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.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class E_Round_196_Div2 {

	public static long MOD = 1000000007;
	static int[][] dp;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		long[] data = new long[n];
		for (int i = 0; i < n; i++) {
			data[i] = in.nextLong();
		}

		if (n > 1) {
			dp = new int[1 << n][1 << n];
			for (int[] a : dp) {
				Arrays.fill(a, -2);
			}
			int result = Integer.MAX_VALUE;
			for (int i = 1; i < (1 << n); i++) {
				int v = cal(i, i, n, data);
				// System.out.println(Integer.toBinaryString(i) + " " + (v));
				if (v != -1)
					result = Math.min(result, v + (Integer.bitCount(i) ==1 ? 0 : 1));
			}
			out.println(result);
		} else {
			out.println(count(data[0], true) + 1);
		}
		out.close();
	}

	public static int cal(int mask, int child, int n, long[] data) {
		if (dp[mask][child] != -2) {
			return dp[mask][child];
		}
		if (Integer.bitCount(mask) == n) {
			int result = 0;
			for (int i = 0; i < n; i++) {
				if (((1 << i) & child) != 0) {
					result += count(data[i] , true) + 1;
				}
			}
			return dp[mask][child] = result;
		}
		if (Integer.bitCount(child) == 0) {
			return -1;
		}
		int result = -1;
		for (int i = 0; i < n; i++) {
			if (((1 << i) & child) != 0) {
				int v = cal(mask, child ^ (1 << i), n, data);
				if (v != -1) {

					result = v + count(data[i], true) + 1;
				}
				for (int j = 1; j < (1 << n); j++) {
					if ((~mask & j) == j) {
						long other = canMatch(j, i, data);
						if (other != -1) {
							int tmp = cal(mask | j, (child | j) ^ (1 << i), n,
									data);
							if (tmp != -1) {
								tmp += count(other, false) + 1;
								if (result == -1 || result > tmp) {
									result = tmp;
								}
							}
						}
					}
				}
				break;
			}
		}
		return dp[mask][child] = result;
	}

	public static int count(long v, boolean direct) {
		if (v == 1) {
			return 0;
		}
		int c = 0;
		boolean prime = true;
		for (long i = 2; i * i <= v; i++) {
			while (v % i == 0) {
				prime = false;
				v /= i;
				c++;
			}
		}
		if (prime) {
			return direct ? 0 : 1;
		}
		return (v == 1 ? c : c + 1);
	}

	public static long canMatch(int mask, int index, long[] data) {
		long cur = data[index];
		for (int j = 0; j < data.length; j++) {
			if (((1 << j) & mask) != 0) {
				if (cur % data[j] != 0) {
					return -1;
				}
				cur /= data[j];
			}
		}
		return cur;
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return x - o.x;
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

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

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}
