Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
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.StringTokenizer;
import java.util.Map;
import java.util.NoSuchElementException;
import java.io.PrintWriter;
import java.util.Iterator;
import java.util.Set;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.AbstractMap;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskB {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            IntList list = new IntArrayList(n);
            for (int i = 0; i < n; i++) {
                list.add(in.nextInt());
            }
            list.sort(IntComparator.REVERSE);

            Counter<Integer> counter = new Counter<>();
            for (int x : list) {
                counter.add(x);
            }

            int ans = 0;
            for (int x : list) {
                if (counter.get(x) == 0) continue;

                int another = (((Integer.highestOneBit(x) << 1) - 1) ^ x) + 1;
                if (counter.get(another) > 0 && (x != another || counter.get(another) >= 2)) {
                    ans++;
                    counter.add(x, -1);
                    counter.add(another, -1);
                }
            }

            out.println(ans);
        }

    }

    static interface IntStream extends Iterable<Integer>, Comparable<IntStream> {
        public IntIterator intIterator();

        default public Iterator<Integer> iterator() {
            return new Iterator<Integer>() {
                private IntIterator it = intIterator();

                public boolean hasNext() {
                    return it.isValid();
                }

                public Integer next() {
                    int result = it.value();
                    it.advance();
                    return result;
                }
            };
        }

        default public int compareTo(IntStream c) {
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                int i = it.value();
                int j = jt.value();
                if (i < j) {
                    return -1;
                } else if (i > j) {
                    return 1;
                }
                it.advance();
                jt.advance();
            }
            if (it.isValid()) {
                return 1;
            }
            if (jt.isValid()) {
                return -1;
            }
            return 0;
        }

    }

    static class Sorter {
        private static final int INSERTION_THRESHOLD = 16;

        private Sorter() {
        }

        public static void sort(IntList list, IntComparator comparator) {
            quickSort(list, 0, list.size() - 1, (Integer.bitCount(Integer.highestOneBit(list.size()) - 1) * 5) >> 1,
                    comparator);
        }

        private static void quickSort(IntList list, int from, int to, int remaining, IntComparator comparator) {
            if (to - from < INSERTION_THRESHOLD) {
                insertionSort(list, from, to, comparator);
                return;
            }
            if (remaining == 0) {
                heapSort(list, from, to, comparator);
                return;
            }
            remaining--;
            int pivotIndex = (from + to) >> 1;
            int pivot = list.get(pivotIndex);
            list.swap(pivotIndex, to);
            int storeIndex = from;
            int equalIndex = to;
            for (int i = from; i < equalIndex; i++) {
                int value = comparator.compare(list.get(i), pivot);
                if (value < 0) {
                    list.swap(storeIndex++, i);
                } else if (value == 0) {
                    list.swap(--equalIndex, i--);
                }
            }
            quickSort(list, from, storeIndex - 1, remaining, comparator);
            for (int i = equalIndex; i <= to; i++) {
                list.swap(storeIndex++, i);
            }
            quickSort(list, storeIndex, to, remaining, comparator);
        }

        private static void heapSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = (to + from - 1) >> 1; i >= from; i--) {
                siftDown(list, i, to, comparator, from);
            }
            for (int i = to; i > from; i--) {
                list.swap(from, i);
                siftDown(list, from, i - 1, comparator, from);
            }
        }

        private static void siftDown(IntList list, int start, int end, IntComparator comparator, int delta) {
            int value = list.get(start);
            while (true) {
                int child = ((start - delta) << 1) + 1 + delta;
                if (child > end) {
                    return;
                }
                int childValue = list.get(child);
                if (child + 1 <= end) {
                    int otherValue = list.get(child + 1);
                    if (comparator.compare(otherValue, childValue) > 0) {
                        child++;
                        childValue = otherValue;
                    }
                }
                if (comparator.compare(value, childValue) >= 0) {
                    return;
                }
                list.swap(start, child);
                start = child;
            }
        }

        private static void insertionSort(IntList list, int from, int to, IntComparator comparator) {
            for (int i = from + 1; i <= to; i++) {
                int value = list.get(i);
                for (int j = i - 1; j >= from; j--) {
                    if (comparator.compare(list.get(j), value) <= 0) {
                        break;
                    }
                    list.swap(j, j + 1);
                }
            }
        }

    }

    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 interface IntReversableCollection extends IntCollection {
    }

    static interface IntIterator {
        public int value() throws NoSuchElementException;

        public boolean advance();

        public boolean isValid();

    }

    static interface IntComparator {
        public static final IntComparator REVERSE = (first, second) -> {
            if (first > second) {
                return -1;
            }
            if (first < second) {
                return 1;
            }
            return 0;
        };

        public int compare(int first, int second);

    }

    static class IntArrayList extends IntAbstractStream implements IntList {
        private int size;
        private int[] data;

        public IntArrayList() {
            this(3);
        }

        public IntArrayList(int capacity) {
            data = new int[capacity];
        }

        public IntArrayList(IntCollection c) {
            this(c.size());
            addAll(c);
        }

        public IntArrayList(IntStream c) {
            this();
            if (c instanceof IntCollection) {
                ensureCapacity(((IntCollection) c).size());
            }
            addAll(c);
        }

        public IntArrayList(IntArrayList c) {
            size = c.size();
            data = c.data.clone();
        }

        public IntArrayList(int[] arr) {
            size = arr.length;
            data = arr.clone();
        }

        public int size() {
            return size;
        }

        public int get(int at) {
            if (at >= size) {
                throw new IndexOutOfBoundsException("at = " + at + ", size = " + size);
            }
            return data[at];
        }

        private void ensureCapacity(int capacity) {
            if (data.length >= capacity) {
                return;
            }
            capacity = Math.max(2 * data.length, capacity);
            data = Arrays.copyOf(data, capacity);
        }

        public void addAt(int index, int value) {
            ensureCapacity(size + 1);
            if (index > size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size) {
                System.arraycopy(data, index, data, index + 1, size - index);
            }
            data[index] = value;
            size++;
        }

        public void removeAt(int index) {
            if (index >= size || index < 0) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            if (index != size - 1) {
                System.arraycopy(data, index + 1, data, index, size - index - 1);
            }
            size--;
        }

        public void set(int index, int value) {
            if (index >= size) {
                throw new IndexOutOfBoundsException("at = " + index + ", size = " + size);
            }
            data[index] = value;
        }

    }

    static interface IntCollection extends IntStream {
        public int size();

        default public void add(int value) {
            throw new UnsupportedOperationException();
        }

        default public IntCollection addAll(IntStream values) {
            for (IntIterator it = values.intIterator(); it.isValid(); it.advance()) {
                add(it.value());
            }
            return this;
        }

    }

    static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        public InputReader(InputStream inputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            st = new StringTokenizer("");
        }

        public String nextString() {
            while (!st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextString());
        }

    }

    static abstract class IntAbstractStream implements IntStream {
        public String toString() {
            StringBuilder builder = new StringBuilder();
            boolean first = true;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                if (first) {
                    first = false;
                } else {
                    builder.append(' ');
                }
                builder.append(it.value());
            }
            return builder.toString();
        }

        public boolean equals(Object o) {
            if (!(o instanceof IntStream)) {
                return false;
            }
            IntStream c = (IntStream) o;
            IntIterator it = intIterator();
            IntIterator jt = c.intIterator();
            while (it.isValid() && jt.isValid()) {
                if (it.value() != jt.value()) {
                    return false;
                }
                it.advance();
                jt.advance();
            }
            return !it.isValid() && !jt.isValid();
        }

        public int hashCode() {
            int result = 0;
            for (IntIterator it = intIterator(); it.isValid(); it.advance()) {
                result *= 31;
                result += it.value();
            }
            return result;
        }

    }

    static interface IntList extends IntReversableCollection {
        public abstract int get(int index);

        public abstract void set(int index, int value);

        public abstract void addAt(int index, int value);

        public abstract void removeAt(int index);

        default public void swap(int first, int second) {
            if (first == second) {
                return;
            }
            int temp = get(first);
            set(first, get(second));
            set(second, temp);
        }

        default public IntIterator intIterator() {
            return new IntIterator() {
                private int at;
                private boolean removed;

                public int value() {
                    if (removed) {
                        throw new IllegalStateException();
                    }
                    return get(at);
                }

                public boolean advance() {
                    at++;
                    removed = false;
                    return isValid();
                }

                public boolean isValid() {
                    return !removed && at < size();
                }

                public void remove() {
                    removeAt(at);
                    at--;
                    removed = true;
                }
            };
        }

        default public void add(int value) {
            addAt(size(), value);
        }

        default public IntList sort(IntComparator comparator) {
            Sorter.sort(this, comparator);
            return this;
        }

    }

    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 void add(K key, long delta) {
            put(key, get(key) + delta);
        }

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

    }
}

