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.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.nio.ByteBuffer;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Stack;


 public class Main{

    
    static int gcd(int a, int b) {
        if(b==0) return a;
        return gcd(b,a%b);
    }
     
     
     public static void main(String[] args) throws IOException {
         String IN = "C:\\Users\\ugochukwu.okeke\\Desktop\\in.file";
         String OUT = "C:\\Users\\ugochukwu.okeke\\Desktop\\out.file";
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
         
        bw.append("YES\n");
        int n = Integer.parseInt(br.readLine());
        int[]a = new int[n];
        String[] in=br.readLine().split(" ");
        for(int i=0;i<n;i++) a[i] = Integer.parseInt(in[i]);
        
        int r=a[0];
        for(int i=1;i<n;i++) r =gcd(r,a[i]);
        if(r>1) bw.append("0\n");
        else{
            int cnt = 0;
            for(int i=0;i<n-1;i++) {
                if(a[i]%2==1) {
                    int tmp1 = a[i];
                    int tmp2 = a[i+1];
                    if(a[i+1]%2==1) {
                        a[i] = tmp1-tmp2;
                        a[i+1] = tmp1+tmp2;
                        cnt++;
                    }
                    else{
                        a[i] = -2*tmp2;
                        a[i+1] = 2*tmp1;
                        cnt+=2;
                        i++;
                    }
                }
            }
            if(a[n-1]%2==1) {
                cnt+=2;
            }
            bw.append(cnt+"\n");
        }
        
        bw.close();
        //done then
         
     }

    

    

 }