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.
input()

sequence = list(map(int, input().split()))
repeated_even_numbers = {}
repeated_odd_numbers = {}
sum = 0

for number in sequence:
    if number % 2 == 0:
        for index in range(31):
            sum += repeated_even_numbers.get((1 << index) - number, 0)
        repeated_even_numbers[number] = repeated_even_numbers.get(number, 0) + 1
    else:
        for index in range(31):
            sum += repeated_odd_numbers.get((1 << index) - number, 0)
        repeated_odd_numbers[number] = repeated_odd_numbers.get(number, 0) + 1

print(sum)