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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#include <unordered_map>
   
using namespace std;
typedef long long int ll;
typedef pair<int, int> P;
   
const int MAX_N=1<<17;

const ll INF=1e9;
    
ll mn[2*MAX_N-1], part[2*MAX_N-1];
bool mada[2*MAX_N-1];
int m;
   
void init(int n){
    m=1;
    while(m<n) m*=2;
}
  
void eval(int k, int l, int r){
    if(mada[k]){
        mn[k]+=part[k];
        if(k<m-1){
            part[2*k+1]+=part[k];
            part[2*k+2]+=part[k];
          mada[2*k+1]=1; mada[2*k+2]=1;
        }
        mada[k]=0;
      part[k]=0;
    }
}
    
void add(int a, int b, ll x, int k, int l, int r){
	eval(k, l, r);
	if(r<=a || b<=l) return;
    if(a<=l && r<=b){
        part[k]=x;
      mada[k]=1;
        eval(k, l, r);
    }else{
        add(a, b, x, k*2+1, l, (l+r)/2);
        add(a, b, x, k*2+2, (l+r)/2, r);
        mn[k]=min(mn[2*k+1], mn[2*k+2]);
    }
}
    
ll find(int a, int b, int k, int l, int r){
	eval(k, l, r);
    if(b<=l || r<=a){
        return INF;
    }
    if(a<=l && r<=b){
        return mn[k];
    }else{
        return min(find(a, b, 2*k+1, l, (l+r)/2), find(a, b, 2*k+2, (l+r)/2, r));
    }
}
   
int main()
{
    int n, q;
    cin>>n>>q;
    init(n);
    for(int i=0; i<q; i++){
        int tp;
        cin>>tp;
        if(tp==0){
            int s, t; ll x;
            cin>>s>>t>>x;
            add(s, t+1, x, 0, 0, m);
        }else{
            int s, t;
            cin>>s>>t;
            cout<<find(s, t+1, 0, 0, m)<<endl;
        }
    }
    return 0;
}