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
n = int(input())
d = input()
# 1234 can be given as _ _ _ _ 
# where each place is single digit 
a  = {'2':'2' ,'3':'3','4':'322','5':'5','6':'53','7':'7','8':'7222','9':'7332'}
# so when we get the one digit we can change it in possible fact and and then sort
arr = []
for i in d:
    if int(i) != 1 and int(i) != 0:
        for j in a[i]:
            arr.append(int(j))
arr.sort(reverse = True)
result = ''
for i in arr:
    result += str(i)
print(result)











