Background

yltx has once again come up with a problem that they cannot solve...

Problem Description

yltx defines that if a prime pair $(x,y)$ satisfies that $x\times y-3\times (x-y)$ is prime, then it is called a yltx pair.

He gives you $T$ pairs $(x,y)$. Please check whether they are yltx pairs.

The data is given in the form of a seed $(x_0,y_0)$.

Perform $T$ times of $x_0\leftarrow (7x_0+13)\ \mathrm{xor}\ (x_0\div 13-7)$. For the value obtained in the $i$-th execution, first take modulo $10^4$, add $10^4$, take modulo $10^4$ again, then add $1$, and you get the $x$ of the $i$-th test case. Here division means integer division, and $x_0$ is treated as a 32-bit signed integer.

Use the same method to get $y$.

Data generation template:

#include<bits/stdc++.h>
using namespace std;
int T,x_0,y_0;
int main() {
	scanf("%d%d%d",&T,&x_0,&y_0);
	while(T--){
		x_0=((7*x_0+13)^(x_0/13-7));
		y_0=((7*y_0+13)^(y_0/13-7));
		int x=(x_0%10000+10000)%10000+1,y=(y_0%10000+10000)%10000+1;
		//x,y即为一组(x,y)。
	}
	return 0;
}

Input Format

The first line contains three integers $T,x_0,y_0$.

Output Format

$1$ line. Output how many pairs are yltx pairs.

100000 1 2

321

Hint

The Constraints for each test point are as follows:

Each Subtask is tested as a bundled group of test points.

This problem provides testdata for download, but we hope you will use the data to do the right thing.

Translated by ChatGPT 5