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())
a = [int(x) for x in input().split()]
cnt = 0
D = {}
MAX = max(a)
for i in range(0, n):
    D[a[i]] = D.get(a[i],0) + 1
DK = D.keys()
for k in DK:
    e0 = 0
    while 1<<e0 <= k:
        e0 += 1
    for e in range(e0,32):
        pow2 = 1<<e
        if pow2-k>MAX:
            break
        nk = D.get(k,0)
        if k==pow2-k:
            cnt += nk*(nk-1)
        else:
            np = D.get(pow2-k,0)
            cnt += nk*np
print(cnt//2)
