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;
int n, cnt[10];
char str[22];
int main() {
  scanf("%d", &n);
  scanf("%s", str);
  for (int i = 0; i < n; ++i) ++cnt[str[i] - '0'];
  while (cnt[4]) cnt[4]--, ++cnt[2], ++cnt[2], ++cnt[3];
  while (cnt[6]) cnt[6]--, ++cnt[3], ++cnt[5];
  while (cnt[8]) cnt[8]--, ++cnt[2], ++cnt[2], ++cnt[2], ++cnt[7];
  while (cnt[9]) cnt[9]--, ++cnt[3], ++cnt[3], ++cnt[2], ++cnt[7];
  for (int i = 9; i >= 2; --i)
    while (cnt[i]--) putchar('0' + i);
  puts("");
}
