// 重要!!!!!!!!!!!! // 何故か配列じゃないと動かないので、必ず使うときには配列に移してから使うこと!! // v.data()みたいなのではバグる!!!!!!TODO なおす // // あと、出力がintになっていることが多いので、long longキャストに注意!!!! #include <bits/stdc++.h> #include <sys/time.h> using namespace std; #define rep(i,n) for(long long i = 0; i < (long long)(n); i++) #define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++) #define pb push_back #define all(x) (x).begin(), (x).end() #define fi first #define se second #define mt make_tuple #define mp make_pair template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); } template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } #define exists find_if #define forall all_of using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>; using ld = long double; using vld = vector<ld>; using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; } using Pos = complex<double>; template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) { o << "(" << v.first << ", " << v.second << ")"; return o; } template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{}; template<class Ch, class Tr, class Tuple, size_t... Is> void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; } template<class Ch, class Tr, class... Args> auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; } ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; } template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; } template <typename T> ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template <typename T, typename U> ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; } template <typename T, typename U, typename V> ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; } vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; } template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;} string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); return s; } template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;}; string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); } struct ci : public iterator<forward_iterator_tag, ll> { ll n; ci(const ll n) : n(n) { } bool operator==(const ci& x) { return n == x.n; } bool operator!=(const ci& x) { return !(*this == x); } ci &operator++() { n++; return *this; } ll operator*() const { return n; } }; size_t random_seed; namespace std { using argument_type = P; template<> struct hash<argument_type> { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash<ll>{}(x.fi); seed ^= (hash<ll>{}(x.se) << 1); return seed; } }; }; // hash for various class namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template <typename T> struct myhash{ std::size_t operator()(const T& val) const { return (hash<T>{}(val)%mod_key)^hash_key; } }; }; template <typename T> class uset:public std::unordered_set<T,myhash::myhash<T>> { using SET=std::unordered_set<T,myhash::myhash<T>>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} }; template <typename T,typename U> class umap:public std::unordered_map<T,U,myhash::myhash<T>> { public: using MAP=std::unordered_map<T,U,myhash::myhash<T>>; umap():MAP(){MAP::rehash(myhash::Bsizes[rand()%20]);} }; struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; } struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); srand((unsigned int)time(NULL)); random_seed = RAND_MAX / 2 + rand() / 2; }} init__; static const double EPS = 1e-14; static const long long INF = 1e18; static const long long mo = 1e9+7; #define ldout fixed << setprecision(40) #define double long double /*****************/ // Dictionary /*****************/ // Nはバケット数 template<int N> class FID { static const int bucket = 512, block = 16; // 整数iのpopcountをO(1)で求めるためのテーブル // popcount[i] = __builtin_popcount(i), i<65536 static char popcount[]; // B[i]: s[0:512*i)のビット1の総数 int n, B[N/bucket+10]; // bs[i]: s[16*i:16*(i+1)]のビット列そのもの unsigned short bs[N/block+10] = {}; // b[i]: s[i/32*512:i/32*512+i%32*32)のビット1の総数 // bs[i]を512bitずつリセットしながら、累積和を取ってる感じ。 unsigned short b[N/block+10] = {}; public: FID(){} FID(int n, bool s[]) : n(n) { if(!popcount[1]) for (int i = 0; i < (1<<block); i++) popcount[i] = __builtin_popcount(i); bs[0] = B[0] = b[0] = 0; for (int i = 0; i < n; i++) { if(i%block == 0) { bs[i/block+1] = 0; if(i%bucket == 0) { B[i/bucket+1] = B[i/bucket]; b[i/block+1] = b[i/block] = 0; } else b[i/block+1] = b[i/block]; } bs[i/block] |= short(s[i])<<(i%block); b[i/block+1] += s[i]; B[i/bucket+1] += s[i]; } if(n%bucket == 0) b[n/block] = 0; } // number of val in [0,r), O(1) // 大ブロックの累積和(512bit)+中ブロックの累積和(16bit)+「余り分に適切なbitmaskをかけてpopcount」 int count(bool val, int r) { return val? B[r/bucket]+b[r/block]+popcount[bs[r/block]&((1<<(r%block))-1)]: r-count(1,r); } // number of val in [l,r), O(1) int count(bool val, int l, int r) { return count(val,r)-count(val,l); } // position of ith in val, 0-indexed, O(log n) // 範囲外を示していたら-1を返す int select(bool val, int i) { if(i < 0 or count(val,n) <= i) return -1; i++; int lb = 0, ub = n, md; while(ub-lb>1) { md = (lb+ub)>>1; if(count(val,md) >= i) ub = md; else lb = md; } return ub-1; } int select(bool val, int i, int l) { return select(val,i+count(val,l)); } bool operator[](int i) { return bs[i/block]>>(i%block)&1; } void print(void) { /* rep(i, 1+(N-1)/bucket) { cout << B[i] << " "; } cout << endl; rep(i, 1+(N-1)/block) { cout << b[i] << " "; } cout << endl; */ rep(i, 1+(N-1)/block) { cout << bits_to_string(bs[i], (i != (N-1)/block ? 16 : N - (N-1)/block*block)) << " "; } cout << endl; } }; template<int N> char FID<N>::popcount[1<<FID<N>::block]; /*****************/ // Wavelet Matrix /*****************/ // 長さNで、値域[0, m=2^D)の整数を管理する //#define ENABLE_SUM template<class T, int N, int D> class wavelet { int n, zs[D]; FID<N> dat[D]; public: wavelet(void) { } #ifdef ENABLE_SUM T raw_data[D+1][N] = {}; T sum_data[D+1][N+1] = {}; wavelet(int n, T seq[]) : n(n) { T l[N] = {}, r[N] = {}; bool b[N] = {}; memcpy(raw_data[0], seq, sizeof(T)*n); for (int d = 0; d < D; d++) { int lh = 0, rh = 0; for (int i = 0; i < n; i++) { b[i] = (raw_data[d][i]>>(D-d-1))&1; if(b[i]) r[rh++] = raw_data[d][i]; else l[lh++] = raw_data[d][i]; } dat[d] = FID<N>(n,b); zs[d] = lh; swap(l,raw_data[d+1]); memcpy(raw_data[d+1]+lh, r, rh*sizeof(T)); } rep(d, D+1) rep(i, N) sum_data[d][i+1] = sum_data[d][i] + raw_data[d][i]; } // 深さdでの列の[l, r)での累積和を求める T getSum(int d, int l, int r) { return sum_data[d][r] - sum_data[d][l]; } // get sum of elements in [l,r) in [a,b) // O(log m) T sum_dfs(int d, int l, int r, T val, T a, T b) { // Wavelet Matrixの深さdで、 // [l, r)が[val, nv) = [val, val+(1ll<<(D-d)))の値域を表現している時、 // [a, b)の値域のものの和は? if(l == r) return 0; // valは無いので0を返す if(d == D) return (a <= val and val < b)? (r-l)*val: 0; // 深さDでは全部の値が同じなので、そのままかけて返す T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv; if(nnv < a or b <= val) // どんなに1を選んでもaに満たなかったり、すでに最大を超えていたら0 return 0; if (a <= val and nnv < b) // これからどう選んでも a <= [l, r) < bの場合、累積和を返す return getSum(d, l, r); int lc = dat[d].count(1,l), rc = dat[d].count(1,r); return sum_dfs(d+1,l-lc,r-rc,val,a,b)+ sum_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b); } T sum(int l, int r, T a, T b) { return sum_dfs(0,l,r,0,a,b); } #else wavelet(int n, T seq[]) : n(n) { T f[N], l[N], r[N]; bool b[N]; memcpy(f, seq, sizeof(T)*n); for (int d = 0; d < D; d++) { int lh = 0, rh = 0; for (int i = 0; i < n; i++) { bool k = (f[i]>>(D-d-1))&1; if(k) r[rh++] = f[i]; else l[lh++] = f[i]; b[i] = k; } dat[d] = FID<N>(n,b); zs[d] = lh; swap(l,f); memcpy(f+lh, r, rh*sizeof(T)); } } #endif void print(void) { rep(i, D) cout << zs[i] << " "; cout << endl; rep(i, D) dat[i].print(); /* cout << "Raw" << endl; rep(d, D+1) { rep(i, N) cout << raw_data[d][i] << " "; cout << endl; } cout << "Sum" << endl; rep(d, D+1) { rep(i, N+1) cout << sum_data[d][i] << " "; cout << endl; } */ } // get, []: i番目の要素 // O(1) T get(int i) { T ret = 0; bool b; for (int d = 0; d < D; d++) { ret <<= 1; b = dat[d][i]; ret |= b; i = dat[d].count(b,i)+b*zs[d]; } return ret; } T operator[](int i) { return get(i); } // rank: 区間[0,r)にあるvalの個数 // O(log m) int count(T val, int l, int r) { for (int d = 0; d < D; d++) { // ここで[l, r)にxのd桁目までが全て入っていることを保証(d>0) bool b = (val>>(D-d-1))&1; l = dat[d].count(b,l)+b*zs[d]; r = dat[d].count(b,r)+b*zs[d]; } return r-l; } int count(T val, int r) { return count(val,0,r); } // select: i番目のvalの位置 // O(log m log log m) int select(T val, int k) { int ls[D], rs[D], l = 0, r = n; for (int d = 0; d < D; d++) { ls[d] = l; rs[d] = r; bool b = val>>(D-d-1)&1; l = dat[d].count(b,l)+b*zs[d]; r = dat[d].count(b,r)+b*zs[d]; } for (int d = D-1; d >= 0; d--) { bool b = val>>(D-d-1)&1; k = dat[d].select(b,k,ls[d]); if(k >= rs[d] or k < 0) return -1; k -= ls[d]; } return k; } int select(T val, int k, int l) { return select(val,k+count(val,l)); } // maximum: 区間[l,r)で大きい順にk個 // O(k log m) void list_max_dfs(int d, int l, int r, int &k, T val, vector<T> &vs) { if(l >= r or !k) return; if(d == D) { while(l++ < r and k > 0) vs.push_back(val), k--; return; } int lc = dat[d].count(1,l), rc = dat[d].count(1,r); // if min, change this order list_max_dfs(d+1, lc+zs[d], rc+zs[d], k, 1ULL<<(D-d-1)|val,vs); list_max_dfs(d+1, l-lc, r-rc, k, val, vs); } vector<T> list_max(int l, int r, int k) { if (r-l < k) k = r-l; if(k < 0) return {}; vector<T> ret; list_max_dfs(0,l,r,k,0,ret); return ret; } // 添字[l, r)の要素で、値が[a, b)のもののうち最大値を求める // valは上からd bit決めて他0を埋めた時の値。 // // O(log m) T rangemax_dfs(int d, int l, int r, T val, T a, T b) { if(r-l <= 0 or val >= b) return -1; if(d == D) return val>=a? val: -1; int lc = dat[d].count(1,l), rc = dat[d].count(1,r); T ret = rangemax_dfs(d+1, lc+zs[d], rc+zs[d], 1ULL<<(D-d-1)|val, a, b); if(~ret) return ret; // 1側を見て見つかったならそれに越したことはない return rangemax_dfs(d+1, l-lc, r-rc, val, a, b); // なければ0側を見る } T rangemax(int l, int r, T a, T b) { return rangemax_dfs(0,l,r,0,a,b); } // k is 0-indexed!!!! // quantile: 区間[l,r)でk番目に大きい数 // O(log m) T quantile(int l, int r, int k) { if(r-l <= k or k < 0) return -1; T ret = 0; for (int d = 0; d < D; d++) { int lc = dat[d].count(1,l), rc = dat[d].count(1,r); // lc - rc = [l, r)で立っている1の数 if(rc-lc > k) { // 1の数にkが収まっていれば l = lc+zs[d], r = rc+zs[d]; // 1側に遷移 ret |= 1ULL<<(D-d-1); } else { // 0側ならば k -= rc-lc; // 1側にあった数だけkを削って次へ l -= lc, r -= rc; } } return ret; } T min(int l, int r) { return quantile(l, r, 0); } T max(int l, int r) { return quantile(l, r, r-l-1); } // freq_list: 区間[l,r)で値が[lb,ub)になる値とその出現回数の組のリスト // O(k log m), kはヒット数 void list_freq_dfs(int d, int l, int r, T val, T a, T b, vector<pair<T,int>> &vs) { if(val >= b or r-l <= 0) return; if(d == D) { if(a <= val) vs.push_back(make_pair(val,r-l)); return; } T nv = val|(1LL<<(D-d-1)), nnv = nv|(((1LL<<(D-d-1))-1)); if(nnv < a) return; int lc = dat[d].count(1,l), rc = dat[d].count(1,r); list_freq_dfs(d+1,l-lc,r-rc,val,a,b,vs); list_freq_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b,vs); } vector<pair<T,int>> list_freq(int l, int r, T a, T b) { vector<pair<T,int>> ret; list_freq_dfs(0,l,r,0,a,b,ret); return ret; } // get_rect: 区間[l,r)で値が[lb,ub)になる要素の位置とその値の組(つまり矩形内にある点の座標)のリスト // O(k log m), kはヒット数 vector<pair<int,T>> get_rect(int l, int r, T a, T b) { vector<pair<T,int>> res = list_freq(l,r,a,b); vector<pair<int,T>> ret; for(auto &e: res) for (int i = 0; i < e.second; i++) ret.push_back(make_pair(select(e.first,i,l), e.first)); return ret; } // number of elements in [l,r) in [a,b) // O(log m) ll freq_dfs(int d, int l, int r, T val, T a, T b) { if(l == r) return 0; if(d == D) return (a <= val and val < b)? r-l: 0; T nv = 1ULL<<(D-d-1)|val, nnv = ((1ULL<<(D-d-1))-1)|nv; if(nnv < a or b <= val) return 0; if(a <= val and nnv < b) return r-l; int lc = dat[d].count(1,l), rc = dat[d].count(1,r); return freq_dfs(d+1,l-lc,r-rc,val,a,b)+ freq_dfs(d+1,lc+zs[d],rc+zs[d],nv,a,b); } ll freq(int l, int r, T a, T b) { return freq_dfs(0,l,r,0,a,b); } // TODO // 普通に // https://www.slideshare.net/pfi/ss-15916040 // rangemaxk, rangemink, prevvalue, nextvalue, intersectを実装するのが良さそう }; // 二次元点群が与えられた時、 // 閉矩形領域の点群の数え上げをO(log n)で行う。 // 静的オンラインクエリ。 // // 使い方 // rep(i, num_of_points) // pc.insert(x[i], y[i]); // pc.build(); // // cout << pc.count(左下x, 左下y, 右上x, 右上y) << endl; // 閉矩形領域 // #define SIZE 100010 #define BITS 18 class PointCloud2D { // デバッグ用 ll countBrutal(ll ax, ll ay, ll bx, ll by) { if (ax > bx || ay > by) return 0; ll ret = 0; rep(i, n) { ret += (ax <= xy[i].fi && xy[i].fi <= bx && ay <= xy[i].se && xy[i].se <= by); } return ret; } public: ll n; ll* data; wavelet<ll, SIZE, BITS> w; vector<P> xy; vll sx, ty; map<ll, ll> xs; map<ll, ll> yt; void insert(ll x, ll y) { xy.push_back(P(x, y)); } void build(void) { xy.pb(P(2ll*INF, 2ll*INF)); n = xy.size(); assert(n < SIZE); assert(SIZE < (1ll<<BITS)); data = new ll[SIZE]; sx.resize(n), ty.resize(n); sort(all(xy), [&](P& x, P& y){return x.se < y.se;}); rep(i, n) if (!yt.count(xy[i].se)) { ll tmp = yt.size(); yt[xy[i].se] = tmp; ty[tmp] = xy[i].se; } sort(all(xy)); rep(i, n) sx[i] = xy[i].fi; rep(i, n) if (!xs.count(xy[i].fi)) xs[xy[i].fi] = i; rep(i, n) { data[i] = yt[xy[i].se]; } w = wavelet<ll, SIZE, BITS>(n, data); } // 左下が(ax, ay), 右上が(bx, by)であるような閉矩形領域内部の点の数 // O(log n) ll count(ll ax, ll ay, ll bx, ll by) { if (ax > bx || ay > by) return 0; // ax以上の最小のs ll as = xs.lower_bound(ax)->se; // bx以上の最小のs ll bs = xs.upper_bound(bx)->se; // ay以上の最小のt ll at = yt.lower_bound(ay)->se; // by以上の最小のt ll bt = yt.upper_bound(by)->se; ll ret = w.freq(as, bs, at, bt); /* if (ret != countBrutal(ax, ay, bx, by)) { cout << "HIT " << mt(ax, ay, bx, by) << " "<< mt(as, bs, at, bt) << endl; cout << "yours : " << ret << " v.s. brutal : " << countBrutal(ax, ay, bx, by)<<endl; } */ return ret; } PointCloud2D(void) { } }; int main(void) { ll n, m; cin >> n >> m; assert(1<=n&&n<=1e5), assert(1<=m&&m<=2e5); vll a(m, -1); map<ll, ll> freq; rep(i, n) { ll x, y; cin >> x >> y; a[x] = i; a[y] = i; freq[x]++, freq[y]++; } for (auto x : freq) { assert(x.se <= 1); } vll p; vector<P> pos(n, P(-1, -1)); rep(i, m) if (a[i] != -1) { if (pos[a[i]].fi < 0) pos[a[i]].fi = i; else pos[a[i]].se = i; p.pb(a[i]); } PointCloud2D pc; rep(i, n) { pc.insert(pos[i].fi, pos[i].se); } pc.build(); vll ret(n, -1); rep(i, n) { ll l = pos[i].fi, r = pos[i].se; ret[i] = pc.count(l+1, -INF, r-1, INF) + pc.count(-INF, l+1, INF, r-1) - 2 * pc.count(l+1, l+1, r-1, r-1); } cout << accumulate(all(ret), 0ll) / 2ll << endl; return 0; }