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.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

/**
 * Created by fly on 9/4/17.
 */
public class Main {
    public static int mod = 1_000_000_007;
    public static int size = 2_000_000;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = in.nextInt();
        int[]  num = new int[n];
        int res = 0;
        for(int i = 0; i < n; ++i) {
            num[i] = in.nextInt();
            res = gcd(res, num[i]);
            num[i] %= 2;
        }
        if(res == 1) {
            ArrayList<Integer> count = new ArrayList<>();
            int cur = 0;
            while(cur < n) {
                int add = 0;
                while(cur < n && num[cur] == 0) ++cur;
                while(cur < n && num[cur] == 1) {++add;++cur;}
                count.add(add);
            }
            int ret = 0;
            for(int each : count) {
                ret += (each + 1)/2 + each % 2;
            }
            out.print("YES\n" + ret);
        } else {
            out.print("YES\n0");
        }
        out.close();
    }

    public static int gcd(int a, int b) {
        if(b > a) {
            int temp = a;
            a = b;
            b = temp;
        }
        if(b == 0) return a;
        else return gcd(b, a%b);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}
