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 fractions import gcd
from datetime import date
from math import factorial
import functools
from heapq import*
from collections import deque
import collections
import math
from collections import defaultdict, Counter
import sys
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
inf = float("inf")


def main():
    n = int(input())
    a = list(map(int, input().split()))
    d = Counter(a)
    ans = 0
    for k in a:
        d[k] -= 1
        for i in range(32):
            if 2 ** i - k < 0:
                continue
            if d[2 ** i - k] > 0:
                ans += d[2 ** i - k]
    print(ans)


if __name__ == '__main__':
    main()
