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())
s = input()
z = ''
for x in range(0,n,1):
    if s[x] is '2':
        z += '2'
    elif s[x] is '3':
        z += '3'
    elif s[x] is '4':
        z += '322'
    elif s[x] is '5':
        z += '5'
    elif s[x] is '6':
        z += '53'
    elif s[x] is '7':
        z += '7'
    elif s[x] is '8':
        z += '7222'
    elif s[x] is '9':
        z += '7332'
c = list(z)
c.sort(reverse=True)
x = ''.join(c)
print(x)