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B. Powers of Two

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given *n* integers *a* _{1}, *a* _{2}, ..., *a* _{ n}. Find the number of pairs of indexes *i*, *j* ( *i* < *j*) that *a* _{ i} + *a* _{ j} is a power of 2 (i. e. some integer *x* exists so that *a* _{ i} + *a* _{ j} = 2^{ x}).

Input

The first line contains the single positive integer *n* (1 ≤ *n* ≤ 10^{5}) — the number of integers.

The second line contains *n* positive integers *a* _{1}, *a* _{2}, ..., *a* _{ n} (1 ≤ *a* _{ i} ≤ 10^{9}).

Output

Print the number of pairs of indexes *i*, *j* ( *i* < *j*) that *a* _{ i} + *a* _{ j} is a power of 2.

Examples

Input

4

7 3 2 1

Output

2

Input

3

1 1 1

Output

3

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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