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())
c = list(map(int, input().split()))
p = list()
for i in range(1, int(1e9)):
    if 2 ** i > int(1e9) * 2:
        break
    p.append(2 ** i)
v = dict()
d = dict()
for x in c:
    for y in p:
        if 2 * x == y:
            d[x] = d.get(x, 0) + 1
            continue
        v[y - x] = v.get(y - x, 0) + 1
r = 0
for x in c:
    r += v.get(x, 0)
for x in d.values():
    r += (x * (x - 1))
print(r // 2)
