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.math.BigInteger;
import java.util.*;

public class Solution {
    private static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
//        int t = 0;
//        if (sc.hasNext())
//            t = sc.nextInt();
//        while (t-- > 0) {
        int n = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = sc.nextLong();
        solve(n, a);
        // }
    }

    private static void solve(int n, long[] a) {
        int index = -1, k = 0;
        for (int i = 1; i < n; i++) {
            if (a[i] < a[i - 1]) {
                index = i;
                k++;
            }
        }
        if (k == 0)
            System.out.println("0");
        else if (k > 1)
            System.out.println("-1");
        else if (k == 1 && a[n - 1] <= a[0])
            System.out.println(n - index);
        else
            System.out.println(-1);
    }
}
