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()
import sys
a=list(map(int,sys.stdin.readline().split()))
b={}
for i in a:
    if i not in b:
        b[i]=1
    else:
        b[i]+=1
ans=0
s=0
#print(b)
for i in set(a):
    for j in range(0,32):
        y=2**j-i
        if y==i   and i in b:
            s+=((b[i]*(b[i]-1))//2)
        elif  y in b:
            ans+=(b[i])*(b[y])
            
print(s + ans//2)
    