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E - Find Permutation

Score : $500$ points

Problem Statement

There is a length-$N$ sequence $A=(A_1,\ldots,A_N)$ that is a permutation of $1,\ldots,N$.

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 $A$.

Constraints

• $2 \leq N \leq 2\times 10^5$
• $1 \leq M \leq 2\times 10^5$
• $1\leq X_i,Y_i \leq N$
• All values in the input are integers.
• There is an $A$ consistent with the input.

Input

The input is given from Standard Input in the following format:

$N$ $M$

$X_1$ $Y_1$

$\vdots$

$X_M$ $Y_M$

Output

If $A$ can be uniquely determined, print Yes in the first line. Then, print $A_1,\ldots,A_N$ in the second line, separated by spaces.

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

3 2
3 1
2 3

Yes
3 1 2

We can uniquely determine that $A=(3,1,2)$.

3 2
3 1
3 2

No

Two sequences $(2,3,1)$ and $(3,2,1)$ can be $A$.

4 6
1 2
1 2
2 3
2 3
3 4
3 4

Yes
1 2 3 4