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 C {
	
	public static void main(String[] args) {
	
		Scanner qwe = new Scanner(System.in);
		int n = qwe.nextInt();
		int[] a = new int[n];
		int gcd = 0;
		for (int i = 0; i < a.length; i++) {
			a[i] =qwe.nextInt();
			gcd = gcd(a[i],gcd);
		}
		
		if(gcd != 1) System.out.println("YES\n"+0);
		else{
			int ans = 0;
			for (int i = 0; i < a.length-1; i++) {
				if(a[i] % 2 == 1){
					ans++;
					int x = a[i];
					int y = a[i+1];
					a[i] = Math.abs(x-y);
					a[i+1] = x+y;
					i--;
				}
			}
			if(a[a.length-1] % 2 == 1) ans+= 2;
			
			System.out.println("YES\n"+ans);
			
		}
		
		
	}
	
	static int gcd(int a, int b){
		if(b == 0) return a;
		return gcd(b, a%b);
	}

}
