#include <bits/stdc++.h>
using namespace std;
struct fact {
  int a;
  int b;
  int c;
  int d;
};
int find(int n, int m) { return ((n / m) + (n / (m * m)) + (n / (m * m * m))); }
int main() {
  struct fact r[10];
  int n;
  cin >> n;
  r[0].a = r[0].b = r[0].c = r[0].d = 0;
  for (int i = 1; i < 10; i++) {
    r[i].a = find(i, 2);
    r[i].b = find(i, 3);
    r[i].c = find(i, 5);
    r[i].d = find(i, 7);
  }
  string s;
  cin >> s;
  int w, x, y, z;
  w = x = y = z = 0;
  for (size_t i = 0; i < s.length(); i++) {
    int temp = s[i] - '0';
    w = w + (r[temp].a);
    x = x + (r[temp].b);
    y = y + (r[temp].c);
    z = z + (r[temp].d);
  }
  while (z != 0) {
    cout << "7";
    z--;
    y--;
    x -= 2;
    w -= 4;
  }
  while (y != 0) {
    cout << "5";
    y--;
    x--;
    w -= 3;
  }
  while (x != 0) {
    cout << "3";
    x--;
    w--;
  }
  while (w != 0) {
    cout << "2";
    w--;
  }
  cout << endl;
  return 0;
}

### Prompt

Please formulate a CPP solution to the following problem:

Drazil is playing a math game with Varda.

Let's define <image> for positive integer x as a product of factorials of its digits. For example, <image>.

First, they choose a decimal number a consisting of n digits that contains at least one digit larger than 1. This number may possibly start with leading zeroes. Then they should find maximum positive number x satisfying following two conditions:

1. x doesn't contain neither digit 0 nor digit 1.

2. <image> = <image>.

Help friends find such number.

Input

The first line contains an integer n (1 ≤ n ≤ 15) — the number of digits in a.

The second line contains n digits of a. There is at least one digit in a that is larger than 1. Number a may possibly contain leading zeroes.

Output

Output a maximum possible integer satisfying the conditions above. There should be no zeroes and ones in this number decimal representation.

Examples

Input

4
1234


Output

33222


Input

3
555


Output

555

Note

In the first case, <image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
struct fact {
  int a;
  int b;
  int c;
  int d;
};
int find(int n, int m) { return ((n / m) + (n / (m * m)) + (n / (m * m * m))); }
int main() {
  struct fact r[10];
  int n;
  cin >> n;
  r[0].a = r[0].b = r[0].c = r[0].d = 0;
  for (int i = 1; i < 10; i++) {
    r[i].a = find(i, 2);
    r[i].b = find(i, 3);
    r[i].c = find(i, 5);
    r[i].d = find(i, 7);
  }
  string s;
  cin >> s;
  int w, x, y, z;
  w = x = y = z = 0;
  for (size_t i = 0; i < s.length(); i++) {
    int temp = s[i] - '0';
    w = w + (r[temp].a);
    x = x + (r[temp].b);
    y = y + (r[temp].c);
    z = z + (r[temp].d);
  }
  while (z != 0) {
    cout << "7";
    z--;
    y--;
    x -= 2;
    w -= 4;
  }
  while (y != 0) {
    cout << "5";
    y--;
    x--;
    w -= 3;
  }
  while (x != 0) {
    cout << "3";
    x--;
    w--;
  }
  while (w != 0) {
    cout << "2";
    w--;
  }
  cout << endl;
  return 0;
}

```