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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.util.*;

public class Main {

    public static void main(String args[]) {

        // 入力
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        Integer[] a = new Integer[n];
        Arrays.setAll(a, i -> Integer.parseInt(sc.next()));
        sc.close();

        // 主処理
        Set<Integer> numset = new HashSet<>();
        for (int i = 0; i < n; i++) {
            numset.add(i);
        }
        Set<Set<Integer>> set = combination(numset, 2);

        int result = 0;
        for (Set<Integer> s : set) {
            List<Integer> numlist = new ArrayList<>(s);
            int h = a[numlist.get(0)] + a[numlist.get(1)];
            int diff = Math.abs((numlist.get(0) + 1) - (numlist.get(1) + 1));
            if (h == diff) {
                result++;
            }
        }

        // 出力
        System.out.println(result);
    }

    public static <T> Set<Set<T>> combination(Set<T> src, int k) {
        if (src.size() <= k) {
            Set<Set<T>> set = new HashSet<>();
            set.add(src);
            return set;
        } else {
            return _combination(new HashSet<T>(), k, src);
        }
    }

    private static <T> Set<Set<T>> _combination(Set<T> selected, int depth, Set<T> pool) {
        if (depth == 0)
            return apply(new HashSet<>(), Operation.add, selected); // 選択済みのもののみ要素に持つ集合をかえす
        Set<Set<T>> result = new HashSet<Set<T>>();
        for (T item : pool) {
            result.addAll(_combination(apply(selected, Operation.add, item), // item を選択済みに変更
                    depth - 1, apply(pool, Operation.remove, item) // pool の中からは取り除く
            ));
        }
        return result;
    }

    private static <T> Set<T> apply(Set<T> src, Operation operation, T item) {
        Set<T> result = new HashSet<T>(src);
        if (Operation.add == operation)
            result.add(item);
        if (Operation.remove == operation)
            result.remove(item);
        return result;
    }

    private enum Operation {
        add, remove
    };
}