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>
def main():
    length = int(input())
    n = [int(digit) for digit in input() if digit != '0' and digit != '1']
    factorial = {2: [2], 3: [3], 4: [2, 2, 3], 5: [5], 6: [5, 3], 7: [7], 8: [7, 2, 2, 2], 9: [7, 3, 3, 2]}
    result = []
    for number in n:
        result += factorial[number]
    result = sorted(result, reverse=True)
    result = map(str, result)
    print(''.join(result))


main()
