# Nothing Is Absolute, Everything Is Relative!

Ada Lovelace National Gir...
Limits 1.5s, 512 MB

You are given an integer array, $A[ ]$ of size $N$, and an integer $M$. Then you have to perform a total of $M$ operations on the array. The operations can be of $2$ types. They are:

Operation type 1:
$1$ $L$ $R$ $X$
Add $X$ to each element of the sub-array $[L,R]$. For example, if the current array is $A[ ] = [1, 3, 8, 5, 10, 6]$, after performing the operation $1$ $2$ $5$ $3$ the updated array will be $A[ ] = [1, 6, 11, 8, 13, 6]$.

Operation type 2:
$2$ $L$ $R$
Find the summation of absolute differences between the adjacent elements of the sub-array $[L,R]$. More formally, find the value of $|A_L - A_{L+1}| + |A_{L+1} - A_{L+2}| + \ldots + |A_{R-1} - A_R|$. Here, $|x|$ means absolute (non-negative) value of $x$.

## Input

The first line contains two space-separated integers $N$ and $M$, the size of the array and the number of operations, respectively. The second line contains $N$ space-separated integers denoting the array. The $i^{th}$ integer represents the $i^{th}$ element, $A[i]$ of the array. After that $M$ lines follow. The $j^{th}$ line represents the $j^{th}$ operation.

Constraints:
$2 \leq N,M \leq 5\times10^5$
$1 \leq L \leq R \leq N$
$-10^7 \leq A[i],X \leq 10^7$
In case of operation type $2$, $L \neq R$.

## Output

Output the answer of each operation type $2$ in a separated line.

## Sample

InputOutput
6 5
1 3 8 5 10 6
2 1 6
1 4 5 3
2 1 3
1 1 2 10
2 2 4

19
7
5