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>
ds = [[], # 0
      [], # 1
      [2], # 2
      [3], # 3
      [3, 2, 2], # 4
      [5], # 5
      [5, 3], # 6
      [7], # 7
      [7, 2, 2, 2], # 8
      [7, 2, 3, 3]] # 9

n = int(input())
xs = input()

rs = []
for x in xs:
    rs.extend(ds[int(x)])

rs.sort(reverse=True)
print(''.join(map(str, rs)))
