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 collections import  defaultdict
def f(arr,n):
    answer=0
    pp=[2**i for i in range(40)]
    dct={}
    # dct[0] = 1
    pref=0
    for i in range(0, len(arr)):
        for  num in pp:
            need=num-arr[i]
            # if dct[need]:
                # print(dct[need],need,arr[i],num)
            answer+=dct.get(need,0)
        dct[arr[i]]=dct.get(arr[i],0)+1
    return answer
a=int(input())
l=list(map(int,input().strip().split()))
print(f(l,a))