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;

//5:20
public class C {
	
	public C() {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int[] nums = new int[n];
		
		boolean[] even = new boolean[n];
		for (int i = 0; i < n; i++) {
			nums[i] = s.nextInt();
			if (nums[i] % 2 == 0) {
				even[i] = true;
			}
		}
		
		int cur = nums[0];
		for (int i = 1; i < nums.length; i++) {
			cur = gcd(cur, nums[i]);
		}
		if (cur > 1) {
			System.out.println("YES");
			System.out.println(0);
			System.exit(0);
		}
		
		int doubles = 0;
		for (int i = 0; i < even.length - 1; i++) {
			if (!even[i] && !even[i+1]) {
				doubles++;
				i++;
			}
		}
		
		int odds = 0;
		for (int i = 0; i < even.length; i++) {
			if (!even[i]) {
				odds++;
			}
		}
		System.err.println(odds);
		System.err.println(doubles);
		odds -= doubles*2;
		System.out.println("YES");
		System.out.println(2*odds + (doubles));
	}
	
	public int gcd(int a, int b)  {
		if (a < b) {
			int temp = a;
			a = b;
			b = temp;
		}
		if (b == 0) {
			return a;
		}
		return gcd(a % b, b);
	}
	
	public static void main(String[] args) {
		new C();
	}
}
