#include "walk.h"
#include <stdlib.h>
#include <string.h>
using namespace std;
typedef vector<int> vi;
const int N = 100000, M = 100000, N_ = 1 << 18, N1 = 4000000, M_ = 4000000; /* N_ = pow2(ceil(log2(N))) */
const long long INF = 0x3f3f3f3f3f3f3f3f;
long long min(long long a, long long b) { return a < b ? a : b; }
unsigned int X = 12345;
int rand_() {
return (X *= 3) >> 1;
}
int ii[N], hh[M * 2];
int *aa;
void sort(int *ii, int l, int r) {
while (l < r) {
int i = l, j = l, k = r, i_ = ii[l + rand_() % (r - l)], tmp;
while (j < k)
if (aa[ii[j]] == aa[i_])
j++;
else if (aa[ii[j]] < aa[i_]) {
tmp = ii[i], ii[i] = ii[j], ii[j] = tmp;
i++, j++;
} else {
k--;
tmp = ii[j], ii[j] = ii[k], ii[k] = tmp;
}
sort(ii, l, i);
l = k;
}
}
int ij[M_], ww[M_], m_;
int *eh[N1], eo[N1], n_;
void append(int i, int h) {
int o = eo[i]++;
if (o >= 2 && (o & o - 1) == 0)
eh[i] = (int *) realloc(eh[i], o * 2 * sizeof *eh[i]);
eh[i][o] = h;
}
int newnode() {
eh[n_] = (int *) malloc(2 * sizeof *eh[n_]);
return n_++;
}
void add(int i, int j, int w) {
int h = m_++;
ij[h] = i ^ j, ww[h] = w;
append(i, h), append(j, h);
}
int pp[N], qq[N], top[N], yy1[N];
void push(int i, int y) {
int t = newnode();
add(top[i], t, y - yy1[i]);
top[i] = t, yy1[i] = y;
}
long long dd[N1]; int pq[N1], iq[1 + N1], cnt;
int lt(int i, int j) {
return dd[i] < dd[j];
}
int p2(int p) {
return (p *= 2) > cnt ? 0 : (p < cnt && lt(iq[p + 1], iq[p]) ? p + 1 : p);
}
void pq_up(int i) {
int p, q, j;
for (p = pq[i]; (q = p / 2) && lt(i, j = iq[q]); p = q)
iq[pq[j] = p] = j;
iq[pq[i] = p] = i;
}
void pq_dn(int i) {
int p, q, j;
for (p = pq[i]; (q = p2(p)) && lt(j = iq[q], i); p = q)
iq[pq[j] = p] = j;
iq[pq[i] = p] = i;
}
void pq_add_last(int i) {
iq[pq[i] = ++cnt] = i;
}
int pq_remove_first() {
int i = iq[1], j = iq[cnt--];
if (j != i)
pq[j] = 1, pq_dn(j);
pq[i] = 0;
return i;
}
long long dijkstra(int s, int t) {
memset(dd, 0x3f, n_ * sizeof *dd);
dd[s] = 0, pq_add_last(s);
while (cnt) {
int i = pq_remove_first(), o;
if (i == t)
return dd[i];
for (o = eo[i]; o--; ) {
int h = eh[i][o], j = i ^ ij[h];
long long d = dd[i] + ww[h];
if (dd[j] > d) {
if (dd[j] == INF)
pq_add_last(j);
dd[j] = d, pq_up(j);
}
}
}
return -1;
}
int xx[N], yy[N], ll[M], rr[M], xx1[M * 2], zz[M], idx[M], zz1[M];
long long solve_using_dijkstra(vi xx_, vi yy_, vi ll_, vi rr_, vi zz_, int s, int t) {
int n = xx_.size(), m = zz_.size(), h, i;
for (i = 0; i < n; i++) {
xx[i] = xx_[i], yy[i] = yy_[i];
ii[i] = i;
}
aa = yy, sort(ii, 0, n);
for (h = 0; h < m; h++) {
ll[h] = ll_[h], rr[h] = rr_[h], zz[h] = zz_[h];
hh[h] = h;
}
aa = zz, sort(hh, 0, m);
for (i = 0; i < n; i++) {
pp[i] = i - 1, qq[i] = i + 1;
top[i] = newnode(), yy1[i] = 0;
}
for (h = 0, i = 0; h < m; h++) {
int h_ = hh[h], i_;
while (i < n && yy[i_ = ii[i]] < zz[h_]) {
if (pp[i_] != -1)
qq[pp[i_]] = qq[i_];
if (qq[i_] != n)
pp[qq[i_]] = pp[i_];
i++;
}
for (i_ = ll[h_]; i_ != rr[h_]; i_ = qq[i_])
push(i_, zz[h_]);
push(i_, zz[h_]);
for (i_ = ll[h_]; i_ != rr[h_]; i_ = qq[i_])
add(top[i_], top[qq[i_]], xx[qq[i_]] - xx[i_]);
}
for (i = 0; i < n; i++)
push(i, yy[i]);
return dijkstra(s, t);
}
long long st1[N_ * 2], st2[N_ * 2];
void pul(int i) {
int l = i << 1, r = l | 1;
st1[i] = min(st1[l], st1[r]), st2[i] = min(st2[l], st2[r]);
}
void update(int i, long long x) {
if (x == INF)
st1[n_ + i] = st2[n_ + i] = INF;
else
st1[n_ + i] = x - zz1[i], st2[n_ + i] = x + zz1[i];
i += n_;
while (i > 1)
pul(i >>= 1);
}
long long query(int i) {
long long x, y;
int l, r;
x = INF;
for (l = 0 + n_, r = i + n_; l <= r; l >>= 1, r >>= 1) {
if ((l & 1) == 1)
x = min(x, st1[l++]);
if ((r & 1) == 0)
x = min(x, st1[r--]);
}
y = INF;
for (l = i + n_, r = n_ - 1 + n_; l <= r; l >>= 1, r >>= 1) {
if ((l & 1) == 1)
y = min(y, st2[l++]);
if ((r & 1) == 0)
y = min(y, st2[r--]);
}
return min(x == INF ? INF : x + zz1[i], y == INF ? INF : y - zz1[i]);
}
long long dp[M];
long long solve_using_segtree(vi xx_, vi ll_, vi rr_, vi zz_) {
long long ans;
int n = xx_.size(), m = zz_.size(), h, i;
for (i = 0; i < n; i++)
xx[i] = xx_[i];
for (h = 0; h < m; h++) {
ll[h] = ll_[h], rr[h] = rr_[h], zz[h] = zz_[h];
hh[h] = h;
}
aa = zz, sort(hh, 0, m);
for (h = 0; h < m; h++)
idx[hh[h]] = h, zz1[h] = zz[hh[h]];
for (h = 0; h < m * 2; h++) {
xx1[h] = (h & 1) == 0 ? ll[h >> 1] << 1 | 0 : rr[h >> 1] << 1 | 1;
hh[h] = h;
}
aa = xx1, sort(hh, 0, m * 2);
n_ = 1;
while (n_ < m)
n_ <<= 1;
memset(st1, 0x3f, n_ * 2 * sizeof *st1), memset(st2, 0x3f, n_ * 2 * sizeof *st2);
ans = INF;
for (h = 0; h < m * 2; h++) {
int h_ = hh[h] >> 1;
if ((hh[h] & 1) == 0)
dp[h_] = xx1[hh[h]] == 0 ? zz[h_] : query(idx[h_]), update(idx[h_], dp[h_]);
else {
update(idx[h_], INF);
if (xx1[hh[h]] == (n - 1 << 1 | 1))
ans = min(ans, dp[h_] + zz[h_] + xx[n - 1] - xx[0]);
}
}
return ans == INF ? -1 : ans;
}
long long min_distance(vi xx_, vi yy_, vi ll_, vi rr_, vi zz_, int s, int t) {
int n = xx_.size();
return s == 0 && t == n - 1 ? solve_using_segtree(xx_, ll_, rr_, zz_) : solve_using_dijkstra(xx_, yy_, ll_, rr_, zz_, s, t);
}
