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>
n = int(input())
digits = list(input())

digits = filter(lambda x: x not in ('0', '1'), digits)


digit_map = {
    '1': [1],
    '2': [2],
    '3': [3],
    '4': [3, 2, 2],
    '5': [5],
    '6': [3, 5],
    '7': [7],
    '8': [7, 2, 2, 2],
    '9': [7, 3, 3, 2]
}

new_number_digits = []

for digit in digits:
    new_number_digits.extend(digit_map[digit])

new_number_digits.sort(reverse=True)
# print(new_number_digits)
print("".join(map(str, new_number_digits)))