There are n jobs that can be executed in parallel on a processor, where the execution time of the i-th job is executionTime[i]. To speed up execution, the following strategy is used.

• In one operation, a job is chosen, the major job, and is executed for x seconds.
• All other jobs are executed for y seconds where y < x.

A job is complete when it has been executed for at least executionTime[i] seconds, then it exits the pool. Find the minimum number of operations s in which the processor can completely execute all the jobs if run optimally.

Example

Consider n = 5, executionTime = [3, 4, 1, 7, 6], x = 4 and y = 2.

The following strategy is optimal using 1-based indexing:

1. Choose job 4 as the major job and reduce the execution times of job 4 by x = 4 and other jobs by y = 2.
   • New executionTime = [1, 2, -1, 3, 4]
   • Job 3 is complete, so it is removed.
2. Choose job 4 again.
   • New executionTime = [-1, 0, -1, -1, 2]
   • Jobs 1, 2, and 4 are now complete.
3. Choose job 5.
   • New executionTime = [-1, -1, -1, -1, -1]
   • Job 5 is complete.

The total number of operations required is 3.

Given a tree with n nodes, rooted at node 0 (nodes are numbered from 0 to n-1), with values assigned to nodes such that values[i] denotes the value of node i, find the maximal sum of values along any downward path starting at some node u and going only down the tree. In other words, only consider child nodes u1, u2, u3, ... uk where each node ui is a direct child of node u (1 ≤ k ≤ r).

For example, given the following tree (labeled as node number/value):

      0/5
     /   \
   1/7   3/4
   /  \
 2/-10  4/15

Possible paths:

1. 0 → 1 → 2 → 3 has a sum of 5 + 7 + (-10) + 4 = 6
2. 1 → 2 → 3 has a sum of 7 + (-10) + 4 = 1
3. The highest sum path is 0 → 4 with a sum of 5 + 15 = 20.

Function Description

Complete the function bestSumDownwardTreePath in the editor below.

It must return an integer that denotes the largest sum of values along a path down the tree from some node u.

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