Polycarp has a variety of (n is even) integers a1,a2,… ,an. Polycarp thought about a positive integer k. From that point forward, Polycarp started playing out the accompanying procedure on the cluster: take a file I (1≤i≤n) and diminish the number simulated intelligence by k. After Polycarp played out a few (potentially zero) number of such activities, it worked out that all numbers in the exhibit turned into something similar. Track down the most extreme k at
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Polycarp has a variety of (n is even) integers a1,a2,… ,an. Polycarp thought about a positive integer k. From that point forward, Polycarp started playing out the accompanying procedure on the cluster: take a file I (1≤i≤n) and diminish the number simulated intelligence by k.
After Polycarp played out a few (potentially zero) number of such activities, it worked out that all numbers in the exhibit turned into something similar. Track down the most extreme k at which such a circumstance is conceivable, or print −1 if a particularly number can be subjectively huge.
Input :The principal line contains one integer t (1≤t≤10) — the number of experiments. Then, at that point, t experiments follow. Each experiment comprises of two lines. The principal line contains an even integer n (4≤n≤40) (n is even). The subsequent line contains n integers a1,a2,… an (−106≤
It is ensured that the amount of all n indicated in the given experiments doesn't surpass 100.
Output :For each experiment output on a different line an integer k (k≥1) — the greatest conceivable number that Polycarp utilized in procedure on the cluster, or −1, if a particularly number can be subjectively huge.
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