⠀⠀⠀⡴⣶⣿⣟⡻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢋⡟⢉⣴⣿⣿⠿⣿⣟⠉⠉⠀⠀⠀⠉⠻⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⢁⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠁⠀⠀⢀⣿⣴⡟⠁⠀⠀⢀⣸⣿⣶⣀⣀⡀⠀⠀⠀⣹⡿⡿⡿⣭⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⠿⠳⠎⠀⣴⣾⣿⣿⡿⠋⠉⠉⠻⣶⣾⠋⠀⠀⠈⠈⣿⡄⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡿⠿⢛⣻⣽⣾⣿⠟⠁⠀⠀⠀⠀⢀⡤⠖⠛⠉⠀⢸⣿⠄⠀⠀⠠⢿⣿⣿⡏⠃⠀⠠⠀⠀⣸⣿⣷⣄⣠⠀⠀⣸⣿⡀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⣋⣡⣴⣶⣿⣿⣿⣟⣁⣀⣀⣀⣀⡤⠚⠁⠀⠀⢀⣠⠤⠼⣧⣤⣤⠀⢠⡅⣹⣿⣧⣄⣀⣀⣀⠀⣳⣿⣿⡿⠉⢀⢀⣽⣿⠙⣄⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⣠⡴⠚⡿⠁⠀⠀⠙⠻⣧⣞⣀⣾⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣉⣠⣶⣯⣾⣿⠻⣆⠈⢧⡘⢿⡟⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠙⠧⣈⠉⠛⠿⢿⣿⣿⣿⡃⠀⠘⢧⠈⣧⠀⢿⣄⠀⠀⠈⠉⠙⠲⠦⣤⣀⠀⠀⠀ ⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣠⠏⣠⠟⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠈⢧⢸⣆⠘⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⠈⠀⠒ ⢀⡤⠼⣆⠀⠀⠀⠀⠀⡸⢁⡞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠈⠃⠿⠀⢿⡟⠛⠿⠿⣿⣿⣿⣷⣦⣤⣀⠀ ⠏⠀⠀⠹⡀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢄⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠈⣷⣤⣀⡀⠀⠉⠛⠛⢿⣿⣿⣷ ⠀⠀⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢯⣦⠀⠀⠀⠀⢀⠹⣿⡆⠀⠀⠀⢹⣿⣿⣿⣷⣦⣄⠀⠀⠘⣿⣿ ⠀⠀⠀⠀⠀⠙⣆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠘⡆⠹⣿⣆⠀⠀⢸⣇⠈⠹⣿⣿⣿⣆⣴⣾⣿⣿ ⠀⠀⠀⠀⠀⣠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⣦⡀⠘⢷⣄⠀⠀⠑⠦⠀⠀⠂⠀⠀⠹⡄⠀⠀⠀⢹⣆⠘⣿⣧⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⡄⠀⡀⠀⠀⠀⢹⡽⢤⡈⠻⡝⠢⢄⣀⠀⠀⠀⠀⠀⠁⢻⡀⠀⠀⠘⡟⠳⣌⢿⣷⡀⢸⣦⣾⢿⣿⣿⣿⣿⣿⠿⠿ ⠀⠀⠀⠀⡎⢠⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠘⣤⠘⠀⠀⠀⠀⢳⡀⠑⢦⣙⢦⡔⠛⠙⠒⠦⣤⣄⡀⠘⡇⠀⠀⠀⣿⣦⠈⢷⠛⢿⣾⣿⣶⡿⠛⠉⠛⢉⣡⣶⣿ ⠀⠀⠀⠀⠇⢸⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⢣⡀⠀⠀⠀⠈⢷⠀⠀⠈⠓⢽⣆⡀⠀⣠⣴⣶⣯⣝⣻⡀⡄⠀⠸⣿⠀⠓⠢⣤⣽⣿⡅⠀⣠⣴⣾⣿⣿⣿⣿ ⠀⠀⠀⠸⠀⢸⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣀⣀⡠⠝⢦⣠⡀⠀⠈⢷⠀⠀⠀⠀⢀⣩⣿⣿⡿⣌⠉⠻⣿⡇⡇⠀⡆⣿⣇⠀⠀⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⢸⣯⡇⠀⠀⢱⠀⠀⣧⠀⠀⡇⢸⡤⠞⠋⠁⠀⠀⠀⠀⠑⢽⣦⡀⠫⠳⡀⠀⠈⢱⢿⣿⣿⣷⣿⡇⠰⢻⣇⡇⠀⣿⡟⣿⠀⠀⡇⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣾⣿⡇⠀⠀⢸⡀⠀⢹⡀⠀⣧⡟⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠿⣦⣄⠹⣆⠀⠈⠘⣿⣿⣿⢿⡇⠀⢸⣿⡇⠀⣿⣷⢿⡀⢀⠀⠀⣿⣿⣿⣟⣿⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⣿⣯⡇⠀⠀⢸⣧⠀⠈⣇⠀⣿⡇⣠⣤⣶⣶⣶⣶⣶⣭⡀⠀⠀⠀⠈⠉⠑⠾⣷⣄⠀⠈⠓⠛⠉⠀⠀⢸⣿⡇⢠⣿⡏⢿⣇⣼⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢹⡟⡇⠀⢀⣾⣿⡀⠀⢹⡄⢧⣿⣿⡏⠹⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠀⠀⡞⢹⡇⢸⣿⡇⠀⢻⡟⠀⡠⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣇⡇⢸⣼⣿⣾⣇⠀⠈⢿⣾⡟⠿⣇⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣸⢻⡇⠀⢸⠟⢠⣇⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⢀⡿⣻⣿⠡⢿⣧⠀⠈⢿⣧⠀⠀⠉⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⡟⣼⠀⠀⣿⠀⣸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⠟⣠⠟⠁⠀⠈⣿⣧⡀⠛⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⢀⣾⣇⡟⢠⡏⠀⢰⡇⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⢿⠀⠁⢀⣠⣴⣾⢿⣿⣷⡄⢹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⣱⠏⠀⠀⢠⣿⣸⢿⠇⢸⠁⠀⣾⣥⣤⠟⠓⢒⣦⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡀⢸⣶⣾⢿⣋⣽⣾⠿⠟⣯⠹⣆⢿⣾⡿⠟⠢⣀⠀⠀⠀⠀⠀⠀⠈⠻⠧⢤⡤⠴⠚⠁⠀⢀⡴⠃⣻⡏⡼⢀⡏⠀⠀⢿⠀⠀⠀⠀⠘⢉⣩⠾⠿⠻⢷⡀⠀⠀ ⠀⠀⠀⠀⡀⠀⡇⠈⣷⣾⠿⠟⠉⠀⢀⣠⣼⠿⣿⣿⢿⡀⠀⠀⢀⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠘⣿⢰⠇⢸⣏⠀⠀⠈⠀⣠⣦⣴⡶⠋⠀⠀⠀⠀⠀⠈⠢⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⢀⣠⣴⣿⡛⣉⢰⡾⣿⠃⠀⠙⢦⡀⣼⣿⠇⢰⣿⠁⠉⢻⣿⡒⠦⠤⠤⠤⠞⠁⠀⠀⡼⠁⡼⠀⡇⠈⢳⣄⣠⣼⠟⣩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢟⣻⣿⣿⣿⣷⣷⣿⡟⠀⠀⠀⠀⢈⣿⠇⠀⢸⣿⠀⠀⠀⢻⡳⡄⠀⠀⠀⠀⠀⢠⠞⠁⠀⡇⠀⠁⢀⣿⣿⡿⢁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡭⣫⣍⣿⡿⣟⣿⡇⠀⠀⠀⠀⣸⣿⠀⠀⣾⣿⡀⠀⠀⠀⠹⣜⠆⠀⠀⣠⠞⠉⠀⠀⠀⡇⠀⣀⣾⡿⠋⣠⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⡾⣟⣫⠷⠿⠋⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡏⢇⠀⠀⣀⣀⣈⣷⣴⡚⠁⠀⠀⠀⠀⠀⣇⣧⣻⣏⣴⣾⣿⣿⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⠁⠸⠋⡙⠠⢀⡰⣿⠀⠀⠀⠀⠸⣿⡇⣀⡤⢿⣧⠼⠚⠉⠁⢠⡏⠀⢀⡟⠛⢷⡦⣀⡀⢀⠿⠇⢸⣿⠋⢾⣿⠛⣦⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠀⠀⠀⢻⠀⠀⠀⠀⠰⣧⡇⡟⠀⠀⠀⣠⠴⢛⠋⠁⠚⠁⠀⠀⠀⣠⠞⠋⣤⠀⠸⠳⡄⠀⠙⠓⠟⠻⣀⠘⣿⣿⠴⠟⣿⡿⠋⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀