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())
 
a = input()
 
nums = []
 
for i in range(n):
    c = int(a[i])
    if c == 4:
        nums.extend([3,2,2])
    elif c == 6:
        nums.extend([3,5])
    elif c == 8:
        nums.extend([2,2,2,7])
    elif c == 9:
        nums.extend([7,3,3,2])
    elif c > 1:
        nums.append(c)
 
print(''.join([str(x) for x in sorted(nums, reverse=True)]))