import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.ArrayDeque; import java.util.ArrayList; import java.util.Comparator; import java.util.List; import java.util.NoSuchElementException; //@Japanese /* PriorityQueueは拡張for文で出すとsortされてない順番で出てくる * longのbit演算は1L<=0; i--) { as[i]--; bs[i]--; int l1 = min(as[i], bs[i]); int r1 = max(as[i], bs[i]); int llas = max(lban[i+1]-1,-1); if(l1==(llas+1)) llas++; if(r1==(llas+1)) llas++; lban[i]=llas; int rlas = min(rban[i+1]+1,n); if(r1==(rlas-1)) rlas--; if(l1==(rlas-1)) rlas--; rban[i]=rlas; if(llas == (n-1)) { possi=false; break; } if(rlas == 0) { possi = false; break; } } /* for(int i=0; i=0) { for(int j=0; j<=lban[i]; j++) { out.print("X"); } } if(max(lban[i]+1,0)pos) p1=false; if(lban[i]>=pos) z=false; if((lban[i]+1)>=pos) m1=false; if(rban[i]= 0) ? a : -a; } private static long abs(long a) { return (a >= 0L) ? a : -a; } private static double abs(double a) { return (a >= 0.0) ? a : -a; } private static int min(int a, int b) { return (a < b) ? a : b; } private static long min(long a, long b) { return (a < b) ? a : b; } private static double min(double a, double b) { return (a < b) ? a : b; } private static int max(int a, int b) { return (a > b) ? a : b; } private static long max(long a, long b) { return (a > b) ? a : b; } private static double max(double a, double b) { return (a > b) ? a : b; } private static int pow2(int num2pow) { if (num2pow > 4e4) throw new IllegalArgumentException("Input is to Large. Use Long."); return num2pow * num2pow; } private static long pow2(long num2pow) { if (num2pow > 1e8) throw new IllegalArgumentException("Input is to Large. Use PowP."); return num2pow * num2pow; } private static int pow(int num_powered, int index) { int ans = 1; for (int i = 0; i < index; i++) { if (ans >= (INTMAX / num_powered)) throw new IllegalArgumentException("Input is to Large. Use Long."); ans *= num_powered; } return ans; } private static long pow(long num_powered, int index) { long ans = 1L; for (int i = 0; i < index; i++) { if (ans >= (LONGMAX / num_powered)) throw new IllegalArgumentException("Input is to Large. Use PowP."); ans *= num_powered; } return ans; } private static long powP(long num_powered, long index, long p) { // O(log(index)) // @Japanese 繰り返し二乗法 if (num_powered == 0L) return 0L; if (index == 0L) return 1L; if (index == 2L) { return (pow2(num_powered) % p); } int d = getDigit2(index); long[] num_done_by2 = new long[d + 1]; num_done_by2[0] = num_powered; for (int i = 1; i <= d; i++) { num_done_by2[i] = num_done_by2[i - 1] * num_done_by2[i - 1]; num_done_by2[i] %= p; } long ans = 1L; for (int i = d; i >= 0; i--) { long cf = (1L << (long) i); if (index >= cf) { index -= cf; ans = ans * num_done_by2[i]; ans %= p; } } return ans; } private static double hypod(double a, double b) { return Math.sqrt(a * a + b * b); } private static int getDigit2(long num2know) { // O(log(n)) long compare4 = 1L; int digit = 0; while (num2know >= compare4) { digit++; compare4 = (1L << (long) digit); } return digit; // num < 2^digit } private static int getDigit10(long num2know) { // O(log10(n)) if(num2know<0L) throw new IllegalArgumentException("Input is Negative"); if(num2know>=1000000000000000000L) return 19; long compare4 = 1L; int digit = 0; while (num2know >= compare4) { digit++; compare4 *= 10L; } return digit; // @Japanese num は digit桁の数で、10^digit未満 } private static int divceil(int numerator, int denominator) { return (numerator + denominator - 1) / denominator; } private static long divceil(long numerator, long denominator) { return (numerator + denominator - 1L) / denominator; } private static long factorial(int n) { // O(n) long ans = 1L; for (long i = 2; i <= n; i++) { if (ans >= (LONGMAX / i)) throw new IllegalArgumentException("Input is to Large. Use facP."); ans *= i; } return ans; } private static long facP(int n, long p) { // O(n) see also PermulationCombination:O(max_sz)+Q long ans = 1L; for (long i = 2; i <= n; i++) { ans *= i; ans %= p; } return ans; } private static long lcm(long m, long n) { long ans = m / gcd(m, n); if (ans >= (LONGMAX / n)) throw new IllegalArgumentException("Input is to Large."); ans *= n; return ans; } private static long gcd(long m, long n) { // O(log(m+n)) if ((m <= 0L) || (n <= 0L)) throw new IllegalArgumentException("m and n should be natural."); while ((m > 0L) && (n > 0L)) { if (m >= n) m %= n; else n %= m; } if (m > 0L) return m; else return n; } private static boolean is_prime(long n2check) { // @Japanese O(√n) if (n2check == 1L) return false; for (long i = 2L; i <= Math.sqrt(n2check); i++) { if (n2check % i == 0L) return false; } return true; } private static int isSquare(long n) { double sq = Math.sqrt(n); long ans = (long)sq; if((ans *ans) == n) return (int)ans; else return -1; } private static int safe_mod(int n, int p) { n %= p; if (n >= 0) return n; return (n + p); } private static long safe_mod(long n, long p) { n %= p; if (n >= 0L) return n; return (n + p); } private static long modinv(long n, long p) { // @Japanese 逆元を求める // O(10log(n)) // pは素数でなくてもよい // ネットから拾ってきたのが理解不能だったので、行列計算を用いて非効率的アルゴリズムを書いた n %= p; if ((p == 1L) || (gcd(n, p) != 1L)) throw new IllegalArgumentException("n and p should be coprime."); // @Japanese // yn≡1(mod p) // <-> xp+yn=1; (n 1) { long quo = a / b, rem = a % b; a = b; b = rem; long s2 = s * quo + u, t2 = t * quo + v; u = s; v = t; s = s2; t = t2; } long det = s * v - t * u; if (abs(det) != 1L) throw new ArithmeticException("My algorithm was Wrong!!"); s /= det; s %= p; if (s < 0L) s += p; return s; } private static int minAll(int[] dt4min) { // O(n) int min = INF; for (int element : dt4min) { if (element < min) min = element; } return min; } private static long minAll(long[] dt4min) { // O(n) long min = INFL; for (long element : dt4min) { if (element < min) min = element; } return min; } private static int maxAll(int[] dt4max) { // O(n) int max = -INF; for (int element : dt4max) { if (element > max) max = element; } return max; } private static long maxAll(long[] dt4max) { // O(n) long max = -INFL; for (long element : dt4max) { if (element > max) max = element; } return max; } private static int sumAll(int[] dt4sum) { // O(n) int sum_of_dt = 0; for (int element : dt4sum) { if (sum_of_dt > (INTMAX - element)) throw new IllegalArgumentException("Input is to Large. Use Long."); sum_of_dt += element; } return sum_of_dt; } private static long sumAll(long[] dt4sum) { // O(n) long sum_of_dt = 0L; for (long element : dt4sum) { if (sum_of_dt > (LONGMAX - element)) throw new IllegalArgumentException("Input is to Large."); sum_of_dt += element; } return sum_of_dt; } private static int sumAll(ArrayList dt4sum) { int sum_of_dt = 0; for (long element : dt4sum) { if (sum_of_dt > (INTMAX - element)) throw new IllegalArgumentException("Input is to Large. Use Long."); sum_of_dt += element; } return sum_of_dt; } private static int[] reverse(int[] as) { int ln = as.length; int[] bs = new int[ln]; for (int i = 0; i < ln; i++) bs[i] = as[ln - i - 1]; return bs; } private static void reverseSub(int[] as, int S_include, int Gnot_include) { // O(G-S) int ln = Gnot_include - S_include; int[] bs = new int[ln]; for (int i = S_include; i < Gnot_include; i++) bs[i - S_include] = as[i]; for (int i = 0; i < ln; i++) as[i + S_include] = bs[ln - i - 1]; } private static boolean is_in_area(int y, int x, int height, int width) { if (y < 0) return false; if (x < 0) return false; if (y >= height) return false; if (x >= width) return false; return true; } private static boolean is_in_area(Vector v, int height, int width) { if (v.y < 0) return false; if (v.x < 0) return false; if (v.y >= height) return false; if (v.x >= width) return false; return true; } private static int nC2(int n) { return ((n * (n - 1)) / 2); } private static long nC2(long n) { return ((n * (n - 1L)) / 2L); } private static int iflag(int pos) { if (pos >= 32) throw new IllegalArgumentException("Input is to Large. Use Long."); return (1 << pos); } private static long flag(int pos) { if (pos >= 64) throw new IllegalArgumentException("Input is to Large. Use Long."); return (1L << (long) pos); } private static boolean isFlaged(int bit, int pos) { if (pos >= 32) throw new IllegalArgumentException("Input is to Large."); return ((bit & (1 << pos)) != 0); } private static boolean isFlaged(long bit, int pos) { if (pos >= 64) throw new IllegalArgumentException("Input is to Large."); return ((bit & (1L << (long) pos)) != 0L); } private static int deflag(int bit, int pos) { return (bit & (~(1 << pos))); } private static int countFlaged(int bit) { int ans = 0; for (int i = 0; i < 31; i++) { if ((bit & (1 << i)) != 0) ans++; } return ans; } private static int countFlaged(long bit) { int ans = 0; for (long i = 0L; i < 63L; i++) { if ((bit & (1L << i)) != 0L) ans++; } return ans; } private static int[] Xdir4 = { 1, 0, 0, -1 }; private static int[] Ydir4 = { 0, 1, -1, 0 }; private static int[] Xdir8 = { 1, 1, 1, 0, 0, -1, -1, -1 }; private static int[] Ydir8 = { 1, 0, -1, 1, -1, 1, 0, -1 }; public static int biSearch(int[] dt, int target) { // O(log(dt.length)) // dt should be sorted in 0->INF // return adress of target int left = 0, right = dt.length - 1; int mid = -1; while (left <= right) { mid = ((right + left) / 2); if (dt[mid] == target) return mid; if (dt[mid] < target) left = (mid + 1); else right = (mid - 1); } return -1; } public static int biSearchMax(long[] dt, long target) { // O(log(dt.length)) // dt should be sorted in 0->INF int left = -1, right = dt.length, mid = -1; while ((right - left) > 1) { mid = ((right + left) / 2); if (dt[mid] <= target) left = mid; else right = mid; } return left; // @Japanese target以下の最大のaddress } public static int biSearchMin(long[] dt, long target) { // O(log(dt.length)) // dt should be sorted in 0->INF int left = -1, right = dt.length, mid = -1; while ((right - left) > 1) { mid = ((right + left) / 2); if (dt[mid] <= target) left = mid; else right = mid; } return right; // @Japanese targetより大きい最小のaddress } private static void fill(boolean[] target, boolean reset) { for (int i = 0; i < target.length; i++) target[i] = reset; } private static void fill(int[] target, int reset) { for (int i = 0; i < target.length; i++) target[i] = reset; } private static void fill(long[] target, long reset) { for (int i = 0; i < target.length; i++) target[i] = reset; } private static void fill(char[] target, char reset) { for (int i = 0; i < target.length; i++) target[i] = reset; } private static void fill(double[] target, double reset) { for (int i = 0; i < target.length; i++) target[i] = reset; } private static void fill(boolean[][] target, boolean reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { target[i][j] = reset; } } } private static void fill(int[][] target, int reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { target[i][j] = reset; } } } private static void fill(long[][] target, long reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { target[i][j] = reset; } } } private static void fill(char[][] target, char reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { target[i][j] = reset; } } } private static void fill(double[][] target, double reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { target[i][j] = reset; } } } private static void fill(int[][][] target, int reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { for (int k = 0; k < target[i][j].length; k++) { target[i][j][k] = reset; } } } } private static void fill(long[][][] target, long reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { for (int k = 0; k < target[i][j].length; k++) { target[i][j][k] = reset; } } } } private static void fill(double[][][] target, double reset) { for (int i = 0; i < target.length; i++) { for (int j = 0; j < target[i].length; j++) { for (int k = 0; k < target[i][j].length; k++) { target[i][j][k] = reset; } } } } private static void fill_parent(int[] parent) { for (int i = 0; i < parent.length; i++) { parent[i] = i; } } private static void showBit(int bit) { for (int i = 0; i < getDigit2(bit); i++) { if (isFlaged(bit, i)) System.out.print("O"); else System.out.print("."); } System.out.println(); } private static void showBit(long bit) { for (int i = 0; i < getDigit2(bit); i++) { if (isFlaged(bit, i)) System.out.print("O"); else System.out.print("."); } System.out.println(); } static void show2(boolean[][] dt, String cmnt) { for (int i = 0; i < dt.length; i++) { for (int j = 0; j < dt[i].length; j++) { if (dt[i][j]) System.out.print("O"); else System.out.print("."); } if (!cmnt.equals("")) System.out.print("<-" + cmnt); System.out.println(" :" + i); } } static void show2(int[][] dt, String cmnt) { for (int i = 0; i < dt.length; i++) { for (int j = 0; j < dt[i].length; j++) System.out.print(dt[i][j] + ","); if (!cmnt.equals("")) System.out.print("<-" + cmnt); System.out.println(" :" + i); } } static void show2(long[][] dt, String cmnt) { for (int i = 0; i < dt.length; i++) { for (int j = 0; j < dt[i].length; j++) System.out.print(dt[i][j] + ","); if (!cmnt.equals("")) System.out.print("<-" + cmnt); System.out.println(" :" + i); } } static void show2(ArrayDeque dt) { long element = 0; while (dt.size() > 0) { element = dt.removeFirst(); System.out.print(element); } System.out.println("\n"); } static void show2(List dt) { for (int i = 0; i < dt.size(); i++) System.out.print(dt.get(i) + ","); System.out.println("\n"); } private static void prtlnas(int[] array, PrintWriter out) { for (int e: array) out.println(e); out.flush(); } private static void prtlnas(long[] array, PrintWriter out) { for (long e: array) out.println(e); out.flush(); } private static void prtlnas(ArrayList array, PrintWriter out) { for (Object e: array) out.println(e); out.flush(); } private static void prtspas(int[] array, PrintWriter out) { out.print(array[0]); for (int i = 1; i < array.length; i++) out.print(" " + array[i]); out.println(); out.flush(); } private static void prtspas(long[] array, PrintWriter out) { out.print(array[0]); for (int i = 1; i < array.length; i++) out.print(" " + array[i]); out.println(); out.flush(); } private static void prtspas(double[] array, PrintWriter out) { out.print(array[0]); for (int i = 1; i < array.length; i++) out.print(" " + array[i]); out.println(); out.flush(); } private static void prtspas(List array, PrintWriter out) { if (array.isEmpty()) return; out.print(array.get(0)); for (int i = 1; i < array.size(); i++) out.print(" " + array.get(i)); out.println(); out.flush(); } static class Vector { int x, y; public Vector(int sx, int sy) { this.x = sx; this.y = sy; } public boolean equals(Vector v) { return (this.x == v.x && this.y == v.y); } public void show2() { System.out.println(this.x + ", " + this.y); } public static int dist2(Vector a, Vector b) { int dx = abs(a.x - b.x); int dy = abs(a.y - b.y); if (dx > 3e4) throw new IllegalArgumentException("Input is to Large. Use Long."); if (dy > 3e4) throw new IllegalArgumentException("Input is to Large. Use Long."); return (dx * dx + dy * dy); } } static class CompVector implements Comparator { public int compare(Vector a, Vector b) { if (a.x == b.x) return a.y - b.y; else return a.x - b.x; } } static class FastScanner { //@Japanese ネットから拾ってきた。よく分からん。 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 static boolean isPrintableChar(int c) { return (33 <= c) && (c <= 126); } public boolean hasNext() { while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; 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 nexL() { 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) || b == ':') { return minus ? -n : n; } else { throw new NumberFormatException(); } b = readByte(); } } public int nexI() { long nl = nexL(); if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) { throw new NumberFormatException(); } return (int) nl; } public double nexD() { return Double.parseDouble(next()); } public int[] ai(int ln) { int[] as = new int[ln]; for (int i = 0; i < ln; i++) { as[i]=nexI(); } return as; } public long[] al(int ln) { long[] as = new long[ln]; for (int i = 0; i < ln; i++) { as[i]=nexL(); } return as; } // a means array public void ai(int[]... array) { for (int i = 0; i < array[0].length; i++) { for (int j = 0; j < array.length; j++) { array[j][i] = nexI(); } } return; } public void al(long[]... array) { for (int i = 0; i < array[0].length; i++) { for (int j = 0; j < array.length; j++) { array[j][i] = nexL(); } } return; } public void aimin1(int[] array) { for (int i = 0; i < array.length; i++) { array[i] = nexI() - 1; } return; } public void aD(double[]... array) { for (int i = 0; i < array[0].length; i++) { for (int j = 0; j < array.length; j++) { array[j][i] = nexD(); } } return; } public void ai2d(int[][] array) { for (int i = 0; i < array.length; i++) { for (int j = 0; j < array[0].length; j++) { array[i][j] = nexI(); } } return; } public void al2d(long[][] array) { for (int i = 0; i < array.length; i++) { for (int j = 0; j < array[0].length; j++) { array[i][j] = nexL(); } } return; } } } // END OF THE CODE