#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #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; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; constexpr ll mod = 998244353; //constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } typedef long double ld; typedef pair LDP; const ld eps = 1e-8; const ld pi = acosl(-1.0); int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 100005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } //----------------------------------------- struct Seg2T { private: vector node; int sz; vector vy; const ll init_c = -INF; public: ll f(ll a, ll b) { return max(a, b); } void add(int y) { vy.push_back(y); } void complete() { sort(vy.begin(), vy.end()); vy.erase(unique(vy.begin(), vy.end()), vy.end()); int n = vy.size(); sz = 1; while (sz < n)sz *= 2; node.resize(2 * sz - 1, init_c); } void update(int k, ll c) { k = lower_bound(vy.begin(), vy.end(), k) - vy.begin(); k += sz - 1; //f(a_{0,3},a_{1,3})=node[k]なこともあるので注意すること node[k] = f(node[k], c); while (k > 0) { k = (k - 1) / 2; node[k] = f(node[k * 2 + 1], node[k * 2 + 2]); } } ll query(int a, int b, int k, int l, int r) { if (r <= a || b <= l)return init_c; if (a <= l && r <= b)return node[k]; else { ll vl = query(a, b, k * 2 + 1, l, (l + r) / 2); ll vr = query(a, b, k * 2 + 2, (l + r) / 2, r); return f(vl, vr); } } ll query(int a, int b) { a = lower_bound(vy.begin(), vy.end(), a) - vy.begin(); b = lower_bound(vy.begin(), vy.end(), b) - vy.begin(); return query(a, b, 0, 0, sz); } }; struct SegT { private: int sz; vector node; const ll init_c = -INF; public: ll f(ll a, ll b) { return max(a, b); } SegT(vector

v, int n) { sz = 1; while (sz < n)sz *= 2; node.resize(sz * 2 - 1); rep(i, v.size()) { int k = v[i].first, y = v[i].second; k += sz - 1; node[k].add(y); while (k > 0) { k = (k - 1) / 2; node[k].add(y); } } rep(i, 2 * sz - 1)node[i].complete(); } void update(int x, int y, ll c) { x += sz - 1; node[x].update(y, c); while (x) { x = (x - 1) / 2; node[x].update(y, c); } } ll query(int a, int b, int x, int y, int k = 0, int l = 0, int r = -1) { if (r < 0)r = sz; if (r <= a || b <= l)return init_c; else if (a <= l && r <= b)return node[k].query(x, y); else { ll vl = query(a, b, x, y, k * 2 + 1, l, (l + r) / 2); ll vr = query(a, b, x, y, k * 2 + 2, (l + r) / 2, r); return f(vl, vr); } } }; void solve(){ int n; cin >> n; using ar = array; vector v(n); rep(i, n)rep(j, 3)cin >> v[i][j]; sort(all(v)); vector vx; rep(i, n) { vx.push_back(v[i][1]); } vx.push_back(0); sort(all(vx)); vx.erase(unique(all(vx)), vx.end()); vector

orile, oriri; rep(i, n) { int x = v[i][1]; x = lower_bound(all(vx), x) - vx.begin(); int y = v[i][0] - v[i][1]; orile.push_back({ x,y }); y = v[i][0] + v[i][1]; oriri.push_back({ x,y }); } int loc0 = lower_bound(all(vx), 0) - vx.begin(); orile.push_back({ loc0,0 }); oriri.push_back({ loc0,0 }); SegT stle(orile, vx.size()), stri(oriri, vx.size()); stle.update(loc0, 0, 0); stri.update(loc0, 0, 0); ll ans = 0; rep(i, n) { int x = lower_bound(all(vx), v[i][1]) - vx.begin(); ll val = -INF; int y = v[i][0] - v[i][1]; ll valle = stle.query(0, x, 0, y + 1); y = v[i][0] + v[i][1]; ll valri = stri.query(x, vx.size(), 0, y + 1); val = max(valle, valri) + v[i][2]; chmax(ans, val); y = v[i][0] - v[i][1]; stle.update(x, y, val); y = v[i][0] + v[i][1]; stri.update(x, y, val); } cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(10); //init_f(); //init(); //while(true) //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }