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Problem 1544 Cow Hurdles

## Problem Description

Farmer John wants the cows to prepare for the county jumping competition, so Bessie and the gang are practicing jumping over hurdles. They are getting tired, though, so they want to be able to use as little energy as possible to jump over the hurdles.

Obviously, it is not very difficult for a cow to jump over several very short hurdles, but one tall hurdle can be very stressful. Thus, the cows are only concerned about the height of the tallest hurdle they have to jump over.

The cows' practice room has N(1<=N<=300) stations, conveniently labeled 1..N. A set of M(1<=M<=25,000) one-way paths connects pairs of stations; the paths are also conveniently labeled 1..M. Path i travels from station S_i to station E_i and contains exactly one hurdle of height H_i(1<=H_i<=1,000,000). Cows must jump hurdles in any path they traverse. The cows have T (1<=T<=40,000) tasks to complete. Task i comprises two distinct numbers, A_i and B_i (1<=A_i<=N;1<=B_i<=N), which connote that a cow has to travel from station A_i to station B_i (by traversing over one or more paths over some route). The cows want to take a path the minimizes the height of the tallest hurdle they jump over when traveling from A_i to B_i. Your job is to write a program that determines the path whose tallest hurdle is smallest and report that height.

## Input

The input will consist of several datasets.
Each dataset contains tree parts:
*Line 1: Three space-separated integers: N, M, and T.
*Lines 2..M+1: Line i+1 contains three space-separated integers: S_i, E_i, and H_i.
*Lines M+2..M+T+1: Line i+M+1 contains two space-separated integers that describe task i: A_i and B_i.
Input is terminated by end of file.

## Output

For each dataset,you should output T lines.
*Lines 1..T: Line i contains the result for task i and tells the smallest possible maximum height necessary to travel between the stations. Output -1 if it is impossible to travel between the two stations.

## Sample Input

5 6 3 1 2 12 3 2 8 1 3 5 2 5 3 3 4 4 2 4 8 3 4 1 2 5 1

4 8 -1

## Hint

Output Details:
Query #1: The best way is to simply travel on the path from station 3 to station 4.
Query #2: There is a path from station 1 to station 2, but a better way would be to travel from station 1 to station 3 and then to station 2.
Query #3: There are no paths that start at station 5, so it is clear that there is no way to reach station 1 from station 5.

## Source

USACO 2007 November

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