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 SolutionB {
	public void solve(){
		int n = nextInt();
		int ar[] = new int[n];
                for (int i = 0; i < n; i++) {
                ar[i] = nextInt();
                }
                int j = 0;
                while(j+1< n && ar[j]<=ar[j+1])
                    j++;
                if(j == n - 1){
                    out.println(0);
                    return;
                }
                for(int i = j+1 ; i < n - 1  ; i++){
                    if(ar[i] > ar[i+1]){
                        out.println(-1);
                        return;
                    }
                }
                if(ar[n-1]>ar[0])
                    out.println(-1);
                else
                    out.println(n-j-1);
	}
	public void run(){
		solve();
		out.close();
	}
	public static void main(String args[]){
		new SolutionB().run();
	}
	BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
	PrintWriter out = new PrintWriter(System.out);
	String line;
	StringTokenizer st;
	public String nextLine(){
		try {
			line = bf.readLine();
			st = new StringTokenizer(line);
		} catch (IOException e) {
			return null;
		}
		return line;
	}
	public String nextString(){
		while (st == null || !st.hasMoreElements()) {
            try {
                line = bf.readLine();
                st = new StringTokenizer(line);
            } catch (IOException e) {
                return null;
            }
        }
        return st.nextToken();
	}
	public int nextInt(){
		return Integer.parseInt(nextString());
	}
	public long nextLong(){
		return Long.parseLong(nextString());
	}
	public double nextDouble(){
		return Double.parseDouble(nextString());
	}
}