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 LittlePonyandSortbyShift {
	public static boolean isSorted(int n,int arr[],int index) {
		for (int i = index; i < arr.length-1; i++) {
			if(arr[i]>arr[i+1]) {
				return false;
			}
		}
		return true;
	}
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int arr[] = new int[n];
		for (int i = 0; i < arr.length; i++) {
			arr[i] = sc.nextInt();
		}
		if(isSorted(n, arr,0)) {
			System.out.println(0);
		}
		else {
			int mid = -1;
			for (int i = 0; i < arr.length-1; i++) {
				if(arr[i]>arr[i+1]) {
					mid = i;
					break;
				}
			}
			if(isSorted(n, arr,mid+1)) {
				if(arr[n-1]<=arr[0]) {
				System.out.println(n-(mid+1));
				}
				else {
					System.out.println(-1);
				}
			}
			else {
				System.out.println(-1);
			}
		}
	}

}
