#include <pointblank>

In a town called "Fernando Pessoa", during the year of 2050, there was a game named PointBlank that has became very popular in the city. It was a classic online FPS game, where people of each team had to kill the players of the other team. The winner of a game was the one that killed the most amount of players after the end of all rounds.

The game was divided in M rounds, each one with N players in different positions. Kurohitsugi, the best player in the town was challenged to kill all the other N players in each round. He knows that he has only one chance: if he dies once, he loses.

According to a very experient captain, Sr. Anonymate, the best position where a player can stay in is exactly a point x that minimizes the sum of the squares of the distances to the other players. And, magically, we know that the probability of killing an oponent is exactly this point 'x' divided by 100.

He wants to calculate the probability sum of killing all the soldiers in all the M rounds if he stays in the point x, but he isn't good in math or programming, so he asked for your help. 

Input

The first line will contain two integers, N and M (1 <= N <= 20, 1 <= M <= 10^6): the amount of players and the amount of rounds. Each of the next M lines will contain N integers Xi (1 <= Xi <= 100): the positions of the players.

Output

You have to print the sum of the probabilities of killing all the N players in each round.

Example