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.


def solution():
    n = int(input())
    a = list(map(int, input().split()))

    pow2 = [2 ** i for i in range(61)]

    total = 0
    dic = {}
    for i in range(n):
        for j in range(60):
            if pow2[j] - a[i] in dic:
                total += dic[pow2[j] - a[i]]

        if a[i] in dic:
            dic[a[i]] += 1
        else:
            dic[a[i]] = 1

    print(total)


solution()
