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 collections import Counter
n = int(input())
k = list(map(int, input().split()))
cnt = Counter(k)
exp = [2 ** i for i in range(32)]
pair = 0
for i in k:
    if cnt[i] > 0:
        cnt[i] -= 1
    for j in exp:
        if j - i in cnt:
            pair += cnt[j - i]
print(pair)
