package main

import (
	"bufio"
	"fmt"
	"os"
)

func generateData(p []int64) []Pair64 {
	n, A, B, C, D, x0, y0, M := p[0], p[1], p[2], p[3], p[4], p[5], p[6], p[7]
	result := make([]Pair64, n)
	result[0] = Pair64{x0, y0}
	for i := 1; int64(i) < n; i++ {
		result[i]._1 = (A*result[i-1]._1 + B) % M
		result[i]._2 = (C*result[i-1]._2 + D) % M
	}
	return result
}

func cropTriangle(scanner *bufio.Scanner) []int {
	caseCnt := ReadInt(scanner)
	answer := make([]int, caseCnt)
	for i := 0; i < caseCnt; i++ {
		params := ReadInt64s(scanner)
		pts := generateData(params)
		bucket := make([]int, 9)
		for _, p := range pts {
			x, y := p._1%3, p._2%3
			bucket[y*3+x]++
		}
		// 3 cases: 3 points in same class;
		// 2 same, 1 diffrent (impossible); 3 diffrent.
		for j := 0; j < 9; j++ {
			answer[i] += bucket[j] * (bucket[j] - 1) * (bucket[j] - 2) / 6
		}
		for j := 0; j < 9; j++ {
			for k := j + 1; k < 9; k++ {
				for l := k + 1; l < 9; l++ {
					if (j/3+k/3+l/3)%3 == 0 && (j%3+k%3+l%3)%3 == 0 {
						answer[i] += bucket[j] * bucket[k] * bucket[l]
					}
				}
			}
		}
	}
	return answer
}

func main() {
	inputFiles := []string{"A-small-practice.in", "A-large-practice.in", "test.in"}
	outputFiles := []string{"result-small.out", "result-large.out", "test.out"}
	const (
		small = iota
		large
		test
	)

	fileType := test

	fin, _ := os.Open(inputFiles[fileType])
	defer fin.Close()

	scanner := bufio.NewScanner(fin)
	answer := cropTriangle(scanner)

	fout, _ := os.Create(outputFiles[fileType])
	defer fout.Close()

	for i, v := range answer {
		s := fmt.Sprintf("Case #%d: %d\n", i+1, v)
		fout.WriteString(s)
	}
}