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.*;
import java.io.*;
import java.math.*;
public class Solution {
    
    public static int MOD = 1000000007;
    public static int MAX = 1000002;
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out,true);
        int n = Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        int[] a = new int[n];
        int min = Integer.MAX_VALUE,l=0,count = 0;
        for(int i =0;i<n;i++){
            a[i] = Integer.parseInt(st.nextToken());    
        }
        int pos = 1;
        for(;pos<n;pos++){
            if(a[pos]<a[pos-1])
                break;
        }
        for(int p = pos+1;p<n;p++){
            if(a[p]<a[p-1]){
                out.println("-1");
                return;
            }
        }
        if(pos == n || a[n-1]<=a[0]){
            out.println(n-pos);
        }
        else{
            out.println("-1");
        }
    }       

}
