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.
def powers_of_two(n, a):
    c = {}
    s = 0
    for x in a:
        for p in range(32):
            s += c.get((1 << p) - x, 0)
        c[x] = c.get(x, 0) + 1
    return s


if __name__ == "__main__":
    n = int(input())
    a = map(int, input().split())
    print(powers_of_two(n, a))
