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.
"""
Code of Ayush Tiwari
Codeforces: servermonk
Codechef: ayush572000

"""
import sys
input = sys.stdin.buffer.readline
from collections import Counter
def solution():
    po=[2**i for i in range(31)]
    n=int(input())
    l=list(map(int,input().split()))
    c=Counter(l)
    ans=0
    for i in range(n):
        for j in po:
            x=j-l[i]
            if c.get(x,0)>0:
                # print(l[i],x)
                if x==l[i]:
                    ans+=(c[x]-1)
                else:
                    ans+=c[x]
    print(ans//2)




solution()