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.
def get_next(val):
    n= val
    k = 0
    while n:
        k += 1
        n >>= 1
    return 2**k


l = int(raw_input())
nums = [int(x) for x in raw_input().split(' ')]
#nums = sorted(nums)
from collections import defaultdict
import math
dic = defaultdict(list)
res = 0
for i, n in enumerate(nums):
    dic[n].append(i)

for n in dic:
    next = get_next(n) - n
    ind = dic.get(next, [])
    if next == n and len(ind) == 1:
        continue
    if next == n:
        res += (len(ind) * (len(ind) - 1) / 2)
        continue
    res += len(ind) * len(dic[n])
print res