Problem:
Score: 500 points

Problem Statement

You are the top spy of AtCoder Kingdom. To prevent the stolen secret from being handed to AlDebaran Kingdom, you have sneaked into the party where the transaction happens.

There are N attendees in the party, and they are given attendee numbers from 1 through N. The height of Attendee i is A_i.

According to an examination beforehand, you know that a pair of attendees satisfying the condition below will make the transaction.

The absolute difference of their attendee numbers is equal to the sum of their heights.

There are \frac{N(N-1)}{2} ways to choose two from the N attendees and make a pair. Among them, how many satisfy the condition above?

P.S.: We cannot let you know the secret.

Constraints

All values in input are integers.

2 \leq N \leq 2 \times 10^5

1 \leq A_i \leq 10^9\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the number of pairs satisfying the condition.

Sample Input 1

6
2 3 3 1 3 1

Sample Output 1

3

A_1 + A_4 = 3, so the pair of Attendee 1 and 4 satisfy the condition.

A_2 + A_6 = 4, so the pair of Attendee 2 and 6 satisfy the condition.

A_4 + A_6 = 2, so the pair of Attendee 4 and 6 satisfy the condition.

No other pair satisfies the condition, so you should print 3.

Sample Input 2

6
5 2 4 2 8 8

Sample Output 2

0

No pair satisfies the condition, so you should print 0.

Sample Input 3

32
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5

Sample Output 3

22

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

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE BangPatterns, BinaryLiterals, CPP, DerivingStrategies      #-}
{-# LANGUAGE DerivingVia, FlexibleContexts, FlexibleInstances           #-}
{-# LANGUAGE GeneralizedNewtypeDeriving, ImplicitParams, KindSignatures #-}
{-# LANGUAGE LambdaCase, MagicHash, MultiParamTypeClasses, MultiWayIf   #-}
{-# LANGUAGE NumericUnderscores, OverloadedStrings, PatternSynonyms     #-}
{-# LANGUAGE RankNTypes, RecordWildCards, ScopedTypeVariables           #-}
{-# LANGUAGE StandaloneDeriving, TupleSections, TypeApplications        #-}
{-# LANGUAGE TypeFamilies, TypeInType, UnboxedTuples, ViewPatterns      #-}

import           Control.Applicative
import           Control.Exception
import           Control.Monad
import           Control.Monad.Primitive
import           Control.Monad.ST
import           Control.Monad.State.Strict
import           Data.Bool
import qualified Data.ByteString               as B
import qualified Data.ByteString.Builder       as B
import qualified Data.ByteString.Char8         as C
import qualified Data.ByteString.Internal      as B
import qualified Data.ByteString.Unsafe        as B
import           Data.Char
import qualified Data.Foldable                 as F
import           Data.Function
import           Data.Functor.Identity
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntSet                   as IS
import qualified Data.List                     as L
import qualified Data.Map.Strict               as M
import           Data.Monoid
import           Data.Ord
import           Data.Primitive
import           Data.Ratio
import           Data.Semigroup
import qualified Data.Set                      as S
import           Data.Tuple
import qualified Data.Vector                   as V
import qualified Data.Vector.Generic           as G
import qualified Data.Vector.Generic.Mutable   as GM
import qualified Data.Vector.Mutable           as VM
import qualified Data.Vector.Primitive         as P
import qualified Data.Vector.Primitive.Mutable as PM
import qualified Data.Vector.Unboxed           as U
import qualified Data.Vector.Unboxed.Mutable   as UM
import           Debug.Trace
import           Foreign                       hiding (void)
import           GHC.Exts
import qualified System.IO                     as IO
import           Unsafe.Coerce

main :: IO ()
main = do
    n <- readLn :: IO Int
    xs <- U.unfoldrN n (runParser int) <$> C.getLine
    print $ solve n xs

solve :: Int -> U.Vector Int -> Int
solve n xs = U.sum $ U.zipWith (*) freqL freqR
  where
    ls = U.filter (<n)  $ U.imap (+) xs
    rs = U.filter (>=0) $ U.imap (-) xs
    freqL = U.accumulate (+) (U.replicate (n+1) 0)
        $ U.map ((,1)) ls
    freqR = U.accumulate (+) (U.replicate (n+1) 0)
        $ U.map ((,1)) rs
    f i x
        | i - x >= 0, xs U.! (i - x) == i - x = 1
        | otherwise = 0



-------------------------------------------------------------------------------
-- Utils
-------------------------------------------------------------------------------
rep :: Monad m => Int -> (Int -> m ()) -> m ()
rep !n = U.forM_ $ U.generate n id
{-# INLINE rep #-}
rev :: Monad m => Int -> (Int -> m ()) -> m ()
rev !n = U.forM_ $ U.iterateN n (subtract 1) (n - 1)
{-# INLINE rev #-}
infixl 8 `shiftRL`, `unsafeShiftRL`
shiftRL = unsafeShiftRL
{-# INLINE shiftRL #-}
unsafeShiftRL (I# x#) (I# i#) = I# (uncheckedIShiftRL# x# i#)
{-# INLINE unsafeShiftRL #-}
type Parser a = StateT C.ByteString Maybe a
runParser :: Parser a -> C.ByteString -> Maybe (a, C.ByteString)
runParser = runStateT
{-# INLINE runParser #-}
int :: Parser Int
int = coerce $ C.readInt . C.dropWhile isSpace
{-# INLINE int #-}
int1 :: Parser Int
int1 = fmap (subtract 1) int
{-# INLINE int1 #-}
char :: Parser Char
char = coerce C.uncons
{-# INLINE char #-}
byte :: Parser Word8
byte = coerce B.uncons
{-# INLINE byte #-}