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 ACB {
	public static void main(String args[]) throws Exception {
	//	System.out.println("Hiiiii");
		Scanner scn = new Scanner(System.in);
		int n = scn.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();
		}

		int idx = 0;
		boolean swap = false,print=false;
		

		int i;
		for (i = 0; i < n - 1; i++) {
			if (!swap && arr[i + 1] < arr[i]) {
				idx = i;
				swap = true;
				i++;
			}
			if(i<n-1 && swap && arr[i+1]<arr[i]) {
				System.out.println(-1);
				print=true;
				break;
			}
		}
	//	System.out.println(i);
		if (!swap && !print) {
			System.out.println(0);
		} else {
			if (arr[n - 1] > arr[0] && !print)
				System.out.println(-1);
			else
				if(!print)
				System.out.println((n - idx - 1));
		}
	}
}
