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(t) for t in input().split()]
counts = dict()
for num in a:
    counts[num] = counts.setdefault(num, 0) + 1

m = max(counts)
pows = [2]
while pows[-1] < m:
    pows.append(2*pows[-1])
pows.append(2*pows[-1])

total = 0
for a in counts:
    matchesFora = 0
    for p in pows:
        if p - a in counts:
            matchesFora += counts[p - a]
            if p - a == a:
                matchesFora -= 1
    total += matchesFora * counts[a]
total //= 2

print(total)