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.util.Scanner;

public class LadderB {

	static Scanner scn = new Scanner(System.in);

	public static void main(String[] args) {
	    int n = scn.nextInt();
		int[] arr = new int[n];
		int min = 0;
		boolean check = true;
		

		for (int i = 0; i < n; i++) {
			arr[i] = scn.nextInt();
			
			if(i!=0 && check == true){
				if(arr[i] != arr[i-1]){
					check = false;
				}
			}
		}
		
		if(check == true){
			System.out.println(0);
			return;
		}

		if (arr[n - 1] > arr[0]) {
			for (int i = n - 1; i > 0; i--) {
				if (arr[i - 1] > arr[i]) {
					min = -1;
					break;
				}

			}
		} else {
			
			min++;

			int i = n - 2;

			while (i >= 0) {
				if (arr[i + 1] >= arr[i]) {
					min++;
					i--;
				} else {
					while (i != 0) {
						if (arr[i - 1] > arr[i]) {
							min = -1;
							break;
						}
						i--;
					}
					break;
				}
			}
		}

		System.out.println(min);
	}

}
