#include <bits/stdc++.h>
using namespace std;
bool debug = false;
int n;
string s;
int fac[5];
void facSim(int x, int v = -1) {
  while (x % 2 == 0) {
    x /= 2;
    fac[0] += v;
  }
  while (x % 3 == 0) {
    x /= 3;
    fac[1] += v;
  }
  while (x % 5 == 0) {
    x /= 5;
    fac[2] += v;
  }
  while (x % 7 == 0) {
    x /= 7;
    fac[3] += v;
  }
}
void facAdd(int x) {
  for (int i = 1; i <= x; i++) {
    facSim(i, 1);
  }
}
int main(int argc, char* argv[]) {
  cin >> n >> s;
  for (int i = 0; i < n; i++) {
    facAdd(s[i] - '0');
  }
  string out;
  int cnt = 0;
  for (int i = 0; i < fac[3]; i++) {
    out += "7";
    for (int j = 1; j <= 6; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[2]; i++) {
    out += "5";
    for (int j = 1; j <= 4; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[1]; i++) {
    out += "3";
    for (int j = 1; j <= 2; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[0]; i++) {
    out += "2";
    for (int j = 1; j <= 1; j++) {
      facSim(j);
    }
  }
  cout << out;
  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;
bool debug = false;
int n;
string s;
int fac[5];
void facSim(int x, int v = -1) {
  while (x % 2 == 0) {
    x /= 2;
    fac[0] += v;
  }
  while (x % 3 == 0) {
    x /= 3;
    fac[1] += v;
  }
  while (x % 5 == 0) {
    x /= 5;
    fac[2] += v;
  }
  while (x % 7 == 0) {
    x /= 7;
    fac[3] += v;
  }
}
void facAdd(int x) {
  for (int i = 1; i <= x; i++) {
    facSim(i, 1);
  }
}
int main(int argc, char* argv[]) {
  cin >> n >> s;
  for (int i = 0; i < n; i++) {
    facAdd(s[i] - '0');
  }
  string out;
  int cnt = 0;
  for (int i = 0; i < fac[3]; i++) {
    out += "7";
    for (int j = 1; j <= 6; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[2]; i++) {
    out += "5";
    for (int j = 1; j <= 4; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[1]; i++) {
    out += "3";
    for (int j = 1; j <= 2; j++) {
      facSim(j);
    }
  }
  for (int i = 0; i < fac[0]; i++) {
    out += "2";
    for (int j = 1; j <= 1; j++) {
      facSim(j);
    }
  }
  cout << out;
  return 0;
}

```