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 B454 {
    static int []a=new int[100001];
   static int []vt=new int[100001];

    static int n;
    
    public static void main (String argv[]){
    
        Scanner input=new Scanner(System.in);
     n=input.nextInt();
    int h=1000000;
      boolean kt=true;
    int k=0;
    int []a=new int[n+1];
    for (int i=0;i++<n;){
    a[i]=input.nextInt();
    if (a[i]<h)h=a[i];
    if ((i>0)&(a[i]<a[i-1])) kt=false;
    }
    if (kt==true) System.out.print("0");
    else{
        kt=true;
    for (int i=0;i++<n;)
        if (a[i]==h){        
            k=i;break;}
    if (k==1){
    int m=n;
    while (m>1){
    if (a[m]==a[1]) m--;
    else break;
    }
    for (int i=1;i++<m;)
        if (a[i]<a[i-1]) kt=false;
    k=m+1;
    }
    else {
       kt=true;
    if (a[n]>a[1]) kt=false;
    else {
    for (int i=k;i++<n;) if (a[i]<a[i-1]){kt=false;break;} 
    if (k>1)
    for (int j=1;j++<k-1;)
        if (a[j]<a[j-1]){kt=false;break;}
        }
    }
    if (kt==false) System.out.print("-1");
    else 
    System.out.print(n-k+1);
    
    }
    } 
    }
    
    
    

