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())
a = [int(x) for x in input().split()]
p2 = [2**i for i in range(31)]

d = {}
for i in a:
    if i in d:
        d[i] += 1
    else:
        d[i] = 1
k = 0
for i in d:
    for p in p2:
        j = p - i
        if j > i:
            break
        if j in d:
            if i == j:
                k += d[i] * (d[i] - 1) // 2
            else:
                k += d[i] * d[j]
print(k)