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(input())
a = input().split()
a = [int(i) for i in a]
#d = dict()
ans = 0
'''
for i in range(n):
    ans += d.get(a[i],0)
    for j in range(1,31):
        val = 2**j - a[i]
        if val > 0:
            if val not in d:
                d[val] = 1
            else:
                d[val] += 1
print(ans)
'''
d = Counter()
for i in range(n):
    for j in range(1,31):
        val = 2**j - a[i]
        if val > 0:
            if val in d:
                ans += d[val]
    d[a[i]] +=1
print(ans)