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>
l = int(input())
number = list(input())
i = 0
length = len(number)
while(i < length):
    # print(''.join(number))
    if number[i] == '0' or number[i] == '1':
        number[i:i+1] = []
        i -= 1
    elif number[i] == '4':
        number[i:i+1] = ['2', '2', '3']
    elif number[i] == '6':
        number[i:i+1] = ['5', '3']
    elif number[i] == '8':
        number[i:i+1] = ['7', '2', '2', '2']
    elif number[i] == '9':
        number[i:i+1] = ['7', '3', '3', '2']
    i += 1
    length = len(number)
    # print(''.join(number))
number.sort(reverse=True)
print(''.join(number))
