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
from collections import Counter

N = int(input())
A = list(map(int, input().split()))

maxPow = (1 << (max(A) * 2).bit_length())
cntA = Counter(A)

ans = 0
while maxPow > 0:
    for a in A:
        if maxPow - a == a:
            if cntA[a] >= 2:
                ans += cntA[a] // 2
                cntA[a] %= 2
        elif cntA[a] > 0 and cntA[maxPow - a] > 0:
            ans += 1
            cntA[a] -= 1
            cntA[maxPow - a] -= 1
    maxPow //= 2

print(ans)