C. A Tale of Two Lands

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

题目链接：https://codeforces.com/contest/1166/problem/C?csrf_token=012e3bb8b804d22d9adf102601bd183f

The legend of the foundation of Vectorland talks of two integers xx and yy. Centuries ago, the array king

placed two markers at points |x||x|and |y||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||x−y| and |x+y||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||z| denotes the absolute value of zz.

Now, Jose is stuck on a question of his history exam: "What are the values of xx and yy?" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to nn integers a1,a2,…,ana1,a2,…,an. Now, he wants to know the number of unordered pairs formed by two different elements from these nn integers such that the legend could be true if xx and yy 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.

Input

The first line contains a single integer nn (2≤n≤2⋅1052≤n≤2⋅105) — the number of choices.

The second line contains nn pairwise distinct integers a1,a2,…,ana1,a2,…,an (−109≤ai≤109−109≤ai≤109) — the choices Jose is considering.

Output

Print a single integer number — the number of unordered pairs {x,y}{x,y} formed by different numbers from Jose's choices that could make the legend true.

Examples

input

Copy

3

2 5 -3

output

Copy

input

Copy

2

3 6

output

Copy

Note

Consider the first sample. For the pair {2,5}{2,5}, the situation looks as follows, with the Arrayland markers at |2|=2|2|=2 and |5|=5|5|=5, while the Vectorland markers are located at |2−5|=3|2−5|=3 and |2+5|=7|2+5|=7:

The legend is not true in this case, because the interval [2,3][2,3] is not conquered by Vectorland. For the pair {5,−3}{5,−3} the situation looks as follows, with Arrayland consisting of the interval [3,5][3,5] and Vectorland consisting of the interval [2,8][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}{2,−3}, for a total of two pairs.

In the second sample, the only pair is {3,6}{3,6}, and the situation looks as follows:

Note that even though Arrayland and Vectorland share 33 as endpoint, we still consider Arrayland to be completely inside of Vectorland.

思路：

本来我用了map加基排序原理写，没想到直接用sort也能过。主要思路就是负数和正数效果一样，注意点是相同数字也算成功的一组。所以输入完数据以后就sort排序，用坐标相减可以得出答案。

代码：

#include<bits/stdc++.h>

using namespace std;

long long x[200005];

int main() {

         int n;

         cin >> n;

         int a, b;

         for (int i = 0; i < n; i++) {

                  cin >> x[i];

                  if (x[i] < 0) {

                          x[i] *= -1;

                  }

         }

         sort(x, x + n);

         a = 0;

         b = 1;

         long long sum = 0;

         while (b < n) {

                  if (x[b] - x[a] <= x[a]) {

                          sum += b - a;

                          b++;

                  }

                  else {

                          a++;

                  }

         }

         cout << sum;

}