title: Maximize Volume Cuboid Given Sum Sides
signature: function maximize_volume_cuboid_given_sum_sides(s)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(s, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(s) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver(67, 11132)
      print(string.format("TEST-0...%s",result))
  
      result = driver(48, 4096)
      print(string.format("TEST-1...%s",result))
  
      result = driver(59, 7600)
      print(string.format("TEST-2...%s",result))
  
      result = driver(22, 392)
      print(string.format("TEST-3...%s",result))
  
      result = driver(14, 100)
      print(string.format("TEST-4...%s",result))
  
      result = driver(66, 10648)
      print(string.format("TEST-5...%s",result))
  
      result = driver(1, 0)
      print(string.format("TEST-6...%s",result))
  
      result = driver(75, 15625)
      print(string.format("TEST-7...%s",result))
  
      result = driver(58, 7220)
      print(string.format("TEST-8...%s",result))
  
      result = driver(78, 17576)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
source_py: def maximize_volume_cuboid_given_sum_sides(s):
      maxvalue = 0
      i = 1
      for i in range((s - 1)):
          j = 1
          for j in range(s):
              k = ((s - i) - j)
              maxvalue = max(maxvalue, ((i * j) * k))
      return maxvalue
source_cpp: int maximize_volume_cuboid_given_sum_sides(int s) {
    int maxvalue = 0;
    for ( int i = 1;
    i <= s - 2;
    i ++ ) {
      for ( int j = 1;
      j <= s - 1;
      j ++ ) {
        int k = s - i - j;
        maxvalue = max ( maxvalue, i * j * k );
      }
    }
    return maxvalue;
  }