This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define md ((l + r) >> 1)
const int inf = 1e9;
int y = -1, mncnt = 2, mxcnt = 2;
struct nodemn {
int l, r, v;
nodemn() {l = 0, r = 0, v = 1e9;}
} segmn[5'000'005];
struct nodemx {
int l, r, v;
nodemx() {l = 0, r = 0, v = -1e9;}
} segmx[5'000'005];
void updmn(int i, int l, int r, int x, int v) {
if (l == r) {
segmn[i].v = min(segmn[i].v, v);
return;
}
if (x <= md) {
if (!segmn[i].l) {
segmn[i].l = mncnt++;
}
updmn(segmn[i].l, l, md, x, v);
} else {
if (!segmn[i].r) {
segmn[i].r = mncnt++;
}
updmn(segmn[i].r, md + 1, r, x, v);
}
segmn[i].v = min(segmn[segmn[i].l].v, segmn[segmn[i].r].v);
}
void updmx(int i, int l, int r, int x, int v) {
if (l == r) {
segmx[i].v = max(segmx[i].v, v);
return;
}
if (x <= md) {
if (!segmx[i].l) {
segmx[i].l = mxcnt++;
}
updmx(segmx[i].l, l, md, x, v);
} else {
if (!segmx[i].r) {
segmx[i].r = mxcnt++;
}
updmx(segmx[i].r, md + 1, r, x, v);
}
segmx[i].v = max(segmx[segmx[i].l].v, segmx[segmx[i].r].v);
}
int getmn(int i, int l, int r, int s, int e) {
if (i == 0 || r < s || e < l) {
return 1e9;
}
if (s <= l && r <= e) {
return segmn[i].v;
}
return min(getmn(segmn[i].l, l, md, s, e), getmn(segmn[i].r, md + 1, r, s, e));
}
int getmx(int i, int l, int r, int s, int e) {
if (i == 0 || r < s || e < l) {
return -1e9;
}
if (s <= l && r <= e) {
return segmx[i].v;
}
return max(getmx(segmx[i].l, l, md, s, e), getmx(segmx[i].r, md + 1, r, s, e));
}
int get(int i, int l, int r, int s, int e, int k) {
if (l == r) {
return l;
}
if (md + 1 <= e && getmn(1, 0, 1e8, md + 1, min(r, e)) < k) {
return get(segmn[i].r, md + 1, r, s, e, k);
} else {
return get(segmn[i].l, l, md, s, e, k);
}
}
int main() {
ios_base::sync_with_stdio(0), cin.tie(0);
int n;
cin >> n;
array<int, 3> a[n];
for (int i = 0; i < n; i++) {
cin >> a[i][0] >> a[i][1] >> a[i][2];
}
sort(a, a + n);
int ans = -1;
int cur = 0;
for (int i = 0; i < n; i++) {
while (a[cur][0] < a[i][0]) {
updmn(1, 0, 1e8, a[cur][1], a[cur][2]);
updmx(1, 0, 1e8, a[cur][1], a[cur][2]);
if (getmx(1, 0, 1e8, 0, a[cur][1] - 1) > a[cur][2]) {
y = max(y, a[cur][1]);
}
if (a[cur][1] + 1 != int(1e8) && getmn(1, 0, 1e8, a[cur][1] + 1, 1e8) < a[cur][2]) {
int newy = get(1, 0, 1e8, a[cur][1] + 1, 1e8, a[cur][2]);
y = max(y, newy);
}
cur++;
}
// while (a[cur][0] < a[i][0]) {
// mx[a[cur][1]] = max(mx[a[cur][1]], a[cur][2]);
// mn[a[cur][1]] = min(mn[a[cur][1]], a[cur][2]);
// for (int newy = 304; newy > a[cur][1]; newy--) {
// if (mn[newy] < a[cur][2]) {
// y = max(y, newy);
// break;
// }
// }
// for (int newy = 0; newy < a[cur][1]; newy++) {
// if (mx[newy] > a[cur][2]) {
// y = max(y, a[cur][1]);
// break;
// }
// }
// cur++;
// }
if (y >= max(1, a[i][1] + 1)) {
int z = getmx(1, 0, 1e8, 0, y - 1);
if (a[i][2] < z) {
ans = max(ans, a[i][0] + z + y);
}
}
}
cout << ans << '\n';
return 0;
}
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