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 PonyShift454B
{
    public static void main(String[] args) 
    {
        // Set up scanner
        Scanner sc = new Scanner(System.in); 
        // System.out.println("Enter n");
        int n = sc.nextInt();
        
        int[] a = new int[n];
        
        for (int i=0; i<n; i++)
        {
            // System.out.println("Enter next value");
            a[i] = sc.nextInt();
        }
        
        int i = 0;
        while (i<n-1 && a[i] <= a[i+1])    // Go to first bad spot
        {
            i++;
        }
        // Is it sorted to start with?
        if (i==n-1)
        {
            System.out.println(0);
            return;
        }
        
        // Now check to see if the rest is increasing
        int possibleanswer = n-i-1;
        i++;    // Skip over bad one
        while (i<n-1 && a[i] <= a[i+1])    // Is the rest increasing?
        {
            i++;
        }
        
        if (i == n-1 && a[n-1] <= a[0])
        {
            System.out.println(possibleanswer);
        }
        else
        {
            System.out.println(-1);
        }
    }
}
            
            
        
        
        
        
        