/** * author: tsuyu93 * started: 2021-07-23 21:45:38 * 継続は力なり、雨だれ石を穿つ * make the impossible possible **/ #pragma GCC optimize("Ofast") #include // #include // #include // namespace mpb = boost::multiprecision; // using bint = mpb::cpp_int; // // 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする) // using Real = mpb::number>; #ifdef __HOGE__ #pragma region macro #endif using namespace std; using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned; using pll = pair; using pli = pair; using pii = pair; using pld = pair; using ppiii = pair; using ppiill = pair; using ppllll = pair; using pplii = pair; using mii = map; using dll = deque; using qll = queue; using pqll = priority_queue; using pqrll = priority_queue, greater>; using pqrpll = priority_queue, greater>; using vint = vector; using vbool = vector; using vstr = vector; using vll = vector; using vld = vector; using vpll = vector; using vvll = vector>; using vvint = vector>; using vvld = vector>; using vvbool = vector; using vvstr = vector; using vvpll = vector>; template using PQ = priority_queue; template using PQR = priority_queue,greater>; #define REP(i,n) for(ll i=0;i=0;i--) #define FOR(i,a,b) for(ll i=a;i<=ll(b);i++) #define FORD(i,a,b) for(ll i=a;i>=ll(b);i--) #define overload4(_1,_2,_3,_4,name,...) name #define overload3(_1,_2,_3,name,...) name #define rep1(n) for(ll dont_use_this_twice=0;dont_use_this_twice(a);) #define rrep4(i,a,b,c) for(ll i=(a)+((b)-(a)-1)/(c)*(c);i>=(a);i-=c) #define rrep(...) overload4(__VA_ARGS__,rrep4,rrep3,rrep2,rrep1)(__VA_ARGS__) #define each1(i,a) for(auto&&i:a) #define each2(x,y,a) for(auto&&[x,y]:a) #define each3(x,y,z,a) for(auto&&[x,y,z]:a) #define each(...) overload4(__VA_ARGS__,each3,each2,each1)(__VA_ARGS__) #define all1(i) begin(i),end(i) #define all2(i,a) begin(i),begin(i)+a #define all3(i,a,b) begin(i)+a,begin(i)+b #define all(...) overload3(__VA_ARGS__,all3,all2,all1)(__VA_ARGS__) #define rall1(i) (i).rbegin(),(i).rend() #define rall2(i,k) (i).rbegin(),(i).rbegin()+k #define rall3(i,a,b) (i).rbegin()+a,(i).rbegin()+b #define rall(...) overload3(__VA_ARGS__,rall3,rall2,rall1)(__VA_ARGS__) #define SUM(...) accumulate(all(__VA_ARGS__),0LL) #define ALL(x) x.begin(),x.end() #define rALL(x) x.rbegin(),x.rend() #define SIZE(x) ll(x.size()) #define Sort(a) sort(all(a)) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__) #define STR(...) string __VA_ARGS__;in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;in(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)int scan(){ return getchar(); } #define fs first #define sc second #define endl '\n' #define elif else if #define ADD_OVERFLOW(a, b) __builtin_add_overflow_p (a, b, (decltype((a)+(b))) 0) #define SUB_OVERFLOW(a, b) __builtin_sub_overflow_p (a, b, (decltype((a)+(b))) 0) #define MUL_OVERFLOW(a, b) __builtin_mul_overflow_p (a, b, (decltype((a)+(b))) 0) void scan(int& a){ scanf("%d", &a); } void scan(unsigned& a){ scanf("%u", &a); } void scan(long& a){ scanf("%ld", &a); } void scan(long long& a){ scanf("%lld", &a); } void scan(unsigned long long& a){ scanf("%llu", &a); } void scan(char& a){ do{ a = getchar(); }while(a == ' ' || a == '\n'); } void scan(float& a){ scanf("%f", &a); } void scan(double& a){ scanf("%lf", &a); } void scan(long double& a){ scanf("%Lf", &a); } void scan(vector& a){ for(unsigned i = 0; i < a.size(); i++){ int b; scan(b); a[i] = b; } } void scan(char a[]){ scanf("%s", a); } void scan(string& a){ cin >> a; } template void scan(vector&); template void scan(array&); template void scan(pair&); template void scan(T(&)[size]); template void scan(vector& a){ for(auto&& i : a) scan(i); } template void scan(deque& a){ for(auto&& i : a) scan(i); } template void scan(array& a){ for(auto&& i : a) scan(i); } template void scan(pair& p){ scan(p.first); scan(p.second); } template void scan(T (&a)[size]){ for(auto&& i : a) scan(i); } template void scan(T& a){ cin >> a; } template std::istream &operator>>(std::istream &is, std::vector &a) {for (auto &x : a) is >> x;return is;} template std::istream &operator>>(std::istream &is, std::pair &a) { is >> a.first >> a.second; return is;} void in(){} template void in(Head& head, Tail&... tail){ scan(head); in(tail...); } void print(){ putchar(' '); } void print(bool a){ printf("%d", a); } void print(int a){ printf("%d", a); } void print(unsigned a){ printf("%u", a); } void print(long a){ printf("%ld", a); } void print(long long a){ printf("%lld", a); } void print(unsigned long long a){ printf("%llu", a); } void print(char a){ printf("%c", a); } void print(char a[]){ printf("%s", a); } void print(const char a[]){ printf("%s", a); } void print(float a){ printf("%.15f", a); } void print(double a){ printf("%.15f", a); } void print(long double a){ printf("%.15Lf", a); } void print(const string& a){ for(auto&& i : a) print(i); } templateostream &operator<<(ostream &os, const pair&p){return os << p.first << " " << p.second;} template void print(const complex& a){ if(a.real() >= 0) print('+'); print(a.real()); if(a.imag() >= 0) print('+'); print(a.imag()); print('i'); } template void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ putchar(' '); print(*i); } } template void print(const pair& p){ print(p.first); putchar(' '); print(p.second); } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ putchar(' '); print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } template vector make_vec(size_t a, T b) {return vector(a,b);} template auto make_vec(size_t a, Ts... ts) {return vector(ts...))>(a, make_vec(ts...));} #ifdef DEBUG #define debug(...) { print(#__VA_ARGS__); print(":"); out(__VA_ARGS__); } #else #define debug(...) void(0) #endif templatepair& operator+=(pair&s,const pair&t){s.first+=t.first;s.second+=t.second;return s;} templatepair& operator-=(pair&s,const pair&t){s.first-=t.first;s.second-=t.second;return s;} templatepair operator+(const pair&s,const pair&t){auto res=s;return res+=t;} templatepair operator-(const pair&s,const pair&t){auto res=s;return res-=t;} templateT poll(queue &q){auto ret=q.front();q.pop();return ret;} templateT poll(deque &q){auto ret=q.front();q.pop_front();return ret;} templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;} templateT poll(PQR &q){auto ret=q.top();q.pop();return ret;} templateT poll(stack &s){auto ret=s.top();s.pop();return ret;} #define INF32 2147483647 //2.147483647x10^{9}:32bit整数のinf #define INF64 9223372036854775807 //9.223372036854775807x10^{18}:64bit整数のinf const ll MOD = 1000000007; // const ll MOD = 998244353; const int inf = 1e9; const ll INF = (1LL<<61); const ll MAXR = 100000; //10^5:配列の最大のrange const ld PI = acos(-1); constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } inline void OKNG(bool b = true) { cout << (b ? "OK" : "NG") << '\n'; } inline void GAme(bool b = true) { cout << (b ? "First" : "Second") << '\n'; } inline void gAme(bool b = true) { cout << (b ? "first" : "second") << '\n'; } inline void Takahashi_Aoki(bool b = true) { cout << (b ? "Takahashi" : "Aoki") << '\n'; } inline void takahashi_aoki(bool b = true) { cout << (b ? "takahashi" : "aoki") << '\n'; } inline void possible(bool i = true){ cout << (i?"possible":"impossible") << '\n'; } inline void Possible(bool i = true){ cout << (i?"Possible":"Impossible") << '\n'; } inline void POSSIBLE(bool i = true){ cout << (i?"POSSIBLE":"IMPOSSIBLE") << '\n'; } templatevoid print_with_bool(bool x,T1 y,T2 z){if(x)cout< inline bool chmin(A& a, B b) {if (a > b) {a = b;return true;}return false;} template inline bool chmax(A& a, B b) {if (a < b) {a = b;return true;}return false;} template auto min(const T& a){ return *min_element(a.begin(),a.end()); } template auto max(const T& a){ return *max_element(a.begin(),a.end()); } template T power(T a, T b) {T res=1;while (b>0) {if (b&1){res*=a;}b/=2;a*=a;}return res;} long long powmod(long long a, long long b) {long long res=1;while (b>0) {if (b&1){res*=a;res%=MOD;}b/=2;a*=a;a%=MOD;}return res;} template T powmod(T a, T b,T m) {T res=1;while (b>0) {if (b&1){res*=a;res%=m;}b/=2;a*=a;a%=m;}return res%m;} template T nlcm(const vector &a) {T res;res = a[0];for (ll i = 1; i < (ll)a.size(); i++) {res = lcm(res, a[i]);}return res;} template T ngcd(const vector &a){T res;res = a[0];for(ll i = 1; i < (ll)a.size() && res != 1; i++) {res = gcd(a[i], res);}return res;} template T sqr(T x){T r=sqrt(x)-1;while((r+1)*(r+1)<=x)r++;return r;} template T bit_length(T a){T k = 0;while(a){k++;a/=2;}return k;} template T isqrt(T n){T a = 0, r = 0;for(T s = bit_length(n)-(bit_length(n)%2?1:2); s >= 0;s-=2){T t = ((n >> s) & 3);r = ((r << 2) | t);T c = ((a << 2) | 1);int b = (r >= c);if(b){r -= c;}a = ((a << 1) | b);}return a;} int popcount(long long a){return __builtin_popcountll(a);} int popcount(int a){return __builtin_popcount(a);} int poplow(ll x){return __builtin_ctzll(x);} int poplow(int x){return __builtin_ctz(x);} int pophigh(ll x){return 63 - __builtin_clzll(x);} int pophigh(int x){return 31 - __builtin_clz(x);} template T ceil(T a, T b) {if(b < 0) a = -a, b = -b;return (a >= 0 ? (a + b - 1) / b : a / b);} template T floor(T a, T b) {if(b < 0) a = -a, b = -b;return (a >= 0 ? a / b : (a - b + 1) / b);} template T sum_of_digit(T a) {T res = 0;while(a){res += a%10; a /= 10;}return res;} template void add_edge(vector> &G, A a, A b,bool directed = false){G[a].emplace_back(b);if(!directed)G[b].emplace_back(a);} template void add_edge(vector>> &G, A a, A b, A p,bool directed = false){G[a].emplace_back(p,b);if(!directed)G[b].emplace_back(p,a);} #ifdef __HOGE__ #pragma endregion #endif // #include // using namespace atcoder; // using mint = modint1000000007; // using mint = modint998244353; // using vm = vector; // using vvm = vector; #include #include #include #include const double EPS = 1e-8; inline bool eq(double a, double b) { return fabs(b - a) < EPS; } struct Point{ double x, y; Point(): x(0), y(0) {} Point(double _x, double _y): x(_x), y(_y) {} Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); } Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); } Point operator*(const double b) const { return Point(x * b, y * b); } Point operator*(const Point &b) const { return Point(x * b.x - y * b.y, x * b.y + y * b.x); } Point operator/(const double b) const { return Point(x / b, y / b); } bool operator==(const Point &b) const { return eq(x, b.x) && eq(y, b.y); } bool operator<(const Point &b) const { return x != b.x ? x < b.x : y < b.y; } double cross(Point b){return this->x * b.y - this->y * b.x;}//外積 double dot(Point b){return this->x * b.x + this->y * b.y;} //内積 double distance(Point v){return sqrt((this->x - v.x)*(this->x - v.x) + (v.y - this->y)*(v.y - this->y));} double abs(){return sqrt(x * x + y * y);} double abs2(){return x * x + y * y;} double arg() { return atan2(y, x); } Point rotate(double theta) { return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y); } Point rotate90() { return Point(-y, x); } friend ostream &operator<<(ostream &os, Point &p) { return os << "(" << p.x << "," << p.y << ")"; } friend istream &operator>>(istream &is, Point &a) { return is >> a.x >> a.y; } }; double RadianToDegree(double r){ return (r * 180.0 / acos(-1)); } double DegreeToRadian(double d){ return (d * acos(-1) / 180.0); } double area(std::vector vec){ int n = vec.size(); if(n <= 2) return 0; double res = 0; for(int i = 1; i < n; i++){ res += (vec[i].x - vec[i - 1].x) * (vec[i].y + vec[i - 1].y); } res += (vec[0].x - vec[n - 1].x) * (vec[0].y + vec[n - 1].y); return std::abs(res) / 2; } void main_(){ cout << fixed << setprecision(15); double R; cin >> R; vector vec; Point a = {0,R}; Point b = a.rotate(DegreeToRadian(120)); Point c = b.rotate(DegreeToRadian(120)); vec = {a,b,c}; cout << area(vec) << endl; //cout << ans << endl; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t = 1; cin >> t; while(t--) main_(); return 0; }