Mike and Harvey are back together! To celebrate this special occasion, they decided to play a unique game. So, this is how it goes :

Mike gives Harvey an $N \times N$ grid A containing integers and 2 integers K and X. Now, Harvey begins the game by selecting K distinct rows among the N rows. He will then add the integer X to all elements of the selected rows.

Mike will then write N integers on a piece of paper, where the $i^{th}$ integer denotes the maximum integer present in the $i^{th}$ column. He then tells Harvey the sum of all integers written on that piece of paper. Let's call this number Mike tells Harvey as Z

This is where your part comes in. Considering that Harvey selects each distinct tuple of K rows with equal probability, you are to find the Expected Value of Z. Can you do this ?

Your answer will be considered correct if the absolute OR relative error between your answer and the jury's answer is $\le 10^{-9}$ . More formally, let your answer be a and the jury's answer be b. Your solution will be considered correct if $\frac {|a-b|}{max(1,b)} \le 10^{-9}$

Input Format :

The first line contains 3 space separated integers $N, K$ and X respectively.

Each of the next N lines contains N space separated integers, where the $j^{th}$ integer on the $i^{th}$ line denotes $A[i][j]$.

Output Format :

For each test case, print a single real number denoting the answer to the problem.

Constraints :

$2 \le N \le 1000$

$1 \le K \le N$

$0 \le A[i] , X \le 10^6$