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

**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