URI Online Judge | 3070

HyperspaceTM Highways

By RS Serbia

Timelimit: 1

In an unspecified solar system, there are N planets. A space government company has recently hired space contractors to build M bidirectional HyperspaceTM highways, each connecting two different planets. The primary objective, which was to make sure that every planet can be reached from any other planet taking only HyperspaceTM highways, has been completely fulfilled. Unfortunately, lots of space contractors had friends and cousins in the Space Board of Directors of the company, so the company decided to do much more than just connecting all planets.

In order to make spending enormous amounts of space money for HyperspaceTM highways
look necessary, they decided to enforce a strict rule on the HyperspaceTM highway network: whenever there is a way to travel through some planets and return to the starting point without traveling through any planet twice, every pair of planets on the itinerary should be directly connected by a HyperspaceTM highway. In other words, the set of planets in every simple cycle induces a complete subgraph.
You are designing a HyperspaceTM navigational app, and the key technical problem you are facing is finding the minimal number of HyperspaceTM highways one needs to use to travel from planet A to planet B. As this problem is too easy for Bubble Cup, here is a harder task: your program needs to do it for Q pairs of planets.

Input

The first line contains three positive integers (1 ≤ ≤ 100 000), M (1 ≤ M ≤ 500 000) and (1 ≤ Q ≤ 200 000), denoting the number of planets, the number of HyperspaceTM highways, and the number of queries, respectively.
Each of the following M lines contains a highway: highway i is given by two integers ui and vi, meaning the planets ui and vi are connected by a HyperspaceTM highway. It is guaranteed that the network of planets and HyperspaceTM highways forms a simple connected graph.

Each of the following Q lines contains a query: query j is given by two integers aj and b(1 ≤ aj < bj ≤ N), meaning we are interested in the minimal number of HyperspaceTM highways one needs to take to travel from planet aj to planet bj.

Output

Output Q lines: the j-th line of output should contain the minimal number of HyperspaceTM
highways one needs to take to travel from planet aj to planet bj.

Input Samples Output Samples

5 7 2
1 2
1 3
1 4
2 3
2 4
3 4
1 5
1 4
2 5

1
2

8 11 4
1 2
2 3
3 4
4 5
1 3
1 6
3 5
3 7
4 7
5 7
6 8
1 5
2 4
6 7
3 8

2

2

3

3