CF2095E Pair Count

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 \oplus a_j)(a_i^2 \oplus a_j^2) \equiv k \bmod p $ . Here $ \oplus $ denotes the [bitwise XOR operation](https://word.rodeo/?utm_source=share#cvMcraT7fZ6Yj3T3fwWbp8jppto8Pan9HXzC5fWYjPCCvqUMqseEkRFkzttufIM=).

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.

In the first example: $ (0\oplus1)(0^2 \oplus 1^2) = 1 \equiv 1 \bmod 3 $ . $ (0\oplus2)(0^2 \oplus 2^2) = 8 \equiv 2 \bmod 3 $ . $ (1\oplus2)(1^2 \oplus 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) $ , $ (1, 6) $ , $ (3, 6) $ .