Like everyone else, FJ is always thinking up ways to increase his revenue. To this end, he has set up a series of tolls that the cows will pay when they traverse the cowpaths throughout the farm.
The cows move from any of the N (1 <= N <= 250) pastures conveniently numbered 1..N to any other pasture over a set of M (1 <= M <= 10,000) bidirectional cowpaths that connect pairs of different pastures Aj and Bj (1 <= Aj <= N; 1 <= Bj <= N). FJ has assigned a toll Lj (1 <= Lj <= 100,000) to the path connecting pastures Aj and Bj.
While there may be multiple cowpaths connecting the same pair of pastures, a cowpath will never connect a pasture to itself. Best of all, a cow can always move from any one pasture to any other pasture by following some sequence of cowpaths.
In an act that can only be described as greedy, FJ has also assigned a toll Ci (1 <= Ci <= 100,000) to every pasture. The cost of moving from one pasture to some different pasture is the sum of the tolls for each of the cowpaths that were traversed plus a *single additional toll* that is the maximum of all the pasture tolls encountered along the way, including the initial and destination pastures.
The patient cows wish to investigate their options. They want you to write a program that accepts K (1 <= K <= 10,000) queries and outputs the minimum cost of trip specified by each query. Query i is a pair of numbers si and ti (1 <= si <= N; 1 <= ti <= N; si != ti) specifying a starting and ending pasture.
Consider this example diagram with five pastures:
The 'edge toll' for the path from pasture 1 to pasture 2 is 3. Pasture 2's 'node toll' is 5.
To travel from pasture 1 to pasture 4, traverse pastures 1 to 3 to 5 to 4. This incurs an edge toll of 2+1+1=4 and a node toll of 4 (since pasture 5's toll is greatest), for a total cost of 4+4=8.
The best way to travel from pasture 2 to pasture 3 is to traverse pastures 2 to 5 to 3. This incurs an edge toll of 3+1=4 and a node toll of 5, for a total cost of 4+5=9.

* Line 1: Three space separated integers: N, M, and K
* Lines 2..N+1: Line i+1 contains a single integer: Ci
* Lines N+2..N+M+1: Line j+N+1 contains three space separated integers: Aj, Bj, and Lj
* Lines N+M+2..N+M+K+1: Line i+N+M+1 specifies query i using two space-separated integers: si and ti

* Lines 1..K: Line i contains a single integer which is the lowest cost of any route from si to ti

5 7 2 
2 
5 
3 
3 
4 
1 2 3 
1 3 2 
2 5 3 
5 3 1 
5 4 1 
2 4 3 
3 4 4 
1 4 
2 3 

8
9