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())
a = [int(i) for i in input().split()]

def isp2(x):
	return (x >= 1) and ((x & (x - 1)) == 0)

p2 = [2 ** i for i in range(33)]

d = {}
for i in a:
	if i in d:
		d[i] += 1
	else:
		d[i] = 1

k = 0
for i in d:
	for p in p2:
		j = p - i
		if j > i:
			break;
		if j in d:
			if i == j:
				k += d[i] * (d[i] - 1) // 2
			else:
				k += d[i] * d[j]

print(k)
