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 math

inp = input()
mas = [int(s) for s in inp.strip().split(' ')]

n = mas[0]

dim = [
    [],
    [],
    [2],
    [3],
    [2, 2, 3],
    [5],
    [5, 3],
    [7],
    [2, 2, 2, 7],
    [7, 3, 3, 2]
]

inp = input()

res = []

for i in inp:
    q = int(i)
    res.extend(dim[q])

res.sort()
res.reverse()

print(
    ''.join(
        [str(n) for n in res]
    )
)