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.InputStreamReader;
import java.io.IOException;

public class C454B {
    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(reader.readLine());
        String[] items = reader.readLine().split(" ");

        int[] digits = new int[n];
        int idx = 0;
        for (String item: items) {
            digits[idx] = Integer.parseInt(item);
            idx += 1;
        }

        final int stateA = 1;
        final int stateB = 2;
        final int stateC = 3;
        int state = stateA;

        boolean isStoped = false;
        int position = 0;
        for (int i = 1; i < digits.length; i++) {
            switch (state) {
                case stateA:
                    if (digits[i - 1] > digits[i]) {
                        position = i;
                        state = stateB;
                    }
                    break;

                case stateB:
                    if (digits[i - 1] > digits[i]) {
                        state = stateC;
                    }
                    break;

                case stateC:
                    isStoped = true;
                    break;
            }
            if (isStoped) {
                break;
            }
        }

        int answer = -1;
        switch (state) {
            case stateA:
                answer = 0;
                break;

            case stateB:
                if (digits[0] >= digits[digits.length - 1]) {
                    answer = digits.length - position;
                }
                break;

            case stateC:
                answer = -1;
                break;
        }
        System.out.println("" + answer);
    }
}