D. Cycles in producttime limit per test7 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider a tree (that is, an undirected connected graph without loops) T_1 and a tree T_2. Let's define their cartesian product T_1 \times T_2 in a following way.Let V be the set of vertices in T_1 and U be the set of vertices in T_2.Then the set of vertices of graph T_1 \times T_2 is V \times U, that is, a set of ordered pairs of vertices, where the first vertex in pair is from V and the second — from U.Let's draw the following edges: Between (v, u_1) and (v, u_2) there is an undirected edge, if u_1 and u_2 are adjacent in U.  Similarly, between (v_1, u) and (v_2, u) there is an undirected edge, if v_1 and v_2 are adjacent in V. Please see the notes section for the pictures of products of trees in the sample tests.Let's examine the graph T_1 \times T_2. How much cycles (not necessarily simple) of length k it contains? Since this number can be very large, print it modulo 998244353.The sequence of vertices w_1, w_2, ..., w_k, where w_i \in V \times U called cycle, if any neighboring vertices are adjacent and w_1 is adjacent to w_k. Cycles that differ only by the cyclic shift or direction of traversal are still considered different.InputFirst line of input contains three integers — n_1, n_2 and k (2 \le n_1, n_2 \le 4000, 2 \le k \le 75) — number of vertices in the first tree, number of vertices in the second tree and the cycle length respectively.Then follow n_1 - 1 lines describing the first tree. Each of this lines contains two integers — v_i, u_i (1 \le v_i, u_i \le n_1), which define edges of the first tree.Then follow n_2 - 1 lines, which describe the second tree in the same format.It is guaranteed, that given graphs are trees.OutputPrint one integer — number of cycles modulo 998244353.ExamplesInput2 2 21 21 2Output8Input2 2 41 21 2Output32Input2 3 41 21 21 3Output70Input4 2 21 21 31 41 2Output20NoteThe following three pictures illustrate graph, which are products of the trees from sample tests.In the first example, the list of cycles of length 2 is as follows:  «AB», «BA»  «BC», «CB»  «AD», «DA»  «CD», «DC»     
Input2 2 21 21 2
Output8
['combinatorics', 'divide and conquer', 'trees', '*2900']