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.
n = int(input())
lst=map(int, raw_input().split())

_dict = {}
for elem in lst: _dict[elem] = _dict.get(elem, 0) + 1

answer = 0
for key in _dict.keys():
	if _dict[key] > 1:
		x = key << 1;
		if x & (~x + 1) == x:
			answer += _dict[key] * (_dict[key] - 1) / 2

	vx = _dict[key]
	_dict[key] = 0

	for j in range(0, 31):
		v = _dict.get((1 << j) - key, 0)
		if v: answer += vx * v

print answer
