Bus Route Connectivity

In this problem, you are given a network of bus stops and bus routes. The bus stops are numbered from 1 to n, and you are provided with m bus routes. Each route is described by three integers u, v, and d, where:

• u and v are the endpoints of the route.
• d indicates the direction of the route: if d = 0 then the route is bidirectional, and if d = 1 then the route is one-way from u to v.

Your task is to determine whether there exists a path from bus stop 1 to bus stop n.

Formally, you are given integers $n$ and $m$, followed by $m$ triples $(u, v, d)$. Construct a graph with the following rules:

• If $d = 0$, add an edge from $u$ to $v$ and an edge from $v$ to $u$.
• If $d = 1$, add a directed edge from $u$ to $v$ only.

Then, using a graph traversal algorithm (such as Breadth First Search), determine if there is a path from node 1 to node $n$. Output Yes if such a path exists, otherwise output No.

inputFormat

The input is given from stdin and consists of:

1. A line containing two integers $n$ and $m$, where $1 \leq n \leq 10^5$ and $0 \leq m \leq 10^5$.
2. $m$ lines each containing three integers $u$, $v$, and $d$ representing a bus route.

It is guaranteed that $1 \leq u,v \leq n$ and $d \in \{0, 1\}$.

outputFormat

Print to stdout a single line with the answer: Yes if there is a path from bus stop 1 to bus stop $n$, or No otherwise.

## sample

4 4
1 2 0
2 3 1
3 4 0
2 4 1

Yes