divide and conquer

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D. Maximum Sum on Even Positions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an array $$$a$$$ consisting of $$$n$$$ integers. Indices of the array start from zero (i. e. the first element is $$$a_0$$$, the second one is $$$a_1$$$, and so on).

You can reverse at most one subarray (continuous subsegment) of this array. Recall that the subarray of $$$a$$$ with borders $$$l$$$ and $$$r$$$ is $$$a[l; r] = a_l, a_{l + 1}, \dots, a_{r}$$$.

Your task is to reverse such a subarray that the sum of elements on even positions of the resulting array is maximized (i. e. the sum of elements $$$a_0, a_2, \dots, a_{2k}$$$ for integer $$$k = \lfloor\frac{n-1}{2}\rfloor$$$ should be maximum possible).

You have to answer $$$t$$$ independent test cases.

Input

The first line of the input contains one integer $$$t$$$ ($$$1 \le t \le 2 \cdot 10^4$$$) — the number of test cases. Then $$$t$$$ test cases follow.

The first line of the test case contains one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of $$$a$$$. The second line of the test case contains $$$n$$$ integers $$$a_0, a_1, \dots, a_{n-1}$$$ ($$$1 \le a_i \le 10^9$$$), where $$$a_i$$$ is the $$$i$$$-th element of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ does not exceed $$$2 \cdot 10^5$$$ ($$$\sum n \le 2 \cdot 10^5$$$).

Output

For each test case, print the answer on the separate line — the maximum possible sum of elements on even positions after reversing at most one subarray (continuous subsegment) of $$$a$$$.

Example

Input

4 8 1 7 3 4 7 6 2 9 5 1 2 1 2 1 10 7 8 4 5 7 6 8 9 7 3 4 3 1 2 1

Output

26 5 37 5

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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