結果
問題 | No.75 回数の期待値の問題 |
ユーザー |
|
提出日時 | 2020-09-14 09:26:56 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 256 ms / 5,000 ms |
コード長 | 22,940 bytes |
コンパイル時間 | 1,959 ms |
コンパイル使用メモリ | 138,768 KB |
実行使用メモリ | 51,532 KB |
最終ジャッジ日時 | 2024-06-22 00:38:01 |
合計ジャッジ時間 | 7,642 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 16 |
ソースコード
#include <stdio.h>#include <sstream>#include <string.h>#include <vector>#include <map>#include <algorithm>#include <utility>#include <set>#include <cctype>#include <queue>#include <stack>#include <cstdio>#include <cstdlib>#include <cmath>#include <deque>#include <limits>#include <iomanip>#include <ctype.h>#include <unordered_map>#include <random>#include <numeric>#include <iostream>#include <array>#define _USE_MATH_DEFINES#include <iostream>#include <math.h>#include <bitset>using namespace std;typedef long long ll;typedef pair<int, int> pii;typedef pair<ll, ll> pll;typedef pair<ll, double> pld;typedef pair<double, double> pdd;typedef pair<double, ll> pdl;typedef pair<int, char> pic;typedef vector<ll> vl;typedef vector<int> vi;typedef priority_queue<ll, vector<ll>, greater<ll>> llgreaterq;typedef priority_queue<pll, vector<pll>, greater<pll>> pllgreaterq;typedef priority_queue<pair<ll, pll>, vector<pair<ll, pll>>, greater<pair<ll, pll>>> plpllgreaterq;typedef priority_queue<vi, vector<vi>, greater<vi>> vigreaterq;typedef priority_queue<vl, vector<vl>, greater<vl >> vlgreaterq;template <class o, class p, class q>using tuple3q = priority_queue<tuple<o, p, q>, vector<tuple<o, p, q>>, greater<tuple<o, p, q>>>;template <class o, class p, class q, class r>using tuple4q = priority_queue<tuple<o, p, q, r>, vector<tuple<o, p, q, r>>, greater<tuple<o, p, q, r>>>;template <class o, class p, class q, class r, class s>using tuple5q = priority_queue<tuple<o, p, q, r, s>, vector<tuple<o, p, q, r, s>>, greater<tuple<o, p, q, r, s>>>;int dx[] = { -1,0,1,0 };int dy[] = { 0,-1,0,1 };#define bit(x,v) ((ll)x << v)#define rep(x,n) for(ll x = 0;x < n;x++)#define rep2(x,f,v) for(ll x=f;x<v;x++)#define repe(v,x) for(auto v : x)// 許容する誤差ε#define EPS (1e-10)// 2つのスカラーが等しいかどうか#define EQ(a,b) (std::abs(a-b) < EPS)// 2つのベクトルが等しいかどうか#define EQV(a,b) ( EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()) )#define all(a) a.begin(),a.end()#define all0(a) memset(a,0,sizeof(a))#define allm1(a) memset(a,-1,sizeof(a))#define put_float(v) cout << fixed << setprecision(10); \cout << v << endl#define put(v) cout << v << endl#define vinsert(v,p,x) v.insert(v.begin() + p,x)#define vsort(v) sort(all(v));#define vdesc(v) vsort(v); \reverse(all(v))#define dup(v) v.erase(unique(all(v)),v.end())#define ion(i,j) ((i & (1LL << j)) > 0)#define next(i) i++;i%=2#define Len size()#define ull unsignd long long#define psp(a,b) push_back(make_pair(a,b))#define psp2(a,b) push(make_pair(a,b))#define cini(a) a; cin >> a#define infa(a,b) (a + b) % INF#define infm(a,b) (a * b) % INF#define infd(a,b) (a * INFinv(b)) % INF#define infs(a,b) (a + INF - b) % INF#define inf(a) (a) %= INF#define inff(a) ((a) % INF)#define No cout << "No" << endl#define Yes cout << "Yes" << endl#define NO cout << "NO" << endl#define YES cout << "YES" << endl#define smal -INF*INF#define big INF*INFll INF = 1000000007;const int MAX = 2000010;long long fac[MAX], finv[MAX], inv[MAX];void COMinit() {fac[0] = fac[1] = 1;finv[0] = finv[1] = 1;inv[1] = 1;for (int i = 2; i < MAX; i++) {fac[i] = fac[i - 1] * i % INF;inv[i] = INF - inv[INF % i] * (INF / i) % INF;finv[i] = finv[i - 1] * inv[i] % INF;}}// 二項係数計算long long COM(int n, int k) {if (n < k) return 0;if (n < 0 || k < 0) return 0;return fac[n] * (finv[k] * finv[n - k] % INF) % INF;}ll getpow(ll b, ll x, ll md) {ll t = b;ll res = 1;while (x > 0){if (x & 1) {res *= t;res %= md;}x >>= 1;t *= t;t %= md;}return res % md;}ll getpow(ll b, ll x) {return getpow(b, x, INF);}ll modinv(ll x) {return getpow(x, INF - 2);}ll gcd(ll a, ll b) {if (b == 0) return a;return gcd(b, a % b);}class mint {int md = 1000000007;public:long long x;mint(ll x, ll md) {this->md = md;this->x = (x % md + md) % md;}mint(long long x = 0) : x((x% md + md) % md) {}mint operator-() const {return mint(-x);}mint& operator+=(const mint& a) {if ((x += a.x) >= md) x -= md;return *this;}mint& operator-=(const mint& a) {if ((x += md - a.x) >= md) x -= md;return *this;}mint& operator*=(const mint& a) {(x *= a.x) %= md;return *this;}mint operator+(const mint& a) const {mint res(*this);return res += a;}mint operator-(const mint& a) const {mint res(*this);return res -= a;}mint operator*(const mint& a) const {mint res(*this);return res *= a;}mint pow(ll t) const {if (!t) return 1;mint a = pow(t >> 1);a *= a;if (t & 1) a *= *this;return a;}// for prime INFmint inv() const {return pow(md - 2);}mint& operator/=(const mint& a) {return (*this) *= a.inv();}mint operator/(const mint& a) const {mint res(*this);return res /= a;}friend ostream& operator<<(ostream& os, const mint& m) {os << m.x;return os;}};int pr[200010];int lank[200010];void uini(int n) {for (size_t i = 0; i <= n; i++){pr[i] = i;lank[i] = 1;}}int parent(int x) {if (x == pr[x]) return x;return pr[x] = parent(pr[x]);}int same(int x, int y) {return parent(x) == parent(y);}bool unit(int x, int y) {int px = parent(x);int py = parent(y);if (px == py) return false;if (lank[py] < lank[px]) {pr[py] = px;lank[px] += lank[py];}else {pr[px] = py;lank[py] += lank[px];}return true;}ll n, m;int ci = 0;struct Node {int key;int priority;Node* parent, * left, * right;Node(int key, int priority);Node() {}};Node NIL;Node::Node(int key, int priority) : key(key), priority(priority) {left = &NIL;right = &NIL;}Node* root = new Node();void cenrec(Node* k) {if (k->key == NIL.key) return;cenrec(k->left);cout << " " << k->key;cenrec(k->right);}void fastrec(Node* k){if (k->key == NIL.key) return;cout << " " << k->key;fastrec(k->left);fastrec(k->right);}void insert(Node* v) {Node* y = &NIL;Node* x = root;while (x->key != NIL.key){y = x;if (v->key < x->key) {x = x->left;}else {x = x->right;}}v->parent = y;if (y->key == NIL.key) {root = v;}else if (v->key < y->key) {y->left = v;}else {y->right = v;}}Node* find(Node* k, ll v){if (k->key == NIL.key) return &NIL;if (k->key == v) return k;if (v < k->key) return find(k->left, v);return find(k->right, v);}void delp12(Node* x) {if (x->key == NIL.key) return;Node* l = x->left;Node* r = x->right;Node* pr = x->parent;if (l->key == NIL.key&& r->key == NIL.key) {if (pr->left == x) {pr->left = &NIL;}else pr->right = &NIL;}else if (l->key != NIL.key) {if (pr->left == x) {pr->left = l;}else pr->right = l;l->parent = pr;}else if (r->key != NIL.key) {if (pr->left == x) {pr->left = r;}else pr->right = r;r->parent = pr;}}Node* get_next(Node* k) {if (k->key == NIL.key) return &NIL;Node* res = get_next(k->left);if (res->key != NIL.key) return res;return k;}void del(Node* x) {if (x->key == NIL.key) return;Node* l = x->left;Node* r = x->right;Node* pr = x->parent;if (l->key != NIL.key && r->key != NIL.key) {Node* nex = get_next(r);x->key = nex->key;delp12(nex);}else {delp12(x);}}Node* rightRotate(Node* t) {Node* s = t->left;t->left = s->right;s->right = t;return s;}Node* leftRotate(Node* t) {Node* s = t->right;t->right = s->left;s->left = t;return s;}Node* _insert(Node* t, int key, int priority) {if (t->key == NIL.key) {return new Node(key, priority);}if (key == t->key) {return t;}if (key < t->key) {t->left = _insert(t->left, key, priority);if (t->priority < t->left->priority) {t = rightRotate(t);}}else {t->right = _insert(t->right, key, priority);if (t->priority < t->right->priority) {t = leftRotate(t);}}return t;}Node* delete1(Node* t, int key);Node* _delete(Node* t, int key) {if (t->left->key == NIL.key && t->right->key == NIL.key) {return &NIL;}else if (t->left->key == NIL.key) {t = leftRotate(t);}else if (t->right->key == NIL.key) {t = rightRotate(t);}else{if (t->left->priority > t->right->priority) {t = rightRotate(t);}elset = leftRotate(t);}return delete1(t, key);}Node* delete1(Node* t, int key) {if (t->key == NIL.key) {return &NIL;}if (key < t->key) {t->left = delete1(t->left, key);}else if (key > t->key) {t->right = delete1(t->right, key);}else return _delete(t, key);return t;}int H;int left(int i) {return i * 2 + 1;}int right(int i) {return i * 2 + 2;}class edge {public:int from, to, i;ll val;edge() {}edge(ll to) : to(to) {}edge(ll to, ll i) : to(to), i(i) {}edge(ll from, ll to, ll val) : from(from), to(to), val(val) {}};class LCA {private:vector<vector<edge>> v;vector<vector<int>> parent;vector<int> depth;void dfs(int n, int m, int d) {parent[0][n] = m;depth[n] = d;for (auto x : v[n]) {if (x.to != m) dfs(x.to, n, d + 1);}}public:LCA(ll N, ll root, vector<vector<edge>>& tree) {v = tree;parent = vector<vector<int>>(21, vector<int>(N + 1, 0));depth = vector<int>(N + 1, 0);dfs(root, -1, 0);for (int j = 0; j + 1 < 20; j++) {for (int i = 1; i <= N; i++) {if (parent[j][i] < 0) parent[j + 1][i] = -1;else parent[j + 1][i] = parent[j][parent[j][i]];}}}int lca(int n, int m) {if (depth[n] > depth[m]) swap(n, m);for (int j = 0; j < 20; j++) {if ((depth[m] - depth[n]) >> j & 1) m = parent[j][m];}if (n == m) return n;for (int j = 19; j >= 0; j--) {if (parent[j][n] != parent[j][m]) {n = parent[j][n];m = parent[j][m];}}return parent[0][n];}int dep(int n) { return depth[n]; }};ll k;int _rank[1010];int temp[1010];bool compare_sa(int i, int j) {if (_rank[i] != _rank[j]) return _rank[i] < _rank[j];else {int ri = i + k <= n ? _rank[i + k] : -1;int rj = j + k <= n ? _rank[j + k] : -1;return ri < rj;}}void construct_sa(string S, int* sa) {n = S.length();for (size_t i = 0; i <= n; i++){sa[i] = i;_rank[i] = i < n ? S[i] : -1;}for (k = 1; k <= n; k *= 2){sort(sa, sa + n + 1, compare_sa);// saはソート後の接尾辞の並びになっている、rankは元の位置のindexを保持したまま、更新されている。// ピンとこなかった部分temp[sa[0]] = 0;for (size_t i = 1; i <= n; i++){temp[sa[i]] = temp[sa[i - 1]] + (compare_sa(sa[i - 1], sa[i]) ? 1 : 0);}for (size_t i = 0; i <= n; i++){_rank[i] = temp[i];}}}bool contain(string S, int* sa, string T) {int a = 0, b = S.length();// sa は 接尾辞が辞書順に並んでいる、入っているのはその位置のインデックスwhile (b - a > 1) {int c = (a + b) / 2;if (S.compare(sa[c], T.length(), T) < 0) a = c;else b = c;}return S.compare(sa[b], T.length(), T) == 0;}#define bit(x,v) ((ll)x << v)class BIT {static const int MAX_N = 500010;public:BIT() { memset(bit, 0, sizeof(bit)); }ll bit[MAX_N + 1], n;ll sum(int i) {ll s = 0;while (i > 0){s += bit[i];i -= i & -i;}return s;}void add(int i, int x) {while (i <= n){bit[i] += x;i += i & -i;}}};struct UnionFind {vector<int> A;UnionFind(int n) : A(n, -1) {}int find(int x) {if (A[x] < 0) return x;return A[x] = find(A[x]);}void unite(int x, int y) {x = find(x), y = find(y);if (x == y) return;if (A[x] > A[y]) swap(x, y);A[x] += A[y];A[y] = x;}int ngroups() {int ans = 0;for (auto a : A) if (a < 0) ans++;return ans;}};vector<ll> getp(ll n) {vector<ll> res;ll a = 2;if (n % 2 == 0) {res.push_back(2);while (n % 2 == 0)n /= 2;}for (ll i = 3; i * i <= n; i += 2){if (n % i == 0) {res.push_back(i);while (n % i == 0)n /= i;}}if (n != 1) res.push_back(n);return res;}vector<ll> getp2(ll n) {vector<ll> res;ll a = 2;if (n % 2 == 0) {while (n % 2 == 0) { n /= 2; res.push_back(2); }}for (ll i = 3; i * i <= n; i += 2){if (n % i == 0) {while (n % i == 0) { n /= i; res.push_back(i); }}}if (n != 1) res.push_back(n);return res;}vector<pll> getp3(ll n) {vector<pll> res;ll a = 2;int si = 0;if (n % 2 == 0) {res.push_back(make_pair(2, 0));while (n % 2 == 0) { n /= 2; res[si].second++; }si++;}for (ll i = 3; i * i <= n; i += 2){if (n % i == 0) {res.push_back(make_pair(i, 0));while (n % i == 0) { n /= i; res[si].second++; }si++;}}if (n != 1) { res.push_back(make_pair(n, 1)); }return res;}vector<ll> getDivisors(ll n) {vector<ll> res;ll a = 2;res.push_back(1);for (ll i = 2; i * i <= n; i++){if (n % i == 0) {res.push_back(i);if (n / i != i)res.push_back(n / i);}}return res;}struct ve {public:vector<ve> child;int _t = INF;ve(int t) :_t(t) {}ve(ve _left, ve _right) {_t = _left._t + _right._t;child.push_back(_left);child.push_back(_right);}bool operator<(const ve& t) const {return _t > t._t;}};vector<bool> elas(ll n) {vector<bool> r(n);fill(r.begin(), r.end(), 1);r[0] = 0;r[1] = 0;for (ll i = 2; i * i < n; i++){if (!r[i]) continue;ll ti = i * 2;while (ti < n){r[ti] = false;ti += i;}}return r;}bool isPrime(ll v) {for (ll i = 2; i * i <= v; i++){if (v % i == 0) return false;}return true;}class SegTree {public:const static int MAX_N = 100010;const static int DAT_SIZE = (1 << 18) - 1;int N, Q;int A[MAX_N];ll data[DAT_SIZE], datb[DAT_SIZE];void init(int _n) {N = 1;while (N < _n) N <<= 1;memset(data, 0, sizeof(data));memset(datb, 0, sizeof(datb));}void init(int _n, ll iv) {N = 1;while (N < _n) N <<= 1;rep(i, DAT_SIZE) {data[i] = iv;datb[i] = iv;}}void add(int a, int b, int x) {add(a, b + 1, x, 0, 0, N);}void add(int a, int b, int x, int k, int l, int r) {if (a <= l && r <= b) {data[k] += x;}else if (l < b && a < r) {datb[k] += (min(b, r) - max(a, l)) * x;add(a, b, x, k * 2 + 1, l, (l + r) / 2);add(a, b, x, k * 2 + 2, (l + r) / 2, r);}}void change(int a, int b, int x) {change(a, b + 1, x, 0, 0, N);}void change(int a, int b, int x, int k, int l, int r) {if (a <= l && r <= b) {data[k] = x;}else if (l < b && a < r) {datb[k] = x;change(a, b, x, k * 2 + 1, l, (l + r) / 2);change(a, b, x, k * 2 + 2, (l + r) / 2, r);}}ll sum(int a, int b) {return sum(a, b + 1, 0, 0, N);}ll sum(int a, int b, int k, int l, int r) {if (b <= l || r <= a) {return 0;}if (a <= l && r <= b) {return data[k] * (r - l) + datb[k];}ll res = (min(b, r) - max(a, l)) * data[k];res += sum(a, b, k * 2 + 1, l, (l + r) / 2);res += sum(a, b, k * 2 + 2, (l + r) / 2, r);return res;}};class Segment;class Circle;class Point {public:double x, y;Point(double x = 0, double y = 0) :x(x), y(y) {}Point operator + (Point p) { return Point(x + p.x, y + p.y); }Point operator - (Point p) { return Point(x - p.x, y - p.y); }Point operator * (double a) { return Point(a * x, a * y); }Point operator / (double a) { return Point(x / a, y / a); }double abs() { return sqrt(norm()); }double norm() { return x * x + y * y; }bool operator < (const Point& p)const {return x != p.x ? x < p.x : y < p.y;}bool operator == (const Point& p) const {return fabs(x - p.x) < EPS && fabs(y - p.y) < EPS;}static double dot(Point a, Point b) {return a.x * b.x + a.y * b.y;}static double cross(Point a, Point b) {return a.x * b.y - a.y * b.x;}static bool isOrthogonal(Point a, Point b) {return EQ(dot(a, b), 0.0);}static bool isOrthogonal(Point a1, Point a2, Point b1, Point b2) {return isOrthogonal(a1 - a2, b1 - b2);}static bool isOrthogonal(Segment s1, Segment s2);static bool isPalallel(Point a, Point b) {return EQ(cross(a, b), 0.0);}static bool isPalallel(Point a1, Point a2, Point b1, Point b2) {return isPalallel(a1 - a2, b1 - b2);}static bool isPalallel(Segment s1, Segment s2);static const int COUNTER_CLOCKWISE = 1;static const int CLOCKWISE = -1;static const int ONLINE_BACK = 2;static const int ONLINE_FRONT = -2;static const int ON_SEGMENT = 0;static int ccw(Point p0, Point p1, Point p2) {// 線分はp0とp1でp2がどこにあるかを探るPoint a = p1 - p0;Point b = p2 - p0;if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;if (cross(a, b) < -EPS) return CLOCKWISE;if (dot(a, b) < -EPS) return ONLINE_BACK;if (a.norm() < b.norm()) return ONLINE_FRONT;return ON_SEGMENT;}static bool intersect(Point p1, Point p2, Point p3, Point p4) {return (ccw(p1, p2, p3) * ccw(p1, p2, p4) <= 0&& ccw(p3, p4, p1) * ccw(p3, p4, p2) <= 0);}static bool intersect(Segment s1, Segment s2);static Point project(Segment s, Point p);static Point reflect(Segment s, Point p);static Point getDistance(Point a, Point b) {return (a - b).abs();}static double getDistanceLP(Segment s, Point p);static double getDistanceSP(Segment s, Point p);static double getDistance(Segment s1, Segment s2);static Point getIntersection(Segment s1, Segment s2);static pair<Point, Point> crossPoints(Circle c, Segment s);static int contains(vector<Point> g, Point p) {int n = g.size();bool x = false;rep(i, n) {Point a = g[i] - p, b = g[(i + 1) % n] - p;// 線の上に載っているかif (std::abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;// pを基準として上下にあるか// または外積が正か?(→にあるか)if (a.y > b.y) swap(a, b);if (a.y < EPS && EPS < b.y && cross(a, b) > EPS) x = !x;}return x ? 2 : 0;}static vector<Point> andrewScan(vector<Point> s) {vector<Point> u, l;if (s.size() < 3) return s;sort(all(s));u.push_back(s[0]);u.push_back(s[1]);l.push_back(s[s.size() - 1]);l.push_back(s[s.size() - 2]);for (int i = 2; i < s.size(); i++) {for (int _n = u.size(); _n >= 2 && ccw(u[_n - 2], u[_n - 1], s[i]) > CLOCKWISE; _n--) {u.pop_back();}u.push_back(s[i]);}for (int i = s.size() - 3; i >= 0; i--) {for (int _n = l.size(); _n >= 2 && ccw(l[_n - 2], l[_n - 1], s[i]) > CLOCKWISE; _n--) {l.pop_back();}l.push_back(s[i]);}reverse(all(l));for (int i = u.size() - 2; i >= 1; i--){l.push_back(u[i]);}return l;}void get_cin() {cin >> x >> y;}};class Segment {public:Point p1, p2;Segment() {}Segment(Point p1, Point p2) :p1(p1), p2(p2) {}void get_cin() {cin >> p1.x >> p1.y >> p2.x >> p2.y;}Point p1tp2() {return p2 - p1;}Point p2tp1() {return p1 - p2;}double abs() {return std::abs(norm());}double norm() {return (p2 - p1).norm();}};bool Point::isOrthogonal(Segment s1, Segment s2) {return EQ(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);}bool Point::isPalallel(Segment s1, Segment s2) {return EQ(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0);}bool Point::intersect(Segment s1, Segment s2) {return intersect(s1.p1, s1.p2, s2.p1, s2.p2);}Point Point::project(Segment s, Point p) {Point base = s.p2 - s.p1;double r = Point::dot(p - s.p1, base) / base.norm();return s.p1 + base * r;}Point Point::reflect(Segment s, Point p) {return (project(s, p) * 2) - p;}double Point::getDistanceLP(Segment s, Point p) {return std::abs(cross(s.p2 - s.p1, p - s.p1) / (s.p2 - s.p1).abs());}double Point::getDistanceSP(Segment s, Point p) {if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return (p - s.p1).abs();if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return (p - s.p2).abs();return getDistanceLP(s, p);}double Point::getDistance(Segment s1, Segment s2) {if (intersect(s1, s2)) return 0.0;return min({ getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2),getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2) });}Point Point::getIntersection(Segment s1, Segment s2) {// (s1.p1 - s2.p1).norm()auto bs = s1.p2 - s1.p1;auto n1 = s2.p1 - s1.p1;auto n2 = s2.p2 - s1.p1;auto c1 = std::abs(cross(n1, bs)) / bs.norm();auto c2 = std::abs(cross(n2, bs)) / bs.norm();return s2.p1 + (s2.p2 - s2.p1) * (c1 / (c1 + c2));// c1:c2=t:1-t// c2t=(1-t)c1// t/(1-t)=c1/(c1+c2)//}double arg(Point p) { return atan2(p.y, p.x); }Point polar(double a, double r) { return Point(cos(r) * a, sin(r) * a); }class Circle {public:Point c;double r;Circle(Point c = Point(), double r = 0.0) : c(c), r(r) {}void get_cin() {cin >> c.x >> c.y >> r;}static pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {double d = (c1.c - c2.c).abs(); // 中心点どうしの距離double a = acos((c1.r * c1.r + d * d - c2.r * c2.r) / (2 * c1.r * d));double t = arg(c2.c - c1.c);return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));}};pair<Point, Point> Point::crossPoints(Circle c, Segment s) {auto pp = project(s, c.c);auto f = (pp - c.c).norm();auto mu = sqrt(c.r * c.r - f);auto e = s.p1tp2() / s.p1tp2().abs();return make_pair(pp + e * mu, pp - e * mu);}ll divRm(string s, ll x) {ll r = 0;for (ll i = 0; i < s.size(); i++){r *= 10;r += s[i] - '0';r %= x;}return r;}ll cmbi(ll x, ll b) {ll res = 1;for (size_t i = 0; i < b; i++){res *= x - i;res %= INF;res *= inv[b - i];res %= INF;}return res;}ll digsum(ll x) {ll res = 0;while (x > 0){res += x % 10;x /= 10;}return res;}bool check_parindrome(string s) {int n = s.size();rep(i, n / 2) {if (s[i] != s[n - i - 1]) {return false;}}return true;}ll npr(ll n, ll r) {if (r == 0)return 1;return inff(fac[n] * modinv(fac[n - r]));}vl zalgo(string s) {ll c = 0;vl a(s.size());ll si = s.size();rep2(i, 1, s.size()) {if (i + a[i - c] < c + a[c]){a[i] = a[i - c];}else {ll j = max(0LL, a[c] - (i - c));while (i + j < si && s[j] == s[i + j]){j++;}a[i] = j;c = i;}}a[0] = s.size();return a;}string decStrNum(string s) {ll si = s.size();for (int i = si - 1; i >= 0; i--){if (s[i] == '0') {s[i] = '9';continue;}s[i] = s[i] - 1;break;}return s;}// ここまでライブラリ// ここからコードvoid solv() {cin >> n;double hi = 201;double lo = 0;while (hi-lo>EPS){double md = (hi + lo) / 2;double dp[201]; all0(dp);rep2(i, 1, n + 1) {dp[i] = 1;rep2(j, 1, 7) {if (i < j) {dp[i] += md / 6.0;}else {dp[i] += dp[i - j] / 6.0;}}}if (md > dp[n]) {hi = md;}else {lo = md;}}put_float(lo);}int main(){COMinit();solv();return 0;}