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