[Usaco2017 Open]Switch Grass

Farmer John has recently been experimenting with cultivating different types of grass on his farm, r

ealizing that different types of cows like different types of grass. However, he must be careful to 

ensure that different types of grass are planted sufficiently far away from each-other, in order to 

prevent them from being inextricably mixed.FJ's farm consists of Nfields (1≤N≤200,000), where M pa

irs of fields are connected by bi-directional pathways (1≤M≤200,000). Using these pathways, it is 

possible to walk from any field to any other field. Each pathway has an integer length in the range 

1…1,000,000. Any pair of fields will be linked by at most one direct pathway.In each field, FJ init

ially plants one of Ktypes of grass (1≤K≤N). Over time, however, he might decide to switch the gra

ss in some field to a different type. He calls this an "update" operation. He might perform several 

updates over the course of time, which are all cumulative in nature.After each update, FJ would like

 to know the length of the shortest path between two fields having different grass types. That is, a

mong all pairs of fields having different grass types, he wants to know which two are closest. Ideal

ly, this number is large, so he can prevent grass of one type from mixing with grass of another type

. It is guaranteed that the farm will always have at least two fields with different grass types.In 

30 percent of the input cases, each field will be directly connected to at most 10 pathways.

The first line of input contains four integers, N, M, K, and Q, where Q is the number of updates (1

≤Q≤200,000). The next M lines describe the paths; each one contains three integers A, B, and L, in

dicating a path from field A to field B (both integers in the range 1…N) of length L. The next line

 indicates the initial type of grass growing in each field (N integers in the range 1…K). Finally, 

the last Q lines each describe an update, specified by two integers A and B, where the grass in fiel

d A is to be updated to type B

For each update, print the length of the shortest path between two fields with different types of grass

3 2 3 4
1 2 3
2 3 1
1 1 2
3 3
2 3
1 2
2 2

1
3
3
1