Problem Statement  
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You are given a list of integer intervals, ranges, where each interval is specified by a String of the form "<low><high>" (quotes for clarity). Here "<low>" and "<high>" represent nonnegative integers (sequences of characters between '0' and '9' inclusive with no leading zeros) which are separated by a single hyphen ''. Your task is to find the largest integer that is in at least one of the intervals and is a perfect cube. Return this integer in a String with no extra leading zeros and only the digits '0''9'. In other words, find the largest integer in the intervals that is equal to n^{3} for some integer n. If there is no perfect cube in the intervals, return the empty string, "" (quotes for clarity). For example {"11000000000001"} would return "1000000000000" which is 10000^{3}.  
Definition  
 
Notes  
  C++ users: the 64 bit integer type is long long.  
Constraints  
  range will have between 1 and 50 elements inclusive.  
  Each element of range will contain between 3 and 31 characters inclusive.  
  Each element of range will be of the form "<low><high>" where <low> and <high> are separated by exactly one hyphen, ''.  
  Each character of <low> and <high> will be a digit between '0' and '9' inclusive.  
  <low> and <high> will contain no leading zeros.  
  <low> and <high> will be between 0 and 1000000000000000000 (1e15) inclusive.  
  <low> will be less than or equal to <high>  
Examples  
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