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.*;
import java.io.*;

public class Main{


    public static void main(String[] args) throws IOException{
        Reader sc = new Reader();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out), true);
        
        int n = sc.nextInt();

        int[] a = new int[n];
        int[] b = new int[n];

        int ind = -1;

        for(int i=0; i<n; i++){
            int x = sc.nextInt();
            a[i] = x;
            b[i] = x;
            if(i>0 && x<b[i-1] && ind==-1){
                ind = i;
            }
        }

        if(ind==-1){
            out.println(0);
            return;
        }
        //System.out.println(ind);

        Arrays.sort(b);

        int k = a.length - ind;
        //System.out.println(k);

        
        for(int i=0; i<b.length; i++){
            if(i<k){

                if(a[ind+i]!=b[i]){
                    out.println(-1);
                    return;
                }
            }
            else{
                if(b[i]!=a[i-k]){
                    out.println(-1);
                    return;
                }
            }
        }


        out.println(k);



        
    }





    
}




/*Reader class*/
class Reader {
        BufferedReader br;
        StringTokenizer st;
 
        public Reader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }