B"For an array u_1, u_2, ldots, u_n , define You are given three cost arrays: [a_1, a_2, ldots, a_n] , [b_1, b_2, ldots, b_n] , and [c_0, c_1, ldots, c_{n-1}] . Define the cost of an array that has x prefix maximums, y suffix maximums, and z ascents as a_x cdot b_y cdot c_z . Let the sum of costs of all permutations of 1,2, ldots,n be f(n) . Find f(1) , f(2) , ..., f(n) modulo 998 ,244 ,353 . The first line contains an integer n ( 1 <= n <= 700 ). The second line contains n integers a_1, ldots,a_n ( 0 <= a_i<998 ,244 ,353 ). The third line contains n integers b_1, ldots,b_n ( 0 <= b_i<998 ,244 ,353 ). The fourth line contains n integers c_0, ldots,c_{n-1} ( 0 <= c_i<998 ,244 ,353 ). Print n integers: the i -th one is f(i) modulo 998 ,244 ,353 . In the second example: The sum of all permutations' costs is 34 , so f(3)=34 . "...