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(raw_input())
values = list(reversed(sorted(map(int, raw_input().split()))))
delta_count = {}
result = 0
for value in values:
    if value in delta_count:
        result += delta_count[value]
    x = 2
    while x < value:
        x *= x
    while x > value:
        x >>= 1
    delta = (x << 1) - value
    delta_count[delta] = delta_count.setdefault(delta, 0) + 1
print(result)
