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 math

def c(n):
    return math.factorial(n) / (math.factorial(n - 2) * 2)

n = int(input())
a = list(map(int, input().split()))
s = set()
ans = 0

for i in range(33):
    s.add(2 ** i)

d = dict()
for i in range(len(a)):
    if a[i] in d:
        d[a[i]] += 1
    else:
        d[a[i]] = 1

for elem1 in d:
    for elem2 in s:
        if d.get(elem2 - elem1, 0) > 0:
            if elem1 != elem2 - elem1:
                ans += (d[elem1] * d[elem2 - elem1]) / 2
            else:
                if d[elem1] > 1:
                    ans += c(d[elem1]) 


print(int(ans))