣿⣴⣠⡇⣶⣾⣿⣷⣿⠟⣿⣿⠿⣾⣾⣷⠟⣾⢸⡇⣶⣿⣿⣷⣿⣾⣷⡷⣶⢿⡿⣿⣿⣾⣿⡾⣷⣿⣴⣠ ⠀⢸⡇⡇⢸⢸⡇⡆⠀⢸⡆⡇⢈⢸⣹⣟⣴⣷⠻⠀⡇⠀⢸⡇⡇⠸⢸⣷⡇⠀⢸⢸⡇⡆⢸⠀⡇⠀⣿⣿⡇⣸⢸⡇⡇⠀⢸⣷⡇⢸⢸⡏⣯⡶⢧⠙⠀ ⢦⠞⡳⡏⢤⠴⣀⢣⠀⣼⠲⡇⢄⠷⣼⢁⠋⡴⣀⠀⡄⡴⢶⣧⠇⠴⢄⠖⣠⢦⠴⢸⡇⢦⠘⠀⠀⢦⠚⣳⡋⢤⠔⣀⠣⠀⣼⠓⡇⢦⠟⣼⢀⠋⡴⣠⠀ ⠀⢲⡠⢀⠀⠀⠀⡆⠴⢀⠆⡤⠀⡀⣆⣴⢀⠀⠀⠀⠀⠀⠀⠆⡤⠀⠀⠀⠀⠀⠀⢲⡠⠀⠴⢠⠀⠀⢲⣠⠀⠀⠀⠀⡆⠔⢀⡆⡴⠀⡀⣆⣴⢀⠀⠀⠀