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.
pow2=[1]*33
for i in range(1,33):
	pow2[i]=2*pow2[i-1]

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

res=0
dic={}
for a in nums:
	value=dic.get(a,0)
	dic[a]=value+1

for a in nums:
	for b in pow2:
		value=dic.get(b-a,0)
		res+=value
		if (b==2*a):
			res-=1

print res/2