Problem Statement

There are $N$ red stones and $M$ blue stones on a two-dimensional plane. The $i$-th red stone is at coordinates $(RX_i,RY_i)$, and the $j$-th blue stone is at $(BX_j,BY_j)$. There may be multiple stones at the same coordinates.

You can choose a blue stone and move it to anywhere you like, any number of times. The cost of moving a blue stone from $(x, y)$ to $(x',y')$ is $|x-x'|+|y-y'|$.

You want to meet the following condition:

• For every $1 \leq i \leq N$, there are $K$ or more blue stones to the upper right of the $i$-th red stone. More formally, there are $K$ or more indices $1 \leq j \leq M$ such that $RX_i \leq BX'_j$ and $RY_i \leq BY'_j$, where $(BX'_j,BY'_j)$ are the coordinates of the $j$-th blue stone after your operations.

Find the minimum total cost needed to achieve your objective.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq M \leq 10^5$
• $1 \leq K \leq \min(M,10)$
• $0 \leq RX_i,RY_i,BX_j,BY_j \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M K
RX_1 RY_1
RX_2 RY_2
\vdots
RX_N RY_N
BX_1 BY_1
BX_2 BY_2
\vdots
BX_M BY_M

Output

Print the answer.