⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⡇⠈⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣶⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡈⠉⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠘⠲⠆⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣭⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠋⠀⠀⠀⠀⣤⣀⠤⠤⠤⠤⠔⠒⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⢸⣿⡆⠀⠈⠓⠤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⢀⡶⠁⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠞⠁⠀⠀⢸⣿⠀⠀⢠⠶⣏⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠀⢠⡞⠠⠊⠀⠀⠀⠉⢳⢦⣤⣀⣤⠀⠀⡿⠀⠀⠀⠀⡾⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣟⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣾⣥⣤⣴⠶⠁⡴⠁⠀⠀⠀⠀⣰⢃⣴⣫⡶⠟⠉⠀⠀⠀⠛⠀⠀⠀⠘⢀⣰⣿⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⣴⠉⣆⡇⠀⠀⠀⢹⡟⢿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡞⠀⠀⠀⠀⢰⠀⠀⣴⣟⣛⣯⠥⠤⣤⠶⢺⡄⠀⠀⠀⠀⢀⣤⠿⣿⠃⢀⣴⣿⡀⠀⠀⠀⠀⠀⠀⢿⠀⠹⢱⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⣸⠃⠀⠀⠀⠀⣸⠀⢰⣿⡿⠛⠁⠀⢸⡟⠘⣦⣷⠀⠀⠀⠀⡟⠁⣰⡯⢶⣿⡿⠈⣧⠀⢸⣄⠀⡀⠀⠘⡆⠀⠈⢧⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣼⡏⠀⠀⠀⠀⢠⡇⢠⣿⡏⠀⠀⠀⠀⣼⠀⠀⠘⣾⡆⠀⠀⠀⣧⠞⠋⢀⣾⡿⠁⠀⠸⡄⢸⠹⣦⣇⠀⠀⠘⠀⠀⠈⣇⠀⠙⠲⠙⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢋⡼⣁⡇⠀⠀⡀⣼⡧⡾⠁⠻⣄⠀⠀⢀⢿⠀⣀⠀⠙⣇⠀⠀⢠⡇⠀⢀⣾⡟⠡⢀⡀⠀⣳⣾⠀⠹⣿⠀⠀⠀⠀⡀⠀⣿⠀⠀⢿⡖⠚⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣡⣿⠀⠀⠀⣷⣟⣹⣧⣶⣶⣿⣮⡀⠀⢸⠀⣾⡀⠀⠸⠀⠀⢸⡇⠀⣾⡟⠀⠀⠀⣹⢾⣉⣿⠀⠀⢻⡇⠀⠀⢀⡇⢰⣿⠀⢠⣻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣠⣿⣼⠀⠀⣿⣿⣿⣿⣟⣻⣭⣟⣿⣦⣸⡿⠻⡇⠀⠀⠀⠀⢸⢷⣼⡟⠀⢀⣴⣾⣵⣶⣾⣿⣄⠀⠀⡇⠀⠀⣾⣧⣼⣿⡄⡟⢻⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⣹⣆⢘⣿⣿⣧⡾⠋⠁⠀⠈⠙⠻⣿⣿⣤⣻⠀⣦⠀⠀⢸⣷⣿⣠⣶⠿⠋⣉⣀⣀⣀⠉⣻⣷⣼⡇⠀⢠⣿⣿⡿⠿⣿⡁⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠁⡟⣿⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⢹⣶⡿⣆⠀⢸⣿⣿⣯⡷⠚⠉⠁⠀⠀⠉⠛⢯⣽⣿⡇⠀⣼⣿⣿⡁⠀⢹⡷⠐⠀⠀⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⢳⡉⢻⣷⢟⣆⠀⠀⠀⠀⠀⢾⣿⡇⠈⠹⡇⣿⠃⠘⣆⣼⡿⠟⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⣿⠃⢠⣿⡿⠉⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡈⢷⡈⣻⡆⠹⣥⠀⢠⣄⠀⠘⣿⡗⠀⠀⠀⠛⠀⠀⠘⣿⠀⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⡟⠀⣰⠇⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠁⠙⢧⣽⣿⣿⡀⠈⠛⠛⠒⠒⠓⠒⠚⠉⠀⢀⣸⡀⠀⠀⠘⠧⣀⣈⣛⡁⠀⠀⠀⠀⠀⢀⡼⠃⣼⣿⠟⣠⡼⠃⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠒⠒⠉⠀⣰⠟⠋⠩⢁⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⢹⣇⠀⠀⠀⠀⠀⢠⣶⠶⢦⣤⣤⣄⣀⣀⣀⣤⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣖⡿⠟⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡷⣾⣏⠻⣦⣌⠂⠄⡀⣟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣼⠻⢿⡀⠈⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⡏⢽⣻⣿⣆⣈⣛⣿⣦⣄⣿⣦⣄⣀⣠⡴⠖⠋⠈⠉⡝⠋⠉⢛⣿⠀⠀⡀⣄⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⣿⠸⣻⠇⣉⣿⠉⠉⠉⠉⣸⣟⠙⠿⢽⣽⣽⠿⠻⣛⡿⠻⠛⣛⣛⣯⣧⡷⠟⢛⣿⡏⠛⠷⣦⣴⠶⠿⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣭⣿⣿⡀⠀⠀⣠⡏⠹⣆⢀⣠⡟⠙⣿⣶⣾⣶⣾⣿⡿⠋⣽⠏⠀⣠⠞⢹⠀⠀⠀⠀⠀⢠⠄⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣼⠁⠀⠈⢉⣭⣿⡇⠀⢠⠏⣼⣳⡿⠟⠛⠷⣶⡞⠉⠙⢻⣟⣿⣄⣴⣃⣠⠞⠁⠀⣾⠀⠀⠀⠀⢠⠇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣰⠇⠀⢀⣴⠟⠁⢿⡇⠠⢿⡾⢛⣛⣥⠶⢾⣿⢿⣿⠛⠶⢶⣽⡋⠙⢿⡉⠹⢮⡳⡀⡿⠀⢀⠀⠀⣸⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⡀⠀⣠⠞⠀⠀⣰⠃⢀⡴⠋⠀⠀⢀⢿⡇⢠⠏⣠⣾⡟⠀⠰⠦⣾⠀⣿⠔⠒⠒⠛⡿⣧⡀⢳⡀⠀⠙⢿⣣⠀⣼⠀⢠⡇⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⡖⠁⠀⢀⣼⠃⡴⠋⠀⠀⠀⣴⢻⠸⡇⣯⣴⣿⢤⣷⠀⠀⠀⢸⡄⢹⠀⠀⠀⢠⡧⢹⣧⠈⡇⠀⠀⠀⠙⠀⡷⠀⣼⡇⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⣼⢁⠞⠁⠀⠀⣠⠞⠁⢀⣴⠟⠁⢀⡟⢸⠸⣆⠀⠀⠘⡇⢸⠀⠀⠀⣸⣥⠖⡿⠀⡇⠀⠀⠀⠀⠀⣧⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⡷⠋⠀⠀⣰⠞⠁⢀⡴⠛⠁⠀⢠⡞⠀⣼⡄⠘⡗⣆⠀⣿⢸⢀⡠⢾⠁⠸⡀⢹⣼⣧⡀⠀⠀⠀⢀⣿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣼⠋⣠⠴⠋⠀⠀⢀⡴⣫⣶⣾⣿⡇⠀⡇⠸⣶⣿⢿⣾⠀⢸⡀⠀⣧⣠⣿⣷⢳⣀⠀⠀⢸⣿⡿⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣧⠀⢘⣿⠋⢁⡀⠀⣠⣴⣿⣾⣿⡿⢾⡇⠁⣿⣇⣠⣿⣿⣾⣿⣤⣼⣷⠻⣿⣟⢦⣙⣷⠇⠙⠣⣿⣿⠇⠀⠈⢷⡀⣠⣴⣾⠿⠷⣤⣄⡀⣹⡀⠀⠀⠀⠀⠀