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F. Parametric MST

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$. For any real number $$$t$$$, consider the complete weighted graph on $$$n$$$ vertices $$$K_n(t)$$$ with weight of the edge between vertices $$$i$$$ and $$$j$$$ equal to $$$w_{ij}(t) = a_i \cdot a_j + t \cdot (a_i + a_j)$$$.

Let $$$f(t)$$$ be the cost of the minimum spanning tree of $$$K_n(t)$$$. Determine whether $$$f(t)$$$ is bounded above and, if so, output the maximum value it attains.

Input

The input consists of multiple test cases. The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 10^4$$$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$2 \leq n \leq 2 \cdot 10^5$$$) — the number of vertices of the graph.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^6 \leq a_i \leq 10^6$$$).

The sum of $$$n$$$ for all test cases is at most $$$2 \cdot 10^5$$$.

Output

For each test case, print a single line with the maximum value of $$$f(t)$$$ (it can be shown that it is an integer), or INF if $$$f(t)$$$ is not bounded above.

Example

Input

5 2 1 0 2 -1 1 3 1 -1 -2 3 3 -1 -2 4 1 2 3 -4

Output

INF -1 INF -6 -18

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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