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(raw_input())
A = map(int, list(raw_input()))
factors = [0]*10
mapping = {0:[], 1:[], 2:[2], 3:[3], 4:[2,2], 5:[5], 6:[2,3], 7:[7], 8:[2,2,2], 9:[3,3]}

# For every digit of A
for n in range(N):
    # Iterate over range (0, digit)
    for i in range(A[n]+1):
        # Add one for each factor
        for j in mapping[i]:
            factors[j] += 1

result = []

for n in range(9,1,-1):
    # Must add the factorial of this to our result
    count = factors[n]
    if count != 0:
        result.extend([n]*count)

        # Iterate over range (0,n), removing the appropriate number of factors
        for i in range(n+1):
            # Remove factors[n] for each factor
            for j in mapping[i]:
                factors[j] -= count

print "".join(map(str,result))