⡀⠀⢻⣅⢧⣾⣯⣯⣽⣶⣷⣞⣷⣏⣿⡳⣿⣿⣷⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⡟⣾⣧⣿⣿⣿⣧⣿⣧⣻⣿⡿⣿⣻⣧⠀⢀⣠⠴⠚⠉⠉⠉⠉⠉⠙⠲⠤⠦⠔⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣾⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠹⡷⢻⣷⣿⠗⠋⢀⣠⠴⠒⠚⠛⠛⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⣣⡟⡿⣿⣻⣾⣷⣿⣾⣿⡟⣾⣿⣿⣿⠀⢳⡿⠋⠁⠀⠐⠋⢀⣤⡲⠯⠭⣑⠢⡈⠳⠀⢀⣠⢤⣤⣄⡀⠀⠀⠀⠈⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀ ⣡⣿⡏⣼⢱⣿⣾⣿⣤⣿⣿⣞⣻⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⣠⡿⠟⠉⣉⣠⠼⢻⣀⠀⠤⡍⠺⣅⢀⡈⠙⠻⣦⡀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀ ⡒⣽⢣⡇⠸⣖⣿⣿⣾⣿⡿⣿⣻⠃⣅⡟⠁⣠⠀⠀⣠⣴⣶⡟⠉⣀⣴⣾⠟⢁⡴⣿⣿⡟⠀⢹⡀⠈⢳⣏⠳⣦⡈⢿⣆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠿⠷⠶⠿⠿⠿⠿⠿⠷⠶⠿⠾⡟⠀⡼⠁⢠⠞⣱⣿⠋⢀⣾⣿⣿⠏⢀⡞⢹⣿⢹⡇⠀⢸⡇⠀⠀⣏⣧⠘⣷⡀⠻⣇⠀⠀⠀⠸⡶⠶⠶⠶⠦⠦⠦⠤⠤⠤⠤⠤⠴⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸⠀⡴⠁⣠⡿⠁⣰⣻⡿⢃⡏⠀⡞⠀⣿⡇⠘⡇⠀⢘⣷⠀⠀⢸⢸⣇⢸⣳⠘⣾⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠁⢸⢁⣼⡿⠁⡼⣱⡿⠁⣾⠁⣸⠃⢰⢻⠇⠀⡇⠀⢧⣿⡀⠀⠈⡇⣿⠀⡇⣇⠘⣧⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⡆⣠⡞⣼⠇⡼⢡⣿⠁⠰⡏⠀⣿⠀⢸⢸⠀⢠⢳⠀⢸⢇⣇⠀⠀⠃⢱⡇⢸⠘⡄⢸⠳⣄⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠞⣰⢳⠁⣿⢰⣡⢼⡗⠒⠒⣷⠲⣷⠄⢸⣸⠀⢸⡼⡆⠈⢿⡼⡄⠀⢸⡈⡇⢸⡄⢧⠀⡇⢿⢧⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡶⠋⢠⢿⡆⡆⢻⣾⠁⠘⠇⠀⠀⠻⠄⠿⡄⠀⢿⡆⠀⢳⣻⡉⠙⢿⡻⣦⣌⣧⡇⢸⢣⢸⢀⠿⣼⠀⢣⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡿⠋⠀⠀⡏⣼⢳⠘⢎⠹⣄⠀⢀⣀⣀⣀⡀⠀⠀⠀⠈⠛⠀⠀⠙⠓⠀⠀⠓⠜⠋⠹⣷⣼⡈⢦⣿⠄⢻⡀⠈⣇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⢰⠏⠀⢀⡞⠁⣿⢹⣾⡷⡌⢧⠘⢿⣿⣶⠾⢾⣽⣿⠀⠀⠀⠀⠀⠀⢀⣤⢤⠤⣤⣀⠀⠀⠘⢿⣇⠀⢻⠇⠀⣇⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⢠⡏⠀⠀⡇⡸⡿⡇⡇⠈⡇⢸⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⠿⠛⠻⢷⣿⣷⣄⠀⢸⣟⢆⠘⢧⠀⡜⠀⡟⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⢸⣄⣿⠀⠀⠀⡇⡇⣸⣰⠃⢠⠇⡼⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢠⠿⣿⣯⣧⠈⢳⣇⢰⡃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠈⣿⣹⠀⠀⣸⣧⣿⠟⠁⣠⢞⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⣠⡿⣣⢃⡇⢻⠀⠀⣿⡜⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠃⠀⢿⣏⡇⢰⠻⡟⠁⣠⠞⣵⠟⡿⣄⠀⠀⠀⠸⡷⠒⠒⠲⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⣰⣟⠛⣡⠎⡇⢸⠀⢠⢻⡇⢸⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠁⠀⢀⣯⣿⢸⡟⠀⡇⢰⠃⢸⡟⠀⠹⡟⣦⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⢀⣼⣿⡯⡟⢹⢸⠃⡼⢀⡎⣜⡇⠸⣆⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⢠ ⠀⡤⠞⠉⢀⣀⣠⣴⣻⢿⣿⣸⠱⡇⣟⢿⡀⢻⣇⠀⠀⢳⣏⣷⣄⠀⠀⠹⢤⣀⣀⡤⠞⠁⠀⠀⣠⡴⢻⣏⡿⡸⢁⡏⣼⣰⣣⢞⣴⣿⡀⠀⠙⣷⡄⠀⠀⠙⣄⠀⠀⠀⠀⠀⣾ ⠞⢀⢔⣿⠖⢛⡟⢩⠋⢛⣼⠇⠀⣹⢹⠀⢿⡦⡝⢧⣀⢸⢿⡏⠈⠳⣄⠀⠙⠒⠒⠀⠀⣀⡴⢻⣿⢃⣏⣿⡗⣡⠏⢀⣿⣿⢻⡘⡏⠘⢷⣄⠀⠈⢿⡄⠀⠀⢹⠀⠀⠀⠀⢰⠙ ⠀⡛⠙⡆⢠⡏⠀⠀⣠⡾⢋⣤⡾⢁⣾⠀⡌⡇⠘⢦⠹⣯⠀⠀⠀⠀⠈⠳⠦⣤⡤⠔⠋⠁⢀⣿⣿⢸⣼⣻⡇⢀⣴⣯⡏⢸⠀⢣⠘⣄⠀⠈⠳⡄⠈⣷⠀⠀⢸⡇⠀⠀⠀⠈⠀ ⣀⠄⠓⠦⣼⡅⣴⡟⠁⠠⢻⠋⣠⣞⣋⣼⣿⠇⠀⢸⠀⣏⡇⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠻⣼⡞⣿⠃⣾⢁⣿⡇⠈⡇⠀⢇⠘⡆⠀⠀⡇⠀⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⠏⠀⣟⡇⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠻⣅⠀⢧⠘⣿⡇⠀⡇⠀⢸⠀⡇⠀⢀⠇⡼⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠒⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⣀⠴⠚⠁⢀⣼⠟⠀⠀⠀⠀⣀⣈⡆⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⣈⣷⣌⣷⣌⠳⣔⠁⢀⠎⣰⠃⣠⢎⡜⠁⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠻⣿⣿⣿⣿⣿⡟⠁⣠⣴⡾⠋⠁⠀⠀⠀⠀⣰⠃⣿⠁⠀⠀⢀⡿⡌⢆⠀⠀⢀⡞⠁⢰⡿⢹⠈⣧⠈⣦⢋⡞⠁⣠⠀⡞⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⡰⢹⣿⠀⠀⠀⠀⠀⠀⣠⠻⣶⡿⠀⠀⠀⠀⠳⡇⠈⣆⢠⠏⠀⠀⡏⢀⠎⢰⠿⡇⢸⠉⠀⡼⠁⢸⢧⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠆⢸⣿⣿⣿⣿⣿⣆⡇⣿⠘⣆⠀⠀⠀⢀⡴⢧⡀⠙⣧⠀⠀⠀⠀⢠⠿⡄⠘⢿⡆⠀⠀⣧⣡⠀⢀⣽⠇⡜⠀⣼⠁⠀⠈⢯⣦⡀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠋⠀⣾⣿⣿⣿⣿⣿⣿⣷⣧⡳⣌⠙⢦⣠⣾⣷⠀⠳⣄⠬⡳⡄⠀⠀⡘⠀⢱⡀⣨⣿⣄⠀⢻⣿⣷⣯⣏⡴⠃⠀⡟⡄⠀⠀⠀⠙⠺⣷⡀⠀⠀⠘⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⡴⠃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⢹⣿⣿⡇⠀⠈⠳⣴⠃⠀⡰⠃⢀⡴⢻⣿⣿⣿⣧⡘⣿⣿⣿⢟⠙⢦⠀⠹⣝⣆⠀⠀⠀⠀⠙⣿⠀⠀⠀⣽⡇⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣰⣿⣿⣿⡀⠀⠀⢸⣇⣼⡡⠖⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⢬⣇⡀⠈⠛⣷⡄⠀⠀⢠⣿⠀⠀⣰⡿⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⡀⠀⠀⣿⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢤⣤⠀⣿⡟⢦⠀⠈⣿⠀⣠⡿⠃⠀⣰⡃⠁⠀⠀⠀⠀ ⠀⠈⠃⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⢛⣵⣿⣿⣿⣿⣿⣿⣷⡀⠀⣉⣦⡀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⡏⣿⠈⡇⠀⣹⣷⣻⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀