A divisor tree is a rooted tree that meets the following conditions: 

  * Each vertex of the tree contains a positive integer number. 
  * The numbers written in the leaves of the tree are prime numbers. 
  * For any inner vertex, the number within it is equal to the product of the numbers written in its children. 



Manao has n distinct integers a1, a2, ..., an. He tries to build a divisor tree which contains each of these numbers. That is, for each ai, there should be at least one vertex in the tree which contains ai. Manao loves compact style, but his trees are too large. Help Manao determine the minimum possible number of vertices in the divisor tree sought.

Input

The first line contains a single integer n (1 ≤ n ≤ 8). The second line contains n distinct space-separated integers ai (2 ≤ ai ≤ 1012).

Output

Print a single integer — the minimum number of vertices in the divisor tree that contains each of the numbers ai.

Examples

Input

2
6 10


Output

7


Input

4
6 72 8 4


Output

12


Input

1
7


Output

1

Note

Sample 1. The smallest divisor tree looks this way: <image>

Sample 2. In this case you can build the following divisor tree: <image>

Sample 3. Note that the tree can consist of a single vertex.
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
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;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskC {
    int n;
    long[] a;
    int[] count;
    int[] next;
    int cur;
    int cntRoots;
    int opt;

    public void solve(int testNumber, InputReader in, OutputWriter out) {
        n = in.nextInt();
        a = new long[n];
        for (int i = 0; i < n; ++i)
            a[i] = in.nextLong();
        Arrays.sort(a);
        count = new int[n];
        for (int i = 0; i < n; ++i) {
            long x = a[i];
            for (long y = 2; y * y <= x; ++y) {
                while (x % y == 0) {
                    x /= y;
                    ++count[i];
                }
            }
            if (x > 1) ++count[i];
        }
        next = new int[n];
        cur = 0;
        opt = 1000 * 1000 * 1000;
        cntRoots = 0;
        dfs(0);
        out.printLine(opt + n);
    }

    private void dfs(int ind) {
        if (ind >= n) {
            int val = cur;
            if (cntRoots > 1) ++val;
            if (val < opt) opt = val;
            return;
        }
        int w = count[ind];
        long y = a[ind];
        for (int i = 0; i < ind; ++i)
            if (next[i] == ind) {
                if (y % a[i] != 0) return;
                y /= a[i];
                w -= count[i];
            }
        if (count[ind] == 1) w = 0; // prime
        cur += w;
        for (int i = ind; i < n; ++i) {
            next[ind] = i;
            if (i == ind) ++cntRoots;
            dfs(ind + 1);
            if (i == ind) --cntRoots;
        }
        cur -= w;
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buffer = new byte[10000];
    private int cur;
    private int count;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public static boolean isSpace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    public int read() {
        if (count == -1) {
            throw new InputMismatchException();
        }
        try {
            if (cur >= count) {
                cur = 0;
                count = stream.read(buffer);
                if (count <= 0)
                    return -1;
            }
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        return buffer[cur++];
    }

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

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

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

    }

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                writer.print(' ');
            }
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    }
