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>
#!/usr/bin/python3 -SOO
import math,string,itertools,fractions,re,array,bisect
from heapq import *
from collections import *

n = int(input())
fac = [1]
a = 1
for i in range(1,11):
    fac.append(i*fac[-1])
l = []
for x in input().strip():
    if x=='0' or x=='1': continue
    if x=='4':
        l += ['3','2','2']
    elif x=='6':
        l += ['5','3']
    elif x=='8':
        l += ['7','2','2','2']
    elif x=='9':
        l += ['7','3','3','2']
    else:
        l += [x]
print(''.join(sorted(l,reverse=True)))
