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.
n = int(input())
dictionary = dict()
for i in input().split():
    if int(i) in dictionary:
        dictionary[int(i)]+=1
    else:
        dictionary[int(i)]=1       
powerslist = []
ans = 0  
for i in range(1,32):
    powerslist.append(2**i)
 
for i in dictionary:
    for j in powerslist:
        if j-i in dictionary:
            if j-i!=i:
                ans+=dictionary[j-i]*dictionary[i]
            else:
                ans+=(dictionary[i]-1)*(dictionary[i])
            
print(ans//2)
