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(raw_input())
a=map(int,raw_input().split())
powers=[2**i for i in xrange(1,32)]
c=0
dic={}
for value in a:
	for pow2 in powers:
		if pow2>value:
			if pow2-value in dic:
				c+=dic[pow2-value]
	if value in dic:
		dic[value]+=1
	else:
		dic[value]=1
print c			