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 = map(int, input().split())

pow2 = []
x = 1
for i in range(32):
    x <<= 1
    pow2.append(x)

ans = 0
cnt = {}
for x in a:
    for y in pow2:
        need = y - x
        if need in cnt:
            ans += cnt[need]
    cnt[x] = cnt.get(x, 0) + 1
print(ans)

