B. Powers of Twotime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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).InputThe 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).OutputPrint the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.ExamplesInput47 3 2 1Output2Input31 1 1Output3NoteIn 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.
Input47 3 2 1
Output2
['brute force', 'data structures', 'implementation', 'math', '*1500']