Codeforces Round #292 (Div. 2) C. Drazil and Factorial 515C

C. Drazil and Factorial

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Drazil is playing a math game with Varda.

Let's define  for positive integer x as a product of factorials of its digits. For example, .

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.  = .

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

Copy

4
1234

output

Copy

33222

input

Copy

3
555

output

Copy

555

Note

In the first case, 

题意 给出数x，得出x各位数阶乘的乘积；求得出的各位数乘积和与x得出的各位数阶乘的乘积相等的最大数

先打表ch[i] F[i]=F[p]最大值p，排序，反转

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
int main(){
    int n;
    scanf("%d",&n);
    string str;
    cin>>str;
    string str1 = "";
    string ch[10]={"","","2","3","223","5","53","7","7222","7332"};
    for(int i = 0; i < n; i++){
        str1 += ch[str[i]-'0'];
    }
    sort(str1.begin(),str1.end());
    reverse(str1.begin(),str1.end());
    cout<<str1<<endl;
    return 0;
}