#include <bits/stdc++.h>
using namespace std;
int main(int argc, char* argv[]) {
  map<int, vector<int>> m;
  m[2] = vector<int>(1, 2);
  for (int i = 3; i <= 9; ++i) {
    m[i] = m[i - 1];
    auto tmp = i;
    int j = 2;
    for (; j * j <= i; ++j)
      if (tmp % j == 0)
        while (tmp % j == 0) {
          m[i].push_back(j);
          tmp /= j;
        }
    if (tmp != 1) m[i].push_back(tmp);
    sort(m[i].begin(), m[i].end());
  }
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> mm;
  auto T = 1ULL;
  for (auto c : s)
    if (c > '1') mm.insert(mm.end(), m[c - '0'].begin(), m[c - '0'].end());
  sort(mm.begin(), mm.end());
  string ans;
  while (!mm.empty()) {
    vector<int> tmp;
    ans += string(1, '0' + mm.back());
    set_difference(mm.begin(), mm.end(), m[mm.back()].begin(),
                   m[mm.back()].end(), back_inserter(tmp));
    mm = tmp;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Create a solution in Cpp for 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 main(int argc, char* argv[]) {
  map<int, vector<int>> m;
  m[2] = vector<int>(1, 2);
  for (int i = 3; i <= 9; ++i) {
    m[i] = m[i - 1];
    auto tmp = i;
    int j = 2;
    for (; j * j <= i; ++j)
      if (tmp % j == 0)
        while (tmp % j == 0) {
          m[i].push_back(j);
          tmp /= j;
        }
    if (tmp != 1) m[i].push_back(tmp);
    sort(m[i].begin(), m[i].end());
  }
  int n;
  cin >> n;
  string s;
  cin >> s;
  vector<int> mm;
  auto T = 1ULL;
  for (auto c : s)
    if (c > '1') mm.insert(mm.end(), m[c - '0'].begin(), m[c - '0'].end());
  sort(mm.begin(), mm.end());
  string ans;
  while (!mm.empty()) {
    vector<int> tmp;
    ans += string(1, '0' + mm.back());
    set_difference(mm.begin(), mm.end(), m[mm.back()].begin(),
                   m[mm.back()].end(), back_inserter(tmp));
    mm = tmp;
  }
  cout << ans << endl;
  return 0;
}

```