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 = input()
v = [0] * 8

for digit in a:
    if int(digit) == 2:
        v[int(digit)] += 1
    elif int(digit) == 3:
        v[int(digit)] += 1
    elif int(digit) == 4:
        v[3] += 1
        v[2] += 2
    elif int(digit) == 5:
        v[int(digit)] += 1
    elif int(digit) == 6:
        v[5] += 1
        v[3] += 1
    elif int(digit) == 7:
        v[int(digit)] += 1
    elif int(digit) == 8:
        v[7] += 1
        v[2] += 3
    elif int(digit) == 9:
        v[7] += 1
        v[3] += 2
        v[2] += 1

for i in range (7, 0, -1):
    while v[i] != 0:
        print(i, end="")
        v[i] -= 1
