Codeforces 979C - Kuro and Walking Route [dfs + 思维]

C. Kuro and Walking Route

time limit per test : 2 seconds

memory limit per test : 256 megabytes

input : standard input

output : standard output

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 $(u,v)$ ($u\ne v$) 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 $y$ ($1\le n\le 3\cdot {10}^5,1\le x,y\le n$, $x\ne y$) - 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 $b$ ($1\le a,b\le n$, $a\ne b$), 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.

Examples

input

Copy

3 1 3
1 2
2 3

output

Copy

5

input

Copy

3 1 3
1 2
1 3

output

Copy

4

Note

On the first example, Kuro can choose these pairs:

• $(1,2)$: his route would be $1\to 2$,
• $(2,3)$: his route would be $2\to 3$,
• $(3,2)$: his route would be $3\to 2$,
• $(2,1)$: his route would be $2\to 1$,
• $(3,1)$: his route would be $3\to 2\to 1$.

Kuro can't choose pair $(1,3)$ since his walking route would be $1\to 2\to 3$, 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 $1\to 2$,
• $(2,1)$: his route would be $2\to 1$,
• $(3,2)$: his route would be $3\to 1\to 2$,
• $(3,1)$: his route would be $3\to 1$. 

题意：给n个顶点，有n - 1条边，显然是一棵树（我也没看出来），给两个点x, y；问有多少最短路径，不包含从x->y的路径；

这样子就是个组合问题啦。。。总共n*(n-1)，减去不满足题意的就可以啦。。。

代码：

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