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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;

public class Main {

	public static void main(String[] args) {
		IO io = new IO();
		int n = io.nextInt();
		int[] a = io.nextIntArray(n);
		Arrays.sort(a);
		HashMap<Integer, Integer> count = new HashMap<>();
		for(int i=0;i<n;i++) {
			count.put(a[i], count.getOrDefault(a[i], 0) + 1);
		}
		int ans = 0;
		for(int i=n-1;i>=0;i--) {
			int x = a[i];
			int c1 = count.getOrDefault(x, 0);
			if (c1 <= 0) continue;
			count.put(x, c1-1);

			int y = Integer.highestOneBit(x);
			if (x != y) {
				y = (y << 1) - x;
			}
			int c = count.getOrDefault(y, 0);
			if (c > 0) {
				count.put(y, c - 1);
				ans++;
			}
		}
		System.out.println(ans);
	}

}
class IO extends PrintWriter {
	private final InputStream in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	public IO() {
		this(System.in);
	}

	public IO(InputStream source) {
		super(System.out);
		this.in = source;
	}

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	private static boolean isNewLine(int c) {
		return c == '\n' || c == '\r';
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public boolean hasNextLine() {
		while (hasNextByte() && isNewLine(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public char[] nextCharArray(int len) {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		char[] s = new char[len];
		int i = 0;
		int b = readByte();
		while (isPrintableChar(b)) {
			if (i == len) {
				throw new InputMismatchException();
			}
			s[i++] = (char) b;
			b = readByte();
		}
		return s;
	}

	public String nextLine() {
		if (!hasNextLine()) {
			throw new NoSuchElementException();
		}
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (!isNewLine(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) {
			throw new NumberFormatException();
		}
		return (int) nl;
	}

	public char nextChar() {
		if (!hasNext()) {
			throw new NoSuchElementException();
		}
		return (char) readByte();
	}

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

	public int[] nextIntArray(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public long[] nextLongArray(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public double[] nextDoubleArray(int n) {
		double[] a = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public void nextIntArrays(int[]... a) {
		for (int i = 0; i < a[0].length; i++)
			for (int j = 0; j < a.length; j++)
				a[j][i] = nextInt();
	}

	public int[][] nextIntMatrix(int n, int m) {
		int[][] a = new int[n][];
		for (int i = 0; i < n; i++)
			a[i] = nextIntArray(m);
		return a;
	}

	public char[][] nextCharMap(int n, int m) {
		char[][] a = new char[n][];
		for (int i = 0; i < n; i++)
			a[i] = nextCharArray(m);
		return a;
	}

	public void close() {
		super.close();
		try {
			in.close();
		} catch (IOException e) {
		}
	}
}
