結果
| 問題 | No.1551 誕生日の三角形 |
| ユーザー |
 re_re0101
|
| 提出日時 | 2021-06-18 21:22:17 |
| 言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 1,000 ms |
| コード長 | 29,731 bytes |
| コンパイル時間 | 1,995 ms |
| コンパイル使用メモリ | 198,964 KB |
| 実行使用メモリ | 6,948 KB |
| 最終ジャッジ日時 | 2024-06-22 19:47:19 |
| 合計ジャッジ時間 | 2,447 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge2 |
（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
6,944 KB |
| testcase_02 | AC | 1 ms
6,940 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 1 ms
6,948 KB |
| testcase_05 | AC | 1 ms
6,940 KB |
| testcase_06 | AC | 2 ms
6,944 KB |
| testcase_07 | AC | 2 ms
6,940 KB |
| testcase_08 | AC | 2 ms
6,944 KB |
| testcase_09 | AC | 2 ms
6,944 KB |
| testcase_10 | AC | 2 ms
6,940 KB |
ソースコード
// #pragma GCC optimize ("O3")
// #pragma GCC target("avx512f")
// #pragma GCC optimize("unroll-loops")
// #ifndef ONLINE_JUDGE
// #define _GLIBCXX_DEBUG
// #endif
#include<bits/stdc++.h>
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// #include <boost/rational.hpp>
// namespace mp = boost::multiprecision;
// using Bint=mp::cpp_int;
// using Real = mp::number<mp::cpp_dec_float<1024>>;
// #include<atcoder/all>
using namespace std;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define bit(n,k) (((ll)n>>(ll)k)&1) /*nのk bit目*/
#define pb push_back
#define pf push_front
#define fi first
#define se second
#define eb emplace_back
#define endl '\n'
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define PI 3.14159265359
const double eps = 1e-12;
const long long INF= (long long)1e18+20;
const int inf= 1010101010;
typedef long double D; // 座標値の型。doubleかlong doubleを想定
typedef complex<D> Point; // Point
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vl>vvl;
typedef vector<vvl>vvvl;
typedef vector<vvvl>vvvvl;
typedef vector<vvvvl>vvvvvl;
typedef vector<int>vi;
typedef vector<vi>vvi;
typedef vector<vvi>vvvi;
typedef vector<vvvi>vvvvi;
typedef vector<vvvvi>vvvvvi;
typedef pair<ll,ll> P;
// typedef double D;
template<class T> using minpq=priority_queue<T,vector<T>,greater<T>>;
const ll MOD=1000000007LL;
// const ll MOD=998244353LL;
const ll mod=MOD;
vl dx={0,0,1,-1,1,1,-1,-1};
vl dy={1,-1,0,0,-1,1,-1,1};
template<class T> vector<T> make_vec(size_t a) { return vector<T>(a); }
template<class T, class... Ts> auto make_vec(size_t a, Ts... ts) {
return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));
}
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}
//素因数分解O(√n)
map<ll,ll>prime_factor(ll n){
map<ll,ll>res;
for(ll i=2;i*i<=n;i++){
while(n%i==0){
res[i]++;
n/=i;
}
}
if(n!=1)res[n]=1;
return res;
}
const ll MAX = 5000010;
long long fac[MAX], finv[MAX], inv[MAX];
//finvが階乗の逆元
// テーブルを作る前処理
void COMinit() {
fac[0] = fac[1] = 1;
finv[0] = finv[1] = 1;
inv[1] = 1;
for (ll 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(ll n, ll k){
if (n < k) return 0;
if (n < 0 || k < 0) return 0;
return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
}
ll modpow(ll a, ll n,ll mod=MOD) {
ll res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
/*Eratosthenes()
ll N=2000010;
vl arr(N);
void Eratosthenes(){
for(ll i = 0; i < N; i++){
arr[i] = 1;
}
arr[1]=0;
for(ll i = 2; i < sqrt(N); i++){
if(arr[i]){
for(ll j = 0; i * (j + 2) < N; j++){
arr[i *(j + 2)] = 0;
}
}
}
}*/
//素数判定O(√n)
bool is_prime(ll n){
for(ll i=2;i*i<=n;i++){
if(n%i==0)return false;
}
return n!=1;
}
//約数の列挙O(√n)
vector<ll>divisor(ll n){
vector<ll>res;
for(ll i=1;i*i<=n;i++){
if(n%i==0){
res.push_back(i);
if(i != n/i) res.push_back(n/i);
}
}
return res;
}
/* Trie 木： 文字の種類(char_size)、int型で0に対応する文字(base)
insert(word): 単語 word を Trie 木に挿入する
search(word): 単語 word が Trie 木にあるか判定する
start_with(prefix): prefix が一致する単語が Trie 木にあるか判定する
count(): 挿入した単語の数を返す
size(): Trie 木の頂点数を返す
計算量：insert, search ともに O(M)（Mは単語の長さ）
*/
template <int char_size, int base>
struct Trie {
struct Node { // 頂点を表す構造体
vector<int> next; // 子の頂点番号を格納。存在しなければ-1
vector<int> accept; // 末端がこの頂点になる単語の word_id を保存
int c; // base からの間隔をint型で表現したもの
int common; // いくつの単語がこの頂点を共有しているか
Node(int c_) : c(c_), common(0) {
next.assign(char_size, -1);
}
};
vector<Node> nodes; // trie 木本体
int root;
Trie() : root(0) {
nodes.push_back(Node(root));
}
// 単語の挿入
void insert(const string &word, int word_id) {
int node_id = 0;
for (int i = 0; i < (int)word.size(); i++) {
int c = (int)(word[i] - base);
int &next_id = nodes[node_id].next[c];
if (next_id == -1) { // 次の頂点が存在しなければ追加
next_id = (int)nodes.size();
nodes.push_back(Node(c));
}
++nodes[node_id].common;
node_id = next_id;
}
++nodes[node_id].common;
nodes[node_id].accept.push_back(word_id);
}
void insert(const string &word) {
insert(word, nodes[0].common);
}
// 単語とprefixの検索
bool search(const string &word, bool prefix = false) {
int node_id = 0;
for (int i = 0; i < (int)word.size(); i++) {
int c = (int)(word[i] - base);
int &next_id = nodes[node_id].next[c];
if (next_id == -1) { // 次の頂点が存在しなければ終了
return false;
}
node_id = next_id;
}
return (prefix) ? true : nodes[node_id].accept.size() > 0;
}
// prefix を持つ単語が存在するかの検索
bool start_with(const string &prefix) {
return search(prefix, true);
}
// 挿入した単語の数
int count() const {
return (nodes[0].common);
}
// Trie木のノード数
int size() const {
return ((int)nodes.size());
}
};
// //Lowest Common Ancestor
// struct Edge{
// int to;
// Edge(int to):to(to){}
// };
// using Graph = vector<vector<Edge>>;
// class lca {
// public:
// const int n = 0;
// const int log2_n = 0;
// vector<vector<int>> parent;
// vector<int> depth;
// lca() {}
// //g:グラフ root:根
// lca(const Graph &g, int root)
// : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, vector<int>(n)), depth(n) {
// dfs(g, root, -1, 0);
// for (int k = 0; k + 1 < log2_n; k++) {
// for (int v = 0; v < (int)g.size(); v++) {
// if (parent[k][v] < 0)
// parent[k + 1][v] = -1;
// else
// parent[k + 1][v] = parent[k][parent[k][v]];
// }
// }
// }
// void dfs(const Graph &g, int v, int p, int d) {
// parent[0][v] = p;
// depth[v] = d;
// for (auto &e : g[v]) {
// if (e.to != p) dfs(g, e.to, v, d + 1);
// }
// }
// //uとvのlcaを取得
// int get(int u, int v) {
// if (depth[u] > depth[v]) swap(u, v);
// for (int k = 0; k < log2_n; k++) {
// if ((depth[v] - depth[u]) >> k & 1) {
// v = parent[k][v];
// }
// }
// if (u == v) return u;
// for (int k = log2_n - 1; k >= 0; k--) {
// if (parent[k][u] != parent[k][v]) {
// u = parent[k][u];
// v = parent[k][v];
// }
// }
// return parent[0][u];
// }
// int dep(int i) {
// return depth[i];
// }
// int dist(int u,int v){
// return depth[u]+depth[v]-depth[get(u,v)]*2;
// }
// };
// union by size + path having
class UnionFind {
public:
vector <ll> par; // 各元の親を表す配列
vector <ll> siz; // 素集合のサイズを表す配列(1 で初期化)
// Constructor
UnionFind(ll sz_): par(sz_), siz(sz_, 1LL) {
for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
}
void init(ll sz_) {
par.resize(sz_);
siz.assign(sz_, 1LL); // resize だとなぜか初期化されなかった
for (ll i = 0; i < sz_; ++i) par[i] = i; // 初期では親は自分自身
}
// Member Function
// Find
ll root(ll x) { // 根の検索
while (par[x] != x) {
x = par[x] = par[par[x]]; // x の親の親を x の親とする
}
return x;
}
// Union(Unite, Merge)
bool merge(ll x, ll y) {
x = root(x);
y = root(y);
if (x == y) return false;
// merge technique（データ構造をマージするテク．小を大にくっつける）
if (siz[x] < siz[y]) swap(x, y);
siz[x] += siz[y];
par[y] = x;
return true;
}
bool issame(ll x, ll y) { // 連結判定
return root(x) == root(y);
}
ll size(ll x) { // 素集合のサイズ
return siz[root(x)];
}
};
// 0-indexed parmutation only
vvl cycle_partition(const vl &p){
ll n=p.size();
vvl ret;
vector<bool> check(n,false);
rep(i,n)if(!check[p[i]]){
vl v;
ll pos=p[i];
v.pb(i);
check[i]=true;
while(pos!=i){
v.pb(pos);
check[pos]=true;
pos=p[pos];
}
ret.pb(v);
}
return ret;
}
vl Z_algorithm(vl s){
ll c=0,n=s.size();
vl Z(n,0);
for(ll i=1;i<n;i++){
ll l=i-c;
if(i+Z[l]<c+Z[c]){
Z[i]=Z[l];
}else{
ll j=max(0LL,c+Z[c]-i);
while(i+j<n && s[j]==s[i+j])j++;
Z[i]=j;
c=i;
}
}
Z[0]=n;
return Z;
}
//Manachar 修理中
// vl Manachar(string S){
// ll c=0,n=S.size();
// vl R(n,1);
// for(ll i=0;i<n;i++){
// ll l=c-(i-c);
// if(i+R[l]<c+R[c]){
// R[i]=R[l];
// }else{
// ll j=c+R[c]-i;
// while(i-j>=0 && i+j<n && S[i-j] == S[i+j])j++;
// R[i]=j;
// c=i;
// }
// }
// return R;
// }
template <typename T>
T pow(T a, long long n, T e = 1) {
T ret = e;
while (n) {
if (n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
template <int mod>
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(long long x_) {
if ((x = x_ % mod + mod) >= mod) x -= mod;
}
ModInt& operator+=(ModInt rhs) {
if ((x += rhs.x) >= mod) x -= mod;
return *this;
}
ModInt& operator-=(ModInt rhs) {
if ((x -= rhs.x) < 0) x += mod;
return *this;
}
ModInt& operator*=(ModInt rhs) {
x = (unsigned long long)x * rhs.x % mod;
return *this;
}
ModInt& operator/=(ModInt rhs) {
x = (unsigned long long)x * rhs.inv().x % mod;
return *this;
}
ModInt operator-() const { return -x < 0 ? mod - x : -x; }
ModInt operator+(ModInt rhs) const { return ModInt(*this) += rhs; }
ModInt operator-(ModInt rhs) const { return ModInt(*this) -= rhs; }
ModInt operator*(ModInt rhs) const { return ModInt(*this) *= rhs; }
ModInt operator/(ModInt rhs) const { return ModInt(*this) /= rhs; }
bool operator==(ModInt rhs) const { return x == rhs.x; }
bool operator!=(ModInt rhs) const { return x != rhs.x; }
ModInt inv() const { return pow(*this, mod - 2); }
friend ostream& operator<<(ostream& s, ModInt<mod> a) {
s << a.x;
return s;
}
friend istream& operator>>(istream& s, ModInt<mod>& a) {
s >> a.x;
return s;
}
};
using mint = ModInt<MOD>;
typedef vector<mint> vm;
typedef vector<vector<mint> >vvm;
typedef vector<vector<vector<mint> > >vvvm;
template <typename T>
struct segment_tree_beats{
int N;
vector<T> max1, max2, min1, min2, add, sum;
vector<int> maxc, minc, len;
void update_max(int i, T x){
sum[i] += (x - max1[i]) * maxc[i];
if (max1[i] == min1[i]){
min1[i] = x;
} else if (max1[i] == min2[i]){
min2[i] = x;
}
max1[i] = x;
}
void update_min(int i, T x){
sum[i] += (x - min1[i]) * minc[i];
if (min1[i] == max1[i]){
max1[i] = x;
} else if (min1[i] == max2[i]){
max2[i] = x;
}
min1[i] = x;
}
void update_add(int i, T x){
max1[i] += x;
if (max2[i] != -INF){
max2[i] += x;
}
min1[i] += x;
if (min2[i] != INF){
min2[i] += x;
}
sum[i] += x * len[i];
add[i] += x;
}
void push(int i){
if (i >= N - 1){
return;
}
int l = i * 2 + 1;
int r = i * 2 + 2;
if (add[i] != 0){
update_add(l, add[i]);
update_add(r, add[i]);
add[i] = 0;
}
if (max1[i] < max1[l]){
update_max(l, max1[i]);
}
if (min1[i] > min1[l]){
update_min(l, min1[i]);
}
if (max1[i] < max1[r]){
update_max(r, max1[i]);
}
if (min1[i] > min1[r]){
update_min(r, min1[i]);
}
}
void update(int i){
int l = i * 2 + 1;
int r = i * 2 + 2;
sum[i] = sum[l] + sum[r];
if (max1[l] > max1[r]){
max1[i] = max1[l];
max2[i] = max(max2[l], max1[r]);
maxc[i] = maxc[l];
} else if (max1[l] < max1[r]){
max1[i] = max1[r];
max2[i] = max(max1[l], max2[r]);
maxc[i] = maxc[r];
} else {
max1[i] = max1[l];
max2[i] = max(max2[l], max2[r]);
maxc[i] = maxc[l] + maxc[r];
}
if (min1[l] < min1[r]){
min1[i] = min1[l];
min2[i] = min(min2[l], min1[r]);
minc[i] = minc[l];
} else if (min1[l] > min1[r]){
min1[i] = min1[r];
min2[i] = min(min1[l], min2[r]);
minc[i] = minc[r];
} else {
min1[i] = min1[l];
min2[i] = min(min2[l], min2[r]);
minc[i] = minc[l] + minc[r];
}
}
segment_tree_beats(vector<T> A){
int n = A.size();
N = 1;
while (N < n){
N *= 2;
}
max1 = vector<T>(N * 2 - 1, -INF);
max2 = vector<T>(N * 2 - 1, -INF);
min1 = vector<T>(N * 2 - 1, INF);
min2 = vector<T>(N * 2 - 1, INF);
add = vector<T>(N * 2 - 1, 0);
sum = vector<T>(N * 2 - 1, 0);
maxc = vector<int>(N * 2 - 1, 1);
minc = vector<int>(N * 2 - 1, 1);
len = vector<int>(N * 2 - 1, 1);
for (int i = 0; i < n; i++){
max1[N - 1 + i] = A[i];
min1[N - 1 + i] = A[i];
sum[N - 1 + i] = A[i];
}
for (int i = N - 2; i >= 0; i--){
len[i] = len[i * 2 + 1] + len[i * 2 + 2];
update(i);
}
}
void range_chmin(int L, int R, T x, int i, int l, int r){
if (r <= L || R <= l || x >= max1[i]){
return;
} else if (L <= l && r <= R && x > max2[i]){
update_max(i, x);
return;
}
push(i);
int m = (l + r) / 2;
range_chmin(L, R, x, i * 2 + 1, l, m);
range_chmin(L, R, x, i * 2 + 2, m, r);
update(i);
}
void range_chmax(int L, int R, T x, int i, int l, int r){
if (r <= L || R <= l || x <= min1[i]){
return;
} else if (L <= l && r <= R && x < min2[i]){
update_min(i, x);
return;
}
push(i);
int m = (l + r) / 2;
range_chmax(L, R, x, i * 2 + 1, l, m);
range_chmax(L, R, x, i * 2 + 2, m, r);
update(i);
}
void range_add(int L, int R, T x, int i, int l, int r){
if (r <= L || R <= l){
return;
} else if (L <= l && r <= R){
update_add(i, x);
return;
}
push(i);
int m = (l + r) / 2;
range_add(L, R, x, i * 2 + 1, l, m);
range_add(L, R, x, i * 2 + 2, m, r);
update(i);
}
T range_sum(int L, int R, int i, int l, int r){
if (r <= L || R <= l){
return 0;
} else if (L <= l && r <= R){
return sum[i];
}
push(i);
int m = (l + r) / 2;
return range_sum(L, R, i * 2 + 1, l, m) + range_sum(L, R, i * 2 + 2, m, r);
}
void range_chmin(int L, int R, T x){
range_chmin(L, R, x, 0, 0, N);
}
void range_chmax(int L, int R, T x){
range_chmax(L, R, x, 0, 0, N);
}
void range_add(int L, int R, T x){
range_add(L, R, x, 0, 0, N);
}
T range_sum(int L, int R){
return range_sum(L, R, 0, 0, N);
}
};
struct PartiallyPersistentUnionFind {
vector<ll> par, last;
vector<vector<P> > history;
PartiallyPersistentUnionFind(ll n) : par(n, -1), last(n, -1), history(n) {
for (auto &vec : history) vec.emplace_back(-1, -1);
}
void init(ll n) {
par.assign(n, -1); last.assign(n, -1); history.assign(n, vector<P>());
for (auto &vec : history) vec.emplace_back(-1, -1);
}
ll root(ll t, ll x) {
if (last[x] == -1 || t < last[x]) return x;
return root(t, par[x]);
}
bool issame(ll t, ll x, ll y) {
return root(t, x) == root(t, y);
}
bool merge(ll t, ll x, ll y) {
x = root(t, x); y = root(t, y);
if (x == y) return false;
if (par[x] > par[y]) swap(x, y); // merge technique
par[x] += par[y];
par[y] = x;
last[y] = t;
history[x].emplace_back(t, par[x]);
return true;
}
ll size(ll t, ll x) {
x = root(t, x);
return -prev(lower_bound(history[x].begin(), history[x].end(), make_pair(t, 0LL)))->second;
}
};
// matrix
template<class T> struct Matrix {
vector<vector<T> > val;
Matrix(int n = 1, int m = 1, T v = 0) : val(n, vector<T>(m, v)) {}
void init(int n, int m, T v = 0) {val.assign(n, vector<T>(m, v));}
void resize(int n, int m) {
val.resize(n);
for (int i = 0; i < n; ++i) val[i].resize(m);
}
Matrix<T>& operator = (const Matrix<T> &A) {
val = A.val;
return *this;
}
size_t size() const {return val.size();}
vector<T>& operator [] (int i) {return val[i];}
const vector<T>& operator [] (int i) const {return val[i];}
friend ostream& operator << (ostream& s, const Matrix<T>& M) {
s << endl;
for (int i = 0; i < (int)M.size(); ++i) s << M[i] << endl;
return s;
}
};
template<class T> Matrix<T> operator * (const Matrix<T> &A, const Matrix<T> &B) {
Matrix<T> R(A.size(), B[0].size());
for (int i = 0; i < A.size(); ++i)
for (int j = 0; j < B[0].size(); ++j)
for (int k = 0; k < B.size(); ++k)
R[i][j] += A[i][k] * B[k][j];
return R;
}
template<class T> Matrix<T> pow(const Matrix<T> &A, long long n) {
Matrix<T> R(A.size(), A.size());
auto B = A;
for (int i = 0; i < A.size(); ++i) R[i][i] = 1;
while (n > 0) {
if (n & 1) R = R * B;
B = B * B;
n >>= 1;
}
return R;
}
template<class T> vector<T> operator * (const Matrix<T> &A, const vector<T> &B) {
vector<T> v(A.size());
for (int i = 0; i < A.size(); ++i)
for (int k = 0; k < B.size(); ++k)
v[i] += A[i][k] * B[k];
return v;
}
template<class T> Matrix<T> operator + (const Matrix<T> &A, const Matrix<T> &B) {
Matrix<T> R(A.size(), A[0].size());
for (int i = 0; i < A.size(); ++i)
for (int j = 0; j < A[0].size(); ++j)
R[i][j] = A[i][j] + B[i][j];
return R;
}
template<class T> Matrix<T> operator - (const Matrix<T> &A, const Matrix<T> &B) {
Matrix<T> R(A.size(), A[0].size());
for (int i = 0; i < A.size(); ++i)
for (int j = 0; j < A[0].size(); ++j)
R[i][j] = A[i][j] - B[i][j];
return R;
}
const int MAX_ROW = 510; // to be set appropriately
const int MAX_COL = 510; // to be set appropriately
struct BitMatrix {
int H, W;
bitset<MAX_COL> val[MAX_ROW];
BitMatrix(int m = 1, int n = 1) : H(m), W(n) {}
inline bitset<MAX_COL>& operator [] (int i) {return val[i];}
};
int GaussJordan(BitMatrix &A, bool is_extended = false) {
int rank = 0;
for (int col = 0; col < A.W; ++col) {
if (is_extended && col == A.W - 1) break;
int pivot = -1;
for (int row = rank; row < A.H; ++row) {
if (A[row][col]) {
pivot = row;
break;
}
}
if (pivot == -1) continue;
swap(A[pivot], A[rank]);
for (int row = 0; row < A.H; ++row) {
if (row != rank && A[row][col]) A[row] ^= A[rank];
}
++rank;
}
return rank;
}
int linear_equation(BitMatrix A, vector<int> b, vector<int> &res) {
int m = A.H, n = A.W;
BitMatrix M(m, n + 1);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) M[i][j] = A[i][j];
M[i][n] = b[i];
}
int rank = GaussJordan(M, true);
// check if it has no solution
for (int row = rank; row < m; ++row) if (M[row][n]) return -1;
// answer
res.assign(n, 0);
for (int i = 0; i < rank; ++i) res[i] = M[i][n];
return rank;
}
ll exp(ll n,ll r){
if(r==0)return 1;
return n*exp(n,r-1);
}
ll factorial(int n){
if(n==0)return 1;
return n*factorial(n-1);
}
void input_vvi(int n){
vector<string>s(n);
string ans;
ans+="vector<vector<int>> dp={";
rep(i,n){
cin>>s[i];
ans+="{";
ans+=s[i];
ans+="}";
if(i!=n-1)ans+=",";
}
ans+="};";
cout<<ans<<endl;
}
/**
* @brief Rolling-Hash(ローリングハッシュ)
* @see https://qiita.com/keymoon/items/11fac5627672a6d6a9f6
* @docs docs/rolling-hash.md
*/
struct RollingHash {
static const uint64_t mod = (1ull << 61ull) - 1;
using uint128_t = __uint128_t;
vector< uint64_t > power;
const uint64_t base;
static inline uint64_t add(uint64_t a, uint64_t b) {
if((a += b) >= mod) a -= mod;
return a;
}
static inline uint64_t mul(uint64_t a, uint64_t b) {
uint128_t c = (uint128_t) a * b;
return add(c >> 61, c & mod);
}
static inline uint64_t generate_base() {
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
return rand(mt);
}
inline void expand(size_t sz) {
if(power.size() < sz + 1) {
int pre_sz = (int) power.size();
power.resize(sz + 1);
for(int i = pre_sz - 1; i < sz; i++) {
power[i + 1] = mul(power[i], base);
}
}
}
explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}
vector< uint64_t > build(const string &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
template< typename T >
vector< uint64_t > build(const vector< T > &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
uint64_t query(const vector< uint64_t > &s, int l, int r) {
expand(r - l);
return add(s[r], mod - mul(s[l], power[r - l]));
}
uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
expand(h2len);
return add(mul(h1, power[h2len]), h2);
}
int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
int len = min(r1 - l1, r2 - l2);
int low = 0, high = len + 1;
while(high - low > 1) {
int mid = (low + high) / 2;
if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
else high = mid;
}
return low;
}
};
struct SuccinctIndexableDictionary {
size_t length;
size_t blocks;
vector< unsigned > bit, sum;
SuccinctIndexableDictionary() = default;
SuccinctIndexableDictionary(size_t length) : length(length), blocks((length + 31) >> 5) {
bit.assign(blocks, 0U);
sum.assign(blocks, 0U);
}
void set(int k) {
bit[k >> 5] |= 1U << (k & 31);
}
void build() {
sum[0] = 0U;
for(int i = 1; i < blocks; i++) {
sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
}
}
bool operator[](int k) {
return (bool((bit[k >> 5] >> (k & 31)) & 1));
}
int rank(int k) {
return (sum[k >> 5] + __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
}
int rank(bool val, int k) {
return (val ? rank(k) : k - rank(k));
}
};
/*
* @brief Wavelet-Matrix(ウェーブレット行列)
* @docs docs/wavelet-matrix.md
*/
template< typename T, int MAXLOG >
struct WaveletMatrix {
size_t length;
SuccinctIndexableDictionary matrix[MAXLOG];
int mid[MAXLOG];
WaveletMatrix() = default;
WaveletMatrix(vector< T > v) : length(v.size()) {
vector< T > l(length), r(length);
for(int level = MAXLOG - 1; level >= 0; level--) {
matrix[level] = SuccinctIndexableDictionary(length + 1);
int left = 0, right = 0;
for(int i = 0; i < length; i++) {
if(((v[i] >> level) & 1)) {
matrix[level].set(i);
r[right++] = v[i];
} else {
l[left++] = v[i];
}
}
mid[level] = left;
matrix[level].build();
v.swap(l);
for(int i = 0; i < right; i++) {
v[left + i] = r[i];
}
}
}
pair< int, int > succ(bool f, int l, int r, int level) {
return {matrix[level].rank(f, l) + mid[level] * f, matrix[level].rank(f, r) + mid[level] * f};
}
// v[k]
T access(int k) {
T ret = 0;
for(int level = MAXLOG - 1; level >= 0; level--) {
bool f = matrix[level][k];
if(f) ret |= T(1) << level;
k = matrix[level].rank(f, k) + mid[level] * f;
}
return ret;
}
T operator[](const int &k) {
return access(k);
}
// count i s.t. (0 <= i < r) && v[i] == x
int rank(const T &x, int r) {
int l = 0;
for(int level = MAXLOG - 1; level >= 0; level--) {
tie(l, r) = succ((x >> level) & 1, l, r, level);
}
return r - l;
}
// k-th(0-indexed) smallest number in v[l,r)
T kth_smallest(int l, int r, int k) {
assert(0 <= k && k < r - l);
T ret = 0;
for(int level = MAXLOG - 1; level >= 0; level--) {
int cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);
bool f = cnt <= k;
if(f) {
ret |= T(1) << level;
k -= cnt;
}
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// k-th(0-indexed) largest number in v[l,r)
T kth_largest(int l, int r, int k) {
return kth_smallest(l, r, r - l - k - 1);
}
// count i s.t. (l <= i < r) && (v[i] < upper)
int range_freq(int l, int r, T upper) {
int ret = 0;
for(int level = MAXLOG - 1; level >= 0; level--) {
bool f = ((upper >> level) & 1);
if(f) ret += matrix[level].rank(false, r) - matrix[level].rank(false, l);
tie(l, r) = succ(f, l, r, level);
}
return ret;
}
// count i s.t. (l <= i < r) && (lower <= v[i] < upper)
int range_freq(int l, int r, T lower, T upper) {
return range_freq(l, r, upper) - range_freq(l, r, lower);
}
// max v[i] s.t. (l <= i < r) && (v[i] < upper)
T prev_value(int l, int r, T upper) {
int cnt = range_freq(l, r, upper);
return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
}
// min v[i] s.t. (l <= i < r) && (lower <= v[i])
T next_value(int l, int r, T lower) {
int cnt = range_freq(l, r, lower);
return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
}
};
template< typename T, int MAXLOG >
struct CompressedWaveletMatrix {
WaveletMatrix< int, MAXLOG > mat;
vector< T > ys;
CompressedWaveletMatrix(const vector< T > &v) : ys(v) {
sort(begin(ys), end(ys));
ys.erase(unique(begin(ys), end(ys)), end(ys));
vector< int > t(v.size());
for(int i = 0; i < v.size(); i++) t[i] = get(v[i]);
mat = WaveletMatrix< int, MAXLOG >(t);
}
inline int get(const T& x) {
return lower_bound(begin(ys), end(ys), x) - begin(ys);
}
T access(int k) {
return ys[mat.access(k)];
}
T operator[](const int &k) {
return access(k);
}
int rank(const T &x, int r) {
auto pos = get(x);
if(pos == ys.size() || ys[pos] != x) return 0;
return mat.rank(pos, r);
}
T kth_smallest(int l, int r, int k) {
return ys[mat.kth_smallest(l, r, k)];
}
T kth_largest(int l, int r, int k) {
return ys[mat.kth_largest(l, r, k)];
}
int range_freq(int l, int r, T upper) {
return mat.range_freq(l, r, get(upper));
}
int range_freq(int l, int r, T lower, T upper) {
return mat.range_freq(l, r, get(lower), get(upper));
}
T prev_value(int l, int r, T upper) {
auto ret = mat.prev_value(l, r, get(upper));
return ret == -1 ? T(-1) : ys[ret];
}
T next_value(int l, int r, T lower) {
auto ret = mat.next_value(l, r, get(lower));
return ret == -1 ? T(-1) : ys[ret];
}
};
pair<long long,long long>roop_search(vl next_index,ll first_point){
ll idx=first_point;
map<ll,ll>mp;
mp[idx]=0;
ll cur=1;
ll roop_begin=-1;
ll roop_size=-1;
while(true){
idx=next_index[idx];
if(mp.count(idx)){
roop_begin=mp[idx];
roop_size=cur-roop_begin;
break;
}
mp[idx]=cur++;
}
return {roop_begin,roop_size};
}
ll functional(ll x){
if(x==0)return 1;
else return x*functional(x-1);
}
int main(){
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(13);
//CDEは制約を読もう！
//主客転倒！二重和のときは一番内側の物が何回使われるか
//√Nで分けるテク
//絶対値は外して2通りの式にした後、変数ごとにまとめる
//組み合わせが少ないそうなものはdfsで実行してみる（典型25）
/*--------------------------------*/
double a;cin>>a;
a/=3;
cout<<a*a*sqrt(3)/4<<endl;
}