// need #include #include // data structure #include #include #include #include #include #include #include #include #include //#include #include #include #include // stream //#include //#include //#include #include // etc #include #include #include #include #include #include #include // input #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t) { std::cin >> t; } templatevoid MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } templatevoid MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } templatevoid MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define VEC(type, c, n) std::vector c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& r:c)for(auto& i:r)std::cin>>i; // output #define OUT(dist) std::cout<<(dist); #define FOUT(n, dist) std::cout<=(a);--i) #define REP(i, n) for(int i=0;i=0;--i) #define FORLL(i, a, n) for(ll i=ll(a);i=ll(a);--i) #define REPLL(i, n) for(ll i=0;i=0;--i) #define IN(a, x, b) (a<=x && x inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } #define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]" #define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;} void CHECKTIME(std::function f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast((end - start)).count(); std::cerr << "[Time:" << res << "ns (" << res / (1.0e9) << "s)]\n"; } // test template std::vector> VV(int n, int m, T init = T()) { return std::vector>(n, std::vector(m, init)); } template std::ostream& operator<<(std::ostream& os, std::pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } // type/const //#define int ll using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair; using PAIRLL = std::pair; constexpr int INFINT = 1 << 30; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-10; constexpr int MOD = 1000000007; constexpr double PI = 3.141592653589793238462643383279; template void FILL(T(&a)[N], const T& val) { for (auto& x : a) x = val; } template void FILL(ARY(&a)[N][M], const T& val) { for (auto& b : a) FILL(b, val); } template void FILL(std::vector& a, const T& val) { for (auto& x : a) x = val; } template void FILL(std::vector>& a, const T& val) { for (auto& b : a) FILL(b, val); } // ------------>8------------------------------------->8------------ // https://www.dropbox.com/sh/9lknvq4xay709cn/AAAX61z5W1m20MPkJ8V53l5ma/%23WaveletMatrix.cpp?dl=0 using namespace std; typedef unsigned int u32; inline int popcount(u32 x) { x = x - ((x >> 1) & 0x55555555); x = (x & 0x33333333) + ((x >> 2) & 0x33333333); return ((x + (x >> 4) & 0xF0F0F0F) * 0x1010101) >> 24; } //(k+1)番目の1の立っている位置(最下位から)を返す //http://graphics.stanford.edu/~seander/bithacks.html#SelectPosFromMSBRank を参考にした inline int select32(u32 x, int k) { u32 a, b, c; int t, s; a = (x & 0x55555555) + ((x >> 1) & 0x55555555); b = (a & 0x33333333) + ((a >> 2) & 0x33333333); c = (b & 0x0f0f0f0f) + ((b >> 4) & 0x0f0f0f0f); t = (c & 0xff) + ((c >> 8) & 0xff); s = 0; s += ((t - k - 1) & 128) >> 3; k -= t & ((t - k - 1) >> 8); //if(k >= t) s += 16, k -= t; t = (c >> s) & 0xf; s += ((t - k - 1) & 128) >> 4; k -= t & ((t - k - 1) >> 8); //if(k >= t) s += 8, k -= t; t = (b >> s) & 0x7; s += ((t - k - 1) & 128) >> 5; k -= t & ((t - k - 1) >> 8); //if(k >= t) s += 4, k -= t; t = (a >> s) & 0x3; s += ((t - k - 1) & 128) >> 6; k -= t & ((t - k - 1) >> 8); //if(k >= t) s += 2, k -= t; t = (x >> s) & 0x1; s += ((t - k - 1) & 128) >> 7; //if(k >= t) s += 1; return s; } //※静的なデータ構造 //constructした後setを何回か呼び、その後buildを呼んだ後にrank,selectが行える struct FullyIndexableDictionary { static const int NOTFOUND = -1; static const int SELECTT_INTERVAL = 32; //SELECTT_INTERVAL >= 32 int length, blockslength, count; vector blocks; vector ranktable, selecttable0, selecttable1; FullyIndexableDictionary(int len) : length(len) { blocks.resize((blockslength = (len + 31) / 32) + 1); } inline void set(int i) { blocks[i / 32] |= 1 << i % 32; } void build() { if (length == 0) { count = 0; return; } ranktable.assign(blockslength + 1, 0); selecttable0.clear(); selecttable1.clear(); int prev0 = 0, prev1 = 0, count0 = 0, count1 = 0; for (int i = 0; i < blockslength; i++) { ranktable[i] = count1; count1 += popcount(blocks[i]); count0 = 32 * (i + 1) - count1; if (prev1 < (count1 + SELECTT_INTERVAL - 1) / SELECTT_INTERVAL) selecttable1.push_back(i), prev1 = (count1 + SELECTT_INTERVAL - 1) / SELECTT_INTERVAL; if (prev0 < (count0 + SELECTT_INTERVAL - 1) / SELECTT_INTERVAL) selecttable0.push_back(i), prev0 = (count0 + SELECTT_INTERVAL - 1) / SELECTT_INTERVAL; } ranktable[blockslength] = count1; selecttable1.push_back(blockslength - 1); selecttable0.push_back(blockslength - 1); count = count1; } inline bool access(int pos) const { return blocks[pos / 32] >> pos % 32 & 1; } inline int rank(int pos) const { //[0..pos)の1の個数 int block_idx = pos / 32; return ranktable[block_idx] + popcount(blocks[block_idx] & (1U << pos % 32) - 1); } inline int rank(bool b, int pos) const { return b ? rank(pos) : pos - rank(pos); } inline int rank(bool b, int left, int right) const { return rank(b, right) - rank(b, left); } //O(log n)は重いよねえ。expect O(1) (たぶん) ならできるけど最悪ケースがなあ //あるいはメモリ4*32*n bytes でO(1)でもできるけど…ハッシュテーブルでうまくやればうまくできるか? template int select(int k) const { //(k+1)番目のbの位置 if ((b ? count : length - count) <= k) return NOTFOUND; int selecttable_index = k / SELECTT_INTERVAL; int l = (b ? selecttable1 : selecttable0)[selecttable_index], u = (b ? selecttable1 : selecttable0)[selecttable_index + 1] + 1; //ブロックを二分探索 while (l + 1 < u) { int m = (l + u) / 2; ((b ? ranktable[m] : m * 32 - ranktable[m]) <= k ? l : u) = m; } return l * 32 + select32(b ? blocks[l] : ~blocks[l], k - (b ? ranktable[l] : 32 * l - ranktable[l])); } inline int select(bool b, int k) const { return b ? select(k) : select(k); } inline int select(bool b, int k, int left) const { return select(b, rank(b, left) + k); } }; /* WaveletMatrix。たしかにこっちの方が「常に」使うべきな気がする */ inline unsigned int BITMASK(int i) { return (1 << i) - 1; } //※メモリ, 時間はだいたい支配的な部分のみ書く //メモリ: (length * bitsize / 8) bytes struct WaveletMatrix { typedef unsigned long long Val; static const int NOTFOUND = -1; static const Val UNDEFINED = Val(-1); static const int MAX_BITSIZE = 64; int length, bitsize; Val maxval; vector dicts; vector mids; //追加メモリ: (2 * length * sizeof Val) bytes //時間: bitsize * length * 大きめ void init(const vector& data) { length = data.size(); maxval = *max_element(data.begin(), data.end()); if (1ULL << (8 * sizeof(Val) - 1) <= maxval) bitsize = 8 * sizeof(Val); else for (bitsize = 0; Val(1) << bitsize <= maxval; bitsize++); dicts.assign(bitsize, length); mids.assign(bitsize, 0); vector datacurrent(data), datanext(length); for (int bit = 0; bit < bitsize; bit++) { int pos = 0; for (int i = 0; i < length; i++) if ((datacurrent[i] >> (bitsize - bit - 1) & 1) == 0) datanext[pos++] = datacurrent[i]; mids[bit] = pos; for (int i = 0; i < length; i++) if ((datacurrent[i] >> (bitsize - bit - 1) & 1) != 0) dicts[bit].set(i), datanext[pos++] = datacurrent[i]; dicts[bit].build(); datacurrent.swap(datanext); } } Val access(int pos) const { Val val = 0; for (int bit = 0; bit < bitsize; bit++) { bool dir = dicts[bit].access(pos); val = val << 1 | (dir ? 1 : 0); pos = dicts[bit].rank(dir, pos); if (dir) pos += mids[bit]; } return val; } int rank(Val val, int left, int right) const { if (val > maxval) return 0; for (int bit = 0; bit < bitsize; bit++) { bool dir = val >> (bitsize - bit - 1) & 1; left = dicts[bit].rank(dir, left), right = dicts[bit].rank(dir, right); if (dir) left += mids[bit], right += mids[bit]; } return right - left; } int rank(Val val, int right) const { return rank(val, 0, right); } int rank_all(Val val, int left, int right, int& out_lt, int& out_gt) const { if (val > maxval) { out_lt = right - left; out_gt = 0; return 0; } out_lt = out_gt = 0; for (int bit = 0; bit < bitsize; bit++) { bool dir = val >> (bitsize - bit - 1) & 1; int leftcount = dicts[bit].rank(dir, left), rightcount = dicts[bit].rank(dir, right); (dir ? out_lt : out_gt) += (right - left) - (rightcount - leftcount); left = leftcount, right = rightcount; if (dir) left += mids[bit], right += mids[bit]; } return right - left; } inline int rank_lt(Val val, int left, int right) const { int tmp_lt, tmp_gt; rank_all(val, left, right, tmp_lt, tmp_gt); return tmp_lt; } inline int rangefreq(int left, int right, Val bottom, Val up) { return rank_lt(up, left, right) - rank_lt(bottom, left, right); } //O(bitsize log length) (FID::selectがlog nで最悪の場合) int select(Val val, int k) const { if (val > maxval) return NOTFOUND; static int lefts[MAX_BITSIZE], rights[MAX_BITSIZE]; int left = 0, right = length; for (int bit = 0; bit < bitsize; bit++) { lefts[bit] = left, rights[bit] = right; bool dir = val >> (bitsize - bit - 1) & 1; left = dicts[bit].rank(dir, left), right = dicts[bit].rank(dir, right); if (dir) left += mids[bit], right += mids[bit]; } for (int bit = bitsize - 1; bit >= 0; bit--) { k = dicts[bit].select(val >> (bitsize - bit - 1) & 1, k, lefts[bit]); if (k == FullyIndexableDictionary::NOTFOUND || k >= rights[bit]) return NOTFOUND; k -= lefts[bit]; } return k; } int select(Val val, int k, int left) const { return select(val, k + rank(val, left)); } void quantile(int left, int right, int k, Val& out_val, int& out_k) const { if (right - left <= k) { out_val = UNDEFINED; out_k = NOTFOUND; return; } Val val = 0; for (int bit = 0; bit < bitsize; bit++) { int count = dicts[bit].rank(true, left, right); bool dir = k < count; val = val << 1 | (dir ? 1 : 0); if (!dir) k -= count; left = dicts[bit].rank(dir, left), right = dicts[bit].rank(dir, right); if (dir) left += mids[bit], right += mids[bit]; } out_val = val; out_k = k; } struct IdxVal { int idx; Val val; IdxVal() {} IdxVal(int i, Val v) : idx(i), val(v) {} }; inline Val quantile(int left, int right, int k) const { Val tmp_val; int tmp_k; quantile(left, right, k, tmp_val, tmp_k); return tmp_val; } inline IdxVal quantile_idxval(int left, int right, int k) const { Val tmp_val; int tmp_k; quantile(left, right, k, tmp_val, tmp_k); return IdxVal(select(tmp_val, tmp_k, left), tmp_val); } inline Val maximum(int left, int right) const { return quantile(left, right, 0); } inline Val minimum(int left, int right) const { return quantile(left, right, right - left - 1); } //区間がかぶってるとkとかがintより大きくなるよね void quantile_ranges(const vector& lefts0, const vector& rights0, int k, Val& out_val, int& out_k) const { int n = lefts0.size(); int width = 0; for (int i = 0; i < n; i++) width += rights0[i] - lefts0[i]; if (width <= k) { out_val = UNDEFINED; out_k = NOTFOUND; return; } static vector lefts, rights; //自動変数だとメモリ確保の時間…と思ったけどこれだとどうだろう? lefts.assign(lefts0.begin(), lefts0.end()); rights.assign(rights0.begin(), rights0.end()); Val val = 0; for (int bit = 0; bit < bitsize; bit++) { int count = 0; for (int i = 0; i < n; i++) { count += dicts[bit].rank(true, lefts[i], rights[i]); } bool dir = k < count; val = val << 1 | (dir ? 1 : 0); if (!dir) k -= count; for (int i = 0; i < n; i++) { lefts[i] = dicts[bit].rank(dir, lefts[i]); rights[i] = dicts[bit].rank(dir, rights[i]); if (dir) lefts[i] += mids[bit], rights[i] += mids[bit]; } } out_val = val; out_k = k; } //区間がかぶってるとバグる //区間がソートされていないとバグる inline IdxVal quantile_ranges_idxval(const vector& lefts, const vector& rights, int k) const { int n = lefts.size(); Val tmp_val; int tmp_k; quantile_ranges(lefts, rights, k, tmp_val, tmp_k); for (int i = 0; i < n; i++) { if (tmp_k < rights[i] - lefts[i]) { return IdxVal(select(tmp_val, tmp_k, lefts[i]), tmp_val); } tmp_k -= rights[i] - lefts[i]; } return IdxVal(NOTFOUND, UNDEFINED); } struct Range { int left, right; int bit; Val val; Range(int l, int r, int b, Val v) : left(l), right(r), bit(b), val(v) {} }; //O(bitsize min(length, maxval) log min(length, maxval))? //priority_queueではやはり最悪ケースが… //でもランダムで適当(バラけすぎとかが無い)なデータに対しては結構速い template int rectbfsk(const F& f, int left, int right, Val bottom, Val up, int k, FOut& out) const { int k0 = k; up = min(up, maxval + 1); priority_queue, F> q(f); q.push(Range(left, right, 0, 0)); while (k && !q.empty()) { Range t = q.top(); q.pop(); if (t.bit == bitsize) { f.pushvalues(out, t, k); } else { int leftcount = dicts[t.bit].rank(false, t.left); int rightcount = dicts[t.bit].rank(false, t.right); if (rightcount - leftcount != 0 && bottom <= ((t.val << (bitsize - t.bit)) | BITMASK(bitsize - t.bit - 1))) q.push(Range(leftcount, rightcount, t.bit + 1, t.val << 1)); if ((t.right - t.left) - (rightcount - leftcount) != 0 && (((t.val << 1 | 1) << (bitsize - t.bit - 1))) < up) { q.push(Range( (t.left - leftcount) + mids[t.bit], (t.right - rightcount) + mids[t.bit], t.bit + 1, t.val << 1 | 1)); } } } return k0 - k; } struct ValCount { Val val; int count; ValCount(Val v, int c) : val(v), count(c) {} ValCount() {} }; struct FreqList { inline bool operator()(const Range& x, const Range& y) const { return x.right - x.left < y.right - y.left || (x.right - x.left == y.right - y.left && x.val > y.val); } inline void pushvalues(vector& out, const Range& t, int& k) const { out.push_back(ValCount(t.val, t.right - t.left)); k--; } }; inline int topk(int left, int right, Val bottom, Val up, int k, vector& out) const { return rectbfsk >(FreqList(), left, right, bottom, up, k, out); } template struct DfsInfo { const F& f; FOut& out; Val bottom, up; DfsInfo(const F& f_, FOut& o, Val b, Val u) : f(f_), out(o), bottom(b), up(u) {} }; //O(min(k bitsize, min(length, maxval)))? //minじゃなくてもう少しなめらかな関数で上界得られそうだけど…kつの中で幅に入らない分は共有されるイメージ //でもO(k bitsize)はやはり心強いな。k=1ならO(bitsize)となるわけだし template void rectdfsk_dfs(const DfsInfo& info, int bit, Val val, int left, int right, int& k) const { if (bit == bitsize) { info.f.pushvalues(info.out, val, right - left, k); return; } int leftcount = dicts[bit].rank(left); int rightcount = dicts[bit].rank(right); if (F::MAXF) { if (k > 0 && rightcount - leftcount != 0 && (((val << 1 | 1) << (bitsize - bit - 1)) < info.up)) rectdfsk_dfs(info, bit + 1, val << 1 | 1, leftcount + mids[bit], rightcount + mids[bit], k); if (k > 0 && (right - left) - (rightcount - leftcount) != 0 && (info.bottom <= ((val << (bitsize - bit)) | BITMASK(bitsize - bit - 1)))) rectdfsk_dfs(info, bit + 1, val << 1, left - leftcount, right - rightcount, k); } else { if (k > 0 && (right - left) - (rightcount - leftcount) != 0 && (info.bottom <= ((val << (bitsize - bit)) | BITMASK(bitsize - bit - 1)))) rectdfsk_dfs(info, bit + 1, val << 1, left - leftcount, right - rightcount, k); if (k > 0 && rightcount - leftcount != 0 && (((val << 1 | 1) << (bitsize - bit - 1)) < info.up)) rectdfsk_dfs(info, bit + 1, val << 1 | 1, leftcount + mids[bit], rightcount + mids[bit], k); } } template struct MinMaxList { enum { MAXF = maxf }; inline void pushvalues(vector& out, Val val, int count, int& k) const { out.push_back(ValCount(val, min(k, count))); k -= min(k, count); } }; template int rectdfsk(const F& f, int left, int right, Val bottom, Val up, int k, FOut& out) const { rectdfsk_dfs(DfsInfo(f, out, bottom, up), 0, 0, left, right, k); return k; } template int rectminmaxk(int left, int right, Val bottom, Val up, int k, vector& out) const { return rectdfsk, vector >(MinMaxList(), left, right, bottom, up, k, out); } }; signed main() { INIT; VAR(int, n); VEC(int, a, n); VEC_ROW(int, n, L, R); std::vector b(n); REP(i, n) b[i] = a[i] + R[i]; WaveletMatrix wav; wav.init(b); ll cnt = 0; FOR(j, 1, n) { int i = std::lower_bound(ALL(a), a[j] - L[j]) - a.begin(); if (i >= j) continue; // [i, j)をチェック cnt += wav.rangefreq(i, j, a[j], INFINT_LIM); } OUT(cnt)BR; return 0; }