#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define _USE_MATH_DEFINES #include #include using namespace std; #define rep(x,n) for(int x = 0;x < n;x++) typedef long long ll; typedef pair pii; typedef pair pll; typedef pair pic; int dx[] = { -1,0,1,0 }; int dy[] = { 0,-1,0,1 }; #define bit(x,v) ((ll)x << v) const ll INF = 1000000007; const int MAX = 1000010; const int MOD = 1000000007; 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 % MOD; inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } // 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] % MOD) % MOD; } ll gcd(ll a, ll b) { if (b == 0) return a; return gcd(b, a % b); } int pr[100010]; int lank[100010]; 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 bit[200010]; int max_n = 200000; int pm = 0; void add(int x) { while (max_n >= x) { bit[x]++; x += x & -x; } } void sub(int x) { while (max_n >= x) { bit[x]--; x += x & -x; } } ll merge(ll* a, int left, int mid, int right) { ll n1 = mid - left; ll n2 = right - mid; vector L(n1 + 1); vector R(n2 + 1); for (size_t i = 0; i < n1; i++) { L[i] = a[left + i]; } for (size_t i = 0; i < n2; i++) { R[i] = a[mid + i]; } L[n1] = INF; R[n2] = INF; ll i = 0; ll j = 0; ll r = 0; for (size_t k = left; k < right; k++) { if (L[i] <= R[j]) { a[k] = L[i]; i++; } else { a[k] = R[j]; r += n1 - i; j++; } } return r; } ll merge2(pair* a, int left, int mid, int right) { ll n1 = mid - left; ll n2 = right - mid; vector> L(n1 + 1); vector> R(n2 + 1); for (size_t i = 0; i < n1; i++) { L[i] = a[left + i]; } for (size_t i = 0; i < n2; i++) { R[i] = a[mid + i]; } L[n1] = make_pair(INF, ' '); R[n2] = make_pair(INF, ' '); ll i = 0; ll j = 0; ll r = 0; for (size_t k = left; k < right; k++) { if (L[i].first <= R[j].first) { a[k] = L[i]; i++; } else { a[k] = R[j]; r += n1 - i; j++; } } return r; } ll mergeSort2(pair* a, int left, int right) { ll res = 0; if (left + 1 < right) { int mid = (left + right) / 2; res = mergeSort2(a, left, mid); res += mergeSort2(a, mid, right); res += merge2(a, left, mid, right); } return res; } ll mergeSort(ll* a, int left, int right) { ll res = 0; if (left + 1 < right) { int mid = (left + right) / 2; res = mergeSort(a, left, mid); res += mergeSort(a, mid, right); res += merge(a, left, mid, right); } return res; } int partition(pair* a, int p, int r) { pair x = a[r]; int i = p - 1; for (size_t j = p; j < r; j++) { if (a[j].first <= x.first) { i++; swap(a[i], a[j]); } } swap(a[i + 1], a[r]); return i + 1; } void quick(pair* a, int p, int r) { if (p < r) { int q = partition(a, p, r); quick(a, p, q - 1); quick(a, q + 1, r); } } ll n; int ci = 0; ll P[1000010]; 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); } else t = 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; } struct edge { int from, to; ll val; edge(int from, int to, ll val) : from(from), to(to), val(val) {} }; int 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 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; } }; void yes() { cout << "Yes\n"; exit(0); } void no() { cout << "No\n"; exit(0); } vector getp(ll n) { vector 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 getp2(ll n) { vector 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 getp3(ll n) { vector 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 getDivisors(ll n) { vector 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 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 elas(ll n) { vector 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; } 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; } ll getpow(ll b, ll x) { return getpow(b, x, INF); } 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; } }; ll divRm(string s, ll x) { ll r = 0; for (size_t 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; } void solv() { cin >> n; double dp[300]; memset(dp, 0, sizeof(dp)); rep(i, 1000) { for (int i = 1; i <= n; i++) { double tmp = 1; for (int j = 1; j <= 6; j++) { if (i == j) continue; if (i < j) { tmp += dp[n] / 6.0; } else { tmp += dp[i - j] / 6.0; } } dp[i] = tmp; } } cout << fixed << setprecision(10) << dp[n] << endl; } int main() { //COMinit(); solv(); return 0; }