#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } //////////////////////////////////////////////////////////////////////////////// template struct ModInt { static constexpr unsigned M = M_; unsigned x; constexpr ModInt() : x(0U) {} constexpr ModInt(unsigned x_) : x(x_ % M) {} constexpr ModInt(unsigned long long x_) : x(x_ % M) {} constexpr ModInt(int x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} constexpr ModInt(long long x_) : x(((x_ %= static_cast(M)) < 0) ? (x_ + static_cast(M)) : x_) {} ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; } ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; } ModInt &operator*=(const ModInt &a) { x = (static_cast(x) * a.x) % M; return *this; } ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); } ModInt pow(long long e) const { if (e < 0) return inv().pow(-e); ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b; } ModInt inv() const { unsigned a = M, b = x; int y = 0, z = 1; for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast(q) * z; y = z; z = w; } assert(a == 1U); return ModInt(y); } ModInt operator+() const { return *this; } ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; } ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); } ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); } ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); } ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); } template friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); } template friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); } template friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); } template friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); } explicit operator bool() const { return x; } bool operator==(const ModInt &a) const { return (x == a.x); } bool operator!=(const ModInt &a) const { return (x != a.x); } friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; } }; //////////////////////////////////////////////////////////////////////////////// constexpr unsigned MO = 1'000'000'007; using Mint = ModInt; int N; vector> P; Mint solve() { sort(P.begin(), P.end()); // cerr<<"P = ";pv(P.begin(),P.end()); vector xs(N); for (int i = 0; i < N; ++i) { const Int x = P[i].first - P[i].second; xs[i] = x; } sort(xs.begin(), xs.end()); xs.erase(unique(xs.begin(), xs.end()), xs.end()); const int xsLen = xs.size(); // cerr<<" xs = ";pv(xs.begin(),xs.end()); vector> yss(xsLen); for (int i = 0; i < N; ++i) { const Int x = P[i].first - P[i].second; const Int y = P[i].first + P[i].second; const int posX = lower_bound(xs.begin(), xs.end(), x) - xs.begin(); for (int e = posX; e < xsLen; e |= e + 1) { yss[e].push_back(y); } } vector> bit1(xsLen), bitA(xsLen); for (int e = 0; e < xsLen; ++e) { auto &ys = yss[e]; sort(ys.begin(), ys.end()); ys.erase(unique(ys.begin(), ys.end()), ys.end()); const int ysLen = ys.size(); bit1[e].assign(ysLen, 0); bitA[e].assign(ysLen, 0); } Mint ans = 0; for (int i = 0, j; i < N; ++i) { for (j = i; j < N && P[i].first == P[j].first; ++j) {} for (int k = i; k < j; ++k) { const Int x = P[k].first - P[k].second; const Int y = P[k].first + P[k].second; // cerr<<" get "<= 0; e = (e & (e + 1)) - 1) { auto &ys = yss[e]; const int posY = lower_bound(ys.begin(), ys.end(), y) - ys.begin(); for (int f = posY - 1; f >= 0; f = (f & (f + 1)) - 1) { sum1 += bit1[e][f]; sumA += bitA[e][f]; } } ans += (sum1 * P[k].first - sumA); } for (int k = i; k < j; ++k) { const Int x = P[k].first - P[k].second; const Int y = P[k].first + P[k].second; // cerr<<" add "<