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.
n = int(input())
A = list(map(int, input().split()))
cnt = {}

for a in A:
    if a in cnt:
        cnt[a] += 1
    else:
        cnt[a] = 1

c = 0
for a in A:
    cnt[a] -= 1
    for n in range(1, 32):
        cur = 2**n
        if cur <= a:
            continue
        if cur - a in cnt:
            c += cnt[cur - a]

print(c)
