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 int ll;
ll INF=100000000000;

int N,Q;
struct LazySegmentTree{
  private:
  int n; vector<ll> node,lazy;
  
  public:
  LazySegmentTree(vector<ll> v){
    int sz=(int)v.size();
    n=1;  while(n<sz)n*=2;
    node.resize(2*n-1);
    lazy.resize(2*n-1,0);
    for(int i=0;i<sz;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 eval(int k,int l,int 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];}
      lazy[k]=0;
    }
  }
  void add(int a,int b,ll x,int k=0,int l=0,int r=-1){
    if(r<0)r=n;
    eval(k,l,r);
    if(b<=l || r<=a)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);
      node[k]=min(node[2*k+1],node[2*k+2]);
    }
  }
  ll getsum(int a,int b,int k=0,int l=0,int r=-1){
    if(r<0)r=n;
    eval(k,l,r);
    if(b<=l || r<=a)return INF;
    if(a<=l && r<=b)return node[k];
    ll vl=getsum(a,b,2*k+1,l,(l+r)/2);
    ll vr=getsum(a,b,2*k+2,(l+r)/2,r);
    return min(vl,vr);
  }
};

int main(){
  cin >> N >> Q;
  LazySegmentTree seg(vector<ll>(N,0));
  for(int i=0;i<Q;i++){
    int q; cin >> q;
    if(q==0){
      int s,t,x; cin >> s >> t >> x;
      seg.add(s,t+1,x);
    }
    else{
      int s,t; cin >> s >> t;
      cout << seg.getsum(s,t+1) << endl;
    }
  }
}