#include <bits/stdc++.h>
using namespace std;
#define pb push_back
typedef vector<int> vi;
typedef long long ll;
struct SegmentTree {
vi a, t;
SegmentTree(int n, const vi& a) {
this->a = a;
t = vi(4*n);
build(1, 0, n-1);
}
void build(int v, int tl, int tr) {
if (tl == tr) {
t[v] = a[tl];
} else {
int tm = (tl+tr)/2;
build(2*v, tl, tm);
build(2*v+1, tm+1, tr);
t[v] = 0;
}
}
int get(int v, int tl, int tr, int pos) {
if (tl == tr) return t[v];
else {
int tm = (tl+tr)/2;
if (pos <= tm)
return t[v] + get(2*v, tl, tm, pos);
else
return t[v] + get(2*v+1, tm+1, tr, pos);
}
}
void update(int v, int tl, int tr, int l, int r, int add) {
if (l > r) return;
else if (l == tl && r == tr) t[v] += add;
else {
int tm = (tl+tr)/2;
update(2*v, tl, tm, l, min(r, tm), add);
update(2*v+1, tm+1, tr, max(tm+1, l), r, add);
}
}
};
// pair<int, vi> toLeft(int n, vi S, vi especial) {
// ll res1 = 0;
// vi pos(n);
// vi mapper(n+1, -1);
// for (int i = 0; i < n; i++) {
// int v = abs(S[i]);
// if (mapper[v] != -1) {
// pos[i] = mapper[v];
// pos[mapper[v]] = i;
// } else {
// mapper[v] = i;
// }
// }
// vi dist(n);
// for (int i = 0; i < n; i++) {
// dist[i] = abs(pos[i]-i) - (!especial[i]);
// }
// SegmentTree tree(n, dist);
// vi nxt(n, -1), prev(n, -1);
// for (int i = 0; i < n; i++) {
// if (i > 0) prev[i] = i-1;
// if (i < n-1) nxt[i] = i+1;
// }
// for (int i = 0; i < 5; i++) {
// if (pos[i] < i || S[i] > 0 || tree.get(1, 0, n-1, pos[i]) <= 0) continue;
// res1 += tree.get(1, 0, n-1, pos[i]);
// tree.update(1, 0, n-1, pos[i]+1, n-1, -1);
// if (nxt[i] == pos[i]) continue;
// int tmp = nxt[i];
// if (nxt[i] != -1) prev[nxt[i]] = pos[i];
// nxt[i] = pos[i];
// if (nxt[pos[i]] != -1) prev[nxt[pos[i]]] = prev[pos[i]];
// if (prev[pos[i]] != -1) nxt[prev[pos[i]]] = nxt[pos[i]];
// nxt[pos[i]] = tmp;
// prev[pos[i]] = i;
// }
// int zero = 0;
// for (int i = 0; i < n; i++) {
// if (prev[i] == -1) zero = i;
// }
// int idx = 0;
// vi newS(n);
// // cout << res1 << endl;
// for (int i = zero; ; i = nxt[i]) {
// newS[idx] = S[i];
// idx++;
// if (nxt[i] == -1) break;
// }
// S = newS;
// return {max(0LL, res1), newS};
// }
pair<int, vi> toLeft(int n, vi S, vi especial) {
ll res1 = 0;
vi pos(n);
vi mapper(n+1, -1);
for (int i = 0; i < n; i++) {
int v = abs(S[i]);
if (mapper[v] != -1) {
pos[i] = mapper[v];
pos[mapper[v]] = i;
} else {
mapper[v] = i;
}
}
vi dist(n);
for (int i = 0; i < n; i++) {
dist[i] = abs(i-pos[i])-(!especial[i]);
}
SegmentTree tree1(n, dist), tree2(n, dist);
vi nxt(n, -1), prev(n, -1);
for (int i = 0; i < n; i++) {
if (i > 0) prev[i] = i-1;
if (i < n-1) nxt[i] = i+1;
}
for (int i = 0; i < n; i++) {
int d = (tree1.get(1, 0, n-1, i)+tree2.get(1, 0, n-1, pos[i]))-dist[i];
if (pos[i] < i || S[i] > 0 || d <= 0) continue;
res1 += d;
tree1.update(1, 0, n-1, i+1, pos[i]-1, -1);
tree2.update(1, 0, n-1, i+1, pos[i]-1, +1);
if (nxt[i] == pos[i]) continue;
int tmp = nxt[i];
if (nxt[i] != -1) prev[nxt[i]] = pos[i];
nxt[i] = pos[i];
if (nxt[pos[i]] != -1) prev[nxt[pos[i]]] = prev[pos[i]];
if (prev[pos[i]] != -1) nxt[prev[pos[i]]] = nxt[pos[i]];
nxt[pos[i]] = tmp;
prev[pos[i]] = i;
}
int zero = 0;
for (int i = 0; i < n; i++) {
if (prev[i] == -1) zero = i;
}
int idx = 0;
vi newS(n);
for (int i = zero; ; i = nxt[i]) {
newS[idx] = S[i];
idx++;
if (nxt[i] == -1) break;
}
return {max(0LL, res1), newS};
}
pair<int, vi> toRight(int n, vi S, vi especial) {
ll res1 = 0;
vi pos(n);
vi mapper(n+1, -1);
for (int i = 0; i < n; i++) {
int v = abs(S[i]);
if (mapper[v] != -1) {
pos[i] = mapper[v];
pos[mapper[v]] = i;
} else {
mapper[v] = i;
}
}
vi dist(n);
for (int i = 0; i < n; i++) {
dist[i] = abs(i-pos[i])-(!especial[i]);
}
SegmentTree tree1(n, dist), tree2(n, dist);
vi nxt(n, -1), prev(n, -1);
for (int i = 0; i < n; i++) {
if (i > 0) prev[i] = i-1;
if (i < n-1) nxt[i] = i+1;
}
for (int i = n-1; i >= 0; i--) {
int d = (tree1.get(1, 0, n-1, i)+tree2.get(1, 0, n-1, pos[i]))-dist[i];
if (pos[i] > i || S[i] > 0 || d <= 0) continue;
res1 += d;
tree1.update(1, 0, n-1, pos[i]+1, i-1, -1);
tree2.update(1, 0, n-1, pos[i]+1, i-1, +1);
if (nxt[i] == pos[i]) continue;
int tmp = nxt[i];
if (nxt[i] != -1) prev[nxt[i]] = pos[i];
nxt[i] = pos[i];
if (nxt[pos[i]] != -1) prev[nxt[pos[i]]] = prev[pos[i]];
if (prev[pos[i]] != -1) nxt[prev[pos[i]]] = nxt[pos[i]];
nxt[pos[i]] = tmp;
prev[pos[i]] = i;
}
int zero = 0;
for (int i = 0; i < n; i++) {
if (prev[i] == -1) zero = i;
}
int idx = 0;
vi newS(n);
for (int i = zero; ; i = nxt[i]) {
newS[idx] = S[i];
idx++;
if (nxt[i] == -1) break;
}
return {max(0LL, res1), newS};
}
ll count_swaps(vi S) {
int n = S.size();
vector<pair<vi, vi>> mapper(n+1, pair<vi, vi>());
for (int i = 0; i < n; i++) {
int v = abs(S[i]);
if (S[i] < 0) {
mapper[v].first.pb(i);
} else
mapper[v].second.pb(i);
}
int idx = 1;
vi pos(n), especial(n);
for (int i = 1; i <= n; i++) {
for (int j = 0; j < mapper[i].first.size(); j++) {
S[mapper[i].first[j]] = -idx;
S[mapper[i].second[j]] = idx;
if (mapper[i].first[j] > mapper[i].second[j]) {
especial[mapper[i].first[j]] = especial[mapper[i].second[j]] = true;
S[mapper[i].first[j]] = -S[mapper[i].first[j]];
S[mapper[i].second[j]] = -S[mapper[i].second[j]];
}
pos[mapper[i].first[j]] = mapper[i].second[j];
pos[mapper[i].second[j]] = mapper[i].first[j];
idx++;
}
}
// for (int i = 0; i < n; i++) cout << S[i] << " ";
// cout << endl;
ll res1 = 0, res2 = 0;
// All to left
pair<int, vi> tmp = toLeft(n, S, especial);
res1 = tmp.first;
for (int i = 0;i < n; i++) S[i] = -S[i];
// All to right
tmp = toRight(n, S, especial);
res2 = tmp.first;
return min(res1, res2);
}
