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())
rdl = input()
toAnswer =[[0],[0],[2],[3],[3,2,2],[5],[5,3],[7],[7,2,2,2],[7,3,3,2]]
answer = []
for i in range(len(rdl)):
    answer.append(toAnswer[int(rdl[i])])
for i in answer:
    i.sort()
    i = i[::-1]
answer.sort()
answer = answer[::-1]
newanwer = []
for i in answer:
    for j in i:
        newanwer.append(j)
newanwer.sort()
while newanwer[0] == 0:
    newanwer = newanwer[1:]
newanwer = newanwer[::-1]
for i in newanwer:
        print(i, end='')
