Number of Components

1000ms

262144K

Description:

The Kingdom of Kremland is a tree (a connected undirected graph without cycles) consisting of $$$n$$$ vertices. Each vertex $$$i$$$ has its own value $$$a_i$$$. All vertices are connected in series by edges. Formally, for every $$$1 \leq i < n$$$ there is an edge between the vertices of $$$i$$$ and $$$i+1$$$.

Denote the function $$$f(l, r)$$$, which takes two integers $$$l$$$ and $$$r$$$ ($$$l \leq r$$$):

We leave in the tree only vertices whose values range from $$$l$$$ to $$$r$$$.
The value of the function will be the number of connected components in the new graph.

Your task is to calculate the following sum: $$$$$$\sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) $$$$$$

Input:

The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$) — the number of vertices in the tree.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq n$$$) — the values of the vertices.

Output:

Print one number — the answer to the problem.

Sample Input:

3
2 1 3

Sample Output:

Sample Input:

4
2 1 1 3

Sample Output:

Sample Input:

10
1 5 2 5 5 3 10 6 5 1

Sample Output:

Note:

In the first example, the function values will be as follows:

$$$f(1, 1)=1$$$ (there is only a vertex with the number $$$2$$$, which forms one component)
$$$f(1, 2)=1$$$ (there are vertices $$$1$$$ and $$$2$$$ that form one component)
$$$f(1, 3)=1$$$ (all vertices remain, one component is obtained)
$$$f(2, 2)=1$$$ (only vertex number $$$1$$$)
$$$f(2, 3)=2$$$ (there are vertices $$$1$$$ and $$$3$$$ that form two components)
$$$f(3, 3)=1$$$ (only vertex $$$3$$$)

Totally out $$$7$$$.

In the second example, the function values will be as follows:

$$$f(1, 1)=1$$$
$$$f(1, 2)=1$$$
$$$f(1, 3)=1$$$
$$$f(1, 4)=1$$$
$$$f(2, 2)=1$$$
$$$f(2, 3)=2$$$
$$$f(2, 4)=2$$$
$$$f(3, 3)=1$$$
$$$f(3, 4)=1$$$
$$$f(4, 4)=0$$$ (there is no vertex left, so the number of components is $$$0$$$)

Totally out $$$11$$$.

Informação

Provedor Codeforces

Código CF1151E