結果
| 問題 |
No.3180 angles sum
|
| ユーザー |
 erbowl
|
| 提出日時 | 2025-06-29 16:26:43 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 30,007 bytes |
| コンパイル時間 | 4,206 ms |
| コンパイル使用メモリ | 304,464 KB |
| 実行使用メモリ | 7,848 KB |
| 最終ジャッジ日時 | 2025-06-29 16:26:58 |
| 合計ジャッジ時間 | 14,197 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 12 WA * 5 |
ソースコード
// ギリギリな時に
#pragma GCC optimize("O3")
typedef long long ll;
typedef long double ld;
#include <bits/stdc++.h>
using namespace std;
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// modint
template <int MOD>
struct Fp {
// inner value
long long val;
// constructor
constexpr Fp() : val(0) {}
constexpr Fp(long long v) : val(v % MOD) {
if (val < 0) val += MOD;
}
// getter
constexpr long long get() const { return val; }
constexpr int get_mod() const { return MOD; }
// comparison operators
constexpr bool operator==(const Fp &r) const { return this->val == r.val; }
constexpr bool operator!=(const Fp &r) const { return this->val != r.val; }
// arithmetic operators
constexpr Fp &operator+=(const Fp &r) {
val += r.val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp &operator-=(const Fp &r) {
val -= r.val;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp &operator*=(const Fp &r) {
val = val * r.val % MOD;
return *this;
}
constexpr Fp &operator/=(const Fp &r) {
long long a = r.val, b = MOD, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
val = val * u % MOD;
if (val < 0) val += MOD;
return *this;
}
constexpr Fp operator+() const { return Fp(*this); }
constexpr Fp operator-() const { return Fp(0) - Fp(*this); }
constexpr Fp operator+(const Fp &r) const { return Fp(*this) += r; }
constexpr Fp operator-(const Fp &r) const { return Fp(*this) -= r; }
constexpr Fp operator*(const Fp &r) const { return Fp(*this) *= r; }
constexpr Fp operator/(const Fp &r) const { return Fp(*this) /= r; }
// other operators
constexpr Fp &operator++() {
++val;
if (val >= MOD) val -= MOD;
return *this;
}
constexpr Fp &operator--() {
if (val == 0) val += MOD;
--val;
return *this;
}
constexpr Fp operator++(int) {
Fp res = *this;
++*this;
return res;
}
constexpr Fp operator--(int) {
Fp res = *this;
--*this;
return res;
}
friend constexpr istream &operator>>(istream &is, Fp<MOD> &x) {
is >> x.val;
x.val %= MOD;
if (x.val < 0) x.val += MOD;
return is;
}
friend constexpr ostream &operator<<(ostream &os, const Fp<MOD> &x) {
return os << x.val;
}
// other functions
constexpr Fp pow(long long n) const {
Fp res(1), mul(*this);
while (n > 0) {
if (n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
constexpr Fp inv() const {
Fp res(1), div(*this);
return res / div;
}
friend constexpr Fp<MOD> pow(const Fp<MOD> &r, long long n) {
return r.pow(n);
}
friend constexpr Fp<MOD> inv(const Fp<MOD> &r) { return r.inv(); }
};
// Binomial coefficient
template <class mint>
struct BiCoef {
vector<mint> fact_, inv_, finv_;
constexpr BiCoef() {}
constexpr BiCoef(int n) : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); }
constexpr void init(int n) {
fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1);
int MOD = fact_[0].get_mod();
for (int i = 2; i < n; i++) {
fact_[i] = fact_[i - 1] * i;
inv_[i] = -inv_[MOD % i] * (MOD / i);
finv_[i] = finv_[i - 1] * inv_[i];
}
}
constexpr mint com(int n, int k) const {
if (n < k || n < 0 || k < 0) return 0;
return fact_[n] * finv_[k] * finv_[n - k];
}
constexpr mint fact(int n) const {
if (n < 0) return 0;
return fact_[n];
}
constexpr mint inv(int n) const {
if (n < 0) return 0;
return inv_[n];
}
constexpr mint finv(int n) const {
if (n < 0) return 0;
return finv_[n];
}
};
// Lazy Segment Tree
template <class Monoid, class Action>
struct LazySegmentTree {
// various function types
using FuncOperator = function<Monoid(Monoid, Monoid)>;
using FuncMapping = function<Monoid(Action, Monoid)>;
using FuncComposition = function<Action(Action, Action)>;
// core member
int N;
FuncOperator OP;
FuncMapping MAPPING;
FuncComposition COMPOSITION;
Monoid IDENTITY_MONOID;
Action IDENTITY_ACTION;
// inner data
int log, offset;
vector<Monoid> dat;
vector<Action> lazy;
// constructor
LazySegmentTree() {}
LazySegmentTree(int n, const FuncOperator op, const FuncMapping mapping,
const FuncComposition composition,
const Monoid &identity_monoid,
const Action &identity_action) {
init(n, op, mapping, composition, identity_monoid, identity_action);
}
LazySegmentTree(const vector<Monoid> &v, const FuncOperator op,
const FuncMapping mapping, const FuncComposition composition,
const Monoid &identity_monoid,
const Action &identity_action) {
init(v, op, mapping, composition, identity_monoid, identity_action);
}
void init(int n, const FuncOperator op, const FuncMapping mapping,
const FuncComposition composition, const Monoid &identity_monoid,
const Action &identity_action) {
N = n, OP = op, MAPPING = mapping, COMPOSITION = composition;
IDENTITY_MONOID = identity_monoid, IDENTITY_ACTION = identity_action;
log = 0, offset = 1;
while (offset < N) ++log, offset <<= 1;
dat.assign(offset * 2, IDENTITY_MONOID);
lazy.assign(offset * 2, IDENTITY_ACTION);
}
void init(const vector<Monoid> &v, const FuncOperator op,
const FuncMapping mapping, const FuncComposition composition,
const Monoid &identity_monoid, const Action &identity_action) {
init((int)v.size(), op, mapping, composition, identity_monoid,
identity_action);
build(v);
}
void build(const vector<Monoid> &v) {
assert(N == (int)v.size());
for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
for (int k = offset - 1; k > 0; --k) pull_dat(k);
}
int size() const { return N; }
// basic functions for lazy segment tree
void pull_dat(int k) { dat[k] = OP(dat[k * 2], dat[k * 2 + 1]); }
void apply_lazy(int k, const Action &f) {
dat[k] = MAPPING(f, dat[k]);
if (k < offset) lazy[k] = COMPOSITION(f, lazy[k]);
}
void push_lazy(int k) {
apply_lazy(k * 2, lazy[k]);
apply_lazy(k * 2 + 1, lazy[k]);
lazy[k] = IDENTITY_ACTION;
}
void pull_dat_deep(int k) {
for (int h = 1; h <= log; ++h) pull_dat(k >> h);
}
void push_lazy_deep(int k) {
for (int h = log; h >= 1; --h) push_lazy(k >> h);
}
// setter and getter, update A[i], i is 0-indexed, O(log N)
void set(int i, const Monoid &v) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
dat[k] = v;
pull_dat_deep(k);
}
Monoid get(int i) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
return dat[k];
}
Monoid operator[](int i) { return get(i); }
// apply f for index i
void apply(int i, const Action &f) {
assert(0 <= i && i < N);
int k = i + offset;
push_lazy_deep(k);
dat[k] = MAPPING(f, dat[k]);
pull_dat_deep(k);
}
// apply f for interval [l, r)
void apply(int l, int r, const Action &f) {
assert(0 <= l && l <= r && r <= N);
if (l == r) return;
l += offset, r += offset;
for (int h = log; h >= 1; --h) {
if (((l >> h) << h) != l) push_lazy(l >> h);
if (((r >> h) << h) != r) push_lazy((r - 1) >> h);
}
int original_l = l, original_r = r;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) apply_lazy(l++, f);
if (r & 1) apply_lazy(--r, f);
}
l = original_l, r = original_r;
for (int h = 1; h <= log; ++h) {
if (((l >> h) << h) != l) pull_dat(l >> h);
if (((r >> h) << h) != r) pull_dat((r - 1) >> h);
}
}
// get prod of interval [l, r)
Monoid prod(int l, int r) {
assert(0 <= l && l <= r && r <= N);
if (l == r) return IDENTITY_MONOID;
l += offset, r += offset;
for (int h = log; h >= 1; --h) {
if (((l >> h) << h) != l) push_lazy(l >> h);
if (((r >> h) << h) != r) push_lazy(r >> h);
}
Monoid val_left = IDENTITY_MONOID, val_right = IDENTITY_MONOID;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) val_left = OP(val_left, dat[l++]);
if (r & 1) val_right = OP(dat[--r], val_right);
}
return OP(val_left, val_right);
}
Monoid all_prod() { return dat[1]; }
// get max r such that f(v) = True (v = prod(l, r)), O(log N)
// f(IDENTITY) need to be True
int max_right(const function<bool(Monoid)> f, int l = 0) {
if (l == N) return N;
l += offset;
push_lazy_deep(l);
Monoid sum = IDENTITY_MONOID;
do {
while (l % 2 == 0) l >>= 1;
if (!f(OP(sum, dat[l]))) {
while (l < offset) {
push_lazy(l);
l = l * 2;
if (f(OP(sum, dat[l]))) {
sum = OP(sum, dat[l]);
++l;
}
}
return l - offset;
}
sum = OP(sum, dat[l]);
++l;
} while ((l & -l) != l); // stop if l = 2^e
return N;
}
// get min l that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int min_left(const function<bool(Monoid)> f, int r = -1) {
if (r == 0) return 0;
if (r == -1) r = N;
r += offset;
push_lazy_deep(r - 1);
Monoid sum = IDENTITY_MONOID;
do {
--r;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(OP(dat[r], sum))) {
while (r < offset) {
push_lazy(r);
r = r * 2 + 1;
if (f(OP(dat[r], sum))) {
sum = OP(dat[r], sum);
--r;
}
}
return r + 1 - offset;
}
sum = OP(dat[r], sum);
} while ((r & -r) != r);
return 0;
}
// debug stream
friend ostream &operator<<(ostream &s, LazySegmentTree seg) {
for (int i = 0; i < (int)seg.size(); ++i) {
s << seg[i];
if (i != (int)seg.size() - 1) s << " ";
}
return s;
}
// dump
void dump() {
for (int i = 0; i <= log; ++i) {
for (int j = (1 << i); j < (1 << (i + 1)); ++j) {
cout << "{" << dat[j] << "," << lazy[j] << "} ";
}
cout << endl;
}
}
};
// Segment Tree
template <class Monoid>
struct SegmentTree {
using Func = function<Monoid(Monoid, Monoid)>;
// core member
int N;
Func OP;
Monoid IDENTITY;
// inner data
int log, offset;
vector<Monoid> dat;
// constructor
SegmentTree() {}
SegmentTree(int n, const Func &op, const Monoid &identity) {
init(n, op, identity);
}
SegmentTree(const vector<Monoid> &v, const Func &op, const Monoid &identity) {
init(v, op, identity);
}
void init(int n, const Func &op, const Monoid &identity) {
N = n;
OP = op;
IDENTITY = identity;
log = 0, offset = 1;
while (offset < N) ++log, offset <<= 1;
dat.assign(offset * 2, IDENTITY);
}
void init(const vector<Monoid> &v, const Func &op, const Monoid &identity) {
init((int)v.size(), op, identity);
build(v);
}
void pull(int k) { dat[k] = OP(dat[k * 2], dat[k * 2 + 1]); }
void build(const vector<Monoid> &v) {
assert(N == (int)v.size());
for (int i = 0; i < N; ++i) dat[i + offset] = v[i];
for (int k = offset - 1; k > 0; --k) pull(k);
}
void clear() { dat.assign(dat.size(), IDENTITY); }
int size() const { return N; }
Monoid operator[](int i) const { return dat[i + offset]; }
// update A[i], i is 0-indexed, O(log N)
void set(int i, const Monoid &v) {
assert(0 <= i && i < N);
int k = i + offset;
dat[k] = v;
while (k >>= 1) pull(k);
}
// get [l, r), l and r are 0-indexed, O(log N)
Monoid prod(int l, int r) {
assert(0 <= l && l <= r && r <= N);
Monoid val_left = IDENTITY, val_right = IDENTITY;
l += offset, r += offset;
for (; l < r; l >>= 1, r >>= 1) {
if (l & 1) val_left = OP(val_left, dat[l++]);
if (r & 1) val_right = OP(dat[--r], val_right);
}
return OP(val_left, val_right);
}
Monoid all_prod() { return dat[1]; }
// get max r such that f(v) = True (v = prod(l, r)), O(log N)
// f(IDENTITY) need to be True
int max_right(const function<bool(Monoid)> f, int l = 0) {
if (l == N) return N;
l += offset;
Monoid sum = IDENTITY;
do {
while (l % 2 == 0) l >>= 1;
if (!f(OP(sum, dat[l]))) {
while (l < offset) {
l = l * 2;
if (f(OP(sum, dat[l]))) {
sum = OP(sum, dat[l]);
++l;
}
}
return l - offset;
}
sum = OP(sum, dat[l]);
++l;
} while ((l & -l) != l); // stop if l = 2^e
return N;
}
// get min l that f(get(l, r)) = True (0-indexed), O(log N)
// f(IDENTITY) need to be True
int min_left(const function<bool(Monoid)> f, int r = -1) {
if (r == 0) return 0;
if (r == -1) r = N;
r += offset;
Monoid sum = IDENTITY;
do {
--r;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(OP(dat[r], sum))) {
while (r < offset) {
r = r * 2 + 1;
if (f(OP(dat[r], sum))) {
sum = OP(dat[r], sum);
--r;
}
}
return r + 1 - offset;
}
sum = OP(dat[r], sum);
} while ((r & -r) != r);
return 0;
}
// debug
friend ostream &operator<<(ostream &s, const SegmentTree &seg) {
for (int i = 0; i < (int)seg.size(); ++i) {
s << seg[i];
if (i != (int)seg.size() - 1) s << " ";
}
return s;
}
};
// Union-Find
struct UnionFind {
// core member
vector<int> par;
// constructor
UnionFind() {}
UnionFind(int n) : par(n, -1) {}
void init(int n) { par.assign(n, -1); }
// core methods
int root(int x) {
if (par[x] < 0)
return x;
else
return par[x] = root(par[x]);
}
bool same(int x, int y) { return root(x) == root(y); }
bool merge(int x, int y) {
x = root(x), y = root(y);
if (x == y) return false;
if (par[x] > par[y]) swap(x, y); // merge technique
par[x] += par[y];
par[y] = x;
return true;
}
int size(int x) { return -par[root(x)]; }
// get groups
vector<vector<int>> groups() {
vector<vector<int>> member(par.size());
for (int v = 0; v < (int)par.size(); ++v) {
member[root(v)].push_back(v);
}
vector<vector<int>> res;
for (int v = 0; v < (int)par.size(); ++v) {
if (!member[v].empty()) res.push_back(member[v]);
}
return res;
}
// debug
friend ostream &operator<<(ostream &s, UnionFind uf) {
const vector<vector<int>> &gs = uf.groups();
for (const vector<int> &g : gs) {
s << "group: ";
for (int v : g) s << v << " ";
s << endl;
}
return s;
}
};
namespace NTT {
long long modpow(long long a, long long n, int mod) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mod;
a = a * a % mod;
n >>= 1;
}
return res;
}
long long modinv(long long a, int mod) {
long long b = mod, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b, swap(a, b);
u -= t * v, swap(u, v);
}
u %= mod;
if (u < 0) u += mod;
return u;
}
int calc_primitive_root(int mod) {
if (mod == 2) return 1;
if (mod == 167772161) return 3;
if (mod == 469762049) return 3;
if (mod == 754974721) return 11;
if (mod == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
long long x = (mod - 1) / 2;
while (x % 2 == 0) x /= 2;
for (long long i = 3; i * i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) x /= i;
}
}
if (x > 1) divs[cnt++] = x;
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (modpow(g, (mod - 1) / divs[i], mod) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
int get_fft_size(int N, int M) {
int size_a = 1, size_b = 1;
while (size_a < N) size_a <<= 1;
while (size_b < M) size_b <<= 1;
return max(size_a, size_b) << 1;
}
// number-theoretic transform
template <class mint>
void trans(vector<mint> &v, bool inv = false) {
if (v.empty()) return;
int N = (int)v.size();
int MOD = v[0].get_mod();
int PR = calc_primitive_root(MOD);
static bool first = true;
static vector<long long> vbw(30), vibw(30);
if (first) {
first = false;
for (int k = 0; k < 30; ++k) {
vbw[k] = modpow(PR, (MOD - 1) >> (k + 1), MOD);
vibw[k] = modinv(vbw[k], MOD);
}
}
for (int i = 0, j = 1; j < N - 1; j++) {
for (int k = N >> 1; k > (i ^= k); k >>= 1);
if (i > j) swap(v[i], v[j]);
}
for (int k = 0, t = 2; t <= N; ++k, t <<= 1) {
long long bw = vbw[k];
if (inv) bw = vibw[k];
for (int i = 0; i < N; i += t) {
mint w = 1;
for (int j = 0; j < t / 2; ++j) {
int j1 = i + j, j2 = i + j + t / 2;
mint c1 = v[j1], c2 = v[j2] * w;
v[j1] = c1 + c2;
v[j2] = c1 - c2;
w *= bw;
}
}
}
if (inv) {
long long invN = modinv(N, MOD);
for (int i = 0; i < N; ++i) v[i] = v[i] * invN;
}
}
// for garner
static constexpr int MOD0 = 754974721;
static constexpr int MOD1 = 167772161;
static constexpr int MOD2 = 469762049;
using mint0 = Fp<MOD0>;
using mint1 = Fp<MOD1>;
using mint2 = Fp<MOD2>;
static const mint1 imod0 = 95869806; // modinv(MOD0, MOD1);
static const mint2 imod1 = 104391568; // modinv(MOD1, MOD2);
static const mint2 imod01 = 187290749; // imod1 / MOD0;
// small case (T = mint, long long)
template <class T>
vector<T> naive_mul(const vector<T> &A, const vector<T> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
vector<T> res(N + M - 1);
for (int i = 0; i < N; ++i)
for (int j = 0; j < M; ++j) res[i + j] += A[i] * B[j];
return res;
}
// mul by convolution
template <class mint>
vector<mint> mul(const vector<mint> &A, const vector<mint> &B) {
if (A.empty() || B.empty()) return {};
int N = (int)A.size(), M = (int)B.size();
if (min(N, M) < 30) return naive_mul(A, B);
int MOD = A[0].get_mod();
int size_fft = get_fft_size(N, M);
if (MOD == 998244353) {
vector<mint> a(size_fft), b(size_fft), c(size_fft);
for (int i = 0; i < N; ++i) a[i] = A[i];
for (int i = 0; i < M; ++i) b[i] = B[i];
trans(a), trans(b);
vector<mint> res(size_fft);
for (int i = 0; i < size_fft; ++i) res[i] = a[i] * b[i];
trans(res, true);
res.resize(N + M - 1);
return res;
}
vector<mint0> a0(size_fft, 0), b0(size_fft, 0), c0(size_fft, 0);
vector<mint1> a1(size_fft, 0), b1(size_fft, 0), c1(size_fft, 0);
vector<mint2> a2(size_fft, 0), b2(size_fft, 0), c2(size_fft, 0);
for (int i = 0; i < N; ++i)
a0[i] = A[i].val, a1[i] = A[i].val, a2[i] = A[i].val;
for (int i = 0; i < M; ++i)
b0[i] = B[i].val, b1[i] = B[i].val, b2[i] = B[i].val;
trans(a0), trans(a1), trans(a2), trans(b0), trans(b1), trans(b2);
for (int i = 0; i < size_fft; ++i) {
c0[i] = a0[i] * b0[i];
c1[i] = a1[i] * b1[i];
c2[i] = a2[i] * b2[i];
}
trans(c0, true), trans(c1, true), trans(c2, true);
mint mod0 = MOD0, mod01 = mod0 * MOD1;
vector<mint> res(N + M - 1);
for (int i = 0; i < N + M - 1; ++i) {
int y0 = c0[i].val;
int y1 = (imod0 * (c1[i] - y0)).val;
int y2 = (imod01 * (c2[i] - y0) - imod1 * y1).val;
res[i] = mod01 * y2 + mod0 * y1 + y0;
}
return res;
}
}; // namespace NTT
// Formal Power Series
template <typename mint>
struct FPS : vector<mint> {
using vector<mint>::vector;
// constructor
constexpr FPS(const vector<mint> &r) : vector<mint>(r) {}
// core operator
constexpr FPS pre(int siz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), siz));
}
constexpr FPS rev() const {
FPS res = *this;
reverse(begin(res), end(res));
return res;
}
constexpr FPS &normalize() {
while (!this->empty() && this->back() == 0) this->pop_back();
return *this;
}
// basic operator
constexpr FPS operator-() const noexcept {
FPS res = (*this);
for (int i = 0; i < (int)res.size(); ++i) res[i] = -res[i];
return res;
}
constexpr FPS operator+(const mint &v) const { return FPS(*this) += v; }
constexpr FPS operator+(const FPS &r) const { return FPS(*this) += r; }
constexpr FPS operator-(const mint &v) const { return FPS(*this) -= v; }
constexpr FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
constexpr FPS operator*(const mint &v) const { return FPS(*this) *= v; }
constexpr FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
constexpr FPS operator/(const mint &v) const { return FPS(*this) /= v; }
constexpr FPS operator/(const FPS &r) const { return FPS(*this) /= r; }
constexpr FPS operator%(const FPS &r) const { return FPS(*this) %= r; }
constexpr FPS operator<<(int x) const { return FPS(*this) <<= x; }
constexpr FPS operator>>(int x) const { return FPS(*this) >>= x; }
constexpr FPS &operator+=(const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] += v;
return *this;
}
constexpr FPS &operator+=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] += r[i];
return this->normalize();
}
constexpr FPS &operator-=(const mint &v) {
if (this->empty()) this->resize(1);
(*this)[0] -= v;
return *this;
}
constexpr FPS &operator-=(const FPS &r) {
if (r.size() > this->size()) this->resize(r.size());
for (int i = 0; i < (int)r.size(); ++i) (*this)[i] -= r[i];
return this->normalize();
}
constexpr FPS &operator*=(const mint &v) {
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= v;
return *this;
}
constexpr FPS &operator*=(const FPS &r) {
return *this = NTT::mul((*this), r);
}
constexpr FPS &operator/=(const mint &v) {
assert(v != 0);
mint iv = modinv(v);
for (int i = 0; i < (int)this->size(); ++i) (*this)[i] *= iv;
return *this;
}
// division, r must be normalized (r.back() must not be 0)
constexpr FPS &operator/=(const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
if (this->size() < r.size()) {
this->clear();
return *this;
}
int need = (int)this->size() - (int)r.size() + 1;
*this = (rev().pre(need) * r.rev().inv(need)).pre(need).rev();
return *this;
}
constexpr FPS &operator%=(const FPS &r) {
assert(!r.empty());
assert(r.back() != 0);
this->normalize();
FPS q = (*this) / r;
return *this -= q * r;
}
constexpr FPS &operator<<=(int x) {
FPS res(x, 0);
res.insert(res.end(), begin(*this), end(*this));
return *this = res;
}
constexpr FPS &operator>>=(int x) {
FPS res;
res.insert(res.end(), begin(*this) + x, end(*this));
return *this = res;
}
constexpr mint eval(const mint &v) {
mint res = 0;
for (int i = (int)this->size() - 1; i >= 0; --i) {
res *= v;
res += (*this)[i];
}
return res;
}
// advanced operation
// df/dx
constexpr FPS diff() const {
int n = (int)this->size();
FPS res(n - 1);
for (int i = 1; i < n; ++i) res[i - 1] = (*this)[i] * i;
return res;
}
// \int f dx
constexpr FPS integral() const {
int n = (int)this->size();
FPS res(n + 1, 0);
for (int i = 0; i < n; ++i) res[i + 1] = (*this)[i] / (i + 1);
return res;
}
// inv(f), f[0] must not be 0
constexpr FPS inv(int deg) const {
assert((*this)[0] != 0);
if (deg < 0) deg = (int)this->size();
FPS res({mint(1) / (*this)[0]});
for (int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * pre(i << 1)).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS inv() const { return inv((int)this->size()); }
// log(f) = \int f'/f dx, f[0] must be 1
constexpr FPS log(int deg) const {
assert((*this)[0] == 1);
FPS res = (diff() * inv(deg)).integral();
res.resize(deg);
return res;
}
constexpr FPS log() const { return log((int)this->size()); }
// exp(f), f[0] must be 0
constexpr FPS exp(int deg) const {
assert((*this)[0] == 0);
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = res * (pre(i << 1) - res.log(i << 1) + 1).pre(i << 1);
}
res.resize(deg);
return res;
}
constexpr FPS exp() const { return exp((int)this->size()); }
// pow(f) = exp(e * log f)
constexpr FPS pow(long long e, int deg) const {
if (e == 0) {
FPS res(deg, 0);
res[0] = 1;
return res;
}
long long i = 0;
while (i < (int)this->size() && (*this)[i] == 0) ++i;
if (i == (int)this->size() || i > (deg - 1) / e) return FPS(deg, 0);
mint k = (*this)[i];
FPS res = ((((*this) >> i) / k).log(deg) * e).exp(deg) * mint(k).pow(e)
<< (e * i);
res.resize(deg);
return res;
}
constexpr FPS pow(long long e) const { return pow(e, (int)this->size()); }
// sqrt(f), f[0] must be 1
constexpr FPS sqrt_base(int deg) const {
assert((*this)[0] == 1);
mint inv2 = mint(1) / 2;
FPS res(1, 1);
for (int i = 1; i < deg; i <<= 1) {
res = (res + pre(i << 1) * res.inv(i << 1)).pre(i << 1);
for (mint &x : res) x *= inv2;
}
res.resize(deg);
return res;
}
constexpr FPS sqrt_base() const { return sqrt_base((int)this->size()); }
// friend operators
friend constexpr FPS diff(const FPS &f) { return f.diff(); }
friend constexpr FPS integral(const FPS &f) { return f.integral(); }
friend constexpr FPS inv(const FPS &f, int deg) { return f.inv(deg); }
friend constexpr FPS inv(const FPS &f) { return f.inv((int)f.size()); }
friend constexpr FPS log(const FPS &f, int deg) { return f.log(deg); }
friend constexpr FPS log(const FPS &f) { return f.log((int)f.size()); }
friend constexpr FPS exp(const FPS &f, int deg) { return f.exp(deg); }
friend constexpr FPS exp(const FPS &f) { return f.exp((int)f.size()); }
friend constexpr FPS pow(const FPS &f, long long e, int deg) {
return f.pow(e, deg);
}
friend constexpr FPS pow(const FPS &f, long long e) {
return f.pow(e, (int)f.size());
}
friend constexpr FPS sqrt_base(const FPS &f, int deg) {
return f.sqrt_base(deg);
}
friend constexpr FPS sqrt_base(const FPS &f) {
return f.sqrt_base((int)f.size());
}
};
using Graph = vector<vector<int>>;
struct LCA {
vector<vector<int>> parent; // parent[d][v] := 2^d-th parent of v
vector<int> depth;
LCA() {}
LCA(const Graph &G, int r = 0) { init(G, r); }
void init(const Graph &G, int r = 0) {
int V = (int)G.size();
int h = 1;
while ((1 << h) < V) ++h;
parent.assign(h, vector<int>(V, -1));
depth.assign(V, -1);
dfs(G, r, -1, 0);
for (int i = 0; i + 1 < (int)parent.size(); ++i)
for (int v = 0; v < V; ++v)
if (parent[i][v] != -1) parent[i + 1][v] = parent[i][parent[i][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 != p) dfs(G, e, v, d + 1);
}
int get(int u, int v) {
if (depth[u] > depth[v]) swap(u, v);
for (int i = 0; i < (int)parent.size(); ++i)
if ((depth[v] - depth[u]) & (1 << i)) v = parent[i][v];
if (u == v) return u;
for (int i = (int)parent.size() - 1; i >= 0; --i) {
if (parent[i][u] != parent[i][v]) {
u = parent[i][u];
v = parent[i][v];
}
}
return parent[0][u];
}
};
// ローリングハッシュ
struct RollingHash {
static const int base1 = 1007, base2 = 2009;
static const int mod1 = 1000000007, mod2 = 1000000009;
vector<long long> hash1, hash2, power1, power2;
// construct
RollingHash(const string &S) {
int n = (int)S.size();
hash1.assign(n + 1, 0), hash2.assign(n + 1, 0);
power1.assign(n + 1, 1), power2.assign(n + 1, 1);
for (int i = 0; i < n; ++i) {
hash1[i + 1] = (hash1[i] * base1 + S[i]) % mod1;
hash2[i + 1] = (hash2[i] * base2 + S[i]) % mod2;
power1[i + 1] = (power1[i] * base1) % mod1;
power2[i + 1] = (power2[i] * base2) % mod2;
}
}
// get hash value of S[left:right]
inline long long get(int l, int r) const {
long long res1 = hash1[r] - hash1[l] * power1[r - l] % mod1;
if (res1 < 0) res1 += mod1;
long long res2 = hash2[r] - hash2[l] * power2[r - l] % mod2;
if (res2 < 0) res2 += mod2;
return res1 * mod2 + res2;
}
// get hash value of S
inline long long get() const { return hash1.back() * mod2 + hash2.back(); }
// get lcp of S[a:] and S[b:]
inline int getLCP(int a, int b) const {
int len = min((int)hash1.size() - a, (int)hash1.size() - b);
int low = 0, high = len;
while (high - low > 1) {
int mid = (low + high) >> 1;
if (get(a, a + mid) != get(b, b + mid))
high = mid;
else
low = mid;
}
return low;
}
// get lcp of S[a:] and T[b:]
inline int getLCP(const RollingHash &T, int a, int b) const {
int len = min((int)hash1.size() - a, (int)hash1.size() - b);
int low = 0, high = len;
while (high - low > 1) {
int mid = (low + high) >> 1;
if (get(a, a + mid) != T.get(b, b + mid))
high = mid;
else
low = mid;
}
return low;
}
};
int main() {
// 1<<iに注意！1LL<<iを必ず使う
// endlの代わりに'\n'を使う
// map,unordered_mapを安易に使わない遅いから
// multisetにすべきところをsetにして壊れるやつ
// これがないと落ちることがある
// using mint = Fp<998244353>;
// using mint = ld;
ios_base::sync_with_stdio(false);
cin.tie(0);
ll t;
cin >> t;
while (t--) {
ld ax, ay, bx, by, cx, cy;
cin >> ax >> ay >> bx >> by >> cx >> cy;
ld a = atan(ay / (ax + 0.000000001));
ld b = atan(by / (bx + 0.000000001));
ld c = atan(cy / (cx + 0.000000001));
// cerr << a << " " << b << " " << c << endl;
if (abs(a + b - c) < 0.000000001 ||
abs(abs(a + b - c) - M_PI) < 0.000000001) {
cout << "Yes" << endl;
} else {
cout << "No" << endl;
}
}
}