# Trees: Depth First Search

# Intervals on Tree

We have a tree with **n** vertices and **n** − **1** edges, respectively numbered **1**, **2**, ..., **n** and **1**, **2**, ..., **n** − **1**. Edge **i** connects vertices `u`

and _{i}`v`

._{i}

For integers **L**, **R** (**1** ≤ **L** ≤ **R** ≤ **n**), let us define a function f(**L**, **R**) as follows:

- Let
**S**be the set of the vertices numbered**L**through**R**. f(**L**,**R**) represents the number of connected components in the subgraph formed only from the vertex set S and the edges whose endpoints both belong to**S**.

Compute

#### Input

The first line contains number **n** (**1** ≤ **n** ≤ **2** * `10`

). Each of the next ^{5}**n** - **1** lines contains two vertices (`u`

, _{i}`v`

) (_{i}**1** ≤ `u`

, _{i}`v`

≤ _{i}**n**) - an edge in the graph.

#### Output

Print the value of the sum.

#### Example

We have six possible pairs (**L**, **R**) as follows:

For **L** = **1**, R = **1**, **S** = {**1**} and we have **1** connected component.

For **L** = **1**, **R** = **2**, **S** = {**1**, **2**} and we have **2** connected components.

For **L** = **1**, **R** = **3**, **S** = {**1**, **2**, **3**} and we have **1** connected component, since **S** contains both endpoints of each of the edges **1**, **2**.

For **L** = **2**, **R** = **2**, **S** = {**2**} and we have **1** connected component.

For **L** = **2**, **R** = **3**, **S** = {**2**, **3**} and we have **1** connected component, since **S** contains both endpoints of Edge **2**.

For **L** = **3**, **R** = **3**, **S** = {**3**} and we have **1** connected component.

The sum of these is **7**.

3 1 3 2 3

7