HandsOn $>$Max Queries

There is an array a containing $n$ integers.

Let's define occ$(i,j,x)$ as the number of occurrences of $x$ in the subarray from $i$ to $j.$ We define beauty $(l,r,x)$ as the maximum value of occ$(i,j,x)$ over all possible pairs $)ij(r$ satisfying that the maximum element in the subarray from $i$ to $j$ is x$.$

You are also given $q$ queries, each query contains three values $,$ x$)$ where $)||r({10}^5$ and $)x({10}^5.$ The answer to each query is the beauty $(l,r,x).$

Find the sum of answers to all queries. Since the answer might be large return it modulo ${10}^{{?}^{{?}^{?}}}9+7.$

Input Format

The first line contains an integer, $n,$ denoting the number of elements in a$.$

Each line $i$ of the $n$ subsequent lines $($where $a[i]q0i$