⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡌⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣘⠒⣿⣛⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⡿⣌⣳⣞⠀⠳⡀⠉⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠙⣷⡀⠀⠀⠀⠀⠀⠀⢳⢸⠀⢯⠳⣄⢈⢦⡈⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡘⢿⡄⠀⠀⠀⠀⢸⣻⣿⠁⢸⡄⠈⠳⡇⠑⢼⡆⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣀⠀⠀⣀⣀⡀⠀⠈⢿⣌⢿⣷⣄⠀⠀⠀⠙⠮⣦⡀⡇⠀⠀⠈⣦⣤⣋⡆⠀ ⠀⠀⠀⠀⣿⠻⢤⡀⠀⠀⠙⠛⠛⢛⣻⣯⡟⠒⠒⠚⠉⢦⢁⣿⣦⡀⠀⠀⢰⠻⡙⣷⣄⠀⠀⣼⣿⡍⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠙⢆⣀⣀⡠⢴⡟⠉⣻⣿⣶⣯⠋⠽⢻⣦⡹⠉⢿⡆⠀⣾⣤⠟⠛⣽⠆⠀⡇⢸⣿⡄⠀ ⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⡰⠋⠀⡀⣿⢹⠋⢧⡀⠀⠀⠹⣷⡄⠸⣿⠟⠻⠿⣄⠀⢸⠀⢀⣱⠈⣿⣿⠀ ⠀⠀⠀⠀⠈⠙⠷⣦⣀⣠⣾⠁⠀⠀⢸⠀⣾⣆⠀⢼⢶⣤⣀⣉⠙⣦⣴⣦⡀⠀⠀⠙⣿⣧⡏⣹⡤⡇⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣷⣤⡀⡼⣄⣯⡀⣀⣠⢈⠷⢄⡀⣐⣿⠁⠸⣅⣀⠀⠀⠈⣻⣥⣷⣿⢿⣿⡭ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⠞⣟⣿⣧⡴⣿⣗⣾⣿⣯⣻⡀⢰⣿⣯⣤⠀⠀⠉⠻⣿⣿⣡⢿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⣿⣄⠜⣿⡇⠀⠜⠙⢿⣷⠈⢹⣿⣿⣿⣿⣧⣀⠀⢀⣴⣿⠏⣿⠨⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣾⣿⣿⣛⣿⣿⠞⣻⡷⠚⠉⠉⠉⠙⢧⣽⣿⡻⠿⣿⣿⣿⣿⣿⣷⡿⠀⠿⠀⠀ ⠀⠀⢀⣤⡶⠟⣻⠛⠋⠉⠉⠉⠻⢿⣿⣙⣾⣿⣤⣀⣠⣤⣄⣀⣼⣿⣟⣁⣠⣾⡿⢻⣿⣏⣻⡇⢸⢶⡆⠀ ⢀⣶⠟⠁⢀⡞⠁⠀⠀⠀⢀⣀⣀⡀⠀⠙⣷⡄⠉⣉⣉⣭⣿⣿⠛⠉⠻⠋⠙⢉⣣⣿⣿⣿⣿⣿⡉⣼⡟⣷ ⡾⢃⠀⠀⠈⡄⠀⢠⣶⣿⣿⢿⢻⣿⣧⣀⣻⣿⡟⠛⠉⠁⣿⡧⣤⣈⣤⣤⣶⢾⣿⣿⣿⣿⣿⡿⣿⣿⠃⠁ ⠻⣿⢷⡄⠀⠘⠦⣈⠛⠻⠿⢋⣿⣿⣿⣿⠟⠀⠀⠀⠀⢘⡿⠯⠽⣯⣍⡁⠀⠀⢇⠸⠿⣿⣿⣰⣿⡟⡰⠁ ⠀⣸⠀⠹⣆⠀⠀⠈⠉⠛⠛⠓⢻⣿⡟⠛⢦⡀⠀⠀⠀⢸⠁⠀⠀⠀⠈⠛⠷⣦⣈⣶⣾⣿⣿⣿⣧⠗⠁⠀ ⠀⠹⣇⠀⠈⠻⢶⣤⣄⠀⠐⢚⡿⣿⠇⢠⡀⢣⠀⠀⢀⢸⣶⣶⣶⣶⣶⣶⣦⣨⣿⣿⣿⠿⠛⠛⣿⡇⠀⠀ ⠀⠀⠙⢷⣄⡀⠀⠀⠉⠉⣡⣿⡁⣿⠀⠀⠈⠛⠲⠴⠷⠚⠛⠿⠿⢯⣍⠉⠉⠉⠉⡴⠃⠀⠀⣰⡿⠁⠀⠀ ⠀⠀⠀⠀⠉⠛⠿⠷⣶⡞⠁⡸⢛⣿⡀⠀⡠⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢷⣾⣧⡀⢀⣾⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣷⠋⠀⣧⡞⠈⢧⠀⠈⠓⠲⠤⣤⣄⣀⣾⠋⠑⣶⣼⣿⣿⣿⣋⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⡇⠀⠀⠘⢷⠀⠈⢣⠀⢀⣴⣾⣻⣿⠋⠁⠀⣠⢿⣿⣿⣿⣿⣿⡉⠉⠉⣑⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⡶⠲⢯⣴⣊⡥⠞⠋⢩⣉⠉⠁⠈⠉⠉⣥⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠹⡄⠈⠙⢻⡐⣦⣀⠀⣹⣷⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⢹⠀⢀⣠⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⢸⣾⢿⣿⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣴⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠹⣿⣿⡿⠿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡀⠀⢿⣿⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣗⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢿⣇⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠘⢿⣷⣤⣀⣲⡿⠟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⠉⢿⡟⠁⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⠞⢧⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀