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:
//遅延セグ木早書きチャレンジ0:00~
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;

using namespace std;
#define N (1<<17)
class RAQxRMQ{
private:
    ll dat[N*2],laz[N*2];
    void eval(int k){
	dat[k]+=laz[k];
	if(k<N-1){
	    laz[k*2+1]+=laz[k];
	    laz[k*2+2]+=laz[k];
	}
	laz[k]=0;
    }
    ll dfs(int l,int r,int a,int b,int k){
	eval(k);
	if(l<=a&&b<=r)return dat[k];
	if(b<=l||r<=a)return (ll)mod*(ll)mod;
	ll vl=dfs(l,r,a,(a+b)/2,k*2+1);
	ll vr=dfs(l,r,(a+b)/2,b,k*2+2);
	return min(vl,vr);
    }
    void ufs(int l,int r,int a,int b,int k,ll x){
	eval(k);
	if(l<=a&&b<=r){laz[k]+=x;eval(k);return;}
	if(b<=l||r<=a)return;
	ufs(l,r,a,(a+b)/2,k*2+1,x);
	ufs(l,r,(a+b)/2,b,k*2+2,x);
	dat[k]=min(dat[k*2+1],dat[k*2+2]);
    }
public:
    void Init(){
	lol(i,2*N)dat[i]=laz[i]=0;
    }
    void Add(int l,int r,ll x){
	ufs(l,r+1,0,N,0,x);
    }
    ll Min(int l,int r){
	return dfs(l,r+1,0,N,0);
    }
};
int main(){
    int n,q;cin>>n>>q;
    RAQxRMQ seg;seg.Init();
    while(q--){
	ll z,a,b,c;
	cin>>z;
	if(z==0){
	    cin>>a>>b>>c;
	    seg.Add(a,b,c);
	}
	if(z==1){
	    cin>>a>>b;
	    cout<<seg.Min(a,b)<<endl;
	}
    }
    return 0;
}