You are given $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ representing points on a number line. Paco has a token that starts at coordinate $$$0$$$.
Reflecting the token about a point moves it to the other side of that point, keeping the same distance from it. If the token is already at that point, it stays there.
Paco's token (blue) being reflected about a point (red). Choose an integer $$$p$$$. Paco's token is reflected about the points with coordinates $$$p, a_1, a_2, \ldots, a_n$$$, in this order, exactly once each.
Help Paco find $$$p$$$ such that his token ends at exactly coordinate $$$0$$$. This is very important for him. It can be shown that exactly one such integer exists.
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 $$$n$$$ ($$$1 \le n \le 10^5$$$).
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^4 \le a_i \le 10^4$$$).
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.
For each test case, print the integer $$$p$$$.
51322 532 7 14-3 0 -3 010
3-3-4-60
In the first test case, choose $$$p=3$$$. Paco's token moves from $$$0$$$ to $$$6$$$ and then back to $$$0$$$.
In the second test case, choose $$$p=-3$$$. Paco's token visits coordinates $$$0 \to -6 \to 10 \to 0$$$.
In the third test case, choose $$$p=-4$$$. Paco's token visits coordinates $$$0 \to -8 \to 12 \to 2 \to 0$$$.
