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Chef Chick loves to jump a lot. Once, it realised that it was on an infinitely long road, and decided to travel along this road by jumping.

Let's view the road as the $x$-axis in a 1D coordinate system. Initially, Chef Chick is at the coordinate $x=0$, and it wants to move only in the positive $x$-direction. Moreover, Chef Chick has $N$ favourite integers $a_{1}, a_{2}, \ldots, a_{N}$, and it wants to jump on the coordinates that are multiples of these favourite numbers — when its current position is $x$, it jumps to the smallest coordinate $y > x$ such that $y$ is an integer multiple of at least one of the values $a_{1}, a_{2}, \ldots, a_{N}$; the length of such a jump is $y-x$.

This way, Chef Chick keeps jumping along the road forever in the positive $x$-direction. You need to find the length of the longest jump it will make, i.e. the largest integer $d$ such that Chef Chick makes at least one jump with length $d$ and never makes any jump with a greater length. It can be proved that such an integer always exists.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $a_{1}, a_{2}, \ldots, a_{N}$.

------ Output ------
For each test case, print a single line containing one integer — the length of the longest jump that Chick will make.

------ Constraints ------
$1 ≤ T ≤ 100$
$1 ≤ N ≤ 100$
$1 ≤ a_{i} ≤ 10^{5}$ for each valid $i$
$a_{1}, a_{2}, \ldots, a_{N}$ are pairwise distinct

----- Sample Input 1 ------
1

2

2 3
----- Sample Output 1 ------
2
----- explanation 1 ------
Example case 1: The sequence of coordinates on which Chef Chick would jump starts with $(0, 2, 3, 4, 6, \ldots)$. A longest jump is e.g. from $4$ to $6$, with length $2$.

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