You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.TreeSet;
 
public class Main {
	public static void main(String arg[]){
		InputReader in = new InputReader(System.in);
		OutputWriter out = new OutputWriter(System.out);
		int n = in.readInt();
		int a[] = IOUtils.readIntArray(in, n);
		
		long pow[] = new long[33];
		pow[0] = 2;
		for(int i = 1; i < 33; i++)
			pow[i] = 2L*pow[i-1];

		HashMap<Long, Long> map = new HashMap<Long, Long>();
		for(int i = 0; i < n; i++){
			if(map.containsKey((long)a[i]))
				map.put((long)a[i],map.get((long)a[i])+1);
			else
				map.put((long)a[i], (long) 1);
		}
		
		long count = 0;
		for(int ele : a){
			for(int i = 0; i < 33; i++){
				if(map.containsKey((pow[i]-ele))){
					if(pow[i] - ele == ele)
						count += map.get(pow[i]-ele)-1;
					else
						count += map.get(pow[i]-ele);
				}
			}
		}
		out.printLine(count/2);
		out.flush();
		out.close();
	}	
}
class InputReader {
	 
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private 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 {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}
 
	
 
	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
 
	public String next() {
		return readString();
	}
 
	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}
 
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 print(Object...objects) {
		for (int i = 0; i < objects.length; i++) {
			if (i != 0)
				writer.print(' ');
			writer.print(objects[i]);
		}
	}
 
	public void printLine(Object...objects) {
		print(objects);
		writer.println();
	}
 
	public void close() {
		writer.close();
	}
 
	public void flush() {
		writer.flush();
	}
} 
class IOUtils {
	 
	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

}