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 defaultdict as dd
from math import log
n = input()
a = map(int,raw_input().split())
m = max(a)
ans = 0
d = dd(int)
for i in range(n):
    d[a[i]]+=1
for i in range(n):
    p = int(log(a[i],2))
    p+=1
    while 1:
        q = 2**p - a[i]
        if q > m:
            break
        if q==a[i]:
            if d[q]>=2:
                ans +=d[q]-1
        else:
            if d[q]>=1:
                ans +=d[q]
        p+=1
print ans/2
