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.util.*;
import java.io.*;

public class Main {

    static int gcd(int a, int b) {
        if (a < b) {
            int temp = a;
            a = b;
            b = temp;
        }
        return b == 0 ? a : gcd(b, a % b);
    }
    public static void main(String[] args) throws IOException {
        //BufferedReader in = new BufferedReader(new FileReader("input.in"));
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        //PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.out")));
        StringTokenizer st = new StringTokenizer(in.readLine());
        int n = Integer.parseInt(st.nextToken());
        int arr[] = new int[n];
        st = new StringTokenizer(in.readLine());
        int d = 0;
        int moves = 0;
        for (int i = 0; i < n; i++) {
            arr[i] = Integer.parseInt(st.nextToken());
            d = gcd(arr[i], d);
        }
        out.println("YES");
        if (d != 1) {
            out.println(moves);
            out.close();
            System.exit(0);
        }
        for (int i = 0; i < n - 1; i++) {
            if (arr[i] % 2 == 1 && arr[i+1] % 2 == 1) {
                arr[i] = 2;
                arr[i+1] = 2;
                moves++;
            }
        }

        for (int i = 0; i < n - 1; i++) {
            if ((arr[i+1] % 2 == 1 && arr[i] % 2 == 0) || (arr[i+1] % 2 == 0 && arr[i] % 2 == 1)) {
                moves += 2;
                arr[i] = 2;
                arr[i+1] = 2;
            }
        }
        out.println(moves);
        out.close();
        System.exit(0);
    }
}
