B'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 n x m , consisting of exactly nm nodes: 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 ^{ dagger dagger} 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. ^{ dagger} A 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 ge 0 ). ^{ dagger dagger} . 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 . The first line contains three integers n , m , and q ( 1 <= n, m <= 3 cdot 10^5 , 0 <= q <= 3 cdot 10^5 ) -- the number of horizontal threads, the number of vertical threads, and the numb'...