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.*;

public class TestClass {

    static PrintWriter out = new PrintWriter(System.out);
    public static void main(String[] args) throws Exception{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        String s[] = in.readLine().split(" ");
        int a[] = new int[n];
        for(int i=0;i<n;i++)
        {
        	a[i] = Integer.parseInt(s[i]);
        }
        int g = gcd(a[0],a[1]);
        for(int i=2;i<n;i++)
        {
        	g = gcd(g,a[i]);
        }
        if(g>1)
        {
        	out.println("YES");
        	out.println(0);
        	out.close();
        	System.exit(0);
        }
        int cnt=0;
        int i=0;
        while(i<n-1)
        {
        	if(a[i]%2==1)
        	{
        		int x = Math.abs(a[i]-a[i+1]);
        		int y = a[i]+a[i+1];
        		a[i] = x;
        		a[i+1] = y;
        		cnt++;
        	}
        	else
        	{
        		i++;
        	}
        	
        }
        if(a[n-1]%2==1)
    	{
    		cnt +=2;
    	}
    
        out.println("YES");
        out.println(cnt);
        out.close();
    } 
    public static int gcd(int a,int b)
    {
    	if(b==0)
    	{
    		return a;
    	}
    	return gcd(b,a%b);
    }
 
  
}
