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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Div2_410C {

	public static void main(String[] args) throws IOException {
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter printer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

		int numE = Integer.parseInt(reader.readLine());
		int[] elements = new int[numE];
		StringTokenizer inputData = new StringTokenizer(reader.readLine());
		for (int i = 0; i < numE; i++) {
			elements[i] = Integer.parseInt(inputData.nextToken());
		}

		int gcd = elements[0];
		for (int i = 1; i < numE; i++) {
			gcd = gcd(gcd, elements[i]);
		}

		if (gcd > 1) {
			printer.println("YES");
			printer.println(0);
			printer.close();
			return;
		}

		int cnt = 0;
		for (int i = 0; i < numE; i++) {
			if ((elements[i] & 1) == 1) {
				if (i + 1 < numE && (elements[i + 1] & 1) == 1) {
					cnt++;
					i++;
				} else {
					cnt += 2;
				}
			}
		}
		printer.println("YES");
		printer.println(cnt);
		printer.close();
	}

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

}
