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;
import java.util.ArrayList;
import java.util.LinkedList;
import java.util.StringTokenizer;


public class PonyShift {

	static StringBuilder out = new StringBuilder();
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static StringTokenizer st;
	static int n;
	static int arr[];
	public static void main(String[] args)throws Throwable {
		// TODO Auto-generated method stub

		n = Integer.parseInt(br.readLine());
		st = new StringTokenizer(br.readLine());
		arr = new int[n];
		for(int i=0;i<n;i++) arr[i]= Integer.parseInt(st.nextToken());
		int l = n;
		boolean ok = true;
		for(int i=0;i<n;i++){
			if(i+1<n&&arr[i]>arr[i+1]){
				l = i;
				ok = false;
				break;
			}

		}
		if(ok){
			System.out.print("0");
			return;
		}
		l++;
	//	System.err.println(l);
		boolean invalid = false;
		for(int j=0;j<n-1;j++){
			int curr = (j+l)%n;
			int next = (j+l+1)%n;
			//if(curr==l)break;
			if(arr[next]<arr[curr]){
			//	System.out.println(arr[next]+" "+arr[curr]);
				invalid = true;
				break;
			}
		}
		if(invalid) System.out.print("-1");
		else System.out.print(n-l);
	}
}

