A9001 | Sereja and Subsequences

Sereja has a sequence that consists of $n$ positive integers, $a_{1},a_{2},...,a_{n}$ .

First Sereja took a piece of squared paper and wrote all distinct non-empty non-decreasing subsequences of sequence $a$ . Then for each sequence written on the squared paper, Sereja wrote on a piece of lines paper all sequences that do not exceed it.

A sequence of positive integers $x=x_{1},x_{2},...,x_{r}$ doesn't exceed a sequence of positive integers $y=y_{1},y_{2},...,y_{r}$ , if the following inequation holds: $x_{1}<=y_{1},x_{2}<=y_{2},...,x_{r}<=y_{r}$ .

Now Sereja wonders, how many sequences are written on the lines piece of paper. Help Sereja, find the required quantity modulo $1000000007$ $(10^{9}+7)$ .

The first line contains integer $n$ $(1<=n<=10^{5})$ . The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ $(1<=a_{i}<=10^{6})$ .

In the single line print the answer to the problem modulo $1000000007$ $(10^{9}+7)$ .