OpenKattis
National University of Singapore

Topovi

Mirko is a huge fan of chess and programming, but typical chess soon became boring for him, so he started having fun with rook pieces.

He found a chessboard with $N$ rows and $N$ columns and placed $K$ rooks on it. Mirko’s game is made of the following rules:

  1. Each rook’s power is determined by an integer.

  2. A rook sees all the fields that are in his row or column except its own field.

  3. We say that a field is attacked if the binary XOR of all the powers of the rooks that see the field is greater than $0$.

Notice that the field a rook is at can be attacked or not.

Initially, Mirko placed the rooks in a certain layout on the board and will make $P$ moves. After each move, determine how many fields are attacked. Every rook can be moved to any free field on the whole board (not only across column and row).

Input

The first line of input contains integers $N$, $K$, $P$ ($1 \leq N \leq 1\ 000\ 000\ 000$, $1 \leq K \leq 100\ 000$, $1 \leq P \leq 100\ 000$). Each of the following $K$ lines contains three integers $R$, $C$, $X$ ($1 \leq R, C \leq N$, $1 \leq X \leq 1\ 000\ 000\ 000$) which denote that initially there is a rook of power $X$ on the field $(R, C)$. Each of the following $P$ lines contains four integers $R_1$, $C_1$, $R_2$, $C_2$ ($1 \leq R_1, C_1, R_2, C_2 \leq N$) which denote that the rook has moved from field $(R_1, C_1 )$ to field $(R_2, C_2 )$. It is guaranteed that there will not be two rooks on one field at any point.

Output

The output must consist of $P$ lines, the $k$-th line containing the total number of attacked fields after $k$ moves.

Sample Input 1 Sample Output 1
2 2 2
1 1 1
2 2 1
2 2 2 1
1 1 1 2
4
0
Sample Input 2 Sample Output 2
2 2 2
1 1 1
2 2 2
2 2 2 1
1 1 1 2
4
2
Sample Input 3 Sample Output 3
3 3 4
1 1 1
2 2 2
2 3 3
2 3 3 3
3 3 3 1
1 1 1 2
3 1 3 2
6
7
7
9