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.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class TaskC {
        int gcd(int a, int b) {
            a = a < 0 ? -a : a;
            b = b < 0 ? -b : b;
            if (a == 0) {
                return b;
            }
            return gcd(b % a, a);
        }

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int[] a = in.getIntArray1D(n);
            int gcd = gcd(a[0], a[1]);
            for (int i = 2; i < n; ++i) {
                gcd = gcd(gcd, a[i]);
            }
            if (gcd > 1) {
                out.println("YES");
                out.println(0);
                return;
            }
            int ones = 0;
            for (int i = 0; i < n; ++i) {
                if (a[i] == 1) {
                    ++ones;
                }
            }

            int ans = 0;
            for (int i = 0; i < n; ++i) {
                a[i] = a[i] % 2;
            }
            for (int i = 0; i < n; ++i) {
                if (a[i] == 1) {
                    if (i > 0 && a[i - 1] == 1) {
                        ++ans;
                        a[i] = a[i - 1] = 0;
                    } else if (i < n - 1 && a[i + 1] == 1) {
                        ++ans;
                        a[i] = a[i + 1] = 0;
                    } else if (i > 0 && a[i - 1] == 0) {
                        ans += 2;
                        a[i] = a[i - 1] = 0;
                    } else if (i < n - 1 && a[i + 1] == 0) {
                        ans += 2;
                        a[i] = a[i + 1] = 0;
                    }
                }
            }
            out.println("YES");
            out.println(ans);
        }

    }

    static class InputReader implements AutoCloseable {
        private final InputStream in;
        private int capacity;
        private byte[] buffer;
        private int len = 0;
        private int cur = 0;

        public InputReader(InputStream stream) {
            this(stream, 100_000);
        }

        public InputReader(InputStream stream, int capacity) {
            this.in = stream;
            this.capacity = capacity;
            buffer = new byte[capacity];
        }

        private boolean update() {
            if (cur >= len) {
                try {
                    cur = 0;
                    len = in.read(buffer, 0, capacity);
                    if (len <= 0)
                        return false;
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return true;
        }

        private int read() {
            if (update())
                return buffer[cur++];
            else return -1;
        }

        private boolean isSpace(int c) {
            return c == '\n' || c == '\t' || c == '\r' || c == ' ';
        }

        private int readSkipSpace() {
            int c;
            do {
                c = read();
            } while (isSpace(c));
            return c;
        }

        public int nextInt() {
            int c = readSkipSpace();
            if (c < 0)
                throw new InputMismatchException();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c == -1) break;
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res = res * 10 + c - '0';
                if (res < 0)
                    throw new InputMismatchException();
                c = read();
            } while (!isSpace(c));
            res *= sgn;
            return res;
        }

        public int[] getIntArray1D(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; ++i) {
                array[i] = nextInt();
            }
            return array;
        }


        public void close() throws IOException {
            in.close();
        }

    }
}

