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.Arrays;
import java.util.StringTokenizer;

public class Solution {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(br.readLine());
        String str = br.readLine();
        StringTokenizer st = new StringTokenizer(str, " ");
        int[] arr = new int[n];
        int[] newArr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(st.nextToken());
            newArr[i] = arr[i];
        }
        Arrays.sort(newArr);
        int count = 0, current = arr[0], index = arr.length - 1;
        while (index >= 0 && arr[index] <= current) {
            current = arr[index];
            index--;
            count++;
        }
        int[] array = new int[n];
        int in = 0;
        for (int i = index + 1; i < n; i++) {
            array[in++] = arr[i];
        }
        for (int i = 0; i <= index; i++) {
            array[in++] = arr[i];
        }
        int i;
        for (i = 0; i < n; i++) {
            if (array[i] != newArr[i]) {
                bw.write(-1 + "\n");
                break;
            }
        }
        if (i == n) {
            bw.write(count%n + "\n");
        }
        bw.flush();
    }
}

