⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⡒⠋⣉⡍⠉⣉⠽⠛⢉⡠⠖⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠖⢉⡴⠊⢁⡴⠊⢁⡤⠚⠉⢀⡠⠔⢺⡩⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⣴⠥⠤⠭⣤⣀⣉⠀⠰⠋⠀⣀⠔⠋⠀⢀⡤⠳⡙⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠀⡾⠀⡾⠀⢰⠆⠀⡟⠳⢶⣜⡃⠀⣠⡶⠛⣀⡴⠿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣥⣧⣤⣧⣤⣥⣤⣼⣀⣀⠃⠀⣸⠈⢙⠧⣍⠀⠼⠋⢀⠜⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡞⠀⡸⠑⢤⡐⠁⢠⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠋⠙⣿⣿⡿⠛⠉⠈⠹⠿⠿⠋⠑⠧⡠⠏⠙⣶⡁⢠⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠷⠒⠊⠉⠁⠀⠙⠉⠀⠰⠤⠤⢄⣀⠀⠀⠀⢸⣿⣦⡴⠁⡽⢇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠔⠒⠒⢦⠀⢀⡀⠀⠀⠀⣀⣀⣀⡈⠁⠀⠀⠀⣸⣿⣿⣾⣁⣜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡸⣄⠘⠇⡰⢣⠏⠀⠀⠀⢾⠁⢶⡄⠉⡆⠀⠀⠀⣹⣿⣿⢋⡼⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠈⠉⠉⠀⡏⠀⠀⠀⠀⠈⠲⠥⠤⠚⠁⠀⠀⠀⢀⠙⢣⡯⡄⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠻⠀⠘⠖⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠯⣀⡀⠀⡀⢲⡀⠀⠀⠀⠀⢠⡀⢀⠀⢠⣄⣸⠦⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡜⢇⠸⣠⠀⣳⠚⣟⢪⣤⡄⡆⢰⡆⠈⠁⠛⠀⠈⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣇⠈⠳⢥⣀⡃⠆⠐⢆⣀⠷⠻⡦⠀⣶⠀⣶⠀⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⡄⠀⠀⠉⠉⠉⠉⠀⢀⡄⠀⠀⢠⡄⢠⢠⠋⣿⣻⣿⡶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡃⠈⠇⠀⡄⠠⠿⠀⠘⠃⠀⣤⠈⠁⡼⠃⢠⣿⢿⣽⣻⢷⣯⣟⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣻⡹⠀⡤⠁⢠⡄⠀⠿⠀⠀⢀⡤⠺⡆⠀⠰⣿⣻⢾⣽⡻⣾⢽⡿⣽⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣶⣦⣤⡤⡴⠖⣶⠚⣉⠁⠿⠀⠀⠀⢸⡛⠫⣿⣾⣽⣳⢯⣟⣿⢷⣻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⣽⣿⣽⣾⡟⣣⠈⣆⠈⣀⠘⠃⠀⠀⠀⠀⢸⡙⣦⠈⢳⣿⣼⣻⣞⣿⣯⣷⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⠏⢰⢻⣴⣿⠀⠿⠀⣤⠀⠀⠀⠀⠈⠁⠘⡇⢸⣿⢿⡿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢐⣿⡽⣯⣿⣿⠀⡏⠀⢁⡈⠺⡀⠀⠛⠀⠀⠀⠀⠀⠀⣸⠁⣾⢯⣟⣽⡿⣾⣽⣟⡿⣷⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⣿⣽⣳⣿⠘⡄⢣⠀⠈⠁⣀⢻⠆⠀⠀⠀⠀⠀⢀⡴⢁⢜⣿⣟⣾⢿⣽⣳⣯⢿⣽⢿⡽⣯⣷⡀⠀⠀ ⠀⠀⢠⣾⢯⣟⣿⣞⣷⣻⣧⠘⣄⢣⡀⠀⠉⠀⠀⠀⠀⢀⡠⠒⣁⠔⠁⣼⣿⢿⣽⣻⣾⢿⡽⣯⡿⣯⣟⡷⣯⢷⠀⠀ ⠀⢀⣿⡽⣾⣽⣻⢿⣞⣷⣻⣧⡈⢆⠵⡀⠀⠀⣠⠔⠚⡡⠔⣊⣥⣴⡿⣿⣽⣻⣾⣻⣞⣯⣟⣿⣽⣳⢯⡿⣽⣻⡇⠀ ⠀⣸⣯⢗⡿⣾⢯⣟⡿⣞⡷⣯⢷⡀⢣⠙⠔⢋⠤⠒⣩⣴⡿⣿⣽⣳⣟⣷⣟⣯⢷⣻⣞⡷⣯⣿⣳⢯⡿⣽⣳⢯⣿⡀ ⠀⣿⣞⣯⢷⣿⣻⢾⣽⣻⢿⣽⣻⢿⡄⠡⠖⢁⣴⡿⣯⢷⣻⣷⣯⣷⢿⣻⢾⡽⣯⢷⣯⣟⡷⣿⡽⣯⣟⡷⣯⣟⡾⡇ ⢸⣿⢾⡽⣞⣯⣟⡿⣾⡽⣯⣟⡿⣯⣿⡆⣠⡿⣾⣽⣿⣻⣟⣷⣻⣞⣯⣟⣯⢿⣽⣻⢾⣽⣻⣯⣟⡷⣯⣟⡷⣯⣟⣿ ⣸⣯⢿⣽⣫⣿⣽⣻⢷⣻⢷⣯⢿⣽⣻⣟⣻⣿⣽⣳⢯⣷⣻⣞⣷⣻⢾⡽⣞⡿⣾⣽⣻⣞⡷⣿⣽⣻⠷⣯⣟⣷⣛⣾