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.
#!/usr/bin/python

from collections import deque

def ir():
    return int(raw_input())

def ia():
    line = raw_input()
    line = line.split()
    return map(int, line)

n = ir()
a = ia()

d = {}
for e in a:
    d[e] = d.get(e, 0) + 1

ans  = 0
for e in a:
    p = 1
    for k in range(0, 31):
        p *= 2
        rst = p - e
        if rst not in d: continue
        if rst != e: ans += d[p - e]
        else       : ans += d[p - e] - 1

print ans // 2
