Chef gives an array A with N elements to Babla. Babla's task is to find the maximum non-negative integer X such that: No element in the array belongs to the range[−X,X]. In other words, for all (1≤i≤N), either Ai​<−X or Ai​>X. Help Babla to find the maximum non-negative integer X for which the given condition is satisfied or determine if no such X exists. Input Format The first line of input will contain a single integer T, denoting the number of test cases. Each test case consists of multiple lines of input. The first line of each test case contains an integer N — the number of elements in the array. The second line of each test case contains N space-separated integers A1​,A2​,…,AN​ representing the array A. Output Format For each test case, output on a new line, the maximum non-negative integer X, satisfying the above condition. If no such X exists, output −1 instead. Constraints 1≤T≤105 1≤N≤105 −109≤Ai​≤109 Sum of N over all test cases does not exceed 2⋅105.

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Random Variables

A random variable Z is a real valued function of the type Z: S → R on a sample space S. That means the function assigns a real number to every primitive event in the sample space. In other words, a random variable is a function mapping a sample space S to a set of real numbers R.