You are given n integers a1,a2,...,an. Find the number of pairs of indexes i,j (i \lt j) that ai+aj is a power of 2 (i. e. some integer x exists so that ai+aj=2x).

The first line contains the single positive integer n (1 \le n \le 105) - the number of integers.

The second line contains n positive integers a1,a2,...,an (1 \le ai \le 109).

Print the number of pairs of indexes i,j (i \lt j) that ai+aj is a power of 2.

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 \lt j) include in answer.