#pragma GCC optimize("O1") #pragma GCC optimize("O2") #pragma GCC optimize("O3") #include<bits/stdc++.h> // #include<atcoder/modint> // #include<atcoder/convolution> #define pb push_back #define eb emplace_back #define mp make_pair #define F first #define S second #define rs resize #define ft front() #define bk back() // #define int long long #define vi vector<int> #define vvi vector<vector<int>> #define pii pair<int, int> #define vpii vector<pair<int, int>> #define vc vector<char> #define vb vector<bool> #define mii map<int,int> #define f0r(i,n) for(int i=0;i<n;i++) #define FOR(i,k,n) for(int i=k;i<n;i++) #define r0f(i,n) for(int i = n-1; i >= 0; i--) #define R0F(i,k,n) for(int i = n-1; i >= k; i--) #define all(v) (v).begin(),(v).end() #define rall(v) (v).rbegin(),(v).rend() #define SUM(v) (accumulate(all(v), 0LL)) #define in(a) int a; cin>>a #define in2(a,b) int a,b; cin>>a>>b #define in3(a,b,c) int a,b,c; cin>>a>>b>>c #define in4(a,b,c,d) int a,b,c,d; cin>>a>>b>>c>>d #define vin(v,n); vi v(n); f0r(i,n){cin>>v[i];} #define out(a) cout<<a<<'\n' #define out2(a,b) cout<<a<<' '<<b<<'\n' #define out3(a,b,c) cout<<a<<' '<<b<<' '<<c<<'\n' #define out4(a,b,c,d) cout<<a<<' '<<b<<' '<<c<<' '<<d<<'\n' #define pout(a) cout<<a.first<<' '<<a.second<<'\n' #define vout(v) for(auto u : v){cout<<u<<' ';} cout<<endl #define dout(a) cout<<a<<' '<<#a<<endl #define dout2(a,b) cout<<a<<' '<<#a<<' '<<b<<' '<<#b<<endl #define YN(x); if(x){cout<<"YES"<<'\n';}else{cout<<"NO"<<'\n';} #define yn(x); if(x){cout<<"Yes"<<'\n';}else{cout<<"No"<<'\n';} #define p2(x) (1LL << (x)) #define pct(x) (__builtin_popcountll((x))) #define ist(x,y) (((x) >> (y)) & 1) template<class T, class U> bool ckmin(T& a, const U& b) { return (T)b < a ? a = (T)b, 1 : 0; } template<class T, class U> bool ckmax(T& a, const U& b) { return a < (T)b ? a = (T)b, 1 : 0; } const int leg = 1e9 + 7; const int mod = 998244353; using namespace std; // using namespace atcoder; // using mint = modint998244353; // using mint = modint1000000007; const int mxn = 3e5 + 5; // mint fact[mxn], inv[mxn]; // mint C(int n, int r){return fact[n] * inv[n-r] * inv[r];} // mint snb(int n, int r){return C(n + r, n);} int n; int ans = 2e9; //vi cf, fi, se, A, B; int cf[mxn], fi[mxn*2], se[mxn*2], A[mxn], B[mxn]; pii intersect(pii a, pii b){ // if(b.F > b.S || a.F > a.S)return {1,0}; if(a.F > b.F)swap(a,b); if(a.S < b.F)return {1,0}; if(a.S > b.S)return a; return {b.F, a.S}; return {max(a.F, b.F), min(a.S, b.S)}; } void prt(vi &v){ int cur = 0; f0r(i, v.size()){cur += v[i]; cout<<cur<<' '; }cout<<'\n'; } inline int get(int x, int t){ if(x < n){ if(t <= x)return A[max(x-t, fi[x])]; else return B[min(x+(n-t), se[x])]; } else{ if(t <= x - n)return B[min(2*n-1-x + t, fi[x])]; else return A[max(2*n-1-x - (n-t), se[x])]; } } void put(int l, int r){if(l <= r){cf[l]++; cf[r+1]--;}} void solve(vi v, vi a, vi b){ sort(all(a)); sort(all(b)); f0r(i,n)A[i]=a[i],B[i]=b[i];//A = a, B = b; f0r(i,2*n)fi[i]=se[i]=0; f0r(i,n){ int lo = n-1, hi = n*2-1; while(lo < hi){ int mid = lo + (hi - lo + 1) / 2; if(v[mid] >= v[i])lo=mid; else hi=mid-1; } fi[i] = max(0, i - (lo - (n-1))); lo = n, hi = n*2; while(lo < hi){ //first one less than v[i] int mid = lo + (hi - lo) / 2; if(v[mid] < v[i])hi = mid; else lo = mid + 1; } se[i] = min(i + (n*2-lo), n-1); } FOR(i,n,2*n){ int lo = -1, hi = n-1; while(lo < hi){ int mid = lo + (hi - lo + 1) / 2; if(v[mid] <= v[i])lo=mid; else hi=mid-1; } fi[i] = min(2*n-1-i + lo + 1, n-1); lo = 0, hi = n; while(lo < hi){ int mid = lo + (hi - lo) / 2; if(v[mid] > v[i])hi=mid; else lo=mid+1; } se[i] = max(0, 2*n-1-i-(n-lo)); } //vout(fi); // dout(get(0,1)); // f0r(t,n+1){ // f0r(i,2*n)cout<<get(i,t)<<' '; cout<<'\n'; // } int tm = 0; f0r(i,n)ckmax(tm, abs(a[i]-v[i])); FOR(i,n,2*n)ckmax(tm,abs(b[2*n-1-i]-v[i])); int lo = 0, hi = tm; while(lo < hi){ int k = lo + (hi - lo) / 2; f0r(i,n+2)cf[i]=0; bool ok = 1; f0r(i,2*n){ int sp; if(i < n)sp = i; else sp = i-n; if(i < n){ int l = 0, r = sp+1; while(l < r){ int mid = l + (r - l) / 2; if(get(i,mid) - v[i] <= k)r=mid; else l=mid+1; } int L = l; l = -1, r = sp; while(l < r){ int mid = l + (r - l + 1) / 2; if(get(i,mid) - v[i] >= -k)l=mid; else r=mid-1; } int R = l; put(L, R); l = sp+1, r = n+1; while(l < r){ int mid = l + (r - l) / 2; if(get(i,mid) - v[i] <= k)r=mid; else l=mid+1; } L = l; l = sp, r = n; while(l < r){ int mid = l + (r - l + 1) / 2; if(get(i,mid) - v[i] >= -k)l=mid; else r=mid-1; } R = l; put(L, R); } else{ int l = 0, r = sp+1; while(l < r){ int mid = l + (r - l) / 2; if(get(i,mid) - v[i] >= -k)r=mid; else l=mid+1; } int L = l; l = -1, r = sp; while(l < r){ int mid = l + (r - l + 1) / 2; if(get(i,mid) - v[i] <= k)l=mid; else r=mid-1; } int R = l; put(L, R); l = sp+1, r = n+1; while(l < r){ int mid = l + (r - l) / 2; if(get(i,mid) - v[i] >= -k)r=mid; else l=mid+1; } L = l; l = sp, r = n; while(l < r){ int mid = l + (r - l + 1) / 2; if(get(i,mid) - v[i] <= k)l=mid; else r=mid-1; } R = l; put(L, R); } // if(k==4)prt(cf); } /* f0r(i,n){ int l = 0, r = n-i; while(l < r){ int mid = l + (r-l) / 2; if(a[i] - v[i+mid] <= k)r = mid; else l = mid + 1; } int L = l; l = -1, r = n-i-1; while(l < r){ int mid = l + (r-l+1) / 2; if(a[i] - v[i+mid] >= -k)l = mid; else r = mid - 1; } int R = l; // if(k==7)dout2(L,R); if(abs(v[n+n-1-i] - a[i]) <= k){ //[L, R] [n-i, n] if(L>R)cf[n-i]++, cf[n+1]--; else cf[L]++, cf[R+1]--, cf[n-i]++, cf[n+1]--; //if(k==1){dout2(L, n);} // if(L == n-i || R == -1)can = intersect(can, mp(n-i, n)); // else can = intersect(can, mp(L, n));//if(k==1){dout2(L, n);} } else{ if(L <= R)cf[L]++, cf[R+1]--; else ok = 0; // if(L <= R)can = intersect(can, mp(L, R)); else can = {1,0}; //if(k==1){dout2(L, R);} } if(k==7){prt(cf);} } f0r(i,n){ int l = 0, r = i+1; while(l < r){ int mid = l + (r-l) / 2; if(b[i] - v[2*n-1-(i-mid)] >= -k)r = mid; else l = mid + 1; } int L = l; l = -1, r = i; while(l < r){ int mid = l + (r-l+1) / 2; if(b[i] - v[2*n-1-(i-mid)] <= k)l = mid; else r = mid - 1; } int R = l; if(abs(v[i] - b[i]) <= k){ //[L,R] [i+1,n] if(L>R)cf[i+1]++, cf[n+1]--; else cf[L]++, cf[R+1]--, cf[i+1]++, cf[n+1]--; // if(L == i+1 || R == -1)can = intersect(can, mp(i+1, n)); // else can = intersect(can, mp(L, n));//if(k==1){dout2(L, n);} } else{ if(L <= R)cf[L]++, cf[R+1]--; else ok = 0;//if(k==1){dout2(L, R);} } if(k==7){prt(cf);} } */ // if(k==2)out3(k, can.F, can.S); // if(k==3)dout(ok); int cur = 0; bool bb = 0; f0r(i,n+2){ cur += cf[i]; if(cur == (n<<1))bb = 1; } if(!bb)ok=0; if(ok)hi = k; else lo = k + 1; } ckmin(ans, lo); /* f0r(i,n+1){ vi t1, t2; f0r(j,i)t1.pb(v[j]); FOR(j,i,i+n)t2.pb(v[j]); FOR(j,i+n,2*n)t1.pb(v[j]); sort(all(t1)); sort(all(t2)); int cur = 0; f0r(j, n)ckmax(cur,abs(t1[j] - a[j])), ckmax(cur,abs(t2[j] - b[j])); ckmin(ans, cur); } */ } signed main(){ ios::sync_with_stdio(false); cin.tie(NULL); //ifstream cin(".in"); //ofstream cout(".out"); // fact[0]=1;FOR(i,1,mxn)fact[i]=fact[i-1]*i;inv[mxn-1]=fact[mxn-1].inv();r0f(i,mxn-1)inv[i]=inv[i+1]*(i+1); // in(t); while(t--){ cin>>n; ans = 2e9; vin(v,2*n); vin(a,n); vin(b,n); solve(v,a,b); solve(v,b,a); out(ans); // } }