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 bisect import bisect
from math import log2
n = int(input())
a = [int(i) for i in input().split()]
a,x,ans = sorted(a),[1]*n,0
for i in range(n-1,-1,-1):
	if x[i]:
		m = 2**(int(log2(a[i]))+1)
		b = bisect(a,m-a[i],hi=i)-1
		if b+1 and a[b]==m-a[i]: x[b],ans,a[b],a[i] = 0,ans+1,a[b]+0.1,a[i]+0.1
print(ans)