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>
w = int(input())
s = input()
F = [1] * 18
for i in range(1, 18):
    F[i] = i * F[i - 1]
a = 0
b = 0
c = 0
d = 0
for i in range(w):
    z = int(s[i])
    if z > 8:
        b += 2
    if z > 7:
        a += 3
    if z > 6:
        d += 1
    if z > 5:
        a += 1
        b += 1
    if z > 4:
        c += 1
    if z > 3:
        a += 2
    if z > 2:
        b += 1
    if z > 1:
        a += 1
ans = ''
a -= d * 4
b -= d * 2
c -= d
ans += '7' * d
b -= c
a -= c * 3
ans += '5' * c
a -= b
ans += '3' * b
ans += '2' * a
print(ans)

    
    
