A. DIY Wooden Laddertime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet'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?InputThe first line contains a single integer T (1 \le T \le 100) — the number of queries. The queries are independent.Each query consists of two lines. The first line contains a single integer n (2 \le n \le 10^5) — the number of planks you have.The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 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.OutputPrint 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.ExampleInput
4
4
1 3 1 3
3
3 3 2
5
2 3 3 4 2
3
1 1 2
Output
2
1
2
0
NoteExamples for the queries 1-3 are shown at the image in the legend section.The Russian meme to express the quality of the ladders:  
4
4
1 3 1 3
3
3 3 2
5
2 3 3 4 2
3
1 1 2

2 1 2 0 
['greedy', 'math', 'sortings', '*900']