Rotten Ropes

We have $n$ ropes of equal length and we want to use them to lift a heavy object. Each rope has an associated tear-off weight $t$: if we try to lift an object heavier than $t$ with that single rope, the rope tears off. However, we may fasten several ropes to the object in parallel and lift it with all of them together. When $k$ ropes are used to lift an object of weight $w$, each of the $k$ ropes -- regardless of its own tear-off weight -- is assumed to carry a weight of $w/k$. If $w/k > t$ for a rope whose tear-off weight is $t$, that rope tears off.

For example, three ropes with tear-off weights $1$, $10$, and $15$, when all three are fastened to one object, cannot lift an object heavier than $3$ unless the weakest rope tears off; but the second rope alone can lift an object of weight at most $10$.

Given the tear-off weights of the $n$ ropes, find the weight of the heaviest object that can be lifted by fastening some subset of the ropes so that none of them tears off.

The first line contains a single integer $t$ ($1 \le t \le 10$), the number of test cases, followed by the data for each test case. The first line of each test case contains a single integer $n$ ($1 \le n \le 1000$), the number of ropes. The next line contains $n$ integers between $1$ and $10000$, the tear-off weights of the ropes, separated by spaces.

For each test case, output on its own line a single number: the largest weight that can be lifted without tearing off any chosen rope.