English · Original
Chinese · Translation
Formal · Original
Kuro is living in a country called Uberland, consisting of $n$ towns, numbered from $1$ to $n$, and $n - 1$ bidirectional roads connecting these towns. It is possible to reach each town from any other. Each road connects two towns $a$ and $b$. Kuro loves walking and he is planning to take a walking marathon, in which he will choose a pair of towns $(u, v)$ ($u \neq v$) and walk from $u$ using the shortest path to $v$ (note that $(u, v)$ is considered to be different from $(v, u)$).
Oddly, there are 2 special towns in Uberland named Flowrisa (denoted with the index $x$) and Beetopia (denoted with the index $y$). Flowrisa is a town where there are many strong-scent flowers, and Beetopia is another town where many bees live. In particular, Kuro will avoid any pair of towns $(u, v)$ if on the path from $u$ to $v$, he reaches Beetopia after he reached Flowrisa, since the bees will be attracted with the flower smell on Kuro’s body and sting him.
Kuro wants to know how many pair of city $(u, v)$ he can take as his route. Since he’s not really bright, he asked you to help him with this problem.
## Input
The first line contains three integers $n$, $x$ and $y$ ($1 \leq n \leq 3 \cdot 10^5$, $1 \leq x, y \leq n$, $x \ne y$) - the number of towns, index of the town Flowrisa and index of the town Beetopia, respectively.
$n - 1$ lines follow, each line contains two integers $a$ and $b$ ($1 \leq a, b \leq n$, $a \ne b$), describes a road connecting two towns $a$ and $b$.
It is guaranteed that from each town, we can reach every other town in the city using the given roads. That is, the given map of towns and roads is a tree.
## Output
A single integer resembles the number of pair of towns $(u, v)$ that Kuro can use as his walking route.
[samples]
## Note
On the first example, Kuro can choose these pairs:
* $(1, 2)$: his route would be $1 \rightarrow 2$,
* $(2, 3)$: his route would be $2 \rightarrow 3$,
* $(3, 2)$: his route would be $3 \rightarrow 2$,
* $(2, 1)$: his route would be $2 \rightarrow 1$,
* $(3, 1)$: his route would be $3 \rightarrow 2 \rightarrow 1$.
Kuro can't choose pair $(1, 3)$ since his walking route would be $1 \rightarrow 2 \rightarrow 3$, in which Kuro visits town $1$ (Flowrisa) and then visits town $3$ (Beetopia), which is not allowed (note that pair $(3, 1)$ is still allowed because although Kuro visited Flowrisa and Beetopia, he did not visit them in that order).
On the second example, Kuro can choose the following pairs:
* $(1, 2)$: his route would be $1 \rightarrow 2$,
* $(2, 1)$: his route would be $2 \rightarrow 1$,
* $(3, 2)$: his route would be $3 \rightarrow 1 \rightarrow 2$,
* $(3, 1)$: his route would be $3 \rightarrow 1$.
Kuro 生活在一个名为 Uberland 的国家，该国有 $n$ 个城镇，编号从 $1$ 到 $n$，以及 $n - 1$ 条双向道路连接这些城镇。任意两个城镇之间都可以互相到达。每条道路连接两个城镇 $a$ 和 $b$。Kuro 热爱散步，他计划参加一场步行马拉松，他将选择一对城镇 $(u, v)$（$u \ne v$），并从 $u$ 沿最短路径走到 $v$（注意 $(u, v)$ 与 $(v, u)$ 被视为不同的配对）。
奇怪的是，Uberland 中有两个特殊城镇，分别名为 Flowrisa（编号为 $x$）和 Beetopia（编号为 $y$）。Flowrisa 是一个有许多浓香花朵的城镇，而 Beetopia 是一个有许多蜜蜂生活的城镇。具体来说，如果 Kuro 在从 $u$ 到 $v$ 的路径上，先经过 Flowrisa 后再经过 Beetopia，他将避免选择这样的城镇对 $(u, v)$，因为蜜蜂会被 Kuro 身上的花香吸引并蜇他。
Kuro 想知道有多少对城镇 $(u, v)$ 可以作为他的步行路线。由于他并不聪明，他请你帮他解决这个问题。
第一行包含三个整数 $n$、$x$ 和 $y$（$1 \le n \le 3 \cdot 10^5$，$1 \le x, y \le n$，$x \ne y$），分别表示城镇数量、Flowrisa 城镇的编号和 Beetopia 城镇的编号。
接下来 $n - 1$ 行，每行包含两个整数 $a$ 和 $b$（$1 \le a, b \le n$，$a \ne b$），描述一条连接城镇 $a$ 和 $b$ 的道路。
保证从每个城镇都可以通过给定的道路到达其他所有城镇。也就是说，给定的城镇和道路地图是一棵树。
输出一个整数，表示 Kuro 可以作为步行路线的城镇对 $(u, v)$ 的数量。
在第一个例子中，Kuro 可以选择以下配对：
Kuro 不能选择配对 $(1, 3)$，因为他的步行路线是 $1 \to 2 \to 3$，其中他先经过城镇 $1$（Flowrisa），再经过城镇 $3$（Beetopia），这是不允许的（注意配对 $(3, 1)$ 仍然是允许的，因为虽然 Kuro 经过了 Flowrisa 和 Beetopia，但他没有按这个顺序经过它们）。
在第二个例子中，Kuro 可以选择以下配对：
## Input
第一行包含三个整数 $n$、$x$ 和 $y$（$1 \le n \le 3 \cdot 10^5$，$1 \le x, y \le n$，$x \ne y$），分别表示城镇数量、Flowrisa 城镇的编号和 Beetopia 城镇的编号。接下来 $n - 1$ 行，每行包含两个整数 $a$ 和 $b$（$1 \le a, b \le n$，$a \ne b$），描述一条连接城镇 $a$ 和 $b$ 的道路。保证从每个城镇都可以通过给定的道路到达其他所有城镇。也就是说，给定的城镇和道路地图是一棵树。
## Output
输出一个整数，表示 Kuro 可以作为步行路线的城镇对 $(u, v)$ 的数量。
[samples]
## Note
在第一个例子中，Kuro 可以选择以下配对：$(1, 2)$：他的路线是 $1 \to 2$；$(2, 3)$：他的路线是 $2 \to 3$；$(3, 2)$：他的路线是 $3 \to 2$；$(2, 1)$：他的路线是 $2 \to 1$；$(3, 1)$：他的路线是 $3 \to 2 \to 1$。Kuro 不能选择配对 $(1, 3)$，因为他的步行路线是 $1 \to 2 \to 3$，其中他先经过城镇 $1$（Flowrisa），再经过城镇 $3$（Beetopia），这是不允许的（注意配对 $(3, 1)$ 仍然是允许的，因为虽然 Kuro 经过了 Flowrisa 和 Beetopia，但他没有按这个顺序经过它们）。
在第二个例子中，Kuro 可以选择以下配对：$(1, 2)$：他的路线是 $1 \to 2$；$(2, 1)$：他的路线是 $2 \to 1$；$(3, 2)$：他的路线是 $3 \to 1 \to 2$；$(3, 1)$：他的路线是 $3 \to 1$。
**Definitions**
Let $ T = (V, E) $ be a tree with $ n $ vertices (towns), labeled $ 1 $ to $ n $.
Let $ x, y \in V $, $ x \ne y $, denote the special towns Flowrisa and Beetopia, respectively.
Let $ P(u, v) $ denote the unique simple path from vertex $ u $ to vertex $ v $ in $ T $.
Let $ \text{order}(P(u, v)) $ denote the sequence of vertices along $ P(u, v) $, starting at $ u $ and ending at $ v $.
**Constraints**
1. $ 1 \le n \le 3 \cdot 10^5 $
2. $ 1 \le x, y \le n $, $ x \ne y $
3. The graph is a tree: connected and acyclic.
**Forbidden Condition**
A pair $ (u, v) $, $ u \ne v $, is **forbidden** if and only if in $ \text{order}(P(u, v)) $, vertex $ x $ appears **before** vertex $ y $.
**Objective**
Compute the number of ordered pairs $ (u, v) $, $ u \ne v $, such that $ (u, v) $ is **not forbidden**, i.e., either:
- $ x $ does not appear on $ P(u, v) $, or
- $ y $ appears on $ P(u, v) $ before $ x $, or
- neither $ x $ nor $ y $ is on $ P(u, v) $.
Equivalently, count:
$$
\left| \left\{ (u, v) \in V \times V \mid u \ne v \text{ and } \text{if } x, y \in P(u, v) \text{ then } y \text{ precedes } x \text{ in } \text{order}(P(u, v)) \right\} \right|
$$
**Note**: Total possible pairs: $ n(n - 1) $.
Let $ F $ be the set of forbidden pairs: $ F = \{ (u, v) \mid x \text{ appears before } y \text{ on } P(u, v) \} $.
Then the answer is:
$$
n(n - 1) - |F|
$$
API Response (JSON)
{
"problem": {
"name": "C. Kuro and Walking Route",
"description": {
"content": "Kuro is living in a country called Uberland, consisting of $n$ towns, numbered from $1$ to $n$, and $n - 1$ bidirectional roads connecting these towns. It is possible to reach each town from any other",
"description_type": "Markdown"
},
"platform": "Codeforces",
"limit": {
"time_limit": 2000,
"memory_limit": 262144
},
"difficulty": "None",
"is_remote": true,
"is_sync": true,
"sync_url": null,
"sign": "CF979C"
},
"statements": [
{
"statement_type": "Markdown",
"content": "Kuro is living in a country called Uberland, consisting of $n$ towns, numbered from $1$ to $n$, and $n - 1$ bidirectional roads connecting these towns. It is possible to reach each town from any other...",
"is_translate": false,
"language": "English"
},
{
"statement_type": "Markdown",
"content": "Kuro 生活在一个名为 Uberland 的国家，该国有 $n$ 个城镇，编号从 $1$ 到 $n$，以及 $n - 1$ 条双向道路连接这些城镇。任意两个城镇之间都可以互相到达。每条道路连接两个城镇 $a$ 和 $b$。Kuro 热爱散步，他计划参加一场步行马拉松，他将选择一对城镇 $(u, v)$（$u \\ne v$），并从 $u$ 沿最短路径走到 $v$（注意 $(u, v)$ 与 $(v...",
"is_translate": true,
"language": "Chinese"
},
{
"statement_type": "Markdown",
"content": "**Definitions** \nLet $ T = (V, E) $ be a tree with $ n $ vertices (towns), labeled $ 1 $ to $ n $. \nLet $ x, y \\in V $, $ x \\ne y $, denote the special towns Flowrisa and Beetopia, respectively. \n\n...",
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}