Find Permutation

There is a length $n$ sequence $A=(a_1,a_2,...,a_n)$​ that is a permutation of $1,2,...,n$.

While you do not know $A$, you know that $A_{x_i}<A_{y_i}$ for $m$ pairs of integers $(x_i,y_i)$.

Can $A$ be uniquely determined? If it is possible, find $A$.

Input

The first line contains two numbers $n(2\le n\le 2\cdot 10^5)$ and $m(1\le m\le 2\cdot 10^5)$.

Each of the next $m$ lines contains a pair of integers $(x_i,y_i)$, $1\le x_i,y_i\le n$.

Output

If $A$ can be uniquely determined, print Yes in the first line. Then, print $a_1,a_2,...,a_n$ in the second line.

If $A$ cannot be uniquely determined, just print No.

Examples