#include namespace { #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic pop using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; using mint = modint998244353; constexpr int FACT_SIZE = 1000000; mint Fact[FACT_SIZE + 1]; mint iFact[FACT_SIZE + 1]; const auto fact_init = [] { Fact[0] = mint::raw(1); for(int i = 1; i <= FACT_SIZE; ++i) { Fact[i] = Fact[i-1] * i; } iFact[FACT_SIZE] = Fact[FACT_SIZE].inv(); for(int i = FACT_SIZE; i; --i) { iFact[i-1] = iFact[i] * i; } return false; }(); mint comb(int n, int k) { if (k == 0) return mint::raw(1); assert(n >= 0 && k >= 0); if (k > n) return mint::raw(0); return Fact[n] * iFact[n - k] * iFact[k]; } mint icomb(int n, int k) { return iFact[n] * Fact[n - k] * Fact[k]; } mint fact(int n) {return Fact[n];} mint perm(int n, int k) { assert(0 <= n); return Fact[n] * iFact[n - k]; } } int main() { ios::sync_with_stdio(false); cin.tie(0); int n, q; cin >> n >> q; scc_graph g(n + 1); rep(_, q) { int l, r; cin >> l >> r; l--; for(int i = l; i <= r; i++) { g.add_edge(i, l); g.add_edge(i, r); } } vector done(n); mint ans = 1; for(auto& c: g.scc()) { sort(all(c)); int l = -1; for(int r: c) { if (l == -1) { l = r; continue; } int cnt = 0; for(int i = l; i < r; i++) { cnt += !done[i]; done[i] = true; } if (cnt % 2) { cout << 0 << '\n'; return 0; } ans *= comb(cnt, cnt / 2) - comb(cnt, cnt / 2 - 1); l = r; } } int rest = n - accumulate(all(done), 0); if (rest) { int a = (rest + 1) / 2, b = rest - a; mint v = comb(a + b, a); if (b - 1 >= 0) v -= comb(a + b, b - 1); ans *= v; } ans *= fact(n / 2); ans *= fact((n + 1) / 2); cout << ans.val() << '\n'; }