Drazil and Factorial

2000ms

262144K

Description:

Drazil is playing a math game with Varda.

Let's define $\text{[math]}$ for positive integer x as a product of factorials of its digits. For example, $\text{[math]}$ .

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. $\text{[math]}$ = $\text{[math]}$ .

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.

Sample Input:

4
1234

Sample Output:

Sample Input:

3
555

Sample Output:

Note:

In the first case, $\text{[math]}$

Informação

Provedor Codeforces

Código CF515C