import java.util.*; import java.io.*; import java.math.*; public class Main { static boolean DEBUG; public static void main(String[] args) { DEBUG = args.length > 0 && args[0].equals("-DEBUG"); Solver solver = new Solver(); solver.solve(); solver.exit(); } static class FastScanner { 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 32 <= 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(); } } } static class Solver { FastScanner sc = new FastScanner(); public Solver() { } String ns() { return sc.next(); } String[] ns(int n) { String a[] = new String[n]; for(int i = 0; i < n; i ++) { a[i] = ns(); } return a; } String[][] ns(int n, int m) { String a[][] = new String[n][m]; for(int i = 0; i < n; i ++) { a[i] = ns(m); } return a; } char[] nc(int n) { String str = ns(); char a[] = new char[max(n, str.length())]; for(int i = 0; i < str.length(); i ++) { a[i] = str.charAt(i); } return a; } char[][] nc(int n, int m) { char a[][] = new char[n][m]; for(int i = 0; i < n; i ++) { a[i] = nc(m); } return a; } boolean[] nb(int n, char t) { char c[] = nc(-1); if(n < 0) n = c.length; boolean a[] = new boolean[n]; for(int i = 0; i < n; i ++) { a[i] = c[i] == t; } return a; } boolean[][] nb(int n, int m, char t) { boolean a[][] = new boolean[n][m]; for(int i = 0; i < n; i ++) { a[i] = nb(m, t); } return a; } int ni() { return (int)sc.nextLong(); } int[] ni(int n) { int a[] = new int[n]; for(int i = 0; i < n; i ++) { a[i] = ni(); } return a; } int[][] ni(int n, int m) { int a[][] = new int[n][m]; for(int i = 0; i < n; i ++) { a[i] = ni(m); } return a; } long nl() { return sc.nextLong(); } long[] nl(int n) { long a[] = new long[n]; for(int i = 0; i < n; i ++) { a[i] = nl(); } return a; } long[][] nl(int n, int m) { long a[][] = new long[n][m]; for(int i = 0; i < n; i ++) { a[i] = nl(m); } return a; } double nd() { return Double.parseDouble(sc.next()); } double[] nd(int n) { double a[] = new double[n]; for(int i = 0; i < n; i ++) { a[i] = nd(); } return a; } double[][] nd(int n, int m) { double a[][] = new double[n][m]; for(int i = 0; i < n; i ++) { a[i] = nd(m); } return a; } PrintWriter out = new PrintWriter(System.out); PrintWriter err = new PrintWriter(System.err); void prt() { out.print(""); } void prt(T a) { out.print(a); } void prtln() { out.println(""); } void prtln(T a) { out.println(a); } void prtln(int... a) { StringBuilder sb = new StringBuilder(); for(int element : a){ sb.append(element+" "); } prtln(sb.toString().trim()); } void prtln(long... a) { StringBuilder sb = new StringBuilder(); for(long element : a){ sb.append(element+" "); } prtln(sb.toString().trim()); } void prtln(double... a) { StringBuilder sb = new StringBuilder(); for(double element : a){ sb.append(element+" "); } prtln(sb.toString().trim()); } void prtln(String... a) { StringBuilder sb = new StringBuilder(); for(String element : a){ sb.append(element+" "); } prtln(sb.toString().trim()); } void prtln(char... a) { StringBuilder sb = new StringBuilder(); for(char element : a){ sb.append(element); } prtln(sb.toString().trim()); } void prtln(int[][] a) { for(int[] element : a){ prtln(element); } } void prtln(long[][] a) { for(long[] element : a){ prtln(element); } } void prtln(double[][] a) { for(double[] element : a){ prtln(element); } } void prtln(String[][] a) { for(String[] element : a){ prtln(element); } } void prtln(char[][] a) { for(char[] element : a){ prtln(element); } } String errconvert(int a) { return isINF(a) ? "_" : String.valueOf(a); } String errconvert(long a) { return isINF(a) ? "_" : String.valueOf(a); } void errprt(int a) { if(DEBUG) { err.print(errconvert(a)); } } void errprt(long a) { if(DEBUG) { err.print(errconvert(a)); } } void errprt() { if(DEBUG) { err.print(""); } } void errprt(T a) { if(DEBUG) { err.print(a); } } void errprt(boolean a) { if(DEBUG) { errprt(a ? "#" : "."); } } void errprtln() { if(DEBUG) { err.println(""); } } void errprtln(int a) { if(DEBUG) { err.println(errconvert(a)); } } void errprtln(long a) { if(DEBUG) { err.println(errconvert(a)); } } void errprtln(T a) { if(DEBUG) { err.println(a); } } void errprtln(boolean a) { if(DEBUG) { errprtln(a ? "#" : "."); } } void errprtln(int... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(int element : a){ sb.append(errconvert(element)+" "); } errprtln(sb.toString().trim()); } } void errprtln(long... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(long element : a){ sb.append(errconvert(element)+" "); } errprtln(sb.toString().trim()); } } void errprtln(double... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(double element : a){ sb.append(element+" "); } errprtln(sb.toString().trim()); } } void errprtln(String... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(String element : a){ sb.append(element+" "); } errprtln(sb.toString().trim()); } } void errprtln(char... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(char element : a){ sb.append(element); } errprtln(sb.toString().trim()); } } void errprtln(boolean... a) { if(DEBUG) { StringBuilder sb = new StringBuilder(); for(boolean element : a){ sb.append((element ? "#" : ".")+" "); } errprtln(sb.toString().trim()); } } void errprtln(int[][] a) { if(DEBUG) { for(int[] element : a){ errprtln(element); } } } void errprtln(long[][] a) { if(DEBUG) { for(long[] element : a){ errprtln(element); } } } void errprtln(double[][] a) { if(DEBUG) { for(double[] element : a){ errprtln(element); } } } void errprtln(String[][] a) { if(DEBUG) { for(String[] element : a){ errprtln(element); } } } void errprtln(char[][] a) { if(DEBUG) { for(char[] element : a){ errprtln(element); } } } void errprtln(boolean[][] a) { if(DEBUG) { for(boolean[] element : a){ errprtln(element); } } } void reply(boolean b) { prtln(b ? "Yes" : "No"); } void REPLY(boolean b) { prtln(b ? "YES" : "NO"); } void flush() { out.flush(); if(DEBUG) { err.flush(); } } void exit() { flush(); System.exit(0); } void assertion(boolean b) { if(!b) throw new AssertionError(); } int min(int a, int b) { return Math.min(a, b); } long min(long a, long b) { return Math.min(a, b); } double min(double a, double b) { return Math.min(a, b); } int min(int... x) { int min = x[0]; for(int val : x) { min = min(min, val); } return min; } long min(long... x) { long min = x[0]; for(long val : x) { min = min(min, val); } return min; } double min(double... x) { double min = x[0]; for(double val : x) { min = min(min, val); } return min; } int max(int a, int b) { return Math.max(a, b); } long max(long a, long b) { return Math.max(a, b); } double max(double a, double b) { return Math.max(a, b); } int max(int... x) { int max = x[0]; for(int val : x) { max = max(max, val); } return max; } long max(long... x) { long max = x[0]; for(long val : x) { max = max(max, val); } return max; } double max(double... x) { double max = x[0]; for(double val : x) { max = max(max, val); } return max; } long sum(int... a) { long sum = 0; for(int element : a) { sum += element; } return sum; } long sum(long... a) { long sum = 0; for(long element : a) { sum += element; } return sum; } double sum(double... a) { double sum = 0; for(double element : a) { sum += element; } return sum; } long[] sums(int[] a) { long sum[] = new long[a.length + 1]; sum[0] = 0; for(int i = 0; i < a.length; i ++) { sum[i + 1] = sum[i] + a[i]; } return sum; } long[] sums(long[] a) { long sum[] = new long[a.length + 1]; sum[0] = 0; for(int i = 0; i < a.length; i ++) { sum[i + 1] = sum[i] + a[i]; } return sum; } double[] sums(double[] a) { double sum[] = new double[a.length + 1]; sum[0] = 0; for(int i = 0; i < a.length; i ++) { sum[i + 1] = sum[i] + a[i]; } return sum; } int abs(int x) { return x >= 0 ? x : - x; } long abs(long x) { return x >= 0 ? x : - x; } double abs(double x) { return x >= 0 ? x : - x; } int signum(int x) { return x > 0 ? 1 : x < 0 ? -1 : 0; } int signum(long x) { return x > 0 ? 1 : x < 0 ? -1 : 0; } int signum(double x) { return x > 0 ? 1 : x < 0 ? -1 : 0; } long round(double x) { return Math.round(x); } long floor(double x) { return (long)Math.floor(x); } int divfloor(int a, int b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); } long divfloor(long a, long b) { return signum(a) == signum(b) ? a / b : - divceil(abs(a), abs(b)); } long ceil(double x) { return (long)Math.ceil(x); } int divceil(int a, int b) { return a >= 0 && b > 0 ? (a + b - 1) / b : a < 0 && b < 0 ? divceil(abs(a), abs(b)) : - divfloor(abs(a), abs(b)); } long divceil(long a, long b) { return a >= 0 && b > 0 ? (a + b - 1) / b : a < 0 && b < 0 ? divceil(abs(a), abs(b)) : - divfloor(abs(a), abs(b)); } double sqrt(int x) { return Math.sqrt((double)x); } double sqrt(long x) { return Math.sqrt((double)x); } double sqrt(double x) { return Math.sqrt(x); } double pow(double x, double y) { return Math.pow(x, y); } long pow(long x, long y) { if(y == 0) { return 1; }else { long tmp = pow(x, y / 2); return tmp * tmp * (y % 2 == 0 ? 1 : x); } } int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); } long lcm(long a, long b) { return a / gcd(a, b) * b; } int gcd(int[] array) { int gcd = 0; for(int i = 0; i < array.length; i ++) { gcd = gcd(gcd, array[i]); } return gcd; } long gcd(long[] array) { long gcd = 0; for(int i = 0; i < array.length; i ++) { gcd = gcd(gcd, array[i]); } return gcd; } int upperToInt(char a) { return a - 'A'; } int lowerToInt(char a) { return a - 'a'; } int numToInt(char a) { return a - '0'; } int charToInt(char a) { return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a); } char intToUpper(int a) { return (char)(a + 'A'); } char intToLower(int a) { return (char)(a + 'a'); } char intToNum(int a) { return (char)(a + '0'); } int[] charToInt(char[] a) { int array[] = new int[a.length]; for(int i = 0; i < a.length; i ++) { array[i] = charToInt(a[i]); } return array; } long[] div(long a) { List divList = new ArrayList(); for(long i = 1; i * i <= a; i ++) { if(a % i == 0) { divList.add(i); if(i * i != a) { divList.add(a / i); }; } } long div[] = new long[divList.size()]; for(int i = 0; i < divList.size(); i ++) { div[i] = divList.get(i); } return div; } long[][] factor(long a) { List factorList = new ArrayList(); List degreeList = new ArrayList(); for(long i = 2; i * i <= a; i ++) { if(a % i == 0) { long count = 0; while(a % i == 0) { a /= i; count ++; } factorList.add(i); degreeList.add(count); } } if(a > 1) { factorList.add(a); degreeList.add(1L); } long factor[][] = new long[factorList.size()][2]; for(int i = 0; i < factorList.size(); i ++) { factor[i][0] = factorList.get(i); factor[i][1] = degreeList.get(i); } Arrays.sort(factor, (sort1, sort2) -> Long.compare(sort1[0], sort2[0])); return factor; } boolean isPrime(long x) { boolean ok = x > 1; for(long i = 2; i * i <= x; i ++) { ok &= x % i != 0; if(!ok) return ok; } return ok; } boolean[] prime(int num) { boolean prime[] = new boolean[num]; fill(prime, true); prime[0] = false; prime[1] = false; for(int i = 2; i < num; i ++) { if(prime[i]) { for(int j = 2; i * j < num; j ++) { prime[i * j] = false; } } } return prime; } long[][] countElements(long[] a, boolean sort) { int len = a.length; long array[] = new long[len]; for(int i = 0; i < len; i ++) { array[i] = a[i]; } if(sort) { Arrays.sort(array); } List elem = new ArrayList(); List cnt = new ArrayList(); long tmp = 1; for(int i = 1; i <= len; i ++) { if(i == len || array[i] != array[i - 1]) { elem.add(array[i - 1]); cnt.add(tmp); tmp = 1; }else { tmp ++; } } long counts[][] = new long[elem.size()][2]; for(int i = 0; i < elem.size(); i ++) { counts[i][0] = elem.get(i); counts[i][1] = cnt.get(i); } return counts; } long[][] countElements(String str, boolean sort) { int len = str.length(); char array[] = str.toCharArray(); if(sort) { Arrays.sort(array); } List elem = new ArrayList(); List cnt = new ArrayList(); long tmp = 1; for(int i = 1; i <= len; i ++) { if(i == len || array[i] != array[i - 1]) { elem.add((long)array[i - 1]); cnt.add(tmp); tmp = 1; }else { tmp ++; } } long counts[][] = new long[elem.size()][2]; for(int i = 0; i < elem.size(); i ++) { counts[i][0] = elem.get(i); counts[i][1] = cnt.get(i); } return counts; } int[] baseConvert(long x, int n) { long tmp = x; int len = 0; while(tmp > 0) { tmp /= n; len ++; } int digit[] = new int[len]; int i = 0; tmp = x; while(tmp > 0) { digit[i ++] = (int)(tmp % n); tmp /= n; } return digit; } int[] baseConvert(int x, int n) { int tmp = x; int len = 0; while(tmp > 0) { tmp /= n; len ++; } int digit[] = new int[len]; int i = 0; tmp = x; while(tmp > 0) { digit[i ++] = (int)(tmp % n); tmp /= n; } return digit; } int numDigits(long a) { return Long.toString(a).length(); } long bitFlag(int a) { return 1L << (long)a; } boolean isFlagged(long x, int a) { return (x & bitFlag(a)) != 0; } long countString(String str, String a) { return (str.length() - str.replace(a, "").length()) / a.length(); } long countStringAll(String str, String a) { return str.length() - str.replaceAll(a, "").length(); } int lowerBound(long[] array, long key) { return BS(array, key, true, true, true); } int lowerBound(long[] array, long key, int ng, int ok) { return BS(array, key, true, true, true, ng, ok); } int upperBound(long[] array, long key) { return BS(array, key, true, true, false); } int upperBound(long[] array, long key, int ng, int ok) { return BS(array, key, true, true, false, ng, ok); } int cntBS(long[] array, long key, boolean ascending, boolean greater, boolean equals) { return BS(array, key, ascending, greater, equals, true); } int cntBS(long[] array, long key, boolean ascending, boolean greater, boolean equals, int ng, int ok) { return BS(array, key, ascending, greater, equals, true, ng, ok); } int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals) { return BS(array, key, ascending, greater, equals, false); } int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, int ng, int ok) { return BS(array, key, ascending, greater, equals, false, ng, ok); } int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, boolean count) { int ng = ascending ^ greater ? array.length : -1; int ok = ascending ^ greater ? -1 : array.length; return BS(array, key, ascending, greater, equals, count, ng, ok); } int BS(long[] array, long key, boolean ascending, boolean greater, boolean equals, boolean count, int ng, int ok) { int index = binarySearch(array, key, greater, equals, ng, ok); return count ? (int)abs(ok - index) : index; } int binarySearch(long[] array, long key, boolean greater, boolean equals, int ng, int ok) { while (abs(ok - ng) > 1) { int mid = (ok + ng) / 2; if(isOKforBinarySearch(array, mid, key, greater, equals)) { ok = mid; }else { ng = mid; } } return ok; } boolean isOKforBinarySearch(long[] array, int index, long key, boolean greater, boolean equals) { return (array[index] > key && greater) || (array[index] < key && !greater) || (array[index] == key && equals); } void reverse(String[] array) { String reversed[] = new String[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void reverse(int[] array) { int reversed[] = new int[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void reverse(long[] array) { long reversed[] = new long[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void reverse(double[] array) { double reversed[] = new double[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void reverse(boolean[] array) { boolean reversed[] = new boolean[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void reverse(Object[] array) { Object reversed[] = new Object[array.length]; for(int i = 0; i < array.length; i ++) { reversed[array.length - i - 1] = array[i]; } for(int i = 0; i < array.length; i ++) { array[i] = reversed[i]; } } void fill(int[] array, int x) { Arrays.fill(array, x); } void fill(long[] array, long x) { Arrays.fill(array, x); } void fill(double[] array, double x) { Arrays.fill(array, x); } void fill(boolean[] array, boolean x) { Arrays.fill(array, x); } void fill(int[][] array, int x) { for(int[] a : array) { fill(a, x); } } void fill(long[][] array, long x) { for(long[] a : array) { fill(a, x); } } void fill(double[][] array, double x) { for(double[] a : array) { fill(a, x); } } void fill(boolean[][] array, boolean x) { for(boolean[] a : array) { fill(a, x); } } void fill(int[][][] array, int x) { for(int[][] a : array) { fill(a, x); } } void fill(long[][][] array, long x) { for(long[][] a : array) { fill(a, x); } } void fill(double[][][] array, double x) { for(double[][] a : array) { fill(a, x); } } void fill(boolean[][][] array, boolean x) { for(boolean[][] a : array) { fill(a, x); } } void shuffleArray(int[] array){ int n = array.length; Random rnd = new Random(); for(int i = 0; i < n; i ++){ int tmp = array[i]; int randomPos = i + rnd.nextInt(n - i); array[i] = array[randomPos]; array[randomPos] = tmp; } } void shuffleArray(long[] array){ int n = array.length; Random rnd = new Random(); for(int i = 0; i < n; i ++){ long tmp = array[i]; int randomPos = i + rnd.nextInt(n - i); array[i] = array[randomPos]; array[randomPos] = tmp; } } void shuffleArray(double[] array){ int n = array.length; Random rnd = new Random(); for(int i = 0; i < n; i ++){ double tmp = array[i]; int randomPos = i + rnd.nextInt(n - i); array[i] = array[randomPos]; array[randomPos] = tmp; } } void swap(int[] array, int i, int j) { int tmp = array[i]; array[i] = array[j]; array[j] = tmp; } void swap(long[] array, int i, int j) { long tmp = array[i]; array[i] = array[j]; array[j] = tmp; } void swap(double[] array, int i, int j) { double tmp = array[i]; array[i] = array[j]; array[j] = tmp; } long INF = (long)1e18 + 7; boolean isINF(long a) { return abs(a) > INF / 1000; } boolean isPlusINF(long a) { return a > 0 && isINF(a); } boolean isMinusINF(long a) { return isPlusINF(- a); } int I_INF = (int)1e9 + 7; boolean isINF(int a) { return abs(a) > I_INF / 1000; } boolean isPlusINF(int a) { return a > 0 && isINF(a); } boolean isMinusINF(int a) { return isPlusINF(- a); } // mods long MOD = (long)1e9 + 7; // 998244353; public long mod(long i) { i %= MOD; return i + (i < 0 ? MOD : 0); } long pow_m(long x, long y) { if(y == 0) { return 1; }else { long tmp = pow_m(x, y / 2); return mod(mod(tmp * tmp) * (y % 2 == 0 ? 1 : x)); } } long[] pows_m(long x, int max) { long pow[] = new long[max + 1]; pow[0] = 1; for(int i = 0; i < max; i ++) { pow[i + 1] = mod(pow[i] * x); } return pow; } int MAX_INV_SIZE = 100_100; HashMap invMap = new HashMap<>(); long inv(long x) { x = mod(x); if(invMap.containsKey(x)) { return invMap.get(x); } if(invMap.size() >= MAX_INV_SIZE) { return calInv(x); } invMap.put(x, calInv(x)); return invMap.get(x); } long calInv(long x) { return pow_m(x, MOD - 2); } int MAX_FACT = 5_000_100; long fact[]; long invFact[]; boolean isFactPrepared = false; HashMap factMap; void prepareFact() { fact = new long[MAX_FACT]; Arrays.fill(fact, 0); invFact = new long[MAX_FACT]; Arrays.fill(invFact, 0); fact[0] = 1; int maxIndex = min(MAX_FACT, (int)MOD); for(int i = 1; i < maxIndex; i ++) { fact[i] = mod(fact[i - 1] * i); } invFact[maxIndex - 1] = inv(fact[maxIndex - 1]); for(int i = maxIndex - 1; i > 0; i --) { invFact[i - 1] = mod(invFact[i] * i); } factMap = new HashMap<>(); isFactPrepared = true; } long P(int n, int r) { if(!isFactPrepared) { prepareFact(); } if(n < 0 || r < 0 || n < r) { return 0; } if(n >= MAX_FACT) { if(!factMap.containsKey(n)) { long largeFact[] = new long[MAX_FACT]; factMap.put(n, largeFact); fill(largeFact, -INF); largeFact[0] = 1; } long largeFact[] = factMap.get(n); int i = r; while(isINF(largeFact[i])) { i --; } for(; i < r; i ++) { largeFact[i + 1] = mod(largeFact[i] * (n - i)); } return largeFact[r]; } return mod(fact[n] * invFact[n - r]); } long C(int n, int r) { if(!isFactPrepared) { prepareFact(); } if(n < 0 || r < 0 || n < r) { return 0; } return mod(P(n, r) * invFact[r]); } long H(int n, int r) { return C((n - 1) + r, r); } // grid class Grids { int h; int w; Grid[][] gs; Grids(int h, int w) { this.h = h; this.w = w; gs = new Grid[h][w]; for(int i = 0; i < h; i ++) { for(int j = 0; j < w; j ++) { gs[i][j] = new Grid(i, j, h, w); } } } void init(boolean[][] b) { for(int i = 0; i < h; i ++) { for(int j = 0; j < w; j ++) { gs[i][j].b = b[i][j]; } } } void init(long[][] val) { for(int i = 0; i < h; i ++) { for(int j = 0; j < w; j ++) { gs[i][j].val = val[i][j]; } } } int dx[] = {0, -1, 1, 0, 0, -1, 1, -1, 1}; int dy[] = {0, 0, 0, -1, 1, -1, -1, 1, 1}; Grid next(Grid g, int i) { return isValid(g.x + dx[i], g.y + dy[i], g.h, g.w) ? gs[g.x + dx[i]][g.y + dy[i]] : null; } } class Grid implements Comparable { int x; int y; int h; int w; int i; boolean b; long val; Grid() { } Grid(int x, int y, int h, int w) { init(x, y, h, w, false, 0); } Grid(int x, int y, int h, int w, boolean b) { init(x, y, h, w, b, 0); } Grid(int x, int y, int h, int w, long val) { init(x, y, h, w, false, val); } Grid(int x, int y, int h, int w, boolean b, long val) { init(x, y, h, w, b, val); } void init(int x, int y, int h, int w, boolean b, long val) { this.x = x; this.y = y; this.h = h; this.w = w; this.b = b; this.val = val; i = x * w + y; } @Override public int compareTo(Grid g) { return Long.compare(this.val, g.val); } } boolean isValid(int x, int y, int h, int w) { return x >= 0 && x < h && y >= 0 && y < w; } boolean isValid(Grid g) { return isValid(g.x, g.y, g.h, g.w); } // graph class Graph { int numNode; int numEdge; boolean directed; Edge edges[]; Node nodes[]; Node reversedNodes[]; Graph(int numNode, int numEdge, boolean directed) { this.numNode = numNode; this.numEdge = numEdge; this.directed = directed; nodes = new Node[numNode]; reversedNodes = new Node[numNode]; for(int i = 0; i < numNode; i ++) { nodes[i] = new Node(i); reversedNodes[i] = new Node(i); } } void init(Edge[] edges) { this.edges = edges; for(Edge edge : edges) { nodes[edge.source].add(edge.target, edge.cost); if(directed) { reversedNodes[edge.target].add(edge.source, edge.cost); }else { nodes[edge.target].add(edge.source, edge.cost); } } } void clearNodes() { for(Node n : nodes) { n.clear(); } for(Node n : reversedNodes) { n.clear(); } } } class Node extends ArrayList { int id; Node(int id) { this.id = id; } void add(int target, long cost) { add(new Edge(id, target, cost)); } } class Edge implements Comparable { int source; int target; long cost; Edge(int source, int target, long cost) { this.source = source; this.target = target; this.cost = cost; } @Override public int compareTo(Edge e) { return Long.compare(this.cost, e.cost); } } public void solve() { String str = ns(); char c[] = new char[str.length()]; for(int i = 0; i < c.length; i ++) { c[i] = str.charAt(i); } // int num = c.length; // boolean ans = false; // boolean aaa = true; // if(num <= 1) { // prtln("NO"); return; // } // for(int i = 0; i < num; i ++) { // aaa &= c[i] == ' ' || (c[i] >= 'a' && c[i] <= 'z'); // } // if(!aaa) { // prtln("NO"); return; // } // for(int i = 0; i <= num; i ++) { // for(int j = i + 2; j <= num; j ++) { // boolean ok = true; // boolean b[][] = new boolean[2][26]; // for(int k = 0; k < i; k ++) { // if(c[k] != ' ') { // b[1][charToInt(c[k])] = true; // } // } // for(int k = i; k < j; k ++) { // if(c[k] == ' ') { // ok &= (k - i) % 2 != 0; // }else { // b[(k - i) % 2 == 0 ? 0 : 1][charToInt(c[k])] = true; // } // } // for(int k = j; k < num; k ++) { // if(c[k] != ' ') { // b[1][charToInt(c[k])] = true; // } // } // for(int k = 0; k < 26; k ++) { // ok &= !b[0][k] || !b[1][k]; // } // ans |= ok; // } // } // prtln(ans ? "Yes" : "NO"); } } }