/** author: shobonvip created: 2025.02.21 22:21:43 **/ #include<bits/stdc++.h> using namespace std; //* ATCODER #include<atcoder/all> using namespace atcoder; typedef modint998244353 mint; //*/ /* BOOST MULTIPRECISION #include<boost/multiprecision/cpp_int.hpp> 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 <typename T> bool chmin(T &a, const T &b) { if (a <= b) return false; a = b; return true; } template <typename T> bool chmax(T &a, const T &b) { if (a >= b) return false; a = b; return true; } template <typename T> T max(vector<T> &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmax(ret, a[i]); return ret; } template <typename T> T min(vector<T> &a){ assert(!a.empty()); T ret = a[0]; for (int i=0; i<(int)a.size(); i++) chmin(ret, a[i]); return ret; } template <typename T> T sum(vector<T> &a){ T ret = 0; for (int i=0; i<(int)a.size(); i++) ret += a[i]; return ret; } template< typename Mint > vector< Mint > lagrange_polynomial(const vector< Mint > &x, const vector< Mint > &y) { int k = (int) x.size() - 1; vector< Mint > f(k + 1), dp(k + 2); dp[0] = 1; for(int j = 0; j <= k; j++) { for(int l = k + 1; l > 0; l--) { dp[l] = dp[l] * -x[j] + dp[l - 1]; } dp[0] *= -x[j]; } for(int i = 0; i <= k; i++) { Mint d = 1; for(int j = 0; j <= k; j++) { if(i != j) { d *= x[i] - x[j]; } } Mint mul = y[i] / d; if(x[i] == 0) { for(int j = 0; j <= k; j++) { f[j] += dp[j + 1] * mul; } } else { Mint inv = Mint(1) / (-x[i]), pre = 0; for(int j = 0; j <= k; j++) { Mint cur = (dp[j] - pre) * inv; f[j] += cur * mul; pre = cur; } } } return f; } int main(){ ios_base::sync_with_stdio(false); cin.tie(NULL); ll n,m; cin >> n >> m; vector<ll> a(m),b(m),c(m),e(m); rep(i,0,m){ cin>>a[i]>>b[i]>>c[i]>>e[i]; } vector<mint> lpt(4); lpt[0]=1; rep(d,1,4){ rep(x,-15*d,15*d+1){ rep(y,-15*d,15*d+1){ rep(z,-15*d,15*d+1){ bool mode=1; rep(i,0,m){ if(a[i]*x+b[i]*y+c[i]*z+d*e[i]<0){ mode=0; break; } } if(mode){ lpt[d]++; } } } } } vector<mint> ehr_poly = lagrange_polynomial({0,1,2,3},lpt); mint ans=0; rep(i,0,4){ ans+=ehr_poly[i]*mint(-n).pow(i); } ans*=-1; cout<<ans.val()<<endl; }