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.StringTokenizer;

public class MikeAndGcdProblem {

	public static FastScanner in = new FastScanner(System.in);

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

		public FastScanner(InputStream i) {
			reader = new BufferedReader(new InputStreamReader(i));
			tokenizer = new StringTokenizer("");
		}

		public String next() throws IOException {
			while (!tokenizer.hasMoreTokens())
				tokenizer = new StringTokenizer(reader.readLine());
			return tokenizer.nextToken();
		}

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

		public void close() throws IOException {
			reader.close();
		}
	}

	public static int gcd(int a, int b) {
		return b == 0 ? a : a % b == 0 ? b : gcd(b, a % b);
	}

	public static void main(String[] args) {
		try {
			int n = in.nextInt();
			int[] l = new int[n + 1];
			int minGcd = 0;
			for (int i = 0; i < n; i++) {
				l[i] = in.nextInt();
				minGcd = gcd(minGcd, l[i]);
			}
			int nbMove = 0;
			if (minGcd == 1) {
				for (int i = 0; i < n; i++)
					if (l[i] % 2 == 1)
						if (l[i + 1] % 2 == 1) {
							nbMove++;
							l[i] = 0;
							l[i + 1] = 0;
						} else {
							nbMove += 2;
							l[i] = 0;
						}
			}
			System.out.println("YES");
			System.out.println(nbMove);
			in.close();
		} catch (

		Exception e) {
			e.printStackTrace();
		}
	}

}