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 . 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)).