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>
fprimes = [[],[],[2],[3],[2,2,3],[5],[3,5],[7],[2,2,2,7],[3,3,2,7]]
n = input()
inp = raw_input()
b = sorted([str(i) for j in map(int, list(inp)) for i in fprimes[j]])
b.reverse()
s = ''.join(b) if len(b) else '0'
print s if (int(s) > int(inp) or '0' in inp or '1' in inp) else inp