### Problem Statement

The digits 4 and 7 are lucky digits, and all other digits are unlucky. A second level lucky number is a positive integer whose decimal representation contains either all 4's or all 7's. John and Brus have a set of integers, and they would like to find the subset whose sum is a second level lucky number.

You are given int[] numbers, the set of integers that John and Brus have. Return a int[] containing the subset whose sum is a second level lucky number. The return value must be sorted in ascending order. If there are multiple possible return values, return the one with the largest sum. If there is a tie, return the one that comes earliest lexicographically. A int[] a1 comes before a int[] a2 lexicographically if a1 contains a smaller number at the first index where they differ. If there are no possible subsets, return an empty int[] instead.

### Definition

 Class: TheLuckyNumbersLevelTwo Method: find Parameters: int[] Returns: int[] Method signature: int[] find(int[] numbers) (be sure your method is public)

### Constraints

-numbers will contain between 1 and 34 elements, inclusive.
-Each element of numbers will be between 1 and 1,000,000,000, inclusive.
-All elements in numbers will be distinct.

### Examples

0)

 `{1, 2, 3, 4}`
`Returns: {1, 2, 4 }`
 Here it's possible to get two second level lucky numbers - 4 and 7. There are two subsets with a sum of 7 - {3, 4} and {1, 2, 4}. We will choose the last one because it is lexicographically smaller.
1)

 `{12, 43, 29}`
`Returns: { }`
 There are no subsets whose sum is a second level lucky number.
2)

 `{4, 7}`
`Returns: {7 }`
3)

 `{41, 2, 28, 44, 7, 42, 21}`
`Returns: {7, 28, 42 }`
4)

 `{15, 10, 28, 3, 13, 27, 7}`
`Returns: {7, 15, 27, 28 }`
5)

 `{18, 45, 6}`
`Returns: { }`
6)

 `{34, 20, 26, 28, 33, 23, 44, 40, 25, 10, 36, 14, 7, 29, 21, 27, 17, 13, 19, 24, 32, 41, 31}`
`Returns: {7, 10, 13, 14, 17, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 44 }`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10833

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14247&pm=10833

Vasyl[alphacom]

#### Testers:

PabloGilberto , ivan_metelsky , StevieT

#### Problem categories:

Recursion, Sorting