$N$ people numbered $1,2,\dots,N$ are standing in a row. Person $i$ wears Color $A_i$. Answer $Q$ queries of the format below. - You are given integers $l$ and $r$. Considering only Person $l,l+1,\dots,r$, how many pairs of people wearing the same color can be formed at most? ### Constraints - All values in input are integers. - $1 \le N \le 10^5$ - $1 \le Q \le 10^6$ - $1 \le A_i \le N$ - $1 \le l \le r \le N$ in each query.

Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\dots$ $A_N$ $Q$ $\mathrm{Query}_1$ $\mathrm{Query}_2$ $\vdots$ $\mathrm{Query}_Q$ Here, $\mathrm{Query}_i$ represents the $i$\-th query. Each query is in the following format: $l$ $r$

Print $Q$ lines. The $i$\-th line should contain the answer for the $i$\-th query as an integer. The use of fast input and output methods is recommended because of potentially large input and output.