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 = raw_input()
A = [int(i) for i in A.split(' ')]

two = []
i = 1
while(i <= 100000000000):
	two += [i]
	i *= 2

ans = 0	
d = dict()
for i in A:
	for j in two:
		ans += d.get(j-i,0)
	d[i] = d.get(i,0) + 1
	
print(str(ans))