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
;(function () {

    print(function () {
        var n = +readline(),
            a = readline().split(' ').map(Number),
            d = 0, r = null;

        if (n === 2) {
            return a[0] <= a[1] ? 0 : 1;
        }

        a = a.concat([a[0]]);

        a.forEach(function (e, i, a) {
            if (i === 0) return;
            if (e < a[i - 1]) {
                d++;
                r = i;
            }
        });

        if (d === 0) return 0;
        if (d > 1) return -1;
        return n - r;
    }.call(this));

}.call(this));
