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 = input()
ss = str(input())
a = []

for ch in ss:
    if ch == '2' or ch == '3' or ch == '5' or ch == '7':
        a.append(ch)
    elif ch == '4':
        a.extend(['3','2','2'])
    elif ch == '8':
        a.extend(['7', '2', '2', '2'])
    elif ch == '6':
        a.extend(['5', '3'])
    elif ch == '9':
        a.extend(['7', '3', '3', '2'])
a.sort()
a.reverse()
d = ''.join(a)
print(d)