During a programming contest, Mr. Search Tree (a.k.a. MST) forgot how to implement Kruskal's and Prim's algorithms. In a moment of desperation, he wrote a DFS that always follows the smallest available edge first. Strangely enough, it passed.

Now he wonders: for which starting nodes does his "Most Stupid Technique" accidentally produce a correct minimum spanning tree$$$^\dagger$$$ ?

Formally, given a connected undirected graph with $$$n$$$ nodes and $$$m$$$ edges, the $$$i$$$-th edge has weight $$$i$$$, and here is the algorithm he used:

vis := array of n booleans
s := set of edges

function dfs(u):
    vis[u] := true
    for each edge (u, v) connected to u in increasing order of edge weight:
        if not vis[v]:
            add edge (u, v) to s
            dfs(v)

function findMST(u):
    reset vis to all false
    clear the edge set s
    dfs(u)
    return s

In other words, findMST(u) performs a DFS starting from vertex $$$u$$$, always choosing the smallest-weight unvisited edge from the current node and includes it in the tree.

Although this always produces a spanning tree, it doesn't always yield a minimum one.

Your task is to determine, for each node $$$i$$$ from $$$1$$$ to $$$n$$$, whether findMST(i) returns a minimum spanning tree.

$$$^\dagger$$$ A minimum spanning tree (MST) of a connected undirected graph is a subset of the edges that forms a tree connecting all the vertices and has the minimum possible total edge weight among all such trees.