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).
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).
Print the number of pairs of indexes i,j (i<j) that ai+aj is a power of 2.
4
7 3 2 1
2
3
1 1 1
3
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.