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.
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Jul 27 10:52:28 2020

@author: shailesh
"""


from collections import defaultdict
N = int(input())

A = [int(i) for i in input().split()]

d = {}
d = defaultdict(lambda :0,d)


power_table = [2**i for i in range(31)]
sum_val= 0
for i in A:
    for pow_2 in power_table:
        sum_val += d[pow_2 - i]
    d[i] += 1

print(sum_val)