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.
t = input
p = print
r = range
n = int(t())
a = list(map(int, t().split()))
c = 0
co = {x: 0 for x in range(100000)}
po = [2 ** x for x in range(33)]
for i in range(n):
    if a[i] in co:
        c += co.get(a[i])
    for j in range(len(po)):
        if a[i] < po[j]:
            co.update({po[j] - a[i]: co.get(po[j] - a[i], 0) + 1})
p(c)