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.

from collections import Counter
wczytane = []
MAXN = 0
m = Counter()
def wczytaj():
	global wczytane
	wczytane = []
	S = raw_input()
	i = 0
	n = len(S)
	while i < n:	
		a = 0
		ujemne = False
		while i < n and S[i] != ' ':
			a *= 10
			if S[i] == '-':
				ujemne = True
				i += 1
			a += int(S[i])
			i += 1
		i += 1
		if ujemne:
			wczytane.append(-a)
		else: wczytane.append(a)

n = input()

wczytaj()
t = wczytane
for i in range(n):
	m[t[i]] += 1
	MAXN = max(MAXN,t[i])

MAXN *= 2

wyn = 0
for w in range(n):
	a = t[w]
	R = 1
	while R <= MAXN:
		if R - a < 1:
			R *= 2
			continue
		if a != R - a:
			wyn += m[R - a]
		else:
			wyn += m[R - a] - 1
		R *= 2
print wyn // 2 

	
