Uber plans to expand Green Zones (EV-only zones).

You are given:

road_nodes — number of zones

road_from[i], road_to[i] — bidirectional roads

road_weight[i] — travel distance

partner[i] — partner managing zone i

minGap — minimum shortest-path distance required between any two active Green Zones

If Uber selects a partner, all zones managed by that partner become Green Zones.

Constraint:

No two active Green Zones may be within minGap distance (shortest path distance).

Return the number of valid partner combinations.

int countGreenZonePlans( int road_nodes, int[] road_from, int[] road_to, int[] road_weight, int minGap, int[] partner )

Example 1

road_nodes = 3 road_from = [1,2,3] road_to = [2,3,1] road_weight = [3,2,5] minGap = 4 partner = [1,2,3]

Output: 4

Valid plans: {1} {2} {3} {1,3}

Example 2

Input: road_nodes = 2 road_from = [1] road_to = [2] road_weight = [5] minGap = 4 partner = [1,2]

Output: 3

Valid subsets: {} {1} {2} {1,2}

(Note: exclude empty set if required by interpretation)