Gambling

2000ms

262144K

Description:

Marian is at a casino. The game at the casino works like this.

Before each round, the player selects a number between $$$1$$$ and $$$10^9$$$. After that, a dice with $$$10^9$$$ faces is rolled so that a random number between $$$1$$$ and $$$10^9$$$ appears. If the player guesses the number correctly their total money is doubled, else their total money is halved.

Marian predicted the future and knows all the numbers $$$x_1, x_2, \dots, x_n$$$ that the dice will show in the next $$$n$$$ rounds.

He will pick three integers $$$a$$$, $$$l$$$ and $$$r$$$ ($$$l \leq r$$$). He will play $$$r-l+1$$$ rounds (rounds between $$$l$$$ and $$$r$$$ inclusive). In each of these rounds, he will guess the same number $$$a$$$. At the start (before the round $$$l$$$) he has $$$1$$$ dollar.

Marian asks you to determine the integers $$$a$$$, $$$l$$$ and $$$r$$$ ($$$1 \leq a \leq 10^9$$$, $$$1 \leq l \leq r \leq n$$$) such that he makes the most money at the end.

Note that during halving and multiplying there is no rounding and there are no precision errors. So, for example during a game, Marian could have money equal to $$$\dfrac{1}{1024}$$$, $$$\dfrac{1}{128}$$$, $$$\dfrac{1}{2}$$$, $$$1$$$, $$$2$$$, $$$4$$$, etc. (any value of $$$2^t$$$, where $$$t$$$ is an integer of any sign).

Input:

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 100$$$) — the number of test cases.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2\cdot 10^5$$$) — the number of rounds.

The second line of each test case contains $$$n$$$ integers $$$x_1, x_2, \dots, x_n$$$ ($$$1 \leq x_i \leq 10^9$$$), where $$$x_i$$$ is the number that will fall on the dice in the $$$i$$$-th round.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output:

For each test case, output three integers $$$a$$$, $$$l$$$, and $$$r$$$ such that Marian makes the most amount of money gambling with his strategy. If there are multiple answers, you may output any of them.

Sample Input:

4
5
4 4 3 4 4
5
11 1 11 1 11
1
1000000000
10
8 8 8 9 9 6 6 9 6 6

Sample Output:

4 1 5
1 2 2
1000000000 1 1
6 6 10

Note:

For the first test case, the best choice is $$$a=4$$$, $$$l=1$$$, $$$r=5$$$, and the game would go as follows.

Marian starts with one dollar.
After the first round, he ends up with $$$2$$$ dollars because the numbers coincide with the chosen one.
After the second round, he ends up with $$$4$$$ dollars because the numbers coincide again.
After the third round, he ends up with $$$2$$$ dollars because he guesses $$$4$$$ even though $$$3$$$ is the correct choice.
After the fourth round, he ends up with $$$4$$$ dollars again.
In the final round, he ends up $$$8$$$ dollars because he again guessed correctly.

There are many possible answers for the second test case, but it can be proven that Marian will not end up with more than $$$2$$$ dollars, so any choice with $$$l = r$$$ with the appropriate $$$a$$$ is acceptable.

Informação

Provedor Codeforces

Código CF1692H