B - Powers of two /

問題文

ただし、正整数が 2 べきであるとは、ある非負整数 t を用いて 2^t と書けることを指します。

制約

• 1 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^9
• A_i は整数

入力

N
A_1 A_2 ... A_N


出力

2 つのボールに書かれた数の和が 2 べきとなるペアの個数として考えられる最大値を出力せよ。

入力例 1

3
1 2 3


出力例 1

1


1 番目のボールと 3 番目のボールをペアにすることで、書かれた数の和が 4 となるペアを 1 つ作ることができます。 2 番目のボール同士をペアにできないことに注意してください。

入力例 2

5
3 11 14 5 13


出力例 2

2


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