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 Main {

	
	public static void main(String[] args) {

		BufferedReader br = new BufferedReader( new InputStreamReader( System.in) , 8* 1024);
		Scanner sc = new Scanner( br);
		int n = sc.nextInt();
		int [] array = new int[n];
		
		for(int i = 0 ; i < n ; ++i )
			array[i] = sc.nextInt();
		
		int twist = -1;
		
		for(int i = 1 ; i < n ; ++i  )
			if( array[i ] < array[i-1])
			{
				twist = i ; 
				break;
			}
		
		if( twist == -1 )
		{
			System.out.println("0");
			return;
		}
		
		else
		{
			if( !isSorted(array,twist,n-1))
			{
				System.out.println("-1");
				return ;
			}
			
			else
			{
				if(  array[n-1] > array[0])
				{
				
					System.out.println("-1");
					return ;// mismathcl
				}
					
				else
				{
					System.out.println( n- twist );
					return;
				}
			}
			
		}
		

	}
	
	static boolean isSorted( int[] array , int start , int end ){
		
		if( start == end) return true;
		
		for( int i = start + 1; i <= end ; ++i )
			if( array[i] < array[i-1]) return false;

		return true;
	}

}
