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.
x = 2
b = []
for i in xrange(50):
    b.append(x)
    x *= 2
n = input()
a = map(int,raw_input().split())
d = {}
ans = 0
for i in xrange(n) :
    d[a[i]] = d.get(a[i],0) + 1

for i in xrange(n):
    d[a[i]] -= 1
    for j in xrange(len(b)):
        if b[j] - a[i] >= 0 and d.get(b[j] - a[i],-1) != -1:
            ans += d[b[j] - a[i]]
print ans
    