#include <bits/stdc++.h>
int a[10][4] = {{0, 0, 0, 0}, {1, 0, 0, 0}, {2, 0, 0, 0}, {3, 0, 0, 0},
                {3, 2, 2, 0}, {5, 0, 0, 0}, {5, 3, 0, 0}, {7, 0, 0, 0},
                {7, 2, 2, 2}, {7, 3, 3, 2}};
void countsort(int a[], int length) {
  int b[10] = {0};
  int i = 0;
  for (i = 0; i < length; i++) {
    b[a[i]]++;
  }
  for (i = 9; i >= 2; i--) {
    while (b[i]--) {
      printf("%d", i);
    }
  }
  printf("\n");
}
int main() {
  int s[100] = {0};
  int i = 0, digit = 0;
  long long number = 0;
  while (~scanf("%d %I64d", &digit, &number)) {
    memset(s, 0, sizeof(s));
    i = 0;
    while (digit--) {
      if (number % 10 > 1) {
        if (a[number % 10][0] != 0) {
          s[i] = a[number % 10][0];
          i++;
        }
        if (a[number % 10][1] != 0) {
          s[i] = a[number % 10][1];
          i++;
        }
        if (a[number % 10][2] != 0) {
          s[i] = a[number % 10][2];
          i++;
        }
        if (a[number % 10][3] != 0) {
          s[i] = a[number % 10][3];
          i++;
        }
      }
      number = number / 10;
    }
    countsort(s, 100);
  }
}

### 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>
int a[10][4] = {{0, 0, 0, 0}, {1, 0, 0, 0}, {2, 0, 0, 0}, {3, 0, 0, 0},
                {3, 2, 2, 0}, {5, 0, 0, 0}, {5, 3, 0, 0}, {7, 0, 0, 0},
                {7, 2, 2, 2}, {7, 3, 3, 2}};
void countsort(int a[], int length) {
  int b[10] = {0};
  int i = 0;
  for (i = 0; i < length; i++) {
    b[a[i]]++;
  }
  for (i = 9; i >= 2; i--) {
    while (b[i]--) {
      printf("%d", i);
    }
  }
  printf("\n");
}
int main() {
  int s[100] = {0};
  int i = 0, digit = 0;
  long long number = 0;
  while (~scanf("%d %I64d", &digit, &number)) {
    memset(s, 0, sizeof(s));
    i = 0;
    while (digit--) {
      if (number % 10 > 1) {
        if (a[number % 10][0] != 0) {
          s[i] = a[number % 10][0];
          i++;
        }
        if (a[number % 10][1] != 0) {
          s[i] = a[number % 10][1];
          i++;
        }
        if (a[number % 10][2] != 0) {
          s[i] = a[number % 10][2];
          i++;
        }
        if (a[number % 10][3] != 0) {
          s[i] = a[number % 10][3];
          i++;
        }
      }
      number = number / 10;
    }
    countsort(s, 100);
  }
}

```