Mike has a sequence A = [a1, a2, ..., an] of length n. He considers the sequence B = [b1, b2, ..., bn] beautiful if the gcd of all its elements is bigger than 1, i.e. <image>. 

Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 ≤ i < n), delete numbers ai, ai + 1 and put numbers ai - ai + 1, ai + ai + 1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence A beautiful if it's possible, or tell him that it is impossible to do so.

<image> is the biggest non-negative number d such that d divides bi for every i (1 ≤ i ≤ n).

Input

The first line contains a single integer n (2 ≤ n ≤ 100 000) — length of sequence A.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.

Output

Output on the first line "YES" (without quotes) if it is possible to make sequence A beautiful by performing operations described above, and "NO" (without quotes) otherwise.

If the answer was "YES", output the minimal number of moves needed to make sequence A beautiful.

Examples

Input

2
1 1


Output

YES
1


Input

3
6 2 4


Output

YES
0


Input

2
1 3


Output

YES
1

Note

In the first example you can simply make one move to obtain sequence [0, 2] with <image>.

In the second example the gcd of the sequence is already greater than 1. 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class MikeAndGcdProblem {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());
        int gcd = 0;
        boolean[] isEven = new boolean[n];
        String[] line = br.readLine().split("\\s+");
        for (int i = 0; i < n; i++) {
            int num = Integer.parseInt(line[i]);
            gcd = gcd(gcd, num);
            isEven[i] = (num & 1) == 0;
        }

        if (gcd > 1) {
            System.out.println("YES\n0");
            return;
        }

        int moves = 0;
        for (int i = 0, l = n - 1; i < l; i++) {
            if (!isEven[i]) {
                moves += isEven[i + 1] ? 2 : 1;
                isEven[i + 1] = true;
            }
        }
        if (!isEven[n - 1]) {
            moves += 2;
        }

        System.out.println("YES\n" + moves);
    }

    private static int gcd(int a, int b) {
        if (a < b) {
            return gcd(b, a);
        }
        while (b != 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
}
