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.*;
import java.util.*;

public class b1 {
	public static void main(String[] args) throws FileNotFoundException {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}
		int ind = 0;
		while (ind < n - 1 && (a[ind + 1] > a[ind] || a[ind] == a[ind + 1])){
			ind++;
		}
		if (ind == n - 1){
			out.print(0);
		}
		else{
			if (a[ind + 1] > a[0]){
				out.print(-1);
			}
			else{
				int ind1 = ind;
				ind++;
				while (ind < n - 1 && (a[ind + 1] > a[ind] || a[ind] == a[ind + 1])){
					ind++;
				}
				if (ind == n - 1 && a[n - 1] <= a[0]){
					out.print(n - ind1 - 1);
				}
				else{
					out.print(-1);
				}
			}
		}
		out.close();
	}
}
