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())
a = sorted([int(i) for i in input().split()])
d = {}
for i in range(n):
    if a[i]in d:
        d[a[i]]+=1
    else:
        d[a[i]]=1
ans=0
for i in range(32):
    t=2**i
    for j in d:
        if t-j in d:
            if j==t-j:
                ans+=(d[j]-1)*d[j]
            else:
                ans+=d[j]*d[t-j]
print(ans//2)