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
import math
N = int(input())
A = sorted([int(_) for _ in input().split()], reverse=True)
dp = {}
for a in A:
    dp[a] = dp.get(a, 0) + 1
ans = 0
for a in A:
    if dp[a]:
        dp[a] -= 1
        if dp.get(2**int(math.log2(a) + 1) - a, 0) > 0:
            dp[2**int(math.log2(a) + 1) - a] -= 1
            ans += 1
print(ans)