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.
import collections

n = int(input())
s = list(map(int, input().split()))
c = collections.Counter()
for i in s:
    c[i] += 1

pow = [2**x for x in range(1,32)]

ans = 0
for i in s:
    for j in pow:
        if i >= j:
            continue
        elif i == j//2:
            ans += c[i]-1
        elif j-i in c:
            ans += c[j-i]

print(ans//2)