Memory Match

You are playing the game “Memory Match”.

This game revolves around a set of $N$ picture cards. The cards are organized in pairs: there are $N/2$ different pictures, each picture occurring on exactly two cards.

At the beginning of the game, the cards are shuffled and laid face down on the table. Players then take turns in guessing a pair of cards with the same picture. Each turn consists of picking a face-down card and turning it over to reveal its picture, then picking another face-down card and turning that card over as well. If the pictures on the two turned cards are identical, the cards remain face-up, the player scores a point and may take another turn. If the pictures are different, both cards are turned face-down again and the turn goes to the next player.

It is now your turn! Given a description of all previous actions in the game, pick as many matching pairs as possible.

The first line contains an even integer $N$, the number of cards on the table ($2 \leq N \leq 1000$).

The second line contains an integer $K$, the number of turns played thus far in the game ($0 \leq K \leq 1000$).

The following $K$ lines
each describe a turn. A turn is described by integers
$C_1$ and $C_2$ followed by words $P_1$ and $P_2$. The numbers $C_1$ and $C_2$ refer to card positions on the
table ($1 \leq C_1, C_2 \leq
N$ and $C_1 \neq
C_2$). The words describe the pictures on the two
selected cards. Each word consists of between $1$ and $20$ lowercase letters in range
‘`a`’ …‘`z`’.
If $P_1 = P_2$, the two
cards stay face-up and the corresponding positions $C_1$ and $C_2$ may not be chosen again.

The input is such that at least two cards are still in face-down position.

Output one line with an integer $S$, the number of matching pairs you can score with certainty.

Sample Input 1 | Sample Output 1 |
---|---|

8 5 1 3 earth sun 2 6 mars sun 6 3 sun sun 7 5 earth moon 2 7 mars earth |
3 |

Sample Input 2 | Sample Output 2 |
---|---|

10 6 1 2 moon earth 9 10 venus sun 8 7 moon venus 1 8 moon moon 4 10 sun sun 9 6 venus mars |
3 |

Sample Input 3 | Sample Output 3 |
---|---|

8 2 1 3 moon earth 2 6 sun earth |
1 |