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())

arr = [int(z) for z in input().split()]

arr.sort()

occ = {}
for i in set(arr):
    occ[i] = 0

for i in arr:
    occ[i] += 1

res = 0
for power in range(32):
    for i in arr:
        if not occ.get(2**power - i):
            continue
        if 2**power - i == i:
            res += (occ[i] - 1)
        else:
            res += occ[2**power - i]

print(res//2)

