import java.io.*; import java.util.*; class Trie{ /** Node class **/ static class Node{ private final int R = 26; Node[] links; private boolean isEnd; int idx; Node(){ links = new Node[R]; } boolean containsKey(char ch) { return links[ch - 'a'] != null; } Node get(char ch) { return links[ch - 'a']; } void put(char ch, Node node) { links[ch - 'a'] = node; } void setEnd() { isEnd = true; } boolean isEnd() { return isEnd; } } Node root; int[] cNum; public Trie(int m){ root = new Node(); cNum = new int[m]; } /** Inserts a word into the trie **/ void insert(int idx, String word) { Node node = root; for(int i=0;iout.print(i + " ")); out.println(); } static void printAll(long[] a) { Arrays.stream(a).forEach(i->out.print(i + " ")); out.println(); } static void printAll(int[] a, int add) { Arrays.stream(a).forEach(i->out.print(i + add + " ")); out.println(); } static void printAll(long[] a, long add) { Arrays.stream(a).forEach(i->out.print(i + add + " ")); out.println(); } static List[] makeTree(List[] graph, int vertexNum, int edgeNum) { graph = new ArrayList[vertexNum]; for(int i=0;i(); for(int i=0;i void reverse(List ls) { int sz = ls.size(); for (int i = 0; i < sz / 2; i++) { T t = ls.get(i); ls.set(i, ls.get(sz - 1 - i)); ls.set(sz - 1 - i, t); } } static void reverse(T[] ar) { int len = ar.length; for (int i = 0; i < len / 2; i++) { T t = ar[i]; ar[i] = ar[len - 1 - i]; ar[len - 1 - i] = t; } } static void sbnl() {//StringBuilderに改行文字をappendする sb.append("\n"); } static int lowerBound(int[] a, int x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] < x) { l = c; } else { r = c; } } return r; } static int upperBound(int[] a, int x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] <= x) { l = c; } else { r = c; } } return r; } static int rlowerBound(int[] a, int x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] > x) { l = c; } else { r = c; } } return r; } static int rupperBound(int[] a, int x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] >= x) { l = c; } else { r = c; } } return r; } static int lowerBound(long[] a, long x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] < x) { l = c; } else { r = c; } } return r; } static int upperBound(long[] a, long x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] <= x) { l = c; } else { r = c; } } return r; } static int rlowerBound(long[] a, long x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] > x) { l = c; } else { r = c; } } return r; } static int rupperBound(long[] a, long x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] >= x) { l = c; } else { r = c; } } return r; } static int lowerBound(double[] a, double x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] < x) { l = c; } else { r = c; } } return r; } static int upperBound(double[] a, double x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] <= x) { l = c; } else { r = c; } } return r; } static int rlowerBound(double[] a, double x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] > x) { l = c; } else { r = c; } } return r; } static int rupperBound(double[] a, double x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] >= x) { l = c; } else { r = c; } } return r; } static int lowerBound(char[] a, char x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] < x) { l = c; } else { r = c; } } return r; } static int upperBound(char[] a, char x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] <= x) { l = c; } else { r = c; } } return r; } static int rlowerBound(char[] a, char x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] > x) { l = c; } else { r = c; } } return r; } static int rupperBound(char[] a, char x) { int l = -1, r = a.length; while (r - l > 1) { int c = (l + r) / 2; if (a[c] >= x) { l = c; } else { r = c; } } return r; } static int lowerBound(List ls, T x) throws RuntimeException { if (ls.size() == 0) return -1; if (ls.get(0) instanceof Integer) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) >= 0 ? 1 : -1); } else if (ls.get(0) instanceof Long) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) >= 0 ? 1 : -1); } else if (ls.get(0) instanceof Double) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) >= 0 ? 1 : -1); } else { System.err.println( String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName())); throw new RuntimeException(); } } static int upperBound(List ls, T x) throws RuntimeException { if (ls.size() == 0) return -1; if (ls.get(0) instanceof Integer) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) > 0 ? 1 : -1); } else if (ls.get(0) instanceof Long) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) > 0 ? 1 : -1); } else if (ls.get(0) instanceof Double) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) > 0 ? 1 : -1); } else { System.err.println( String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName())); throw new RuntimeException(); } } static int rupperBound(List ls, T x) throws RuntimeException { if (ls.size() == 0) return -1; if (ls.get(0) instanceof Integer) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) < 0 ? 1 : -1); } else if (ls.get(0) instanceof Long) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) < 0 ? 1 : -1); } else if (ls.get(0) instanceof Double) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) < 0 ? 1 : -1); } else { System.err.println( String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName())); throw new RuntimeException(); } } static int rlowerBound(List ls, T x) { if (ls.size() == 0) return -1; if (ls.get(0) instanceof Integer) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Integer) t1).compareTo((Integer) t2) <= 0 ? 1 : -1); } else if (ls.get(0) instanceof Long) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Long) t1).compareTo((Long) t2) <= 0 ? 1 : -1); } else if (ls.get(0) instanceof Double) { return ~Collections.binarySearch(ls, x, (t1, t2) -> ((Double) t1).compareTo((Double) t2) <= 0 ? 1 : -1); } else { System.err.println( String.format("%s:数値でないリストを二分探索しています。", Thread.currentThread().getStackTrace()[1].getMethodName())); throw new RuntimeException(); } } static int[] concat(int x, int arr[]) { int ret[] = new int[arr.length + 1]; System.arraycopy(arr, 0, ret, 1, ret.length - 1); ret[0] = x; return ret; } static int[] concat(int arr[], int x) { int ret[] = new int[arr.length + 1]; System.arraycopy(arr, 0, ret, 0, ret.length - 1); ret[ret.length - 1] = x; return ret; } static long[] concat(long x, long arr[]) { long ret[] = new long[arr.length + 1]; System.arraycopy(arr, 0, ret, 1, ret.length - 1); ret[0] = x; return ret; } static long[] concat(long arr[], long x) { long ret[] = new long[arr.length + 1]; System.arraycopy(arr, 0, ret, 0, ret.length - 1); ret[ret.length - 1] = x; return ret; } static char[] concat(char x, char arr[]) { char ret[] = new char[arr.length + 1]; System.arraycopy(arr, 0, ret, 0, ret.length - 1); ret[ret.length - 1] = x; return ret; } static char[] concat(char arr[], char x) { char ret[] = new char[arr.length + 1]; System.arraycopy(arr, 0, ret, 0, ret.length - 1); ret[ret.length - 1] = x; return ret; } static int max(int x, int y) { return Math.max(x, y); } static int min(int x, int y) { return Math.min(x, y); } static int max(int x, int y, int z) { x = Math.max(x, y); x = Math.max(x, z); return x; } static int min(int x, int y, int z) { x = Math.min(x, y); x = Math.min(x, z); return x; } static long max(long x, long y) { return Math.max(x, y); } static long min(long x, long y) { return Math.min(x, y); } static long max(long x, long y, long z) { x = Math.max(x, y); x = Math.max(x, z); return x; } static long min(long x, long y, long z) { x = Math.min(x, y); x = Math.min(x, z); return x; } static double max(double x, double y) { return Math.max(x, y); } static double min(double x, double y) { return Math.min(x, y); } static double max(double x, double y, double z) { x = Math.max(x, y); x = Math.max(x, z); return x; } static double min(double x, double y, double z) { x = Math.min(x, y); x = Math.min(x, z); return x; } static void sort(int[] ar) { Arrays.sort(ar); } static void sort(long[] ar) { Arrays.sort(ar); } static void sort(double[] ar) { Arrays.sort(ar); } static void sort(char[] ar) { Arrays.sort(ar); } static void rsort(int[] ar) { Arrays.sort(ar); int len = ar.length; for (int i = 0; i < len / 2; i++) { int tmp = ar[i]; ar[i] = ar[len - 1 - i]; ar[len - 1 - i] = tmp; } } static void rsort(long[] ar) { Arrays.sort(ar); int len = ar.length; for (int i = 0; i < len / 2; i++) { long tmp = ar[i]; ar[i] = ar[len - 1 - i]; ar[len - 1 - i] = tmp; } } static void rsort(double[] ar) { Arrays.sort(ar); int len = ar.length; for (int i = 0; i < len / 2; i++) { double tmp = ar[i]; ar[i] = ar[len - 1 - i]; ar[len - 1 - i] = tmp; } } static void rsort(char[] ar) { Arrays.sort(ar); int len = ar.length; for (int i = 0; i < len / 2; i++) { char tmp = ar[i]; ar[i] = ar[len - 1 - i]; ar[len - 1 - i] = tmp; } } static void fill(int arr[], int x) { Arrays.fill(arr, x); } static void fill(long arr[], long x) { Arrays.fill(arr, x); } static void fill(boolean arr[], boolean x) { Arrays.fill(arr, x); } static void fill(double arr[], double x) { Arrays.fill(arr, x); } static void fill(int arr[][], int x) { for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x); } static void fill(long arr[][], long x) { for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x); } static void fill(double arr[][], double x) { for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x); } static void fill(boolean arr[][], boolean x) { for (int i = 0; i < arr.length; i++) Arrays.fill(arr[i], x); } //MOD culc static long plus(long x, long y) { long res = (x + y) % mod; return res < 0 ? res + mod : res; } static long sub(long x, long y) { long res = (x - y) % mod; return res < 0 ? res + mod : res; } static long mul(long x, long y) { long res = (x * y) % mod; return res < 0 ? res + mod : res; } static long div(long x, long y) { long res = x * pow(y, mod - 2) % mod; return res < 0 ? res + mod : res; } static long pow(long x, long y) { if (y < 0) return 0; if (y == 0) return 1; if (y % 2 == 1) return (x * pow(x, y - 1)) % mod; long root = pow(x, y / 2); return root * root % mod; } public static void main(String[] args) throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); solve(); out.flush(); } //input static InputStream is; static PrintWriter out; static String INPUT = ""; private static byte[] inbuf = new byte[1024]; static int lenbuf = 0, ptrbuf = 0; private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private static int skip() { int b; while ((b = readByte()) != -1 && isSpaceChar(b)) ; return b; } @SuppressWarnings("unused") private static double nd() { return Double.parseDouble(ns()); } @SuppressWarnings("unused") private static char nc() { return (char) skip(); } private static String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while (!(isSpaceChar(b))) { sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private static 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); } @SuppressWarnings("unused") private static char[][] nm(int n, int m) { char[][] map = new char[n][]; for (int i = 0; i < n; i++) map[i] = ns(m); return map; } @SuppressWarnings("unused") private static int[] na(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++) a[i] = ni(); return a; } @SuppressWarnings("unused") private static long[] nla(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++) a[i] = nl(); return a; } @SuppressWarnings("unused") private static int[][] na(int n, int m){ int[][] res = new int[n][m]; for(int i=0;i= '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(); } } @SuppressWarnings("unused") private static 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(); } } }