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.
import math
from collections import defaultdict
def solve():
    n = int(input())
    arr = list(map(int, input().split(" ")))

    freq = defaultdict(int)
    total = 0

    power_of_twos = []
    count = 1
    while 2**count <= 2 * 10**9:
        power_of_twos.append(2**count)
        count += 1

    for i in arr:
        if i in freq:
            total += freq[i]

        for j in power_of_twos:
            if j - i > 0:
                freq[j - i] += 1

    print(total)

solve()