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.Iterator;
import java.util.LinkedList;
import java.util.List;
import java.util.Scanner;

//https://codeforces.com/problemset/problem/798/C
public class Solution {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt(), gcd = -1;
        boolean[] arr = new boolean[n];
        LinkedList<Integer> arr1 = new LinkedList<>();
        int last=-1;
        for (int j = 0; j < n; j++) {
            int a = scanner.nextInt();
            gcd = gcd(a, gcd == -1 ? a : gcd);
            arr[j] = a%2==0;

            a=a%2;
            if (last==-1 && a==1)arr1.addLast(1);
            else if (a==1&&last==1) {
                arr1.addLast(arr1.removeLast()+1);
            } else if (a==1)
                arr1.addLast(1);
            last=a;
        }
        //System.out.println(arr1);
        int ans = 0;
        if (gcd == 1) {
            Iterator<Integer> it = arr1.iterator();
            while (it.hasNext()) {
                int num = it.next();
                if (num%2==0)
                    ans += num/2;
                else {
                    ans += (num/2)+2;
                }
                //System.out.println(ans);
            }
        }
        System.out.println("YES");
        System.out.println(ans);
        scanner.close();
    }
    public static int gcd(int x,int y){
        int a = x,  b = y,t;

        while (b != 0) {
            t = b;
            b = a % b;
            a = t;
        }

        return a;
    }
}
