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()
x=input()
a,b=[0]*10,[0]*10
for i in range(2,10):
    a[i]=x.count(str(i))
    
b[2]=a[2]+2*a[4]+3*a[8]+a[9]
b[3]=a[3]+a[4]+a[6]+2*a[9]
b[5]=a[5]+a[6]
b[7]=a[7]+a[8]+a[9]
print('7'*b[7]+'5'*b[5]+'3'*b[3]+'2'*b[2])
