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(raw_input())
a = raw_input()

digit_count = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
commands = [{}, {}, {}, {}, {2: 2, 3: 1}, {}, {5: 1, 3: 1}, {}, {7: 1, 2: 3}, {7: 1, 3: 2, 2: 1}]
for c in a:
    cap = ord(c) - ord('0')
    digit_count[cap] += 1

s = ''
for i in xrange(9, 1, -1):
    if commands[i] == {}:
        s += str(i) * digit_count[i]
    else:
        for key in commands[i]:
            digit_count[key] += digit_count[i] * commands[i][key]

print s
