Number of Components

时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

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: $$$$$$\sum_{l=1}^{n} \sum_{r=l}^{n} f(l, r) $$$$$$

输入描述:

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.

输出描述:

Print one number — the answer to the problem.

示例1

输入

复制

3
2 1 3

输出

复制

示例2

输入

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4
2 1 1 3

输出

复制

示例3

输入

复制

10
1 5 2 5 5 3 10 6 5 1

输出

复制

备注:

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 $$$11$$$.