#include using namespace std; #define rep(i, n) for (int i = 0; i < (n); i++) #define per(i, n) for (int i = (n)-1; i >= 0; i--) #define rep2(i, l, r) for (int i = (l); i < (r); i++) #define per2(i, l, r) for (int i = (r)-1; i >= (l); i--) #define each(e, v) for (auto &e : v) #define MM << " " << #define pb push_back #define eb emplace_back #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; template using minheap = priority_queue, greater>; template using maxheap = priority_queue; template bool chmax(T &x, const T &y) { return (x < y) ? (x = y, true) : false; } template bool chmin(T &x, const T &y) { return (x > y) ? (x = y, true) : false; } template int flg(T x, int i) { return (x >> i) & 1; } int popcount(int x) { return __builtin_popcount(x); } int popcount(ll x) { return __builtin_popcountll(x); } int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template void print(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' '); if (v.empty()) cout << '\n'; } template void printn(const vector &v, T x = 0) { int n = v.size(); for (int i = 0; i < n; i++) cout << v[i] + x << '\n'; } template int lb(const vector &v, T x) { return lower_bound(begin(v), end(v), x) - begin(v); } template int ub(const vector &v, T x) { return upper_bound(begin(v), end(v), x) - begin(v); } template void rearrange(vector &v) { sort(begin(v), end(v)); v.erase(unique(begin(v), end(v)), end(v)); } template vector id_sort(const vector &v, bool greater = false) { int n = v.size(); vector ret(n); iota(begin(ret), end(ret), 0); sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; }); return ret; } template void reorder(vector &a, const vector &ord) { int n = a.size(); vector b(n); for (int i = 0; i < n; i++) b[i] = a[ord[i]]; swap(a, b); } template T floor(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? x / y : (x - y + 1) / y); } template T ceil(T x, T y) { assert(y != 0); if (y < 0) x = -x, y = -y; return (x >= 0 ? (x + y - 1) / y : x / y); } template pair operator+(const pair &p, const pair &q) { return make_pair(p.first + q.first, p.second + q.second); } template pair operator-(const pair &p, const pair &q) { return make_pair(p.first - q.first, p.second - q.second); } template istream &operator>>(istream &is, pair &p) { S a; T b; is >> a >> b; p = make_pair(a, b); return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } struct io_setup { io_setup() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; constexpr int inf = (1 << 30) - 1; constexpr ll INF = (1LL << 60) - 1; // constexpr int MOD = 1000000007; constexpr int MOD = 998244353; template struct Mod_Int { int x; Mod_Int() : x(0) {} Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} static int get_mod() { return mod; } Mod_Int &operator+=(const Mod_Int &p) { if ((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator-=(const Mod_Int &p) { if ((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator*=(const Mod_Int &p) { x = (int)(1LL * x * p.x % mod); return *this; } Mod_Int &operator/=(const Mod_Int &p) { *this *= p.inverse(); return *this; } Mod_Int &operator++() { return *this += Mod_Int(1); } Mod_Int operator++(int) { Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator--() { return *this -= Mod_Int(1); } Mod_Int operator--(int) { Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator-() const { return Mod_Int(-x); } Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; } Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; } Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; } Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; } bool operator==(const Mod_Int &p) const { return x == p.x; } bool operator!=(const Mod_Int &p) const { return x != p.x; } Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod - 2); } Mod_Int pow(long long k) const { Mod_Int now = *this, ret = 1; for (; k > 0; k >>= 1, now *= now) { if (k & 1) ret *= now; } return ret; } friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; } friend istream &operator>>(istream &is, Mod_Int &p) { long long a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; template struct Combination { static vector _fac, _ifac; Combination() {} static void init(int n) { _fac.resize(n + 1), _ifac.resize(n + 1); _fac[0] = 1; for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i; _ifac[n] = _fac[n].inverse(); for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i; } static T fac(int k) { return _fac[k]; } static T ifac(int k) { return _ifac[k]; } static T inv(int k) { return fac(k - 1) * ifac(k); } static T P(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k); } static T C(int n, int k) { if (k < 0 || n < k) return 0; return fac(n) * ifac(n - k) * ifac(k); } // n 個の区別できる箱に、k 個の区別できない玉を入れる場合の数 static T H(int n, int k) { if (n < 0 || k < 0) return 0; return k == 0 ? 1 : C(n + k - 1, k); } // n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数 static T second_stirling_number(int n, int k) { T ret = 0; for (int i = 0; i <= k; i++) { T tmp = C(k, i) * T(i).pow(n); ret += ((k - i) & 1) ? -tmp : tmp; } return ret * ifac(k); } // n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数 static T bell_number(int n, int k) { if (n == 0) return 1; k = min(k, n); vector pref(k + 1); pref[0] = 1; for (int i = 1; i <= k; i++) { if (i & 1) { pref[i] = pref[i - 1] - ifac(i); } else { pref[i] = pref[i - 1] + ifac(i); } } T ret = 0; for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i]; return ret; } }; template vector Combination::_fac = vector(); template vector Combination::_ifac = vector(); using comb = Combination; template struct Binary_Indexed_Tree { vector bit; const int n; Binary_Indexed_Tree(const vector &v) : n((int)v.size()) { bit.resize(n + 1); copy(begin(v), end(v), begin(bit) + 1); build(); } Binary_Indexed_Tree(int n, T x = 0) : Binary_Indexed_Tree(vector(n, x)) {} void set(int i, const T &x) { bit[i + 1] = x; } void build() { for (int a = 2; a <= n; a <<= 1) { for (int b = a; b <= n; b += a) bit[b] += bit[b - a / 2]; } } void add(int i, const T &x) { for (i++; i <= n; i += (i & -i)) bit[i] += x; } void change(int i, const T &x) { add(i, x - query(i, i + 1)); } T sum(int i) const { i = min(i, n); if (i <= 0) return 0; T ret = 0; for (; i > 0; i -= (i & -i)) ret += bit[i]; return ret; } T query(int l, int r) const { l = max(l, 0), r = min(r, n); if (l >= r) return 0; return sum(r) - sum(l); } T operator[](int i) const { return query(i, i + 1); } // v[0]+...+v[r] >= x を満たす最小の r (なければ n) int lower_bound(T x) const { int ret = 0; for (int k = 31 - __builtin_clz(n); k >= 0; k--) { if (ret + (1 << k) <= n && bit[ret + (1 << k)] < x) x -= bit[ret += (1 << k)]; } return ret; } // v[0]+...+v[r] > x を満たす最小の r (なければ n) int upper_bound(T x) const { int ret = 0; for (int k = 31 - __builtin_clz(n); k >= 0; k--) { if (ret + (1 << k) <= n && bit[ret + (1 << k)] <= x) x -= bit[ret += (1 << k)]; } return ret; } }; template long long inversion_number(const vector &a) { int n = a.size(); vector v(n); iota(begin(v), end(v), 0); sort(begin(v), end(v), [&](int i, int j) { if (a[i] != a[j]) return a[i] < a[j]; return i < j; }); Binary_Indexed_Tree bit(n, 0); long long ret = 0; for (int i = 0; i < n; i++) { ret += bit.query(v[i] + 1, n); bit.add(v[i], 1); } return ret; } // a を b に変換するのに必要な最小バブルソート回数 template long long inversion_number(const vector &a, const vector &b) { int n = a.size(); assert(b.size() == n); vector u(n), v(n); iota(begin(u), end(u), 0); sort(begin(u), end(u), [&](int i, int j) { if (a[i] != a[j]) return a[i] < a[j]; return i < j; }); iota(begin(v), end(v), 0); sort(begin(v), end(v), [&](int i, int j) { if (b[i] != b[j]) return b[i] < b[j]; return i < j; }); vector w(n); for (int i = 0; i < n; i++) { if (a[u[i]] != b[v[i]]) return -1; w[v[i]] = u[i]; } Binary_Indexed_Tree bit(n, 0); long long ret = 0; for (int i = 0; i < n; i++) { ret += bit.query(w[i] + 1, n); bit.add(w[i], 1); } return ret; } void solve() { int N, M; cin >> N >> M; comb::init(N); mint ans = 0; vector p(N, -1); // i の位置 vector q(N, -1); // i 番目が何か rep(i, M) { int x, t; cin >> x >> t; x--, t--; p[x] = t; q[t] = x; } vector v; int cnt = 0; rep(i, N) { if (q[i] != -1) v.eb(q[i]); if (q[i] == -1) cnt++; } vector ids; rep(i, N) { if (p[i] == -1) ids.eb(i); } ans += inversion_number(v); int c1 = 0; rep(i, N) { if (q[i] != -1) { int j = q[i]; int d1 = lb(ids, j); int d2 = cnt - d1; int c2 = cnt - c1; ans += mint(d1) * mint(c2) / mint(cnt); ans += mint(d2) * mint(c1) / mint(cnt); } else { c1++; } } ans += mint(cnt) * mint(cnt - 1) / 4; ans *= comb::fac(cnt); cout << ans << '\n'; } int main() { int T = 1; // cin >> T; while (T--) solve(); }