#P1520D. Same Differences
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ID: 5902
Type: RemoteJudge
2000ms
256MiB
Tried: 0
Accepted: 0
Difficulty: (None)
Uploaded By:
Hydro
Tags> Same Differences
No submission language available for this problem.
Description
You are given an array $a$ of $n$ integers. Count the number of pairs of indices $(i, j)$ such that $i < j$ and $a_j - a_i = j - i$.
The first line contains one integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case output the number of pairs of indices $(i, j)$ such that $i < j$ and $a_j - a_i = j - i$.
Input
The first line contains one integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.
The first line of each test case contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$).
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$) — array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case output the number of pairs of indices $(i, j)$ such that $i < j$ and $a_j - a_i = j - i$.
Samples
4
6
3 5 1 4 6 6
3
1 2 3
4
1 3 3 4
6
1 6 3 4 5 6
1
3
3
10