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.
raw_input()
# holding all input integers
array = map(int, raw_input().split())
# a dictionary: <value, occurance>, updated as position moves
d = {}
counter = 0

# pre-compute 2 to the power of 30
test = [2**i for i in xrange(32)]

for val in array:
    for pow2 in test:
        if pow2 >= val:
            if (pow2 - val) in d:
                counter += d[pow2 - val]
    if val in d:
        d[val] += 1
    else:
        d[val] = 1
        
print counter
