B. Count Pairs
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $(a_i + a_j)(a_i^2 + a_j^2) \equiv k \bmod p$.

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.

Examples
Input
3 3 0
0 1 2

Output
1
Input
6 7 2
1 2 3 4 5 6

Output
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: $(1, 5)$, $(2, 3)$, $(4, 6)$.