// O(K^2N^3) ... のはず // これは落としたい!! #include using namespace std; //* ATCODER #include using namespace atcoder; typedef modint998244353 mint; //*/ /* BOOST MULTIPRECISION #include using namespace boost::multiprecision; //*/ typedef long long ll; #define rep(i, s, n) for (int i = (int)(s); i < (int)(n); i++) #define rrep(i, s, n) for (int i = (int)(n)-1; i >= (int)(s); i--) #define all(v) v.begin(), v.end() template bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } template T max(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]); return ret; } template T min(vector &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]); return ret; } template T sum(vector &a){ T ret = 0; for (int i=0; i<(int)a.size(); i++) ret += a[i]; return ret; } // https://nyaannyaan.github.io/library/fps/nth-term.hpp.html template vector BerlekampMassey(const vector &s) { const int N = (int)s.size(); vector 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; } // https://yukicoder.me/wiki/black_box_linear_algebra template mint sparse_det(int n, vector> &a) { random_device seed_gen; mt19937 engine(seed_gen()); uniform_int_distribution dist(1, mint::mod() - 1); if ((int)a.size() == 0) return 0; vector d(n); mint ddet = 1; for (int i=0; i g(0); vector b(n), c(n); for (int i=0; i f(2 * n); for (int i=0; i<2*n; i++) { for (int z=0; z nb(n); for (int z=0; z(f); if (n % 2 == 1) g.back() *= -1; return g.back() / ddet; } int main(){ ios_base::sync_with_stdio(false); cin.tie(NULL); int k; cin >> k; int cnt = 2; vector a, b; vector s, t; for(int i=0; i> n >> m; a.push_back(0); b.push_back(cnt); a.push_back(1); b.push_back(cnt + 1); for (int j=0; j> x >> y; x--; y--; a.push_back(x + cnt); b.push_back(y + cnt); } cnt += n; } vector vals; map,int> mp; auto add = [&](int x, int y, mint val) -> void { if (mp.find(pair(x,y)) == mp.end()){ mp[pair(x,y)] = (int)vals.size(); vals.push_back(0); } vals[mp[pair(x,y)]] += val; }; for (int i=0; i<(int)a.size(); i++) { if (a[i] - 1 >= 0 && b[i] - 1 >= 0) { add(a[i]-1,b[i]-1,-1); add(b[i]-1,a[i]-1,-1); } if (a[i] - 1 >= 0) { add(a[i]-1,a[i]-1,+1); } if (b[i] - 1 >= 0) { add(b[i]-1,b[i]-1,+1); } } vector> mat; for (auto[x,v]:mp)mat.push_back(make_tuple(x.first,x.second,vals[v])); cout << sparse_det(cnt-1, mat).val() << endl; }