Sums and Differences

Interview

Time limit1sMemory limit128 MB

Summary

Count ordered pairs from distinct positions where the difference exceeds the sum, which holds exactly when the second element is negative.

Level: Easy2 of 10
Topics: Math, Combinatorics
Solved: No attempts yet

Problem

You are given $n$ integers. Count how many ordered pairs $(a, b)$ satisfy $a - b > a + b$ , where $a$ and $b$ are two elements taken from different positions (the same position cannot be used for both $a$ and $b$ ).

Input

The first line contains an integer $n$ ( $1 \le n \le 10^6$ ). The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $-10^9 \le a_i \le 10^9$ ) separated by spaces.

Output

Print the number of ordered pairs whose difference is greater than their sum.

Hint

When the numbers are $-1, 2, 3$ , the possible ordered pairs are $(-1, 2), (-1, 3), (2, -1), (2, 3), (3, -1), (3, 2)$ , six in total. Among them, $(2, -1)$ and $(3, -1)$ satisfy the condition.

Examples3

Example 1
Input
```
3
-1 2 3
```
Expected output
```
2
```
Example 2
Input
```
4
1 2 3 4
```
Expected output
```
0
```
Example 3
Input
```
3
-1 -2 -3
```
Expected output
```
6
```