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<algorithm>
#include<vector>
#include<queue>
#include<string>
using namespace std;
typedef long long ll;
struct lazy_segtree{
private:
  int sz;
  vector<ll> node,lazy;
  ll seg_inf;
public:
  lazy_segtree(int n){
    sz=1;
    while(sz<n) sz*=2;
    node.resize(sz*2-1,0);
    lazy.resize(sz*2-1,0);
    seg_inf=0xffffffffffffff;
  }
  void eval(int k){
    node[k]+=lazy[k];
    if(k<sz-1){
      lazy[2*k+1]+=lazy[k];
      lazy[2*k+2]+=lazy[k];
    }
    lazy[k]=0;
  }
  void plus(int a,int b,ll x,int k,int l,int r){
    eval(k);
    if(r<=a||b<=l) return;
    if(a<=l&&r<=b){
      lazy[k]+=x;
      eval(k);
    }
    else{
      plus(a,b,x,2*k+1,l,(l+r)/2);
      plus(a,b,x,2*k+2,(l+r)/2,r);
      node[k]=min(node[2*k+1],node[2*k+2]);
    }
  }
  void add(int a,int b,ll x){
    plus(a,b,x,0,0,sz);
  }
  ll get_min(int a,int b,int k,int l,int r){
    eval(k);
    if(r<=a||b<=l) return seg_inf;
    if(a<=l&&r<=b) return node[k];
    else return min(get_min(a,b,2*k+1,l,(l+r)/2),get_min(a,b,2*k+2,(l+r)/2,r));
  }
  ll find(int s,int t){
    return get_min(s,t,0,0,sz);
  }
  void debug(int f){
    if(f==0){
      cout<<"node:";
      for(int i=0;i<node.size();i++) cout<<node[i]<<" ";
    }
    else{
      cout<<"lazy:";
      for(int i=0;i<lazy.size();i++) cout<<lazy[i]<<" ";
    }
    cout<<endl;
  }
};
int main(){
  int n,q;
  cin>>n>>q;
  lazy_segtree seg=lazy_segtree(n);
  for(int i=0;i<q;i++){
    int f;
    cin>>f;
    if(f==0){
      int s,t; ll x;
      cin>>s>>t>>x;
      //s++; t++;
      seg.add(s,t+1,x);
    }
    else{
      int s,t;
      cin>>s>>t;
      //s++; t++;
      cout<<seg.find(s,t+1)<<endl;
    }
    //seg.debug(0);
    //seg.debug(1);
  }
}