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.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class MikeAndGCD 
{

	static int n;
	static int arr[];

	static int gcd(int a,int b)
	{
		if(a == 0)
			return b;
		return gcd(b % a,a);
	}
	public static void main(String[]args) throws Throwable
	{
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt(); arr = new int[n];
		for(int i = 0 ; i < n ; ++i)
			arr[i] = sc.nextInt();
		int g = arr[0];
		for(int i = 1; i < n ; ++i)
			g = gcd(arr[i],g);
		if(g != 1)
		{
			System.out.println("YES\n0");
			return;
		}
		int ans = 0;
		for(int i = 0 ; i < n ; ++i)
			arr[i] = arr[i] & 1;
		for(int i = 0 ; i < n - 1; ++i)
		{
			if(arr[i] % 2 == 1)
			{
				if(arr[i + 1] % 2 == 1)
				{
					arr[i] = arr[i + 1] = 0;
					ans++; ++i;
				}
				else
				{
					arr[i] = arr[i + 1] = 0;
					ans += 2;
				}
			}

		}
		if(arr[n - 1] == 1)
			ans += 2;
		System.out.println("YES");
		System.out.println(ans);

	}
	static class Scanner
	{
		BufferedReader br;
		StringTokenizer st;


		Scanner(InputStream s)  { br = new BufferedReader(new InputStreamReader(s)); }

		String next() throws IOException
		{

			while(st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();

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



	}
}
