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.
from sys import stdin, stdout
n = int(stdin.readline())
power = [2 ** i for i in range(31)]
d = {}
ans = 0

for value in map(int, stdin.readline().split()):
    for m in power:
        if m >= value and m - value in d:
            ans += d[m - value]
    if value in d:
        d[value] += 1
    else:
        d[value] = 1

stdout.write(str(ans))