#line 2 "template.hpp" // #pragma GCC target("avx2") // #pragma GCC optimize("O3") // #pragma GCC optimize("unroll-loops") #include using namespace std; // https://xn--kst.jp/blog/2019/08/29/cpp-comp/ // debug methods // usage: debug(x,y); // vector 出力できるように修正 template ostream& debug_print(ostream& os, const vector& v) { os << "["; for (size_t i = 0; i < v.size(); ++i) { os << v[i]; if (i < v.size() - 1) os << ", "; } os << "]"; return os; } template ostream& debug_print(ostream& os, const T& var) { os << var; return os; } #define CHOOSE(a) CHOOSE2 a #define CHOOSE2(a0, a1, a2, a3, a4, x, ...) x #define debug_1(x1) { cout << #x1 << ": "; debug_print(cout, x1) << endl; } #define debug_2(x1, x2) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << endl; } #define debug_3(x1, x2, x3) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << endl; } #define debug_4(x1, x2, x3, x4) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << endl; } #define debug_5(x1, x2, x3, x4, x5) { cout << #x1 << ": "; debug_print(cout, x1) << ", " << #x2 << ": "; debug_print(cout, x2) << ", " << #x3 << ": "; debug_print(cout, x3) << ", " << #x4 << ": "; debug_print(cout, x4) << ", " << #x5 << ": "; debug_print(cout, x5) << endl; } #ifdef LOCAL #define debug(...) CHOOSE((__VA_ARGS__, debug_5, debug_4, debug_3, debug_2, debug_1, ~))(__VA_ARGS__) #else #define debug(...) #endif using ll = long long; using vl = vector; using Graph = vector>; using P = pair; #define all(v) v.begin(), v.end() template inline bool chmax(T &a, T b) { return ((a < b) ? (a = b, true) : (false)); } template inline bool chmin(T &a, T b) { return ((a > b) ? (a = b, true) : (false)); } #define rep1(i, n) for(ll i = 1; i <= ((ll)n); ++i) // https://trap.jp/post/1224/ template constexpr auto min(T... a) { return min(initializer_list>{a...}); } template constexpr auto max(T... a) { return max(initializer_list>{a...}); } template void input(T &...a) { (cin >> ... >> a); } template void input(vector &a) { for(T &x : a) cin >> x; } void print() { cout << '\n'; } template void print(const T &a, const Ts &...b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } void print(const string &s) { cout << s << '\n'; } template struct is_container : std::false_type {}; template struct is_container().begin()), decltype(std::declval().end())>> : std::true_type {}; template typename enable_if::value>::type print(const Container& x) { if (!x.empty()) { auto it = x.begin(); for (; it != prev(x.end()); ++it) { cout << *it << " "; } cout << *it << "\n"; // 最後の要素を出力して改行 } } #define INT(...) \ int __VA_ARGS__; \ input(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ input(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ input(__VA_ARGS__) #define REP1(a) for(ll i = 0; i < a; i++) #define REP2(i, a) for(ll i = 0; i < a; i++) #define REP3(i, a, b) for(ll i = a; i < b; i++) #define REP4(i, a, b, c) for(ll i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__) ll inf = 3e18; vl dx = {1, -1, 0, 0}; vl dy = {0, 0, 1, -1}; #line 3 "math/factorial.hpp" // https://suisen-cp.github.io/cp-library-cpp/library/math/factorial.hpp template struct factorial { factorial() {}; void ensure(const int n) { int sz = size(fac); if(sz > n) { return; } int new_sz = max(2 * sz, n + 1); fac.resize(new_sz), fac_inv.resize(new_sz); for(int i = sz; i < new_sz; i++) { if(i == 0) { fac[i] = 1; continue; } fac[i] = fac[i - 1] * i; } fac_inv[new_sz - 1] = T(1) / fac[new_sz - 1]; for(int i = new_sz - 2; i >= sz; i--) { fac_inv[i] = fac_inv[i + 1] * (i + 1); } return; } T get(int i) { ensure(i); return fac[i]; } T operator[](int i) { return get(i); } T inv(int i) { ensure(i); return fac_inv[i]; } T binom(int n, int i) { if(n < 0 || i < 0 || n < i) { return T(0); } ensure(n); return fac[n] * fac_inv[i] * fac_inv[n - i]; } T perm(int n, int i) { if(n < 0 || i < 0 || n < i) { return T(0); } ensure(n); return fac[n] * fac_inv[n - i]; } private: vector fac, fac_inv; }; #line 3 "poly/shift_of_sampling_points.hpp" #include // https://suisen-cp.github.io/cp-library-cpp/library/polynomial/shift_of_sampling_points.hpp template vector shift_of_sampling_points(const vector &f, const int m, const int c) { // n次未満の多項式fのn個の点f(0),...,f(n-1)に対して // f(c),...,f(c+m-1)を計算 factorial fac; const int n = f.size(); auto a = [&] { vector a1(n), a2(n); rep(i, n) { a1[i] = f[i] * fac.inv(i); a2[i] = ((i & 1) ? -1 : 1) * fac.inv(i); } auto a = convolution(a1, a2); a.resize(n); return a; }(); vector a_(n); rep(i, n) { a_[i] = a[n - 1 - i] * fac[n - 1 - i]; } vector b2 = [&] { // b2[i] = c*(c-1)*...*(c-i+1)/i! vector b2(n); Mint ci = 1; b2[0] = ci; for(int i = 1; i < n; i++) { ci *= c - i + 1; b2[i] = ci * fac.inv(i); } return b2; }(); auto b = convolution(a_, b2); vector fc = [&] { vector f1(n); vector f2(m); rep(i, n) { f1[i] = b[n - 1 - i] * fac.inv(i); } rep(i, m) { f2[i] = fac.inv(i); } return convolution(f1, f2); }(); vector res(m); rep(i, m) { res[i] = fac[i] * fc[i]; } return res; } #line 4 "math/factorial_large.hpp" #include template struct factorial_large { const ll K = 9; vector> f; vector g; factorial_large() { // f_i(x) = (2^i x + 1) * ... * (2^i x + 2^i - 1) // f_i(0) , ... , f_i(2^i - 1) の値が分かればシフトできる f = vector(K + 1, vector()); f[0] = {1}; // f_0(x) = 1 rep(i, K) { // cul f_(i+1) ll ti = 1LL << i; auto f1 = shift_of_sampling_points(f[i], 3 * ti, ti); f[i].insert(f[i].end(), all(f1)); f[i + 1].resize(2 * ti); rep(j, 2 * ti) { f[i + 1][j] = f[i][2 * j] * f[i][2 * j + 1] * ti * (2 * j + 1); } } // g_i = (i*2^K)! { ll sz = ll(mint::mod()) / (1LL << K) + 1; auto g1 = shift_of_sampling_points(f[K], sz - 1, 0); g.resize(sz); g[0] = 1; mint tK = 1 << K; for(int i = 1; i < sz; i++) { g[i] = g[i - 1] * g1[i - 1] * tK * i; } } } mint fac(ll n) { if(n >= mint::mod()) return 0; ll r = n / (1LL << K); ll q = n - (1LL << K) * r; mint res = g[r]; for(ll i = (1LL << K) * r + 1; i <= n; i++) { res *= i; } return res; } }; #line 5 "/home/y_midori/cp/yukicoder/455/c.cpp" // using namespace atcoder; using mint = atcoder::modint998244353; factorial fac; factorial_large fac_large; mint cul_fac(ll n) { if(n < 1e6) { return fac[n]; } else return fac_large.fac(n); } void solve() { LL(k); ll sum = 0; mint ans = 1; rep(i, k) { LL(l, m); sum += l * m; ans *= cul_fac(m).inv(); ans *= cul_fac(l).inv().pow(m); } ans *= cul_fac(sum); print(ans.val()); } int main() { ios::sync_with_stdio(false); std::cin.tie(nullptr); cout << std::setprecision(16); int t = 1; rep(_, t) { solve(); } }