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

n=int(raw_input())
array=map(int, raw_input().split())

positions=defaultdict(list)

for i, item in enumerate (array):
    positions[item].append (i)

    
counter=0

for a in xrange (32):
    for item in positions:
        if 2**a-item in positions:
            if 2**a-item==item:
                counter+=(1+len(positions[item])-1)*(len(positions[item])-1)/2
            else:
                for i, pos in enumerate (positions[item]):
                    position=len (positions[2**a-item])
                    for x, posx in enumerate (positions[2**a-item]):
                        if posx > pos:
                            position=x
                            break
                    counter+=len (positions[2**a-item])-position
                
                        
            
            
               
            
            
print counter