Sereja has a sequence that consists of n positive integers, a₁, a₂, ..., 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 = x₁, x₂, ..., x_r doesn't exceed a sequence of positive integers y = y₁, y₂, ..., y_r, if the following inequation holds: x₁ ≤ y₁, x₂ ≤ y₂, ..., 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 (10⁹ + 7).

Input

The first line contains integer n (1 ≤ n ≤ 10⁵). The second line contains n integers a₁, a₂, ..., a_n (1 ≤ a_i ≤ 10⁶).

Output

In the single line print the answer to the problem modulo 1000000007 (10⁹ + 7).

Sereja and Subsequences

Examples