#ABC126E. [ABC126E] 1 or 2

[ABC126E] 1 or 2

Score : 500500 points

Problem Statement

There are NN cards placed face down in a row. On each card, an integer 11 or 22 is written.

Let AiA_i be the integer written on the ii-th card.

Your objective is to guess A1,A2,...,ANA_1, A_2, ..., A_N correctly.

You know the following facts:

  • For each i=1,2,...,Mi = 1, 2, ..., M, the value AXi+AYi+ZiA_{X_i} + A_{Y_i} + Z_i is an even number.

You are a magician and can use the following magic any number of times:

Magic: Choose one card and know the integer AiA_i written on it. The cost of using this magic is 11.

What is the minimum cost required to determine all of A1,A2,...,ANA_1, A_2, ..., A_N?

It is guaranteed that there is no contradiction in given input.

Constraints

  • All values in input are integers.
  • 2N1052 \leq N \leq 10^5
  • 1M1051 \leq M \leq 10^5
  • 1Xi<YiN1 \leq X_i < Y_i \leq N
  • 1Zi1001 \leq Z_i \leq 100
  • The pairs (Xi,Yi)(X_i, Y_i) are distinct.
  • There is no contradiction in input. (That is, there exist integers A1,A2,...,ANA_1, A_2, ..., A_N that satisfy the conditions.)

Input

Input is given from Standard Input in the following format:

NN MM

X1X_1 Y1Y_1 Z1Z_1

X2X_2 Y2Y_2 Z2Z_2

\vdots

XMX_M YMY_M ZMZ_M

Output

Print the minimum total cost required to determine all of A1,A2,...,ANA_1, A_2, ..., A_N.

3 1
1 2 1
2

You can determine all of A1,A2,A3A_1, A_2, A_3 by using the magic for the first and third cards.

6 5
1 2 1
2 3 2
1 3 3
4 5 4
5 6 5
2
100000 1
1 100000 100
99999