Problem Statement

The cardinality of a binary number is given as the total number of "ones" it contains. For example, the cardinality of binary 10100 (decimal 20) is 2, because there are 2 "ones". The cardinality of binary 11110 (decimal 30) is 4, because there are 4 "ones".

Given a int[] of decimal numbers arrange them in ascending order of binary cardinality and return this arranged int[]. If two numbers have the same binary cardinality, then the smaller number must come first in the arranged int[].

Definition

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

Constraints

-numbers will have between 1 and 50 elements inclusive.
-each element of numbers will be between 0 and 1000000 inclusive.

Examples

0)

 `{4}`
`Returns: { 4 }`
 There is only one element in the array, so it must be returned.
1)

 `{31,15,7,3,2}`
`Returns: { 2,  3,  7,  15,  31 }`
 We start by converting the above set of decimals into binary numbers. We get the following array: {11111, 1111, 111, 11, 10}. Now we can calculate the cardinality of each number: {5, 4, 3, 2, 1}. So 2 has the lowest binary cardinality, followed by 3, 7, 15 and finally 31.
2)

 `{10,9,8,7,6,5,4,3,2,1}`
`Returns: { 1,  2,  4,  8,  3,  5,  6,  9,  10,  7 }`
 The cardinality array is {2, 2, 1, 3, 2, 2, 1, 2, 1, 1}. Note that although 10 and 3 have the same cardinality of 2, 3 must come earlier because it is smaller in value.
3)

 `{811385,340578,980086,545001,774872,855585,13848,863414,419523,190151,784903,127461}`
```Returns:
{ 13848,  340578,  545001,  855585,  419523,  811385,  127461,  190151,  774872,  863414,  784903,  980086 }```

Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1519

Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4635&pm=1519