Given an equation “x=y”, for example, “111=12”, you need to add pluses inside x to make the equation correct. In our example “111=12”, we can add one plus “11+1=12” and the equation becomes correct. You need to find the minimum number of pluses to add to x to make the equation correct. If there is no answer print -1.

Note that the value of y won’t exceed 5000. The numbers in the corrected equation may contain arbitrary amounts of leading zeros.

Input Format

The first line contains a string, A as described in the problem statement.

Constraints

1 <= length(A) <= 10^3