CF1900E.Transitive Graph

You are given a directed graph $G$ with $n$ vertices and $m$ edges between them.

Initially, graph $H$ is the same as graph $G$ . Then you decided to perform the following actions:

• If there exists a triple of vertices $a$ , $b$ , $c$ of $H$ , such that there is an edge from $a$ to $b$ and an edge from $b$ to $c$ , but there is no edge from $a$ to $c$ , add an edge from $a$ to $c$ .
• Repeat the previous step as long as there are such triples.

Note that the number of edges in $H$ can be up to $n^2$ after performing the actions.

You also wrote some values on vertices of graph $H$ . More precisely, vertex $i$ has the value of $a_i$ written on it.

Consider a simple path consisting of $k$ distinct vertices with indexes $v_1, v_2, \ldots, v_k$ . The length of such a path is $k$ . The value of that path is defined as $\sum_{i = 1}^k a_{v_i}$ .

A simple path is considered the longest if there is no other simple path in the graph with greater length.

Among all the longest simple paths in $H$ , find the one with the smallest value.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ). The description of the test cases follows.

The first line of each test case contains two integers $n$ and $m$ ( $1 \le n,m \le 2 \cdot 10^5$ ) — the number of vertices and the number of edges.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 10^9$ ) — the numbers written on the vertices of graph $H$ .

The $i$ -th of the next $m$ lines contains two integers $v_i$ and $u_i$ ( $1 \le v_i, u_i \le n$ ) — meaning that there is an edge going from vertex $v_i$ to vertex $u_i$ in graph $G$ . Note that edges are directed. Also note that the graph may have self-loops and multiple edges.

It is guaranteed that neither the sum of $n$ nor the sum of $m$ over all test cases exceeds $2 \cdot 10^5$ .

For each test case, output two numbers — the length of the longest simple path in $H$ and the minimal possible value of such path.

In the first test case, the longest path in both graphs is $1 \to 3 \to 4 \to 5 \to 2$ . As the path includes all vertices, the minimal possible value of the longest path is the sum of values on all vertices, which is $12$ .

In the second test case, the longest possible path is $1 \to 2 \to 3 \to 4 \to 6 \to 7$ . As there are no longest paths with vertex $5$ in them, this path has the minimal possible value of $5\,999\,999\,995$ .

In the third test case, it can be proven that there is no path longer than $11$ and that the value of the longest path cannot be less than $37$ . Also, notice that the given graph has both self-loops and multiple edges.