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

n = int(input())
a = list(map(int, input().split()))

l = [int(math.pow(2, i)) for i in range(1, 32)]

s = dict()
for i in a:
    if i in s.keys():
        s[i] += 1
    else:
        s[i] = 1

c = 0
for k in s.keys():
    for j in l:
        if (j - k) in s.keys():
            if (j - k) == k:
                c += s[k] * (s[j - k] - 1)
            else:
                c += s[k] * s[j - k]
print(c // 2)
