Just Another Range Query

This is another simple range query problem where you will perform some updates and answer some queries. Let's take an array $A$ of length $N$. Initially, $A[i] = i$ for each $i$ in the range $[1,N]$.

You will have to perform $Q$ operations on this array. There will be two types of operations:

• $\texttt{1 L R V}$ - which means that you will have to subtract $V$ from all $A[i]$ such that $L ≤ i ≤ R$.
• $\texttt{2 L R}$ - which means that you will have to print the sum of all $A[i]$ such that $L ≤ i ≤ R$.

Input

In the first line of input, there will be two integers $N$ and $Q$ ($1 \le N \le 10^9$, $1 \le Q \le 10^5$) which are the length of the array and number of operations to perform respectively.

Next Q lines will contain the description of the operations to perform in the format $\texttt{1 L R V}$ or $\texttt{2 L R}$ ($1 \le L \le R \le N$, $1 \le V \le 10^5$).

Output

For each operation of the format $\texttt{2 L R}$, print the answer of the query in a single line.

Sample

Input	Output
10 5 2 1 5 1 4 8 10 2 2 7 1 1 10 1 2 1 10	15 -13 -5