{"raw_statement":[{"iden":"problem statement","content":"There is a length-$N$ sequence $A=(A_1,\\ldots,A_N)$ that is a permutation of $1,\\ldots,N$.\nWhile you do not know $A$, you know that $A_{X_i}<A_{Y_i}$ for $M$ pairs of integers $(X_i,Y_i)$.\nCan $A$ be uniquely determined? If it is possible, find $A$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq M \\leq 2\\times 10^5$\n*   $1\\leq X_i,Y_i \\leq N$\n*   All values in the input are integers.\n*   There is an $A$ consistent with the input."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$\n$X_1$ $Y_1$\n$\\vdots$\n$X_M$ $Y_M$"},{"iden":"sample input 1","content":"3 2\n3 1\n2 3"},{"iden":"sample output 1","content":"Yes\n3 1 2\n\nWe can uniquely determine that $A=(3,1,2)$."},{"iden":"sample input 2","content":"3 2\n3 1\n3 2"},{"iden":"sample output 2","content":"No\n\nTwo sequences $(2,3,1)$ and $(3,2,1)$ can be $A$."},{"iden":"sample input 3","content":"4 6\n1 2\n1 2\n2 3\n2 3\n3 4\n3 4"},{"iden":"sample output 3","content":"Yes\n1 2 3 4"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}