Mr. Nine and his love for mangoes

Mr. Nine was roaming casually in the Parallel Universe in his mid-semester breaks, suddenly he comes across a mango tree. He loves mangoes so he decides to pluck some mangoes from it but suddenly a fairy appears and tells him to solve a complex problem to get the mangoes. She tells him that there are $n$ nodes in the tree and he is given two nodes $u$ and $v$. Now she asks him how many pairs of nodes are present in tree in which shortest path between them does not contain node $v$ after node $u$ (for example u → a → b → v is also not allowed where $a$ and $b$ are two different nodes). If he is able to tell the correct number of pairs of nodes then he will get all the mangoes, but he is unable to do so and needs your help.

Examples

There are $5$ possible pairs that can be chosen:

$(1,2)$ : his route would be 1 → 2

$(2,3)$ : his route would be 2 → 3

$(3,2)$ : his route would be 3 → 2

$(2,1)$ : his route would be 2 → 1

$(3,1)$ : his route would be 3 → 2 → 1

He cannot choose $(1,3)$ as a pair because the shortest path between them will be 1 → 2 → 3 and this is not acceptable as it contains v = 3 after u = 1 and thus it is not acceptable.

Example 1

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