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 = input()
a = map(int, raw_input().split())
cnt = {}
for i in a:
	if i not in cnt: cnt[i] = 1
	else: cnt[i] += 1
ans = 0
for i in a:
	for p in range(1, 32): 
		cur = 2 ** p
		if cur - i in cnt: 
			#print 'cur=', cur, 'i=', i, 'cur-i=', cur - i
			if cur - i == i:
				ans += cnt[cur - i] - 1
			else: ans += cnt[cur - i]
	cnt[i] -= 1
#print cnt
print ans
		