In this problem you will have to deal with a very special network.

The network consists of two parts: part A and part B. Each part consists of n vertices; i-th vertex of part A is denoted as A_i, and i-th vertex of part B is denoted as B_i.

For each index i (1 ≤ i < n) there is a directed edge from vertex A_i to vertex A_i + 1, and from B_i to B_i + 1, respectively. Capacities of these edges are given in the input. Also there might be several directed edges going from part A to part B (but never from B to A).

You have to calculate the maximum flow value from A₁ to B_n in this network. Capacities of edges connecting A_i to A_i + 1 might sometimes change, and you also have to maintain the maximum flow value after these changes. Apart from that, the network is fixed (there are no changes in part B, no changes of edges going from A to B, and no edge insertions or deletions).

Take a look at the example and the notes to understand the structure of the network better.

The first line contains three integer numbers n, m and q (2 ≤ n, m ≤ 2·10⁵, 0 ≤ q ≤ 2·10⁵) — the number of vertices in each part, the number of edges going from A to B and the number of changes, respectively.

Then n - 1 lines follow, i-th line contains two integers x_i and y_i denoting that the edge from A_i to A_i + 1 has capacity x_i and the edge from B_i to B_i + 1 has capacity y_i (1 ≤ x_i, y_i ≤ 10⁹).

Then m lines follow, describing the edges from A to B. Each line contains three integers x, y and z denoting an edge from A_x to B_y with capacity z (1 ≤ x, y ≤ n, 1 ≤ z ≤ 10⁹). There might be multiple edges from A_x to B_y.

And then q lines follow, describing a sequence of changes to the network. i-th line contains two integers v_i and w_i, denoting that the capacity of the edge from A_vi to A_vi + 1 is set to w_i (1 ≤ v_i < n, 1 ≤ w_i ≤ 10⁹).

Firstly, print the maximum flow value in the original network. Then print q integers, i-th of them must be equal to the maximum flow value after i-th change.