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;
#define rep(i,a,b) for(int i=(a);i<b;i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;

const int inf=2147483647;

int N;
vector<int> val,laz;
vector<bool> flg;
void init(int sz){
   N=1; while(N<sz)N<<=1;
   val.resize(2*N,0); laz.resize(2*N,0);
   flg.resize(2*N,false);
}
void eval(int k,int l,int r){
   if(flg[k]){
      val[k]+=laz[k];
      if(r-l>1){
         laz[2*k+1]+=laz[k]; laz[2*k+2]+=laz[k];
         flg[2*k+1]=1; flg[2*k+2]=1;
      } laz[k]=0; flg[k]=0;
   }
}
void upd(int a,int b,int x,int k=0,int l=0,int r=N){
   eval(k,l,r);
   if(b<=l||r<=a)return;
   if(a<=l&&r<=b){
      laz[k]+=x; flg[k]=1; eval(k,l,r);
   }
   else{
      upd(a,b,x,2*k+1,l,(l+r)/2);
      upd(a,b,x,2*k+2,(l+r)/2,r);
      val[k]=min(val[2*k+1],val[2*k+2]);
   }
}
int que(int a,int b,int k=0,int l=0,int r=N){
   eval(k,l,r);
   if(b<=l||r<=a)return inf;
   if(a<=l&&r<=b)return val[k];
   int lb=que(a,b,2*k+1,l,(l+r)/2);
   int rb=que(a,b,2*k+2,(l+r)/2,r);
   return min(lb,rb);
}

int main(){
   int n,q; scanf("%d%d",&n,&q);
   init(n);
   rep(i,0,q){
      int tmp; scanf("%d",&tmp);
      if(tmp==0){
         int s,t,x; scanf("%d%d%d",&s,&t,&x); t++;
         upd(s,t,x);
      }
      else{
         int s,t; scanf("%d%d",&s,&t); t++;
         printf("%d\n",que(s,t));
      }
   }
   return 0;
}