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())
num = str(input())
primes = {2: 0, 3: 0, 5: 0, 7: 0}
for i in range(n):
    k = int(num[i])
    if (k <= 1):
        continue
    primes[2] += 1
    if (k >= 3):
        primes[3] += 1
        if (k >= 4):
            primes[2] += 2
            if (k >= 5):
                primes[5] += 1
                if (k >= 6):
                    primes[2] += 1
                    primes[3] += 1
                    if (k >= 7):
                        primes[7] += 1
                        if (k >= 8):
                            primes[2] += 3
                            if (k == 9):
                                primes[3] += 2
for i in range(primes[7]):
    print(7, end='')
    primes[2] -= 4
    primes[3] -= 2
    primes[5] -= 1
for i in range(primes[5]):
    print(5, end='')
    primes[2] -= 3
    primes[3] -= 1
for i in range(primes[3]):
    print(3, end='')
    primes[2] -= 1
for i in range(primes[2]):
    print(2, end='')
print("\n")