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.
def binary(x):
	b_left = -1
	b_right = x-1
	b_power = power(mas[x])
	while b_right!=b_left:
		b_middle = (b_left+b_right+1)//2
		if mas[b_middle]+mas[x]>=b_power:
			b_right = b_middle-1
		else:
			b_left = b_middle
	left_border = b_left
	b_right = x
	b_left = 0
	while b_right!=b_left:
		b_middle = (b_left+b_right)//2
		if mas[b_middle]+mas[x]>b_power:
			b_right = b_middle
		else:
			b_left = b_middle+1
	right_border = b_right
	return (right_border-left_border-1)

def power(x):
	p_answer = 2
	while x!=1:
		x = x//2
		p_answer = p_answer*2
	return (p_answer)

N = int(input())
mas = [int(x) for x in input().split()]
mas.sort()
answer = 0
for i in range(N-1, 0, -1):
	answer = answer+binary(i)
print(answer)
