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Time Limit: 4.0 Seconds Memory Limit: 65536K

Total Runs: 597 Accepted Runs: 134 Multiple test files

Case Time Limit: 2.0 Seconds

N cities (2 ≤ N ≤ 10 000) are connected by a network of M one-way
roads (1 ≤ M < 100 000). It is known that these roads do not
cross outside the cities. The numeration of the cities and the roads starts from
1. There is at most one road from any city to another one. The length of each
road does not exceed 10 000.
### Input

### Output

### Example of input data

### Example of output data

The company for which you work sends you on a business trip from city 1 to city N on your personal car. The trip expenses will be compensated to you only if the distance you drive will differ from the shortest possible by no more than K (0 ≤ K ≤ 10 000).

The task is to determine on which roads you can drive to have the right to the compensation. That means the list of all roads that appear on at least one route from city 1 to city N where the length of the route does not exceed the length of the shortest route by more than K.

Input data consists of M+1 lines. The first line contains the numbers N, M, and K. Each next line describes one road and contains the initial city number, the final city number and the length of the road. All numbers are integers and separated from each other by one or more spaces.

Output data consists of several lines. The first line contains the integer L — the number of roads you can use. The following L lines contain the numbers of the roads in ascending order.

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

4 1 3 4 5

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