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())
array = list(map(int, input().split()))
d = {}
powers = [2 ** i for i in range(1, 32)]
s = 0
for i in range(n):
    e = array[i]
    if i > 0:
        for p in powers:
            if p > e:
                # if d.get(p - e, 0) > 0:
                    # print (e, p - e, d, d.get(p - e, 0))
                s += d.get(p - e, 0)
    if e not in d:
        d[e] = 0
    d[e] += 1
print (s)