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 sys, threading

sys.setrecursionlimit(10 ** 6)

scan = lambda: map(int, input().split())

n = int(input())
ans = 0
hash = {}
for i in scan():
    tmp = 1
    while tmp*2<=1e12:
        tmp *=2
        ans += hash.get(tmp-i, 0)
    if hash.get(i, 0):
        hash[i] += 1
    else:
        hash[i] = 1
print(ans)