#include <bits/stdc++.h>
using namespace std;
int n, cnt[8];
long long x;
void checkmax(int &x, int y) {
  if (x < y) {
    x = y;
  }
}
void modify(int x) {
  switch (x) {
    case 4:
      cnt[2] += 2;
      break;
    case 6:
      cnt[2]++;
      cnt[3]++;
      break;
    case 8:
      cnt[2] += 3;
      break;
    case 9:
      cnt[3] += 2;
      break;
    default:
      cnt[x]++;
      break;
  }
}
void del(int x, int y) {
  switch (x) {
    case 7:
      cnt[7] -= y;
      cnt[5] -= y;
      cnt[3] -= 2 * y;
      cnt[2] -= 4 * y;
      break;
    case 5:
      cnt[5] -= y;
      cnt[3] -= y;
      cnt[2] -= 3 * y;
      break;
    case 3:
      cnt[3] -= y;
      cnt[2] -= y;
      break;
    default:
      cnt[2] -= y;
      break;
  }
}
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cin >> n >> x;
  while (x) {
    for (int i = x % 10; i >= 2; i--) {
      modify(i);
    }
    x /= 10;
  }
  for (int i = 1; i <= cnt[7]; i++) {
    cout << 7;
  }
  del(7, cnt[7]);
  for (int i = 1; i <= cnt[5]; i++) {
    cout << 5;
  }
  del(5, cnt[5]);
  for (int i = 1; i <= cnt[3]; i++) {
    cout << 3;
  }
  del(3, cnt[3]);
  for (int i = 1; i <= cnt[2]; i++) {
    cout << 2;
  }
  del(2, cnt[2]);
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
int n, cnt[8];
long long x;
void checkmax(int &x, int y) {
  if (x < y) {
    x = y;
  }
}
void modify(int x) {
  switch (x) {
    case 4:
      cnt[2] += 2;
      break;
    case 6:
      cnt[2]++;
      cnt[3]++;
      break;
    case 8:
      cnt[2] += 3;
      break;
    case 9:
      cnt[3] += 2;
      break;
    default:
      cnt[x]++;
      break;
  }
}
void del(int x, int y) {
  switch (x) {
    case 7:
      cnt[7] -= y;
      cnt[5] -= y;
      cnt[3] -= 2 * y;
      cnt[2] -= 4 * y;
      break;
    case 5:
      cnt[5] -= y;
      cnt[3] -= y;
      cnt[2] -= 3 * y;
      break;
    case 3:
      cnt[3] -= y;
      cnt[2] -= y;
      break;
    default:
      cnt[2] -= y;
      break;
  }
}
int main(int argc, char const *argv[]) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cout.tie(nullptr);
  cin >> n >> x;
  while (x) {
    for (int i = x % 10; i >= 2; i--) {
      modify(i);
    }
    x /= 10;
  }
  for (int i = 1; i <= cnt[7]; i++) {
    cout << 7;
  }
  del(7, cnt[7]);
  for (int i = 1; i <= cnt[5]; i++) {
    cout << 5;
  }
  del(5, cnt[5]);
  for (int i = 1; i <= cnt[3]; i++) {
    cout << 3;
  }
  del(3, cnt[3]);
  for (int i = 1; i <= cnt[2]; i++) {
    cout << 2;
  }
  del(2, cnt[2]);
  return 0;
}

```