Truth only exists within my range
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠔⠂⠀⠀⠀⠀⠐⣂⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⢀⡤⠒⣉⣭⣤⣶⣶⡾⠷⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠖⣡⣶⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠔⣵⡟⠛⠁⠀⡠⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢀⢮⣾⠋⠀⠀⠀⡰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠀⡐⠁⠀⢀⣲⡟⠋⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠘⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⡔⠀⡎⢹⣾⡟⠁⠀⠀⠀⢰⠇⠀⢀⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠀⢁⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠰⠀⠘⡘⠄⠀⣘⣼⣿⢤⠀⠀⠀⢀⡏⠀⡴⠚⡄⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠸⠀⠘⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠄⠀⡇⠀⠶⠐⠀⠰⣽⢿⣿⢺⠀⠀⢀⢘⡵⠊⠀⠀⠃⢀⡏⠁⢺⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢊⣳⡇⠀⣴⡇⠀⠃⠃⠀⣘⢃⠙⡿⡿⠀⠀⢸⢿⢶⣤⣤⣀⡈⢼⢷⠀⠞⣧⠀⠀⠀⡀⢠⠙⠀⣀⢀⠈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠎⣇⠁⠀⢏⡇⠀⠀⠀⢠⡝⠖⣶⠁⣧⠀⠀⡘⠈⢸⠿⣿⠿⠛⢾⠀⡀⠀⣏⠀⠀⠀⢈⣎⠁⢠⡈⠈⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢸⠀⠀⢸⣦⡀⠣⣇⣸⣿⣀⠇⠀⠸⣧⡀⢀⠃⠀⠀⠉⠀⠀⠀⠀⠰⠀⠿⢀⡀⡀⡿⠂⡠⠁⠀⡇⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢸⠀⠠⠈⣿⡷⣌⢾⣿⣿⣿⠂⠀⠀⠘⠈⠪⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢟⡿⣡⣞⡔⠀⣸⠠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢃⣦⠀⢣⠘⡇⣿⣗⣻⣿⡧⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠃⢈⣿⣿⠏⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠈⣷⢄⠻⡗⣿⣿⢷⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢁⣠⢾⢏⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠌⡳⣔⡂⢿⣎⠙⣿⠘⢠⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⣻⠟⢁⡊⠀⠈⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⣌⠑⠷⣝⡀⣷⢸⡄⠁⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣴⡑⣿⡇⣿⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠉⠐⣦⣤⡥⠤⢿⢾⡎⡧⠀⣿⣿⣿⣿⣿⣷⣦⣀⣤⠶⡙⢽⡷⠁⢯⢊⠏⢰⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠘⣿⣇⠢⡀⠓⣿⣾⣅⢻⣝⣿⣿⠟⢉⡘⠋⢁⡴⢺⣯⣁⣂⠃⠈⠀⡆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢬⣿⠮⣵⣽⣛⣛⠻⢽⣿⣿⣷⣿⣿⡁⠀⠀⠈⠢⠀⠃⡖⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢸⣿⠀⠀⣠⣿⠋⠒⢟⡋⠈⠀⠀⠀⠙⢿⣿⣄⠙⣷⡄⠀⠀⠀⢄⡴⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⠀⣰⣿⠏⠀⠀⠀⠈⠑⠢⡀⠀⠀⠌⠈⢻⣧⡈⢷⡀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⣦⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠷⣦⣤⣤⣶⡶⢿⠛⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣆⠂⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡀⠀⠉⠀⠰⠀⠀⢠⠒⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣼⣴⣶⡶⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠎⠂⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣞⠩⠀⠤⡆⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠋⠀⠘⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⠒⣤⣀⣠⠒⠂⢐⠄⠂⠠⠠⠖⢰⠼⡃⠴⠸⠉⠑⠈⠀⡨⢩⡔⣾⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⣾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⣿⡟⠀⣿⠈⠀⠀⠀⠊⠐⠀⠈⠀⠀⠁⠁⠈⠈⠈⠀⠲⣿⠃⣿⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡞⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡈⣿⡇⢸⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⡈⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⣁⣿⠇⣸⠧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡏⢸⢗⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⠀⣿⢀⡿⠆⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⣒⣼⢣⣟⠖⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣻⣇⣼⡇⣁⣀⣀⣠⣤⣾⣿⠧⢀⡀⠀⠀⠀⠀⠀⢀⣾⠷⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠿⣛⡜⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⣿⣿⣿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⣧⢿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀