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())
a = int(input())
a = str(a)
factorials = {'0': 1, '1': 1, '2': 2, '3': 6, '4': 24, '5': 120,
              '6': 720, '7': 5040, '8': 40320, '9': 362880}

f = 1
for i in a:
    f *= factorials[i]

digits = {'7': 0, '5': 0, '3': 0, '2': 0}
for digit in digits:
    while f % factorials[digit] == 0:
        f //= factorials[digit]
        digits[digit] += 1
for digit, number in digits.items():
    for i in range(number):
        print(digit, end='')
