Managing Difficulties

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Time limit2sMemory limit512 MB

Summary

Count triples of increasing indices i < j < k where a[j] - a[i] equals a[k] - a[j], so a[i] + a[k] = 2*a[j].

Level: Medium5 of 10
Topics: Hash map, Combinatorics, Array, Brute force
Solved: No attempts yet

Problem

Every day a new programming problem is published on Codehorses. Thus, n problems will be published in the following n days: the difficulty of the i-th problem is ai.

Polycarp wants to choose exactly three days i, j and k (i < j < k) so that the difference of difficulties on the day j and the day i is equal to the difference of difficulties on the day k and day j. In other words, Polycarp wants equality aj − ai = ak − aj to be true.

Determine the number of possible ways for Polycarp to choose the three days in the desired way.

Input

The first line contains an integer t — the number of test cases in the input (1 ≤ t ≤ 10). Then t test case descriptions follow.

The first line of a test case contains an integer n — the number of the days (3 ≤ n ≤ 2000). The second line of the test case contains n integers a1, a2, . . . , an, where ai is the difficulty of the problem on the i-th day (1 ≤ ai ≤ 109).

Output

Output t integers — the answers for each of the test cases in the input, in the order they are given. The answer to a test case is the number of triples of indices i, j, and k such that 1 ≤ i < j < k ≤ n and ak − aj = aj − ai.

Examples1

Example 1

Input

4
5
1 2 1 2 1
3
30 20 10
5
1 2 2 3 4
9
3 1 4 1 5 9 2 6 5

Expected output