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 collections as cc
import bisect as bi
I = lambda : list(map(int, input().split()))

# for tc in range(int(input())):
n, = I()
ar = I()
mapping = cc.defaultdict(int)
ans = 0
for i in range(len(ar)):
	for j in range(32):
		target = pow(2, j)
		curr = target - ar[i]
		if curr in mapping:
			ans += mapping[curr]
	mapping[ar[i]] += 1
print(ans)