#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep(i,n) for(int i=0; i<(n); i++) #define rrep(i,n) for(int i=(n)-1; i>=0; i--) #define FOR(i,a,b) for(int i=(a); i<(b); i++) #define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % mod) { if (val < 0) val += mod; } constexpr int getmod() { return mod; } constexpr Fp operator - () const noexcept { return val ? mod - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= mod) val -= mod; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += mod; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % mod; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { 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 bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int mod = fact_[0].getmod(); 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 T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T perm(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; //const int mod = 1e9+7; const int mod = 998244353; using mint = Fp; BiCoef bc; int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int n,q; in(n,q); bc.init(n+5); vector cat(n+1); rep(i,n+1) if(i%2==0) cat[i] = bc.com(i,i/2) * bc.inv(i/2+1); vector f(n+1); vector bin; bin.pb(0); bin.pb(n); rep(i,q){ int l,r; in(l,r); l--; f[l] ^= (1LL << i); f[r] ^= (1LL << i); bin.pb(l); bin.pb(r); } rep(i,n) f[i+1] ^= f[i]; sort(ALL(bin)); UNIQUE(bin); map mp; rep(i, (int)bin.size()-1){ int l = bin[i], r = bin[i+1]; mp[f[l]] += r-l; } mint ans = 1; for(auto [val, len] : mp){ if(val == 0){ if(len%2 == 0) ans *= cat[len]; else ans *= bc.com(len, (len+1)/2) - bc.com(len, (len+3)/2); } else{ ans *= cat[len]; } } if(n%2){ ans *= bc.fact((n+1)/2); ans *= bc.fact((n-1)/2); } else{ ans *= bc.fact(n/2); ans *= bc.fact(n/2); } out(ans); }