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 main():
    n = int(input())
    l = list(map(int, input().split()))
    cnt = {}

    res = 0
    for x in l:
        for i in range(1, 32):
            power = 1 << i
            if power - x in cnt:
                res += cnt[power - x]
        try:
            cnt[x] += 1
        except KeyError:
            cnt[x] = 1

    print(res)


if __name__ == '__main__':
    main()
