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>
Permutacion = { '0':[], '1':[], '2':[2], '3':[ 3 ] , '4' :[ 3,2 , 2 ] , '5':[ 5 ] , '6':[ 5 , 3 ] , '7':[ 7 ] , '8':[7 , 2 , 2 , 2] , '9':[ 7 , 3, 3 , 2 ] }
Limite = input()
Cadena = raw_input()
Rpta = []
indice = 0
while  Limite != indice  :
    Rpta = Rpta + Permutacion[ Cadena[ indice ] ]
    indice += 1

Rpta.sort()
Rpta.reverse()
print ''.join( str(x) for x in Rpta )