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())
digits = list(input())
count = []
for i in range (0, 10):
    count.append(0)

for d in digits:
    if int(d) == 2:
        count[2] += 1
    elif int(d) == 3:
        count[3] += 1
    elif int(d) == 4:
        count[2] += 2
        count[3] += 1
    elif int(d) == 5:
        count[5] += 1
    elif int(d) == 6:
        count[3] += 1
        count[5] += 1
    elif int(d) == 7:
        count[7] += 1
    elif int(d) == 8:
        count[2] += 3
        count[7] += 1
    elif int(d) == 9:
        count[2] += 1
        count[3] += 2
        count[7] += 1

for i in range (9, 1, -1):
    while count[i] != 0:
        print(i, end="")
        count[i] -= 1