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.
#import sys
#sys.stdin = open('in', 'r')
n = int(input())
a = [int(x) for x in input().split()]
#n,m = map(int, input().split())

st2 = [1]
while st2[-1] <= 10**10:
    st2.append(st2[-1]*2)

r = 0
d = {}
for i in range(n):
    for s2 in st2:
        if (s2 - a[i]) in d:
            r += d[s2-a[i]]
    d[a[i]] = d.get(a[i], 0) + 1

print(r)
