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())
l = list(map(int, input().split()))

twos = set()
for i in range(1, 36):
	twos.add(2**i)

dic = {}
for i in range(len(l)):
	if l[i] not in dic:
		dic[l[i]] = 1
	else:
		dic[l[i]] += 1
	
ans = 0
for i in dic:
	for two in twos:
		x = two - i
		if x > 0:
			if x in dic:
				if x == i:
					ans += dic[i] * (dic[i] - 1)
				else:
					ans += dic[i] * dic[x]
				#print (x, i, ans)	
print (int(ans/2))
