New Roads Queries

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

There are $n$ cities in Byteland but no roads between them. However, each day, a new road will be built. There will be a total of $m$ roads.

Your task is to process $q$ queries of the form: "after how many days can we travel from city $a$ to city $b$ for the first time?"

Input

The first input line has three integers $n$, $m$ and $q$: the number of cities, roads and queries. The cities are numbered $1,2,\dots,n$.

After this, there are $m$ lines that describe the roads in the order they are built. Each line has two integers $a$ and $b$: there will be a road between cities $a$ and $b$.

Finally, there are $q$ lines that describe the queries. Each line has two integers $a$ and $b$: we want to travel from city $a$ to city $b$.

Output

For each query, print the number of days, or $-1$ if it is never possible.

Constraints

• $1 \le n, m, q \le 2 \cdot 10^5$
  
• $1 \le a,b \le n$
  

Example

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

Output:
2
-1
4