B'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, ... , x_n that the dice will show in the next n rounds. He will pick three integers a , l and r ( l <= q 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 <= q a <= q 10^9 , 1 <= q l <= q r <= q 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). The first line contains a single integer t ( 1 <= q t <= q 100 ) -- the number of test cases. The first line of each test case contains a single integer n ( 1 <= q n <= q 2 cdot 10^5 ) -- the number of rounds. The second line of each test case contains n integers x_1, x_2, ... , x_n ( 1 <= q x_i <= q 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 . 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'...