Fafa and Array

给出一个序列 $a$，定义函数 $f(a)=\sum_{i=1}^{n-1}|a_i-a_{i+1}|$。 给出两种操作: - $\texttt{1 l r x}$，表示在区间 $[l,r]$ 内找一个位置，使得把这个位置的值加上 $x$ 后，$f(a)$ 最大,求这个最大值。 - $\texttt{2 l r x}$，表示把区间 $[l,r]$ 加上 $x$。 $n\le10^5,q\le10^5,x_i\le10^9$。 感谢@Kelin 提供的翻译

Fafa has an array $ A $ of $ n $ positive integers, the function $ f(A) $ is defined as . He wants to do $ q $ queries of two types: - $ 1lrx $ — find the maximum possible value of $ f(A) $ , if $ x $ is to be added to one element in the range $ [l,r] $ . You can choose to which element to add $ x $ . - $ 2lrx $ — increase all the elements in the range $ [l,r] $ by value $ x $ . Note that queries of type $ 1 $ don't affect the array elements.

The first line contains one integer $ n $ $ (3<=n<=10^{5}) $ — the length of the array. The second line contains $ n $ positive integers $ a_{1},a_{2},...,a_{n} $ $ (0<a_{i}<=10^{9}) $ — the array elements. The third line contains an integer $ q $ $ (1<=q<=10^{5}) $ — the number of queries. Then $ q $ lines follow, line $ i $ describes the $ i $ -th query and contains four integers $ t_{i}l_{i}r_{i}x_{i} $ . It is guaranteed that at least one of the queries is of type $ 1 $ .

For each query of type $ 1 $ , print the answer to the query.

5
1 1 1 1 1
5
1 2 4 1
2 2 3 1
2 4 4 2
2 3 4 1
1 3 3 2

2
8

5
1 2 3 4 5
4
1 2 4 2
2 2 4 1
2 3 4 1
1 2 4 2

6
10