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>
from collections import Counter

input()
s = input()

components = (
    Counter(),
    Counter(),
    Counter((2, )),
    Counter((2, 3)),
    Counter( { 2: 3, 3: 1 } ),
    Counter( { 2: 3, 3: 1, 5: 1 } ),
    Counter( { 2: 4, 3: 2, 5: 1 } ),
    Counter( { 2: 4, 3: 2, 5: 1, 7: 1 } ),
    Counter( { 2: 7, 3: 2, 5: 1, 7: 1 } ),
    Counter( { 2: 7, 3: 4, 5: 1, 7: 1 } ),
)

cn = Counter()
for c in s:
    cn += components[ord(c) - 48]
for n in (7, 5, 3, 2):
    for i in range(cn[n]):
        cn -= components[n]
        print(n, end="")
print()
