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>
P = [0] * 16;
n = int(input())
s = input()

for i in s :
    if (i == '2') :
        P[2] += 1
    if (i == '3') :
        P[3] += 1
    if (i == '4') :
        P[3] += 1
        P[2] += 2
    if (i == '5') :
        P[5] += 1
    if (i == '6') :
        P[5] += 1
        P[3] += 1
    if (i == '7') :
        P[7] += 1
    if (i == '8') :
        P[2] += 3
        P[7] += 1
    if (i == '9') :
        P[7] += 1
        P[3] += 2
        P[2] += 1
for i in range(9, 0, -1) :
    for j in range(P[i]) :
        print(i, end = '')