C. A Tale of Two Landstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.Here |z| denotes the absolute value of z.Now, Jose is stuck on a question of his history exam: "What are the values of x and y?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, \dots, a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.InputThe first line contains a single integer n (2 \le n \le 2 \cdot 10^5)  — the number of choices.The second line contains n pairwise distinct integers a_1, a_2, \dots, a_n (-10^9 \le a_i \le 10^9) — the choices Jose is considering.OutputPrint a single integer number — the number of unordered pairs \{x, y\} formed by different numbers from Jose's choices that could make the legend true.ExamplesInput
3
2 5 -3
Output
2
Input
2
3 6
Output
1
NoteConsider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:  The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:  As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:  Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
3
2 5 -3

2 
['binary search', 'sortings', 'two pointers', '*1500']