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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyBufferedReader in = new MyBufferedReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        public void solve(int testNumber, MyBufferedReader in, PrintWriter out) {
            int n = in.getAnInt();
            int[] a = in.getALineOfInts(n);

            out.println("YES");
            if (gcd(a) > 1) {
                out.println(0);
                return;
            }

            int res = 0;
            for (int i = 0; i < n - 1; i++) {
                if (a[i] % 2 != 0) {
                    move(a, i);
                    res++;
                    if (a[i] % 2 != 0) {
                        move(a, i);
                        res++;
                    }
                }
            }

            if (a[n - 1] % 2 != 0) {
                move(a, n - 2);
                res++;
                if (a[n - 1] % 2 != 0) {
                    move(a, n - 2);
                    res++;
                }
            }
            out.println(res);
        }

        private void move(int[] a, int i) {
            int tmp = a[i];
            a[i] -= a[i + 1];
            a[i + 1] += tmp;
        }

        private static int gcd(int a, int b) {
            while (b > 0) {
                int temp = b;
                b = a % b; // % is remainder
                a = temp;
            }
            return a;
        }

        private static int gcd(int[] input) {
            int result = input[0];
            for (int i = 1; i < input.length; i++) result = gcd(result, input[i]);
            return result;
        }

    }

    static class MyBufferedReader {
        BufferedReader in;

        public MyBufferedReader(InputStream s) {
            this.in = new BufferedReader(new InputStreamReader(s));
        }

        public MyBufferedReader(BufferedReader in) {
            this.in = in;
        }

        public int getAnInt() {
            int res = -1;
            try {
                res = Integer.parseInt(new StringTokenizer(in.readLine()).nextToken());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return res;
        }

        public int[] getALineOfInts(int numExpected) {
            if (numExpected == 0) {
                return new int[0];
            }

            int[] res = new int[numExpected];
            StringTokenizer st = null;
            try {
                st = new StringTokenizer(in.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            for (int i = 0; i < numExpected; i++)
                res[i] = Integer.parseInt(st.nextToken());
            return res;
        }

    }
}

