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 number_of_power_of_two_pairs(numbers):
    ret = 0
    dic = dict()
    for num in numbers:
        for i in range(32):
            ret += dic.get(2**i - num, 0)
        dic[num] = dic.get(num, 0) + 1
    return ret


def main():
    n = int(raw_input())
    numbers = map(int, raw_input().split())
    print number_of_power_of_two_pairs(numbers)


if __name__ == '__main__':
    main()
