Smallest Number With Given Digit Product

Given a positive integer n, return a string representing the smallest positive integer such that the product of its digits is equal to n, or "-1" if no such number exists.

 

Example 1:

Input: n = 105
Output: "357"
Explanation: 3 * 5 * 7 = 105. It can be shown that 357 is the smallest number with a product of digits equal to 105. So the answer would be "105".

Example 2:

Input: n = 7
Output: "7"
Explanation: Since 7 has only one digit, its product of digits would be 7. We will show that 7 is the smallest number with a product of digits equal to 7. Since the product of numbers 1 to 6 is 1 to 6 respectively, so "7" would be the answer.

Example 3:

Input: n = 44
Output: "-1"
Explanation: It can be shown that there is no number such that its product of digits is equal to 44. So the answer would be "-1".

 

Constraints:

• 1 <= n <= 1018