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())
val = list(map(int, input().split()))

from collections import Counter
cnt = Counter(val)

powers = [2 ** i for i in range(31)]

ans = 0
for i in cnt.keys():
    for p in range(31):
        temp = powers[p] - i
        if temp > i:
            ans += cnt[i] * cnt.get(temp, 0)
        elif temp == i:
            ans += (cnt[i] * (cnt[i] - 1)) // 2

print(ans)