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 Rust (1.42.0) (judge verdict: Accepted)

extern crate core;

use std::collections::HashMap;
use std::io::{self, Read};

#[macro_export]
macro_rules! input {
  ($s:expr=>$($t:tt)*) => {
    let mut lines=$s.split("\n");
    $(
        line_parse!(lines,$t);
    )*
  };
}

macro_rules! line_parse {
  ($lines:expr,($($name:ident:$t:tt)*)) => {
    let mut line=$lines.next().unwrap().split_whitespace();
    $(value_def!(line,$name,$t);)*
  };

  //複数行
  ($lines:expr,{$n:expr;$name:ident:$t:tt}) => {
    values_def!($lines,$n,$name,$t);
  };
}

macro_rules! value_def {
    ($line:expr, $name:ident, $t:tt) => {
        let $name = value!($line, $t);
    };
}

macro_rules! values_def {
    ($lines:expr, $n:expr, $name:ident, $t:tt) => {
        let $name = {
            let mut vec = Vec::new();
            for i in 0..$n {
                let mut next = $lines.next().unwrap().split_whitespace();
                vec.push(value!(next, $t));
            }
            vec
        };
    };
}

macro_rules! value {
  //配列
  ($line:expr,[$t:tt]) => {
    $line.map(|x|{
      let mut iter=::std::iter::once(x);
      value!(iter,$t)
    }).collect::<Vec<_>>()
  };
  //タプル
  ($line:expr,($($t:tt),*)) => {
    ($(value!($line,$t),)*)
  };
  //文字列
  ($line:expr,#) => {
    $line.next().unwrap()
  };
  //インデックス(-1)
  ($line:expr,@) => {
    $line.next().unwrap().parse::<usize>().unwrap()-1
  };
  //単一値
  ($line:expr,$t:ty) => {
    $line.next().unwrap().parse::<$t>().unwrap()
  };
}

fn main() {
    let mut input = String::new();
    io::stdin().read_to_string(&mut input).unwrap();
    let output = solve(input.trim().to_string());
    println!("{}", output);
}

fn solve(input: String) -> String {
    input!(input=>(n:usize)(list:[i64]));
    /*
    2 3 3 1 3 1

    1 2 (2, -1) (3, 0) (4, 1)
    2 3 (3, -2) (4, -1) (5, 0)
    3 3
    4 1
    5 3
    6 1

    (n_x+a_x)=(n_y-h_y)となるx<yな値の個数
    */
    let list = list
        .into_iter()
        .enumerate()
        .map(|(i, x)| (i as i64 + 1, x))
        .collect::<Vec<_>>();

    let diff_to_n =
        list.iter()
            .map(|(n, a)| (n - a, n))
            .fold(HashMap::new(), |mut acc, (key, v)| {
                acc.entry(key).or_insert(Vec::new()).push(v);
                acc
            });

    list.iter()
        .map(|(n, a)| {
            diff_to_n
                .get(&(n + a))
                .map(|xs| larger_count(xs, &n))
                .unwrap_or(0)
        })
        .sum::<usize>()
        .to_string()
}

macro_rules! tests {
    ($($name:ident: $input:expr=>$output:expr,)*) => {
        mod tests {
            $(
                #[test]
                fn $name() {
                    assert_eq!($output.trim().to_string(),super::solve($input.trim().to_string()));
                }
            )*
        }
    }
}
tests! {
    test1: "6\n2 3 3 1 3 1\n" => "3\n",
    test2: "6\n5 2 4 2 8 8\n" => "0\n",
    test3: "32\n3 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\n" => "22\n",
}

//より大きい
pub fn larger_count<T: Ord>(vec: &Vec<T>, val: &T) -> usize {
    vec.len() - upper_bound(vec, 0, vec.len(), val)
}

//vecは昇順ソート済み
//以上
pub fn lower_bound<T: Ord>(vec: &Vec<T>, mut first: usize, mut last: usize, val: &T) -> usize {
    let mut mid;
    while last - first > 1 {
        mid = (first + last) / 2;
        if &vec[mid] < val {
            first = mid;
        } else {
            last = mid;
        }
    }
    if &vec[first] < val {
        last
    } else {
        first
    }
}

//より大きい
pub fn upper_bound<T: Ord>(vec: &Vec<T>, mut first: usize, mut last: usize, val: &T) -> usize {
    let mut mid;
    while last - first > 1 {
        mid = (first + last) / 2;
        if &vec[mid] <= val {
            first = mid;
        } else {
            last = mid;
        }
    }
    if &vec[first] <= val {
        last
    } else {
        first
    }
}