⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⣷⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿⠀⠀⠈⣿⣦⣄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣞⡇⠀⠀⠀⣼⡿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢿⣽⡀⠀⠉⠛⠁⠀⣰⣾⠿⠿⣦⡀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣞⡿⣞⡅⠀⠀⠀⠀⠘⠏⠓⠒⠒⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⢾⣽⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣶⡻⣞⣿⣺⢯⣽⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣽⣻⢾⣽⣷⣾⣽⣻⣞⣷⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⡀⠀⠀⠀⣀⣲⣴⢶⣞⡿⣽⣞⡷⣯⢿⡽⣞⣿⠟⠋⠁⠉⠈⠳⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢶⣾⣿⡽⣯⣟⡾⣽⡷⣯⣟⡽⡾⣽⡯⠁⠀⠀⠀⠀⠀⠀⢮⣭⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢞⣿⣿⢯⡿⣿⣯⣟⣷⣯⢿⣳⣟⡷⣽⣼⣻⣽⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⡗⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣽⣾⣿⣾⣗⡿⣯⡷⣯⣟⡷⣞⣼⣿⣀⠀⠀⠀⠀⢀⣠⡿⣏⡗⠈⠐⠈⠅⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠏⠉⠉⠽⢟⢿⣿⣿⣿⣿⣷⣻⢾⡽⣞⡷⠄⡹⣶⢿⣻⢿⣻⡽⢯⣼⢦⠶⠁⠈⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠇⠀⠀⠀⠀⠀⠁⣽⣿⣿⣿⣷⣯⣿⣽⣛⡦⠀⠀⢩⣿⣹⢯⣷⢻⣟⠺⢣⡖⣘⠤⠓⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡃⠁⠀⠀⠀⢀⣤⣾⣟⢿⣻⣿⣿⣟⡾⣽⡳⠄⠎⢳⣯⢯⣟⡾⢯⣞⣯⣓⠉⢀⠀⠀⡄⢢⡀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⣶⣳⣶⣺⣿⣿⣳⢯⣟⣿⣿⣳⢯⠛⠅⠃⠀⠀⣴⣿⡿⣬⢶⠾⠙⣊⣥⠾⡒⠊⢁⢠⠣⣌⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡽⣾⡽⣯⣟⣿⡿⣯⣿⣿⣾⢿⣿⠳⢏⣈⢠⠀⠀⣰⢿⡿⣽⣉⡶⠌⠋⠉⣀⡀⠁⠀⠀⠀⣘⡐⣂⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣳⣟⣳⣟⣾⣽⣿⣿⣿⣿⣿⣦⣜⡻⡽⠆⠧⣴⡟⣯⢟⡳⣭⠲⠄⠐⠀⠀⠀⠈⠁⠉⠑⢊⡕⢃⠄⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢧⠀⠹⠾⡵⡞⡽⢢⣃⠐⠀⠀⠄⡐⠀⠀⠀⡘⢦⠘⣌⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⡈⠀⡀⠄⡑⠢⣉⠴⣈⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣏⡴⣶⣵⣢⢤⢠⡀⡄⢠⠐⡰⢌⡱⠀⡁⡀⠆⡥⠆⡥⣛⡽⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⢷⣯⡽⣞⣷⣻⡼⣡⢋⡔⠣⠜⡐⢐⠠⡓⣤⣙⣲⣽⣻⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣞⣷⣻⡴⣣⢜⡱⣊⡕⣊⠠⡙⡰⣭⢷⣯⣿⢿