Rotation-Proof Highway Network

You are given a directed graph representing an aerial highway network. The network is considered rotation-proof if and only if there exists a designated starting station (station 1) such that every other station is reachable from station 1 and station 1 is also reachable from every other station. In other words, the graph is strongly connected.

The first line of input contains two integers n and m, where n is the number of stations and m is the number of highways. Each of the next m lines contains two integers u and v which represent a directed highway from station u to station v.

Your task is to determine whether the highway network is rotation-proof. If it is, output YES; otherwise, output NO.

Note: The necessary condition is that the network must be strongly connected. Additionally, if the number of highways is less than the number of stations, the network cannot be rotation-proof.

inputFormat

The input is given from standard input and is formatted as follows:

n m
u1 v1
u2 v2
... 
um vm

Where:

• n (1 ≤ n ≤ 10⁵) is the number of stations.
• m (1 ≤ m ≤ 10⁵) is the number of highways.
• Each of the next m lines contains two integers u and v (1 ≤ u, v ≤ n), indicating a directed highway from station u to station v.

outputFormat

Print a single line to standard output containing YES if the network is rotation-proof (i.e. strongly connected), or NO otherwise.

## sample

4 5
1 2
2 3
3 4
4 1
1 3

YES