Count Pairs
Description
You are given a prime number $p$, $n$ integers $a_1, a_2, \ldots, a_n$, and an integer $k$.
Find the number of pairs of indexes $(i, j)$ ($1 \le i < j \le n$) for which $(a_i + a_j)(a_i^2 + a_j^2) \equiv k \bmod p$.
The first line contains integers $n, p, k$ ($2 \le n \le 3 \cdot 10^5$, $2 \le p \le 10^9$, $0 \le k \le p-1$). $p$ is guaranteed to be prime.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le p-1$). It is guaranteed that all elements are different.
Output a single integer — answer to the problem.
Input
The first line contains integers $n, p, k$ ($2 \le n \le 3 \cdot 10^5$, $2 \le p \le 10^9$, $0 \le k \le p-1$). $p$ is guaranteed to be prime.
The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($0 \le a_i \le p-1$). It is guaranteed that all elements are different.
Output
Output a single integer — answer to the problem.
Samples
3 3 0
0 1 2
1
6 7 2
1 2 3 4 5 6
3
Note
In the first example:
$(0+1)(0^2 + 1^2) = 1 \equiv 1 \bmod 3$.
$(0+2)(0^2 + 2^2) = 8 \equiv 2 \bmod 3$.
$(1+2)(1^2 + 2^2) = 15 \equiv 0 \bmod 3$.
So only $1$ pair satisfies the condition.
In the second example, there are $3$ such pairs: $(1, 5)$, $(2, 3)$, $(4, 6)$.