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>
#include <bits/stdc++.h>
using namespace std;
const int prime[] = {2, 3, 5, 7};
int a[10];
void get(int x, int y) {
  for (int i = 0; i < 4; i++)
    while (x % prime[i] == 0) {
      a[prime[i]] += y;
      x /= prime[i];
    }
}
char s[20];
int n, i, j;
int main() {
  cin >> n >> s;
  for (i = 0; i < n; i++) {
    int x = s[i] - '0';
    for (j = 1; j <= x; j++) get(j, 1);
  }
  for (i = 3; i >= 0; i--)
    while (a[prime[i]]) {
      for (j = prime[i]; j; j--) get(j, -1);
      cout << prime[i];
    }
}
