Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. AlgoRace

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPMP is getting a warrior. He is practicing a lot, but the results are not acceptable yet. This time instead of programming contests, he decided to compete in a car racing to increase the spirit of victory. He decides to choose a competition that also exhibits algorithmic features.

AlgoRace is a special league of car racing where different teams compete in a country of *n* cities. Cities are numbered 1 through *n*. Every two distinct cities in the country are connected with one bidirectional road. Each competing team should introduce one driver and a set of cars.

The competition is held in *r* rounds. In *i*-th round, drivers will start at city *s*_{i} and finish at city *t*_{i}. Drivers are allowed to change their cars at most *k*_{i} times. Changing cars can take place in any city in no time. One car can be used multiple times in one round, but total number of changes should not exceed *k*_{i}. Drivers can freely choose their path to destination.

PMP has prepared *m* type of purpose-built cars. Beside for PMP’s driving skills, depending on properties of the car and the road, a car traverses each road in each direction in different times.

PMP Warriors wants to devise best strategies of choosing car and roads in each round to maximize the chance of winning the cup. For each round they want to find the minimum time required to finish it.

Input

The first line contains three space-separated integers *n*, *m*, *r* (2 ≤ *n* ≤ 60, 1 ≤ *m* ≤ 60, 1 ≤ *r* ≤ 10^{5}) — the number of cities, the number of different types of cars and the number of rounds in the competition, correspondingly.

Next *m* sets of *n* × *n* matrices of integers between 0 to 10^{6} (inclusive) will follow — describing the time one car requires to traverse different roads. The *k*-th integer in *j*-th line of the *i*-th set is the time that *i*-th car requires to traverse the road from *j*-th city to *k*-th city. These matrices are not necessarily symmetric, but their diagonal is always zero.

Next *r* lines contain description of the rounds. The *i*-th of these lines contains space-separated integers *s*_{i}, *t*_{i}, *k*_{i} (1 ≤ *s*_{i}, *t*_{i} ≤ *n*, *s*_{i} ≠ *t*_{i}, 0 ≤ *k*_{i} ≤ 1000) — the number of starting city, finishing city and the number of possible car changes in *i*-th round, correspondingly.

Output

For each round you should print the minimum required time to complete the round in a single line.

Examples

Input

4 2 3

0 1 5 6

2 0 3 6

1 3 0 1

6 6 7 0

0 3 5 6

2 0 1 6

1 3 0 2

6 6 7 0

1 4 2

1 4 1

1 4 3

Output

3

4

3

Input

4 2 3

0 7 3 3

8 0 10 5

1 1 0 4

8 9 2 0

0 3 3 9

7 0 4 9

3 8 0 4

4 8 9 0

2 3 3

2 1 3

1 2 2

Output

4

5

3

Note

In the first sample, in all rounds PMP goes from city #1 to city #2, then city #3 and finally city #4. But the sequences of types of the cars he uses are (1, 2, 1) in the first round and (1, 2, 2) in the second round. In the third round, although he can change his car three times, he uses the same strategy as the first round which only needs two car changes.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/21/2018 19:58:41 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|