Problem: This problem is different with easy version only by constraints on total answers length

It is an interactive problem

Venya joined a tour to the madhouse, in which orderlies play with patients the following game. Orderlies pick a string s of length n, consisting only of lowercase English letters. The player can ask two types of queries: 

  * ? l r – ask to list all substrings of s[l..r]. Substrings will be returned in random order, and in every substring, all characters will be randomly shuffled. 
  * ! s – guess the string picked by the orderlies. This query can be asked exactly once, after that the game will finish. If the string is guessed correctly, the player wins, otherwise he loses. 



The player can ask no more than 3 queries of the first type.

To make it easier for the orderlies, there is an additional limitation: the total number of returned substrings in all queries of the first type must not exceed \left⌈ 0.777(n+1)^2 \right⌉ (⌈ x ⌉ is x rounded up).

Venya asked you to write a program, which will guess the string by interacting with the orderlies' program and acting by the game's rules.

Your program should immediately terminate after guessing the string using a query of the second type. In case your program guessed the string incorrectly, or it violated the game rules, it will receive verdict Wrong answer.

Note that in every test case the string is fixed beforehand and will not change during the game, which means that the interactor is not adaptive.

Input

First line contains number n (1 ≤ n ≤ 100) — the length of the picked string.

Interaction

You start the interaction by reading the number n.

To ask a query about a substring from l to r inclusively (1 ≤ l ≤ r ≤ n), you should output

? l r

on a separate line. After this, all substrings of s[l..r] will be returned in random order, each substring exactly once. In every returned substring all characters will be randomly shuffled.

In the case, if you ask an incorrect query, ask more than 3 queries of the first type or there will be more than \left⌈ 0.777(n+1)^2 \right⌉ substrings returned in total, you will receive verdict Wrong answer.

To guess the string s, you should output

! s

on a separate line.

After printing each query, do not forget to flush the output. Otherwise, you will get Idleness limit exceeded. To flush the output, you can 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. 



If you received - (dash) as an answer to any query, you need to terminate your program with exit code 0 (for example, by calling exit(0)). This means that there was an error in the interaction protocol. If you don't terminate with exit code 0, you can receive any unsuccessful verdict. 

Hack format

To hack a solution, use the following format:

The first line should contain one integer n (1 ≤ n ≤ 100) — the length of the string, and the following line should contain the string s.

Example

Input


4

a
aa
a

cb
b
c

c

Output


? 1 2

? 3 4

? 4 4

! aabc

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.Iterator;
import java.util.Set;
import java.io.IOException;
import java.util.HashMap;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.util.Map;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            C2MadhouseHardVersion solver = new C2MadhouseHardVersion();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class C2MadhouseHardVersion {
        FastInput in;
        FastOutput out;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            this.in = in;
            this.out = out;

            int n = in.readInt();
            if (n == 1) {
                answer(actual(1));
                return;
            }

            int m = (n + 1) / 2;
            String left = actual(m);
            Map<Summary, Integer> total = ask(1, n);

            char[] ans = new char[n];
            Arrays.fill(ans, 'a');
            for (int i = 0; i < m; i++) {
                ans[i] = left.charAt(i);
            }

            Summary all = null;
            for (Summary s : total.keySet()) {
                if (s.sum == n) {
                    all = s;
                    total.remove(all);
                    break;
                }
            }

            Summary last = all;
            for (int i = n - 1; i >= m; i--) {
                Summary trace = new Summary(all);
                int j;
                for (j = 0; i + j - 1 < n - 1; j++) {
                    trace.dec(ans[j] - 'a');
                }
                for (; j >= 1; j--) {
                    remove(total, trace);
                    trace.inc(ans[j - 1] - 'a');
                    trace.dec(ans[i + j - 1] - 'a');
                }
                Summary now = null;
                for (Summary s : total.keySet()) {
                    if (s.sum == i) {
                        now = s;
                        total.remove(now);
                        break;
                    }
                }

                ans[i] = (char) (last.differIndex(now) + 'a');
                last = now;
            }

            answer(new String(ans));
        }

        public void remove(Map<Summary, Integer> total, Summary s) {
            int remain = total.get(s) - 1;
            if (remain == 0) {
                total.remove(s);
            } else {
                total.put(s, remain);
            }
        }

        public String actual(int m) {
            if (m == 1) {
                Map<Summary, Integer> map = ask(1, 1);
                String s = "" + (char) (map.keySet().iterator().next().differIndex(new Summary("")) + 'a');
                return s;
            }
            Map<Summary, Integer> h1 = ask(1, m);
            Map<Summary, Integer> h2 = ask(2, m);
            for (Summary s : h2.keySet()) {
                int remain = h1.get(s) - h2.get(s);
                if (remain == 0) {
                    h1.remove(s);
                } else {
                    h1.put(s, remain);
                }
            }

            List<Summary> list = new ArrayList<>(h1.keySet());
            list.sort((a, b) -> a.sum - b.sum);
            Summary last = new Summary("");
            StringBuilder ans = new StringBuilder(m);
            for (Summary s : list) {
                ans.append((char) (s.differIndex(last) + 'a'));
                last = s;
            }
            return ans.toString();
        }

        void answer(String ans) {
            out.printf("! %s", ans).println().flush();
        }

        Map<Summary, Integer> ask(int l, int r) {
            int n = r - l + 1;
            int m = n * (n + 1) / 2;
            Map<Summary, Integer> map = new HashMap<>(m);
            out.printf("? %d %d", l, r).println().flush();
            for (int i = 0; i < m; i++) {
                Summary s = new Summary(in.readString());
                map.put(s, map.getOrDefault(s, 0) + 1);
            }
            return map;
        }

    }

    static class SequenceUtils {
        public static boolean equal(int[] a, int al, int ar, int[] b, int bl, int br) {
            if ((ar - al) != (br - bl)) {
                return false;
            }
            for (int i = al, j = bl; i <= ar; i++, j++) {
                if (a[i] != b[j]) {
                    return false;
                }
            }
            return true;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput printf(String format, Object... args) {
            cache.append(String.format(format, args));
            return this;
        }

        public FastOutput println() {
            cache.append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                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 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);
        }

    }

    static class Summary {
        int[] cnts = new int['z' - 'a' + 1];
        int sum;

        public void dec(int i) {
            cnts[i]--;
            sum--;
        }

        public void inc(int i) {
            cnts[i]++;
            sum++;
        }

        public Summary(Summary model) {
            this.cnts = model.cnts.clone();
            this.sum = model.sum;
        }

        public Summary(String s) {
            sum = s.length();
            for (char c : s.toCharArray()) {
                cnts[c - 'a']++;
            }
        }

        public int differIndex(Summary s) {
            for (int i = 0; i < cnts.length; i++) {
                if (cnts[i] != s.cnts[i]) {
                    return i;
                }
            }
            return -1;
        }

        public int hashCode() {
            int hash = 1;
            for (int i = 0; i < cnts.length; i++) {
                hash = hash * 31 + cnts[i];
            }
            return hash;
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof Summary)) {
                return false;
            }
            Summary other = (Summary) obj;
            return SequenceUtils.equal(cnts, 0, cnts.length - 1,
                    other.cnts, 0, cnts.length - 1);
        }

    }
}