Problem: I'm traveling to a country with a rabbit. There are n cities in this country numbered from 1 to n, and the rabbit is now in city 1. City i is a point on the coordinate plane (xi, yi) ).

Rabbits travel to meet the following conditions.

* The travel path is a polygonal line, each part of which must be a line segment connecting two different cities.
* The total length of the travel route must be r or less. The overlapping part of the route is also counted for the number of times it has passed.
* When the direction of movement changes, the bending angle must be less than or equal to θ. There is no limit to the initial direction of movement.



If you move from one city to another, you will get one carrot in the destination city. You can visit the same city multiple times, and you will get a carrot each time you visit. Find the maximum number of carrots you can put in.



Input

One integer n is given on the first line of the input, and two real numbers r and θ are given on the second line, separated by a space.

1 ≤ n ≤ 20
0 <r <104
0 ° <θ <180 °


The following n lines are given the integers xi and yi separated by spaces.

-10 000 ≤ xi, yi ≤ 10 000

The answer does not change even if r and θ are changed within ± 10-3.
The locations of both cities are different.

Output

Output the maximum number of carrots that the rabbit can get on this trip in one line.

Example

Input

5
100.1 90.1
0 0
0 10
5 5
10 0
10 10


Output

10

Solution (in CPP):

Solution:
#include<bits/stdc++.h>

using namespace std;
#define INFS (1LL<<28)
#define DEKAI 1000000007
#define INF 1000000007
//#define MOD 1000000007
#define lp(i,n) for(int i=0;i<n;i++)
#define lps(i,n) for(int i=1;i<=n;i++)
#define all(c) begin(c), end(c)

//#define int long long

namespace {
#define __DECLARE__(C)    \
	    template <typename T> \
	std::ostream &operator<<(std::ostream &, const C<T> &);

#define __DECLAREM__(C)               \
	    template <typename T, typename U> \
	std::ostream &operator<<(std::ostream &, const C<T, U> &);

    __DECLARE__(std::vector)
    __DECLARE__(std::deque)
    __DECLARE__(std::set)
    __DECLARE__(std::stack)
    __DECLARE__(std::queue)
    __DECLARE__(std::priority_queue)
    __DECLARE__(std::unordered_set)
    __DECLAREM__(std::map)
    __DECLAREM__(std::unordered_map)

    template <typename T, typename U>
    std::ostream &operator<<(std::ostream &, const std::pair<T, U> &);
    template <typename... T>
    std::ostream &operator<<(std::ostream &, const std::tuple<T...> &);
    template <typename T, std::size_t N>
    std::ostream &operator<<(std::ostream &, const std::array<T, N> &);

    template <typename Tuple, std::size_t N>
    struct __TuplePrinter__ {
        static void print(std::ostream &os, const Tuple &t) {
            __TuplePrinter__<Tuple, N - 1>::print(os, t);
            os << ", " << std::get<N - 1>(t);
        }
    };

    template <typename Tuple>
    struct __TuplePrinter__<Tuple, 1> {
        static void print(std::ostream &os, const Tuple &t) { os << std::get<0>(t); }
    };

    template <typename... T>
    std::ostream &operator<<(std::ostream &os, const std::tuple<T...> &t) {
        os << '(';
        __TuplePrinter__<decltype(t), sizeof...(T)>::print(os, t);
        os << ')';
        return os;
    }

    template <typename T, typename U>
    std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &v) {
        return os << '(' << v.first << ", " << v.second << ')';
    }

#define __INNER__                             \
	os << '[';                                \
	for (auto it = begin(c); it != end(c);) { \
		os << *it;                            \
		os << (++it != end(c) ? ", " : "");   \
	}                                         \
	return os << ']';

    template <typename T, std::size_t N>
    std::ostream &operator<<(std::ostream &os, const std::array<T, N> &c) {
        __INNER__
    }

#define __DEFINE__(C)                                           \
	    template <typename T>                                       \
	std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
		__INNER__                                               \
	}

#define __DEFINEM__(C)                                             \
	    template <typename T, typename U>                              \
	std::ostream &operator<<(std::ostream &os, const C<T, U> &c) { \
		__INNER__                                                  \
	}

#define __DEFINEW__(C, M1, M2)                                  \
	    template <typename T>                                       \
	std::ostream &operator<<(std::ostream &os, const C<T> &c) { \
		std::deque<T> v;                                        \
		for (auto d = c; !d.empty(); d.pop()) v.M1(d.M2());     \
			return os << v;                                         \
	}

    __DEFINE__(std::vector)
    __DEFINE__(std::deque)
    __DEFINE__(std::set)
    __DEFINEW__(std::stack, push_front, top)
    __DEFINEW__(std::queue, push_back, front)
    __DEFINEW__(std::priority_queue, push_front, top)
    __DEFINE__(std::unordered_set)
    __DEFINEM__(std::map)
    __DEFINEM__(std::unordered_map)
}

#define pii pair<int,int>
#define ll long long
inline ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
inline ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

// modint
template <signed M, unsigned T>
struct mod_int {
    constexpr static signed MODULO = M;
    constexpr static unsigned TABLE_SIZE = T;

    signed x;

    mod_int() : x(0) {}

    mod_int(long long y) : x(static_cast<signed>(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO)) {}

    mod_int(int y) : x(y >= 0 ? y % MODULO : MODULO - (-y) % MODULO) {}

    mod_int &operator+=(const mod_int &rhs) {
        if ((x += rhs.x) >= MODULO) x -= MODULO;
        return *this;
    }

    mod_int &operator-=(const mod_int &rhs) {
        if ((x += MODULO - rhs.x) >= MODULO) x -= MODULO;
        return *this;
    }

    mod_int &operator*=(const mod_int &rhs) {
        x = static_cast<signed>(1LL * x * rhs.x % MODULO);
        return *this;
    }

    mod_int &operator/=(const mod_int &rhs) {
        x = static_cast<signed>((1LL * x * rhs.inv().x) % MODULO);
        return *this;
    }

    mod_int operator-() const { return mod_int(-x); }

    mod_int operator+(const mod_int &rhs) const { return mod_int(*this) += rhs; }

    mod_int operator-(const mod_int &rhs) const { return mod_int(*this) -= rhs; }

    mod_int operator*(const mod_int &rhs) const { return mod_int(*this) *= rhs; }

    mod_int operator/(const mod_int &rhs) const { return mod_int(*this) /= rhs; }

    bool operator<(const mod_int &rhs) const { return x < rhs.x; }

    mod_int inv() const {
        assert(x != 0);
        if (x <= static_cast<signed>(TABLE_SIZE)) {
            if (_inv[1].x == 0) prepare();
            return _inv[x];
        } else {
            signed a = x, b = MODULO, u = 1, v = 0, t;
            while (b) {
                t = a / b;
                a -= t * b;
                std::swap(a, b);
                u -= t * v;
                std::swap(u, v);
            }
            return mod_int(u);
        }
    }

    mod_int pow(long long t) const {
        assert(!(x == 0 && t == 0));
        mod_int e = *this, res = mod_int(1);
        for (; t; e *= e, t >>= 1)
            if (t & 1) res *= e;
        return res;
    }

    mod_int fact() {
        if (_fact[0].x == 0) prepare();
        return _fact[x];
    }

    mod_int inv_fact() {
        if (_fact[0].x == 0) prepare();
        return _inv_fact[x];
    }

    mod_int choose(mod_int y) {
        assert(y.x <= x);
        return this->fact() * y.inv_fact() * mod_int(x - y.x).inv_fact();
    }

    static mod_int _inv[TABLE_SIZE + 1];

    static mod_int _fact[TABLE_SIZE + 1];

    static mod_int _inv_fact[TABLE_SIZE + 1];

    static void prepare() {
        _inv[1] = 1;
        for (int i = 2; i <= (int)TABLE_SIZE; ++i) {
            _inv[i] = 1LL * _inv[MODULO % i].x * (MODULO - MODULO / i) % MODULO;
        }
        _fact[0] = 1;
        for (unsigned i = 1; i <= TABLE_SIZE; ++i) {
            _fact[i] = _fact[i - 1] * int(i);
        }
        _inv_fact[TABLE_SIZE] = _fact[TABLE_SIZE].inv();
        for (int i = (int)TABLE_SIZE - 1; i >= 0; --i) {
            _inv_fact[i] = _inv_fact[i + 1] * (i + 1);
        }
    }
};

template <int M, unsigned F>
std::ostream &operator<<(std::ostream &os, const mod_int<M, F> &rhs) {
    return os << rhs.x;
}

template <int M, unsigned F>
std::istream &operator>>(std::istream &is, mod_int<M, F> &rhs) {
    long long s;
    is >> s;
    rhs = mod_int<M, F>(s);
    return is;
}

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
mod_int<M, F> mod_int<M, F>::_inv_fact[TABLE_SIZE + 1];

template <int M, unsigned F>
bool operator==(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
    return lhs.x == rhs.x;
}

template <int M, unsigned F>
bool operator!=(const mod_int<M, F> &lhs, const mod_int<M, F> &rhs) {
    return !(lhs == rhs);
}

const int MF = 1000010;
const int MOD = 1000000007;

using mint = mod_int<MOD, MF>;

mint binom(int n, int r) { return (r < 0 || r > n || n < 0) ? 0 : mint(n).choose(r); }

mint fact(int n) { return mint(n).fact(); }

mint inv_fact(int n) { return mint(n).inv_fact(); }
const ll mod = 1000000007;
const int MAX_N = 10000;  // 400MB
// const int MAX_N = 1024; // 4MB
// nCr % mod

//#define int long long

inline ll gcds(ll a, ll b) { return b ? gcds(b, a % b) : a; }
inline ll lcms(ll a, ll b) { return a / gcd(a, b) * b; }

#define RK 200000000000
#define LK 300000000000
#define PL 400000000000
#define MI 500000000000
#define KA 600000000000
#define PI acos(-1)
//#define double float
double dist[30][30];

void calc_dist(vector<pair<int,int>> &v){
    lp(i,v.size()){
        lp(j,v.size()){
            double ax=v[i].first;
            double ay=v[i].second;
            double bx=v[j].first;
            double by=v[j].second;
            dist[i][j]=sqrt(abs(ax-bx)*abs(ax-bx)+abs(ay-by)*abs(ay-by));
            //cout<<i<<" "<<j<<" "<<dist[i][j]<<endl;
        }
    }
}

void make_g(vector<vector<vector<int>>> &g,vector<pair<int,int>> &v,double si){
    lp(i,v.size()){
        lp(j,v.size()){
            lp(k,v.size()){
                if(i==j||j==k||i==k)continue;
                //i->j->k
                double ax=v[i].first;
                double ay=v[i].second;
                double bx=v[j].first;
                double by=v[j].second;
                double cx=v[k].first;
                double cy=v[k].second;
                ax-=bx;
                cx-=bx;
                ay-=by;
                cy-=by;
                //cout<<i<<" "<<j<<endl;
                double arc=acos((ax*cx+ay*cy)/(sqrt(ax*ax+ay*ay)*sqrt(cx*cx+cy*cy)));
                arc=arc*180/PI;
                if(arc>180.0)arc-=180.0;
                else arc=180-arc;
                //cout<<i<<" "<<j<<" "<<k<<" "<<arc<<endl;
                if(arc<=si+0.000001){
                    g[i][j].push_back(k);
                }
                if(abs(dist[i][j]+dist[j][k]-dist[i][k])<0.000001){
                    //cout<<i<<" "<<j<<" "<<k<<endl;
                    g[i][j].push_back(k);

                }
            }
        }
    }
}
double dp[20][20][20000];

signed main(){
    int n;
    cin>>n;
    double r,si;
    cin>>r>>si;
    vector<pair<int,int>> v;
    lp(i,n){
        int a,b;
        cin>>a>>b;
        v.push_back({a,b});
    }
    vector<vector<vector<int>>> g;//g[before][index].push_back(next)
    g.resize(n);
    lp(i,n)g[i].resize(n);
    calc_dist(v);
    make_g(g,v,si);
    lp(i,20)lp(j,20)lp(k,20000)dp[i][j][k]=r+100;
    queue<pair<int,pair<int,int>>> q;
    lp(i,n){
        //0->i
        if(i==0)continue;
        if(dist[0][i]>r-0.000001)continue;
        dp[0][i][1]=dist[0][i];
        q.push({0,{i,1}});
    }
    int ans=0;
    while(!q.empty()){
        int bef=q.front().first;
        int now=q.front().second.first;
        int cnt=q.front().second.second;
        q.pop();
        double dist_now=dp[bef][now][cnt];
        //cout<<bef<<" "<<now<<" "<<dist_now<<" "<<cnt<<endl;
        ans=max(cnt,ans);
        lp(i,g[bef][now].size()){
            int next=g[bef][now][i];
            double dist_next=dist_now+dist[now][next];
            if(dp[now][next][cnt+1]<=dist_next)continue;
            if(dist_next>r)continue;
            dp[now][next][cnt+1]=dist_next;
            q.push({now,{next,cnt+1}});
        }
    }
    cout<<ans<<endl;
    return 0;
}