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 bisect

n = int(input())
a = sorted(list(map(int, input().split())))

cnt = {}
for x in a:
    if x in cnt:
        cnt[x] += 1
    else:
        cnt[x] = 1

ans = 0
for i in range(n - 1, -1, -1):
    for d in range(30, -1, -1):
        k = bisect.bisect_left(a, (1 << d) - a[i])
        if k < n and a[i] + a[k] == (1 << d) and (a[i] == a[k] and cnt[a[i]] >= 2 or a[i] != a[k] and cnt[a[i]] >= 1 and cnt[a[k]] >= 1):
            ans += 1
            cnt[a[i]] -= 1
            cnt[a[k]] -= 1

print(ans)