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.io.BufferedInputStream;
import java.util.Scanner;
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;
        FastReader in = new FastReader(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, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = in.nextInt();
            }


            int r = 0;
            int d = a[0];

            for (int i = 1; i < n; i++) {
                d = Math2.gcd(d, a[i]);
            }

            if (d == 1) {
                for (int i = 1; i < n; i++) {
                    if (a[i - 1] % 2 == 0) {
                        continue;
                    }

                    r += a[i] % 2 == 0 ? 2 : 1;
                    a[i] = 0;
                }

                if (a[n - 1] % 2 != 0) {
                    r += 2;
                }
            }

            out.println("YES");
            out.println(r);

        }

    }

    static class FastReader {
        BufferedInputStream bis;

        public FastReader(InputStream in) {
            bis = new BufferedInputStream(in);
        }

        public int nextInt() {
            try {
                boolean negative = false;
                int c = bis.read();
                int result = 0;
                while (c != '-' && (c < '0' || c > '9')) {
                    c = bis.read();
                }

                if (c == '-') {
                    negative = true;
                    c = bis.read();
                }

                while (c >= '0' && c <= '9') {
                    result *= 10;
                    result += c - '0';
                    c = bis.read();
                }

                return negative ? -result : result;
            } catch (Exception ex) {
            }

            return 0;
        }

    }

    static class Math2 {
        public static int gcd(int a, int b) {
            int c;
            while (a != 0) {
                c = a;
                a = b % a;
                b = c;
            }
            return b;
        }

    }
}

