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.
pows=[]
x=1
for i in range(32):
    pows.append(x)
    x*=2

def countPairs(n, d):
    count=0
    x=0
    m=0
    for i in d.keys():
        if i in pows:
            m+=d[i]
    while(x<32):
        curr=pows[x]
        for i in d.keys():
            if curr-i in d.keys():
                count+=d[i]*d[curr-i]
        x+=1
    count=int((count-m)/2)
    return count

n=int(input())
d={}
for i in list(map(int, input().split())):
    if i not in d:
        d[i]=1
    else:
        d[i]+=1
print(countPairs(n, d))
