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.
MAX = 4000000000

n = int(raw_input())

tab = map(int, raw_input().split())

M = {}

sol = 0

for i in range(0, n):
    if tab[i] in M:
        M[tab[i]] += 1
    else:
        M[tab[i]] = 1


for i in range(0, n):
    pot = 1

    while pot < MAX:

        if pot - tab[i] in M:

            sol += M[pot - tab[i]]

            if pot - tab[i] == tab[i]:
                sol -= 1

        pot *= 2

print sol / 2
