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.
input()
a = list(map(int, input().split()))

#a = [7, 3, 2, 1]
a = sorted(a)
total = 0

d = {}

for i in range(len(a)):
    if a[i] in d.keys():
        d[a[i]] += 1
    else:
        d[a[i]] = 1
        
values = set([2 ** i for i in range(1, 33)])

for i in range(len(a)):
    for val in values:
        diff = val-a[i]
        
        if diff in d.keys():
            
            if diff == a[i]:
                total += d[diff]-1
            else:
                total += d[diff]
                
            #print(diff,a[i], val, i, total)
                
            

print(total//2)