package contest180615; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class E { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(); int[] a = na(n); int[] x = na(n); int[] y = na(n); for(int i = 0;i < n;i++){ y[i] = Math.abs(y[i]); } // dp[i] = dp[j] + d(j+1,i+1) // dp[i] = min(dp[j] + |a[i]-x[j+1]|+|y[j+1]|) long[] dp = new long[n+1]; Arrays.fill(dp, Long.MAX_VALUE); dp[0] = 0; EnvelopeManhattan el = new EnvelopeManhattan(n); for(int i = 0;i < n;i++){ el.add(x[i], y[i]+dp[i]); dp[i+1] = el.min(a[i]); } out.println(dp[n]); } public class EnvelopeManhattan { public static final long INF = Long.MIN_VALUE; public long[] xs; public long[] centers, heights; public int p; public EnvelopeManhattan(int n) { xs = new long[n]; centers = new long[n]; heights = new long[n]; p = 0; } public void clear() { p = 0; } public void add(long center, long height) { assert p == 0 || centers[p-1] <= center; if(p > 0 && heights[p-1] + (center - centers[p-1]) <= height)return; while(p > 0){ int i = p-1; if(p > 1 && height + (center - centers[p-1]) <= heights[p-1]){ p--; continue; } // (x-c[i])+h[i] = -(x-C)+H // 2x = H-h[i]+C+c[i] long nx = floor(height-heights[i]+center+centers[i]+1, 2); xs[p] = nx; heights[p] = height; centers[p] = center; p++; return; } xs[p] = INF; heights[p] = height; centers[p] = center; p++; } public long floor(long a, long b) { if(b < 0){ a = -a; b = -b; } return a >= 0 ? a/b : (a-b+1)/b; } public int argmin(int x) { if(p <= 0)return -1; int ind = Arrays.binarySearch(xs, 0, p, x); if(ind < 0)ind = -ind-2; return ind; } public long min(long x) { if(p <= 0)return Long.MIN_VALUE; int ind = Arrays.binarySearch(xs, 0, p, x); if(ind < 0)ind = -ind-2; return Math.abs(centers[ind]-x) + heights[ind]; } } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new E().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if(lenbuf == -1)throw new InputMismatchException(); if(ptrbuf >= lenbuf){ ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if(lenbuf <= 0)return -1; } return inbuf[ptrbuf++]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while(p < n && !(isSpaceChar(b))){ buf[p++] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for(int i = 0;i < n;i++)a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for(int i = 0;i < n;i++)a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for(int i = 0;i < n;i++)map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for(int i = 0;i < n;i++)map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if(b == '-'){ minus = true; b = readByte(); } while(true){ if(b >= '0' && b <= '9'){ num = num * 10 + (b - '0'); }else{ return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }