Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3
1 2 3


Output

1


Input

5
3 11 14 5 13


Output

2
N = int(input())
A = list(map(int, input().split()))
A = sorted(A, reverse = True)
d = {} # d[i] = number of i
ans = 0
for i in A:
	for j in range(31, 0, -1):
		x = 2 ** j - i
		if x in d and d[x] > 0:
			ans = ans + 1
			d[x] -= 1
			break
	else:
		d[i] = d.get(i, 0) + 1
print(ans)