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>
n    = int(input())
a    = [int(i) for i in input()]
u    = [[] for i in range(10)]
u[2] = [2]
u[3] = [3]
u[4] = [2, 2, 3]
u[5] = [5]
u[6] = [3, 5]
u[7] = [7]
u[8] = [2, 2, 2, 7]
u[9] = [2, 3, 3, 7]
c    = []

for i in a:
    if i > 1:
        c += u[i]
c.sort()
c = list(map(str,reversed(c)))
print(''.join(c))