⠀⠀⠀⠀⠀⠀⠈⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢁⢎⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⠀⠀⠀⢈⣄⣰⣬⣆⣤⡼⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⡀⣷⣾⣿⢯⢿⣷⡶⣿⢹⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⡈⠀⠀⠀⠜⢾⣻⣌⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢨⣷⣿⡀⠀⠀⠀⠀⣠⣿⡿⠟⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠄⡾⠛⠛⠒⢶⣾⣿⣿⢿⣅⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠡⠃⠀⢰⡟⣟⣭⣳⣿⣿⣷⣈⡟⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣹⣿⡻⣗⣩⣾⣿⠟⠀⠙⠟⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠉⢻⣿⣿⣷⠀⢤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣛⣿⣄⠀⠀⠀⢀⣶⣿⣿⣿⡇⠇⠁⠀⠠⢿⣷⣯⣷⡤⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣟⡂⢀⣠⣾⣿⠿⠙⠀⠀⠀⢀⢁⣴⣿⡯⢿⣞⣷⡾⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠟⠛⢋⡨⢖⣩⣿⣯⣿⡿⠋⠀⠀⠀⠀⠀⢠⢼⡿⣽⢾⣽⡾⠟⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡴⣾⣯⣿⣿⣿⣿⡿⣽⣻⣧⣄⠠⢄⡠⢀⣸⠋⣿⣯⣿⣳⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠏⣽⣳⡽⣿⣻⣧⣿⢿⣿⣿⣷⣜⠷⠿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⢌⡳⣽⢞⣿⣽⣿⡾⣟⣷⣻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣴⡾⠛⣽⣿⣿⣿⣿⣿⣿⣿⣌⠳⣝⡎⠀⠉⠚⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⣠⣶⠞⠋⠁⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡼⣹⢮⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡗⣧⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣟⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣼⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡽⠻⣿⡇⠀