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. 
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{	
	static int a[];
	public static void main (String[] args)
	{
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = scan.nextInt();
		}
		if (isGood()) {
			System.out.println("YES");
			System.out.println("0");
			return ;
		}
		for (int i = 0; i <n; i++) {
			a[i] = a[i] % 2;
		}
		int ans = 0;
		for (int i = 0; i < n; i++) {
			int cnt = 0;
			while (i < n && a[i] == 1) {
				i++;
				cnt++;
			}
			ans = ans + cnt / 2;
			if (cnt % 2 == 1) {
				ans = ans + 2;
			}
		}
		
		System.out.println("YES");
		System.out.println(ans);
	}
	
	public static boolean isGood() {
		int g = a[0];
		for (int i = 1; i < a.length; i++) {
			g = gcd(g, a[i]);
		}
		return g > 1;
	}
	
	public static int gcd (int a, int b) {
		if (a == 0) 
			return b;
		return gcd(b % a, a);
	}
	
}