Indifferent

We have 2N pots. The market price of the i-th pot (1 ≤ i ≤ 2N) is p_i yen (the currency of Japan).

Now, you and Lunlun the dachshund will alternately take one pot. You will go first, and we will continue until all the pots are taken by you or Lunlun. Since Lunlun does not know the market prices of the pots, she will always choose a pot randomly from the remaining pots with equal probability. You know this behavior of Lunlun, and the market prices of the pots.

Let the sum of the market prices of the pots you take be S yen. Your objective is to maximize the expected value of S. Find the expected value of S when the optimal strategy is adopted.

Constraints

• 1 ≤ N ≤ 10^5
• 1 ≤ p_i ≤ 2 × 10^5
• All input values are integers.

Input

Input is given from Standard Input in the following format:

N p_1 : p_{2N}

Output

Print the expected value of S when the strategy to maximize the expected value of S is adopted. The output is considered correct if its absolute or relative error from the judge's output is at most 10^{-9}.

Examples

Input

1 150000 108

Output

150000.0

Input

2 50000 50000 100000 100000

Output

183333.3333333333

inputFormat

input values are integers.

Input

Input is given from Standard Input in the following format:

N p_1 : p_{2N}

outputFormat

Output

Print the expected value of S when the strategy to maximize the expected value of S is adopted. The output is considered correct if its absolute or relative error from the judge's output is at most 10^{-9}.

Examples

Input

1 150000 108

Output

150000.0

Input

2 50000 50000 100000 100000

Output

183333.3333333333

样例

1
150000
108

150000.0