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.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Random;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class P {

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N];
		int gcd = 0;
		for (int i = 0; i < N; i++) 
			gcd = gcd(gcd, a[i] = sc.nextInt());
		

		if (gcd > 1) {
			System.out.println("YES");
			System.out.println(0);
			return;
		}
		int odds = 0;
		boolean[] odd = new boolean[N];
		for (int i = 0; i < N; i++)
			odds += (odd[i] = (a[i] % 2 != 0)) ? 1 : 0;
		int ans = 0;
		for (int i = 0; i < N - 1;) {
			if (odd[i] && odd[i + 1]) {
				odd[i] = odd[i + 1] = false;
				odds -= 2;
				ans++;
				i += 2;
			} else
				i++;
		}

		ans += odds * 2;
		System.out.println("YES");
		System.out.println(ans);

	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String f) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(f));
		}

		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();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		public int[] nextIntArray1(int n) throws IOException {
			int[] a = new int[n + 1];
			for (int i = 1; i <= n; i++)
				a[i] = nextInt();
			return a;
		}

		public int[] nextIntArraySorted(int n) throws IOException {
			int[] a = nextIntArray(n);
			Random r = new Random();
			for (int i = 0; i < n; i++) {
				int j = i + r.nextInt(n - i);
				int t = a[i];
				a[i] = a[j];
				a[j] = t;
			}
			Arrays.sort(a);
			return a;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		public long[] nextLongArray1(int n) throws IOException {
			long[] a = new long[n + 1];
			for (int i = 1; i <= n; i++)
				a[i] = nextLong();
			return a;
		}

		public long[] nextLongArraySorted(int n) throws IOException {
			long[] a = nextLongArray(n);
			Random r = new Random();
			for (int i = 0; i < n; i++) {
				int j = i + r.nextInt(n - i);
				long t = a[i];
				a[i] = a[j];
				a[j] = t;
			}
			Arrays.sort(a);
			return a;
		}
	}
}