write a go solution for Description:
Anya is engaged in needlework. Today she decided to knit a scarf from semi-transparent threads. Each thread is characterized by a single integer — the transparency coefficient.

The scarf is made according to the following scheme: horizontal threads with transparency coefficients a_1,a_2,ldots,a_n and vertical threads with transparency coefficients b_1,b_2,ldots,b_m are selected. Then they are interwoven as shown in the picture below, forming a piece of fabric of size nxm, consisting of exactly nm nodes:

Example of a piece of fabric for n=m=4.

After the interweaving tightens and there are no gaps between the threads, each node formed by a horizontal thread with number i and a vertical thread with number j will turn into a cell, which we will denote as (i,j). Cell (i,j) will have a transparency coefficient of a_i+b_j.

The interestingness of the resulting scarf will be the number of its sub-squares^dagger in which there are no pairs of neighboring^daggerdagger cells with the same transparency coefficients.

Anya has not yet decided which threads to use for the scarf, so you will also be given q queries to increase/decrease the coefficients for the threads on some ranges. After each query of which you need to output the interestingness of the resulting scarf.

^daggerA sub-square of a piece of fabric is defined as the set of all its cells (i,j), such that x_0<=i<=x_0+d and y_0<=j<=y_0+d for some integers x_0, y_0, and d (1<=x_0<=n-d, 1<=y_0<=m-d, d>=0).

^daggerdagger. Cells (i_1,j_1) and (i_2,j_2) are neighboring if and only if |i_1-i_2|+|j_1-j_2|=1.

Input Format:
The first line contains three integers n, m, and q (1<=n,m<=3*10^5, 0<=q<=3*10^5) — the number of horizontal threads, the number of vertical threads, and the number of change requests.

The second line contains n integers a_1,a_2,ldots,a_n (-10^9<=a_i<=10^9) — the transparency coefficients for the horizontal threads, with the threads numbered from top to bottom.

The third line contains m integers b_1,b_2,ldots,b_m (-10^9<=b_i<=10^9) — the transparency coefficients for the vertical threads, with the threads numbered from left to right.

The next q lines specify the change requests. Each request is described by a quadruple of integers t, l, r, and x (1<=t<=2, l<=r, -10^9<=x<=10^9). Depending on the parameter t in the request, the following actions are required:

- t=1. The transparency coefficients for the horizontal threads in the range [l,r] are increased by x (in other words, for all integers l<=i<=r, the value of a_i is increased by x);
- t=2. The transparency coefficients for the vertical threads in the range [l,r] are increased by x (in other words, for all integers l<=i<=r, the value of b_i is increased by x).

Output Format:
Output (q+1) lines. In the (i+1)-th line (0<=i<=q), output a single integer — the interestingness of the scarf after applying the first i requests.

Note:
In the first example, the transparency coefficients of the cells in the resulting plate are as follows:

2334233434454556

Then there are the following sub-squares that do not contain two neighboring cells with the same transparency coefficient:

- Each of the 16 cells separately;
- A sub-square with the upper left corner at cell (3,1) and the lower right corner at cell (4,2);
- A sub-square with the upper left corner at cell (2,3) and the lower right corner at cell (3,4);
- A sub-square with the upper left corner at cell (2,1) and the lower right corner at cell (3,2);
- A sub-square with the upper left corner at cell (3,3) and the lower right corner at cell (4,4).

In the second example, after the first query, the transparency coefficients of the horizontal threads are [1,2,2]. After the second query, the transparency coefficients of the vertical threads are [2,-4,2].. Output only the code with no comments, explanation, or additional text.