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>
slt = [0]*10
slt[2]=[2]
slt[3]=[3]
slt[4]=[3,2,2]
slt[5]=[5]
slt[6]=[5,3]
slt[7]=[7]
slt[8]=[7,2,2,2]
slt[9]=[7,3,3,2]
n = input()
a = raw_input()
ans=[]
for i in a:
    if(i=='1' or i=='0'):
        continue
    ans+=slt[ord(i)-48]
ans.sort()
ans1=""
for i in ans:
    ans1+=str(i)
print ans1[-1::-1]
