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.sort()
pow2 = [2**i for i in range(1, 31)]
nums = []
counts = {}

for a in A:
	if a not in counts:
		nums.append(a)
		counts[a] = 0
	counts[a] += 1
nums.reverse()
ans = 0
for n in nums:
	if n not in counts:
		continue
	for p in pow2:
		if p > n and (p-n) in counts:
			if n == p - n:
				if counts[p-n] >= 2:
					ans += counts[p-n] // 2
					counts[p-n] = counts[p-n] % 2
			else:
				cnt = min(counts[p-n], counts[n])
				ans += cnt
				counts[p-n] -= cnt
				counts[n] -= cnt
print(ans)