Sequence Operations and Inversion Count

Yoshino gives you a sequence of length $$n$$ with the $$i$$-th element being $$a_i$$. Yoshino will perform $$m$$ operations on the sequence.

Operations are of two types:

1. 1 l r x: Yoshino updates the elements in the range $$[l, r]$$ to form an arithmetic sequence starting from $$x$$ with a common difference of 1. In other words, for every index $$i$$ in $$[l, r]$$, the value is set to $$a_i = x + (i - l)$$.
2. 2: Yoshino queries the current number of inversion pairs in the entire sequence. An inversion pair is defined as a pair of indices $$(i, j)$$ such that $$i a_j$$.

inputFormat

The first line contains two integers $$n$$ and $$m$$: the length of the sequence and the number of operations.

The second line contains $$n$$ integers: $$a_1, a_2, \dots, a_n$$, representing the initial sequence.

Then follow $$m$$ lines, each describing an operation:

• If the operation is of type 1, the line contains four integers: 1 l r x.
• If the operation is of type 2, the line contains a single integer: 2.

outputFormat

For every operation of type 2, output one integer on a new line: the number of inversion pairs in the current sequence.

sample

5 3
1 3 2 5 4
2
1 2 4 0
2

3
4