Codeforces Round 886 (Div. 4) |
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Finished |
Mihai and Slavic were looking at a group of $$$n$$$ frogs, numbered from $$$1$$$ to $$$n$$$, all initially located at point $$$0$$$. Frog $$$i$$$ has a hop length of $$$a_i$$$.
Each second, frog $$$i$$$ hops $$$a_i$$$ units forward. Before any frogs start hopping, Slavic and Mihai can place exactly one trap in a coordinate in order to catch all frogs that will ever pass through the corresponding coordinate.
However, the children can't go far away from their home so they can only place a trap in the first $$$n$$$ points (that is, in a point with a coordinate between $$$1$$$ and $$$n$$$) and the children can't place a trap in point $$$0$$$ since they are scared of frogs.
Can you help Slavic and Mihai find out what is the maximum number of frogs they can catch using a trap?
The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of test cases follows.
The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 2 \cdot 10^5$$$) — the number of frogs, which equals the distance Slavic and Mihai can travel to place a trap.
The second line of each test case contains $$$n$$$ integers $$$a_1, \ldots, a_n$$$ ($$$1 \leq a_i \leq 10^9$$$) — the lengths of the hops of the corresponding frogs.
It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
For each test case output a single integer — the maximum number of frogs Slavic and Mihai can catch using a trap.
751 2 3 4 532 2 263 1 3 4 9 1091 3 2 4 2 3 7 8 511087 11 6 8 12 4 4 8109 11 9 12 1 7 2 5 8 10
3 3 3 5 0 4 4
In the first test case, the frogs will hop as follows:
In the second test case, Slavic and Mihai can put a trap at coordinate $$$2$$$ and catch all three frogs instantly.
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