⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠳⣄⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢶⣌⡳⡆⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣤⡶⠞⠛⠛⠲⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⢀⡟⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣦⣄⣀⡾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠘⣿⡀⠀⠀⠀⠀⣿⡇⠀⢀⣠⠶⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣷⣄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢠⣿⠏⠀⠀⢸⣇⠀⠀⠀⠀⡇⣇⣴⣫⠶⣿⠟⢾⣏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⣿⣿⣿⣿⠟⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡼⣾⣦⣼⠋⠀⠀⠀⠀⣿⡀⠀⠀⠀⡇⣿⣿⡁⠀⣿⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊ ⣷⣶⣤⣀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⡸⣹⣿⠀⠈⠙⣿⣤⣤⣄⣀⣀⢸⣧⠀⠀⠀⡇⣿⣿⣷⣼⡏⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⡴ ⣿⣷⣯⣛⢷⣦⡀⠀⠀⠙⢦⡈⢳⣄⠀⠀⠀⠀⢠⣇⡏⠙⣧⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣤⣴⠶⠿⢿⣿⣿⣿⣷⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣴⠟⠀ ⣿⣿⣿⣿⣷⣽⣿⠀⠀⠀⠀⠙⢦⡙⢷⡀⠀⠀⢸⡿⠁⠀⠈⢷⣄⣠⣿⣿⡿⠟⠋⠁⠀⠀⣀⣀⣠⡴⠾⣿⣿⣯⣻⢿⡄⠀⠀⠀⠀⣀⣀⡤⠤⠶⢖⢲⠀⣠⠞⠁⣰⠟⠁⠀⠀ ⠛⠻⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⡤⠽⠦⠽⠶⠤⠬⠷⣤⣴⣾⣿⣿⣿⣿⡿⠚⠛⠲⢶⣿⣿⣽⡟⠁⠀⠀⠀⠈⠻⣿⣧⣳⡴⠒⠉⠉⠁⠘⣆⠀⠀⠸⡌⢿⠁⣠⠞⠁⠀⠀⠀⠀ ⢶⣿⣿⣿⡿⠛⠃⠀⠀⠀⡿⢸⡆⠀⠀⠀⡼⠀⠀⠀⠀⡇⠘⡿⣯⣿⠏⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡽⢹⡄⠀⠀⠀⠀⢻⣤⡀⠀⢣⢸⡞⠁⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⡇⢸⠀⠀⢀⣀⡇⠀⠀⠀⠀⠇⢸⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠳⢤⡄⠀⠀⠀⡞⠁⠀⢸⡀⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⡀⠀⠀⠀⢰⡇⢸⠀⠀⠘⠫⡀⠀⠀⠰⣜⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣠⡼⠟⠛⠶⢤⣄⣀⣤⣾⣿⣿⠀⠀⠀⡏⠀⠀⠀⠀⢣⠀⠀⢀⡇⣼⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣷⠀⠀⠀⢸⡇⢸⡀⠀⠀⢠⠁⠀⠀⠀⢘⠀⠀⠈⣿⣿⣿⣿⣶⣤⠶⠛⠉⢀⣀⣀⣀⠀⠀⠉⠛⠻⣿⢿⡆⠀⠀⢇⠀⠀⠀⠀⣸⡤⠚⣋⡼⠛⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⠿⠟⠋⠀⠀⠀⠸⣧⣄⡉⠲⢤⣸⡀⠀⠀⠀⢸⠀⠀⠀⢻⣿⡿⠟⢋⣠⣴⠶⠟⠛⠉⠉⠉⠛⠛⠿⠶⣶⣬⣿⣹⠀⠀⠸⣀⡤⠞⠋⣸⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠟⠶⢦⣄⣀⠀⠀⠈⠙⠳⢶⣬⡉⠓⠦⣄⣸⠀⠀⠀⣺⢹⣶⠾⠛⠉⠀⠀⣀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⢻⢹⠀⠀⢰⠃⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶ ⣶⠟⣩⡶⠋⠉⠙⠒⠯⠝⠓⠶⣤⣀⡀⠈⠉⠛⠲⢦⣭⣉⠒⠂⢸⢸⣀⣤⣶⠶⠟⠛⠉⠉⠁⠀⠈⠉⠙⠛⠷⢶⣦⣾⣸⠀⣠⣷⡾⠛⠁⠀⠀⠀⣀⣤⣤⠶⠖⠛⠋⠉⠁⠀⠀ ⣤⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⣀⡈⠉⠛⠳⣾⣟⣯⣁⣀⣀⣤⣤⣤⠴⠶⠆⠴⢶⣤⣤⣤⣤⣼⣯⣿⣾⠟⠁⠀⠀⠀⢰⣾⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⣇⠀⢀⣾⣿⣮⡻⣮⣄⣀⣀⣀⣀⣠⣴⣧⣤⣤⣤⣭⣤⣿⣿⣿⡻⣦⠀⠀⠀⠀⣼⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⣥⣴⣿⣴⣾⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣤⣤⣤⣤⡿⠷⠶⠾⠿⢶⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣄⠀⠀⠀⠀⣀⣠⣤⡶⠿⠟⠛⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⡀⠀ ⠀⠀⣾⣿⣿⢷⣦⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶ ⠓⠢⣿⣿⣿⠀⠈⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠟ ⠀⠀⣿⣿⣿⡆⠀⠀⠀⠈⠉⠛⠻⢶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⡶⠾⠛⠛⠉⠁⠀⠀⠀ ⢶⣤⣿⢸⣿⣧⣤⣤⣤⣤⣤⣤⣄⠀⠀⠉⠉⠙⠛⢛⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣶⣶⣶⣶⠶⠶⠾⠛⠛⠛⠋⣉⣉⣀⣀⡀⠀⠀⠀⢀⠀⠀⣀⣄