Initially there are two arrays $$$a$$$ and $$$b$$$ of length $$$n$$$ filled with zeros. You need to process $$$q$$$ updates and queries of the following types:
1. For each $$$i$$$ such, that $$$l \leq i \leq r$$$ set $$$a[i] := a[i] + c$$$ and then set $$$b[i] := \max(b[i], a[i])$$$
2. For each $$$i$$$ such, that $$$l \leq i \leq r$$$ set $$$a[i] := \max(a[i], d)$$$ and then set $$$b[i] := \max(b[i], a[i])$$$
3. Print $$$\max(b[l], b[l + 1], ..., b[r])$$$
The first line of the input contains a integers $$$n, q$$$ ($$$1 \leq n,q \leq 5 \cdot 10^5$$$).
The following $$$q$$$ lines of the input start with $$$1 \leq t_i \leq 3$$$ indicating query / update type.
If $$$t_i = 1$$$ the line contains integers $$$l_i, r_i, c_i$$$, ($$$1 \leq l_i \leq r_i \leq n, |c_i| \leq 10^6$$$).
If $$$t_i = 2$$$ the line contains integers $$$l_i, r_i, d_i$$$, ($$$1 \leq l_i \leq r_i \leq n, |d_i| \leq 10^{12}$$$).
If $$$t_i = 3$$$ the line contains integers $$$l_i, r_i$$$, ($$$1 \leq l_i \leq r_i \leq n$$$).
The $$$i$$$-th line of the output should contain the answer to the $$$i$$$-th type 3 query.
10 8 1 1 10 1 1 1 2 2 3 1 7 1 1 5 -100 3 1 3 2 1 6 100 3 7 8 3 6 9
3 3 1 100
