Powers of two

Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

• 1 \leq N \leq 2\times 10^5
• 1 \leq A_i \leq 10^9
• A_i is an integer.

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3 1 2 3

Output

1

Input

5 3 11 14 5 13

Output

2

inputFormat

Input

Input is given from Standard Input in the following format:

N A_1 A_2 ... A_N

outputFormat

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Examples

Input

3 1 2 3

Output

1

Input

5 3 11 14 5 13

Output

2

样例

3
1 2 3

1