Problem: This is an interactive problem!

An arithmetic progression or arithmetic sequence is a sequence of integers such that the subtraction of element with its previous element (x_i - x_{i - 1}, where i ≥ 2) is constant — such difference is called a common difference of the sequence.

That is, an arithmetic progression is a sequence of form x_i = x_1 + (i - 1) d, where d is a common difference of the sequence.

There is a secret list of n integers a_1, a_2, …, a_n.

It is guaranteed that all elements a_1, a_2, …, a_n are between 0 and 10^9, inclusive.

This list is special: if sorted in increasing order, it will form an arithmetic progression with positive common difference (d > 0). For example, the list [14, 24, 9, 19] satisfies this requirement, after sorting it makes a list [9, 14, 19, 24], which can be produced as x_n = 9 + 5 ⋅ (n - 1).

Also you are also given a device, which has a quite discharged battery, thus you can only use it to perform at most 60 queries of following two types:

  * Given a value i (1 ≤ i ≤ n), the device will show the value of the a_i.
  * Given a value x (0 ≤ x ≤ 10^9), the device will return 1 if an element with a value strictly greater than x exists, and it will return 0 otherwise.



Your can use this special device for at most 60 queries. Could you please find out the smallest element and the common difference of the sequence? That is, values x_1 and d in the definition of the arithmetic progression. Note that the array a is not sorted.

Interaction

The interaction starts with a single integer n (2 ≤ n ≤ 10^6), the size of the list of integers.

Then you can make queries of two types:

  * "? i" (1 ≤ i ≤ n) — to get the value of a_i.
  * "> x" (0 ≤ x ≤ 10^9) — to check whether there exists an element greater than x



After the query read its result r as an integer.

  * For the first query type, the r satisfies 0 ≤ r ≤ 10^9. 
  * For the second query type, the r is either 0 or 1.
  * In case you make more than 60 queries or violated the number range in the queries, you will get a r = -1.
  * If you terminate after receiving the -1, you will get the "Wrong answer" verdict. Otherwise you can get an arbitrary verdict because your solution will continue to read from a closed stream. 



When you find out what the smallest element x_1 and common difference d, print

  * "! x_1 d" 



And quit after that. This query is not counted towards the 60 queries limit.

After printing any 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 documentation for other languages.



Hacks

For hack, use the following format:

The first line should contain an integer n (2 ≤ n ≤ 10^6) — the list's size.

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — the elements of the list.

Also, after the sorting the list must form an arithmetic progression with positive common difference.

Example

Input


4

0

1

14

24

9

19



Output



&gt; 25

&gt; 15

? 1

? 2

? 3

? 4

! 9 5

Note

Note that the example interaction contains extra empty lines so that it's easier to read. The real interaction doesn't contain any empty lines and you shouldn't print any extra empty lines as well.

The list in the example test is [14, 24, 9, 19].

Solution (in JAVA):

Solution:
//package baobab;

import java.io.*;
import java.util.*;

public class E {

    public static void main(String[] args) {
        Solver solver = new Solver();
    }

    static class Solver {
        IO io;

        public Solver() {
            this.io = new IO();
            try {
                solve();
            } catch (RuntimeException e) {
                if (!e.getMessage().equals("Clean exit")) {
                    throw e;
                }
            } finally {
                io.close();
            }
        }

        /****************************** START READING HERE ********************************/

        List<Long> sample = new ArrayList<>();

        void solve() {
            long n = io.nextInt();
            sample = new ArrayList<>();

            // special case
            if (n <= 60) {
                for (int i=1; i<=n; i++) {
                    sample.add(qGet(i));
                }
                Collections.sort(sample);
                System.out.println("! " + sample.get(0) + " " + (sample.get(1) - sample.get(0)));
                System.out.flush();
                return;
            }
            // normal case below




            // Get random sample
            int sampleSize = 30;
            Random rng = new Random();
            HashSet<Integer> tried = new HashSet<>();
            for (int i=1; i<=sampleSize; i++) {
                while (true) {
                    int index = rng.nextInt((int)n)+1;
                    if (!tried.add(index)) continue;
                    sample.add(qGet(index));
                    break;
                }
            }
            Collections.sort(sample);

            // Find out what is largest
            long largest = binSearch(sample.get(sample.size()-1), (long)1e9);

            // Knowing some diffs and the largest, narrow down possibilities
            List<Long> possible = new ArrayList<>();
            long minDiff = Integer.MAX_VALUE;
            for (int i=1; i<sample.size(); i++) {
                minDiff = Math.min(minDiff, sample.get(i)-sample.get(i-1));
            }
            long maxD = minDiff;
            for (int i=1; maxD/i>=1; i++) {
                long possibleD = maxD/i;
                if (maxD%i != 0) continue;
                if (!givenDExplainsAllDiffs(possibleD)) continue;
                long smallest = largest - (n-1) * possibleD;
                if (smallest < 0) continue;
                if (smallest > sample.get(0)) continue;
                possible.add(possibleD);
            }

            if (possible.isEmpty()) {
                System.out.println("Bug somewhere, possible is empty");
                return;
            }
            if (possible.size() > 1) {
                System.out.println("Logic may be wrong, more than 1 possibility remaining.");
                return;
            }

            long d = possible.get(0);
            long smallest = largest - (n-1) * d;
            System.out.println("! " + smallest + " " + d);
            System.out.flush();
        }

        boolean givenDExplainsAllDiffs(long d) {
            for (int j=1; j<sample.size(); j++) {
                long diff = sample.get(j) - sample.get(j-1);
                if (diff%d != 0) return false;
            }
            return true;
        }
        
        long binSearch(long min, long max) {
            while (min != max) {
                long guess = min+(max-min+1)/2;
                if (qExistAsLargeAs(guess)) {
                    min = guess;
                } else {
                    max = guess-1;
                }
            }
            return max;
        }        
        
        boolean qExistAsLargeAs(long x) {
            System.out.println("> " + (x-1));
            System.out.flush();
            int reply = io.nextInt();
            return (reply == 1);
        }

        long qGet(int i) {
            System.out.println("? " + i);
            System.out.flush();
            int reply = io.nextInt();
            return reply;
        }

        /************************** UTILITY CODE BELOW THIS LINE **************************/

        long MOD = (long)1e9 + 7;

        boolean closeToZero(double v) {
            // Check if double is close to zero, considering precision issues.
            return Math.abs(v) <= 0.0000000001;
        }

        void draw(boolean[][] d) {
            System.out.print("  ");
            for (int x=0; x<d[0].length; x++) {
                System.out.print(" " + x + " ");
            }
            System.out.println("");
            for (int y=0; y<d.length; y++) {
                System.out.print(y + " ");
                for (int x=0; x<d[0].length; x++) {
                    System.out.print((d[y][x] ? "[x]" : "[ ]"));
                }
                System.out.println("");
            }
        }

        void draw(int[][] d) {
            int max = 1;
            for (int y=0; y<d.length; y++) {
                for (int x=0; x<d[0].length; x++) {
                    max = Math.max(max, ("" + d[y][x]).length());
                }
            }
            System.out.print("  ");
            String format = "%" + (max+2) + "s";
            for (int x=0; x<d[0].length; x++) {
                System.out.print(String.format(format, x) + " ");
            }
            format = "%" + (max) + "s";
            System.out.println("");
            for (int y=0; y<d.length; y++) {
                System.out.print(y + " ");
                for (int x=0; x<d[0].length; x++) {
                    System.out.print(" [" + String.format(format, (d[y][x])) + "]");
                }
                System.out.println("");
            }
        }

        void draw(long[][] d) {
            int max = 1;
            for (int y=0; y<d.length; y++) {
                for (int x=0; x<d[0].length; x++) {
                    max = Math.max(max, ("" + d[y][x]).length());
                }
            }
            System.out.print("  ");
            String format = "%" + (max+2) + "s";
            for (int x=0; x<d[0].length; x++) {
                System.out.print(String.format(format, x) + " ");
            }
            format = "%" + (max) + "s";
            System.out.println("");
            for (int y=0; y<d.length; y++) {
                System.out.print(y + " ");
                for (int x=0; x<d[0].length; x++) {
                    System.out.print(" [" + String.format(format, (d[y][x])) + "]");
                }
                System.out.println("");
            }
        }

        class IDval implements Comparable<IDval> {
            int id;
            long val;

            public IDval(int id, long val) {
                this.val = val;
                this.id = id;
            }

            @Override
            public int compareTo(IDval o) {
                if (this.val < o.val) return -1;
                if (this.val > o.val) return 1;
                return this.id - o.id;
            }
        }

        private class ElementCounter {
            private HashMap<Long, Integer> elements;

            public ElementCounter() {
                elements = new HashMap<>();
            }

            public void add(long element) {
                int count = 1;
                Integer prev = elements.get(element);
                if (prev != null) count += prev;
                elements.put(element, count);
            }

            public void remove(long element) {
                int count = elements.remove(element);
                count--;
                if (count > 0) elements.put(element, count);
            }

            public int get(long element) {
                Integer val = elements.get(element);
                if (val == null) return 0;
                return val;
            }

            public int size() {
                return elements.size();
            }
        }

        class StringCounter {
            HashMap<String, Integer> elements;

            public StringCounter() {
                elements = new HashMap<>();
            }

            public void add(String identifier) {
                int count = 1;
                Integer prev = elements.get(identifier);
                if (prev != null) count += prev;
                elements.put(identifier, count);
            }

            public void remove(String identifier) {
                int count = elements.remove(identifier);
                count--;
                if (count > 0) elements.put(identifier, count);
            }

            public long get(String identifier) {
                Integer val = elements.get(identifier);
                if (val == null) return 0;
                return val;
            }

            public int size() {
                return elements.size();
            }
        }

        class DisjointSet {
            /** Union Find / Disjoint Set data structure. */
            int[] size;
            int[] parent;
            int componentCount;

            public DisjointSet(int n) {
                componentCount = n;
                size = new int[n];
                parent = new int[n];
                for (int i=0; i<n; i++) parent[i] = i;
                for (int i=0; i<n; i++) size[i] = 1;
            }

            public void join(int a, int b) {
                /* Find roots */
                int rootA = parent[a];
                int rootB = parent[b];
                while (rootA != parent[rootA]) rootA = parent[rootA];
                while (rootB != parent[rootB]) rootB = parent[rootB];

                if (rootA == rootB) {
                    /* Already in the same set */
                    return;
                }

                /* Merge smaller set into larger set. */
                if (size[rootA] > size[rootB]) {
                    size[rootA] += size[rootB];
                    parent[rootB] = rootA;
                } else {
                    size[rootB] += size[rootA];
                    parent[rootA] = rootB;
                }
                componentCount--;
            }

        }

        class Trie {
            int N;
            int Z;
            int nextFreeId;
            int[][] pointers;
            boolean[] end;

            /** maxLenSum = maximum possible sum of length of words */
            public Trie(int maxLenSum, int alphabetSize) {
                this.N = maxLenSum;
                this.Z = alphabetSize;
                this.nextFreeId = 1;
                pointers = new int[N+1][alphabetSize];
                end = new boolean[N+1];
            }

            public void addWord(String word) {
                int curr = 0;
                for (int j=0; j<word.length(); j++) {
                    int c = word.charAt(j) - 'a';
                    int next = pointers[curr][c];
                    if (next == 0) {
                        next = nextFreeId++;
                        pointers[curr][c] = next;
                    }
                    curr = next;
                }
                end[curr] = true;
            }

            public boolean hasWord(String word) {
                int curr = 0;
                for (int j=0; j<word.length(); j++) {
                    int c = word.charAt(j) - 'a';
                    int next = pointers[curr][c];
                    if (next == 0) return false;
                    curr = next;
                }
                return end[curr];
            }

        }

        private static class Prob {

            /** For heavy calculations on probabilities, this class
             *  provides more accuracy & efficiency than doubles.
             *  Math explained: https://en.wikipedia.org/wiki/Log_probability
             *  Quick start:
             *      - Instantiate probabilities, eg. Prob a = new Prob(0.75)
             *      - add(), multiply() return new objects, can perform on nulls & NaNs.
             *      - get() returns probability as a readable double */

            /** Logarithmized probability. Note: 0% represented by logP NaN. */
            private double logP;

            /** Construct instance with real probability. */
            public Prob(double real) {
                if (real > 0) this.logP = Math.log(real);
                else this.logP = Double.NaN;
            }

            /** Construct instance with already logarithmized value. */
            static boolean dontLogAgain = true;
            public Prob(double logP, boolean anyBooleanHereToChooseThisConstructor) {
                this.logP = logP;
            }

            /** Returns real probability as a double. */
            public double get() {
                return Math.exp(logP);
            }

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

            /***************** STATIC METHODS BELOW ********************/

            /** Note: returns NaN only when a && b are both NaN/null. */
            public static Prob add(Prob a, Prob b) {
                if (nullOrNaN(a) && nullOrNaN(b)) return new Prob(Double.NaN, dontLogAgain);
                if (nullOrNaN(a)) return copy(b);
                if (nullOrNaN(b)) return copy(a);

                double x = Math.max(a.logP, b.logP);
                double y = Math.min(a.logP, b.logP);
                double sum = x + Math.log(1 + Math.exp(y - x));
                return new Prob(sum, dontLogAgain);
            }

            /** Note: multiplying by null or NaN produces NaN (repping 0% real prob). */
            public static Prob multiply(Prob a, Prob b) {
                if (nullOrNaN(a) || nullOrNaN(b)) return new Prob(Double.NaN, dontLogAgain);
                return new Prob(a.logP + b.logP, dontLogAgain);
            }

            /** Returns true if p is null or NaN. */
            private static boolean nullOrNaN(Prob p) {
                return (p == null || Double.isNaN(p.logP));
            }

            /** Returns a new instance with the same value as original. */
            private static Prob copy(Prob original) {
                return new Prob(original.logP, dontLogAgain);
            }
        }

        class Binary implements Comparable<Binary> {

            /**
             * Use example: Binary b = new Binary(Long.toBinaryString(53249834L));
             *
             * When manipulating small binary strings, instantiate new Binary(string)
             * When just reading large binary strings, instantiate new Binary(string,true)
             * get(int i) returns a character '1' or '0', not an int.
             */

            private boolean[] d;
            private int first; // Starting from left, the first (most remarkable) '1'
            public int length;


            public Binary(String binaryString) {
                this(binaryString, false);
            }
            public Binary(String binaryString, boolean initWithMinArraySize) {
                length = binaryString.length();
                int size = Math.max(2*length, 1);
                first = length/4;
                if (initWithMinArraySize) {
                    first = 0;
                    size = Math.max(length, 1);
                }
                d = new boolean[size];
                for (int i=0; i<length; i++) {
                    if (binaryString.charAt(i) == '1') d[i+first] = true;
                }
            }

            public void addFirst(char c) {
                if (first-1 < 0) doubleArraySize();
                first--;
                d[first] = (c == '1' ? true : false);
                length++;
            }

            public void addLast(char c) {
                if (first+length >= d.length) doubleArraySize();
                d[first+length] = (c == '1' ? true : false);
                length++;
            }

            private void doubleArraySize() {
                boolean[] bigArray = new boolean[(d.length+1) * 2];
                int newFirst = bigArray.length / 4;
                for (int i=0; i<length; i++) {
                    bigArray[i + newFirst] = d[i + first];
                }
                first = newFirst;
                d = bigArray;
            }

            public boolean flip(int i) {
                boolean value = (this.d[first+i] ? false : true);
                this.d[first+i] = value;
                return value;
            }

            public void set(int i, char c) {
                boolean value = (c == '1' ? true : false);
                this.d[first+i] = value;
            }

            public char get(int i) {
                return (this.d[first+i] ? '1' : '0');
            }

            @Override
            public int compareTo(Binary o) {
                if (this.length != o.length) return this.length - o.length;
                int len = this.length;
                for (int i=0; i<len; i++) {
                    int diff = this.get(i) - o.get(i);
                    if (diff != 0) return diff;
                }
                return 0;
            }

            @Override
            public String toString() {
                StringBuilder sb = new StringBuilder();
                for (int i=0; i<length; i++) {
                    sb.append(d[i+first] ? '1' : '0');
                }
                return sb.toString();
            }


        }

        /************************** Range queries **************************/

        class FenwickMin {
            long n;
            long[] original;
            long[] bottomUp;
            long[] topDown;

            public FenwickMin(int n) {
                this.n = n;
                original = new long[n+2];
                bottomUp = new long[n+2];
                topDown = new long[n+2];
            }

            public void set(int modifiedNode, long value) {
                long replaced = original[modifiedNode];
                original[modifiedNode] = value;
                // Update left tree
                int i = modifiedNode;
                long v = value;
                while (i <= n) {
                    if (v > bottomUp[i]) {
                        if (replaced == bottomUp[i]) {
                            v = Math.min(v, original[i]);
                            for (int r=1 ;; r++) {
                                int x = (i&-i)>>>r;
                                if (x == 0) break;
                                int child = i-x;
                                v = Math.min(v, bottomUp[child]);
                            }
                        } else break;
                    }
                    if (v == bottomUp[i]) break;
                    bottomUp[i] = v;
                    i += (i&-i);
                }
                // Update right tree
                i = modifiedNode;
                v = value;
                while (i > 0) {
                    if (v > topDown[i]) {
                        if (replaced == topDown[i]) {
                            v = Math.min(v, original[i]);
                            for (int r=1 ;; r++) {
                                int x = (i&-i)>>>r;
                                if (x == 0) break;
                                int child = i+x;
                                if (child > n+1) break;
                                v = Math.min(v, topDown[child]);
                            }
                        } else break;
                    }
                    if (v == topDown[i]) break;
                    topDown[i] = v;
                    i -= (i&-i);
                }
            }

            public long getMin(int a, int b) {
                long min = original[a];
                int prev = a;
                int curr = prev + (prev&-prev); // parent right hand side
                while (curr <= b) {
                    min = Math.min(min, topDown[prev]); // value from the other tree
                    prev = curr;
                    curr = prev + (prev&-prev);;
                }
                min = Math.min(min, original[prev]);
                prev = b;
                curr = prev - (prev&-prev); // parent left hand side
                while (curr >= a) {
                    min = Math.min(min,bottomUp[prev]); // value from the other tree
                    prev = curr;
                    curr = prev - (prev&-prev);
                }
                return min;
            }

        }

        class FenwickSum {
            public long[] d;

            public FenwickSum(int n) {
                d=new long[n+1];
            }

            /** a[0] must be unused. */
            public FenwickSum(long[] a) {
                d=new long[a.length];
                for (int i=1; i<a.length; i++) {
                    modify(i, a[i]);
                }
            }

            /** Do not modify i=0. */
            void modify(int i, long v) {
                while (i<d.length) {
                    d[i] += v;
                    // Move to next uplink on the RIGHT side of i
                    i += (i&-i);
                }
            }

            /** Returns sum from a to b, *BOTH* inclusive. */
            long getSum(int a, int b) {
                return getSum(b) - getSum(a-1);
            }

            private long getSum(int i) {
                long sum = 0;
                while (i>0) {
                    sum += d[i];
                    // Move to next uplink on the LEFT side of i
                    i -= (i&-i);
                }
                return sum;
            }
        }

        class SegmentTree {

            /* Provides log(n) operations for:
             * - Range query (sum, min or max)
             * - Range update ("+8 to all values between indexes 4 and 94")
             */

            int N;
            long[] lazy;
            long[] sum;
            long[] min;
            long[] max;
            boolean supportSum;
            boolean supportMin;
            boolean supportMax;

            public SegmentTree(int n) {
                this(n, true, true, true);
            }

            public SegmentTree(int n, boolean supportSum, boolean supportMin, boolean supportMax) {
                for (N=2; N<n;) N*=2;
                this.lazy = new long[2*N];
                this.supportSum = supportSum;
                this.supportMin = supportMin;
                this.supportMax = supportMax;
                if (this.supportSum) this.sum = new long[2*N];
                if (this.supportMin) this.min = new long[2*N];
                if (this.supportMax) this.max = new long[2*N];
            }

            void modifyRange(long x, int a, int b) {
                modifyRec(a, b, 1, 0, N-1, x);
            }

            void setRange() {
                //TODO
            }

            long getSum(int a, int b) {
                return querySum(a, b, 1, 0, N-1);
            }

            long getMin(int a, int b) {
                return queryMin(a, b, 1, 0, N-1);
            }

            long getMax(int a, int b) {
                return queryMax(a, b, 1, 0, N-1);
            }

            private long querySum(int wantedLeft, int wantedRight, int i, int actualLeft, int actualRight) {
                if (wantedLeft > actualRight || wantedRight < actualLeft) {
                    return 0;
                }
                if (wantedLeft == actualLeft && wantedRight == actualRight) {
                    int count = wantedRight - wantedLeft + 1;
                    return sum[i] + count * lazy[i];
                }
                if (lazy[i] != 0) propagate(i, actualLeft, actualRight);
                int d = (actualRight - actualLeft + 1) / 2;
                long left = querySum(wantedLeft, min(actualLeft+d-1, wantedRight), 2*i, actualLeft, actualLeft+d-1);
                long right = querySum(max(actualLeft+d, wantedLeft), wantedRight, 2*i+1, actualLeft+d, actualRight);
                return left + right;
            }

            private long queryMin(int wantedLeft, int wantedRight, int i, int actualLeft, int actualRight) {
                if (wantedLeft > actualRight || wantedRight < actualLeft) {
                    return Long.MAX_VALUE;
                }
                if (wantedLeft == actualLeft && wantedRight == actualRight) {
                    return min[i] + lazy[i];
                }
                if (lazy[i] != 0) propagate(i, actualLeft, actualRight);
                int d = (actualRight - actualLeft + 1) / 2;
                long left = queryMin(wantedLeft, min(actualLeft+d-1, wantedRight), 2*i, actualLeft, actualLeft+d-1);
                long right = queryMin(max(actualLeft+d, wantedLeft), wantedRight, 2*i+1, actualLeft+d, actualRight);
                return min(left, right);
            }

            private long queryMax(int wantedLeft, int wantedRight, int i, int actualLeft, int actualRight) {
                if (wantedLeft > actualRight || wantedRight < actualLeft) {
                    return Long.MIN_VALUE;
                }
                if (wantedLeft == actualLeft && wantedRight == actualRight) {
                    return max[i] + lazy[i];
                }
                if (lazy[i] != 0) propagate(i, actualLeft, actualRight);
                int d = (actualRight - actualLeft + 1) / 2;
                long left = queryMax(wantedLeft, min(actualLeft+d-1, wantedRight), 2*i, actualLeft, actualLeft+d-1);
                long right = queryMax(max(actualLeft+d, wantedLeft), wantedRight, 2*i+1, actualLeft+d, actualRight);
                return max(left, right);
            }

            private void modifyRec(int wantedLeft, int wantedRight, int i, int actualLeft, int actualRight, long value) {
                if (wantedLeft > actualRight || wantedRight < actualLeft) {
                    return;
                }
                if (wantedLeft == actualLeft && wantedRight == actualRight) {
                    lazy[i] += value;
                    return;
                }
                if (lazy[i] != 0) propagate(i, actualLeft, actualRight);
                int d = (actualRight - actualLeft + 1) / 2;
                modifyRec(wantedLeft, min(actualLeft+d-1, wantedRight), 2*i, actualLeft, actualLeft+d-1, value);
                modifyRec(max(actualLeft+d, wantedLeft), wantedRight, 2*i+1, actualLeft+d, actualRight, value);
                if (supportSum) sum[i] += value * (min(actualRight, wantedRight) - max(actualLeft, wantedLeft) + 1);
                if (supportMin) min[i] = min(min[2*i] + lazy[2*i], min[2*i+1] + lazy[2*i+1]);
                if (supportMax) max[i] = max(max[2*i] + lazy[2*i], max[2*i+1] + lazy[2*i+1]);
            }

            private void propagate(int i, int actualLeft, int actualRight) {
                lazy[2*i] += lazy[i];
                lazy[2*i+1] += lazy[i];
                if (supportSum) sum[i] += lazy[i] * (actualRight - actualLeft + 1);
                if (supportMin) min[i] += lazy[i];
                if (supportMax) max[i] += lazy[i];
                lazy[i] = 0;
            }

        }

        /***************************** Graphs *****************************/

        List<Integer>[] toGraph(IO io, int n) {
            /* Trees only. */
            List<Integer>[] g = new ArrayList[n+1];
            for (int i=1; i<=n; i++) g[i] = new ArrayList<>();
            for (int i=1; i<=n-1; i++) {
                int a = io.nextInt();
                int b = io.nextInt();
                g[a].add(b);
                g[b].add(a);
            }
            return g;
        }

        class Graph {

            int n;
            List<Integer>[] edges;

            public Graph(int n) {
                this.n = n;
                edges = new ArrayList[n+1];
                for (int i=1; i<=n; i++) edges[i] = new ArrayList<>();
            }

            void addBiEdge(int a, int b) {
                addEdge(a, b);
                addEdge(b, a);
            }

            void addEdge(int from, int to) {
                edges[from].add(to);
            }

            /*********** Strongly Connected Components (Kosaraju) ****************/

            ArrayList<Integer>[] bacw;

            public int getCount() {
                bacw = new ArrayList[n+1];
                for (int i=1; i<=n; i++) {
                    bacw[i] = new ArrayList<Integer>();
                }
                for (int a=1; a<=n; a++) {
                    for (int b : edges[a]) {
                        bacw[b].add(a);
                    }
                }
                int count = 0;
                List<Integer> list = new ArrayList<Integer>();
                boolean[] visited = new boolean[n+1];
                for (int i=1; i<=n; i++) {
                    dfsForward(i, visited, list);
                }
                visited = new boolean[n+1];
                for (int i=n-1; i>=0; i--) {
                    int node = list.get(i);
                    if (visited[node]) continue;
                    count++;
                    dfsBackward(node, visited);
                }
                return count;
            }

            void dfsForward(int i, boolean[] visited, List<Integer> list) {
                if (visited[i]) return;
                visited[i] = true;
                for (int neighbor : edges[i]) {
                    dfsForward(neighbor, visited, list);
                }
                list.add(i);
            }

            void dfsBackward(int i, boolean[] visited) {
                if (visited[i]) return;
                visited[i] = true;
                for (int neighbor : bacw[i]) {
                    dfsBackward(neighbor, visited);
                }
            }

            /************************* Topological Order **********************/

            int UNTOUCHED = 0;
            int FINISHED = 2;
            int INPROGRESS = 1;
            int[] vis;
            List<Integer> topoAns;

            // Returns nodes in topological order or null if cycle was found
            public List<Integer> topoSort() {
                topoAns = new ArrayList<>();
                vis = new int[n+1];
                for (int i=1; i<=n; i++) {
                    if (!topoDFS(i)) return null;
                }
                Collections.reverse(topoAns);
                return topoAns;
            }

            boolean topoDFS(int curr) {
                Integer status = vis[curr];
                if (status == null) status = UNTOUCHED;
                if (status == FINISHED) return true;
                if (status == INPROGRESS) {
                    return false;
                }
                vis[curr] = INPROGRESS;
                for (int next : edges[curr]) {
                    if (!topoDFS(next)) return false;
                }
                vis[curr] = FINISHED;
                topoAns.add(curr);
                return true;
            }

        }

        class LCAFinder {

            /* O(n log n) Initialize: new LCAFinder(graph)
             * O(log n) Queries: find(a,b) returns lowest common ancestor for nodes a and b */

            int[] nodes;
            int[] depths;
            int[] entries;
            int pointer;
            FenwickMin fenwick;

            public LCAFinder(List<Integer>[] graph) {
                this.nodes = new int[(int)10e6];
                this.depths = new int[(int)10e6];
                this.entries = new int[graph.length];
                this.pointer = 1;
                boolean[] visited = new boolean[graph.length+1];
                dfs(1, 0, graph, visited);
                fenwick = new FenwickMin(pointer-1);
                for (int i=1; i<pointer; i++) {
                    fenwick.set(i, depths[i] * 1000000L + i);
                }
            }

            private void dfs(int node, int depth, List<Integer>[] graph, boolean[] visited) {
                visited[node] = true;
                entries[node] = pointer;
                nodes[pointer] = node;
                depths[pointer] = depth;
                pointer++;
                for (int neighbor : graph[node]) {
                    if (visited[neighbor]) continue;
                    dfs(neighbor, depth+1, graph, visited);
                    nodes[pointer] = node;
                    depths[pointer] = depth;
                    pointer++;
                }
            }

            public int find(int a, int b) {
                int left = entries[a];
                int right = entries[b];
                if (left > right) {
                    int temp = left;
                    left = right;
                    right = temp;
                }
                long mixedBag = fenwick.getMin(left, right);
                int index = (int) (mixedBag % 1000000L);
                return nodes[index];
            }
        }

        /**************************** Geometry ****************************/

        class Point {
            int y;
            int x;

            public Point(int y, int x) {
                this.y = y;
                this.x = x;
            }
        }

        boolean segmentsIntersect(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4) {
            // Returns true if segment 1-2 intersects segment 3-4

            if (x1 == x2 && x3 == x4) {
                // Both segments are vertical
                if (x1 != x3) return false;
                if (min(y1,y2) < min(y3,y4)) {
                    return max(y1,y2) >= min(y3,y4);
                } else {
                    return max(y3,y4) >= min(y1,y2);
                }
            }
            if (x1 == x2) {
                // Only segment 1-2 is vertical. Does segment 3-4 cross it? y = a*x + b
                double a34 = (y4-y3)/(x4-x3);
                double b34 = y3 - a34*x3;
                double y = a34 * x1 + b34;
                return y >= min(y1,y2) && y <= max(y1,y2) && x1 >= min(x3,x4) && x1 <= max(x3,x4);
            }
            if (x3 == x4) {
                // Only segment 3-4 is vertical. Does segment 1-2 cross it? y = a*x + b
                double a12 = (y2-y1)/(x2-x1);
                double b12 = y1 - a12*x1;
                double y = a12 * x3 + b12;
                return y >= min(y3,y4) && y <= max(y3,y4) && x3 >= min(x1,x2) && x3 <= max(x1,x2);
            }
            double a12 = (y2-y1)/(x2-x1);
            double b12 = y1 - a12*x1;
            double a34 = (y4-y3)/(x4-x3);
            double b34 = y3 - a34*x3;
            if (closeToZero(a12 - a34)) {
                // Parallel lines
                return closeToZero(b12 - b34);
            }
            // Non parallel non vertical lines intersect at x. Is x part of both segments?
            double x = -(b12-b34)/(a12-a34);
            return x >= min(x1,x2) && x <= max(x1,x2) && x >= min(x3,x4) && x <= max(x3,x4);
        }

        boolean pointInsideRectangle(Point p, List<Point> r, boolean countBorderAsInside) {
            Point a = r.get(0);
            Point b = r.get(1);
            Point c = r.get(2);
            Point d = r.get(3);
            double apd = areaOfTriangle(a, p, d);
            double dpc = areaOfTriangle(d, p, c);
            double cpb = areaOfTriangle(c, p, b);
            double pba = areaOfTriangle(p, b, a);
            double sumOfAreas = apd + dpc + cpb + pba;
            if (closeToZero(sumOfAreas - areaOfRectangle(r))) {
                if (closeToZero(apd) || closeToZero(dpc) || closeToZero(cpb) || closeToZero(pba)) {
                    return countBorderAsInside;
                }
                return true;
            }
            return false;
        }

        double areaOfTriangle(Point a, Point b, Point c) {
            return 0.5 * Math.abs((a.x-c.x)*(b.y-a.y)-(a.x-b.x)*(c.y-a.y));
        }

        double areaOfRectangle(List<Point> r) {
            double side1xDiff = r.get(0).x - r.get(1).x;
            double side1yDiff = r.get(0).y - r.get(1).y;
            double side2xDiff = r.get(1).x - r.get(2).x;
            double side2yDiff = r.get(1).y - r.get(2).y;
            double side1 = Math.sqrt(side1xDiff * side1xDiff + side1yDiff * side1yDiff);
            double side2 = Math.sqrt(side2xDiff * side2xDiff + side2yDiff * side2yDiff);
            return side1 * side2;
        }

        boolean pointsOnSameLine(double x1, double y1, double x2, double y2, double x3, double y3) {
            double areaTimes2 = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2);
            return (closeToZero(areaTimes2));
        }

        class PointToLineSegmentDistanceCalculator {

            // Just call this
            double minDistFromPointToLineSegment(double point_x, double point_y, double x1, double y1, double x2, double y2) {
                return Math.sqrt(distToSegmentSquared(point_x, point_y, x1, y1, x2, y2));
            }

            private double distToSegmentSquared(double point_x, double point_y, double x1, double y1, double x2, double y2) {
                double l2 = dist2(x1,y1,x2,y2);
                if (l2 == 0) return dist2(point_x, point_y, x1, y1);
                double t = ((point_x - x1) * (x2 - x1) + (point_y - y1) * (y2 - y1)) / l2;
                if (t < 0) return dist2(point_x, point_y, x1, y1);
                if (t > 1) return dist2(point_x, point_y, x2, y2);

                double com_x = x1 + t * (x2 - x1);
                double com_y = y1 + t * (y2 - y1);
                return dist2(point_x, point_y, com_x, com_y);
            }

            private double dist2(double x1, double y1, double x2, double y2) {
                return Math.pow((x1 - x2), 2) + Math.pow((y1 - y2), 2);
            }

        }

        /****************************** Math ******************************/

        long pow(long base, int exp) {
            if (exp == 0) return 1L;
            long x = pow(base, exp/2);
            long ans = x * x;
            if (exp % 2 != 0) ans *= base;
            return ans;
        }

        long gcd(long... v) {
            /** Chained calls to Euclidean algorithm. */
            if (v.length == 1) return v[0];
            long ans = gcd(v[1], v[0]);
            for (int i=2; i<v.length; i++) {
                ans = gcd(ans, v[i]);
            }
            return ans;
        }

        long gcd(long a, long b) {
            /** Euclidean algorithm. */
            if (b == 0) return a;
            return gcd(b, a%b);
        }

        int[] generatePrimesUpTo(int last) {
            /* Sieve of Eratosthenes. Practically O(n). Values of 0 indicate primes. */
            int[] div = new int[last+1];
            for (int x=2; x<=last; x++) {
                if (div[x] > 0) continue;
                for (int u=2*x; u<=last; u+=x) {
                    div[u] = x;
                }
            }
            return div;
        }

        long lcm(long a, long b) {
            /** Least common multiple */
            return a * b / gcd(a,b);
        }

        class BaseConverter {

            /* Palauttaa luvun esityksen kannassa base */
            public String convert(Long number, int base) {
                return Long.toString(number, base);
            }

            /* Palauttaa luvun esityksen kannassa baseTo, kun annetaan luku Stringinä kannassa baseFrom */
            public String convert(String number, int baseFrom, int baseTo) {
                return Long.toString(Long.parseLong(number, baseFrom), baseTo);
            }

            /* Tulkitsee kannassa base esitetyn luvun longiksi (kannassa 10) */
            public long longify(String number, int baseFrom) {
                return Long.parseLong(number, baseFrom);
            }
        }

        class BinomialCoefficients {
            /** Total number of K sized unique combinations from pool of size N (unordered)
             N! / ( K! (N - K)! )   */

            /** For simple queries where output fits in long. */
            public long biCo(long n, long k) {
                long r = 1;
                if (k > n) return 0;
                for (long d = 1; d <= k; d++) {
                    r *= n--;
                    r /= d;
                }
                return r;
            }

            /** For multiple queries with same n, different k. */
            public long[] precalcBinomialCoefficientsK(int n, int maxK) {
                long v[] = new long[maxK+1];
                v[0] = 1; // nC0 == 1
                for (int i=1; i<=n; i++) {
                    for (int j=Math.min(i,maxK); j>0; j--) {
                        v[j] = v[j] + v[j-1]; // Pascal's triangle
                    }
                }
                return v;
            }

            /** When output needs % MOD. */
            public long[] precalcBinomialCoefficientsK(int n, int k, long M) {
                long v[] = new long[k+1];
                v[0] = 1; // nC0 == 1
                for (int i=1; i<=n; i++) {
                    for (int j=Math.min(i,k); j>0; j--) {
                        v[j] = v[j] + v[j-1]; // Pascal's triangle
                        v[j] %= M;
                    }
                }
                return v;
            }
        }

        int invertNumber(int a, int k) {
            // Inverts the binary representation of a, using only k last bits e.g. 01101 -> 10010
            int inv32k = ~a;
            int mask = 1;
            for (int i = 1; i < k; ++i) mask |= mask << 1;
            return inv32k & mask;
        }

        /**************************** Strings ****************************/

        class Zalgo {

            public int pisinEsiintyma(String haku, String kohde) {
                char[] s = new char[haku.length() + 1 + kohde.length()];
                for (int i=0; i<haku.length(); i++) {
                    s[i] = haku.charAt(i);
                }
                int j = haku.length();
                s[j++] = '#';
                for (int i=0; i<kohde.length(); i++) {
                    s[j++] = kohde.charAt(i);
                }
                int[] z = toZarray(s);
                int max = 0;
                for (int i=haku.length(); i<z.length; i++) {
                    max = Math.max(max, z[i]);
                }
                return max;
            }

            public int[] toZarray(char[] s) {
                int n = s.length;
                int[] z = new int[n];
                int a = 0, b = 0;
                for (int i = 1; i < n; i++) {
                    if (i > b) {
                        for (int j = i; j < n && s[j - i] == s[j]; j++)  z[i]++;
                    }
                    else {
                        z[i] = z[i - a];
                        if (i + z[i - a] > b) {
                            for (int j = b + 1; j < n && s[j - i] == s[j]; j++) z[i]++;
                            a = i;
                            b = i + z[i] - 1;
                        }
                    }
                }
                return z;
            }

            public List<Integer> getStartIndexesWhereWordIsFound(String haku, String kohde) {
                // this is alternative use case
                char[] s = new char[haku.length() + 1 + kohde.length()];
                for (int i=0; i<haku.length(); i++) {
                    s[i] = haku.charAt(i);
                }
                int j = haku.length();
                s[j++] = '#';
                for (int i=0; i<kohde.length(); i++) {
                    s[j++] = kohde.charAt(i);
                }
                int[] z = toZarray(s);
                List<Integer> indexes = new ArrayList<>();
                for (int i=haku.length(); i<z.length; i++) {
                    if (z[i] < haku.length()) continue;
                    indexes.add(i);
                }
                return indexes;
            }

        }

        class StringHasher {

            class HashedString {
                long[] hashes;
                long[] modifiers;

                public HashedString(long[] hashes, long[] modifiers) {
                    this.hashes = hashes;
                    this.modifiers = modifiers;
                }
            }

            long P;
            long M;

            public StringHasher() {
                initializePandM();
            }

            HashedString hashString(String s) {
                int n = s.length();
                long[] hashes = new long[n];
                long[] modifiers = new long[n];
                hashes[0] = s.charAt(0);
                modifiers[0] = 1;
                for (int i=1; i<n; i++) {
                    hashes[i] = (hashes[i-1] * P + s.charAt(i)) % M;
                    modifiers[i] = (modifiers[i-1] * P) % M;
                }
                return new HashedString(hashes, modifiers);
            }

            /**
             * Indices are inclusive.
             */
            long getHash(HashedString hashedString, int startIndex, int endIndex) {
                long[] hashes = hashedString.hashes;
                long[] modifiers = hashedString.modifiers;
                long result = hashes[endIndex];
                if (startIndex > 0) result -= (hashes[startIndex-1] * modifiers[endIndex-startIndex+1]) % M;
                if (result < 0) result += M;
                return result;
            }

            // Less interesting methods below



            /**
             * Efficient for 2 input parameter strings in particular.
             */
            HashedString[] hashString(String first, String second) {
                HashedString[] array = new HashedString[2];
                int n = first.length();
                long[] modifiers = new long[n];
                modifiers[0] = 1;

                long[] firstHashes = new long[n];
                firstHashes[0] = first.charAt(0);
                array[0] = new HashedString(firstHashes, modifiers);

                long[] secondHashes = new long[n];
                secondHashes[0] = second.charAt(0);
                array[1] = new HashedString(secondHashes, modifiers);

                for (int i=1; i<n; i++) {
                    modifiers[i] = (modifiers[i-1] * P) % M;
                    firstHashes[i] = (firstHashes[i-1] * P + first.charAt(i)) % M;
                    secondHashes[i] = (secondHashes[i-1] * P + second.charAt(i)) % M;
                }
                return array;
            }

            /**
             * Efficient for 3+ strings
             * More efficient than multiple hashString calls IF strings are same length.
             */
            HashedString[] hashString(String... strings) {
                HashedString[] array = new HashedString[strings.length];
                int n = strings[0].length();
                long[] modifiers = new long[n];
                modifiers[0] = 1;
                for (int j=0; j<strings.length; j++) {
                    // if all strings are not same length, defer work to another method
                    if (strings[j].length() != n) {
                        for (int i=0; i<n; i++) {
                            array[i] = hashString(strings[i]);
                        }
                        return array;
                    }

                    // otherwise initialize stuff
                    long[] hashes = new long[n];
                    hashes[0] = strings[j].charAt(0);
                    array[j] = new HashedString(hashes, modifiers);
                }
                for (int i=1; i<n; i++) {
                    modifiers[i] = (modifiers[i-1] * P) % M;
                    for (int j=0; j<strings.length; j++) {
                        String s = strings[j];
                        long[] hashes = array[j].hashes;
                        hashes[i] = (hashes[i-1] * P + s.charAt(i)) % M;
                    }
                }
                return array;
            }

            void initializePandM() {
                ArrayList<Long> modOptions = new ArrayList<>(20);
                modOptions.add(353873237L);
                modOptions.add(353875897L);
                modOptions.add(353878703L);
                modOptions.add(353882671L);
                modOptions.add(353885303L);
                modOptions.add(353888377L);
                modOptions.add(353893457L);
                P = modOptions.get(new Random().nextInt(modOptions.size()));

                modOptions.clear();
                modOptions.add(452940277L);
                modOptions.add(452947687L);
                modOptions.add(464478431L);
                modOptions.add(468098221L);
                modOptions.add(470374601L);
                modOptions.add(472879717L);
                modOptions.add(472881973L);
                M = modOptions.get(new Random().nextInt(modOptions.size()));

            }
        }

        int editDistance(String a, String b) {
            a = "#"+a;
            b = "#"+b;
            int n = a.length();
            int m = b.length();
            int[][] dp = new int[n+1][m+1];
            for (int y=0; y<=n; y++) {
                for (int x=0; x<=m; x++) {
                    if (y == 0) dp[y][x] = x;
                    else if (x == 0) dp[y][x] = y;
                    else {
                        int e1 = dp[y-1][x] + 1;
                        int e2 = dp[y][x-1] + 1;
                        int e3 = dp[y-1][x-1] + (a.charAt(y-1) != b.charAt(x-1) ? 1 : 0);
                        dp[y][x] = min(e1, e2, e3);
                    }
                }
            }
            return dp[n][m];
        }

        /*************************** Technical ***************************/

        private class IO extends PrintWriter {
            private InputStreamReader r;
            private static final int BUFSIZE = 1 << 15;
            private char[] buf;
            private int bufc;
            private int bufi;
            private StringBuilder sb;

            public IO() {
                super(new BufferedOutputStream(System.out));
                r = new InputStreamReader(System.in);

                buf = new char[BUFSIZE];
                bufc = 0;
                bufi = 0;
                sb = new StringBuilder();
            }

            /** Print, flush, return nextInt. */
            private int queryInt(String s) {
                io.println(s);
                io.flush();
                return nextInt();
            }

            /** Print, flush, return nextLong. */
            private long queryLong(String s) {
                io.println(s);
                io.flush();
                return nextLong();
            }

            /** Print, flush, return next word. */
            private String queryNext(String s) {
                io.println(s);
                io.flush();
                return next();
            }

            private void fillBuf() throws IOException {
                bufi = 0;
                bufc = 0;
                while(bufc == 0) {
                    bufc = r.read(buf, 0, BUFSIZE);
                    if(bufc == -1) {
                        bufc = 0;
                        return;
                    }
                }
            }

            private boolean pumpBuf() throws IOException {
                if(bufi == bufc) {
                    fillBuf();
                }
                return bufc != 0;
            }

            private boolean isDelimiter(char c) {
                return c == ' ' || c == '\t' || c == '\n' || c == '\r' || c == '\f';
            }

            private void eatDelimiters() throws IOException {
                while(true) {
                    if(bufi == bufc) {
                        fillBuf();
                        if(bufc == 0) throw new RuntimeException("IO: Out of input.");
                    }

                    if(!isDelimiter(buf[bufi])) break;
                    ++bufi;
                }
            }

            public String next() {
                try {
                    sb.setLength(0);

                    eatDelimiters();
                    int start = bufi;

                    while(true) {
                        if(bufi == bufc) {
                            sb.append(buf, start, bufi - start);
                            fillBuf();
                            start = 0;
                            if(bufc == 0) break;
                        }

                        if(isDelimiter(buf[bufi])) break;
                        ++bufi;
                    }

                    sb.append(buf, start, bufi - start);

                    return sb.toString();
                } catch(IOException e) {
                    throw new RuntimeException("IO.next: Caught IOException.");
                }
            }

            public int nextInt() {
                try {
                    int ret = 0;

                    eatDelimiters();

                    boolean positive = true;
                    if(buf[bufi] == '-') {
                        ++bufi;
                        if(!pumpBuf()) throw new RuntimeException("IO.nextInt: Invalid int.");
                        positive = false;
                    }

                    boolean first = true;
                    while(true) {
                        if(!pumpBuf()) break;
                        if(isDelimiter(buf[bufi])) {
                            if(first) throw new RuntimeException("IO.nextInt: Invalid int.");
                            break;
                        }
                        first = false;

                        if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                            if(ret < -214748364) throw new RuntimeException("IO.nextInt: Invalid int.");
                            ret *= 10;
                            ret -= (int)(buf[bufi] - '0');
                            if(ret > 0) throw new RuntimeException("IO.nextInt: Invalid int.");
                        } else {
                            throw new RuntimeException("IO.nextInt: Invalid int.");
                        }

                        ++bufi;
                    }

                    if(positive) {
                        if(ret == -2147483648) throw new RuntimeException("IO.nextInt: Invalid int.");
                        ret = -ret;
                    }

                    return ret;
                } catch(IOException e) {
                    throw new RuntimeException("IO.nextInt: Caught IOException.");
                }
            }

            public long nextLong() {
                try {
                    long ret = 0;

                    eatDelimiters();

                    boolean positive = true;
                    if(buf[bufi] == '-') {
                        ++bufi;
                        if(!pumpBuf()) throw new RuntimeException("IO.nextLong: Invalid long.");
                        positive = false;
                    }

                    boolean first = true;
                    while(true) {
                        if(!pumpBuf()) break;
                        if(isDelimiter(buf[bufi])) {
                            if(first) throw new RuntimeException("IO.nextLong: Invalid long.");
                            break;
                        }
                        first = false;

                        if(buf[bufi] >= '0' && buf[bufi] <= '9') {
                            if(ret < -922337203685477580L) throw new RuntimeException("IO.nextLong: Invalid long.");
                            ret *= 10;
                            ret -= (long)(buf[bufi] - '0');
                            if(ret > 0) throw new RuntimeException("IO.nextLong: Invalid long.");
                        } else {
                            throw new RuntimeException("IO.nextLong: Invalid long.");
                        }

                        ++bufi;
                    }

                    if(positive) {
                        if(ret == -9223372036854775808L) throw new RuntimeException("IO.nextLong: Invalid long.");
                        ret = -ret;
                    }

                    return ret;
                } catch(IOException e) {
                    throw new RuntimeException("IO.nextLong: Caught IOException.");
                }
            }

            public double nextDouble() {
                return Double.parseDouble(next());
            }

        }

        void print(Object output) {
            io.println(output);
        }

        void done(Object output) {
            print(output);
            done();
        }

        void done() {
            io.close();
            throw new RuntimeException("Clean exit");
        }

        long min(long... v) {
            long ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.min(ans, v[i]);
            }
            return ans;
        }

        double min(double... v) {
            double ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.min(ans, v[i]);
            }
            return ans;
        }

        int min(int... v) {
            int ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.min(ans, v[i]);
            }
            return ans;
        }

        long max(long... v) {
            long ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.max(ans, v[i]);
            }
            return ans;
        }

        double max(double... v) {
            double ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.max(ans, v[i]);
            }
            return ans;
        }

        int max(int... v) {
            int ans = v[0];
            for (int i=1; i<v.length; i++) {
                ans = Math.max(ans, v[i]);
            }
            return ans;
        }

    }

}