Let's define a function (f(a)) for an array (a) of length (n) as ()f(a) = \textrm{cost} + (a_1 - a_2 + a_3 - a_4 \cdots a_n)() where (\textrm{cost}) is zero initially. Now consider the scenario where Alice and Bob are given an array (a) of length (n). They play a game taking at most (10^{100}) turns alternately with Alice going first. In each turn, they must perform any one (only one) of the following operations: End the game for both Alice and Bob. Choose two indices (l,r) with (1 \le l \le r \le n) and swap (a_l) and (a_r); this adds ((r - l)) to the (\textrm{cost}). Assume that Alice tries to maximize (f(a)) and Bob tries to minimize it. Your task is to determine the final value of (f(a)) assuming both players play optimally. Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 10^4)). The description of the test cases follows. The first line of each test case contains a single integer (n) ((1 \le n \le 2\cdot10^5)) — the length of the array (a). The second line contains (n) integers (a_1,a_2,a_3,\ldots,a_n) ((1 \le a_i \le 10^9)) — the elements of the array (a). It is guaranteed that the sum of (n) over all test cases does not exceed (2\cdot10^5). For each testcase, output a single integer — the final value of (f(a)) assuming both players play optimally. For the first testcase, it is optimal for Alice to end the game on her first turn. So the final value of (\textrm{cost} = 0) and (f(a) = 0 + 1000 - 1 = 999). For the fourth testcase, it is optimal for Alice to swap (a_1) and (a_6), and then it is optimal for Bob to end the game on his first turn. So the final value of (\textrm{cost} = 5) and (f(a) = 5 + 15 - 14 + 1 - 14 + 1 - 1=-7).