CF1166C.A Tale of Two Lands

The 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.

Vectorland 建国传说中提到了两个整数 $x$ 和 $y$。几个世纪前，数组之王在数轴上点 $|x|$ 和 $|y|$ 处放置了两个标记，并征服了这两点之间（含端点）的所有土地，将其命名为 Arrayland。多年以后，向量之王在数轴上点 $|x - y|$ 和 $|x + y|$ 处放置了标记，并征服了这两点之间（含端点）的所有土地，将其命名为 Vectorland。他如此操作，使得 Arrayland 的全部领土（含端点）完全包含于 Vectorland 的领土之内。

此处 $|z|$ 表示 $z$ 的绝对值。

现在，Jose 正被历史考试中的一道题难住了：“$x$ 和 $y$ 的值是多少？” Jose 不知道答案，但他相信自己已将可能的答案缩小至 $n$ 个整数 $a_1, a_2, \dots, a_n$。现在，他想知道：从这 $n$ 个整数中任取两个不同元素所构成的无序对中，有多少对满足——若令 $x$ 和 $y$ 分别等于该对中的两个值，则上述传说成立。注意，Jose 可能出错，即可能不存在任何一对数能使传说成立。

The 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.

第一行包含一个整数 $n$（$2 \le n \le 2 \cdot 10^5$）—— 表示选项的数量。

第二行包含 $n$ 个两两不同的整数 $a_1, a_2, \dots, a_n$（$-10^9 \le a_i \le 10^9$）—— 表示 Jose 正在考虑的选项。

Print 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.

输出一个整数——即由何塞所选的不同数字构成的无序对 $\{x, y\}$ 的数量，这些无序对可能使传说成立。

Consider 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.

考虑第一个样例。对于数对 ${2, 5}$，情形如下所示：Arrayland 的标记位于 $|2| = 2$ 和 $|5| = 5$，而 Vectorland 的标记位于 $|2 - 5| = 3$ 和 $|2 + 5| = 7$：

此时传说不成立，因为区间 $[2, 3]$ 并未被 Vectorland 覆盖。对于数对 ${5, -3}$，情形如下所示：Arrayland 对应区间 $[3, 5]$，Vectorland 对应区间 $[2, 8]$：

由于 Vectorland 完全包含了 Arrayland，因此传说成立。同样可以验证，传说对数对 ${2, -3}$ 也成立，总计有两个满足条件的数对。

在第二个样例中，唯一的数对是 ${3, 6}$，情形如下所示：

注意：尽管 Arrayland 和 Vectorland 共享端点 $3$，我们仍认为 Arrayland 完全包含于 Vectorland 之内。