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>
freq = [0 for i in range(10)]
factor = [[], [1], [2], [3], [2, 2], [5], [2, 3], [7], [2, 2, 2], [3, 3]]
n = int(input())
val = list(input())
for i in val:
    v = int(i)
    for j in range(1, v+1):
        for k in factor[j]:
            freq[k] += 1
for i in range(9, 1, -1):
    for j in range(1, i):
        for k in factor[j]:
            freq[k] -= freq[i]
    print(str(i) * freq[i], end="")
print()