Write a program which manipulates a sequence A = {$a_0,a_1,...,a_{n−1}$} with the following operations:

• add(s,t,x) : add x to $a_s,a_{s+1},...,a_t$.
• find(s,t) : report the minimum value in $a_s,a_{s+1},...,a_t$.

Note that the initial values of $a_i\ (i=0,1,...,n−1)$ are 0.

In the first line, n (the number of elements in A) and q (the number of queries) are given. 

Then, i-th query query$_i$ is given in the following format:

0 s t x

or

1 s t

The first digit represents the type of the query. '0' denotes add(s,t,x) and '1' denotes find(s,t).