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.
import sys
input = sys.stdin.readline
from collections import Counter

n = int(input())
a = list(map(int, input().split()))
p = [2]

while p[-1]*2<=10**18:
    p.append(p[-1]*2)

cnt = Counter(a)
ans = 0

for k, v in cnt.items():
    for pi in p:
        k2 = pi-k
        
        if k==k2:
            ans += cnt[k]*(cnt[k]-1)
        else:
            ans += cnt[k]*cnt[k2]

print(ans//2)