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;
import java.util.ArrayList;
import java.util.List;

public class Main {
	
	public static int a, b;
	public static long ans;
	public static boolean vis[][];
	
	public static void main(String[] args) {

		Scanner in = new Scanner( System.in );
		
		int number = in.nextInt();
		int[] array = new int[number + 1];
		int ans = 0;
		
		boolean shaobing = true;
		
		for( int sa = 1; sa <= number; sa ++ ) {
			array[sa] = in.nextInt();
		}
		
		int g = array[1];
		
		for( int sa = 1; sa < number; sa ++ ) {
			g = gcd( g, array[sa + 1] );
//			System.out.println( g );
			if( g == 1 ) {
				shaobing = false;
				break;
			}
		}
		
		if( shaobing ) {
			ans = 0;
		}
		else {
			for( int sa = 1; sa < number; sa ++ ) {
				if( array[sa] % 2 != 0 ) {
					if( array[sa + 1] % 2 != 0 ) {
						ans += 1;
						array[sa + 1] = array[sa] + array[sa + 1];
					}
					else {
						ans += 2;
						array[sa + 1] = array[sa] * 2;
					}
				}
				if( sa == number - 1 && array[sa + 1] % 2 != 0 ) {
					ans += 2;
				}
			}
		}
		
		System.out.println( "YES" );
		System.out.println( ans );
		
	}
	
	public static int gcd( int a, int b ) {
		int ans = 1;
		for( int sa = Math.min( a, b ); sa >= 1; sa -- ) {
			if( a % sa == 0 && b % sa == 0 ) {
				ans = sa;
				break;
			}
		}
		return ans;
	}
	
}