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.*;
public class MikeGCD {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        int n = s.nextInt();
        int numbers[] = new int[n];
        int g = 0;
        for(int i = 0; i < n; ++i) {
            numbers[i] = s.nextInt();
            g = gcd(g, numbers[i]);
        }
        if(g > 1) {
            System.out.println("YES\n0");
            return;
        }
        int oddNumber = 0;
        int moves = 0;
        for(int i = 0; i < n; ++i) {
            if(numbers[i] % 2 == 0) {
                if(oddNumber > 0) {
                    if(oddNumber % 2 == 0) {
                        moves += oddNumber/2;
                    } else {
                        moves += oddNumber/2 + 2;
                    }
                }
                oddNumber = 0;
            } else {
                oddNumber++;
            }
        }
        if(oddNumber > 0) {
            if(oddNumber % 2 == 0) {
                moves += oddNumber/2;
            } else {
                moves += oddNumber/2 + 2;
            }
        }
        oddNumber = 0;
        System.out.println("YES");
        System.out.println(moves);
    }
    
    /**
     * 
     * @param a >= 0
     * @param b >= 0
     * @return returns gcd of two positive integers
     */
    static int gcd(int a, int b) {
        while(b > 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }
}
