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.util.*;
import java.io.*;
public class Main
{
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    public static int gcd(int a,int b)
    {
        if(b%a==0)
        return a;
        return gcd(b%a,a);
    }
    public static void main(String args[])
    {
        FastReader fs=new FastReader();
        PrintWriter pw=new PrintWriter(System.out);
        int n=fs.nextInt();
        int a[]=new int[n];
        for(int i=0;i<n;i++)
        a[i]=fs.nextInt();
        int g=a[0];
        for(int i=1;i<n;i++)
        g=gcd(g,a[i]);
        if(g>1)
        pw.println("YES\n0");
        else
        {
            for(int i=0;i<n;i++)
            a[i]%=2;
            for(int i=1;i<n;i++)
            {
                if(a[i]>0)
                a[i]+=a[i-1];
            }
            int cnt=0;
            for(int i=n-1;i>=0;)
            {
                if(a[i]==0)
                i--;
                else
                {
                    cnt+=a[i]/2;
                    if(a[i]%2!=0)
                    cnt+=2;
                    i-=a[i];
                }
            }
            pw.println("YES");
            pw.println(cnt);
        }
        pw.flush();
        pw.close();
    }
}