Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Lua (5.3.2) (judge verdict: Wrong Answer)

local n = io.read("*n")
local a = {}
local am = {}
for i = 1, n do
  local v = io.read("*n")
  a[i] = v
  if not am[v] then am[v] = 1 else am[v] = am[v] + 1 end
end
table.sort(a)
local ret = 0
local mul = 1
while mul < a[n] do
  mul = mul * 2
end
for i = n, 2, -1 do
  local v = a[i]
  while v + v < mul do
    mul = mul // 2
  end
  if am[v] then
    am[v] = am[v] - 1
    if am[v] == 0 then am[v] = nil end
    local dst = mul - v
    if am[dst] then
      ret = ret + 1
      am[dst] = am[dst] - 1
      if am[dst] == 0 then am[dst] = nil end
    end
  end
end
print(ret)