title: Count Possible Groups Size 2 3 Sum Multiple 3
signature: countPossibleGroupsSize23SumMultiple3 :: [Integer] -> Integer -> Double
  countPossibleGroupsSize23SumMultiple3 arr n = 
test_code: import Text.Printf
  import Control.Exception (catch, SomeException)
  import Data.Typeable
  import qualified Data.List as List
  import qualified Data.Map as Map
  import qualified Data.Set as Set
  
  -- SOLUTION CODE
  -- ============================================
  
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  validateSolution :: Double -> Double -> Bool
  validateSolution actual expected = do
      (abs (actual-expected)) < 1e-06
  
  driver :: [Integer] -> Integer -> Double -> String
  driver arr n expected = do
      if (validateSolution (PLACEHOLDER_FN_NAME arr n) expected)
          then "PASSED"
      else "FAILED"
  
  main = do
      printf "TEST-0...%s\n" (driver ([1, 3, 6, 12, 18, 31, 36, 43, 47, 59, 64, 64, 69, 69, 94, 98, 98]) (12) (90.0) )
  
      printf "TEST-1...%s\n" (driver ([94, 46, 64, 18, 70, 22, -98, 52, -26, 34, -22, 22, 40, 66, -72, -66, 86, 84, 12, -38, 28, -60, -10, -30, -78, 76, 62, 74, 24, -64, 0, 92, -20, -66, -52]) (23) (655.0) )
  
      printf "TEST-2...%s\n" (driver ([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]) (29) (3276.0) )
  
      printf "TEST-3...%s\n" (driver ([68, 96, 74, 38, 70, 70]) (5) (7.0) )
  
      printf "TEST-4...%s\n" (driver ([-88, -74, -70, -64, -64, -64, -58, -52, -18, -10, -6, 4, 4, 28, 44, 48, 52, 54, 64, 72, 76, 94]) (18) (329.0) )
  
      printf "TEST-5...%s\n" (driver ([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1]) (36) (2310.0) )
  
      printf "TEST-6...%s\n" (driver ([9, 12, 14, 21, 27, 28, 45, 50, 54, 57, 58, 62, 78, 82, 91, 92, 95]) (9) (49.0) )
  
      printf "TEST-7...%s\n" (driver ([16, -46, -32, -36, -84, -14, -18, 16, 54, 90, -4]) (8) (24.0) )
  
      printf "TEST-8...%s\n" (driver ([0, 0, 1, 1]) (3) (1.0) )
  
      printf "TEST-9...%s\n" (driver ([53, 32, 54, 84, 79, 37, 44, 30, 92, 53, 89, 95]) (8) (29.0) )
  
source_py: def count_possible_groups_size_2_3_sum_multiple_3(arr, n):
      c = [0, 0, 0]
      res = 0
      for i in range(0, n):
          c[(arr[i] % 3)] += 1
      res += ((c[0] * (c[0] - 1)) >> 1)
      res += (c[1] * c[2])
      res += (((c[0] * (c[0] - 1)) * (c[0] - 2)) / 6)
      res += (((c[1] * (c[1] - 1)) * (c[1] - 2)) / 6)
      res += (((c[2] * (c[2] - 1)) * (c[2] - 2)) / 6)
      res += ((c[0] * c[1]) * c[2])
      return res
source_cpp: int count_possible_groups_size_2_3_sum_multiple_3(vector<int> arr, int n) {
    int c [ 3 ] = {
      0 },
      i;
      int res = 0;
      for ( i = 0;
      i < n;
      i ++ ) c [ arr [ i ] % 3 ] ++;
      res += ( ( c [ 0 ] * ( c [ 0 ] - 1 ) ) >> 1 );
      res += c [ 1 ] * c [ 2 ];
      res += ( c [ 0 ] * ( c [ 0 ] - 1 ) * ( c [ 0 ] - 2 ) ) / 6;
      res += ( c [ 1 ] * ( c [ 1 ] - 1 ) * ( c [ 1 ] - 2 ) ) / 6;
      res += ( ( c [ 2 ] * ( c [ 2 ] - 1 ) * ( c [ 2 ] - 2 ) ) / 6 );
      res += c [ 0 ] * c [ 1 ] * c [ 2 ];
      return res;
    }