Closest Cow Wins

Farmer John owns a long farm along a highway that can be treated as a one-dimensional number line. The farm has $K$ grassy patches ($1 \leq K \leq 2\cdot 10^5$). The $i$-th patch is at position $p_i$ and has tastiness $t_i$ ($0 \leq t_i \leq 10^9$). Farmer Nhoj, Farmer John's rival, has already placed $M$ cows ($1 \leq M \leq 2\cdot 10^5$) at positions $f_1 \ldots f_M$. All $K+M$ positions are distinct integers in $[0,10^9]$.

Farmer John must choose $N$ positions ($1 \leq N \leq 2\cdot 10^5$, not necessarily integers) for his cows. These positions must differ from the positions of Farmer Nhoj's cows, but they may coincide with grassy patches.

Each patch belongs to the owner of the cow closest to it. If a Farmer John cow and a Farmer Nhoj cow are equally close to a patch, Farmer Nhoj claims the patch.

Given the positions of Farmer Nhoj's cows and the positions and tastiness values of the patches, find the maximum total tastiness Farmer John can claim by placing his cows optimally.

The first line contains $K$, $M$, and $N$.

The next $K$ lines each contain two integers $p_i$ and $t_i$.

The next $M$ lines each contain one integer $f_i$.

Print one integer, the maximum total tastiness. The answer can exceed the 32-bit integer range, so use a 64-bit integer type.