#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
#ifdef __GNUC__
#include <ext/hash_map>
#define unordered_map __gnu_cxx::hash_map
#else
#include <unordered_map>
#endif
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
class Mosquitoes { public:
int getMaximum(vector <int> xInit, vector <int> v, int R)
{
vector< pair<double,double> > tx;
for (int i = 0; i < xInit.size(); i++)
for (int j = i+1; j < xInit.size(); j++)
critical_points(xInit[i], v[i], xInit[j], v[j], R, &tx);
int best = 1;
for(int i=0; i<tx.size(); ++i) {
double t = tx[i].first;
double x = tx[i].second;
if( t >= 0 ) {
int cnt = 0;
for (int k = 0; k < xInit.size(); k++)
if( is_in(xInit[k], v[k], t, x, R) )
++cnt;
best = max(best, cnt);
}
}
return best;
}
void critical_points(double x1, double v1, double x2, double v2, double R,
vector< pair<double,double> >* tx)
{
// Compute t such that | (x1 + t v1) - (x2 - t v2) | = 2R
double x = x1 - x2;
double v = v1 - v2;
if( v == 0 ) {
if( abs(x) <= 2*R )
tx->push_back( make_pair(0, (x1+x2)/2) );
} else {
double t1 = (2*R - x) / v;
double t2 = (2*R + x) / (-v);
tx->push_back( make_pair(t1, (func(x1,v1,t1)+func(x2,v2,t1))/2) );
tx->push_back( make_pair(t2, (func(x1,v1,t2)+func(x2,v2,t2))/2) );
}
}
double func(double x, double v, double t)
{
return x + v*t;
}
bool is_in(double x, double v, double t, double c, double R)
{
return abs(func(x,v,t) - c) <= R + 1e-8;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, Mosquitoes().getMaximum(xInit, v, R));}
int main(){
CASE(0)
int xInit_[] = {1, -1};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {1, -1};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 10;
int _ = 2;
END
CASE(1)
int xInit_[] = {100, -100};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {1, -1};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 10;
int _ = 1;
END
CASE(2)
int xInit_[] = {0, -1, 10, -11, 99, -99};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {1, -1, -3, 3, 47, -47};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 3;
int _ = 4;
END
CASE(3)
int xInit_[] = {5};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {2};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 8;
int _ = 1;
END
CASE(4)
int xInit_[] = {12,34,56,78,90};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {-1,2,-3,4,-5};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 6;
int _ = 3;
END
CASE(5)
int xInit_[] = {-29, -27};
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = {25, 61};
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = 7;
int _ = 2;
END
/*
CASE(6)
int xInit_[] = ;
vector <int> xInit(xInit_, xInit_+sizeof(xInit_)/sizeof(*xInit_));
int v_[] = ;
vector <int> v(v_, v_+sizeof(v_)/sizeof(*v_));
int R = ;
int _ = ;
END
*/
}
// END CUT HERE