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 read(func=int, is_list=False):
    if is_list:
        return map(func, raw_input().split())
    else:
        return func(raw_input())

n = read(int, False)
a = read(int, True)

cnt = {}
ans = 0
for x in a:
    it = 0
    while it < 35:
        p = 2**it
        it += 1
        if p <= x:
            continue
        if p - x in cnt:
            ans += cnt[p - x]
    if x not in cnt:
        cnt[x] = 1
    else:
        cnt[x] += 1

print ans
