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 $(i, j)$ ($1 \le i \lt j \le n$) 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.

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.

Note

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: $(1, 5)$, $(1, 6)$, $(3, 6)$.

3 3 2
0 1 2

1

6 11 2
1 3 5 6 7 8

3