Preparando MOJI
The 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:
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 $$$10^9+7$$$.
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.
Print single integer — the number of pairs of good subsegments modulo $$$10^9+7$$$.
3
1 2 3
1
5
1 2 1 2 3
4
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: