Array and Segments (Easy version)
Contest: Codeforces Round 535 (Div. 3)
Difficulty rating: 1800
Tags: brute force, greedy, implementation

The only difference between easy and hard versions is a number of elements in the array.

You are given an array $$$a$$$ consisting of $$$n$$$ integers. The value of the $$$i$$$-th element of the array is $$$a_i$$$.

You are also given a set of $$$m$$$ segments. The $$$j$$$-th segment is $$$[l_j; r_j]$$$, where $$$1 \le l_j \le r_j \le n$$$.

You can choose some subset of the given set of segments and decrease values on each of the chosen segments by one (independently). For example, if the initial array $$$a = [0, 0, 0, 0, 0]$$$ and the given segments are $$$[1; 3]$$$ and $$$[2; 4]$$$ then you can choose both of them and the array will become $$$b = [-1, -2, -2, -1, 0]$$$.

You have to choose some subset of the given segments (each segment can be chosen at most once) in such a way that if you apply this subset of segments to the array $$$a$$$ and obtain the array $$$b$$$ then the value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ will be maximum possible.

Note that you can choose the empty set.

If there are multiple answers, you can print any.

If you are Python programmer, consider using PyPy instead of Python when you submit your code.

Input format:
The first line of the input contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 300, 0 \le m \le 300$$$) — the length of the array $$$a$$$ and the number of segments, respectively.

The second line of the input contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^6 \le a_i \le 10^6$$$), where $$$a_i$$$ is the value of the $$$i$$$-th element of the array $$$a$$$.

The next $$$m$$$ lines are contain two integers each. The $$$j$$$-th of them contains two integers $$$l_j$$$ and $$$r_j$$$ ($$$1 \le l_j \le r_j \le n$$$), where $$$l_j$$$ and $$$r_j$$$ are the ends of the $$$j$$$-th segment.

Output format:
In the first line of the output print one integer $$$d$$$ — the maximum possible value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ if $$$b$$$ is the array obtained by applying some subset of the given segments to the array $$$a$$$.

In the second line of the output print one integer $$$q$$$ ($$$0 \le q \le m$$$) — the number of segments you apply.

In the third line print $$$q$$$ distinct integers $$$c_1, c_2, \dots, c_q$$$ in any order ($$$1 \le c_k \le m$$$) — indices of segments you apply to the array $$$a$$$ in such a way that the value $$$\max\limits_{i=1}^{n}b_i - \min\limits_{i=1}^{n}b_i$$$ of the obtained array $$$b$$$ is maximum possible.

If there are multiple answers, you can print any.

Constraints:
Time limit: 2.0 s
Memory limit: 256.0 MB

Note:
In the first example the obtained array $$$b$$$ will be $$$[0, -4, 1, 1, 2]$$$ so the answer is $$$6$$$.

In the second example the obtained array $$$b$$$ will be $$$[2, -3, 1, -1, 4]$$$ so the answer is $$$7$$$.

In the third example you cannot do anything so the answer is $$$0$$$.

Example input:
5 4
2 -2 3 1 2
1 3
4 5
2 5
1 3

Example output:
6
2
1 4

Example input:
5 4
2 -2 3 1 4
3 5
3 4
2 4
2 5

Example output:
7
2
3 2

Editorial:
Let's divide all segments to four classes. The first class contains segments which covers both minimum and maximum values (the answer) of the resulting array, the second class contains segments which covers only minimum value of the resulting array, the third class contains segments which covers only maximum value of the resulting array and the fourth class contains segments which covers neither maximum nor minimum of the resulting array.
We can easy see that we cannot increase the answer if we apply segments of first and third classes. What is common in this two classes? Right, both of them are cover maximum value.
So we can came up with the solution in $$$O(n^2m)$$$ or $$$O(n(n+m))$$$ (depends on implementation). Let's iterate over position of the supposed maximum value and apply all segments which not cover it. It can be done in $$$O(n^2m)$$$ with straight-forward implementation or in $$$O(n(n+m))$$$ using prefix sums. After we apply all needed segments we can try to update the answer with the value of the obtained array.