CareerCup

We define the following:

There are friends_nodes friends numbered from 1 to friends_nodes.
There are friends_edges pairs of friends, where each (xi, yi) pair of friends is connected by a shared integer token described by friends_weighti.
Any two friends, xi and yi, can be connected by zero or more tokens because if friends xi and yi share token ti and friends yi and zi also share token ti, then xi and zi are also said to share token ti.

Find the maximal product of xi and yi for any directly or indirectly connected (xi, yi) pair of friends such that xi and yi share the maximal number of tokens with each other.

Complete the maxTokens function in the editor. It has four parameters:

Name Type Description
friends_nodes integer The number of friends.
friends_from integer array Each friends_from[i] (where 0 ≤ i < friends_edges) denotes the first friend in pair (friends_from[i], friends_to[i]).
friends_to integer array Each friends_to[i] (where 0 ≤ i < friends_edges) denotes the second friend in pair (friends_from[i], friends_to[i]).
friends_weight integer array Each friends_weight[i] (where 0 ≤ i < friends_edges) denotes the ID number of a token shared by both friends_from[i] and friends_to[i].
Note: friends_edges is the number of pairs of friends that directly share a token.

The function must return an integer denoting the maximal product of xi and yi such that xi and yi are a pair of friends that share the maximal number of tokens with each other.

Input Format
The first line contains two space-separated integers describing the respective values of friends_nodes and friends_edges.
Each line i of the friends_edges subsequent lines (where 0 ≤ i < friends_edges) contains three space-separated integers describing the respective values of friends_fromi, friends_toi, and friends_weighti.

Constraints

2 ≤ friends_nodes ≤ 100
1 ≤ friends_edges ≤ min(200, (friends_nodes × (friends_nodes − 1)) / 2)
1 ≤ friends_weighti ≤ 100
1 ≤ friends_fromi, friends_toi ≤ friends_nodes
1≤ friends_weighti ≤ friends_edges
friends_fromi ≠ friends_toi
Each pair of friends can be connected by zero or more types of tokens.

Output Format
Return an integer denoting the maximal product of xi and yi such that xi and yi are a pair of friends that share the maximal number of tokens with each other.

Sample Input 0
4 5
1 2 1
1 2 2
2 3 1
2 3 3
2 4 3

Sample Output 0
6

Explanation 0
Each pair of n = 4 friends is connected by the following tokens:

Pair (1, 2) shares 2 tokens (i.e., tokens 1 and 2)
Pair (1, 3) shares 1 token (i.e., token 1)
Pair (1, 4) shares 0 tokens
Pair (2, 3) shares 2 tokens (i.e., tokens 1 and 3)
Pair (2, 4) shares 1 token (i.e., token 3)
Pair (3, 4) shares 1 token (i.e., token 3)

The pairs connected by the maximal number of tokens are (1, 2) and (2, 3). Their respective products are 1 × 2 = 2 and 2 × 3 = 6. We then return the largest of these values as our answer, which is 6.