Please help me solve this problem. Please only solve if you are 100 percent sure and please show as much steps as possible, Thank you very much for your help

7, (10%) Cinderella's stepmother has newly bought n bolts and n nuts. The bolts and the nuts are of different sizes, each of them are from size 1 to size n. So, each bolt has exactly one nut just-fitting it. These bolts and nuts have the same appearance, so that we cannot distinguish a bolt from another bolt, or a nut from another nut, just by looking at them. Fortunately, we can compare a bolt with a nut by screwing them together, to see if the size of the bolt is too large, or just fitting, or too small, for the nut. Cinderella wants to join the ball held by Prince Charming. But now, her wicked stepmother has mixed the bolts, and mixed the nuts, and tells her that she can go to the ball unless she can find the largest bolt and the largest nut in time. An obvious way is to compare each bolt with eaclh nut, but that will take (n2) comparisons (which is too long). Can you help Cinderella to find an algorithm requiring only o(n2) comparisons? For instance, (n) comparisons