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())
    num = int(input())
    f = [1] * 10
    ans = []
    lookup = {2: ['2'], 3: ['3'], 4: ['2', '2', '3'],
              5: ['5'], 6: ['3', '5'],
              7: ['7'], 8: ['2', '2', '2', '7'],
              9: ['2', '3', '3', '7']}
    while num != 0:
        if num % 10 > 1:
            ans += lookup[num % 10]
        num = num // 10

    # ans.reverse()
    ans.sort(reverse=True)
    print(''.join(ans))


if __name__ == "__main__":
    main()
