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>
answer = {
    "7": [7],
    "8": [7, 2, 2, 2],
    "9": [7, 3, 3, 2],
    "6": [5, 3],
    "5": [5],
    "4": [3, 2, 2],
    "3": [3],
    "2": [2],
    "1": [],
    "0": []
}
def main():
    _ = input()
    inp = str(input())
    ans = []
    for i in inp:
        ans += answer[i]

    ans.sort()
    for i in reversed(ans):
        print(i, end="")
main()
