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())
ai = list(map(int,input().split()))
nums = {}

ans = 0
for i in range(n):
    num = ai[i]
    length = len(bin(num)[2:])
    for j in range(length, 31):
        num2 = 2 ** j - num
        #print(num,num2)
        num4 = 0
        try :
            num4 = nums[num2]
        except:
            num4 = 0
        ans += num4
    try:
        nums[ai[i]] += 1
    except:
        nums[ai[i]] = 1
print(ans)
