Dr. Henri is looking through his telescope at the MRD Observatory. He is observing a certain star ~Y~ and wants to find its magnitude (a measure of brightness), ~m_Y~. The magnitude of a star can be any real number.

Dr. Henri is using a device called a differential photometer to measure magnitude. Although this device is very precise, it cannot directly measure the magnitude of a star; it can only measure the difference in magnitudes between two stars.

Fortunately, Dr. Henri knows the magnitude ~m_X~ of a certain star ~X~. He decides to find ~m_Y~ by constructing a sequence of ~n + 1~ stars beginning with ~X~ and ending with ~Y~. Then, for each star ~i~ on the list (except ~Y~), he records the difference ~d_i = m_{i + 1} - m_i~ between the magnitudes of the stars ~i + 1~ and ~i~, for a total of ~n~ observations. He can then calculate a value for ~m_Y~ from this sequence.

Dr. Henri knows that he must take multiple measurements in order to ensure accuracy, so he constructs ~K~ such sequences. Sequence ~i~ consists of ~n_i~ observations, and the value of ~m_Y~ calculated from ~i~ is denoted as ~m_{Yi}~. Of course, due to natural error in measuring, the ~m_{Yi}~'s calculated from each sequence may not be exactly the same. So Dr. Henri will use the mean of the ~m_{Yi}~'s, ~\frac{m_{Y1} + m_{Y2} + \dots + m_{YK}}{K}~, as the final ~m_Y~, which he denotes ~m_{Yf}~.

Given ~K~ sequences of observations, please help Dr. Henri find ~m_{Yf}~.

Constraints

~2 \le K \le 1\,000~
~1 \le n_i \le 1\,000~
~-100.0 \le m_X, d_i \le 100.0~

Input Specification

The first line of input will contain one integer, ~K~.
The second line will contain one real number, ~m_X~.
The next ~K~ lines will contain one integer ~n_i~, followed by ~n_i~ space-separated real numbers ~d_{i1}, d_{i2}, \dots, d_{in_i}~, the observations from the ~i~-th list.

Output Specification

A single line containing one real number, ~m_{Yf}~. Your answer will be judged as correct if it has an absolute error of no more than ~10^{-3}~.

Sample Input

3
-1.46
2 4.53 1.20
3 4.77 -1.45 2.35
1 5.69

Sample Output

4.236667