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.
'''input
4
5 5 3 3
'''
from collections import Counter

n = int(input())
arr = list(map(int, input().split()))
highest = max(arr)
freqs = Counter(arr)
count = 0
for e in freqs:
    power = 2
    while power <= highest + e:
        comp = power - e
        comp_freq = freqs[comp]
        if comp > e:
            count += freqs[e] * comp_freq
        elif comp == e:
            count += (comp_freq) * (comp_freq-1) // 2
        power *= 2
print(count)
