{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"Organizing a programming contest is not an easy job. To avoid making the problems too difficult, the organizer usually expect the contest result satisfy the following two terms:\r\u003cbr\u003e1.\tAll of the teams solve at least one problem.\r\u003cbr\u003e2.\tThe champion (One of those teams that solve the most problems) solves at least a certain number of problems.\r\u003cbr\u003e\r\u003cbr\u003eNow the organizer has studied out the contest problems, and through the result of preliminary contest, the organizer can estimate the probability that a certain team can successfully solve a certain problem.\r\u003cbr\u003e\r\u003cbr\u003eGiven the number of contest problems M, the number of teams T, and the number of problems N that the organizer expect the champion solve at least. We also assume that team i solves problem j with the probability Pij (1 \u0026lt;\u003d i \u0026lt;\u003d T, 1\u0026lt;\u003d j \u0026lt;\u003d M). Well, can you calculate the probability that all of the teams solve at least one problem, and at the same time the champion team solves at least N problems?\r\u003cbr\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input consists of several test cases. The first line of each test case contains three integers M (0 \u0026lt; M \u0026lt;\u003d 30), T (1 \u0026lt; T \u0026lt;\u003d 1000) and N (0 \u0026lt; N \u0026lt;\u003d M). Each of the following T lines contains M floating-point numbers in the range of [0,1]. In these T lines, the j-th number in the i-th line is just Pij. A test case of M \u003d T \u003d N \u003d 0 indicates the end of input, and should not be processed."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, please output the answer in a separate line. The result should be rounded to three digits after the decimal point. "}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2 2 2\r\n0.9 0.9\r\n1 0.9\r\n0 0 0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.972\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}