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.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		int n = sc.nextInt();
		
		int a[] = new int[n];
		
		for(int i = 0; i < n; ++i) a[i] = sc.nextInt();
		
		int g = a[0];
		
		for(int i = 1; i < n; ++i)
			g = gcd(g, a[i]);
		
		if(g != 1) {
			out.println("YES");
			out.println(0);
			out.flush();
			return;
		}
		
		int times = 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;
				times++;
			}
		}
		
		for(int i = 0; i < n - 1; ++i) {
			while(a[i] % 2 != 0 || a[i + 1] % 2 != 0) {
				a[i] = 2;
				a[i + 1] = 2;
				times += 2;
			}
		}
		
		trace(Arrays.toString(a));
		
		out.println("YES");
		out.println(times);
		 
		out.flush();
		out.close();
	}
	
	static int gcd(int a, int b) { return (b == 0)?a:gcd(b, a % b); }
	
	static class Scanner{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public Scanner(FileReader r){	br = new BufferedReader(r);}

		public String next() throws IOException 
		{
			while (st == null || !st.hasMoreTokens()) 
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {return Integer.parseInt(next());}

		public long nextLong() throws IOException {return Long.parseLong(next());}

		public String nextLine() throws IOException {return br.readLine();}

		public double nextDouble() throws IOException { return Double.parseDouble(next()); }

		public boolean ready() throws IOException {return br.ready();}
	}
	
	static boolean OJ = System.getProperty("ONLINE_JUDGE") != null;
	static void trace(String s) {
		if(!OJ)	System.out.println(s);
	}
}