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())
N = list(map(int, input().split()))

D = dict()

for i in range(n):
    D[N[i]] = D.get(N[i], 0) + 1

S = {1}
counter = 0
s = 1
for i in range(1, 33):
    s *= 2
    S.add(s)

for elem in D:
    for step in S:
        if D.get(step - elem, 0) > 0:
            if step - elem != elem:
                counter += D[elem]*D[step - elem] / 2
                #print('1-', counter, elem, step - elem)
            elif step - elem == elem and D[elem] > 1: 
                counter += (math.factorial(D[elem]) // (2 * math.factorial(D[elem] - 2) )) 
                #print('2-', counter)
print(int(counter))