結果

問題 No.2179 Planet Traveler
ユーザー 👑 bo9chanbo9chan
提出日時 2023-01-06 23:22:50
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 164 ms / 3,000 ms
コード長 22,782 bytes
コンパイル時間 2,027 ms
コンパイル使用メモリ 161,024 KB
実行使用メモリ 18,524 KB
最終ジャッジ日時 2024-05-07 23:14:08
合計ジャッジ時間 4,429 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,940 KB
testcase_03 AC 1 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,944 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 19 ms
16,768 KB
testcase_12 AC 144 ms
16,384 KB
testcase_13 AC 151 ms
16,896 KB
testcase_14 AC 18 ms
16,896 KB
testcase_15 AC 17 ms
16,896 KB
testcase_16 AC 18 ms
16,896 KB
testcase_17 AC 164 ms
18,524 KB
testcase_18 AC 147 ms
17,496 KB
testcase_19 AC 160 ms
18,524 KB
testcase_20 AC 22 ms
6,944 KB
testcase_21 AC 139 ms
16,972 KB
testcase_22 AC 94 ms
12,976 KB
testcase_23 AC 90 ms
13,144 KB
testcase_24 AC 132 ms
16,904 KB
testcase_25 AC 100 ms
13,312 KB
testcase_26 AC 142 ms
17,512 KB
testcase_27 AC 25 ms
6,940 KB
testcase_28 AC 69 ms
11,008 KB
testcase_29 AC 135 ms
16,776 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#ifdef __LOCAL
#include <mytemplate.hpp>  // プリコンパイル済みヘッダ ~/local/include/mytemplate.hpp.gch
#else
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream> 
#include <iterator>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#endif
using namespace std;
// #include <boost/multiprecision/cpp_int.hpp>
// using bint = boost::multiprecision::cpp_int;
using int128 = __int128_t;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vd = vector<double>;
using vvd = vector<vd>;
using vc = vector<char>;
using vvc = vector<vc>;
using pll = pair<ll, ll>;
#define REP1(i, n) REP3(i, 0, n, 1)
#define REP2(i, s, n) REP3(i, s, n, 1)
#define REP3(i, s, n, d) for(ll i = (ll)(s); i < (ll)(n); i += (d))
#define REP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define rep(...) REP_OVERLOAD(__VA_ARGS__, REP3, REP2, REP1)(__VA_ARGS__)
#define DEP1(i, n) DEP3(i, n, -1, 1)
#define DEP2(i, n, s) DEP3(i, n, s, 1)
#define DEP3(i, n, s, d) for(ll i = (ll)(n); (ll)(s) < i; i -= (d))
#define DEP_OVERLOAD(e1, e2, e3, e4, NAME,...) NAME
#define dep(...) DEP_OVERLOAD(__VA_ARGS__, DEP3, DEP2, DEP1)(__VA_ARGS__)
#define fore(e, a) for (auto&& e: (a))
#define len(a) (ll)(a).size()
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define th third
#define sqrt(x) sqrtl(x)
#define popcount(b) __builtin_popcountll(b)
#define Bit(b, i) (((b) >> (i)) & 1)
#define End(...) do{ print(__VA_ARGS__); exit(0); }while(0)
/*********    C O N S T A N T    **********/
constexpr ll INF = LONG_LONG_MAX / 2 - 10000LL;  // 4,611,686,018,427,377,903  ~= 4.6e+18, 19桁
const double PI = acos(-1);
/*********       P A I R       **********/
template<class T, class U> inline pair<T, U>& operator+=(pair<T, U>& a, const pair<T, U>& b) {a.fi += b.fi; a.se += b.se; return a;}
template<class T, class U> inline pair<T, U>& operator-=(pair<T, U>& a, const pair<T, U>& b) {a.fi -= b.fi; a.se -= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator*=(pair<T, U>& a, const pair<T, U>& b) {a.fi *= b.fi; a.se *= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator/=(pair<T, U>& a, const pair<T, U>& b) {a.fi /= b.fi; a.se /= b.se; return a;}
template<class T, class U> inline pair<T, U>& operator%=(pair<T, U>& a, const pair<T, U>& b) {a.fi %= b.fi; a.se %= b.se; return a;}
template<class T, class U, class V> inline pair<T, U>& operator+=(pair<T, U>& a, const V& b) {a.fi += b; a.se += b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator-=(pair<T, U>& a, const V& b) {a.fi -= b; a.se -= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator*=(pair<T, U>& a, const V& b) {a.fi *= b; a.se *= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator/=(pair<T, U>& a, const V& b) {a.fi /= b; a.se /= b; return a;}
template<class T, class U, class V> inline pair<T, U>& operator%=(pair<T, U>& a, const V& b) {a.fi %= b; a.se %= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator+(pair<T, U> a, const V& b) {a += b; return a;}
template<class T, class U, class V> inline pair<T, U> operator-(pair<T, U> a, const V& b) {a -= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator*(pair<T, U> a, const V& b) {a *= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator/(pair<T, U> a, const V& b) {a /= b; return a;}
template<class T, class U, class V> inline pair<T, U> operator%(pair<T, U> a, const V& b) {a %= b; return a;}
template<class T, class U> inline pair<T, U> operator+(pair<T, U> a) {return a;}
template<class T, class U> inline pair<T, U> operator-(pair<T, U> a) {return a * (-1);}
template<class T, class U> istream& operator >>(istream& stream, pair<T, U>& a) {stream >> a.fi >> a.se; return stream;}
template<class T, class U> ostream& operator <<(ostream &stream, const pair<T, U>& a) { stream << a.fi << " " << a.se; return stream; }
/*********       V E C T O R      **********/
template<class T> inline vector<T>& operator+=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] += b[i]; return a;}
template<class T> inline vector<T>& operator-=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] -= b[i]; return a;}
template<class T> inline vector<T>& operator*=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] *= b[i]; return a;}
template<class T> inline vector<T>& operator/=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] /= b[i]; return a;}
template<class T> inline vector<T>& operator%=(vector<T>& a, const vector<T>& b) {assert(a.size() == b.size()); rep(i, 0, a.size()) a[i] %= b[i]; return a;}
template<class T, class U> inline vector<T>& operator+=(vector<T>& a, const U& b) {fore(e, a) e += b; return a;}
template<class T, class U> inline vector<T>& operator-=(vector<T>& a, const U& b) {fore(e, a) e -= b; return a;}
template<class T, class U> inline vector<T>& operator*=(vector<T>& a, const U& b) {fore(e, a) e *= b; return a;}
template<class T, class U> inline vector<T>& operator/=(vector<T>& a, const U& b) {fore(e, a) e /= b; return a;}
template<class T, class U> inline vector<T>& operator%=(vector<T>& a, const U& b) {fore(e, a) e %= b; return a;}
template<class T, class U> inline vector<T> operator+(vector<T> a, const U& b) {a += b; return a;}
template<class T, class U> inline vector<T> operator-(vector<T> a, const U& b) {a -= b; return a;}
template<class T, class U> inline vector<T> operator*(vector<T> a, const U& b) {a *= b; return a;}
template<class T, class U> inline vector<T> operator/(vector<T> a, const U& b) {a /= b; return a;}
template<class T, class U> inline vector<T> operator%(vector<T> a, const U& b) {a %= b; return a;}
template<class T> inline vector<T> operator+(vector<T> a) {return a;}
template<class T> inline vector<T> operator-(vector<T> a) {return a * (-1);}
template<class T> istream& operator >>(istream& stream, vector<T>& a) {fore(e, a) stream >> e; return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<T>& v) {if(v.size()){stream << v[0]; rep(i, 1, v.size()) cout << " " << v[i];} return stream;}
template<class T> ostream& operator <<(ostream& stream, const vector<vector<T>>& vv) {if(vv.size()){stream << vv[0]; rep(i, 1, vv.size()) cout << '\n' << vv[i];} return stream;}
template<class T> inline T Sum(const vector<T>& v) {return reduce(all(v));}  // v.size() == 0 のとき T() を返す
template<class T> inline T Max(const vector<T>& v) {assert(v.size()); return *max_element(all(v));}
template<class T> inline T Min(const vector<T>& v) {assert(v.size()); return *min_element(all(v));}
template<class T> inline ll Argmax(const vector<T>& v) {assert(v.size()); return max_element(all(v)) - v.begin();}
template<class T> inline ll Argmin(const vector<T>& v) {assert(v.size()); return min_element(all(v)) - v.begin();}
template<class T, class U> inline bool Contains(const vector<T>& v, const U& a) {return find(all(v), a) != v.end();}
template<class T, class U> vector<T> make_vector(int n, U v) { return vector<T>(n, v); }
template <class T, class... Args> auto make_vector(int n, Args... args) {auto val = make_vector<T>(args...); return make_vector<decltype(val)>(n, move(val));}
/*********        S E T        **********/
template<class T> istream& operator >>(istream& stream, set<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const set<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
template<class T> inline T Max(const set<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const set<T>& st) {assert(st.size()); return *st.begin();}
template<class T> inline bool Contains(const set<T>& st, T x) {return st.find(x) != st.end();}
/*********   M U L T I S E T   **********/
template<class T> istream& operator >>(istream& stream, multiset<T>& st) {T e; stream >> e; st.insert(e); return stream;}
template<class T> ostream& operator <<(ostream& stream, const multiset<T>& st) {if(st.size()){auto it=st.begin(); stream << *it++; for(; it!=st.end(); it++) cout << " " << *it;} return stream;}
template<class T> inline T Max(const multiset<T>& st) {assert(st.size()); return *prev(st.end());}
template<class T> inline T Min(const multiset<T>& st) {assert(st.size()); return *st.begin();}
template<class T> inline bool Contains(const multiset<T>& st, T x) {return st.find(x) != st.end();}
template<class T> inline bool EraseOne(multiset<T>& st, T x) {auto it=st.find(x); if (it!=st.end()) {st.erase(it); return true;} else return false;}  // 要素xを1つ削除. 消せたらtrueを返す.
/*********     S T R I N G     **********/
template<class T> inline bool Contains(const string& s, const T& c) {return s.find(c) != string::npos;}  // cはchar, string共に可
inline string ToUpper(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::toupper); return t; }
inline string ToLower(const string& s) {string t; t.resize(s.size()); std::transform(all(s), t.begin(), ::tolower); return t; }
/*********       T R I O       **********/
template<class T1, class T2, class T3> struct trio {
    T1 first; T2 second; T3 third;
    // コンストラクタ・代入演算子
    trio() {first=T1(); second=T2(); third=T3();}
    trio(const T1& x) : first(x), second(x), third(x) {}
    trio(const T1& x, const T2& y, const T3& z) : first(x), second(y), third(z) {}
    trio(const trio& t) {first=t.first; second=t.second; third=t.third;}  // コピーコンストラクタ
    trio& operator =(const trio& t) {first=t.first; second=t.second; third=t.third; return *this;}
    // 比較演算子
    bool operator <(const trio& t) const {return tie(first, second, third) < tie(t.first, t.second, t.third);}
    bool operator ==(const trio& t) const {return tie(first, second, third) == tie(t.first, t.second, t.third);}
    bool operator !=(const trio& other) const { return !(*this == other); }
    bool operator >(const trio& other) const { return other < *this; }
    bool operator <=(const trio& other) const { return !(*this > other); }
    bool operator >=(const trio& other) const { return !(*this < other); }
    // 単項演算子（+ -）
    trio operator +() const { return *this; }
    trio operator -() const { return (-1) * (*this); }
    // 複合代入演算子
    trio& operator +=(const trio& t) {first += t.first; second += t.second; third += t.third; return *this;}
    trio& operator -=(const trio& t) {first -= t.first; second -= t.second; third -= t.third; return *this;}
    trio& operator *=(const trio& t) {first *= t.first; second *= t.second; third *= t.third; return *this;}
    trio& operator /=(const trio& t) {first /= t.first; second /= t.second; third /= t.third; return *this;}
    trio& operator %=(const trio& t) {first %= t.first; second %= t.second; third %= t.third; return *this;}
    // 算術演算子
    friend trio operator +(const trio& lhs, const trio& rhs) {return trio(lhs) += rhs;}
    friend trio operator -(const trio& lhs, const trio& rhs) {return trio(lhs) -= rhs;}
    friend trio operator *(const trio& lhs, const trio& rhs) {return trio(lhs) *= rhs;}
    friend trio operator /(const trio& lhs, const trio& rhs) {return trio(lhs) /= rhs;}
    friend trio operator %(const trio& lhs, const trio& rhs) {return trio(lhs) %= rhs;}
    // 入出力
    friend istream& operator >>(istream &stream, trio& t) {return stream >> t.first >> t.second >> t.third;}
    friend ostream& operator <<(ostream &stream, const trio& t) {return stream << t.first << " " << t.second << " " << t.third;}
};
using tll = trio<ll, ll, ll>;
/*********       P R I N T       **********/
template<class T> void print(const T& e) {cout << e << '\n';}
template<class H, class... T> void print(const H& h, const T&... t) {cout << h << ' '; print(t...);}
/*********       D E B U G       **********/
#ifdef __LOCAL
#define debug(...) if(DEBUG) do{cout << '[' << #__VA_ARGS__ << "] ";debug_(__VA_ARGS__);}while(0)
#else
#define debug(...)
#endif
void dbg_(const long long& e) {if (e == INF) cout << "INF"; else if (e == -INF) cout << "-INF"; else cout << e;}
template<class T> void dbg_(const T& e) {cout << e;}
template<class T, class U> void dbg_(const pair<T, U>& p) {cout << '('; dbg_(p.first); cout << ' '; dbg_(p.second); cout << ')';}
template<class T1, class T2, class T3> void dbg_(const trio<T1, T2, T3>& t) {cout << '('; dbg_(t.first); cout << ' '; dbg_(t.second); cout << ' '; dbg_(t.third); cout << ')';}
template<class T> void debug_(const T& e) {dbg_(e); cout << '\n';}
template<class T> void debug_(const vector<T>& v) {if (v.size()){auto it=v.begin(); dbg_(*it++); for(; it!=v.end(); ++it){cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<vector<T>>& vv) {cout << '\n'; ll cnt=0; for(auto&& v : vv){cout << cnt++ << ": "; debug_(v);}}
template<class T, class U> void debug_(const map<T, U>& mp) {if (mp.size()) {auto it = mp.begin(); dbg_(*it++); for(; it != mp.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T, class U> void debug_(const vector<map<T, U>>& vm){cout << '\n'; ll cnt=0; for(auto&& mp : vm){cout << cnt++ << ": "; debug_(mp);}}
template<class T> void debug_(const set<T>& st) {if(st.size()){auto it=st.begin(); dbg_(*it++); for(; it!=st.end(); ++it) {cout << ' '; dbg_(*it);}}cout << '\n';}
template<class T> void debug_(const multiset<T>& st) {if(st.size()) {auto it=st.begin(); dbg_(*it++); for(; it != st.end(); ++it) {cout << ' '; dbg_(*it);}} cout << '\n';}
template<class T> void debug_(const vector<set<T>>& vs) {cout << '\n'; ll cnt=0; for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class T> void debug_(const vector<multiset<T>>& vs) {cout << '\n'; ll cnt=0;for(auto&& st : vs){cout << cnt++ << ": "; debug_(st);}}
template<class H, class... T> void debug_(const H& h, const T&... t) {dbg_(h); cout << ", "; debug_(t...);}
/*********       O T H E R S       **********/
template<class T, class U> inline bool chmin(T& a, U b) {if (a > b) {a = b; return true;} return false;}  // bは値渡し!
template<class T, class U> inline bool chmax(T& a, U b) {if (a < b) {a = b; return true;} return false;}
template<class T, class U> inline auto Mod(const T& a, const U& m) {return (a % m + m) % m;}  // 負もOK
template<class T, class U> inline auto Ceil(const T& x, const U& y) {return x < 0 ? x/y : (x + y - 1) / y;}  // 負もOK
template<class T, class U> inline auto Floor(const T& x, const U& y) {return -(Ceil(-x, y)); }  // 負もOK
template<class T> inline T Pow(T x, ll n) {assert(n >= 0); T ret = 1; while(1) {if (n % 2) ret *= x; n /= 2; if(!n) return ret; x = x * x;}}  // べき乗 mintもOK
template<class T> inline T Aseries(T a, T d, ll n) {assert(n >= 0); return a * n + n * (n - 1) / 2 * d;}  // 等差級数 mintもOK
template<class T> inline T Gseries(T a, T r, ll n) {assert(n >= 0); if (r == 1) return a * n; else return a * (1 - Pow(r, n)) / (1 - r);}  // 等比級数 mintもOK
template<class T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;
inline ll Mask(ll n) {assert(0 <= n && n < 63); return (1LL << n) - 1LL;}  // [0, n)のbitが立った64bit整数を返す。
inline ll Mask(ll n, ll m) {assert(n >= m); return Mask(n) ^ Mask(m);}  // [m, n)のbitが立った64bit整数を返す。
/*********       M  O  D       **********/
// #include <atcoder/modint>  // https://atcoder.github.io/ac-library/production/document_ja/
// using namespace atcoder;
// using mint = modint998244353;     // modint1000000007;
// istream& operator >>(istream& stream, mint& e) {ll n; stream >> n; e = n; return stream; }
// ostream& operator <<(ostream& stream, const mint& e) { stream << e.val(); return stream; }
// using vm = vector<mint>;
// using vvm = vector<vm>;
/***************************************/
constexpr bool DEBUG = false;



/**************　デ　カ　ル　ト　座　標　構　造　体　**************/
template<class T> struct Point {
    T x, y;
    // コンストラクタ・代入演算子
    Point() { x = T(); y = T(); }
    Point(const T& x_) : x(x_), y(x_) { }
    Point(const T& x_, const T& y_) : x(x_), y(y_) { }
    Point(const pair<T, T> p) : x(p.first), y(p.second) {}
    Point (const Point& p) { x = p.x; y = p.y; }  // コピーコンストラクタ
    Point& operator =(const Point& p) { x = p.x; y = p.y; return *this; }

    // 比較演算子（Pairと同じ）
    bool operator <(const Point& p) const { return tie(x, y) < tie(p.x, p.y); }
    bool operator ==(const Point& p) const { return tie(x, y) == tie(p.x, p.y); }
    bool operator !=(const Point& p) const { return !(*this == p); }
    bool operator >(const Point& p) const { return p < *this; }
    bool operator <=(const Point& p) const { return !(*this > p); }
    bool operator >=(const Point& p) const { return !(*this < p); }

    // 単項演算子（+ -）
    Point operator +() const { return *this; }
    Point operator -() const { return Point(-x, -y); }

    // 複合代入演算子
    Point& operator +=(const Point& p) { x += p.x; y += p.y; return *this; }
    Point& operator -=(const Point& p) { x -= p.x; y -= p.y; return *this; }
    Point& operator *=(const Point& p) { x *= p.x; y *= p.y; return *this; }
    Point& operator /=(const Point& p) { x /= p.x; y /= p.y; return *this; }
    Point& operator %=(const Point& p) { x %= p.x; y %= p.y; return *this; }

    // 算術演算子（+ - * /）
    friend Point operator +(const Point& lhs, const Point& rhs) { return Point(lhs) += rhs; }
    friend Point operator -(const Point& lhs, const Point& rhs) { return Point(lhs) -= rhs; }
    friend Point operator *(const Point& lhs, const Point& rhs) { return Point(lhs) *= rhs; }
    friend Point operator /(const Point& lhs, const Point& rhs) { return Point(lhs) /= rhs; }
    friend Point operator %(const Point& lhs, const Point& rhs) { return Point(lhs) %= rhs; }

    // // 二乗 (x^2, y^2)
    Point sq() const { return Point(x * x, y * y); }
    // 絶対値 (|x|, |y|)
    Point abs() const { return Point(std::abs(x), std::abs(y)); }
    // 大きさの二乗 x^2 + y^2
    T mag2() const { return x * x + y * y; }

    // // 入出力、型変換
    friend istream& operator >>(istream &stream, Point<T>& p) {return stream >> p.x >> p.y; }
    friend ostream& operator <<(ostream &stream, const Point<T>& p) {return stream << p.x << ' ' << p.y; }
    template<class U> operator pair<U, U>() const { pair<U, U> p{x, y}; return p; } 
};

// 内積 x1x2 + y1y2
template<class T> T Dot(const Point<T>& p1, const Point<T>& p2) { return p1.x * p2.x + p1.y * p2.y; }
// クロス積 x1y2 - x2y1
template<class T> T Cross(const Point<T>& p1, const Point<T>& p2) { return p1.x * p2.y - p2.x * p1.y; }
// 距離の二乗 (x2-x1)^2 + (y2-y1)^2
template<class T> T Dist2(const Point<T>& p1, const Point<T>& p2) { return (p2 - p1).mag2(); }

// ベクトルpに対してqのなす角θが 0° < θ < 90° を満たすか
template<class T> bool Acute(const Point<T>& p, const Point<T>& q) {return (Dot(p, q) > 0) && (Cross(p, q) > 0);}

// ベクトルpに対してqのなす角θが θ = 90° を満たすか
template<class T> bool Deg90(const Point<T>& p, const Point<T>& q) {return (Dot(p, q) == 0) && (Cross(p, q) > 0);}

// ベクトルのなす角のうち小さい方（2: 0°, 1: 鋭角, 0: 直角, -1:, 鈍角, -2: 180°）
template<class T> ll TypeOfAngle(const Point<T>& p1, const Point<T>& p2) {
    if (Dot(p1, p2) > 0) return Cross(p1, p2) == 0 ? 2 : 1;
    else if (Dot(p1, p2) == 0) return 0;
    else return Cross(p1, p2) == 0 ? -2 : -1;
}

// 偏角による比較関数. 原点(0, 0)は不可. Arg(p1) < Arg(p2)ならtrue.
template<class T> bool CompareByArg(const Point<T>& p1, const Point<T>& p2) {
    assert((p1.x != 0 || p1.y != 0) && (p2.x != 0 || p2.y != 0));
    if (Cross(p1, p2) == 0 && Dot(p1, p2) > 0) {
        // なす角が0°のとき、ソート結果を一意にするためベクトルの大きさで比較する
        return p1.mag2() < p2.mag2();
    } else {
        auto& [x1, y1] = p1;
        auto& [x2, y2] = p2;
        if (y1 == 0 && y2 == 0) return x1 > 0 && x2 < 0;  // p1が0°, p2が180°でtrue
        else if (y1 >= 0 && y2 < 0) return true;          // p1 <= 180° < p2
        else if (y1 < 0 && y2 >= 0) return false;         // p2 <= 180° < p1
        else return x1 * y2 > x2 * y1;                    // p1, p2 <= 180° or 180° < p1, p2
    }
}

// 凸多角形かどうか
template<class T> bool IsConvex(const vector<Point<T>>& vec) {
    ll n = vec.size();
    for(ll i = 0; i < n; i++) {
        ll j = (i + 1) % n;
        ll k = (i - 1 + n) % n;
        if (Cross(vec[j] - vec[i], vec[k] - vec[i]) <= 0) return false;
    }
    return true;
}

int main() {
    cin.tie(nullptr); cout << fixed << setprecision(10);
    
    ll N;
    cin >> N;
    vector<pair<Point<ll>, ll>> P(N);
    cin >> P;

    auto f = [](const Point<ll>& p1, const Point<ll>& p2, ll s) -> bool {
        return p1.mag2() + p2.mag2() - s <= 2 * sqrt(p1.mag2() * p2.mag2());
    };

    vector<vector<pll>> G(N);  // G[i] = {j, s}
    rep(i, N) {
        rep(j, i + 1, N) {
            auto& [p1, t1] = P[i];
            auto& [p2, t2] = P[j];
            if (t1 == t2) {
                ll s = Dist2(p1, p2);
                G[i].eb(j, s);
                G[j].eb(i, s);
            } else {
                ll l = -1;
                ll r = INF;
                while(r - l > 1) {
                    ll m = (l + r) / 2;
                    if (f(p1, p2, m)) r = m;
                    else l = m;
                }
                ll s = r;
                G[i].eb(j, s);
                G[j].eb(i, s);
            }
        }
    }
    debug(G);

    vl dist(N, INF);
    min_priority_queue<pll> que;  // (d, p)
    que.emplace(0, 0);
    dist[0] = 0;

    while(que.size()) {
        auto [d, p] = que.top();
        que.pop();
        if (dist[p] < d) continue;

        fore(e, G[p]) {
            auto [v, s] = e;
            if (chmin(dist[v], max(dist[p], s))) {
                que.emplace(dist[v], v);
            }
        }
    }
    debug(dist);
    print(dist[N - 1]);
}
0