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.Scanner;

public class Solution3 {
  public static void main(String[] args) throws Exception {
    Scanner in = new Scanner(System.in);
    int n = in.nextInt();
    int[] a = new int[n];
    for(int i = 0; i < n; i++) {
      a[i] = in.nextInt();
    }
    int gcd = a[0];
    for (int i = 1; i < n; i++) {
      gcd = gcd(gcd, a[i]);
    }
    if (gcd > 1) {
      System.out.println("YES");
      System.out.println("0");
      System.exit(0);
    }
    int moves = 0;
    for (int i = 0; i < n - 1; i++) {
      if (a[i] % 2 == 1 && a[i + 1] % 2 == 1) {
        a[i] = 2;
        a[i + 1] = 2;
        moves++;
      }
    }
    for (int i = 0; i < n - 1; i++) {
      if (a[i] % 2 != a[i + 1] % 2) {
        a[i] = 2;
        a[i + 1] = 2;
        moves += 2;
      }
    }
    System.out.println("YES");
    System.out.println(moves);
  }

  public static int gcd(int a, int b) {
    return b == 0 ? a : gcd(b, a % b);
  }
}