Description: You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x). Input Format: The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers. The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109). Output Format: Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2. Note: In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4). In the second example all pairs of indexes (i, j) (where i < j) include in answer.