B'Tenzing has n animal friends. He numbers them from 1 to n . One day Tenzing wants to play with his animal friends. To do so, Tenzing will host several games. In one game, he will choose a set S which is a subset of {1,2,3,...,n } and choose an integer t . Then, he will play the game with the animals in S for t minutes. But there are some restrictions: Tenzing wants to know the maximum total time that he can play with his animal friends. Please find out the maximum total time that Tenzing can play with his animal friends and a way to organize the games that achieves this maximum total time, or report that he can play with his animal friends for an infinite amount of time. Also, Tenzing does not want to host so many games, so he will host at most n^2 games. The first line of input contains two integers n and m ( 2 <= q n <= q 100 , 0 <= q m <= q frac{n(n-1)}{2} ) -- the number of animal friends and the number of special restrictions. The i -th of the following m lines of input contains three integers u_i , v_i and y_i ( 1 <= q u_i<v_i <= q n , 0 <= q y_i <= q 10^9 ) -- describing the i -th special restriction. It is guaranteed that for 1 <= q i < j <= q m , (u_i,v_i) neq (u_j,v_j) . If Tenzing can play with his animal friends for an infinite amount of time, output "inf". (Output without quotes.) Otherwise, in the first line, output the total time T ( 0 <= q t <= q 10^{18} ) and the number of games k ( 0 <= q k <= q n^2 ). In the following k lines of output, output a binary string s of length n and an integer t ( 0 <= q t <= q 10^{18} ) -- representing the set S and the number of minutes this game will be played. If s_i= texttt{1} , then i in S , otherwise if s_i= texttt{0} , then i notin S . Under the constraints of this problem, it can be proven that if '...