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():
    n = int(input())
    a = input().strip()

    remove_digits = {'0', '1'}
    prime_single_digits = {'2', '3', '5', '7'}
    single_digits2prime_factorials = {
        '4': ['2', '2', '3'],
        '6': ['3', '5'],
        '8': ['2', '2', '2', '7'],
        '9': ['2', '3', '3', '7']
    }
    res = []
    for digit in a:
        if digit in remove_digits:
            continue

        if digit in remove_digits:
            continue

        if digit in prime_single_digits:
            res.append(digit)
        else:  # is a single digit that is not prime
            res.extend(single_digits2prime_factorials[digit])
        # print('digit: {}, res: {}'.format(digit, res))

    res.sort(reverse=True)
    print(''.join(res))


if __name__ == '__main__':
    main()
