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 Main {
	static int[] nums;
	static int up(int start) {
		int st = start;
		while(st + 1 < nums.length && nums[st] <= nums[st+1]){
			st++;
		}
		return st;
	}
	static int down(int start) {
		int st = start;
		while(st + 1 < nums.length && nums[st] >= nums[st+1]){
			st++;
		}
		return st;
	}
	public static void main(String[] s) {
		Scanner in = new Scanner(System.in);
		int tot = in.nextInt();
		nums = new int[tot];
		for(int i = 0; i < tot;i ++) {
			nums[i] = in.nextInt();
		}
		int ans = -1;
		int p1 = up(0), p2 = up(p1+1);
		if (p1 == tot - 1 || p2 == tot - 1 && nums[p2] <= nums[0])
			ans = tot - p1 - 1;
		if (ans == -1)System.out.println("-1");
		else System.out.println(ans);
	}
}

	  	   		  			 		 		 	 	 			