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(i) for i in input().split()]
d = {}
for i in A:
    d[i] = d.setdefault(i, 0) + 1

from math import log
l = int(log(max(A))/log(2)) + 2
ans = 0
for i in range(N):
    for j in range(1, l):
        c = (1 << j) - A[i]
        ans += d.get(c, 0)
        ans -= c == A[i]

print(ans//2)
