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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class BetterSortByShift {

    public static int minShift2(int[] list) {

	int fallingPoint = 0;

	boolean fallen = false;

	for (int i = 0; i < list.length - 1; i++) {
	    if (list[i + 1] - list[i] < 0) {
		if (fallen == true) {
		    return -1;
		}
		fallen = true;
		fallingPoint = i + 1;
	    }
	}

	if (list[0] - list[list.length - 1] < 0) {
	    if (fallen == true) {
		return -1;
	    }
	}

	if (fallen == false) {
	    return 0;
	}
	return list.length - fallingPoint;
    }

    public static void main(String[] args) throws NumberFormatException,
	    IOException {

	BufferedReader r = new BufferedReader(new InputStreamReader(System.in));

	int n = Integer.parseInt(r.readLine());
	String[] temp = r.readLine().split(" ");
	int[] list = new int[n];
	for (int i = 0; i < temp.length; i++) {
	    list[i] = Integer.parseInt(temp[i]);
	}
	System.out.println(minShift2(list));

    }

}
