A14431 | Gregor and the Two Painters

Two painters, Amin and Benj, are repainting Gregor's living room ceiling! The ceiling can be modeled as an $n \times m$ grid.

For each $i$ between $1$ and $n$ , inclusive, painter Amin applies $a_i$ layers of paint to the entire $i$ -th row. For each $j$ between $1$ and $m$ , inclusive, painter Benj applies $b_j$ layers of paint to the entire $j$ -th column. Therefore, the cell $(i,j)$ ends up with $a_i+b_j$ layers of paint.

Gregor considers the cell $(i,j)$ to be badly painted if $a_i+b_j \le x$ . Define a badly painted region to be a maximal connected component of badly painted cells, i. e. a connected component of badly painted cells such that all adjacent to the component cells are not badly painted. Two cells are considered adjacent if they share a side.

Gregor is appalled by the state of the finished ceiling, and wants to know the number of badly painted regions.

The first line contains three integers $n$ , $m$ and $x$ ( $1 \le n,m \le 2\cdot 10^5$ , $1 \le x \le 2\cdot 10^5$ ) — the dimensions of Gregor's ceiling, and the maximum number of paint layers in a badly painted cell.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 2\cdot 10^5$ ), the number of paint layers Amin applies to each row.

The third line contains $m$ integers $b_1, b_2, \ldots, b_m$ ( $1 \le b_j \le 2\cdot 10^5$ ), the number of paint layers Benj applies to each column.

Print a single integer, the number of badly painted regions.