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.InputStreamReader;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author msagimbekov
 */
public class Codeforces798C {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        int[] a = new int[n];
        String[] s = br.readLine().split(" ");
        a[0] = Integer.parseInt(s[0]);
        int gcd = a[0];
        for (int i = 1; i < n; i++) {
            a[i] = Integer.parseInt(s[i]);
            gcd = gcd(gcd, a[i]);
        }
        
        if (gcd > 1) {
            System.out.println("YES\n0");
        } else {
            int cnt = 0;
            int one = 0;
            for (int i = 0; i < n; i++) {
                if (a[i] % 2 == 1) {
                    one++;
                } else {
                    if(one > 0) {
                        cnt += (one / 2) + (one % 2 == 1 ? 2 : 0);
                        one = 0;
                    }
                }
            }   
            if(one > 0) {
                cnt += (one / 2) + (one % 2 == 1 ? 2 : 0);
                one = 0;
            }
            System.out.println("YES\n" + cnt);
        }
        br.close();
    }
    
    
    private static int gcd(int a, int b) {
        if (a < b) {
            return gcd(b, a);
        }
        
        if (b == 0) {
            return a;
        }
        
        return gcd(b, a % b);
    }
}
