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(raw_input())
a = map(int, raw_input().split())
poweroftwo = [1<<i for i in xrange(1,33)]
differencedict = dict()
paircount = 0
for i in xrange(n):
    paircount += differencedict.get(a[i],0)
    for twoindex in poweroftwo:
        target = twoindex - a[i]
        if target >0:
            if target not in differencedict:
                differencedict[target] = 1
            else:
                differencedict[target]+=1
print paircount


