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.ArrayList;
import java.util.EmptyStackException;
import java.util.Scanner;

public class Tests{
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        int mas[] = new int[n];
        for (int i = 0; i < n; i++) {
            mas[i] = in.nextInt();
        }
        int g = mas[0];
        int answer = 0;
        for (int i = 1; i < n; ++i) {
            g = gcd(g, mas[i]);
        }
        if (g==1){
            for (int i = 0; i < n; i++) {
                mas[i] = mas[i]%2;
            }
            for (int i = 0; i < n; i++) {
                if (mas[i]==1){
                    if (i==n-1){
                        answer+=2;
                    }
                    else if (mas[i+1]==0){
                        answer+=2;
                        i++;
                    }
                    else if (mas[i+1]==1){
                        answer++;
                        i++;
                    }
                }
            }
        }


        System.out.println("YES");
        System.out.println(answer);






    }
    public static int gcd(int a, int b){
        int t;
        while (b > 0) {
            t = b;
            b = a%b;
            a = t;
        }
        return a;
    }
}
