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. 
//package CF;

import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.LinkedList;
import java.util.Queue;
import java.util.StringTokenizer;

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

    public static void main(String[] args) throws Exception
    {
	Scanner bf = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int n = bf.nextInt(), gcd = 0;
	int[] a = new int[n];
	for (int i = 0; i < n; i++)
	{
	    a[i] = bf.nextInt();
	    gcd = gcd(gcd, a[i]);
	}
	if (gcd > 1)
	    out.println("YES\n0");
	else
	{
	    int ans = 0;
	    for (int i = 0; i < a.length; i++)
	    {
		if((a[i] & 1) != 0)
		{
		    if(i+1 < n && (a[i+1] & 1) != 0) { ans++; i++;}
		    else ans+=2;
		}
	    }
	    out.println("YES\n"+ans);
	}
	out.flush();
	out.close();
    }

    static class Scanner {
	StringTokenizer st;
	BufferedReader br;

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

	public Scanner(FileReader fileReader)
	{
	    br = new BufferedReader(fileReader);
	}

	public String next() throws IOException
	{
	    while (st == null || !st.hasMoreTokens())
		st = new StringTokenizer(br.readLine());
	    return st.nextToken();
	}

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

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

	public String nextLine() throws IOException
	{
	    return br.readLine();
	}

	public boolean ready() throws IOException
	{
	    return br.ready();
	}
    }
}