import java.io.File; import java.io.FileNotFoundException; 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.Collections; import java.util.HashMap; import java.util.NoSuchElementException; import java.util.Random; public class Main { public static void main(String[] args) throws FileNotFoundException { new Main().run(); } int[] range = new int[10000010]; static final long INF = (long) 1e18; long hamsolver(int n, int m, int[] x, int[] d, int[][] y) { HashMap> memo = new HashMap<>(); long leftest_letter = INF, rightest_letter = -INF; long leftest_house = INF, rightest_house = -INF; for (int i = 0; i < m; ++i) { rightest_letter = Math.max(rightest_letter, x[i]); leftest_letter = Math.min(leftest_letter, x[i]); for (int j = 0; j < d[i]; ++j) { rightest_house = Math.max(rightest_house, y[i][j]); leftest_house = Math.min(leftest_house, y[i][j]); if (memo.containsKey(y[i][j])) { memo.get(y[i][j]).add(x[i]); } else { memo.put(y[i][j], new ArrayList<>()); memo.get(y[i][j]).add(x[i]); } } } for (ArrayList list : memo.values()) { Collections.sort(list); } long ret = INF; for (int dummy = 0; dummy < 2; ++dummy) { for (int i = 0; i < 10000010; ++i) range[i] = 0; for (int px : memo.keySet()) { if (dummy == 0) { // 右から左に全部の手紙を拾う if (px - memo.get(px).get(0) <= 0) continue; range[memo.get(px).get(0)]++; range[px]--; } else { // 左から右に全部の手紙を拾う if (memo.get(px).get(memo.get(px).size() - 1) - px <= 0) continue; range[px]++; range[memo.get(px).get(0)]--; } } long minsum = 0; for (int i = 0; i < 10000010 - 1; ++i) { range[i + 1] += range[i]; if (range[i + 1] != 0) minsum++; } // rep(i, 100) { cout << range[i] << " "; } cout << endl; if (dummy == 0) { ret = Math.min(ret, minsum * 2L + rightest_letter - leftest_house); } else { ret = Math.min(ret, minsum * 2L + rightest_house - leftest_letter); } } return ret; } class BruteForce { int[] l, r; public BruteForce(int[] l_, int[] r_) { l = l_; r = r_; } int calc() { ArrayDeque que = new ArrayDeque<>(); for (int i = 0; i < MAX; ++i) { que.add(new State(i, l, r)); } while (!que.isEmpty()) { State s = que.poll(); if (s.cnt > MAX * 2) { continue; } if (s.ok()) { return s.cnt; } for (int dx = -1; dx <= 1; dx += 2) { if (0 <= s.cur + dx && s.cur + dx < MAX) { que.addLast(s.move(s.cur + dx)); } } } throw new AssertionError(); } class State { int cur; boolean[] vis; int[] l; int[] r; int cnt = 0; public State(int cur_, int[] l_, int[] r_) { cur = cur_; l = Arrays.copyOf(l_, l_.length); r = Arrays.copyOf(r_, r_.length); vis = new boolean[MAX]; vis[cur] = true; if (l[cur] == cur) { l[cur] = -1; } if (r[cur] == cur) { r[cur] = -1; } } State move(int dst) { State ret = new State(cur, l, r); ret.vis = Arrays.copyOf(vis, vis.length); ret.cur = dst; ret.vis[ret.cur] = true; ret.cnt = cnt; ret.l = Arrays.copyOf(l, l.length); ret.r = Arrays.copyOf(r, r.length); for (int i = 0; i < MAX; ++i) { if (ret.vis[i] && ret.l[i] == dst) { ret.l[i] = -1; } if (ret.vis[i] && ret.r[i] == dst) { ret.r[i] = -1; } } ret.cnt++; return ret; } boolean ok() { for (int i = 0; i < MAX; ++i) { if (!(r[i] == -1 && l[i] == -1)) return false; } return true; } } } int MAX = 0; int solve(int[] l, int[] r) { int rEdge1 = Integer.MAX_VALUE / 10; int rEdge2 = -Integer.MAX_VALUE / 10; int lEdge1 = Integer.MAX_VALUE / 10; int lEdge2 = -Integer.MAX_VALUE / 10; for (int i = 0; i < MAX; ++i) { if (r[i] != -1) { rEdge1 = i; break; } } for (int i = MAX - 1; i >= 0; --i) { if (r[i] != -1) { rEdge2 = r[i]; break; } } for (int i = MAX - 1; i >= 0; --i) { if (l[i] != -1) { lEdge2 = i; break; } } for (int i = 0; i < MAX; ++i) { if (l[i] != -1) { lEdge1 = l[i]; break; } } for (int i = Math.min(lEdge1, rEdge1) + 1; i < Math.max(lEdge2, rEdge2); ++i) { if (l[i] == i) { l[i] = -1; } if (r[i] == i) { r[i] = -1; } } int[] from = new int[MAX]; Arrays.fill(from, -1); for (int i = 0; i < l.length; ++i) { if (l[i] != -1) { from[l[i]] = i; } } int[] middle = new int[MAX]; for (int i = MAX - 1; i >= 0; --i) { if (l[i] != i && l[i] != -1) { ++middle[i - 1]; if (l[i] > 0) { --middle[l[i] - 1]; } } if (i + 1 < MAX) { middle[i] = middle[i + 1] + middle[i]; } } int[][] s = new int[2][MAX]; for (int i = 0; i < s.length; ++i) { for (int j = 0; j < s[i].length; ++j) { s[i][j] = Integer.MAX_VALUE / 10; } } { for (int i = Math.min(rEdge1, lEdge1); i <= Math.max(rEdge2, lEdge2); ++i) { if (rEdge1 <= i && i < lEdge1) { s[0][i] = i - rEdge1; } if (i < lEdge1 || (l[i] != -1 && middle[i] == 0)) { s[0][i] = Math.min(s[0][i], 2 * Math.abs(i - Math.min(lEdge1, rEdge1))); } if (l[i] == i || (middle[i] == 0 && l[i] == -1 && from[i] == -1)) { if (i == 0) { s[1][i] = 0; s[0][i] = 0; } else { s[1][i] = Math.min(s[1][i], Math.min(s[1][i - 1] + 3, s[0][i - 1] + 1)); s[0][i] = Math.min(s[0][i], Math.min(s[1][i - 1] + 3, s[0][i - 1] + 1)); } } else if (from[i] != -1 && i != 0) { s[1][i] = Math.min(s[1][i], Math.min(s[0][i - 1] + 1, s[1][i - 1] + 3)); } else if (l[i] != -1) { if (i == 0) { throw new AssertionError(); } s[1][i] = Math.min(s[1][i], s[1][i - 1] + 3); s[0][i] = Math.min(s[0][i], s[1][i - 1] + 3); } else if ((middle[i] > 0 || from[i] != -1 || l[i] != -1) && i != 0) { s[1][i] = Math.min(s[1][i], s[1][i - 1] + 3); } else { } } } int ans = 2 * (Math.max(lEdge2, rEdge2) - Math.min(lEdge1, rEdge1)); for (int i = 0; i < MAX; ++i) { ans = Math.min(ans, s[0][i] + 2 * Math.abs(i - Math.max(lEdge2, rEdge2)) - (i == Math.max(lEdge2, rEdge2) ? 0 : 1)); } return ans; } void random() { Random rand = new Random(); int MAX_ = rand.nextInt(10) + 1; int m = rand.nextInt(MAX_) + 1; int[] x = new int[m]; int[] d = new int[m]; int[][] y = new int[m][]; for (int i = 0; i < m; ++i) { x[i] = rand.nextInt(MAX_); d[i] = rand.nextInt(5); y[i] = new int[d[i]]; for (int j = 0; j < d[i]; ++j) { y[i][j] = rand.nextInt(MAX_); } } tr("Comparison", hamsolver(MAX_, m, x, d, y), new BruteForce(lr(MAX_, m, x, d, y)[0], lr(MAX_, m, x, d, y)[1]).calc()); // if (solver(MAX_, m, x, d, y) != new BruteForce(lr(MAX_, m, x, d, // y)[0], lr(MAX_, m, x, d, y)[1]).calc()) { if (hamsolver(MAX_, m, x, d, y) != new BruteForce(lr(MAX_, m, x, d, y)[0], lr(MAX_, m, x, d, y)[1]).calc()) { File file = new File(""); PrintWriter pw; try { pw = new PrintWriter(file); pw.println(MAX_ + " " + m); for (int i = 0; i < m; ++i) { pw.println(x[i] + " " + d[i]); for (int j = 0; j < d[i]; ++j) { pw.print(y[i][j] + (j == d[i] - 1 ? "\n" : " ")); } } pw.close(); } catch (FileNotFoundException e) { // TODO Auto-generated catch block e.printStackTrace(); } System.out.println(solver(MAX_, m, x, d, y)); System.exit(0); } } void run() { Scanner sc = new Scanner(); int MAX_ = sc.nextInt(); if (!(1 <= MAX_ && MAX_ <= 1e7)) { throw new AssertionError(); } int m = sc.nextInt(); if (!(1 <= m && m <= 5 * 1e5)) { throw new AssertionError(); } int[] x = new int[m]; int[] d = new int[m]; int[][] y = new int[m][]; int sumd = 0; for (int i = 0; i < m; ++i) { x[i] = sc.nextInt(); d[i] = sc.nextInt(); if(!(d[i]>0)){ throw new AssertionError(); } if (!(0 <= x[i] && x[i] < MAX_)) throw new AssertionError(); sumd += d[i]; y[i] = new int[d[i]]; for (int j = 0; j < d[i]; ++j) { y[i][j] = sc.nextInt(); if (!(0 <= y[i][j] && y[i][j] < MAX_)) throw new AssertionError(); } } if (!(1 <= sumd && sumd <= 1e6)) { throw new AssertionError(); } // System.out.println(hamsolver(MAX_, m, x, d, y)); // System.out.println(new BruteForce(lr(MAX_, m, x, d, y)[0], lr(MAX_, // m, x, d, y)[1]).calc()); System.out.println(solver(MAX_, m, x, d, y)); } int solver(int MAX_, int m, int[] x, int[] d, int[][] y) { MAX = MAX_; int[] r = lr(MAX_, m, x, d, y)[1]; int[] l = lr(MAX_, m, x, d, y)[0]; int[] invl = new int[MAX]; int[] invr = new int[MAX]; Arrays.fill(invl, -1); Arrays.fill(invr, -1); for (int i = 0; i < MAX; ++i) { if (l[i] != -1) { int src = (MAX - 1) - i; int dst = (MAX - 1) - l[i]; invr[src] = dst; } if (r[i] != -1) { int src = (MAX - 1) - i; int dst = (MAX - 1) - r[i]; invl[src] = dst; } } return Math.min(solve(l, r), solve(invl, invr)); } int[][] lr(int MAX_, int m, int[] x, int[] d, int[][] y) { MAX = MAX_; int[] r = new int[MAX]; int[] l = new int[MAX]; Arrays.fill(r, -1); Arrays.fill(l, -1); for (int i = 0; i < m; ++i) { int ma = r[x[i]] != -1 ? r[x[i]] : x[i] - 1; int mi = l[x[i]] != -1 ? l[x[i]] : x[i] + 1; for (int j = 0; j < d[i]; ++j) { ma = Math.max(ma, y[i][j]); mi = Math.min(mi, y[i][j]); } if (ma >= x[i]) { r[x[i]] = ma; } if (mi <= x[i]) { l[x[i]] = mi; } } { int ma = -1; for (int i = 0; i < MAX; ++i) { if (r[i] == -1) continue; if (ma < r[i]) { ma = r[i]; } else if (ma >= r[i]) { r[i] = -1; } } } { int mi = MAX * 10; for (int i = MAX - 1; i >= 0; --i) { if (l[i] == -1) continue; if (mi > l[i]) { mi = l[i]; } else if (mi <= l[i]) { l[i] = -1; } } } return new int[][] { l, r }; } class Scanner { private final InputStream in = System.in; private final byte[] buffer = new byte[1024]; private int ptr = 0; private int buflen = 0; private boolean hasNextByte() { if (ptr < buflen) { return true; } else { ptr = 0; try { buflen = in.read(buffer); } catch (IOException e) { e.printStackTrace(); } if (buflen <= 0) { return false; } } return true; } private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1; } private boolean isPrintableChar(int c) { return 33 <= c && c <= 126; } private void skipUnprintable() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; } public boolean hasNext() { skipUnprintable(); return hasNextByte(); } public String next() { if (!hasNext()) throw new NoSuchElementException(); StringBuilder sb = new StringBuilder(); int b = readByte(); while (isPrintableChar(b)) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } public long nextLong() { if (!hasNext()) throw new NoSuchElementException(); long n = 0; boolean minus = false; int b = readByte(); if (b == '-') { minus = true; b = readByte(); } if (b < '0' || '9' < b) { throw new NumberFormatException(); } while (true) { if ('0' <= b && b <= '9') { n *= 10; n += b - '0'; } else if (b == -1 || !isPrintableChar(b)) { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } public int nextInt() { return (int) nextLong(); } } static void tr(Object... objects) { System.out.println(Arrays.deepToString(objects)); } }