⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⠀⠀⠉⠁⠂⠢⠧⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⣤⠀⠂⠁⠀⠂⠀⠄⠀⡀⠈⠉⠲⠒⠂⠂⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣴⣿⣿⢦⣀⠁⢠⠈⢀⣀⣠⣤⣴⠆⢡⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⣀⠖⠊⠉⠁⠀⢿⣿⣿⣿⣿⡿⢸⣿⣽⣿⣿⣿⣿⡇⠀⡅⡈⠂ ⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠠⠀⣾⣿⣿⣿⠿⡃⣈⢿⣿⣿⡿⣿⣿⡇⠀⠓⠁⠀ ⠀⠀⠀⠀⠀⡧⠄⠀⠠⠁⢀⠀⠛⣿⡄⣈⡉⢁⠤⢬⣝⣿⣿⣿⣿⠁⢠⠇⠀⠀ ⠀⠀⠀⠀⠀⣥⠀⠐⠀⠠⠀⠀⠄⠀⢷⢛⡠⠫⣀⠅⢢⠙⠸⢹⠁⠐⡜⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠝⡄⠐⠀⡀⠁⠀⠄⠀⠈⠀⠀⠈⠀⣀⣀⠄⠈⡠⠚⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠼⠒⠀⠉⠐⠶⣤⣔⣀⡐⠀⡍⠀⠁⠈⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⠊⠀⠀⡀⠀⠀⠀⠀⠀⠙⠻⠧⡀⠁⠤⢴⡴⣺⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⠠⢢⣶⣾⠀⠈⠉⢰⠀⠀⠀⡬⠀⠈⢀⠀⠈⢻⠽⠛⢀⠀⠀⠀⠀ ⠀⢀⠄⢈⠀⠤⠾⠿⢻⣄⠀⠄⡈⠀⠀⢰⠁⠀⠀⠀⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⠣⣀⠀⠀⠀⠐⢴⣈⢁⠉⠁⠀⠀⠀⢓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⢨⣯⣿⣿⣷⣤⣤⢶⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⡟⠋⠛⠛⠛⠚⠛⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠙⢛⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠁⡄⠑⠢⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣉⠉⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⣂⣀⡱⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢠⡾⠁⢀⣀⡀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠼⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣾⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡉⠉⠉⠉⠛⠲⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣠⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠈⢆⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⠂⢀⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⢠⣶⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⠁⠀⠙⡆⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠁⠉⠁⠀⢸⣿⣿⣿⢉⡀⠙⣿⣯⣿⣿⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣇⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣼⣛⣼⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣡⡄⠈⣿⣿⣿⣇⠀⠀⣿⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣹⡾⣿⠿⢿⡛⠉⠓⣦⠤⠬⢿⣿⣿⣿⣯⣥⣾⣿⣿⣿⠟⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣧⣧⡀⠀⠉⡏⠉⠁⣀⣤⣤⣌⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢹⣏⣿⡏⠉⣿⣿⠁⠰⡽⢞⡝⣿⣿⣟⡿⣿⡟⠳⢄⠀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣽⣘⠎⢱⣣⡻⠁⠘⣿⠇⠀⠛⢃⢿⠇⠀⠀⣱⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣾⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠤⠤⠿⠗⠒⠋⠁⠀⠀⠀⠈⠱⣄⢀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⡖⠤⢀⣀⣠⠼⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⠿⠓⠋⠁⠀⠙⠲⣴⣦⣄⣀⠀⠀⠀⡤⠤⢴⠛⠳⡄⠈⠆⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣍⡉⠙⣿⡁⠀⠸⡀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⣠⠒⠀⠐⠲⡀⠀⠀⠀⠀⠈⠙⠶⣿⢳⡀⠀⠑⠢⠤⢤⣶⣾⣟⣷⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣀⣀⣤⡴⢶⠏⠀⠐⠂⠐⠸⡄⠀⠀⠀⠀⠀⣸⠇⠀⠙⣦⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⢰⡿⢶⠿⣽⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠣⡀⠀⠀⠀⠻⡷⠛⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠈⠳⢤⣀⡀⣾⣷⣶⣿⣿⣀⠀⠐⠒⠒⢢⠃⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠑⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠋⠉⠉⠙⠒⠮⢍⣉⠋⠙⢛⣿⠟⠢⠤⠠⠤⠊⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⣀⣀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠉⠓⢶⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠑⠒⠒⠦⠦⠤⠤⢴⣾⣇⠉⠙⠻⣶⡒⠒⠒⠒⣒⡶⠶⠚⢫⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣷⣤⣼⣟⣉⡛⠛⢻⢯⣀⣀⣴⡿⠟⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⢠⡿⠃⠉⠉⠛⠘⠓⠛⠛⠛⢿⣯⡀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠽⣦⡀⠀⠀⠘⢗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣦⡀⠀⠈⢯⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠋⠛⠶⢤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⡤⠒⠯⣀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⠣⠀⣠⠀⠀⠛⠲⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠷⢤⣿⡀⣀⡀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠋⠉⠉⠁⡀⠈⢍⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⡇⣀⣀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀