E. Pair Counttime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputOutput a single integer — answer to the problem.ExamplesInput3 3 20 1 2Output1 Input6 11 21 3 5 6 7 8Output3 NoteIn 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: $$$(1, 5)$$$, $$$(1, 6)$$$, $$$(3, 6)$$$.