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())
l = list(map(int, input().split()))
dic = {}
for i in range(n):
    x = l[i]
    dic[x] = 0
for i in range(n):
    x = l[i]
    dic[x] += 1
s = max(l)
m = 0
num = 0
while 2 ** m <= s:
    m += 1
for i in range(n):
    a = l[i]
    for j in range(1, m + 1):
        b = 2 ** j - a
        if b in dic:
            if b == a:
                num += dic[b] - 1
            else:
                num += dic[b]
num = int(num/2)
print(num)