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 math
n=int(input())
l=list(map(int,input().split()))
p = [2**i for i in range(1,34)]
d={}
c=0
for i in range(len(l)):
    for j in p:
        if(j-l[i] in d):
            c+=d[j-l[i]]
    if(l[i] in d):
        d[l[i]]+=1
    else:
        d[l[i]]=1
print(c)