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D. The Fair Nut's getting crazy

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Fair Nut has found an array $$$a$$$ of $$$n$$$ integers. We call subarray $$$l \ldots r$$$ a sequence of consecutive elements of an array with indexes from $$$l$$$ to $$$r$$$, i.e. $$$a_l, a_{l+1}, a_{l+2}, \ldots, a_{r-1}, a_{r}$$$.

No one knows the reason, but he calls a pair of subsegments good if and only if the following conditions are satisfied:

- These subsegments should not be nested. That is, each of the subsegments should contain an element (as an index) that does not belong to another subsegment.
- Subsegments intersect and each element that belongs to the intersection belongs each of segments only once.

For example $$$a=[1, 2, 3, 5, 5]$$$. Pairs $$$(1 \ldots 3; 2 \ldots 5)$$$ and $$$(1 \ldots 2; 2 \ldots 3)$$$) — are good, but $$$(1 \dots 3; 2 \ldots 3)$$$ and $$$(3 \ldots 4; 4 \ldots 5)$$$ — are not (subsegment $$$1 \ldots 3$$$ contains subsegment $$$2 \ldots 3$$$, integer $$$5$$$ belongs both segments, but occurs twice in subsegment $$$4 \ldots 5$$$).

Help the Fair Nut to find out the number of pairs of good subsegments! The answer can be rather big so print it modulo $$$10^9+7$$$.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$) — the length of array $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$) — the array elements.

Output

Print single integer — the number of pairs of good subsegments modulo $$$10^9+7$$$.

Examples

Input

3

1 2 3

Output

1

Input

5

1 2 1 2 3

Output

4

Note

In the first example, there is only one pair of good subsegments: $$$(1 \ldots 2, 2 \ldots 3)$$$.

In the second example, there are four pairs of good subsegments:

- $$$(1 \ldots 2, 2 \ldots 3)$$$
- $$$(2 \ldots 3, 3 \ldots 4)$$$
- $$$(2 \ldots 3, 3 \ldots 5)$$$
- $$$(3 \ldots 4, 4 \ldots 5)$$$

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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