Shortest Routes II

• Time limit: 1.00 s
• Memory limit: 512 MB

There are $n$ cities and $m$ roads between them. Your task is to process $q$ queries where you have to determine the length of the shortest route between two given cities.

Input

The first input line has three integers $n$, $m$ and $q$: the number of cities, roads, and queries.

Then, there are $m$ lines describing the roads. Each line has three integers $a$, $b$ and $c$: there is a road between cities $a$ and $b$ whose length is $c$. All roads are two-way roads.

Finally, there are $q$ lines describing the queries. Each line has two integers $a$ and $b$: determine the length of the shortest route between cities $a$ and $b$.

Output

Print the length of the shortest route for each query. If there is no route, print $-1$ instead.

Constraints

• $1 \le n \le 500$
  
• $1 \le m \le n^2$
  
• $1 \le q \le 10^5$
  
• $1 \le a,b \le n$
  
• $1 \le c \le 10^9$
  

Example

Input:
4 3 5
1 2 5
1 3 9
2 3 3
1 2
2 1
1 3
1 4
3 2

Output:
5
5
8
-1
3