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.
import sys


def main():
    ans = 0
    n = int(sys.stdin.readline())
    a = list(map(int, sys.stdin.readline().split(' ')))
    store = {}
    power = {}

    for k, v in enumerate(a):
        store[v] = store.get(v, 0) + 1

    power[1] = 2
    for i in range(2, 32):
        power[i] = power[i-1]*2

    for k, v in enumerate(a):
        store[v] -= 1
        for i in range(1, 32):
            if power[i] > v and (power[i]-v) in store:
                ans += store[power[i]-v]

    return ans

answer = main()
print(answer)
