{"raw_statement":[{"iden":"problem statement","content":"Yosupo loves query problems. He made the following problem:\n\n* * *\n\n> **A Query Problem**\n> We have an integer sequence of length $N$: $a_1,\\ldots,a_N$. Initially, $a_i = 0 (1 \\leq i \\leq N)$. We also have a variable $ans$, which is initially $0$. Here, you will be given $Q$ queries of the following forms:\n> \n> *   Type 1:\n>     *   $t_i (=1)$ $l_i$ $r_i$ $v_i$\n>         \n>     *   For each $j = l_i,\\ldots,r_i$, $a_j := \\min(a_j,v_i)$.\n>         \n> *   Type 2:\n>     *   $t_i (=2)$ $l_i$ $r_i$ $v_i$\n>         \n>     *   For each $j = l_i,\\ldots,r_i$, $a_j := \\max(a_j,v_i)$.\n>         \n> *   Type 3:\n>     *   $t_i (=3)$ $l_i$ $r_i$\n>         \n>     *   Compute $a_{l_i} + \\ldots + a_{r_i}$ and add the result to $ans$.\n>         \n> \n> Print the final value of $ans$.\n> Here, for each query, $1$ $\\leq$ $l_i$ $\\leq$ $r_i$ $\\leq$ $N$ holds. Additionally, for Type 1 and 2, $0$ $\\leq$ $v_i$ $\\leq$ $M-1$ holds.\n\n* * *\n\nMaroon saw this problem, thought it was too easy, and came up with the following problem:\n\n* * *\n\n> **Query Problems**\n> Given are positive integers $N,M,Q$. There are $( \\frac{(N+1)N}{2} \\cdot (M+M+1) )^Q$ valid inputs for \"A Query Problem\". Find the sum of outputs over all those inputs, modulo $998{,}244{,}353$.\n\n* * *\n\nFind it."},{"iden":"constraints","content":"*   $1 \\leq N,M,Q \\leq 200000$\n*   All numbers in input are integers."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $M$ $Q$"},{"iden":"sample input 1","content":"1 2 2"},{"iden":"sample output 1","content":"1\n\nThere are $25$ valid inputs, and just one of them - shown below - results in a positive value of $ans$.\n$t_1 = 2, l_1 = 1, r_1 = 1, v_1 = 1, t_2 = 3, l_2 = 1, r_2 = 1$\n$ans$ will be $1$ in this case, so the answer is $1$."},{"iden":"sample input 2","content":"3 1 4"},{"iden":"sample output 2","content":"0"},{"iden":"sample input 3","content":"111 112 113"},{"iden":"sample output 3","content":"451848306"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}