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>
#include<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<map>
#include<set>
#include<bitset>
using namespace std;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; i++ )
#define rep(i,n) REP(i,0,n)
typedef long long ll;
typedef pair<int,int> pint;
typedef pair<ll,int> pli;
const int inf=1e9+7;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;
int dx[4]={1,0,-1,0} , dy[4]={0,1,0,-1} ;

struct LazySegmentTree{
   int n;
   vector<ll> node,lazy,flag;
public:
   LazySegmentTree(int sz,ll init){
       n=1;
       while(n<sz)n*=2;
       node.resize(2*n-1,init);
       lazy.resize(2*n-1,0);
   }

   void eval(int k,int l,int r){
       if(lazy[k]!=0){
           node[k]+=lazy[k];
       if(r-l>1){
            lazy[2*k+1]+=lazy[k];
           lazy[2*k+2]+=lazy[k];
       }
       }
       lazy[k]=0;
    }
       //[a,b)にxを加算
    void update(int a,int b,ll x,int k=0,int l=0,int r=-1){
        if(r<0)r=n;
        eval(k,l,r);
        if(r<=a||b<=l)return;
        if(a<=l&&r<=b){
           lazy[k]+=x;
           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);
           node[k]=min(node[2*k+1],node[2*k+2]);
        }
    }
   //[a,b)での和を返す
   ll get(int a,int b,int k=0,int l=0,int r=-1){
       if(r<0)r=n;
       eval(k,l,r);
       if(r<=a||b<=l)return longinf;
       if(a<=l&&r<=b)return node[k];
       ll xl=get(a,b,2*k+1,l,(l+r)/2);
       ll xr=get(a,b,2*k+2,(l+r)/2,r);
       return min(xl,xr);
   }
};
int main(){
   int n,q;
   cin>>n>>q;
   LazySegmentTree sg(n,0);
   rep(i,q){
       int t;cin>>t;
       if(t){
           int a,b;
           cin>>a>>b;
           b++;
           cout<<sg.get(a,b)<<endl;
       }
       else {
           int a,b,c;
           cin>>a>>b>>c;
           sg.update(a,b+1,c);
       }
   }
   return 0;
}