Problem:
Score : 200 points

Problem Statement

Let us define the FizzBuzz sequence a_1,a_2,... as follows:

If both 3 and 5 divides i, a_i=\mbox{FizzBuzz}.

If the above does not hold but 3 divides i, a_i=\mbox{Fizz}.

If none of the above holds but 5 divides i, a_i=\mbox{Buzz}.

If none of the above holds, a_i=i.

Find the sum of all numbers among the first N terms of the FizzBuzz sequence.

Constraints

1 \leq N \leq 10^6

Input

Input is given from Standard Input in the following format:

N

Output

Print the sum of all numbers among the first N terms of the FizzBuzz sequence.

Sample Input 1

15

Sample Output 1

60

The first 15 terms of the FizzBuzz sequence are:

1,2,\mbox{Fizz},4,\mbox{Buzz},\mbox{Fizz},7,8,\mbox{Fizz},\mbox{Buzz},11,\mbox{Fizz},13,14,\mbox{FizzBuzz}

Among them, numbers are 1,2,4,7,8,11,13,14, and the sum of them is 60.

Sample Input 2

1000000

Sample Output 2

266666333332

Watch out for overflow.

Solution in Haskell (GHC 8.8.3) (judge verdict: Accepted)

-- {-# LANGUAGE BangPatterns #-}
-- {-# LANGUAGE ScopedTypeVariables #-}
-- {-# LANGUAGE FlexibleContexts #-}
-- {-# LANGUAGE ViewPatterns #-}
-- {-# LANGUAGE OverloadedStrings #-}

import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.Vector.Algorithms.Merge as VAM
import qualified Data.Heap as HP
import qualified Data.ByteString.Char8 as BC
import qualified Data.Map as MP
import qualified Data.Set as ST
import qualified Data.Sequence as SQ
import Data.Array
import Data.Array.Unboxed
import Data.Array.ST
import Data.Array.IO
import Data.Maybe
import Data.Ratio
import Data.Char
import Data.Bits
import Data.List
import Data.Tuple
import Data.Functor
import Data.IORef
import Data.STRef
import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Debug.Trace

--------------------------------------------------------------------------
solve i n
    | i > n = 0
    | mod i 3 == 0 = solve (i+1) n
    | mod i 5 == 0 = solve (i+1) n
    | otherwise = i + solve (i+1) n

main = do
    n <- int
    print $ solve 1 n
--------------------------------------------------------------------------
    
-- Input Util
int :: IO Int
int = readLn 

double :: IO Double
double = readLn 

str :: IO String
str = getLine

strBC :: IO BC.ByteString
strBC = BC.getLine

sLineToIntL :: IO [Int]
sLineToIntL = getLine >>= return . map read . words

sLineToDoubleL :: IO [Double]
sLineToDoubleL = getLine >>= return . map read . words

sLineToIntV :: Int -> IO (VU.Vector Int)
sLineToIntV n = BC.getLine >>= return . VU.unfoldrN n (BC.readInt . BC.dropWhile isSpace)

sLineToDoubleV :: Int -> IO (VU.Vector Double)
sLineToDoubleV n = BC.getLine >>= return . VU.fromList . map (read . BC.unpack) . BC.words

mLinesToIntL :: Int -> IO [Int]
mLinesToIntL n = replicateM n readLn

mLinesToDoubleL :: Int -> IO [Double]
mLinesToDoubleL n = replicateM n readLn

mLinesToIntV :: Int -> IO (VU.Vector Int)
mLinesToIntV n = VU.replicateM n readLn

mLinesToDoubleV :: Int -> IO (VU.Vector Double)
mLinesToDoubleV n = VU.replicateM n (BC.getLine >>= return . read . BC.unpack)

mLinesToTupleL :: Int -> IO [(Int, Int)]
mLinesToTupleL n = replicateM n (getLine >>= return . (\[a,b] -> (a,b)) . map read . words)

mLinesToTupleV :: Int -> IO (VU.Vector (Int, Int))
mLinesToTupleV n = VU.replicateM n $ do
    bs <- strBC
    let
        Just (a, bs') = BC.readInt $ BC.dropWhile isSpace bs
        Just (b, _) = BC.readInt $ BC.dropWhile isSpace bs'
    return (a,b)
    
mLinesToTripleV :: Int -> IO (VU.Vector (Int, Int, Int))
mLinesToTripleV n = VU.replicateM n $ do
    bs <- strBC
    let
        Just (a, bs') = BC.readInt $ BC.dropWhile isSpace bs
        Just (b, bs'') = BC.readInt $ BC.dropWhile isSpace bs'
        Just (c, _) = BC.readInt $ BC.dropWhile isSpace bs''
    return (a,b,c)

-- others
strToChr :: String -> Char
strToChr [x] = x

chrToStr :: Char -> String
chrToStr x = [x]

m1 :: Int -> Int
m1 x = subtract 1 x

toDouble :: Int -> Double
toDouble x = fromIntegral x

toInt :: Double -> Int
toInt x = floor x