A10 Solution

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Problem Statement

Let there exist a country with N cities and M bidirectional roads connecting the cities. Each road is either of the following three types.

  • Passenger transportation road (Type 0) – Only lets the passenger vehicles pass through.

  • Cargo transportation road (Type 1)- Only lets the cargo vehicles pass through.

  • Passenger + cargo transportation road (Type 2)- Lets Both passenger and cargo vehicles pass through.

The cities are numbered from 0 to N-1.

We need to find the maximum number of roads that can be closed down, and all the cities still remain connected for both passenger and cargo transportation.

Input Format

N M

///M lines in the following format

<city1> <city2> <roadType>

Output Format

A single integer denoting the maximum number of roads that can be closed. If the cities cannot be connected, output -1.

Constraints

1≤N ≤105

1≤M≤105

Sample testcases

Input1:

  • 7

0 1 0

1 2 0

1 2 1

1 2 0

1 2 0

0 1 2

0 1 0

Output1:

4

Input2:

  • 6

0 1 0

0 1 1

1 2 1

2 3 1

0 1 2

1 2 0

Output2:

-1

0