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())
a = input()
q = [0] * 10
for d in map(int, a):
	for f in range(2, d + 1):
		if f in (4, 6, 8, 9):
			if f == 4:
				q[2] += 2
			elif f == 6:
				q[2] += 1
				q[3] += 1
			elif f == 8:
				q[2] += 3
			elif f == 9:
				q[3] += 2
		elif f not in (0, 1):
			q[f] += 1
ans = []
for i in range(9, 1, -1):
	for j in range(q[i]):
		ans.append(i)
		for k in range(i + 1):
			if k in (4, 6, 8, 9):
				if k == 4:
					q[2] -= 2
				elif k == 6:
					q[2] -= 1
					q[3] -= 1
				elif k == 8:
					q[2] -= 3
				elif k == 9:
					q[3] -= 3
			else:
				q[k] -= 1
ans.sort(reverse=True)
print(''.join(map(str, ans)))

