結果
| 問題 |
No.2960 Judgement
|
| ユーザー |
 にょぐた
|
| 提出日時 | 2025-01-25 11:48:22 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 777 ms |
| コード長 | 44,816 bytes |
| コンパイル時間 | 6,669 ms |
| コンパイル使用メモリ | 336,176 KB |
| 実行使用メモリ | 6,820 KB |
| 最終ジャッジ日時 | 2025-01-25 11:48:30 |
| 合計ジャッジ時間 | 7,805 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 16 |
ソースコード
#include "bits/stdc++.h"
#include<iostream>
#include <numeric>
#include <atcoder/all>
using namespace std;
using namespace atcoder;
// clang-format off
/* accelration */
// 高速バイナリ生成
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
// cin cout の結びつけ解除, stdioと同期しない(入出力非同期化)
// cとstdの入出力を混在させるとバグるので注意
struct Fast { Fast() { std::cin.tie(0); ios::sync_with_stdio(false); } } fast;
using mint9 = modint998244353;
/* alias */
using ull = unsigned long long;
using ll = long long;
using vi = vector<int>;
using vl = vector<long>;
using vll = vector<long long>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vd = vector<double>;
using vs = vector<string>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<double, double>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vpii = vector<pii>;
using vpll = vector<pll>;
using vpdd = vector<pdd>;
using vm = vector<mint9>;
using vvm = vector<vm>;
using vvvm = vector<vvm>;
using vs = vector<string>;
/* define short */
#define pb push_back
// #define mp make_pair
#define all(obj) (obj).begin(), (obj).end()
#define YESNO(bool) if(bool){cout<<"YES"<<endl;}else{cout<<"NO"<<endl;}
#define yesno(bool) if(bool){cout<<"yes"<<endl;}else{cout<<"no"<<endl;}
#define YesNo(bool) if(bool){cout<<"Yes"<<endl;}else{cout<<"No"<<endl;}
/* REP macro */
#define reps(i, a, n) for (ll i = (a); i < (ll)(n); ++i)
#define rep(i, n) reps(i, 0, n)
#define rrep(i, n) reps(i, 1, n + 1)
#define repd(i,n) for(ll i=n-1;i>=0;i--)
#define rrepd(i,n) for(ll i=n;i>=1;i--)
#define repsd(i, a, n) for(ll i=n;i>=a;i--)
#define fore(i,a) for(auto &i:a)
/* 追加分 */
#define vsort(v) sort(v.begin(), v.end())
#define verase(v) v.erase(unique(v.begin(), v.end()), v.end())
#define vlb(v, x) lower_bound(v.begin(), v.end(), x) - v.begin()
#define argsort(v) sort(xy.begin(), xy.end(), [](const auto &p1, const auto &p2) { return atan2l(p1.second, p1.first) < atan2l(p2.second, p2.first);})
/* debug */
// 標準エラー出力を含む提出はrejectされる場合もあるので注意
#define debug(x) cerr << "\033[33m(line:" << __LINE__ << ") " << #x << ": " << x << "\033[m" << endl;
/* int128 */
#define __int128_t ll
/* func */
inline int in_int() { int x; cin >> x; return x; }
inline ll in_ll() { ll x; cin >> x; return x; }
inline string in_str() { string x; cin >> x; return x; }
// search_length: 走査するベクトル長の上限(先頭から何要素目までを検索対象とするか、1始まりで)
template <typename T> inline bool vector_finder(std::vector<T> vec, T element, unsigned int search_length) {
auto itr = std::find(vec.begin(), vec.end(), element);
size_t index = std::distance(vec.begin(), itr);
if (index == vec.size() || index >= search_length) { return false; }
else { return true; }
}
template <typename T> inline void print(const vector<T>& v, string s = " ")
{
rep(i, v.size()) cout << v[i] << (i != (ll)v.size() - 1 ? s : "\n");
}
template <typename T, typename S> inline void print(const pair<T, S>& p)
{
cout << p.first << " " << p.second << endl;
}
template <typename T> inline void print(const T& x) { cout << x << "\n"; }
// inline void printd(double x) { cout << fixed << setprecision(15) << x << endl; }
template <typename T, typename S> inline void print(const vector<pair<T, S>>& v)
{
for (auto&& p : v) print(p);
}
// 第一引数と第二引数を比較し、第一引数(a)をより大きい/小さい値に上書き
template <typename T> inline bool chmin(T& a, const T& b) { bool compare = a > b; if (a > b) a = b; return compare; }
template <typename T> inline bool chmax(T& a, const T& b) { bool compare = a < b; if (a < b) a = b; return compare; }
// gcd lcm
// C++17からは標準実装
// template <typename T> T gcd(T a, T b) {if (b == 0)return a; else return gcd(b, a % b);}
// template <typename T> inline T lcm(T a, T b) {return (a * b) / gcd(a, b);}
// clang-format on
// 提出の際はコメントアウトすること
// #define __builtin_ctzll _tzcnt_u64
int alt__builtin_clz(unsigned int x)
{
int rank = 0;
while (x) {
rank++;
x >>= 1;
}
return 32 - rank;
}
static inline int alt__builtin_ctz(unsigned int x)
{
rep(i, 32) {
if (x & 1) return i;
x >>= 1;
}
}
static inline int alt__builtin_ctzll(unsigned long long x)
{
rep(i, 64) {
if (x & 1) return i;
x >>= 1;
}
}
template< typename T = int >
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template< typename T = int >
struct Graph {
vector< vector< Edge< T > > > g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const {
return g.size();
}
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false, bool directed = false) {
for (int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted) cin >> c;
if (directed) add_directed_edge(a, b, c);
else add_edge(a, b, c);
}
}
inline vector< Edge< T > >& operator[](const int& k) {
return g[k];
}
inline const vector< Edge< T > >& operator[](const int& k) const {
return g[k];
}
};
template< typename T = int >
using Edges = vector< Edge< T > >;
template< class T >
struct Matrix {
vector< vector< T > > A;
Matrix() {}
Matrix(size_t n, size_t m) : A(n, vector< T >(m, 0)) {}
Matrix(size_t n) : A(n, vector< T >(n, 0)) {};
size_t height() const {
return (A.size());
}
size_t width() const {
return (A[0].size());
}
inline const vector< T >& operator[](int k) const {
return (A.at(k));
}
inline vector< T >& operator[](int k) {
return (A.at(k));
}
static Matrix I(size_t n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix& operator+=(const Matrix& B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] += B[i][j];
return (*this);
}
Matrix& operator-=(const Matrix& B) {
size_t n = height(), m = width();
assert(n == B.height() && m == B.width());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
(*this)[i][j] -= B[i][j];
return (*this);
}
Matrix& operator*=(const Matrix& B) {
size_t n = height(), m = B.width(), p = width();
assert(p == B.height());
vector< vector< T > > C(n, vector< T >(m, 0));
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
for (int k = 0; k < p; k++)
C[i][j] = (C[i][j] + (*this)[i][k] * B[k][j]);
A.swap(C);
return (*this);
}
Matrix& operator^=(long long k) {
Matrix B = Matrix::I(height());
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix& B) const {
return (Matrix(*this) += B);
}
Matrix operator-(const Matrix& B) const {
return (Matrix(*this) -= B);
}
Matrix operator*(const Matrix& B) const {
return (Matrix(*this) *= B);
}
Matrix operator^(const long long k) const {
return (Matrix(*this) ^= k);
}
friend ostream& operator<<(ostream& os, Matrix& p) {
size_t n = p.height(), m = p.width();
for (int i = 0; i < n; i++) {
os << "[";
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() {
Matrix B(*this);
assert(width() == height());
T ret = 1;
for (int i = 0; i < width(); i++) {
int idx = -1;
for (int j = i; j < width(); j++) {
if (B[j][i] != 0) idx = j;
}
if (idx == -1) return (0);
if (i != idx) {
ret *= -1;
swap(B[i], B[idx]);
}
ret *= B[i][i];
T vv = B[i][i];
for (int j = 0; j < width(); j++) {
B[i][j] /= vv;
}
for (int j = i + 1; j < width(); j++) {
T a = B[j][i];
for (int k = 0; k < width(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return (ret);
}
};
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = (u64(0) - u64(mod)) % mod;
static_assert(r* mod == 1, "invalid, r * mod != 1");
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t& b)
: a(reduce(u64(b% mod + mod)* n2)) {};
static constexpr u32 reduce(const u64& b) {
return (b + u64(u32(b) * u32(u32(0) - r)) * mod) >> 32;
}
constexpr mint& operator+=(const mint& b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint& operator-=(const mint& b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint& operator*=(const mint& b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint& operator/=(const mint& b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint& b) const { return mint(*this) += b; }
constexpr mint operator-(const mint& b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint& b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint& b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint& b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint& b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const { return pow(mod - 2); }
friend ostream& operator<<(ostream& os, const mint& b) {
return os << b.get();
}
friend istream& operator>>(istream& is, mint& b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
template <typename mint>
struct NTT {
static constexpr uint32_t get_pr() {
uint32_t _mod = mint::get_mod();
using u64 = uint64_t;
u64 ds[32] = {};
int idx = 0;
u64 m = _mod - 1;
for (u64 i = 2; i * i <= m; ++i) {
if (m % i == 0) {
ds[idx++] = i;
while (m % i == 0) m /= i;
}
}
if (m != 1) ds[idx++] = m;
uint32_t _pr = 2;
while (1) {
int flg = 1;
for (int i = 0; i < idx; ++i) {
u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;
while (b) {
if (b & 1) r = r * a % _mod;
a = a * a % _mod;
b >>= 1;
}
if (r == 1) {
flg = 0;
break;
}
}
if (flg == 1) break;
++_pr;
}
return _pr;
};
static constexpr uint32_t mod = mint::get_mod();
static constexpr uint32_t pr = get_pr();
static constexpr int level = 23;
mint dw[level], dy[level];
void setwy(int k) {
mint w[level], y[level];
w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));
y[k - 1] = w[k - 1].inverse();
for (int i = k - 2; i > 0; --i)
w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];
dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];
for (int i = 3; i < k; ++i) {
dw[i] = dw[i - 1] * y[i - 2] * w[i];
dy[i] = dy[i - 1] * w[i - 2] * y[i];
}
}
NTT() { setwy(level); }
void fft4(vector<mint>& a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
if (k & 1) {
int v = 1 << (k - 1);
for (int j = 0; j < v; ++j) {
mint ajv = a[j + v];
a[j + v] = a[j] - ajv;
a[j] += ajv;
}
}
int u = 1 << (2 + (k & 1));
int v = 1 << (k - 2 - (k & 1));
mint one = mint(1);
mint imag = dw[1];
while (v) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = j1 + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;
}
}
// jh >= 1
mint ww = one, xx = one * dw[2], wx = one;
for (int jh = 4; jh < u;) {
ww = xx * xx, wx = ww * xx;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,
t3 = a[j2 + v] * wx;
mint t0p2 = t0 + t2, t1p3 = t1 + t3;
mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;
a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;
a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;
}
xx *= dw[alt__builtin_ctzll((jh += 4))];
}
u <<= 2;
v >>= 2;
}
}
void ifft4(vector<mint>& a, int k) {
if ((int)a.size() <= 1) return;
if (k == 1) {
mint a1 = a[1];
a[1] = a[0] - a[1];
a[0] = a[0] + a1;
return;
}
int u = 1 << (k - 2);
int v = 1;
mint one = mint(1);
mint imag = dy[1];
while (u) {
// jh = 0
{
int j0 = 0;
int j1 = v;
int j2 = v + v;
int j3 = j2 + v;
for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {
mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;
a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;
a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;
}
}
// jh >= 1
mint ww = one, xx = one * dy[2], yy = one;
u <<= 2;
for (int jh = 4; jh < u;) {
ww = xx * xx, yy = xx * imag;
int j0 = jh * v;
int je = j0 + v;
int j2 = je + v;
for (; j0 < je; ++j0, ++j2) {
mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];
mint t0p1 = t0 + t1, t2p3 = t2 + t3;
mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;
a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;
a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;
}
xx *= dy[alt__builtin_ctzll(jh += 4)];
}
u >>= 4;
v <<= 2;
}
if (k & 1) {
u = 1 << (k - 1);
for (int j = 0; j < u; ++j) {
mint ajv = a[j] - a[j + u];
a[j] += a[j + u];
a[j + u] = ajv;
}
}
}
void ntt(vector<mint>& a) {
if ((int)a.size() <= 1) return;
fft4(a, alt__builtin_ctz(a.size()));
}
void intt(vector<mint>& a) {
if ((int)a.size() <= 1) return;
ifft4(a, alt__builtin_ctz(a.size()));
mint iv = mint(a.size()).inverse();
for (auto& x : a) x *= iv;
}
vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40) {
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
setwy(k);
vector<mint> s(M), t(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(s, k);
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inverse();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
void ntt_doubling(vector<mint>& a) {
int M = (int)a.size();
auto b = a;
intt(b);
mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));
for (int i = 0; i < M; i++) b[i] *= r, r *= zeta;
ntt(b);
copy(begin(b), end(b), back_inserter(a));
}
};
namespace ArbitraryNTT {
using i64 = int64_t;
using u128 = uint64_t;
constexpr int32_t m0 = 167772161;
constexpr int32_t m1 = 469762049;
constexpr int32_t m2 = 754974721;
using mint0 = LazyMontgomeryModInt<m0>;
using mint1 = LazyMontgomeryModInt<m1>;
using mint2 = LazyMontgomeryModInt<m2>;
constexpr int r01 = mint1(m0).inverse().get();
constexpr int r02 = mint2(m0).inverse().get();
constexpr int r12 = mint2(m1).inverse().get();
constexpr int r02r12 = i64(r02) * r12 % m2;
constexpr i64 w1 = m0;
constexpr i64 w2 = i64(m0) * m1;
template <typename T, typename submint>
vector<submint> mul(const vector<T>& a, const vector<T>& b) {
static NTT<submint> ntt;
vector<submint> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = i64(a[i] % submint::get_mod());
for (int i = 0; i < (int)b.size(); ++i) t[i] = i64(b[i] % submint::get_mod());
return ntt.multiply(s, t);
}
template <typename T>
vector<int> multiply(const vector<T>& s, const vector<T>& t, int mod) {
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<int> ret(n);
const int W1 = w1 % mod;
const int W2 = w2 % mod;
for (int i = 0; i < n; i++) {
int n1 = d1[i].get(), n2 = d2[i].get(), a = d0[i].get();
int b = i64(n1 + m1 - a) * r01 % m1;
int c = (i64(n2 + m2 - a) * r02r12 + i64(m2 - b) * r12) % m2;
ret[i] = (i64(a) + i64(b) * W1 + i64(c) * W2) % mod;
}
return ret;
}
template <typename mint>
vector<mint> multiply(const vector<mint>& a, const vector<mint>& b) {
if (a.size() == 0 && b.size() == 0) return {};
if (min<int>(a.size(), b.size()) < 128) {
vector<mint> ret(a.size() + b.size() - 1);
for (int i = 0; i < (int)a.size(); ++i)
for (int j = 0; j < (int)b.size(); ++j) ret[i + j] += a[i] * b[j];
return ret;
}
vector<int> s(a.size()), t(b.size());
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i].get();
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i].get();
vector<int> u = multiply<int>(s, t, mint::get_mod());
vector<mint> ret(u.size());
for (int i = 0; i < (int)u.size(); ++i) ret[i] = mint(u[i]);
return ret;
}
template <typename T>
vector<u128> multiply_u128(const vector<T>& s, const vector<T>& t) {
if (s.size() == 0 && t.size() == 0) return {};
if (min<int>(s.size(), t.size()) < 128) {
vector<u128> ret(s.size() + t.size() - 1);
for (int i = 0; i < (int)s.size(); ++i)
for (int j = 0; j < (int)t.size(); ++j) ret[i + j] += i64(s[i]) * t[j];
return ret;
}
auto d0 = mul<T, mint0>(s, t);
auto d1 = mul<T, mint1>(s, t);
auto d2 = mul<T, mint2>(s, t);
int n = d0.size();
vector<u128> ret(n);
for (int i = 0; i < n; i++) {
i64 n1 = d1[i].get(), n2 = d2[i].get();
i64 a = d0[i].get();
i64 b = (n1 + m1 - a) * r01 % m1;
i64 c = ((n2 + m2 - a) * r02r12 + (m2 - b) * r12) % m2;
ret[i] = a + b * w1 + u128(c) * w2;
}
return ret;
}
} // namespace ArbitraryNTT
template <typename mint>
struct FormalPowerSeries : vector<mint> {
using vector<mint>::vector;
using FPS = FormalPowerSeries;
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;
}
FPS& operator+=(const mint& r) {
if (this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
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;
}
FPS& operator-=(const mint& r) {
if (this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
FPS& operator*=(const mint& v) {
for (int k = 0; k < (int)this->size(); k++) (*this)[k] *= v;
return *this;
}
FPS& operator/=(const FPS& r) {
if (this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
if ((int)r.size() <= 64) {
FPS f(*this), g(r);
g.shrink();
mint coeff = g.back().inverse();
for (auto& x : g) x *= coeff;
int deg = (int)f.size() - (int)g.size() + 1;
int gs = g.size();
FPS quo(deg);
for (int i = deg - 1; i >= 0; i--) {
quo[i] = f[i + gs - 1];
for (int j = 0; j < gs; j++) f[i + j] -= quo[i] * g[j];
}
*this = quo * coeff;
this->resize(n, mint(0));
return *this;
}
return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();
}
FPS& operator%=(const FPS& r) {
*this -= *this / r * r;
shrink();
return *this;
}
FPS operator+(const FPS& r) const { return FPS(*this) += r; }
FPS operator+(const mint& v) const { return FPS(*this) += v; }
FPS operator-(const FPS& r) const { return FPS(*this) -= r; }
FPS operator-(const mint& v) const { return FPS(*this) -= v; }
FPS operator*(const FPS& r) const { return FPS(*this) *= r; }
FPS operator*(const mint& v) const { return FPS(*this) *= v; }
FPS operator/(const FPS& r) const { return FPS(*this) /= r; }
FPS operator%(const FPS& r) const { return FPS(*this) %= r; }
FPS operator-() const {
FPS ret(this->size());
for (int i = 0; i < (int)this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
void shrink() {
while (this->size() && this->back() == mint(0)) this->pop_back();
}
FPS rev() const {
FPS ret(*this);
reverse(begin(ret), end(ret));
return ret;
}
FPS dot(FPS r) const {
FPS ret(min(this->size(), r.size()));
for (int i = 0; i < (int)ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
FPS pre(int sz) const {
return FPS(begin(*this), begin(*this) + min((int)this->size(), sz));
}
FPS operator>>(int sz) const {
if ((int)this->size() <= sz) return {};
FPS ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
FPS operator<<(int sz) const {
FPS ret(*this);
ret.insert(ret.begin(), sz, mint(0));
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
mint one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
const int n = (int)this->size();
FPS ret(n + 1);
ret[0] = mint(0);
if (n > 0) ret[1] = mint(1);
auto mod = mint::get_mod();
for (int i = 2; i <= n; i++) ret[i] = (-ret[mod % i]) * (mod / i);
for (int i = 0; i < n; i++) ret[i + 1] *= (*this)[i];
return ret;
}
mint eval(mint x) const {
mint r = 0, w = 1;
for (auto& v : *this) r += w * v, w *= x;
return r;
}
FPS log(int deg = -1) const {
assert((*this)[0] == mint(1));
if (deg == -1) deg = (int)this->size();
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
FPS pow(int64_t k, int deg = -1) const {
const int n = (int)this->size();
if (deg == -1) deg = n;
if (k == 0) {
FPS ret(deg);
if (deg) ret[0] = 1;
return ret;
}
for (int i = 0; i < n; i++) {
if ((*this)[i] != mint(0)) {
mint rev = mint(1) / (*this)[i];
FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);
ret *= (*this)[i].pow(k);
ret = (ret << (i * k)).pre(deg);
if ((int)ret.size() < deg) ret.resize(deg, mint(0));
return ret;
}
if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));
}
return FPS(deg, mint(0));
}
static void* ntt_ptr;
static void set_fft();
FPS& operator*=(const FPS& r);
void ntt();
void intt();
void ntt_doubling();
static int ntt_pr();
FPS inv(int deg = -1) const;
FPS exp(int deg = -1) const;
};
template <typename mint>
void* FormalPowerSeries<mint>::ntt_ptr = nullptr;
// ここから任意mod
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
ntt_ptr = nullptr;
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
exit(1);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
exit(1);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
exit(1);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
exit(1);
}
template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint>& r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
auto ret = ArbitraryNTT::multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if (deg == -1) deg = (*this).size();
FormalPowerSeries<mint> ret({ mint(1) / (*this)[0] });
for (int i = 1; i < deg; i <<= 1)
ret = (ret + ret - ret * ret * (*this).pre(i << 1)).pre(i << 1);
return ret.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
assert((*this).size() == 0 || (*this)[0] == mint(0));
if (deg == -1) deg = (int)this->size();
FormalPowerSeries<mint> ret({ mint(1) });
for (int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + mint(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
/*
// ここからNTT素数
template <typename mint>
void FormalPowerSeries<mint>::set_fft() {
if (!ntt_ptr) ntt_ptr = new NTT<mint>;
}
template <typename mint>
FormalPowerSeries<mint>& FormalPowerSeries<mint>::operator*=(
const FormalPowerSeries<mint>& r) {
if (this->empty() || r.empty()) {
this->clear();
return *this;
}
set_fft();
auto ret = static_cast<NTT<mint>*>(ntt_ptr)->multiply(*this, r);
return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());
}
template <typename mint>
void FormalPowerSeries<mint>::ntt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::intt() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->intt(*this);
}
template <typename mint>
void FormalPowerSeries<mint>::ntt_doubling() {
set_fft();
static_cast<NTT<mint>*>(ntt_ptr)->ntt_doubling(*this);
}
template <typename mint>
int FormalPowerSeries<mint>::ntt_pr() {
set_fft();
return static_cast<NTT<mint>*>(ntt_ptr)->pr;
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {
assert((*this)[0] != mint(0));
if (deg == -1) deg = (int)this->size();
FormalPowerSeries<mint> res(deg);
res[0] = { mint(1) / (*this)[0] };
for (int d = 1; d < deg; d <<= 1) {
FormalPowerSeries<mint> f(2 * d), g(2 * d);
for (int j = 0; j < min((int)this->size(), 2 * d); j++) f[j] = (*this)[j];
for (int j = 0; j < d; j++) g[j] = res[j];
f.ntt();
g.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = 0; j < d; j++) f[j] = 0;
f.ntt();
for (int j = 0; j < 2 * d; j++) f[j] *= g[j];
f.intt();
for (int j = d; j < min(2 * d, deg); j++) res[j] = -f[j];
}
return res.pre(deg);
}
template <typename mint>
FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {
using fps = FormalPowerSeries<mint>;
assert((*this).size() == 0 || (*this)[0] == mint(0));
if (deg == -1) deg = this->size();
fps inv;
inv.reserve(deg + 1);
inv.push_back(mint(0));
inv.push_back(mint(1));
auto inplace_integral = [&](fps& F) -> void {
const int n = (int)F.size();
auto mod = mint::get_mod();
while ((int)inv.size() <= n) {
int i = inv.size();
inv.push_back((-inv[mod % i]) * (mod / i));
}
F.insert(begin(F), mint(0));
for (int i = 1; i <= n; i++) F[i] *= inv[i];
};
auto inplace_diff = [](fps& F) -> void {
if (F.empty()) return;
F.erase(begin(F));
mint coeff = 1, one = 1;
for (int i = 0; i < (int)F.size(); i++) {
F[i] *= coeff;
coeff += one;
}
};
fps b{ 1, 1 < (int)this->size() ? (*this)[1] : 0 }, c{ 1 }, z1, z2{ 1, 1 };
for (int m = 2; m < deg; m *= 2) {
auto y = b;
y.resize(2 * m);
y.ntt();
z1 = z2;
fps z(m);
for (int i = 0; i < m; ++i) z[i] = y[i] * z1[i];
z.intt();
fill(begin(z), begin(z) + m / 2, mint(0));
z.ntt();
for (int i = 0; i < m; ++i) z[i] *= -z1[i];
z.intt();
c.insert(end(c), begin(z) + m / 2, end(z));
z2 = c;
z2.resize(2 * m);
z2.ntt();
fps x(begin(*this), begin(*this) + min<int>(this->size(), m));
x.resize(m);
inplace_diff(x);
x.push_back(mint(0));
x.ntt();
for (int i = 0; i < m; ++i) x[i] *= y[i];
x.intt();
x -= b.diff();
x.resize(2 * m);
for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = mint(0);
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= z2[i];
x.intt();
x.pop_back();
inplace_integral(x);
for (int i = m; i < min<int>(this->size(), 2 * m); ++i) x[i] += (*this)[i];
fill(begin(x), begin(x) + m, mint(0));
x.ntt();
for (int i = 0; i < 2 * m; ++i) x[i] *= y[i];
x.intt();
b.insert(end(b), begin(x) + m, end(x));
}
return fps{ begin(b), begin(b) + deg };
}
*/
// ここまでNTT素数
// g が sparse を仮定, f * g.inv() を計算
template <typename mint>
FormalPowerSeries<mint> sparse_div(const FormalPowerSeries<mint>& f,
const FormalPowerSeries<mint>& g,
int deg = -1) {
assert(g.empty() == false && g[0] != mint(0));
if (deg == -1) deg = f.size();
mint ig0 = g[0].inverse();
FormalPowerSeries<mint> s = f * ig0;
s.resize(deg);
vector<pair<int, mint>> gs;
for (int i = 1; i < (int)g.size(); i++) {
if (g[i] != 0) gs.emplace_back(i, g[i] * ig0);
}
for (int i = 0; i < deg; i++) {
for (auto& [j, g_j] : gs) {
if (i + j >= deg) break;
s[i + j] -= s[i] * g_j;
}
}
return s;
}
template <typename mint>
FormalPowerSeries<mint> sparse_inv(const FormalPowerSeries<mint>& f,
int deg = -1) {
assert(f.empty() == false && f[0] != mint(0));
if (deg == -1) deg = f.size();
vector<pair<int, mint>> fs;
for (int i = 1; i < (int)f.size(); i++) {
if (f[i] != 0) fs.emplace_back(i, f[i]);
}
FormalPowerSeries<mint> g(deg);
mint if0 = f[0].inverse();
if (0 < deg) g[0] = if0;
for (int k = 1; k < deg; k++) {
for (auto& [j, fj] : fs) {
if (k < j) break;
g[k] += g[k - j] * fj;
}
g[k] *= -if0;
}
return g;
}
template <typename mint>
FormalPowerSeries<mint> sparse_log(const FormalPowerSeries<mint>& f,
int deg = -1) {
assert(f.empty() == false && f[0] == 1);
if (deg == -1) deg = f.size();
vector<pair<int, mint>> fs;
for (int i = 1; i < (int)f.size(); i++) {
if (f[i] != 0) fs.emplace_back(i, f[i]);
}
int mod = mint::get_mod();
static vector<mint> invs{ 1, 1 };
while ((int)invs.size() <= deg) {
int i = invs.size();
invs.push_back((-invs[mod % i]) * (mod / i));
}
FormalPowerSeries<mint> g(deg);
for (int k = 0; k < deg - 1; k++) {
for (auto& [j, fj] : fs) {
if (k < j) break;
int i = k - j;
g[k + 1] -= g[i + 1] * fj * (i + 1);
}
g[k + 1] *= invs[k + 1];
if (k + 1 < (int)f.size()) g[k + 1] += f[k + 1];
}
return g;
}
template <typename mint>
FormalPowerSeries<mint> sparse_exp(const FormalPowerSeries<mint>& f,
int deg = -1) {
assert(f.empty() or f[0] == 0);
if (deg == -1) deg = f.size();
vector<pair<int, mint>> fs;
for (int i = 1; i < (int)f.size(); i++) {
if (f[i] != 0) fs.emplace_back(i, f[i]);
}
int mod = mint::get_mod();
static vector<mint> invs{ 1, 1 };
while ((int)invs.size() <= deg) {
int i = invs.size();
invs.push_back((-invs[mod % i]) * (mod / i));
}
FormalPowerSeries<mint> g(deg);
if (deg) g[0] = 1;
for (int k = 0; k < deg - 1; k++) {
for (auto& [ip1, fip1] : fs) {
int i = ip1 - 1;
if (k < i) break;
g[k + 1] += fip1 * g[k - i] * (i + 1);
}
g[k + 1] *= invs[k + 1];
}
return g;
}
template <typename mint>
FormalPowerSeries<mint> sparse_pow(const FormalPowerSeries<mint>& f,
long long k, int deg = -1) {
if (deg == -1) deg = f.size();
if (k == 0) {
FormalPowerSeries<mint> g(deg);
if (deg) g[0] = 1;
return g;
}
int zero = 0;
while (zero != (int)f.size() and f[zero] == 0) zero++;
if (zero == (int)f.size() or __int128_t(zero) * k >= deg) {
return FormalPowerSeries<mint>(deg, 0);
}
if (zero != 0) {
FormalPowerSeries<mint> suf{ begin(f) + zero, end(f) };
auto g = sparse_pow(suf, k, deg - zero * k);
FormalPowerSeries<mint> h(zero * k, 0);
copy(begin(g), end(g), back_inserter(h));
return h;
}
int mod = mint::get_mod();
static vector<mint> invs{ 1, 1 };
while ((int)invs.size() <= deg) {
int i = invs.size();
invs.push_back((-invs[mod % i]) * (mod / i));
}
vector<pair<int, mint>> fs;
for (int i = 1; i < (int)f.size(); i++) {
if (f[i] != 0) fs.emplace_back(i, f[i]);
}
FormalPowerSeries<mint> g(deg);
g[0] = f[0].pow(k);
mint denom = f[0].inverse();
k %= mint::get_mod();
for (int a = 1; a < deg; a++) {
for (auto& [i, f_i] : fs) {
if (a < i) break;
g[a] += f_i * g[a - i] * ((k + 1) * i - a);
}
g[a] *= denom * invs[a];
}
return g;
}
/**
* @brief sparse な形式的冪級数の演算
*/
template <typename mint>
vector<mint> BerlekampMassey(const vector<mint>& s) {
const int N = (int)s.size();
vector<mint> b, c;
b.reserve(N + 1);
c.reserve(N + 1);
b.push_back(mint(1));
c.push_back(mint(1));
mint y = mint(1);
for (int ed = 1; ed <= N; ed++) {
int l = int(c.size()), m = int(b.size());
mint x = 0;
for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
b.emplace_back(mint(0));
m++;
if (x == mint(0)) continue;
mint freq = x / y;
if (l < m) {
auto tmp = c;
c.insert(begin(c), m - l, mint(0));
for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
b = tmp;
y = x;
}
else {
for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
}
}
reverse(begin(c), end(c));
return c;
}
template <typename mint>
mint LinearRecurrence(long long k, FormalPowerSeries<mint> Q,
FormalPowerSeries<mint> P) {
Q.shrink();
mint ret = 0;
if (P.size() >= Q.size()) {
auto R = P / Q;
P -= R * Q;
P.shrink();
if (k < (int)R.size()) ret += R[k];
}
if ((int)P.size() == 0) return ret;
FormalPowerSeries<mint>::set_fft();
if (FormalPowerSeries<mint>::ntt_ptr == nullptr) {
P.resize((int)Q.size() - 1);
while (k) {
auto Q2 = Q;
for (int i = 1; i < (int)Q2.size(); i += 2) Q2[i] = -Q2[i];
auto S = P * Q2;
auto T = Q * Q2;
if (k & 1) {
for (int i = 1; i < (int)S.size(); i += 2) P[i >> 1] = S[i];
for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];
}
else {
for (int i = 0; i < (int)S.size(); i += 2) P[i >> 1] = S[i];
for (int i = 0; i < (int)T.size(); i += 2) Q[i >> 1] = T[i];
}
k >>= 1;
}
return ret + P[0];
}
else {
int N = 1;
while (N < (int)Q.size()) N <<= 1;
P.resize(2 * N);
Q.resize(2 * N);
P.ntt();
Q.ntt();
vector<mint> S(2 * N), T(2 * N);
vector<int> btr(N);
for (int i = 0, logn = alt__builtin_ctz(N); i < (1 << logn); i++) {
btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (logn - 1));
}
mint dw = mint(FormalPowerSeries<mint>::ntt_pr())
.inverse()
.pow((mint::get_mod() - 1) / (2 * N));
while (k) {
mint inv2 = mint(2).inverse();
// even degree of Q(x)Q(-x)
T.resize(N);
for (int i = 0; i < N; i++) T[i] = Q[(i << 1) | 0] * Q[(i << 1) | 1];
S.resize(N);
if (k & 1) {
// odd degree of P(x)Q(-x)
for (auto& i : btr) {
S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] -
P[(i << 1) | 1] * Q[(i << 1) | 0]) *
inv2;
inv2 *= dw;
}
}
else {
// even degree of P(x)Q(-x)
for (int i = 0; i < N; i++) {
S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] +
P[(i << 1) | 1] * Q[(i << 1) | 0]) *
inv2;
}
}
swap(P, S);
swap(Q, T);
k >>= 1;
if (k < N) break;
P.ntt_doubling();
Q.ntt_doubling();
}
P.intt();
Q.intt();
return ret + (P * (Q.inv()))[k];
}
}
template <typename mint>
mint kitamasa(long long N, FormalPowerSeries<mint> Q,
FormalPowerSeries<mint> a) {
assert(!Q.empty() && Q[0] != 0);
if (N < (int)a.size()) return a[N];
assert((int)a.size() >= int(Q.size()) - 1);
auto P = a.pre((int)Q.size() - 1) * Q;
P.resize(Q.size() - 1);
return LinearRecurrence<mint>(N, Q, P);
}
/**
* @brief 線形漸化式の高速計算
* @docs docs/fps/kitamasa.md
*/
template <typename mint>
mint nth_term(long long n, const vector<mint>& s) {
using fps = FormalPowerSeries<mint>;
auto bm = BerlekampMassey<mint>(s);
return kitamasa(n, fps{ begin(bm), end(bm) }, fps{ begin(s), end(s) });
}
template <typename T> inline void print(const FormalPowerSeries<T>& v, string s = " ")
{
rep(i, v.size()) cout << v[i] << (i != (ll)v.size() - 1 ? s : "\n");
}
// 定数
const ll INF = 1ll << 60;
const vi dd({ -1,0,1,0,-1 });
const double PI = atan(1) * 4;
double eps = 1e-10;
const ll MOD9 = 998244353;
const ll MOD1 = 1000000007;
using fps9 = FormalPowerSeries<LazyMontgomeryModInt<MOD9>>;
using fps1 = FormalPowerSeries<LazyMontgomeryModInt<MOD1>>;
// 最大公約数
ll gcd(ll a, ll b) {
if (!b) return a;
if (a % b == 0) return b;
else return gcd(b, a % b);
}
// 最小公倍数
ll lcm(ll a, ll b) {
return a * b / gcd(a, b);
}
// インタラクティブ用
void question(vll v) {
cout << "?";
rep(i, v.size()) {
cout << " " << v[i];
}
cout << endl;
}
void answer(vll v) {
cout << "!";
rep(i, v.size()) {
cout << " " << v[i];
}
cout << endl;
}
// 等差数列
ll arith_sum1(ll left, ll right, ll d) {
return (left + right) * (right - left + d) / (2 * d);
}
ll arith_sum2(ll left, ll d, ll num) {
return arith_sum1(left, left + d * (num - 1), d);
}
// 座標圧縮 (破壊的)
void comp(vll& a) {
sort(a.begin(), a.end());
a.erase(unique(a.begin(), a.end()), a.end());
}
ll ll_sqrt(ll x) {
ll ans = sqrt(x);
while ((ans + 1) * (ans + 1) <= x) ans++;
while (ans * ans > x) ans--;
return ans;
}
// 区間min(+idx)遅延セグ木テンプレート
struct S {
ll val, idx, cnt;
};
struct F {
ll x;
};
S min_op(S l, S r) {
if (l.val <= r.val) return l;
else return r;
}
S min_e() { return { INF, -1 }; }
S max_op(S l, S r) {
if (l.val > r.val) return l;
else if (l.val < r.val) return r;
else return { l.val, l.idx, l.cnt + r.cnt };
}
S max_e() { return { -INF, -1, 1 }; }
S mapping(F l, S r) { return { l.x + r.val, r.idx, r.cnt }; }
F composition(F l, F r) { return { l.x + r.x }; }
F id() { return { 0 }; }
//lazy_segtree<S, min_op, min_e, F, mapping, composition, id> seg(n);
int main() {
ll cnt = 0;
rep(i, 8) {
string s;
cin >> s;
if (s == "AC" || s == "NoOut") cnt++;
}
if (cnt > 5) print("Win");
else if (cnt == 5) print("Draw");
else print("Lose");
}