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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;

public class temp2 {

	public static void main(String[] args) {

		Scanner scn = new Scanner(System.in);
		int n=scn.nextInt();
		int a[]=new int[n];
		int min=Integer.MAX_VALUE;
		int midx=-1;
		for(int i=0;i<n;i++ ){
			a[i]=scn.nextInt();
			if(min>a[i]){
				min=a[i];
				midx=i;
			}
		}
		int ct=1;
		if(midx==0){
			for(int i=1;i<n;i++){
				if(min==a[i] && a[i-1]>min){
					midx=i;
				}
			}
		}
		int j=midx;
		boolean f=true;
		j=(j+1)%n;
		while(j!=midx){
			if(a[((j-1)%n+n)%n]>a[j]){
				f=false;
				break;
			}
			j=(j+1)%n;
			
		}
		if(f){
			if(midx>0){
			System.out.println(n-midx);
			}
			else {
				System.out.println(0);
			}
		}
		else{
			System.out.println(-1);
		}
		
		
		
		

	}

	

}
