B"Vova has recently learned what a circulaton in a graph is. Recall the definition: let G = (V, E) be a directed graph. A circulation f is such a collection of non-negative real numbers f_e ( e in E ), that for each vertex v in V the following conservation condition holds: sum limits_{e in delta^{-}(v)} f_e = sum limits_{e in delta^{+}(v)} f_e where delta^{+}(v) is the set of edges that end in the vertex v , and delta^{-}(v) is the set of edges that start in the vertex v . In other words, for each vertex the total incoming flow should be equal to the total outcoming flow. Let a lr -circulation be such a circulation f that for each edge the condition l_e <= q f_e <= q r_e holds, where l_e and r_e for each edge e in E are two non-negative real numbers denoting the lower and upper bounds on the value of the circulation on this edge e . Vova can't stop thinking about applications of a new topic. Right now he thinks about the following natural question: let the graph be fixed, and each value l_e and r_e be a linear function of a real variable t : l_e(t) = a_e t + b_e r_e(t) = c_e t + d_e Note that t is the same for all edges. Let t be chosen at random from uniform distribution on a segment [0, 1] . What is the probability of existence of lr -circulation in the graph? The first line contains two integers n , m ( 1 <= q n <= q 1000 , 1 <= q m <= q 2000 ). Each of the next m lines describes edges of the graph in the format u_e , v_e , a_e , b_e , c_e , d_e ( 1 <= q u_e, v_e <= q n , -10^4 <= q a_e, c_e <= q 10^4 , 0 <= q b_e, d_e <= q 10^4 ), where u_e and v_e are the startpoint and the endpoint of the edge e , and the remaining 4 integers describe the linear functions for the upper and lower bound of circu"...