P16249 [Lanqiao Cup 2026 NOI Qualifier Postgraduate Group] Evaluation Vulnerability

"The judge is stuck again!" Xiao Lan frowned and stared at the evaluation error log on the screen. After careful investigation, he found a hidden vulnerability in the checking logic of the judging system: when the system reads two parameters $x$ and $y$ in order, if the combination of these two numbers satisfies a certain arithmetic property, it will cause a memory overflow and then trigger an abnormal termination. Specifically, if two parameters that appear in order, $a_i$ and $a_j$ (where $i < j$), satisfy the following equation, the system will crash: $$ \begin{aligned} (a_i + a_j)^2 = a_i + a_j \end{aligned} $$ To fix this vulnerability, Xiao Lan exported all $n$ test parameters from the current crashing testdata, and arranged them in the input order as $a_1, a_2, \ldots, a_n$. Now he needs you to help count how many index pairs $(i, j)$ in this sequence satisfy $1 \le i < j \le n$ and will trigger the above exception.

The first line contains an integer $n$, which represents the total number of test parameters. The second line contains $n$ integers $a_1, a_2, \ldots, a_n$, which represent the parameter values read in order.

Output one integer, which represents the number of parameter pairs that can trigger the exception.

### Constraints and Notes For $40\%$ of the test cases, $2 \le n \le 1000$. For all test cases, $2 \le n \le 10^5$, $-10^9 \le a_i \le 10^9$. Translated by ChatGPT 5