package adv2019; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayDeque; import java.util.ArrayList; import java.util.Arrays; import java.util.Deque; import java.util.InputMismatchException; import java.util.List; import java.util.Queue; public class D20_4 { InputStream is; PrintWriter out; String INPUT = ""; void solve() { int n = ni(), m = ni(); int[][] g = new int[n][m]; for(int i = 0;i < n;i++) { g[i] = na(m); } int[] R = na(n); int[] C = na(m); List es = new ArrayList<>(); int src = n*m+n+m, sink = src + 1; for(int i = 0;i < n;i++) { for(int j = 0;j < m;j++) { // es.add(new Edge(src, i*m+j, 0L)); es.add(new Edge(i*m+j, sink, g[i][j])); } } for(int i = 0;i < n;i++) { es.add(new Edge(src, n*m+i, R[i])); // es.add(new Edge(n*m+i, sink, 0)); for(int j = 0;j < m;j++) { es.add(new Edge(n*m+i, i*m+j, R[i])); } } for(int i = 0;i < m;i++) { es.add(new Edge(src, n*m+n+i, C[i])); // es.add(new Edge(n*m+n+i, sink, 0)); for(int j = 0;j < n;j++) { es.add(new Edge(n*m+n+i, j*m+i, C[i])); } } for(Edge e : es) { e.flow = e.capacity; } long ans = 0; for(int v : R)ans += v; for(int v : C)ans += v; // ans -= maximumFlowDinicNoRec(compileWD(sink+1, es), src, sink); Edge[][] G = compileWD(sink+1, es); D20_4.g = G; initialize(N = sink+1); ans -= pushRelabel(src, sink, n*m+n+m); out.println(ans); } public static class Edge { public int from, to; public long capacity; public long flow; public Edge complement; public boolean cloned; public Edge(int from, int to, long capacity) { this.from = from; this.to = to; this.capacity = capacity; } } public static void reset(Edge[][] g) { for(Edge[] row : g){ for(Edge e : row){ e.flow = e.cloned ? e.capacity : 0; } } } public static Edge[][] compileWD(int n, List edges) { Edge[][] g = new Edge[n][]; // cloning for(int i = edges.size()-1;i >= 0;i--){ Edge origin = edges.get(i); Edge clone = new Edge(origin.to, origin.from, origin.capacity); clone.flow = 0;//origin.capacity; clone.complement = origin; clone.cloned = true; origin.complement = clone; edges.add(clone); } int[] p = new int[n]; for(Edge e : edges)p[e.from]++; for(int i = 0;i < n;i++)g[i] = new Edge[p[i]]; for(Edge e : edges)g[e.from][--p[e.from]] = e; return g; } static long INF = Long.MAX_VALUE / 100; static int SRC, SINK; static long[] excess; public static long pushRelabel(int source, int sink, int heuristicN) { SRC = source; SINK = sink; N = g.length; excess = new long[N]; excess[source] = INF; excess[sink] = -INF; globalRelabel(); for(Edge e : g[source]) { push(e); } for(;highest >= 0;highest--) { while(!list.get(highest).isEmpty()) { int v = list.get(highest).pollLast(); discharge(v); if(work > 4 * heuristicN) { globalRelabel(); } } } return excess[sink] + INF; } static void discharge(int v) { int nh = N; for(Edge e : g[v]) { if(e.flow > 0) { if(height[v] == height[e.to] + 1) { push(e); if(excess[v] <= 0)return; }else { nh = Math.min(nh, height[e.to] + 1); } } } if(count[height[v]] > 1) { updateHeight(v, nh); }else { for(int i = height[v];i <= highest;i++) { for(int j : gap.get(i)) { updateHeight(j, N); } gap.get(i).clear(); } } } static void push(Edge e) { if(excess[e.to] == 0) { list.get(height[e.to]).add(e.to); } long df = Math.min(excess[e.from], e.flow); e.flow -= df; e.complement.flow += df; excess[e.from] -= df; excess[e.to] += df; } static int N; static int work; static int[] height; static int[] count; static int highest; static Edge[][] g; static List> list; static List> gap; static void initialize(int N) { height = new int[N]; count = new int[N]; list = new ArrayList<>(); gap = new ArrayList<>(); for(int i = 0;i < N+1;i++) { list.add(new ArrayDeque()); gap.add(new ArrayDeque()); } } static void globalRelabel() { work = 0; Arrays.fill(height, N); Arrays.fill(count, 0); for(int i = 0;i < highest;i++) { list.get(i).clear(); gap.get(i).clear(); } height[SINK] = 0; Queue q = new ArrayDeque<>(); q.add(SINK); while(!q.isEmpty()) { int v = q.poll(); for(Edge e : g[v]) { if(height[e.to] == N && e.complement.flow > 0) { q.add(e.to); updateHeight(e.to, height[v] + 1); } } // tr(v, height[v], height); highest = height[v]; } } static void updateHeight(int v, int nh) { work++; if(height[v] != N) { count[height[v]]--; } height[v] = nh; if(nh == N)return; count[nh]++; highest = nh; gap.get(nh).add(v); if(excess[v] > 0) { list.get(nh).add(v); } } void run() throws Exception { // int n = 100, m = 100; // Random gen = new Random(1114); // StringBuilder sb = new StringBuilder(); // sb.append(n + " "); // sb.append(m + " "); // for (int i = 0; i < n*m+n+m; i++) { // if(i < n*m) { // sb.append(gen.nextInt(5000000) + " "); // }else { // sb.append(gen.nextInt(1000000000) + " "); // } // } // INPUT = sb.toString(); 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 D20_4().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)); } }