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

p = [ 2**i for i in range(1,34) ]
n = int(input())
l = list(map(int,input().split()))

d = Counter(l)

ans = 0 
for i in range(n):
    for j in range(33):
        #if p[j] >= l[i]:
        req = p[j] - l[i]
        if d[req] > 0:
            #print('l[i', l[i] , 'req' , req)
            if req == l[i]:
                ans += d[l[i]]-1
            else:
                ans += d[req]
            #print('ans',ans)
            
print(ans//2)
