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>
from math import factorial, log2
from operator import mul
from functools import reduce

def drazil():
  input()
  n = input()
  count = [0 for _ in range(10)]
  for c in n:
    c = int(c)
    while True:
      if c in [2,3,5,7]:
        count[c] += 1
        break
      elif c in [4,8]:
        count[2] += int(log2(c))
      elif c in [0,1]:
        break
      elif c == 6:
        count[3] += 1
      elif c == 9:
        count[3] += 2
        count[2] -= 2
      c -= 1
  s = ''
  for i, n in enumerate(count):
    s = str(i)*n + s
  print(s)

if __name__ == '__main__':
  drazil()
