⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⠒⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠋⠀⠀⢀⣀⢀⡀⠈⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠀⠀⠀⢀⣴⣾⣭⠇⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⢁⡀⣀⣤⣤⠶⠋⣹⡭⠙⠛⠲⣄⠀⠀⠀⠀⠈⠀⠙⠳⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⠾⠃⠀⠀⠠⡿⠟⣉⣀⠀⣸⣄⢠⣤⣄⢄⠘⣆⠀⠀⠀⠀⠀⢤⠀⠙⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢈⣵⠞⠀⢀⣀⣠⣴⠾⠉⠀⣿⡿⢇⣾⡇⢹⣾⣧⣹⣄⠀⠀⠰⣄⠀⠑⠤⣼⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢹⡅⠀⢀⡽⣾⡿⢣⣤⣴⣾⣿⣷⣾⣿⡇⣸⣿⣼⣿⡟⣦⡀⠀⢹⡣⠀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⢁⣶⣾⣿⠋⣼⣿⢟⣩⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡿⠜⢿⡆⢸⡇⢳⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢃⣾⣿⢟⣥⣴⣮⠉⠉⠉⠁⠀⠉⠹⢿⣿⣿⣿⣿⠿⣿⡀⠀⢳⣼⠁⡼⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣷⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⡴⠀⣹⣿⣿⡙⣄⠉⣷⠀⢠⡇⡆⠁⠀⠀⢼⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣁⣾⣿⣿⣿⠇⢠⣴⡶⢶⣤⣤⡴⠋⠀⣰⡟⠁⠀⢸⣌⣰⣹⡆⢸⢳⡇⠀⣀⣀⣹⣟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣸⠿⣿⣿⡟⠀⠀⢸⣷⣷⣿⣤⣽⣦⡾⠋⠀⠾⢉⣋⣉⣙⠿⠇⢸⣼⠃⠀⣻⣿⢹⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡽⠀⡉⣿⠃⠀⠀⢹⣿⣿⣿⠭⠧⣿⡇⠀⠀⢺⣿⣿⣏⡷⠶⡆⢰⡹⡄⠀⠉⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⣴⣣⡇⠀⠀⠁⠉⠙⠋⠀⠀⢡⠇⠁⠳⡄⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⡟⣶⡀⢠⡆⠀⠀⠀⠀⠀⣿⡿⠁⢰⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣷⠀⣧⠀⠀⠀⠀⢸⣿⣿⣤⡬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⣿⠀⢸⡆⠀⠀⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⣰⢟⡹⢦⣀⡼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⡶⠛⢶⢀⣿⡇⠈⢷⡀⠀⢾⣶⣶⠶⠦⣤⣤⣤⣄⡀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡾⣋⣉⠄⠁⢸⣿⠁⠀⠘⣧⡀⠈⠛⠷⢧⣬⡭⠇⠀⡟⠁⠀⣶⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣟⣢⢦⣀⡀⣀⠀⣿⡂⠀⠀⠘⢷⣄⠀⠀⠀⠀⢀⡰⠂⠀⠀⢸⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⢒⡋⠉⠀⠀⢸⣿⡇⠈⠿⣷⣿⠀⠈⠀⠀⠀⠀⠀⠙⠳⢦⣤⣴⢾⡇⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢛⣩⠴⠛⠋⠀⠀⠀⠀⢷⣿⣿⣄⠀⠸⡿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣉⡤⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⢿⣿⣿⡄⠀⠙⡋⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡌⢸⣧⣄⠀⠀⠀⢄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⢁⠼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⢿⣶⣶⣬⣦⣄⠀⠀⠀⠀⠀⠀⢸⢠⠞⠀⢸⣿⣿⠀⢸⠀⠀⡇⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⡾⠋⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⣦⡙⢿⣟⣷⡏⠓⠲⢤⣄⣀⣀⡟⠁⠀⠀⣸⣿⣿⠀⣾⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⣰⠏⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⡀⠀⠀⠈⠻⣦⡙⠙⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⣿⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢱⣏⡀⠆⠀⠀⠀⣀⢿⠄⠀⠀⠀⠀⠀⠀⡀⠀⠙⢻⣦⡀⠀⠀⠈⠻⣆⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣸⠃⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡼⣱⣞⣽⣿⣂⠀⠀⡀⢿⡆⠀⢲⡀⠀⠀⠀⠀⠘⢦⣀⢀⠈⠻⢦⣄⠀⠀⠈⠳⢜⣇⠀⠀⠀⠀⠀⠀⢠⣿⡇⠁⣰⡟⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⣵⣿⣾⣿⡿⢿⠀⣰⣆⠸⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠙⠳⢦⣄⡁⠀⣽⣇⠀⠀⠀⠀⢀⣾⡟⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⢁⣿⣿⣿⣿⡇⢾⠀⠸⣿⡀⣿⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠾⠿⢷⣤⣌⡙⠳⢦⡹⣦⠀⠀⠀⣾⣿⠇⣸⠋⠀⠀⠀⠀⠀⢀⣼⡇⠀⣸⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠰⠁⣼⣿⣿⣿⣿⣇⠚⠀⠀⢿⣷⡘⣷⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣄⡑⢈⢷⡀⣸⣿⠏⣰⠇⠀⠀⠀⠀⠀⠀⢿⡏⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠰⢈⠁⠀⢿⣷⣹⣿⣿⣿⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣿⣟⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠄⠀⠀⠀⠹⣿⣿⣿⣿⣶⣶⡿⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣇⠀⠦⠀⠙⠲⢬⣿⣿⣿⣿⣿⣷⣦⡤⠄⠰⠆⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠘⣷⠾⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢻⡶⠤⠤⠄⣼⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⣶⠀⠀⠀⢀⣀⠴⠆ ⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⠒⣶⣶⣶⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣦⡈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠉⠛⠛⣛⣉⣄⠀⠊ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣴⣿⣿⣿⣿⣿⣦⡄ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢹⠀⠀⠀⠀⠀⠀⣰⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⣠⣴⠿⣝⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡏⠀⠀⠀⠀⠀⢀⡟⣰⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿ ⣿⣼⣿⣿⣿⣿⣿⣿⣿⣟⠻⢟⡉⢙⠛⠛⠿⢿⣿⣿⣿⠿⢿⣿⠟⠿⠿⠿⠿⠾⢿⣿⣿⠚⠒⢶⣶⣦⣤⣄⠀⠀⢀⣾⢻⠇⠀⠀⠀⠀⢈⣈⣡⣿⣿⠿⠛⠛⠋⠉⠀⠀⠀⠀⠀ ⣟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⡿⣃⡐⠂⠐⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⢺⠟⢃⢀⡶⡟⣧⣼⣿⠟⠻⣶⣿⢁⣢⣤⣴⡶⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⠀⠘⢻⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⠀⠀⠀⣀⠀⠀⠀⠀⢾⣦⣾⣿⠷⢿⣟⡉⡏⠀⠀⣼⠿⠛⠉⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀