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 = list(map(int,input().split()))
even = {}
odd = {}
for i in range(len(a)):
    if(a[i]%2==0):
        if(a[i] in even):
            even[a[i]]+=1
        else:
            even[a[i]]=1
    else:
        if(a[i] in odd):
            odd[a[i]]+=1
        else:
            odd[a[i]]=1
count=0
count2=0
for keys,values in even.items():
    for i in range(33):
        p = int(pow(2,i)) - keys
        if(p>0):
            if p in even:
                if(keys==p):
                    count+=((values*(values-1))//2)
                else:
                    count2+=(values*even[p])
for keys,values in odd.items():
    for i in range(33):
        p = int(pow(2,i)) - keys
        if(p>0):
            if p in odd:
                if(keys==p):
                    count+=((values*(values-1))//2)
                else:
                    count2+=(values*odd[p])
print(count + count2//2)
                
