#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #define all(x) (x).begin(),(x).end() #pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } typedef long long ll; const int inf = INT_MAX / 2; const ll infl = 1LL << 60; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b struct SegTree { //[l,r) V comp(V& l, V& r) { return min(l,r); }; vector val; SegTree() { val = vector(NV * 2, def); } V get(int x,int y,int l=0,int r=NV,int k=1){if(r<=x||y<=l)return def;if(x<=l&&r<=y)return val[k]; auto a=get(x,y,l,(l+r)/2,k*2);auto b=get(x,y,(l+r)/2,r,k*2+1);return comp(a,b);} void update(int i, V v) { i+=NV;val[i]=v;while(i>1)i>>=1,val[i]=comp(val[i*2],val[i*2+1]); } void add(int i, V v) { update(i, val[i + NV] + v); } V operator[](int x) { return get(x, x + 1); }}; /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ int N; ll A[301010], X[301010], Y[301010]; ll dp[301010]; SegTree st1, st2; vector dic; //--------------------------------------------------------------------------------------------------- void _main() { cin >> N; rep(i, 1, N + 1) cin >> A[i]; rep(i, 1, N + 1) cin >> X[i]; rep(i, 1, N + 1) cin >> Y[i]; rep(i, 0, N + 1) dp[i] = infl; dp[0] = 0; /* O(N^2) ver1 rep(i, 1, N + 1) { rep(j, 0, i) { ll dx = abs(A[i] - X[j + 1]); ll dy = Y[j + 1]; ll z = dp[j] + dx + dy; chmin(dp[i], z); } }*/ /* O(N^2) ver2 rep(i, 1, N + 1) { rep(j, 0, i) if (A[i] < X[j + 1]) chmin(dp[i], dp[j] + X[j + 1] - A[i] + Y[j + 1]); rep(j, 0, i) if (A[i] >= X[j + 1]) chmin(dp[i], dp[j] + A[i] - X[j + 1] + Y[j + 1]); }*/ rep(i, 1, N + 1) dic.push_back(A[i]); rep(i, 1, N + 1) dic.push_back(X[i]); sort(all(dic)); dic.erase(unique(all(dic)), dic.end()); rep(i, 1, N + 1) { int x = lower_bound(all(dic), X[i]) - dic.begin(); int a = lower_bound(all(dic), A[i]) - dic.begin(); st1.update(x, min(st1[x], dp[i - 1] + X[i] + Y[i])); st2.update(x, min(st2[x], dp[i - 1] - X[i] + Y[i])); chmin(dp[i], st1.get(a, 1 << 20) - A[i]); chmin(dp[i], st2.get(0, a) + A[i]); } cout << dp[N] << endl; }