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()))
twos = []
twos.append(1)
freq = {}
while twos[-1]<int(1e9):
    twos.append(twos[-1]*2)

for i in range(n):
    freq[l[i]]=0
for i in range(n):
    freq[l[i]]+=1

answer=0

for i in range(0, l.__len__()):
    for j in range(0, twos.__len__()):
        if twos[j]>=l[i] and twos[j] - l[i] in freq and\
            twos[j] - l[i] != l[i]:
            answer+=freq[twos[j] - l[i]]
        elif twos[j]>=l[i] and twos[j] - l[i] in freq and\
            twos[j] - l[i] == l[i]:
            answer += (freq[twos[j] - l[i]]-1)

print(answer//2)

