Young Luka is about to enter a house with the evil witch Marica inside. As soon as he enters the house, she asks him questions about her array of $N$ numbers. Luka fearfully asks for a clarification of the questions. Marica explains to him that each query consists of two integers $L$ and $R$ which represent the positions of a contiguous sub-array in her array.

It is Luka’s task to answer for each query what the longest contiguous sub-array of that contiguous sub-array (it can be the entire sub-array) having the property of being magical. An array is called magical if all the values are between the values of the first and last number in that array. For example, $[1\ 3\ 1\ 2\ 4]$ is magical, the same as $[4\ 1\ 1\ 2\ 1]$, whereas $[3\ 3\ 4\ 1]$ is not magical.


The first line of input contains the integer $N$ ($1 \leq N \leq 500\, 000$), the number of numbers in the array. The second line contains $N$ integers $a_ i$ ($1 \leq a_ i \leq 10^9$). The third line contains the integer $Q$ ($1 \leq Q \leq 500\, 000$), the number of queries. Each of the following $Q$ lines contains two integers, $L$ and $R$ ($1 \leq L \leq R \leq N$), representing the sub-array from the query.


The $i$-th line of output must contain a single integer—the answer to the $i$-th query.

Sample Input 1 Sample Output 1
5 4 3 3 2
1 2
1 1
2 4
Sample Input 2 Sample Output 2
6 6 5 1 6 2
4 5
4 6
1 4
CPU Time limit 5 seconds
Memory limit 1024 MB
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License For educational use only

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