The first line of input contains three integers: $$$n$$$, $$$m$$$, and $$$k$$$, representing the number of cities, the number of roads, and the number of distinct teleporter types, respectively. The values adhere to the constraints $$$2 \leq n \leq 2 \cdot 10^5$$$, $$$n - 1 \leq m \leq \min\left(\frac{n(n - 1)}{2}, 2 \cdot 10^5\right)$$$, and $$$0 \leq k \leq 2 \cdot 10^5$$$.

Each of the next $$$m$$$ lines describes an existing road between two cities. Each line contains three integers $$$u$$$, $$$v$$$, and $$$c$$$, indicating that there is a bidirectional road connecting cities $$$u$$$ and $$$v$$$ with a cost of $$$c$$$, where $$$1 \leq u, v \leq n$$$ and $$$1 \leq c \leq 10^9$$$. It is guaranteed that there is at least one path between any two cities using only roads, that there are no two distinct roads connecting the same pair of cities, and that no road connects a city to itself.

Next, for each of the $$$n$$$ cities, there is a line containing an integer $$$t$$$, indicating the number of teleporters available in that city, with $$$0 \leq t \leq 2 \cdot 10^5$$$. This line is followed by $$$t$$$ pairs of integers $$$(u_i, c_i)$$$, representing that a teleporter of type $$$u_i$$$ is available in the city, and the cost to use it from this city is $$$c_i$$$, where $$$1 \leq u_i \leq k$$$ and $$$1 \leq c_i \leq 10^9$$$. A single teleporter type may not exist in any city, exist in only one, or exist in multiple cities.

It is guaranteed that the same teleporter type does not appear twice in the same city and that the total sum of available teleporters across all cities does not exceed $$$\min(nk, 2 \cdot 10^5)$$$.