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 sys
input=sys.stdin.readline
print=sys.stdout.write
n=int(input())
ar=list(map(int,input().split()))
p2=[2**i for i in range(1,64)]
d=dict()
for x in ar:
    try:
        d[x]+=1
    except:
        d[x]=1
ans=0
for x in p2:
    for el in set(ar):
        if el*2 != x:
            try:
                ans+=(d[el]*d[x-el])
            except:
                pass
        else:
            ans+= (d[el]*(d[el]-1))
print(str(int(ans)//2))