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.
from math import log2,ceil
def powerof2(k):
    if(2**(ceil(log2(k)))==k):
        return ceil(log2(k)+1)
    return ceil(log2(k))
n=int(input())
a=list(map(int,input().split()))
d={}
for  i  in a:
    try:
        d[i]+=1
    except:
        d[i]=1
c=0
y=max(a)
for i in a:
    r=powerof2(i)
    for j in range(r,33):
        if(2**j-i>y):
            break
        if(2**j-i==i):
            try:
                if(d[i]>=2):
                    #print("i: ",i,"     j:",2**j-i)
                    c+=d[i]-1
            except:
                pass
        else:
            try:
                if(d[2**j-i]>0):
                    #print("i: ",i,"     j:",2**j-i)
                    c+=d[2**j-i]

            except:
                pass
print(c//2)