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)

{-# LANGUAGE TypeApplications #-}
module Main where
import qualified Data.ByteString.Char8         as BS
import qualified Data.ByteString.Lazy.Char8    as BSL
import qualified Data.ByteString.Builder       as BSB
import           Data.Char                      ( isSpace )
import           Data.List
import qualified Data.Vector.Unboxed           as VU
import qualified Data.Vector.Unboxed.Mutable   as VUM
-- see: https://hackage.haskell.org/package/containers-0.6.2.1/docs/Data-Map-Strict.html
import           Data.Map.Strict                ( Map )
import qualified Data.Map.Strict               as Map
import           Data.IntMap                    ( IntMap )
import qualified Data.IntMap                   as IntMap

main :: IO ()
main = do
  n  <- readLn @Int
  as <- VU.unfoldr (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine
  let xs = histV $ VU.zipWith (-) (VU.enumFromN 1 n) as
  let ys = histV $ VU.zipWith (+) (VU.enumFromN 1 n) as
  print $ solve xs ys
 where
  solve xs ys = go 0 0 0   where
    go cnt i j
      | i >= VU.length xs || j >= VU.length xs = cnt
      | fst (xs VU.! i) < fst (ys VU.! j)      = go cnt (i + 1) j
      | fst (xs VU.! i) > fst (ys VU.! j)      = go cnt i (j + 1)
      | otherwise = go (cnt + snd (xs VU.! i) * snd (ys VU.! j)) (i + 1) (j + 1)

-- create histogram from list
hist :: [Int] -> [(Int, Int)]
hist xs = IntMap.toAscList $ IntMap.fromListWith (+) $ zip xs $ repeat 1

histV :: VU.Vector Int -> VU.Vector (Int, Int)
histV = VU.fromList . hist . VU.toList