Luogu P2421

#include<cstdio>
#include<string>
#include<cstring>
#include<iostream>
#include<algorithm>
#define M 16
using namespace std;

int n,mx;
int c[M],p[M],l[M];

int Exgcd(int a,int b,int &x,int &y){
	if(!b){
		x=1,y=0;
		return a;
	}
	int d=Exgcd(b,a%b,y,x);
	y-=a/b*x;
	return d;
}

bool Check(int x){
	for(int i=1;i<=n;i++)
		for(int j=1+i;j<=n;j++){
			int a=p[i]-p[j];
			int b=x;
			int s=c[j]-c[i];
			int x,y;
			int d=Exgcd(a,b,x,y);
			if(s%d) continue;
			a/=d,b/=d,s/=d;
			if(b<0) b=-b;
			x=(x*s%b+b)%b;
			if(x<=l[i]&&x<=l[j])
				return false;
		}
	return true;
}

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%d%d%d",&c[i],&p[i],&l[i]);
		mx=max(mx,c[i]);		
	}
	for(int i=mx;;i++)
		if(Check(i)){
			printf("%d\n",i);
			return 0;
		}
	return 0;
}