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<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll n,m,k,a,b,c,INF=1000000000;
vector<ll> node,lazy,v;
void ini(ll n){
    m=1;
    while(m<n)m*=2;
    node.resize(2*m-1,0);
    lazy.resize(2*m-1,0);
    //for(int i=n+m-1;i<2*m-1;i++)node[i]=INF;
    //for(int i=m-2;i>=0;i--)node[i]=min(node[2*i+1],node[2*i+2]);
    return ;
}
void eval(ll k,ll l,ll 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];
        }
        //else node[k]+=lazy[k];
        lazy[k]=0;
    }
    return ;
}
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,(r+l)/2);
        add(a,b,x,2*k+2,(r+l)/2,r);
        node[k]=min(node[2*k+1],node[2*k+2]);
    }
    return ;
}
ll getsum(ll a,ll b,ll k,ll l,ll r){
    if(a>=r||l>=b)return INF;
    eval(k,l,r);
    if(a<=l&&r<=b)return node[k];
    ll vl=getsum(a,b,2*k+1,l,(r+l)/2);
    ll vr=getsum(a,b,2*k+2,(r+l)/2,r);
    return min(vr,vl);
}
int main(void){
    cin>>n>>k;
    ini(n);
    for(int i=0;i<k;i++){
        cin>>a;
        if(a==0){
            cin>>a>>b>>c;
            add(a,b+1,c,0,0,m);
        }
        else{
            cin>>a>>b;
            cout<<getsum(a,b+1,0,0,m)<<endl;;
        }
        /*for(int i=0;i<2*m-1;i++){
            if(i==7)cout<<"||";
            cout<<node[i]<<"-"<<lazy[i]<<" ";
        }
        cout<<endl;*/
    }
}