+ Graph と同じく、制約の 1≤u_i<v_i≤10^5 は 1≤u_i<v_i≤n の誤りかと思われます

そのとおりです。申し訳ありません。問題文を修正します。 For international contestants: we are sorry, we are fixing an error in the constraint: “1<=ui<vi<=10^5” -> “1<=ui<vi<=n”.

1≤ui<vi≤10^5,1<=ui<vi<=nの間違いでは?(viがnをこえてもいいんですか?)

そのとおりです。申し訳ありません。問題文を修正しました。

For international contestants: we are sorry, we fixed an error in the constraint: “1<=ui<vi<=10^5” -> “1<=ui<vi<=n”. 

Maybe the output should be $n$ lines instead of $n-1$?

We are very sorry, you are right. There should be n lines for each i = 0, 1, ..., n-1. The English statement is being fixed. EDIT: Now the English statement is correct.

What is the maximum length of S?

Sorry, the constraints are fixed in the English statement. |S| <= 1000.