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(i) for i in map(int, input().split())]
power = [1]
while power[-1] < 2*1e9 + 1:
    power.append(power[-1]*2)
numbers = {str(i):0 for i in set(a)}
for i in a:
    numbers[str(i)] += 1
ans = 0
for i in a:
    number = numbers[str(i)]
    if numbers[str(i)] == 0: continue
    numbers[str(i)] = 0
    for j in power:
        if j <= i: continue
        need = j - i
        if str(need) in numbers:
            if i != need:
                ans += numbers[str(need)] * number
            else:
                ans += (number*(number - 1))//2
print(ans)
