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.
'''
Created on Jul 29, 2016

@author: Md. Rezwanul Haque
'''
#from pip.util import Inf
#import math
''''
n = int(input())
L = list(map(int,input().split()))
cnt  = 0
for i in range(n):
    for j in range(i,n):
        if i<j and (L[i]+L[j])%2 == 0:
            for k in range(31):
                if pow(2, k) == L[i]+L[j]:
                    cnt+=1
                    #print(i,j)
                    break
            
            #cnt+=1
print(cnt)'''


n = int(input())

d = {}

for i in input().split():
    if int(i) in d:
        d[int(i)]+=1
    else:
        d[int(i)] = 1
        
#print(d)
L = []

for i in range(1,33):
    L.append(2**i)
    
ans = 0

for i in d:
    for j in L:
        if j-i in d:
            if j-i!= i:
                #print(d[j-i],d[i])
                ans+=d[j-i]*d[i]
            else:
                #print(d[i]-1,d[i])
                ans+=(d[i]-1)*(d[i])
#print(ans)
print(ans//2)

