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.
from collections import defaultdict

n=int(raw_input())
array=map(int, raw_input().split())

numbers=defaultdict(list)

for i, item in enumerate (array):
    numbers[item].append (i)
    
counter=0

for i in xrange (32):
    for num in numbers:
        if 2**i-num in numbers:
            if 2**i-num==num:
                counter+=(1+len(numbers[num])-1)*(len(numbers[num])-1)/2
            else:
                for pos1 in numbers[num]:
                    positions=len (numbers[2**i-num])
                    for x, pos2 in enumerate (numbers[2**i-num]):
                        if pos2 > pos1:
                            positions=x
                            break
                    counter+=len (numbers[2**i-num])-positions
print counter