New Roads Queries

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