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())
ar = list(map(int,input().split()))
d = {}
for i in ar:
	if i not in d:
		d[i] = 1
	else:
		d[i] = d[i] + 1
# print(d)
ans = 0
for p in d:
	for j in range(31):
		x = 1 << j
		if x == 2*p:
			ans += (d[p]*(d[p]-1))
		elif x - p in d:
			# print("yes",d[x-p])
			ans += d[p]*d[x - p]
print(ans//2)

	
