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.*;
import java.util.*;



public class Test {
    
    public static void main(String[] args) throws Exception {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        String s[] = in.readLine().split(" ");
        int a[] = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = Integer.parseInt(s[i]);
        }
        int i = 0;
        while(i < n-1 && a[i] <= a[i+1])
            i++;
        if(i == n-1){
            System.out.println(0);
            return;
        }
        int lt = i;
        i++;
        while(i < n-1 && a[i] <= a[i+1])
            i++;
        if(i != n-1 || a[n-1] > a[0]){
            System.out.println(-1);
            return;
        }
        System.out.println(n-(lt+1));
        



    } 
}