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.util.*;

public class CF572A {

    public static void main(String[] args) {
        Scanner io = new Scanner(System.in);
        int n = io.nextInt();
        ArrayList<Integer> nums = new ArrayList<Integer>(n);
        for(int i = 0; i < n; i++)
            nums.add(io.nextInt());
        if(n <= 10) {

            if(isOrdered(nums)) {
                System.out.println(0);
                return;
            }
            for(int i = 0; i < n; i++) {
                nums.add(0, nums.remove(n-1));
                if(isOrdered(nums)) {
                    System.out.println(i+1);
                    return;
                }
            }
            System.out.println(-1);
            return;
        } else {
            int flag2 = -1;
            int lO;
            for(lO = 0; lO < n-1; lO++)
                if(nums.get(lO + 1) < nums.get(lO))
                    break;
            if(++lO == n) {
                System.out.println(0);
                return;
            }
            
            if(nums.get(lO) > nums.get(0)) {
                System.out.println(-1);
                return;
            }
                
            if(lO + 1 == n) {
                System.out.println(1);
                return;
            }
            int i;
            for(i = lO; i < n-1; i++) {
                if(nums.get(i+1) < nums.get(i)) {
                    System.out.println(-1);
                    return;
                }
            }
            System.out.println(i-lO+1);
        }
        
    }
    public static boolean isOrdered(ArrayList<Integer> arr) {
        for(int i = 0; i < arr.size()-1; i++)
            if(arr.get(i+1) < arr.get(i))
                return false;
        return true;
    }
}
