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.
#!/usr/bin/python

import sys

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

answer = 0

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

p2 = {}
for i in range(0, 31):
	p2[i] = 2 ** i

i = 0
while i < n:
	x = keys[i] << 1;
	y = _dict[keys[i]]
	if y > 1 and x != 0 and (x & (~x + 1)) == x:
		answer += y * (y - 1) / 2

	x = keys[i];
	vx = _dict[x]
	_dict[x] = 0

	for j in range(0, 31):
		y = p2[j] - x
		v = _dict.get(y, 0)
		if v:
			answer += vx * v
	i += 1

print answer
