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())
d = map(int, input())
fac = [(0, 0, 0, 0), (0, 0, 0, 0), (1, 0, 0, 0),
       (1, 1, 0, 0), (3, 1, 0, 0), (3, 1, 1, 0),
       (4, 2, 1, 0), (4, 2, 1, 1), (7, 2, 1, 1),
       (7, 4, 1, 1)]
count = [0, 0, 0, 0]
for el in d:
    for i in range(4):
        count[i] += fac[el][i]
ans = []
for i, dig in reversed([(0, 2), (1, 3), (2, 5), (3, 7)]):
    while count[i] > 0:
        ans.append(dig)
        for j in range(4):
            count[j] -= fac[dig][j]
print(''.join(map(str, ans)))
