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;
#define i_7 (ll)(1E9+7)
#define i_5 (ll)(1E9+5)
ll mod(ll a){
    ll c=a%i_7;
    if(c>=0)return c;
    else return c+i_7;
}
typedef pair<int,int> i_i;
typedef pair<ll,ll> l_l;
ll inf=(ll)1E17;
#define rep(i,l,r) for(ll i=l;i<=r;i++)
#define pb push_back
ll max(ll a,ll b){if(a<b)return b;else return a;}
ll min(ll a,ll b){if(a>b)return b;else return a;}
void Max(ll &pos,ll val){pos=max(pos,val);}//Max(dp[n],dp[n-1]);
void Min(ll &pos,ll val){pos=min(pos,val);}
void Add(ll &pos,ll val){pos=mod(pos+val);}
long double EPS=1E-8;
////////////////////////////////////////
//区間最大区間加算
struct RBQRAQ{
    ll n;
    vector<ll>data,lazy;
    RBQRAQ(ll vs){
        n=1;
        while(n<vs)n*=2;
        data.resize(2*n-1,0);
        lazy.resize(2*n-1,0);
    }
    void eval(ll k,ll l,ll r){
        if(lazy[k]!=0){
            data[k]+=lazy[k];
            if(r-l>1){
                lazy[2*k+1]+=lazy[k];
                lazy[2*k+2]+=lazy[k];
            }
            lazy[k]=0;
        }
    }
    void add(ll a,ll b,ll x,ll k,ll l,ll r){
        eval(k,l,r);
        if(r<=a||b<=l)return;
        if(a<=l&&r<=b){
            lazy[k]+=x;
            eval(k,l,r);
        }else{
            add(a,b,x,2*k+1,l,(l+r)/2);
            add(a,b,x,2*k+2,(l+r)/2,r);
            data[k]=max(data[2*k+1],data[2*k+2]);
        }
    }
    void add(ll a,ll b,ll x){add(a,b,x,0,0,n);}//[a,b)にxを加える
    ll query(ll a,ll b,ll k,ll l,ll r){
        eval(k,l,r);
        if(r<=a||b<=l)return -inf;
        if(a<=l&&r<=b){
            return data[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 max(vl,vr);
        }
    }
    ll query(ll a,ll b){return query(a,b,0,0,n);}//[a,b)の最大値
};
//////////////////////////////////////////////////////
int main(){
    ll n,q;cin>>n>>q;
    RBQRAQ r(n);
    while(q--){
        ll a,b,c,d;cin>>a;
        if(a==0){
            cin>>b>>c>>d;
            r.add(b,c+1,-d);
        }else{
            cin>>b>>c;
            cout<<-r.query(b,c+1)<<endl;
        }
    }
    
    return 0;
}