You are given an undirected tree rooted at node 0 with n nodes numbered from 0 to n - 1. Each node i has an integer value vals[i], and its parent is given by par[i].
A subset of nodes within the subtree of a node is called good if every digit from 0 to 9 appears at most once in the decimal representation of the values of the selected nodes.
The score of a good subset is the sum of the values of its nodes.
Define an array maxScore of length n, where maxScore[u] represents the maximum possible sum of values of a good subset of nodes that belong to the subtree rooted at node u, including u itself and all its descendants.
Return the sum of all values in maxScore.
Since the answer may be large, return it modulo 109 + 7.
Example 1:
Input: vals = [2,3], par = [-1,0]
Output: 8
Explanation:
{0, 1}. The subset {2, 3} is good as the digits 2 and 3 appear only once. The score of this subset is 2 + 3 = 5.{1}. The subset {3} is good. The score of this subset is 3.maxScore array is [5, 3], and the sum of all values in maxScore is 5 + 3 = 8. Thus, the answer is 8.Example 2:
Input: vals = [1,5,2], par = [-1,0,0]
Output: 15
Explanation:
{0, 1, 2}. The subset {1, 5, 2} is good as the digits 1, 5 and 2 appear only once. The score of this subset is 1 + 5 + 2 = 8.{1}. The subset {5} is good. The score of this subset is 5.{2}. The subset {2} is good. The score of this subset is 2.maxScore array is [8, 5, 2], and the sum of all values in maxScore is 8 + 5 + 2 = 15. Thus, the answer is 15.Example 3:
Input: vals = [34,1,2], par = [-1,0,1]
Output: 42
Explanation:
{0, 1, 2}. The subset {34, 1, 2} is good as the digits 3, 4, 1 and 2 appear only once. The score of this subset is 34 + 1 + 2 = 37.{1, 2}. The subset {1, 2} is good as the digits 1 and 2 appear only once. The score of this subset is 1 + 2 = 3.{2}. The subset {2} is good. The score of this subset is 2.maxScore array is [37, 3, 2], and the sum of all values in maxScore is 37 + 3 + 2 = 42. Thus, the answer is 42.Example 4:
Input: vals = [3,22,5], par = [-1,0,1]
Output: 18
Explanation:
{0, 1, 2}. The subset {3, 22, 5} is not good, as digit 2 appears twice. Therefore, the subset {3, 5} is valid. The score of this subset is 3 + 5 = 8.{1, 2}. The subset {22, 5} is not good, as digit 2 appears twice. Therefore, the subset {5} is valid. The score of this subset is 5.{2}. The subset {5} is good. The score of this subset is 5.maxScore array is [8, 5, 5], and the sum of all values in maxScore is 8 + 5 + 5 = 18. Thus, the answer is 18.
Constraints:
1 <= n == vals.length <= 5001 <= vals[i] <= 109par.length == npar[0] == -10 <= par[i] < n for i in [1, n - 1]par represents a valid tree.