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E. Gregor and the Two Painters

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTwo 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.

Input

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.

Output

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

Examples

Input

3 4 11 9 8 5 10 6 7 2

Output

2

Input

3 4 12 9 8 5 10 6 7 2

Output

1

Input

3 3 2 1 2 1 1 2 1

Output

4

Input

5 23 6 1 4 3 5 2 2 3 1 6 1 5 5 6 1 3 2 6 2 3 1 6 1 4 1 6 1 5 5

Output

6

Note

The diagram below represents the first example. The numbers to the left of each row represent the list $$$a$$$, and the numbers above each column represent the list $$$b$$$. The numbers inside each cell represent the number of paint layers in that cell.

The colored cells correspond to badly painted cells. The red and blue cells respectively form $$$2$$$ badly painted regions.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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