Problem: 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.

Constraints

* $1 ≤ n ≤ 100000$
* $1 ≤ q ≤ 100000$
* $0 ≤ s ≤ t < n$
* $-1000 ≤ x ≤ 1000$

Input


$n$ $q$
$query_1$
$query_2$
:
$query_q$


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 $find(s, t)$.

Output

For each $find$ query, print the minimum value.

Example

Input

6 7
0 1 3 1
0 2 4 -2
1 0 5
1 0 1
0 3 5 3
1 3 4
1 0 5


Output

-2
0
1
-1

Solution (in CPP):

Solution:
#include<iostream>
using namespace std;
#include<vector>
#include<functional>
template<typename T>
struct lazysegtree{
	function<T(T,T)>calcfn,lazycalcfn;
	function<T(T,T,unsigned int)>updatefn;
	int n;
	T defvalue,lazydefvalue;
	vector<T>dat,lazy;
	vector<bool>lazyflag;
	lazysegtree(int n_=0,T defvalue_=0,
		function<T(T,T)>calcfn_=[](T a,T b){return a+b;},
		function<T(T,T)>lazycalcfn_=[](T a,T b){return a+b;},
		function<T(T,T,unsigned int)>updatefn_=[](T a,T b,unsigned int width){return a+b*width;},
		T lazydefvalue_=0
	):defvalue(defvalue_),lazydefvalue(lazydefvalue_),
		calcfn(calcfn_),lazycalcfn(lazycalcfn_),updatefn(updatefn_)
	{
		n=1;
		while(n<n_)n<<=1;
		dat.assign(2*n-1,defvalue);
		lazy.assign(2*n-1,lazydefvalue);
		lazyflag.assign(2*n-1,false);
	}
	void copy(vector<T>v)
	{
		for(int i=0;i<v.size();i++)dat[i+n-1]=v[i];
		for(int i=n-2;i>=0;i--)dat[i]=calcfn(dat[2*i+1],dat[2*i+2]);
	}
	void eval(int i,int l,int r)
	{
		if(lazyflag[i])
		{
			dat[i]=updatefn(dat[i],lazy[i],r-l);
			if(r-l>1)
			{
				lazy[2*i+1]=lazycalcfn(lazy[2*i+1],lazy[i]);
				lazy[2*i+2]=lazycalcfn(lazy[2*i+2],lazy[i]);
				lazyflag[2*i+1]=lazyflag[2*i+2]=true;
			}
			lazy[i]=lazydefvalue;
			lazyflag[i]=false;
		}
	}
	void update(int a,int b,T x,int k=0,int l=0,int r=-1)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return;
		else if(a<=l&&r<=b)
		{
			lazy[k]=lazycalcfn(lazy[k],x);
			lazyflag[k]=true;
			eval(k,l,r);
		}
		else
		{
			update(a,b,x,2*k+1,l,(l+r)/2);
			update(a,b,x,2*k+2,(l+r)/2,r);
			dat[k]=calcfn(dat[2*k+1],dat[2*k+2]);
		}
	}
	T query(int a,int b,int k=0,int l=0,int r=-1)
	{
		if(r<0)r=n;
		eval(k,l,r);
		if(b<=l||r<=a)return defvalue;
		else if(a<=l&&r<=b)return dat[k];
		else return calcfn(
			query(a,b,2*k+1,l,(l+r)/2),
			query(a,b,2*k+2,(l+r)/2,r)
		);
	}
};
int n,q;
int main()
{
	cin>>n>>q;
	lazysegtree<int>P(n,(1LL<<31)-1,[](int a,int b){return a<b?a:b;},[](int a,int b){return a+b;},[](int a,int b,int width){return a+b;});
	vector<int>a(n,0);
	P.copy(a);
	for(int i=0;i<q;i++)
	{
		int c;cin>>c;
		if(c)
		{
			int s,t;cin>>s>>t;
			cout<<P.query(s,t+1)<<endl;
		}
		else
		{
			int s,t,x;cin>>s>>t>>x;
			P.update(s,t+1,x);
		}
	}
}