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())
numbers = list(map(int, input().split()))
sced = set(numbers)
counter = {}
for k in numbers:
  if k in counter:
    counter[k] += 1
  else:
    counter[k] = 1

x = 1
ans = 0

for i in range(32):
  for j in sced:
    if (j <= x):
      if (j == x):
        ans += counter[x] * (counter[x] - 1) // 2
      else:
        if x * 2 - j in counter:
          ans += counter[j] * counter[x * 2 - j]
    
  x *= 2

print(ans)
	  	  		   	 	 		   	 		 	  			