← Home
write a go solution for Description:
Let's denote a k-step ladder as the following structure: exactly k+2 wooden planks, of which

- two planks of length at least k+1 — the base of the ladder;
- k planks of length at least 1 — the steps of the ladder;

Note that neither the base planks, nor the steps planks are required to be equal.

For example, ladders 1 and 3 are correct 2-step ladders and ladder 2 is a correct 1-step ladder. On the first picture the lengths of planks are [3,3] for the base and [1] for the step. On the second picture lengths are [3,3] for the base and [2] for the step. On the third picture lengths are [3,4] for the base and [2,3] for the steps.

You have n planks. The length of the i-th planks is a_i. You don't have a saw, so you can't cut the planks you have. Though you have a hammer and nails, so you can assemble the improvised "ladder" from the planks.

The question is: what is the maximum number k such that you can choose some subset of the given planks and assemble a k-step ladder using them?

Input Format:
The first line contains a single integer T (1<=T<=100) — the number of queries. The queries are independent.

Each query consists of two lines. The first line contains a single integer n (2<=n<=10^5) — the number of planks you have.

The second line contains n integers a_1,a_2,...,a_n (1<=a_i<=10^5) — the lengths of the corresponding planks.

It's guaranteed that the total number of planks from all queries doesn't exceed 10^5.

Output Format:
Print T integers — one per query. The i-th integer is the maximum number k, such that you can choose some subset of the planks given in the i-th query and assemble a k-step ladder using them.

Print 0 if you can't make even 1-step ladder from the given set of planks.

Note:
Examples for the queries 1-3 are shown at the image in the legend section.

The Russian meme to express the quality of the ladders:. Output only the code with no comments, explanation, or additional text.