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## 문제

Consider a set $V = \{1, \ldots, n\}$ of $n$ vertices, and a sequence of directed edges $e_1, \ldots, e_{n - 1}$. Let $G_0, \ldots, G_{n - 1}$ be a sequence of graphs such that $G_0$ is empty, and $G_i$ is obtained by introducing the edge $e_i$ into $G_{i - 1}$ for each $i = 1, \ldots, n - 1$. It is guaranteed that $G_{n - 1}$ is a rooted tree with all edges directed away from the root.

Your task is to find a suitable permutation $p_1, \ldots, p_n$ of the set $\{1, \ldots, n\}$. Let $S_i(v) = \{p_u \mid u$ can be reached from $v$ in $G_i\}$. A permutation $p_1, \ldots, p_n$ is called suitable if for any $i \in \{0, \ldots, n - 1\}$ and for any $v \in V$ we have that $S_i(v)$ consists of consecutive numbers (that is, $S_i(v) = \{l, l + 1, \ldots, r\}$ for some numbers $l$ and $r$).

## 입력

The first line contains a single integer $n$ ($2 \leq n \leq 10^6$).

The next $n - 1$ lines describe the edges $e_1, \ldots, e_{n - 1}$. The $i$-th of these lines contains two integers $u_i$ and $v_i$ --- indices of the source and the target vertices of the edge $e_i$ ($1 \le u_i, v_i \le n$).

It is guaranteed that adding all $n - 1$ edges results in a rooted tree with edges directed away from the root.

## 출력

If there is no suitable permutation, print the only word "No" in the only line.

Otherwise, print "Yes" on the first line. On the second line print $n$ integers $p_1, \ldots, p_n$ describing any suitable permutation.

## 예제 입력 1

4
3 1
1 4
1 2


## 예제 출력 1

Yes
3 1 4 2


## 예제 입력 2

7
1 2
1 3
1 4
2 5
3 6
4 7


## 예제 출력 2

No