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

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

Print the number of pairs of indexes i, j (i < j) that ai + aj 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.
import sys
from collections import defaultdict

if __name__ == "__main__":
    n = sys.stdin.readline().strip().split()
    elements = [int(i) for i in sys.stdin.readline().strip().split()]
    counter_dict = defaultdict(int)
    pairs = 0
    for e in elements:
        for i in xrange(1, 32):
            value = 2**i - e
            if value in counter_dict:
                pairs += counter_dict[value]
        counter_dict[e] += 1
    print pairs




