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.

pows = [1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0, 512.0, 1024.0, 2048.0, 4096.0, 8192.0, 16384.0, 32768.0, 65536.0, 131072.0, 262144.0, 524288.0, 1048576.0, 2097152.0, 4194304.0, 8388608.0, 16777216.0, 33554432.0, 67108864.0, 134217728.0, 268435456.0, 536870912.0, 1073741824.0]

n = int(raw_input())
a = map(int,raw_input().split())

count = 0
x = {}


for i in range(0,n) :
    for p in pows :
        count += x.get(p-a[i],0)
    x[a[i]] = x.get(a[i],0) + 1
print count
