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(input())
import math
a=list(map(int,input().split()))
dic={}

x=max(a)

maxp=math.ceil(math.log2(x))
ans=0
for i in a:
	try:
		dic[i]+=1
	except:
		dic[i]=1
	for j in range(1,maxp+2):
		y=(2**j)-i
		# print(j,i,y)
		if(y<0):
			continue
		else:
			if(y==i):
				if(y in dic and dic[y]>1):
					ans+=dic[y]
					ans-=1
			else:
				if(y in dic):
					ans+=dic[y]
		# print("ans",ans)
print(ans)
