E. Number of Components
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Examples
Input
3
2 1 3

Output
7
Input
4
2 1 1 3

Output
11
Input
10
1 5 2 5 5 3 10 6 5 1

Output
104
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 $11$.