{"raw_statement":[{"iden":"statement","content":"_— This is not playing but duty as allies of justice, Nii-chan!_\n\n_— Not allies but justice itself, Onii-chan!_\n\nWith hands joined, go everywhere at a speed faster than our thoughts! This time, the Fire Sisters — Karen and Tsukihi — is heading for somewhere they've never reached — water-surrounded islands!\n\nThere are three clusters of islands, conveniently coloured red, blue and purple. The clusters consist of _a_, _b_ and _c_ distinct islands respectively.\n\nBridges have been built between some (possibly all or none) of the islands. A bridge bidirectionally connects two different islands and has length 1. For any two islands of the same colour, either they shouldn't be reached from each other through bridges, or the shortest distance between them is **at least 3**, apparently in order to prevent oddities from spreading quickly inside a cluster.\n\nThe Fire Sisters are ready for the unknown, but they'd also like to test your courage. And you're here to figure out the number of different ways to build all bridges under the constraints, and give the answer modulo 998 244 353. Two ways are considered different if a pair of islands exist, such that there's a bridge between them in one of them, but not in the other."},{"iden":"input","content":"The first and only line of input contains three space-separated integers _a_, _b_ and _c_ (1 ≤ _a_, _b_, _c_ ≤ 5 000) — the number of islands in the red, blue and purple clusters, respectively."},{"iden":"output","content":"Output one line containing an integer — the number of different ways to build bridges, modulo 998 244 353."},{"iden":"examples","content":"Input\n\n1 1 1\n\nOutput\n\n8\n\nInput\n\n1 2 2\n\nOutput\n\n63\n\nInput\n\n1 3 5\n\nOutput\n\n3264\n\nInput\n\n6 2 9\n\nOutput\n\n813023575"},{"iden":"note","content":"In the first example, there are 3 bridges that can possibly be built, and no setup of bridges violates the restrictions. Thus the answer is 23 = 8.\n\nIn the second example, the upper two structures in the figure below are instances of valid ones, while the lower two are invalid due to the blue and purple clusters, respectively.\n\n<center>![image](https://espresso.codeforces.com/d17348f21254926225b4b05b4e9024421a83ec02.png)</center>"}],"translated_statement":[{"iden":"statement","content":"_— 这不是玩耍，而是作为正义之盟友的职责，哥哥！_\n\n_— 不是盟友，而是正义本身，哥哥！_\n\n手牵手，以比思想更快的速度奔赴任何地方！这一次，火之姐妹——Karen 和 Tsukihi——正前往她们从未到达过的地方——被水域环绕的岛屿！\n\n有三个岛屿群，分别被方便地染成红色、蓝色和紫色。这三个群分别包含 #cf_span[a]、#cf_span[b] 和 #cf_span[c] 个互不相同的岛屿。\n\n一些（可能是全部或没有）岛屿之间已经建好了桥。每座桥双向连接两个不同的岛屿，长度为 #cf_span[1]。对于任意两个同色岛屿，要么它们之间无法通过桥相互到达，要么它们之间的最短距离 *至少为 #cf_span[3]*，显然这是为了防止异常现象在集群内快速传播。\n\n火之姐妹已准备好面对未知，但她们也想考验你的勇气。而你，正是来计算在约束条件下构建所有桥的不同方式数量，并将答案对 #cf_span[998 244 353] 取模。\n\n两种方式被认为是不同的，当且仅当存在一对岛屿，在其中一种方式中有桥连接，而在另一种方式中没有。\n\n输入的第一行且唯一一行包含三个用空格分隔的整数 #cf_span[a]、#cf_span[b] 和 #cf_span[c]（#cf_span[1 ≤ a, b, c ≤ 5 000]）——分别表示红色、蓝色和紫色岛屿群中的岛屿数量。\n\n输出一行，包含一个整数——满足约束条件的建桥方式总数，对 #cf_span[998 244 353] 取模。\n\n在第一个例子中，共有 #cf_span[3] 座可能修建的桥，且没有任何一种桥的布置违反限制。因此答案是 #cf_span[2^3 = 8]。\n\n在第二个例子中，下图中的上两个结构是合法的实例，而下两个则分别因蓝色和紫色集群而无效。"},{"iden":"input","content":"输入的第一行且唯一一行包含三个用空格分隔的整数 #cf_span[a]、#cf_span[b] 和 #cf_span[c]（#cf_span[1 ≤ a, b, c ≤ 5 000]）——分别表示红色、蓝色和紫色岛屿群中的岛屿数量。"},{"iden":"output","content":"输出一行，包含一个整数——满足约束条件的建桥方式总数，对 #cf_span[998 244 353] 取模。"},{"iden":"examples","content":"输入\n1 1 1\n输出\n8\n\n输入\n1 2 2\n输出\n63\n\n输入\n1 3 5\n输出\n3264\n\n输入\n6 2 9\n输出\n813023575"},{"iden":"note","content":"在第一个例子中，共有 #cf_span[3] 座可能修建的桥，且没有任何一种桥的布置违反限制。因此答案是 #cf_span[2^3 = 8]。\n\n在第二个例子中，下图中的上两个结构是合法的实例，而下两个则分别因蓝色和紫色集群而无效。"}],"sample_group":[],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}