201082: [AtCoder]ARC108 C - Keep Graph Connected

Problem Statement

Given is an undirected connected graph with $N$ vertices numbered $1$ to $N$, and $M$ edges numbered $1$ to $M$. The given graph may contain multi-edges but not self loops.

Each edge has an integer label between $1$ and $N$ (inclusive). Edge $i$ has a label $c_i$, and it connects Vertex $u_i$ and $v_i$ bidirectionally.

Snuke will write an integer between $1$ and $N$ (inclusive) on each vertex (multiple vertices may have the same integer written on them) and then keep only the edges satisfying the condition below, removing the other edges.

Condition: Let $x$ and $y$ be the integers written on the vertices that are the endpoints of the edge. Exactly one of $x$ and $y$ equals the label of the edge.

We call a way of writing integers on the vertices good if (and only if) the graph is still connected after removing the edges not satisfying the condition above. Determine whether a good way of writing integers exists, and present one such way if it exists.

Constraints

• $2 \leq N \leq 10^5$
• $N-1 \leq M \leq 2 \times 10^5$
• $1 \leq u_i,v_i,c_i \leq N$
• The given graph is connected and has no self-loops.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$u_1$ $v_1$ $c_1$
$\vdots$
$u_M$ $v_M$ $c_M$

Output

If there is no good way of writing integers, print No. Otherwise, print $N$ lines. The $i$-th line should contain the integer written on Vertex $i$. Any good way of writing integers will be accepted.

Sample Input 1

3 4
1 2 1
2 3 2
3 1 3
1 3 1

Sample Output 1

1
2
1

• We write $1$, $2$, and $1$ on Vertex $1$, $2$, and $3$, respectively.
• Edge $1$ connects Vertex $1$ and $2$, and its label is $1$.
  • Only the integer written on Vertex $1$ equals the label, so this edge will not get removed.
• Edge $2$ connects Vertex $2$ and $3$, and its label is $2$.
  • Only the integer written on Vertex $2$ equals the label, so this edge will not be removed.
• Edge $3$ connects Vertex $1$ and $3$, and its label is $3$.
  • Both integers written on the vertices differ from the label, so this edge will be removed.
• Edge $4$ connects Vertex $1$ and $3$, and its label is $1$.
  • Both integers written on the vertices equal the label, so this edge will be removed.
• After Edge $3$ and $4$ are removed, the graph will still be connected, so this is a good way of writing integers.