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**单点时限: **4.0 sec

**内存限制: **1024 MB

We always hope things in our lives will run smoothly, and having smooth arrays may help. An array of non-negative integers is -smooth if the sum of every set of consecutive integers is exactly . Unfortunately, not all arrays are -smooth. In fact, all -smooth arrays must contain a repeating pattern of length .

Any array can be made -smooth by changing its elements. In each change one element may be modified to any integer between and , inclusive. You want to make all of your arrays smooth, but you don’t want to make any more changes than necessary. So the question is: What is the minimum number of changes you have to make so that a given array would become -smooth?

The first line of input will consist of three integers of the form:

where is the size of the array.

The remainder of the file will consist of integers, , separated by white space.

All input will be within the following constraints:

- ;
- .

Your program must output a single integer specifying the minimum number of changes that must be made in order to make the array smooth.

Input

3 3 5 1 2 3

Output

1

Input

6 3 5 1 2 3 3 2 1

Output

3

Input

5 1 5 1 2 3 4 5

Output

4