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:
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

//template
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(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 = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
void tostr(ll x,string& res){while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return;}
template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; }
template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; }
//template end

template<typename M,typename N=M>
struct LazySegmentTree{
    using F=function<M(M,M)>; using G=function<M(M,N)>; using H=function<N(N,N)>;
    int sz,height; vector<M> data; vector<N> lazy;
    const F f;const G g; const H h; const M m1; const N n1;
    LazySegmentTree(int n,const F f,const G g,const H h,const M &m1,const N n1):f(f),g(g),h(h),m1(m1),n1(n1){
        sz=1,height=0; while(sz<n)sz<<=1,height++;
        data.assign(2*sz,m1); lazy.assign(2*sz,n1);
    }
    void build(vector<M> v){
        rep(i,0,v.size())data[i+sz]=v[i];
        rrep(k,sz-1,0)data[k]=f(data[2*k],data[2*k+1]);
    }
    M ref(int k){return lazy[k]==n1?data[k]:g(data[k],lazy[k]);}
    void recalc(int k){while(k>>=1)data[k]=f(ref(2*k),ref(2*k+1));}
    void thrust(int k){rrep(i,height,0)eval(k>>i);}
    void eval(int k){
        if(lazy[k]!=n1){
            lazy[2*k]=h(lazy[2*k],lazy[k]); lazy[2*k+1]=h(lazy[2*k+1],lazy[k]);
            data[k]=ref(k); lazy[k]=n1;
        }
    }
    void update(int a,int b,N x){
        thrust(a+=sz); thrust(b+=sz-1);
        for(int l=a,r=b+1;l<r;l>>=1,r>>=1){
            if(l&1)lazy[l]=h(lazy[l],x),++l;
            if(r&1)--r,lazy[r]=h(lazy[r],x);
        }
        recalc(a); recalc(b);
    }
    M query(int a,int b){
        thrust(a+=sz); thrust(b+=sz-1);
        M L=m1,R=m1;
        for(int l=a,r=b+1;l<r;l>>=1,r>>=1){
            if(l&1)L=f(L,ref(l++)); if(r&1)R=f(ref(--r),R);
        } return f(L,R);
    }
};

int main(){
   int n,q; scanf("%d%d",&n,&q);
   LazySegmentTree<ll> seg(n,
   [](ll a,ll b){return min(a,b);},
   [](ll a,ll b){return a+b;},
   [](ll a,ll b){return a+b;},INF,0);
   seg.build(vector<ll>(n,0));
   rep(i,0,q){
       int tmp; scanf("%d",&tmp);
       if(tmp==0){
           int s,t,x; scanf("%d%d%d",&s,&t,&x);
           t++; seg.update(s,t,x);
       }
       else{
           int s,t; scanf("%d%d",&s,&t); t++;
           printf("%d\n",seg.query(s,t));
       }
   }
   return 0;
}