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.

-----Input-----
The first line of input contains the integer $N$ ($1 \leq N \leq 500000$), 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 $Q$ ($1 \leq Q \leq 500000$), 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.

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

-----Examples-----
Sample Input:
5
5 4 3 3 2
3
1 2
1 1
2 4
Sample Output:
2
1
3

Source: kattis | Difficulty: HARD


Solutions: