A series of highways connect n cities numbered from 0 to n - 1. You are given a 2D integer array highways where highways[i] = [city1_i, city2_i, toll_i] indicates that there is a highway that connects city1_i and city2_i, allowing a car to go from city1_i to city2_i and vice versa for a cost of toll_i.

You are also given an integer discounts which represents the number of discounts you have. You can use a discount to travel across the i^th highway for a cost of toll_i / 2 (integer division). Each discount may only be used once, and you can only use at most one discount per highway.

Return the minimum total cost to go from city 0 to city n - 1, or -1 if it is not possible to go from city 0 to city n - 1.

Example 1:

Input: n = 5, highways = [[0,1,4],[2,1,3],[1,4,11],[3,2,3],[3,4,2]], discounts = 1
Output: 9
Explanation:
Go from 0 to 1 for a cost of 4.
Go from 1 to 4 and use a discount for a cost of 11 / 2 = 5.
The minimum cost to go from 0 to 4 is 4 + 5 = 9.

Example 2:

Input: n = 4, highways = [[1,3,17],[1,2,7],[3,2,5],[0,1,6],[3,0,20]], discounts = 20
Output: 8
Explanation:
Go from 0 to 1 and use a discount for a cost of 6 / 2 = 3.
Go from 1 to 2 and use a discount for a cost of 7 / 2 = 3.
Go from 2 to 3 and use a discount for a cost of 5 / 2 = 2.
The minimum cost to go from 0 to 3 is 3 + 3 + 2 = 8.

Example 3:

Input: n = 4, highways = [[0,1,3],[2,3,2]], discounts = 0
Output: -1
Explanation:
It is impossible to go from 0 to 3 so return -1.

Constraints:

2 <= n <= 1000
1 <= highways.length <= 1000
highways[i].length == 3
0 <= city1_i, city2_i <= n - 1
city1_i != city2_i
0 <= toll_i <= 10⁵
0 <= discounts <= 500
There are no duplicate highways.

Minimum Cost to Reach City With Discounts

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