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 bisect
import sys
input=sys.stdin.readline
n=int(input())
seq=sorted([int(i) for i in input().split()])
poi=2
count=0
for i in range(1,n):
    while poi<=seq[i]:
        poi*=2
    indL=bisect.bisect_left(seq,poi-seq[i],0,i)
    indR=bisect.bisect_right(seq,poi-seq[i],0,i)
    count+=(indR-indL)
print(count)
    

	 			 	    		   		 	 			    	 	