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: Accepted)

local N = io.read("n")
local A = {}
local S = {}
for i=1,N do
    local n = io.read("n")
    A[i] = n
    if not S[n] then
        S[n] = 0
    end
    S[n] = S[n] + 1
end
table.sort(A)

local function target(r)
    local r2 = r + 1
    local t = 2
    while t < r2 do
        t = t * 2
    end
    return t, t - r
end

local ans = 0
for i=N,2,-1 do
    local r = A[i]
    local t, c = target(r)
    local hit = false
    if S[r] > 0 then
        S[r] = S[r] - 1
        if S[c] and S[c] > 0 then
            ans = ans + 1
            S[c] = S[c] - 1
            hit = true
        end
    end
    --print(r, t, c, hit)
end
print(ans)