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<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<ll,ll> P;
typedef pair<int,int> Pi;
#define rep(i,n) for(ll i=0;i<n;i++)
#define FOR(i,a,b) for(ll i=a;i<b;i++)
#define fi first
#define se second
#define endl "\n"

template<typename T> inline bool chmax(T &a, T b){if(a<b){a=b;return true;}return false;}
template<typename T> inline bool chmin(T &a, T b){if(a>b){a=b;return true;}return false;}
template<typename T> ostream& operator<<(ostream& s,const complex<T>& d) {return s<<"("<<d.real()<<", "<<d.imag()<< ")";}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const pair<T1,T2>& d) {return s<<"("<<d.first<<", "<<d.second<<")";}
template<typename T> ostream& operator<<(ostream& s, const vector<T>& d){int len=d.size();rep(i,len){s<<d[i];if(i<len-1) s<<" ";}return s;}
template<typename T> ostream& operator<<(ostream& s,const vector<vector<T>>& d){int len=d.size();rep(i,len){s<<d[i]<<endl;}return s;}
template<typename T> ostream& operator<<(ostream& s,const set<T>& v){s<<"{ ";for(auto itr=v.begin();itr!=v.end();++itr) {if (itr!=v.begin()) {s<< ", ";}s<<(*itr);}s<<" }";return s;}
template<typename T> ostream& operator<<(ostream& s,const multiset<T>& v){s<<"{ ";for(auto itr=v.begin();itr!=v.end();++itr) {if (itr!=v.begin()) {s<< ", ";}s<<(*itr);}s<<" }";return s;}
template<typename T1, typename T2> ostream& operator<<(ostream& s,const map<T1,T2>& m){s<<"{"<<endl;for(auto itr=m.begin();itr!=m.end();++itr){s<<" "<<(*itr).first<<" : "<<(*itr).second<<endl;}s<<"}"<<endl;return s;}

const ll mod=1e9+7;
const ll inf=1e17;
const int INF=1e9;
const double EPS=1e-10;
const double PI=acos(-1);

//区間加算と区間最小値
/*
verified by
http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3982764#1
*/
struct StarrySkyTree{
private:
    int n;
    vector<ll> node,lazy;
    vector<bool> lazyFlag;
 
public:
    StarrySkyTree(){
        int sz=100050;
        n=1;
		while(n < sz) n*=2;
        node.resize(2*n-1,0);
        lazy.resize(2*n-1,0);
        lazyFlag.resize(2*n-1,false);
    }
    void build(const vector<ll> &v){
        int m=v.size();
        for(int i=0;i<m;i++) node[i+n-1]=v[i];
        for(int i=n-2;i>=0;i--) node[i]=min(node[2*i+1],node[2*i+2]);
    }
    void lazyEvaluate(int k,int l,int r){
        if(lazyFlag[k]){
            node[k]+=lazy[k];//一様更新なのでminの値もそれ足すだけでok
            if(r-l>1) {
                lazy[k*2+1]+=lazy[k];
                lazy[k*2+2]+=lazy[k];
                lazyFlag[k*2+1]=lazyFlag[k*2+2]=true;
            }
            lazyFlag[k]=false;
            lazy[k]=0;
        }
    }
    void update(int a,int b,ll x,int k=0,int l=0,int r=-1){
        if(r<0) r=n;
        lazyEvaluate(k,l,r);
        if(b<=l || r<=a) return ;
        if(a<=l && r<=b) {
            lazy[k]+=x;
            lazyFlag[k]=true;
            lazyEvaluate(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]);
        }
    }

    ll query(int a,int b,int k=0,int l=0,int r=-1){
      if(r<0) r=n;
      lazyEvaluate(k,l,r);
      if(r<=a || b<=l) return inf;
      if(a<=l && r<=b) return node[k];
      else{
        ll vl=query(a,b,2*k+1,l,(l+r)/2);
        ll vr=query(a,b,2*k+2,(l+r)/2,r);
        return min(vl,vr);
      }
	}
};

int main(){
    cin.tie(0);ios::sync_with_stdio(false);
    int n,q;
    cin>>n>>q;
    StarrySkyTree seg;
    while(q--){
        int c,s,t,x;
        cin>>c>>s>>t;
        if(c){
            cout<<seg.query(s,t+1)<<endl;
        }else{
            cin>>x;
            seg.update(s,t+1,x);
        }
    }
}