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.*;

public class B {
	
	public static void main(String[] args) {
		FastScanner sc = new FastScanner();
		int n = sc.nextInt();
		int arr[] = new int[n];
		for(int i = 0; i < n; i++) {
			arr[i] = sc.nextInt();
		}
		int index = 0;
		for(int i = 0; i < n-1; i++) {
			if(arr[i] > arr[i+1]) {
				index = i+1;
				break;
			}
		}
		if(index == 0) {
			System.out.println(0);
		}
		else {
			boolean ok = false;
//			System.out.println(index);
			for(int i = index; i < n-1; i++) {
				if(arr[i] > arr[i+1] || arr[i] > arr[0] || arr[i+1] > arr[0]) {
					System.out.println(-1);
					ok = true;
					break;
				}
			}
			if(arr[index] > arr[0]) {
				System.out.println(-1);
				ok = true;
			}
			if(!ok) {
				System.out.println(n-index);
			}
		}
		
		
		
	} 


	private static boolean check(int[] arr) {
		for(int i = 0; i < arr.length-1; i++) {
			if(arr[i] > arr[i+1]) {
				return false;
			}
		}
		
		return true;
	}


	private static void rightShift(int[] arr) {
		int n = arr.length;
		int temp = arr[n-1];
		for(int i = n-1; i > 0; i--) {
			arr[i] = arr[i-1];
		}
		arr[0] = temp;
	}








	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	
	
	
	static int gcd(int a, int b) {
		return a%b == 0 ? b : gcd(b,a%b);
	}
	
	static boolean[] sieve(int n) {
		
		boolean isPrime[] = new boolean[n+1];
		for(int i = 2; i <= n; i++) {
			if(isPrime[i]) continue;
			for(int j = 2*i; j <= n; j+=i) {
				isPrime[j] = true;
			}
		
		}
		return isPrime;
		
	}
}