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.awt.List;
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.util.ArrayDeque;

public class SortByShift {

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        OutputStream out = new BufferedOutputStream(System.out);
        int n = Integer.parseInt(br.readLine());
        int[] arr = new int[n];
        String[] l = br.readLine().split("\\s+");

        arr[0] = Integer.parseInt(l[0]);
        int prev = arr[0];
        boolean isSorted = true;

        ArrayDeque<Integer> deq = new ArrayDeque<Integer>();
        deq.add(prev);

        for (int i = 1; i < n; i++) {
            arr[i] = Integer.parseInt(l[i]);
            deq.addLast(arr[i]);

            if (prev > arr[i])
                isSorted = false;
            prev = arr[i];
        }

        int op = 0;
        if (isSorted)
            out.write(("0\n").getBytes());
        else {

            while (deq.getFirst() >= deq.getLast()) {
                op++;

                if (op == n)
                    break;

                deq.addFirst(deq.removeLast());
            }

            if (isSorted(deq))
                out.write((op + "\n").getBytes());
            else
                out.write(("-1\n").getBytes());

        }

        out.flush();
        br.close();

    }

    private static boolean isSorted(ArrayDeque<Integer> deq) {
        boolean isSorted = true;

        boolean isFirst = false;
        int prev = deq.peekFirst();
        for (Integer integer : deq) {
            if (!isFirst)
                isFirst = true;
            else {
                if (prev > integer) {
                    isSorted = false;
                    break;
                }
                prev = integer;
            }

        }

        return isSorted;
    }

}
