Problem:
Score : 200 points

Problem Statement

An integer N is a multiple of 9 if and only if the sum of the digits in the decimal representation of N is a multiple of 9.

Determine whether N is a multiple of 9.

Constraints

0 \leq N < 10^{200000}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

If N is a multiple of 9, print Yes; otherwise, print No.

Sample Input 1

123456789

Sample Output 1

Yes

The sum of these digits is 1+2+3+4+5+6+7+8+9=45, which is a multiple of 9, so 123456789 is a multiple of 9.

Sample Input 2

0

Sample Output 2

Yes

Sample Input 3

31415926535897932384626433832795028841971693993751058209749445923078164062862089986280

Sample Output 3

No

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

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE BinaryLiterals #-}
{-# LANGUAGE MultiWayIf #-}
{-# LANGUAGE NumDecimals #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}

import Control.Applicative
import Control.Arrow
import Control.Monad
import Control.Monad.ST

import Data.Char
import Data.List
import Data.Maybe

import qualified Data.ByteString.Char8 as B

import Data.Array.ST.Safe
import Data.STRef

import Debug.Trace
import Text.Printf

readInt = readLn :: IO Int
readInteger = readLn :: IO Integer
readInts = map ( fst . fromJust . B.readInt ) . B.words <$> B.getLine
readIntegers = map ( fst . fromJust . B.readInteger ) . B.words <$> B.getLine

which a b f = if f then a else b
mp [ a, b ] = ( a, b )

modifyArray a i f = writeArray a i =<< f <$> readArray a i

printList [a] = print a
printList (a:as) = putStr ( show a ) >> putChar ' ' >> printList as

main = readInteger >>= putStrLn . which "Yes" "No" . ( == 0 ) . ( `mod` 9 )