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

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