One day,a beautiful girl ask LYH to help her complete a complicated task—using a new compression method similar to Run Length Encoding(RLE) compress a string.Though the task is difficult, LYH is glad to help her.

The compress rules of the new method is as follows: if a substring S is repeated k times, replace k copies of S by k(S). For example, letsgogogo is compressed into lets3(go). The length of letsgogogo is 10, and the length of lets3(go) is 9. In general, the length of k(S) is (number of digits in k ) + (length of S) + 2. For example, the length of 123(abc) is 8. It is also possible that substring S is a compressed string. For example nowletsgogogoletsgogogoandrunrunrun could be compressed as now2(lets3(go))and3(run).

In order to make the girl happy, LYH solved the task in a short time. Can you solve it?