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.
n=int(raw_input())
a=raw_input().split()
a=[int(i) for i in a]
cnt=0
d=dict()
for i in range(0,n):
	cnt+=d.get(a[i],0)
	for j in range(1,31):
		if(2**j-a[i]>0):
			if 2**j-a[i] not in d:
				d[2**j-a[i]]=1
			else:
				d[2**j-a[i]]+=1
print cnt