Problem: This is an interactive problem.

You're given a tree consisting of n nodes, rooted at node 1. A tree is a connected graph with no cycles.

We chose a hidden node x. In order to find this node, you can ask queries of two types: 

  * d u (1 ≤ u ≤ n). We will answer with the distance between nodes u and x. The distance between two nodes is the number of edges in the shortest path between them. 
  * s u (1 ≤ u ≤ n). We will answer with the second node on the path from u to x. However, there's a plot twist. If u is not an ancestor of x, you'll receive "Wrong answer" verdict! 



Node a is called an ancestor of node b if a ≠ b and the shortest path from node 1 to node b passes through node a. Note that in this problem a node is not an ancestor of itself.

Can you find x in no more than 36 queries? The hidden node is fixed in each test beforehand and does not depend on your queries.

Input

The first line contains the integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of nodes in the tree.

Each of the next n-1 lines contains two space-separated integers u and v (1 ≤ u,v ≤ n) that mean there's an edge between nodes u and v. It's guaranteed that the given graph is a tree.

Output

To print the answer, print "! x" (without quotes).

Interaction

To ask a question, print it in one of the formats above: 

  * d u (1 ≤ u ≤ n), or 
  * s u (1 ≤ u ≤ n). 



After each question, you should read the answer: either the distance or the second vertex on the path, as mentioned in the legend. 

If we answer with -1 instead of a valid answer, that means you exceeded the number of queries, made an invalid query, or violated the condition in the second type of queries. Exit immediately after receiving -1 and you will see Wrong answer verdict. Otherwise, you can get an arbitrary verdict because your solution will continue to read from a closed stream.

After printing a query, do not forget to output end of line and flush the output. Otherwise, you will get Idleness limit exceeded. To do this, use:

  * fflush(stdout) or cout.flush() in C++;
  * System.out.flush() in Java;
  * flush(output) in Pascal;
  * stdout.flush() in Python;
  * See the documentation for other languages.



Hacks:

The first line should contain two integers n and x (2 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ x ≤ n).

Each of the next n-1 lines should contain two integers u and v (1 ≤ u,v ≤ n) that mean there is an edge between nodes u and v. The edges must form a tree.

Example

Input


5
1 2
1 3
3 4
3 5
3
5

Output


d 2
s 3
! 5

Note

In the first example, the hidden node is node 5.

<image>

We first ask about the distance between node x and node 2. The answer is 3, so node x is either 4 or 5. We then ask about the second node in the path from node 3 to node x. Note here that node 3 is an ancestor of node 5. We receive node 5 as the answer. Finally, we report that the hidden node is node 5.

Solution (in JAVA):

Solution:

import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.math.BigInteger;
import java.nio.charset.Charset;
import java.util.*;

public class CFContest {
    public static void main(String[] args) throws Exception {
        boolean local = false;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\DATABASE\\TESTCASE\\Code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        int inf = (int) 1e8;
        MathUtils.BitOperator bitOperator = new MathUtils.BitOperator();

        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        int depth;

        @Override
        public void run() {
            solve();
        }

        int where;

        public void solve() {
            int n = io.readInt();
            Node[] nodes = new Node[n + 1];
            for (int i = 1; i <= n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }
            for (int i = 1; i < n; i++) {
                Node a = nodes[io.readInt()];
                Node b = nodes[io.readInt()];
                a.next.add(b);
                b.next.add(a);
            }
            dfs(nodes[1], null, 0);

            io.cache.append("d ").append(1).append('\n');
            io.flush();
            where = io.readInt();

            find(nodes[1]);
        }

        public void dfs(Node root, Node father, int depth) {
            root.size = 1;
            root.depth = depth;
            for (Node node : root.next) {
                if (node == father) {
                    continue;
                }
                dfs(node, root, depth + 1);
                root.size += node.size;
            }
        }

        public Node findCenter(Node root, Node father, int totalSize) {
            int max = totalSize - root.size;
            for (Node node : root.next) {
                if (node == father) {
                    continue;
                }
                max = Math.max(max, node.size);
                Node result = findCenter(node, root, totalSize);
                if (result != null) {
                    return result;
                }
            }
            if (max <= totalSize / 2) {
                return root;
            }
            return null;
        }

        public void findSize(Node root, Node father) {
            root.size = 1;
            for (Node node : root.next) {
                if (node == father) {
                    continue;
                }
                findSize(node, root);
                root.size += node.size;
            }
        }

        public void findTop(Node root) {
            for (Node node : root.next) {
                if (node.depth == root.depth - 1) {
                    node.next.remove(root);
                    find(node);
                    return;
                }
            }
        }

        public void find(Node root) {
            findSize(root, null);
            root = findCenter(root, null, root.size);

            if (root.depth > where) {
                findTop(root);
                return;
            }

            io.cache.append("d ").append(root.id).append('\n');
            io.flush();
            int dist = io.readInt();
            if (dist == 0) {
                io.cache.append("! ").append(root.id).append('\n');
                return;
            }

            if (where - root.depth != dist) {
                findTop(root);
                return;
            }

            io.cache.append("s ").append(root.id).append('\n');
            io.flush();
            int id = io.readInt();
            for (Node node : root.next) {
                if (node.id == id) {
                    node.next.remove(root);
                    find(node);
                    return;
                }
            }
        }
    }


    public static class Node {
        List<Node> next = new ArrayList<>(2);
        int size;
        int id;
        int depth;

        @Override
        public String toString() {
            return "" + id;
        }
    }


    public static class MathUtils {
        private static Random random = new Random(123456789);

        public static class ExtLucasFactorial {
            int exp;
            int fact;
            int p;
            int pc;
            Modular modular;
            Power power;
            ExtGCD extGCD = new ExtGCD();
            int[] g;

            /**
             * O(pc)
             *
             * @param p  the prime
             * @param pc p^c
             * @param g  buffer
             */
            public ExtLucasFactorial(int p, int pc, int[] g) {
                this.p = p;
                this.pc = pc;
                this.g = g;
                modular = new Modular(pc);
                power = new Power(modular);
                g[0] = 1;
                g[1] = 1;
                for (int i = 2; i <= pc; i++) {
                    if (i % p == 0) {
                        g[i] = g[i - 1];
                    } else {
                        g[i] = modular.mul(g[i - 1], i);
                    }
                }
            }

            /**
             * return m! (mod pc) without any factor which is multiple of p.
             * <br>
             * O(\log_2^2{m})
             */
            private int fact(long m) {
                fact = 1;
                exp = 0;
                while (m > 1) {
                    exp += m / p;
                    fact = modular.mul(fact, power.pow(g[pc], m / pc));
                    fact = modular.mul(fact, g[(int) (m % pc)]);
                    m /= p;
                }
                return fact;
            }

            /**
             * Find C(m,n), it means choose n elements from a set whose size is m.
             * <br>
             * O(\log_2^2{m})
             */
            public int composite(long m, long n) {
                int v = fact(m);
                int e = exp;
                extGCD.extgcd(fact(n), pc);
                v = modular.mul(v, modular.valueOf(extGCD.getX()));
                e -= exp;
                extGCD.extgcd(fact(m - n), pc);
                v = modular.mul(v, modular.valueOf(extGCD.getX()));
                e -= exp;
                v = modular.mul(v, power.pow(p, e));
                return v;
            }
        }

        /**
         * 扩展卢卡斯算法
         */
        public static class ExtLucas {
            PollardRho pr = new PollardRho();
            Map<Integer, ExtLucasFactorial> factorialMap = new HashMap();

            public ExtLucas(int p) {
                Map<Integer, Integer> factors = pr.findAllFactors(p);
                for (Map.Entry<Integer, Integer> entry : factors.entrySet()) {
                    factorialMap.put(entry.getValue(), new ExtLucasFactorial(entry.getKey(), entry.getValue(), new int[entry.getValue() + 1]));
                }
            }

            /**
             * Get C(m, n) % p
             */
            public int composite(long m, long n) {
                ExtCRT extCRT = new ExtCRT();
                for (Map.Entry<Integer, ExtLucasFactorial> entry : factorialMap.entrySet()) {
                    extCRT.add(entry.getValue().composite(m, n), entry.getKey());
                }
                return (int) extCRT.r;
            }
        }

        /**
         * 扩展卢卡斯算法
         */
        public static class LongExtLucas {
            LongPollardRho pr = new LongPollardRho();
            Map<Integer, ExtLucasFactorial> factorialMap = new HashMap();

            public LongExtLucas(long p) {
                Map<Long, Long> factors = pr.findAllFactors(p);
                for (Map.Entry<Long, Long> entry : factors.entrySet()) {
                    factorialMap.put(entry.getValue().intValue(), new ExtLucasFactorial(entry.getKey().intValue(), entry.getValue().intValue(), new int[entry.getValue().intValue() + 1]));
                }
            }

            /**
             * Get C(m, n) % p
             */
            public int composite(long m, long n) {
                ExtCRT extCRT = new ExtCRT();
                for (Map.Entry<Integer, ExtLucasFactorial> entry : factorialMap.entrySet()) {
                    extCRT.add(entry.getValue().composite(m, n), entry.getKey());
                }
                return (int) extCRT.r;
            }
        }

        /**
         * 扩展欧几里得
         */
        public static class ExtGCD extends Gcd {
            private long x;
            private long y;

            public long getX() {
                return x;
            }

            public long getY() {
                return y;
            }

            /**
             * Get g = Gcd(a, b) and find a way to set x and y to match ax+by=g
             */
            public long extgcd(long a, long b) {
                if (a >= b) {
                    return extgcd0(a, b);
                } else {
                    long g = extgcd0(b, a);
                    long tmp = x;
                    x = y;
                    y = tmp;
                    return g;
                }
            }

            private long extgcd0(long a, long b) {
                if (b == 0) {
                    x = 1;
                    y = 0;
                    return a;
                }
                long g = extgcd0(b, a % b);
                long n = x;
                long m = y;
                x = m;
                y = n - m * (a / b);
                return g;
            }
        }

        public static class Gcd {
            public long gcd(long a, long b) {
                return a >= b ? gcd0(a, b) : gcd0(b, a);
            }

            private long gcd0(long a, long b) {
                return b == 0 ? a : gcd0(b, a % b);
            }

            public int gcd(int a, int b) {
                return a >= b ? gcd0(a, b) : gcd0(b, a);
            }

            private int gcd0(int a, int b) {
                return b == 0 ? a : gcd0(b, a % b);
            }
        }

        /**
         * 欧拉筛
         */
        public static class EulerSieve {
            int[] primes;
            boolean[] isComp;
            int primeLength;

            public EulerSieve(int limit) {
                isComp = new boolean[limit + 1];
                primes = new int[limit + 1];
                primeLength = 0;
                for (int i = 2; i <= limit; i++) {
                    if (!isComp[i]) {
                        primes[primeLength++] = i;
                    }
                    for (int j = 0, until = limit / i; j < primeLength && primes[j] <= until; j++) {
                        int pi = primes[j] * i;
                        isComp[pi] = true;
                        if (i % primes[j] == 0) {
                            break;
                        }
                    }
                }
            }
        }

        /**
         * 模运算
         */
        public static class Modular {
            final int m;

            public Modular(int m) {
                this.m = m;
            }

            public int valueOf(int x) {
                x %= m;
                if (x < 0) {
                    x += m;
                }
                return x;
            }

            public int valueOf(long x) {
                x %= m;
                if (x < 0) {
                    x += m;
                }
                return (int) x;
            }

            public int mul(int x, int y) {
                return valueOf((long) x * y);
            }

            public int plus(int x, int y) {
                return valueOf(x + y);
            }

            @Override
            public String toString() {
                return "mod " + m;
            }
        }

        /**
         * 位运算
         */
        public static class BitOperator {
            public int bitAt(int x, int i) {
                return (x >> i) & 1;
            }

            public int bitAt(long x, int i) {
                return (int) ((x >> i) & 1);
            }

            public int setBit(int x, int i, boolean v) {
                if (v) {
                    x |= 1 << i;
                } else {
                    x &= ~(1 << i);
                }
                return x;
            }

            public long setBit(long x, int i, boolean v) {
                if (v) {
                    x |= 1L << i;
                } else {
                    x &= ~(1L << i);
                }
                return x;
            }
        }

        /**
         * 幂运算
         */
        public static class Power {
            final Modular modular;

            public Power(Modular modular) {
                this.modular = modular;
            }

            public int pow(int x, long n) {
                if (n == 0) {
                    return 1;
                }
                long r = pow(x, n >> 1);
                r = modular.valueOf(r * r);
                if ((n & 1) == 1) {
                    r = modular.valueOf(r * x);
                }
                return (int) r;
            }

            public int inverse(int x) {
                return pow(x, modular.m - 2);
            }

            public int pow2(int x) {
                return x * x;
            }

            public long pow2(long x) {
                return x * x;
            }

            public double pow2(double x) {
                return x * x;
            }
        }

        /**
         * 对数
         */
        public static class Log2 {
            public int ceilLog(int x) {
                return 32 - Integer.numberOfLeadingZeros(x - 1);
            }

            public int floorLog(int x) {
                return 31 - Integer.numberOfLeadingZeros(x);
            }

            public int ceilLog(long x) {
                return 64 - Long.numberOfLeadingZeros(x - 1);
            }

            public int floorLog(long x) {
                return 63 - Long.numberOfLeadingZeros(x);
            }
        }

        /**
         * 乘法逆元
         */
        public static class InverseNumber {
            int[] inv;

            public InverseNumber(int[] inv, int limit, Modular modular) {
                this.inv = inv;
                inv[1] = 1;
                int p = modular.m;
                for (int i = 2; i <= limit; i++) {
                    int k = p / i;
                    int r = p % i;
                    inv[i] = modular.mul(-k, inv[r]);
                }
            }

            public InverseNumber(int limit, Modular modular) {
                this(new int[limit + 1], limit, modular);
            }
        }

        /**
         * 排列
         */
        public static class Factorial {
            int[] fact;
            int[] inv;

            public Factorial(int[] fact, int[] inv, InverseNumber in, int limit, Modular modular) {
                this.fact = fact;
                this.inv = inv;
                fact[0] = inv[0] = 1;
                for (int i = 1; i <= limit; i++) {
                    fact[i] = modular.mul(fact[i - 1], i);
                    inv[i] = modular.mul(inv[i - 1], in.inv[i]);
                }
            }

            public Factorial(int limit, Modular modular) {
                this(new int[limit + 1], new int[limit + 1], new InverseNumber(limit, modular), limit, modular);
            }
        }

        /**
         * 组合
         */
        public static class Composite {
            final Factorial factorial;
            final Modular modular;

            public Composite(Factorial factorial, Modular modular) {
                this.factorial = factorial;
                this.modular = modular;
            }

            public Composite(int limit, Modular modular) {
                this(new Factorial(limit, modular), modular);
            }

            public int composite(int m, int n) {
                if (n > m) {
                    return 0;
                }
                return modular.mul(modular.mul(factorial.fact[m], factorial.inv[n]), factorial.inv[m - n]);
            }
        }

        /**
         * 大素数测试
         */
        public static class MillerRabin {
            Modular modular;
            Power power;

            /**
             * 判断n是否是素数
             */
            public boolean mr(int n, int s) {
                if (n == 2) {
                    return true;
                }
                if (n % 2 == 0) {
                    return false;
                }
                modular = new Modular(n);
                power = new Power(modular);
                for (int i = 0; i < s; i++) {
                    int x = random.nextInt(n - 2) + 2;
                    if (!mr0(x, n)) {
                        return false;
                    }
                }
                return true;
            }

            private boolean mr0(int x, int n) {
                int exp = n - 1;
                while (true) {
                    int y = power.pow(x, exp);
                    if (y != 1 && y != n - 1) {
                        return false;
                    }
                    if (y != 1 || exp % 2 == 1) {
                        break;
                    }
                    exp = exp / 2;
                }
                return true;
            }
        }


        public static class LongModular {
            final long m;

            public LongModular(long m) {
                this.m = m;
            }

            public long mul(long a, long b) {
                return b == 0 ? 0 : ((mul(a, b >> 1) << 1) % m + a * (b & 1)) % m;
            }

            public long plus(long a, long b) {
                return valueOf(a + b);
            }

            public long valueOf(long a) {
                a %= m;
                if (a < 0) {
                    a += m;
                }
                return a;
            }
        }

        public static class LongPower {
            final LongModular modular;

            public LongPower(LongModular modular) {
                this.modular = modular;
            }

            long pow(long x, long n) {
                if (n == 0) {
                    return 1;
                }
                long r = pow(x, n >> 1);
                r = modular.mul(r, r);
                if ((n & 1) == 1) {
                    r = modular.mul(r, x);
                }
                return r;
            }

            long inverse(long x) {
                return pow(x, modular.m - 2);
            }
        }

        /**
         * 大素数测试
         */
        public static class LongMillerRabin {
            LongModular modular;
            LongPower power;

            /**
             * 判断n是否是素数
             */
            public boolean mr(long n, int s) {
                if (n == 2) {
                    return true;
                }
                if (n % 2 == 0) {
                    return false;
                }
                modular = new LongModular(n);
                power = new LongPower(modular);
                for (int i = 0; i < s; i++) {
                    long x = (long) (random.nextDouble() * (n - 2) + 2);
                    if (!mr0(x, n)) {
                        return false;
                    }
                }
                return true;
            }

            private boolean mr0(long x, long n) {
                long exp = n - 1;
                while (true) {
                    long y = power.pow(x, exp);
                    if (y != 1 && y != n - 1) {
                        return false;
                    }
                    if (y != 1 || exp % 2 == 1) {
                        break;
                    }
                    exp = exp / 2;
                }
                return true;
            }
        }

        public static class LongPollardRho {
            LongMillerRabin mr = new LongMillerRabin();
            Gcd gcd = new Gcd();
            LongModular modular;

            /**
             * Find a factor of n, if n is returned, it means n is 1 or a prime
             */
            public long findFactor(long n) {
                if (mr.mr(n, 3)) {
                    return n;
                }
                modular = new LongModular(n);
                while (true) {
                    long f = findFactor0((long) (random.nextDouble() * n), (long) (random.nextDouble() * n), n);
                    if (f != -1) {
                        return f;
                    }
                }
            }

            private long findFactor0(long x, long c, long n) {
                long xi = x;
                long xj = x;
                int j = 2;
                int i = 1;
                while (i < n) {
                    i++;
                    xi = modular.plus(modular.mul(xi, xi), c);
                    long g = gcd.gcd(n, Math.abs(xi - xj));
                    if (g != 1 && g != n) {
                        return g;
                    }
                    if (i == j) {
                        j = j << 1;
                        xj = xi;
                    }
                }
                return -1;
            }

            /**
             * Find the representation of n=p1^c1 * p2^c2 * ... * pm ^ cm.
             * <br>
             * The returned map contained such entries: pi -> pi^ci
             */
            public Map<Long, Long> findAllFactors(long n) {
                Map<Long, Long> map = new HashMap();
                findAllFactors(map, n);
                return map;
            }

            private void findAllFactors(Map<Long, Long> map, long n) {
                if (n == 1) {
                    return;
                }
                long f = findFactor(n);
                if (f == n) {
                    Long value = map.get(f);
                    if (value == null) {
                        value = 1L;
                    }
                    map.put(f, value * f);
                    return;
                }
                findAllFactors(map, f);
                findAllFactors(map, n / f);
            }

        }

        /**
         * 扩展中国余数定理
         */
        public static class ExtCRT {
            /**
             * remainder
             */
            long r;
            /**
             * modulus
             */
            long m;
            ExtGCD gcd = new ExtGCD();

            public ExtCRT() {
                r = 0;
                m = 1;
            }

            /**
             * Add a new condition: x % m = r
             */
            public boolean add(long r, long m) {
                long m1 = this.m;
                long x1 = this.r;
                long m2 = m;
                long x2 = ((r % m) + m) % m;
                long g = gcd.extgcd(m1, m2);
                long a = gcd.getX();
                if ((x2 - x1) % g != 0) {
                    return false;
                }
                this.m = m1 / g * m2;
                this.r = BigInteger.valueOf(a).multiply(BigInteger.valueOf((x2 - x1) / g))
                        .multiply(BigInteger.valueOf(m1)).add(BigInteger.valueOf(x1))
                        .mod(BigInteger.valueOf(this.m)).longValue();
                return true;
            }
        }

        /**
         * 卢卡斯定理
         */
        public static class Lucas {
            private final Composite composite;
            private int modulus;

            public Lucas(Composite composite) {
                this.composite = composite;
                this.modulus = composite.modular.m;
            }

            public int composite(long m, long n) {
                if (n == 0) {
                    return 1;
                }
                return composite.modular.mul(composite.composite((int) (m % modulus), (int) (n % modulus)),
                        composite(m / modulus, n / modulus));
            }
        }

        /**
         * 因式分解
         */
        public static class PollardRho {
            MillerRabin mr = new MillerRabin();
            Gcd gcd = new Gcd();
            Random random = new Random(123456789);

            public int findFactor(int n) {
                if (mr.mr(n, 10)) {
                    return n;
                }
                while (true) {
                    int f = findFactor0(random.nextInt(n), random.nextInt(n), n);
                    if (f != -1) {
                        return f;
                    }
                }
            }

            public Map<Integer, Integer> findAllFactors(int n) {
                Map<Integer, Integer> map = new HashMap();
                findAllFactors(map, n);
                return map;
            }

            private void findAllFactors(Map<Integer, Integer> map, int n) {
                if (n == 1) {
                    return;
                }
                int f = findFactor(n);
                if (f == n) {
                    Integer value = map.get(f);
                    if (value == null) {
                        value = 1;
                    }
                    map.put(f, value * f);
                    return;
                }
                findAllFactors(map, f);
                findAllFactors(map, n / f);
            }

            private int findFactor0(int x, int c, int n) {
                int xi = x;
                int xj = x;
                int j = 2;
                int i = 1;
                while (i < n) {
                    i++;
                    xi = (int) ((long) xi * xi + c) % n;
                    int g = gcd.gcd(n, Math.abs(xi - xj));
                    if (g != 1 && g != n) {
                        return g;
                    }
                    if (i == j) {
                        j = j << 1;
                        xj = xi;
                    }
                }
                return -1;
            }
        }
    }

    public static class FastIO {
        public final StringBuilder cache = new StringBuilder();
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        public FastIO(InputStream is, OutputStream os) {
            this(is, os, Charset.forName("ascii"));
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public double readDouble() {
            boolean sign = true;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+';
                next = read();
            }

            long val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            if (next != '.') {
                return sign ? val : -val;
            }
            next = read();
            long radix = 1;
            long point = 0;
            while (next >= '0' && next <= '9') {
                point = point * 10 + next - '0';
                radix = radix * 10;
                next = read();
            }
            double result = val + (double) point / radix;
            return sign ? result : -result;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

        public int readLine(char[] data, int offset) {
            int originalOffset = offset;
            while (next != -1 && next != '\n') {
                data[offset++] = (char) next;
                next = read();
            }
            return offset - originalOffset;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

        public void flush() {
            try {
                os.write(cache.toString().getBytes(charset));
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        public void assertTrue(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (!flag) {
                fail();
            }
        }

        public void fail() {
            throw new RuntimeException();
        }

        public void assertFalse(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (flag) {
                fail();
            }
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}