⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⣷⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣿⠀⠀⠈⣿⣦⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣞⡇⠀⠀⠀⣼⡿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢿⣽⡀⠀⠉⠛⠁⠀⣰⣾⠿⠿⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣞⡿⣞⡅⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⢾⣽⢫⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣶⡻⣞⣿⣺⢯⣽⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣽⣻⢾⣽⣷⣾⣽⣻⣞⣷⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⡀⠀⠀⠀⣀⣲⣴⢶⣞⡿⣽⣞⡷⣯⢿⡽⣞⣿⠟⠋⠁⠉⠈⠳⣟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀get rekt
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢶⣾⣿⡽⣯⣟⡾⣽⡷⣯⣟⡽⡾⣽⡯⠁⠀⠀⠀⠀⠀⠀⢮⣭⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ bozo
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢞⣿⣿⢯⡿⣿⣯⣟⣷⣯⢿⣳⣟⡷⣽⣼⣻⣽⠀⠀⠀⠀⠀⠀⠀⢀⣼⡯⡗⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣯⣽⣾⣿⣾⣗⡿⣯⡷⣯⣟⡷⣞⣼⣿⣀⠀⠀⠀⠀⢀⣠⡿⣏⡗⠈⠐⠈⠅⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠏⠉⠉⠽⢟⢿⣿⣿⣿⣿⣷⣻⢾⡽⣞⡷⠄⡹⣶⢿⣻⢿⣻⡽⢯⣼⢦⠶⠁⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠇⠀⠀⠀⠀⠀⠁⣽⣿⣿⣿⣷⣯⣿⣽⣛⡦⠀⠀⢩⣿⣹⢯⣷⢻⣟⠺⢣⡖⣘⠤⠓⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡃ ⠀⠀⠀⢀⣤⣾⣟⢿⣻⣿⣿⣟⡾⣽⡳⠄⠎⢳⣯⢯⣟⡾⢯⣞⣯⣓⠉⢀⠀⠀⡄⢢⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣷⣶⣳⣶⣺⣿⣿⣳⢯⣟⣿⣿⣳⢯⠛⠅⠃⠀⠀⣴⣿⡿⣬⢶⠾⠙⣊⣥⠾⡒⠊⢁⢠⠣⣌⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡽⣾⡽⣯⣟⣿⡿⣯⣿⣿⣾⢿⣿⠳⢏⣈⢠⠀⠀⣰⢿⡿⣽⣉⡶⠌⠋⠉⣀⡀⠁⠀⠀⠀⣘⡐⣂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣽⣳⣟⣳⣟⣾⣽⣿⣿⣿⣿⣿⣦⣜⡻⡽⠆⠧⣴⡟⣯⢟⡳⣭⠲⠄⠐⠀⠀⠀⠈⠁⠉⠑⢊⡕⢃⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣾⣿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⢧⠀⠹⠾⡵⡞⡽⢢⣃⠐⠀⠀⠄⡐⠀⠀⠀⡘⢦⠘⣌⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⡈⠀⡀⠄⡑⠢⣉⠴⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣏⡴⣶⣵⣢⢤⢠⡀⡄⢠⠐⡰⢌⡱⠀⡁⡀⠆⡥⠆⡥⣛⡽⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣻⢷⣯⡽⣞⣷⣻⡼⣡⢋⡔⠣⠜⡐⢐⠠⡓⣤⣙⣲⣽⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣞⣷⣻⡴⣣⢜⡱⣊⡕⣊⠠⡙⡰⣭⢷⣯⣿⢿