You have a tree rooted at node (1) with (n) nodes. Each node has a lowercase English letter written on it. For each integer (i) from (1) to (n), please solve the following problem independently: Consider the set of strings formed by the following process: Choose any node (u) that is in the subtree of (i) as your starting location. Repeat 0 or more times: Suppose you are currently on node (x). Select a node (v) that is in the subtree(^{\text{∗}}) of node (x), but you may not choose (v=x). Move to node (v). This process can be terminated at any point. The characters obtained from all nodes you passed through (in order) are concatenated to form a string. You performed the above process exactly once for every possible path. Two paths are considered different if one node is visited in one path but not another. Now, you have obtained many strings. You want to know the sum of the square of the number of occurrences for each type of string. Since this answer might be very large, output its value modulo (998\,244\,353). Choose any node (u) that is in the subtree of (i) as your starting location. Repeat 0 or more times: Suppose you are currently on node (x). Select a node (v) that is in the subtree(^{\text{∗}}) of node (x), but you may not choose (v=x). Move to node (v). This process can be terminated at any point. Suppose you are currently on node (x). Select a node (v) that is in the subtree(^{\text{∗}}) of node (x), but you may not choose (v=x). Move to node (v). This process can be terminated at any point. The characters obtained from all nodes you passed through (in order) are concatenated to form a string. You performed the above process exactly once for every possible path. Two paths are considered different if one node is visited in one path but not another. Now, you have obtained many strings. You want to know the sum of the square of the number o