Competitions

# August 18. Kiev Summer School

# The unique Topological Sort

The directed unweighted graph is given. Find out if it has a unique topological ordering of its vertices.

#### Input

The first line contains the number of vertices **n** (**1** ≤ **n** ≤ **2** * `10`

) and the number of edges ^{5}**m** (**1** ≤ **m** ≤ `10`

) in a graph. Each of the next ^{5}**m** lines describes the edge of the graph - two numbers, the initial and final vertex.

#### Output

Print **"YES"** if the vertices of the graph can be uniquely lexicographically sorted and **"NO"** otherwise. If it is impossible to sort graph topologically, print **-1**.

Input example #1

3 2 1 2 2 3

Output example #1

YES

Input example #2

3 2 1 2 1 3

Output example #2

NO