#pragma GCC optimize("Ofast,unroll-loops")
#include "wiring.h"
#include <bits/stdc++.h>
//#define int long long
#define ll long long
#define ull unsigned long long
#define down cout<<'\n';
#define debug cout<<" cucuucucuuu",down
#define modwwe int t;cin>>t; while(t--)
#define bit(i,j) (i>>j&1)
#define sobit(a) __builtin_popcountll(a)
#define task2 "top1apio"
#define task "test"
#define fin(x) freopen(x".inp","r",stdin)
#define fou(x) freopen(x".out","w",stdout)
#define pb push_back
#define mask(k) (1ll<<k)
#define checktime cerr << (double)clock() / CLOCKS_PER_SEC * 1000 << " ms";
using namespace std;
#define getchar_unlocked getchar
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
using i128 = __int128;
int rand(int l, int r)
{
return uniform_int_distribution<int>(l, r)(rd);
}
void phongbeo();
const ll inf = 1e17;
const int mod2 = 998244353;
//const ll base=67;
ll n, m, s1, s2, s4, s3, sf, k, s5, s6, s7, s8, s9, mx2, res, dem2 = 0, dem = 0, s33, dem3, dem4, mid, l2,
r2, center;
ll i, s10, s12, k1, k2, k3, s11, lim, w, l, r, dem5, dem6, dem7, dem9, root,q;
ll el = 19;
struct ib
{
int a,b;
};
vector<ib> v,vc;
ll dp[200007],pre[200007],suff[200007];
vector<ll> hihi[200007];
stack<int> vl;
bool cmp(ib a,ib b)
{
return a.a<b.a;
}
ll min_total_length(vector<int> A,vector<int> B)
{
for(auto x:A)v.pb({x,0});
for(auto x:B)v.pb({x,1});
n=v.size();
sort(v.begin(),v.end(),cmp);
s2=1;
vl.push(v[0].a);
dem=0;
for(int i=1; i<v.size(); i++)
{
if(v[i].b!=v[i-1].b)
{
while(!vl.empty())hihi[dem].pb(vl.top()),vl.pop();
reverse(hihi[dem].begin(),hihi[dem].end());
dem++;
vc.pb({s2,v[i-1].b});
s2=0;
}
vl.push(v[i].a);
s2++;
}
vc.pb({s2,v.back().b});
while(!vl.empty())hihi[dem].pb(vl.top()),vl.pop();
reverse(hihi[dem].begin(),hihi[dem].end());
///x con
///y con
/**
case1: x<=y
{
cost(y)-cost(x)-last(x)*(y-x)
=>cost(y)-last(x)*y-(cost(x)-lats(x)*x)
}
case2: x>y
{
cost(y)-cost(x)+begin(y)*(x-y)
=>(cost(y)-begin(y)*y)-(cost(x)-begin(y)*x)
}
*/
for(int i=0; i<=n; i++)
dp[i]=inf;
dp[0]=0;
for(int i=1; i<=dem; i++)
{
s2=0;
int sz=hihi[i-1].size();
for(int j=0; j<=hihi[i].size(); j++)
pre[j]=-inf,suff[j]=-inf;
for(int j=hihi[i-1].size()-1; j>=0; --j)
{
pre[sz-(j+1)]=s2-hihi[i-1].back()*(sz-(j+1))-dp[j+1];
suff[sz-(j+1)]=s2-hihi[i][0]*(sz-(j+1))-dp[j+1];
s2+=hihi[i-1][j];
}
suff[sz]=s2-hihi[i][0]*sz-dp[0];
pre[sz]=s2-hihi[i-1].back()*sz-dp[0];
for(int j=1; j<=hihi[i].size(); j++)
pre[j]=max(pre[j],pre[j-1]);
for(int j=hihi[i-1].size()-1; j>=1; --j)
suff[j]=max(suff[j],suff[j+1]);
s2=0;
dp[0]=dp[sz];
for(int j=0; j<hihi[i].size(); j++)
{
s2=s2+hihi[i][j];
dp[j+1]=s2-hihi[i-1].back()*(j+1)-pre[j+1];
if(j+1<=hihi[i-1].size())
dp[j+1]=min(dp[j+1],s2-hihi[i][0]*(j+1)-suff[j+1]);
}
}
return dp[hihi[dem].size()];
}
