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.
#!/usr/bin/python3.4
import sys
n = int(input())
a = list(map(int, input().split()))
a.sort()
two = [2 ** i for i in range(32)]
cnt = 0
m = {}
for i in a:
	for j in two:
		cnt += m.get(j - i, 0)
	m[i] = m.get(i, 0) + 1
print(cnt)