#include "bits/extc++.h"
using namespace std;
template <typename T, typename... U>
void dbgh(const T& t, const U&... u) {
cerr << t;
((cerr << " | " << u), ...);
cerr << endl;
}
#ifdef DEBUG
#define dbg(...) \
cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \
dbgh(__VA_ARGS__)
#else
#define dbg(...)
#define cerr \
if (false) \
cerr
#endif
using ll = long long;
#define endl "\n"
#define long int64_t
#define sz(x) int(std::size(x))
struct PSA {
vector<long> psum;
PSA(const vector<int>& arr) : psum(sz(arr) + 1) {
for (int i = 0; i < sz(arr); i++) {
psum[i + 1] = psum[i] + arr[i];
}
}
long query(int l, int r) const {
return psum[r] - psum[l];
}
};
ll min_total_length(vector<int> arr_r, vector<int> arr_b) {
vector<pair<int, bool>> arr;
for (auto& a : arr_r) {
arr.emplace_back(a, false);
}
for (auto& a : arr_b) {
arr.emplace_back(a, true);
}
sort(begin(arr), end(arr));
int n = sz(arr);
long dp[n + 1];
memset(dp, 0x3f, sizeof(dp));
dp[n] = 0;
deque<int> inds[2];
int psum_c[n + 1] {};
for (int i = 0; i < n; i++) {
psum_c[i + 1] = psum_c[i];
if (arr[i].second) {
psum_c[i + 1]++;
} else {
psum_c[i + 1]--;
}
}
int p_occ[n + 1][2];
p_occ[0][0] = p_occ[0][1] = -1;
for (int i = 0; i < n; i++) {
memcpy(p_occ[i + 1], p_occ[i], sizeof(p_occ[i]));
p_occ[i + 1][arr[i].second] = i;
}
PSA psa_w(({
vector<int> v;
for (auto& [t, ty] : arr) {
if (ty) {
v.push_back(t);
} else {
v.push_back(-t);
}
}
v;
}));
map<int, int> last_p;
long dp2[n];
auto upd_dp2 = [&](int j) -> void {
// for (; j < n; j++) {
// dp[i] = min(dp[i], wsum + min(dp[j], dp[j + 1]));
// if (j + 1 < n) {
// if (arr[j + 1].second != arr[j].second) {
// break;
// }
// wsum += arr[j + 1].first - last_m;
// }
// }
dp2[j] = min(dp[j], dp[j + 1]);
if (j + 1 < n) {
if (arr[j + 1].second != arr[j].second) {
return;
}
dp2[j] = min(dp2[j], arr[j + 1].first -
arr[p_occ[j][!arr[j].second]].first +
dp2[j + 1]);
}
};
for (int i = n - 1; i >= 0; i--) {
last_p[psum_c[i + 1]] = i;
if (i + 1 < n) {
inds[arr[i + 1].second].push_front(i + 1);
upd_dp2(i + 1);
}
auto [t, ty] = arr[i];
auto &me = inds[ty], &other = inds[!ty];
auto get_w = [&](int u, int v) -> long {
return abs(arr[u].first - arr[v].first);
};
auto get = [&](const deque<int>& arr, int ind) -> int {
if (ind >= sz(arr)) {
return n;
}
return arr[ind];
};
if (!sz(other)) {
continue;
}
if (get(other, 0) < get(me, 0)) {
long csum = 0;
for (int j = 0; j < sz(other) && get(other, j) < get(me, 0); j++) {
csum += get_w(i, other[j]);
dp[i] = min(dp[i], csum + min(dp[other[j]], dp[other[j] + 1]));
}
} else {
dp[i] = dp[i + 1] + get_w(i, other[0]);
{
int j, cnt = 0;
{
auto it = last_p.find(psum_c[i]);
if (it == last_p.end()) {
cnt = 1;
assert(cnt);
} else {
j = it->second;
}
}
if (!cnt) {
dp[i] = min(dp[i], abs(psa_w.query(i, j + 1)) + dp2[j]);
// for (; j < n; j++) {
// dp[i] = min(dp[i], wsum + min(dp[j], dp[j + 1]));
// if (j + 1 < n) {
// if (arr[j + 1].second != arr[j].second) {
// break;
// }
// wsum += arr[j + 1].first - last_m;
// }
// }
}
}
// long csum = 0;
// me.push_front(i);
// for (int j = 0; j < sz(other) && j < sz(me); j++) {
// long xsum = csum;
// for (int k = j; k < sz(other); k++) {
// xsum += get_w(me[j], other[k]);
// dp[i] =
// min(dp[i],
// xsum + dp[min(get(other, k + 1), get(me, j +
// 1))]);
// }
// csum += get_w(me[j], other[j]);
// }
// me.pop_front();
}
}
return dp[0];
}
