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 FOR(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n)   FOR(i,0,n)
#define pb emplace_back
typedef long long ll;
typedef pair<int,int> pint;

const int MAX_N=1<<17;
const ll INF=(1ll<<31)-1;
//Range Sum Query
class Lz_segtree{
public:
    int n;
    ll e=0;
    ll init=0;
    vector<ll> dat,lz;
    Lz_segtree(int n_):n(n_){
        n=1;
        while(n<n_) n*=2;
        dat.resize(n*2,0);
        lz.resize(n*2,e);
    }
    void update_f(ll& d,ll x){
        d+=x;
    }
    ll dat_propergate(ll l,ll r){
        return min(l,r);
    }
    void lz_propergatef(ll& l,ll& r,ll x){
        l+=x,r+=x;
    }
    void eval(int len,int k){
        if(lz[k]!=e) update_f(dat[k],lz[k]);
        if(len>1){
            lz_propergatef(lz[k*2+1],lz[k*2+2],lz[k]);
        }
        lz[k]=e;
    }
    //range [a,b)
    void update(int a,int b,int k,int l,int r,ll x){
        eval(r-l,k);
        if(r<=a||b<=l) return;
        if(a<=l&&r<=b){
            update_f(lz[k],x);
            eval(r-l,k);
        }
        else{
            update(a,b,k*2+1,l,(l+r)/2,x);
            update(a,b,k*2+2,(l+r)/2,r,x);
            dat[k]=dat_propergate(dat[2*k+1],dat[2*k+2]);
        }
    }
    //range [a,b)
    ll query(int a,int b,int k,int l,int r){
        eval(r-l,k);
        if(r<=a||b<=l) return INF;
        if(a<=l&&r<=b) return dat[k];
        else{
            ll vl=query(a,b,k*2+1,l,(l+r)/2);
            ll vr=query(a,b,k*2+2,(l+r)/2,r);
            return dat_propergate(vl,vr);
        }
    }
    void update(int a,int b,ll x){
        return update(a,b,0,0,n,x);
    }
    ll query(int a,int b){
        return query(a,b,0,0,n);
    }
};

int main(){
    int n,q,c,s,t,x;
    cin>>n>>q;
    Lz_segtree seg(n);
    rep(i,q){
        cin>>c;
        if(c==0){
            cin>>s>>t>>x;
            seg.update(s,t+1,x);
        }
        else{
            cin>>s>>t;
            ll ans=seg.query(s,t+1);
            cout<<ans<<endl;
        }
    }
    return 0;
}