#include "wiring.h"
#include <bits/stdc++.h>
using ll = long long;
using namespace std;
#define all(x) begin(x), end(x)
struct SegTree {
using T = ll;
T f(T a, T b) { return min(a, b); }
static constexpr T UNIT = LLONG_MAX;//neutral value for f
vector<T> s; ll n;
SegTree(ll len) : s(2 * len, UNIT), n(len) {}
void set(ll pos, T val) {
for (s[pos += n] = val; pos /= 2;)
s[pos] = f(s[pos * 2], s[pos * 2 + 1]);
}
T query(ll lo, ll hi) { // hi not included
T ra = UNIT, rb = UNIT;
for (lo+=n, hi+=n; lo < hi; lo/=2, hi/=2) {
if (lo % 2) ra = f(ra, s[lo++]);
if (hi % 2) rb = f(s[--hi], rb);
}
return f(ra, rb);
}
};
long long min_total_length(std::vector<int> r, std::vector<int> b) {
vector<pair<ll, ll>> pts;
for (int x : r)
pts.emplace_back(x, 1);
for (int x : b)
pts.emplace_back(x, 0);
sort(all(pts));
vector<ll> nextDiffColorUp(pts.size());
nextDiffColorUp.back() = -1;
for (ll i = (ll)pts.size() - 2; i >= 0; i--) {
if (pts[i].second != pts[i + 1].second) {
nextDiffColorUp[i] = i + 1;
} else {
nextDiffColorUp[i] = nextDiffColorUp[i + 1];
}
}
vector<ll> nextDiffColorDown(pts.size());
nextDiffColorDown[0] = -1;
for (ll i = 1; i < (ll)pts.size(); i++) {
if (pts[i].second != pts[i - 1].second) {
nextDiffColorDown[i] = i - 1;
} else {
nextDiffColorDown[i] = nextDiffColorDown[i - 1];
}
}
vector<ll> sumDown(pts.size(), 0);
for (ll i = 1; i < (ll)pts.size(); i++) {
if (pts[i].second != pts[i - 1].second) {
sumDown[i] = 0;
} else if (nextDiffColorDown[i] == -1) {
sumDown[i] = 1E9;
} else {
ll dest = nextDiffColorDown[i] + 1;
sumDown[i] = sumDown[i - 1] + (pts[i].first - pts[dest].first);
}
}
vector<ll> sumUp(pts.size(), 0);
for (ll i = (ll)pts.size() - 2; i >= 0; i--) {
if (pts[i].second != pts[i + 1].second) {
sumUp[i] = pts[i + 1].first - pts[i].first;
} else if (nextDiffColorUp[i] == -1) {
sumUp[i] = 1E9;
} else {
ll dest = nextDiffColorUp[i];
sumUp[i] = sumUp[i + 1] + (pts[dest].first - pts[i].first);
}
}
SegTree st(pts.size() + 1); // st[j] = dp[j] + sumDown[j - 1]
st.set(pts.size(), 0 + sumDown[pts.size() - 1]);
vector<ll> dp(pts.size() + 1, 0);
for (ll i = (ll)pts.size() - 1; i >= 0; i--) {
ll ans = LLONG_MAX;
if (nextDiffColorDown[i] != -1) {
ans = dp[i + 1] + (pts[i].first - pts[nextDiffColorDown[i]].first);
}
if (nextDiffColorUp[i] != -1) {
ll nextSegmentEndPlus1 = nextDiffColorUp[nextDiffColorUp[i]];
if (nextSegmentEndPlus1 == -1)
nextSegmentEndPlus1 = pts.size();
ll lenNextSegment = nextSegmentEndPlus1 - nextDiffColorUp[i];
ll maxL = min(
nextDiffColorUp[i] - i, // how many remaining in this segment
lenNextSegment
);
//for (ll L = 1; L <= maxL; L++) {
// ans = min(ans, dp[nextDiffColorUp[i] + L] + sumUp[i] + sumDown[nextDiffColorUp[i] + L - 1]);
//}
ll rangeAns = st.query(nextDiffColorUp[i] + 1, nextDiffColorUp[i] + maxL + 1);
//for (ll j = nextDiffColorUp[i] + 1; j <= nextDiffColorUp[i] + maxL; j++) {
// rangeAns = min(rangeAns, dp[j] + sumDown[j - 1]);
//}
if (rangeAns != LLONG_MAX)
ans = min(rangeAns + sumUp[i], ans);
}
dp[i] = ans;
if (i != 0)
st.set(i, dp[i] + sumDown[i - 1]);
}
return dp[0];
}
