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.
from collections import Counter
n = int(raw_input())
"""
dict = {}
a = map(int, raw_input().split())
ret = 0
for a_i in a:
    x = 1
    for _ in range(31):
        if a_i in dict.keys():
            ret += dict[a_i]
            break
        x <<= 1

    x = 1
    for _ in range(31):
        if x - a_i > 0:
            dict[x - a_i] = dict.get(x - a_i, 0) + 1
        x <<= 1

print ret
"""
c, ret = Counter(), 0
a = map(int, raw_input().split())
for a_i in a:
    ret += sum(c[2 ** i - a_i] for i in range((31)))
    c[a_i] += 1

print ret