E. Number of Componentstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe 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) InputThe 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.OutputPrint one number — the answer to the problem.ExamplesInput
3
2 1 3
Output
7Input
4
2 1 1 3
Output
11Input
10
1 5 2 5 5 3 10 6 5 1
Output
104NoteIn 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.
3
2 1 3

7
['combinatorics', 'data structures', 'dp', 'math', '*2100']