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():
    from collections import Counter
    from bisect import bisect_left
    n, res = int(input()), 0
    cnt = Counter(map(int, input().split()))
    aa, bb = sorted(cnt.keys()), []
    b = 2 << aa[-1].bit_length()
    aa.append(b)
    while b > aa[0]:
        bb.append(b)
        b //= 2
    for a in aa:
        for b in bb:
            c = b - a
            if c < a:
                del bb[-1]
                break
            if aa[bisect_left(aa, c)] == c:
                res += cnt[a] * cnt[c] if a < c else cnt[a] * (cnt[a] - 1) // 2
    print(res)


if __name__ == '__main__':
    main()
