If everybody imagined ‘x’ value as 1, then the person with the highest score with him/her, is the winner of this game. Who is the winner of this game?

Alice and Bob came up with a rather strange game. They have an array of integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛. Alice chooses a certain integer k𝑘 and tells it to Bob, then the following happens:Bob chooses two integers i𝑖 and j𝑗 (1≤i<j≤n1≤𝑖<𝑗≤𝑛), and then finds the maximum among the integers ai,ai+1,…,aj𝑎𝑖,𝑎𝑖+1,…,𝑎𝑗;If the obtained maximum is strictly greater than k𝑘, Alice wins, otherwise Bob wins.Help Alice find the maximum k𝑘 at which she is guaranteed to win.InputEach test consists of multiple test cases. The first line contains a single integer t𝑡 (1≤t≤1041≤𝑡≤104) — the number of test cases. The description of the test cases follows.The first line of each test case contains a single integer n𝑛 (2≤n≤5⋅1042≤𝑛≤5⋅104) — the number of elements in the array.The second line of each test case contains n𝑛 integers a1,a2,…,an𝑎1,𝑎2,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109) — the elements of the array.It is guaranteed that the sum of n𝑛 over all test cases does not exceed 5⋅1045⋅104.OutputFor each test case, output one integer — the maximum integer k𝑘 at which Alice is guaranteed to win.ExampleinputCopy642 4 1 751 2 3 4 521 1337 8 16510 10 10 10 9103 12 9 5 2 3 2 9 8 2outputCopy3101592NoteIn the first test case, all possible subsegments that Bob can choose look as follows: [2,4],[2,4,1],[2,4,1,7],[4,1],[4,1,7],[1,7][2,4],[2,4,1],[2,4,1,7],[4,1],[4,1,7],[1,7]. The maximums on the subsegments are respectively equal to 4,4,7,4,7,74,4,7,4,7,7. It can be shown that 33 is the largest integer such that any of the maximums will be strictly greater than it.In the third test case, the only segment that Bob can choose is [1,1][1,1]. So the answer is 00.

Two players, A and B.A goes first. They roll a dice that has random outputs between 1 and 30. The player who gets the higher number wins, and the loser pays the winner the amount that the winner gets on his dice.1. What is the expected winnings?2. Would you prefer being Player A or Player B? Why?

Consider the two player game described by the payoff matric below.  L RU 3,3 2,xD 2,3 1,2What value must x NOT BE for the iterative elimination of strongly dominated strategies to lead to a single outcome?  Write your answer as an integer (e.g. 5).

Consider the two player game described by the payoff matric below.  L RU 3,3 2,xD 2,3 1,2What value must x NOT BE for the iterative elimination of strongly dominated strategies to lead to a single outcome?  Write your answer as an integer

Suppose we change the game’s rules to the following:Outcome Prize4 red balls +1504 blue balls -150Any other outcome -10What will be the expected value for X (the amount of money won by a player after playing the game once)?-2.5-5+2.5+7.5