#include "train.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = 1e5 + 12;
struct node{
node *l = 0, *r = 0;
int sum = 0;
node(int val) {
sum = val;
}
node(node *L, node *R) {
l = L;
r = R;
sum = L->sum + R->sum;
}
};
int s;
using pnode = node *;
pnode tt[N];
int n, m, w, it = 0, ti = 0;
vector<int> rs, ls;
pnode upd(int pos, pnode v, int tl = 0, int tr = s) {
if(tl == tr) {
return new node(v->sum + 1);
} else {
int tm = (tl + tr) >> 1;
if(pos <= tm) {
return new node(upd(pos, v->l, tl, tm), v->r);
} else {
return new node(v->l, upd(pos, v->r, tm + 1, tr));
}
}
}
int get(int l, int r, pnode v, int tl = 0, int tr = s) {
if(l > r || tl > r || l > tr) return 0;
if(tl >= l && tr <= r) {
return v->sum;
} else {
int tm = (tl + tr) >> 1;
return get(l, r, v->l, tl, tm) + get(l, r, v->r, tm + 1, tr);
}
}
vector<int> t, x, y, a, b, c, vt;
vector<pair<int, int>> f;
struct qwq{
int pos;
ll d;
int l, r, v;
};
deque<qwq> d[N];
ll dp[N];
int col = 0;
const ll inf = 1e18, mx = (int)1e9 + 1;
ll cost(int L, int R) {
int ret = 0, ret1 = 0;
int it = lower_bound(rs.begin(), rs.end(), R) - rs.begin() - 1;
int it1 = upper_bound(ls.begin(), ls.end(), L) - ls.begin() - 1;
if(it < 0) {
ret1 = 0;
} else {
ret1 = it + 1 - get(0, it1, tt[it]);
}
return ret1;
}
ll get_val(qwq q, int x) {
if(x < q.pos) return inf;
return q.d + cost(q.pos, x) * 1ll * t[q.v];
}
ll gdp(int v, int pos) {
while(!d[v].empty() && d[v][0].r < pos) {
d[v].pop_front();
}
if(d[v].empty()) return inf;
ll ret = min(inf, get_val(d[v][0], pos));
d[v][0].l = pos;
return ret;
}
void add(int v, ll dd, int pos) {
qwq nv;
nv.pos = pos;nv.d = dd;nv.v = v;
while(!d[v].empty() && get_val(d[v].back(), d[v].back().l) > get_val(nv, d[v].back().l)) {
d[v].pop_back();
}
if(d[v].empty()) {
d[v].push_back({pos, dd, pos, mx, v});
return;
}
if(get_val(d[v].back(), mx) <= get_val(nv, mx)) {
d[v].back().r = mx;
return;
}
int l = 0, r = (int)vt.size() - 1;
while(r - l > 1) {
int mid = vt[(l + r) >> 1], mid1 = (l + r) >> 1;
if(get_val(d[v].back(), mid) <= get_val(nv, mid)) {
l = mid1;
} else {
r = mid1;
}
}
r = vt[r];
d[v].back().r = r - 1;
if(r <= mx) {
nv.l = r;
nv.r = mx;
d[v].push_back(nv);
}
}
ll get() {
vector<int> e, ej;
for(int i = 0; i < m; i++) {
e.push_back(i);
ej.push_back(i);
}
sort(e.begin(), e.end(), [&](int x, int y){
return a[x] < a[y];
});
sort(ej.begin(), ej.end(), [&](int x, int y){
return b[x] < b[y];
});
add(0, 0, 0);
for(int i:e) {
while(it < m && b[ej[it]] <= a[i]) {
int j = ej[it];
if(dp[j] < inf) add(y[j], dp[j], b[j]);
it++;
}
dp[i] = gdp(x[i], a[i]) + c[i];
}
if(dp[m - 1] >= inf) dp[m - 1] = -1;
return dp[m - 1];
}
pnode build(int tl = 0, int tr = s) {
if(tl == tr) {
return new node(0);
} else {
int tm = (tl + tr) >> 1;
return new node(build(tl, tm), build(tm + 1, tr));
}
}
ll solve(int N, int M, int W, vector<int> _T, vector<int> X, vector<int> Y, vector<int> A, vector<int> B, vector<int> C, vector<int> L,vector<int> R) {
n = N;m = M;w = W;
t.swap(_T);
x.swap(X);
y.swap(Y);
a.swap(A);
b.swap(B);
c.swap(C);
m++;
x.push_back(n - 1);
y.push_back(n - 1);
a.push_back(mx);
b.push_back(mx + 1);
c.push_back(0);
for(int i = 0; i < w; i++) {
f.emplace_back(L[i], R[i]);
rs.push_back(R[i]);
ls.push_back(L[i]);
}
for(int i = 0; i < m; i++) {
vt.push_back(a[i]);
vt.push_back(b[i]);
}
vt.push_back(mx + 1);
vt.push_back(0);
sort(vt.begin(), vt.end());
vt.resize(unique(vt.begin(), vt.end()) - vt.begin());
sort(f.begin(), f.end(), [&](pair<int, int> x, pair<int, int> y){
return x.second < y.second;
});
sort(rs.begin(), rs.end());
sort(ls.begin(), ls.end());
ls.resize(unique(ls.begin(), ls.end()) - ls.begin());
s = (int)ls.size();
pnode rt = build();
for(int i = 0; i < w; i++) {
int it = lower_bound(ls.begin(), ls.end(), f[i].first) - ls.begin();
tt[i] = (i ? upd(it, tt[i - 1]) : upd(it, rt));
}
return get();
}
