One day, Twilight Sparkle is interested in how to sort a sequence of integers a1, a2, ..., an in non-decreasing order. Being a young unicorn, the only operation she can perform is a unit shift. That is, she can move the last element of the sequence to its beginning:

a1, a2, ..., an → an, a1, a2, ..., an - 1.

Help Twilight Sparkle to calculate: what is the minimum number of operations that she needs to sort the sequence?

Input

The first line contains an integer n (2 ≤ n ≤ 105). The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

If it's impossible to sort the sequence output -1. Otherwise output the minimum number of operations Twilight Sparkle needs to sort it.

Examples

Input

2
2 1


Output

1


Input

3
1 3 2


Output

-1


Input

2
1 2


Output

0
import java.io.BufferedReader;
import java.io.InputStreamReader;

/**
 *
 * @author bavudaia
 */
public class CrystalSort {
    public static void main(String[] args)  throws Exception{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        String S[] = br.readLine().split(" ");
        int A[]= new int[n];
        for(int i=0;i<n;i++)
            A[i] = Integer.parseInt(S[i]);
        
        // All Asc
        int i=0;
        while (i<n-1)
        {
            if(A[i]>A[i+1])
              break;
            i++;
        }
        int j=n-1;
        while(j>0)
        {
            if(A[j] < A[j-1])
                break;
            j--;
        }
        if(i==n-1)
        {
            System.out.println(0);
        }
        else if(j==0)
        {
           System.out.println(n);   
        }
        else if(j-i == 1 && A[0] >= A[n-1])
        {
            System.out.println(n-i-1);
        }
        else
            System.out.println(-1);
    }
}
