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.StringTokenizer;
public class Main{
    public static void main(String[] args)throws IOException {
        FastReader sc=new FastReader();
        OutputStream output=System.out;
        PrintWriter out=new PrintWriter(output);
        //InputStream input = System.in;
        //Scanner sc = new Scanner(input);
        int n=sc.nextInt();
        int m=0,k=0;
        int[] arr=new int[n];
        for(int i=0;i<n;i++) {
            arr[i]=sc.nextInt();
        }
        for(int i=0;i<n-1;i++)
            if(arr[i]>arr[i+1]){
                m=i;
                k++;
            }
        if (arr[n - 1] > arr[0]) {
                m=n-1;
                k++;
        }
        if(k==0)
            out.println("0");
        else if(k>1)
            out.println("-1");
        else
            out.println(n-1-m);
        out.close();
        }

    static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            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;
        }
    }
}