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.
# -*- coding: utf-8 -*-

# Baqir Khan
# Software Engineer (Backend)

from collections import defaultdict
from sys import stdin

inp = stdin.readline

n = int(inp())
a = list(map(int, inp().split()))
freq = defaultdict(int)
ans = 0

for i in range(n):
    freq[a[i]] += 1

for i in range(n):
    freq[a[i]] -= 1
    for j in range(32):
        power_of_2 = 1 << j
        if power_of_2 - a[i] in freq:
            ans += freq[power_of_2 - a[i]]

print(ans)
