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>
import sys


def main():
    get_fr = {"0" : "",
              "1" : "",
              "2" : "2",
              "3" : "3",
              "4" : "322",
              "5" : "5",
              "6" : "53",
              "7" : "7",
              "8" : "7222",
              "9" : "7332"}

    n = input()
    st = input()
    answer = []
    for i in st:
        answer += list(get_fr[i])
    answer.sort(reverse = True)
    
    print("".join(answer))

main()
