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 <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <queue>
#include <stack>
#include <tuple>
#include <cmath>
#include <iomanip>
#include <map>
#include <cstring> //memset(dp,0,sizeof(dp))
#include <functional>
#include <cctype>
#include <locale>
#define ll long long
#define rep(i,n) for(int i=0;i<(n);i++)
#define rrep(i,n) for(int i=n-1;i>=0;i--)
#define fi first
#define se second
#define pb push_back
#define ALL(a) (a).begin(),(a).end()
using namespace std;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
typedef pair<int,int> P;
typedef pair<long long,long long> Pll;
#define fout(num) cout << fixed << setprecision(20) << (num) << endl
//s[i]=tolower(s[i]); islower(s[i]); cout << tolower(s[i])はバグ
//vector<vector<ll>> dp(n,vector<ll>(n))
//exist x map o setconst ll MOD = 1e9+7;return fac[n]*(finv[k]*finv[n-k] % MOD) % MOD;

template<typename T>
struct LazySegmentTree{
private:
    int n;
    vector<T> node,lazy;
public:
    T SUP=0; /* 初期値　*/
    T merge(T x,T y){
        return min(x,y);
    }
    LazySegmentTree(vector<T> 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]=merge(node[2*i+1],node[2*i+2]);
        }
    }
    void eval(int idx,int l,int r){
        if(lazy[idx]!=0){
            node[idx]+=lazy[idx];
            if(r-l>1){
                /* node[idx]からの伝播  */
                lazy[2*idx+1]+=lazy[idx];
                lazy[2*idx+2]+=lazy[idx];
                
            }
            lazy[idx]=0;
        }
    }
    void update(int a,int b,T x,int idx=0,int l=0,int r=-1){
        if(r<0) r=n;
        eval(idx,l,r);
        if(b<=l||r<=a) return;
        if(a<=l&&r<=b){
            lazy[idx]+=x;
            eval(idx,l,r);
        }else{
            update(a,b,x,2*idx+1,l,(l+r)/2);
            update(a,b,x,2*idx+2,(l+r)/2,r);
            node[idx]=merge(node[2*idx+1],node[2*idx+2]);
        }
    }
    T query(int a,int b,int idx=0,int l=0,int r=-1){
        if(r<0) r=n;
        if(b<=l || r<=a) return 1e15;
        eval(idx,l,r);
        if(a<=l && r<=b) return node[idx];
        T vl = query(a,b,2*idx+1,l,(l+r)/2);
        T vr = query(a,b,2*idx+2,(l+r)/2,r);
        return merge(vl,vr);
    };
};



signed main(){
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int n,q; cin >> n >> q;
    vector<ll> v(n,0);
    LazySegmentTree<ll> lsg(v);
    rep(i,q){
        int x; cin >> x;
        if(x==0){
            int s,t,y; cin >> s >> t >> y;
            t++;
            lsg.update(s,t,y);
        }else{
            int s,t; cin >> s >> t;
            t++;
            cout << lsg.query(s,t) << "\n";
        }
    }

    
}