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 <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
template<class T> void chmin(T &a,const T &b){if(a>b) a=b;}
template<class T> void chmax(T &a,const T &b){if(a<b) a=b;}

#include <functional>

template< typename T, typename S >
struct LazySegmentTree{
    int n;
    vector<T> data;
    vector<S> lazy;
    T te;
    S se;

    inline void merge_functions(S& lazy,S& val){
        lazy+=val;
        //lazy=val;
    }
    inline void operate(T& data,S& val,int len){
        //data+=val*len;
        data+=val;
        //data=val;
    }
    inline T merge_values(T& x,T& y){
        //return x+y;
        return min(x,y);
        //return max(x,y);
    }

    LazySegmentTree(){}
    LazySegmentTree(int sz,T te,S se):te(te),se(se){
        n=1;
        while(n<sz) n*=2;
        data.resize(2*n-1,te);
        lazy.resize(2*n-1,se);
    }

    void build(vector<T> &A){
        for(int k=0;k<int(A.size());k++) data[k+n-1]=A[k];
        for(int k=n-2;k>=0;k--) data[k]=merge_values(data[2*k+1],data[2*k+2]);
    }

    void eval(int k,int l,int r){
        if(lazy[k]==se) return;
        operate(data[k],lazy[k],r-l);
        if(r-l>1){
            merge_functions(lazy[2*k+1],lazy[k]);
            merge_functions(lazy[2*k+2],lazy[k]);
        }
        lazy[k]=se;
    }

    void update(int a,int b,S val,int k=0,int l=0,int r=-1){
        if(r<0) r=n;
        eval(k,l,r);
        if(b<=l||r<=a) return;
        if(a<=l&&r<=b){
            merge_functions(lazy[k],val);
            eval(k,l,r);
        }else{
            update(a,b,val,2*k+1,l,(l+r)/2);
            update(a,b,val,2*k+2,(l+r)/2,r);
            data[k]=merge_values(data[2*k+1],data[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 te;
        if(a<=l&&r<=b) return data[k];

        T vl=query(a,b,2*k+1,l,(l+r)/2);
        T vr=query(a,b,2*k+2,(l+r)/2,r);
        return merge_values(vl,vr);
    }
};

const ll INF=1e18;

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N,Q;
  cin>>N>>Q;

  LazySegmentTree<ll,ll> seg(N,INF,0);

  vector<ll> init(N,0);
  seg.build(init);

  for(int q=0;q<Q;q++){
      int t;cin>>t;
      if(t==0){
          int a,b;
          ll x;
          cin>>a>>b>>x;
          seg.update(a,b+1,x);
      }else{
          int a,b;
          cin>>a>>b;
          cout<<seg.query(a,b+1)<<"\n";
      }
  }

  return 0;
}