Scalar Queries
Description
You are given an array $a_1, a_2, \dots, a_n$. All $a_i$ are pairwise distinct.
Let's define function $f(l, r)$ as follows:
- let's define array $b_1, b_2, \dots, b_{r - l + 1}$, where $b_i = a_{l - 1 + i}$;
- sort array $b$ in increasing order;
- result of the function $f(l, r)$ is $\sum\limits_{i = 1}^{r - l + 1}{b_i \cdot i}$.
Calculate $\left(\sum\limits_{1 \le l \le r \le n}{f(l, r)}\right) \mod (10^9+7)$, i.e. total sum of $f$ for all subsegments of $a$ modulo $10^9+7$.
The first line contains one integer $n$ ($1 \le n \le 5 \cdot 10^5$) — the length of array $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$, $a_i \neq a_j$ for $i \neq j$) — array $a$.
Print one integer — the total sum of $f$ for all subsegments of $a$ modulo $10^9+7$
Input
The first line contains one integer $n$ ($1 \le n \le 5 \cdot 10^5$) — the length of array $a$.
The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$, $a_i \neq a_j$ for $i \neq j$) — array $a$.
Output
Print one integer — the total sum of $f$ for all subsegments of $a$ modulo $10^9+7$
Samples
4
5 2 4 7
167
3
123456789 214365879 987654321
582491518
Note
Description of the first example:
- $f(1, 1) = 5 \cdot 1 = 5$;
- $f(1, 2) = 2 \cdot 1 + 5 \cdot 2 = 12$;
- $f(1, 3) = 2 \cdot 1 + 4 \cdot 2 + 5 \cdot 3 = 25$;
- $f(1, 4) = 2 \cdot 1 + 4 \cdot 2 + 5 \cdot 3 + 7 \cdot 4 = 53$;
- $f(2, 2) = 2 \cdot 1 = 2$;
- $f(2, 3) = 2 \cdot 1 + 4 \cdot 2 = 10$;
- $f(2, 4) = 2 \cdot 1 + 4 \cdot 2 + 7 \cdot 3 = 31$;
- $f(3, 3) = 4 \cdot 1 = 4$;
- $f(3, 4) = 4 \cdot 1 + 7 \cdot 2 = 18$;
- $f(4, 4) = 7 \cdot 1 = 7$;