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.
from sys import stdin
n = int(stdin.readline())
a = map(int,stdin.readline().split())
di = {}
for i in a:
 di[i] = di.get(i,0)+1
ans = 0
b = []
for i in xrange(33):
 b.append(2**i)

for i in a:
 for j in b:
  x = j-i
  r= di.get(x,0)
  if x!=i:
   ans+=r
  else:
   ans+=r-1
print ans/2