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>
my_dict = {
  "0": "",
  "1": "", 
  "2": "2", 
  "3": "3", 
  "4":"322",
  "5": "5",
  "6": "53",
  "7": "7",
  "8": "7222",
  "9": "7332"
  }

n = int(input())
f =""
for digit in input():
  f+=my_dict[digit]

print("".join(map(str, sorted(list(f), reverse=True))))