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.
twoPowers = [2 << x for x in range(32)]
numbers = {}

n = input()

for x in [int(x) for x in input().split()]:
    if x not in numbers:
        numbers[x] = 0
    numbers[x] += 1

sum = 0

for twoPower in twoPowers:
    for key in numbers:
        if key <= twoPower >> 1:
            oppositeKey = twoPower - key
            if key == oppositeKey:
                sum += numbers[key] * (numbers[key]-1 ) // 2
            elif oppositeKey in numbers:
                sum += numbers[key] * numbers[oppositeKey]

print(sum)