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 *
n = int(input())
a = []
s = int(input())
s = str(s)
for i in s :
    a.append(int(i))
m = len(a)
f = []
ff = 1
for i in a :
    f.append(factorial(i))
    ff *= f[len(f) - 1]
vf = [factorial(i) for i in range(0, 10)]
ans = []
d = [7, 5, 3, 2]
for k in d :
    dl = int(vf[k])
    while (ff % dl) == 0 :
        ff = ff // dl
        ans.append(k)
for i in ans :
    print(i, end = '')

