Problem: You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

* The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

* 1 \leq N \leq 18
* The length of S is 2N.
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the number of ways to paint the string that satisfy the condition.

Examples

Input

4
cabaacba


Output

4


Input

11
mippiisssisssiipsspiim


Output

504


Input

4
abcdefgh


Output

0


Input

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


Output

9075135300

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.AbstractSet;
import java.util.InputMismatchException;
import java.util.Random;
import java.util.Map;
import java.io.OutputStreamWriter;
import java.util.NoSuchElementException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Iterator;
import java.io.BufferedWriter;
import java.util.Set;
import java.io.IOException;
import java.util.AbstractMap;
import java.util.Map.Entry;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        CStringColoring solver = new CStringColoring();
        solver.solve(1, in, out);
        out.close();
    }

    static class CStringColoring {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            String s = in.readString();
            Counter<Pair<String, String>> first = compute(s.substring(0, n), n);
            Counter<Pair<String, String>> second = compute(StringUtils.reverse(s.substring(n)), n);
            long answer = 0;
            for (Map.Entry<Pair<String, String>, Long> entry : first.entrySet()) {
                if (second.containsKey(entry.getKey())) {
                    answer += entry.getValue() * second.get(entry.getKey());
                }
            }
            out.printLine(answer);
        }

        private Counter<Pair<String, String>> compute(String s, int n) {
            Counter<Pair<String, String>> counter = new Counter<>();
            for (int i = 1; i < (1 << n); i += 2) {
                StringBuilder red = new StringBuilder();
                StringBuilder blue = new StringBuilder();
                for (int j = 0; j < n; j++) {
                    if ((i >> j & 1) == 1) {
                        red.append(s.charAt(j));
                    } else {
                        blue.append(s.charAt(j));
                    }
                }
                String r = red.toString();
                String b = blue.toString();
                counter.add(Pair.makePair(r, b));
                counter.add(Pair.makePair(b, r));
            }
            return counter;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }

    }

    static class EHashMap<E, V> extends AbstractMap<E, V> {
        private static final int[] shifts = new int[10];
        private int size;
        private EHashMap.HashEntry<E, V>[] data;
        private int capacity;
        private Set<Entry<E, V>> entrySet;

        static {
            Random random = new Random(System.currentTimeMillis());
            for (int i = 0; i < 10; i++) {
                shifts[i] = 1 + 3 * i + random.nextInt(3);
            }
        }

        public EHashMap() {
            this(4);
        }

        private void setCapacity(int size) {
            capacity = Integer.highestOneBit(4 * size);
            //noinspection unchecked
            data = new EHashMap.HashEntry[capacity];
        }

        public EHashMap(int maxSize) {
            setCapacity(maxSize);
            entrySet = new AbstractSet<Entry<E, V>>() {

                public Iterator<Entry<E, V>> iterator() {
                    return new Iterator<Entry<E, V>>() {
                        private EHashMap.HashEntry<E, V> last = null;
                        private EHashMap.HashEntry<E, V> current = null;
                        private EHashMap.HashEntry<E, V> base = null;
                        private int lastIndex = -1;
                        private int index = -1;

                        public boolean hasNext() {
                            if (current == null) {
                                for (index++; index < capacity; index++) {
                                    if (data[index] != null) {
                                        base = current = data[index];
                                        break;
                                    }
                                }
                            }
                            return current != null;
                        }

                        public Entry<E, V> next() {
                            if (!hasNext()) {
                                throw new NoSuchElementException();
                            }
                            last = current;
                            lastIndex = index;
                            current = current.next;
                            if (base.next != last) {
                                base = base.next;
                            }
                            return last;
                        }

                        public void remove() {
                            if (last == null) {
                                throw new IllegalStateException();
                            }
                            size--;
                            if (base == last) {
                                data[lastIndex] = last.next;
                            } else {
                                base.next = last.next;
                            }
                        }
                    };
                }


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

        public EHashMap(Map<E, V> map) {
            this(map.size());
            putAll(map);
        }

        public Set<Entry<E, V>> entrySet() {
            return entrySet;
        }

        public void clear() {
            Arrays.fill(data, null);
            size = 0;
        }

        private int index(Object o) {
            return getHash(o.hashCode()) & (capacity - 1);
        }

        private int getHash(int h) {
            int result = h;
            for (int i : shifts) {
                result ^= h >>> i;
            }
            return result;
        }

        public V remove(Object o) {
            if (o == null) {
                return null;
            }
            int index = index(o);
            EHashMap.HashEntry<E, V> current = data[index];
            EHashMap.HashEntry<E, V> last = null;
            while (current != null) {
                if (current.key.equals(o)) {
                    if (last == null) {
                        data[index] = current.next;
                    } else {
                        last.next = current.next;
                    }
                    size--;
                    return current.value;
                }
                last = current;
                current = current.next;
            }
            return null;
        }

        public V put(E e, V value) {
            if (e == null) {
                return null;
            }
            int index = index(e);
            EHashMap.HashEntry<E, V> current = data[index];
            if (current != null) {
                while (true) {
                    if (current.key.equals(e)) {
                        V oldValue = current.value;
                        current.value = value;
                        return oldValue;
                    }
                    if (current.next == null) {
                        break;
                    }
                    current = current.next;
                }
            }
            if (current == null) {
                data[index] = new EHashMap.HashEntry<E, V>(e, value);
            } else {
                current.next = new EHashMap.HashEntry<E, V>(e, value);
            }
            size++;
            if (2 * size > capacity) {
                EHashMap.HashEntry<E, V>[] oldData = data;
                setCapacity(size);
                for (EHashMap.HashEntry<E, V> entry : oldData) {
                    while (entry != null) {
                        EHashMap.HashEntry<E, V> next = entry.next;
                        index = index(entry.key);
                        entry.next = data[index];
                        data[index] = entry;
                        entry = next;
                    }
                }
            }
            return null;
        }

        public V get(Object o) {
            if (o == null) {
                return null;
            }
            int index = index(o);
            EHashMap.HashEntry<E, V> current = data[index];
            while (current != null) {
                if (current.key.equals(o)) {
                    return current.value;
                }
                current = current.next;
            }
            return null;
        }

        public boolean containsKey(Object o) {
            if (o == null) {
                return false;
            }
            int index = index(o);
            EHashMap.HashEntry<E, V> current = data[index];
            while (current != null) {
                if (current.key.equals(o)) {
                    return true;
                }
                current = current.next;
            }
            return false;
        }

        public int size() {
            return size;
        }

        private static class HashEntry<E, V> implements Entry<E, V> {
            private final E key;
            private V value;
            private EHashMap.HashEntry<E, V> next;

            private HashEntry(E key, V value) {
                this.key = key;
                this.value = value;
            }

            public E getKey() {
                return key;
            }

            public V getValue() {
                return value;
            }

            public V setValue(V value) {
                V oldValue = this.value;
                this.value = value;
                return oldValue;
            }

        }

    }

    static class Pair<U, V> implements Comparable<Pair<U, V>> {
        public final U first;
        public final V second;

        public static <U, V> Pair<U, V> makePair(U first, V second) {
            return new Pair<U, V>(first, second);
        }

        private Pair(U first, V second) {
            this.first = first;
            this.second = second;
        }

        public boolean equals(Object o) {
            if (this == o) {
                return true;
            }
            if (o == null || getClass() != o.getClass()) {
                return false;
            }

            Pair pair = (Pair) o;

            return !(first != null ? !first.equals(pair.first) : pair.first != null) &&
                    !(second != null ? !second.equals(pair.second) : pair.second != null);
        }

        public int hashCode() {
            int result = first != null ? first.hashCode() : 0;
            result = 31 * result + (second != null ? second.hashCode() : 0);
            return result;
        }

        public String toString() {
            return "(" + first + "," + second + ")";
        }

        public int compareTo(Pair<U, V> o) {
            int value = ((Comparable<U>) first).compareTo(o.first);
            if (value != 0) {
                return value;
            }
            return ((Comparable<V>) second).compareTo(o.second);
        }

    }

    static class StringUtils {
        public static String reverse(String sample) {
            StringBuilder result = new StringBuilder(sample);
            result.reverse();
            return result.toString();
        }

    }

    static class Counter<K> extends EHashMap<K, Long> {
        public Counter() {
            super();
        }

        public Counter(int capacity) {
            super(capacity);
        }

        public long add(K key) {
            long result = get(key);
            put(key, result + 1);
            return result + 1;
        }

        public Long get(Object key) {
            if (containsKey(key)) {
                return super.get(key);
            }
            return 0L;
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                if (Character.isValidCodePoint(c)) {
                    res.appendCodePoint(c);
                }
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}