Shortest Routes II

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