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>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(kbrni,n)cout<<" "<<a[kbrni];cout<<endl
#define svec(v) cout<<#v<<":";rep(kbrni,v.size())cout<<" "<<v[kbrni];cout<<endl
#define svecp(v) cout<<#v<<":";each(kbrni,v)cout<<" {"<<kbrni.first<<":"<<kbrni.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(kbrni,s)cout<<" "<<kbrni;cout<<endl
#define smap(m) cout<<#m<<":";each(kbrni,m)cout<<" {"<<kbrni.first<<":"<<kbrni.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template<typename T> class segtree {
private:
    int n,sz,h;
    vector<T> node, lazy;
    void eval(int k) {
        if(lazy[k]){
            node[k] += lazy[k];
            if(k < n) {
                lazy[k*2] += lazy[k], lazy[k*2+1] += lazy[k];
            }
            lazy[k] = 0;
        }
    }

public:
    segtree(vector<T>& v) : sz((int)v.size()), h(0) {
        n = 1;
        while(n < sz) n *= 2, h++;
        node.resize(2*n, numeric_limits<T>::max());
        lazy.resize(2*n, 0);
        for(int i = 0; i < sz; i++) node[i+n] = v[i];
        for(int i = n-1; i >= 1; i--) node[i] = min(node[2*i], node[2*i+1]);
    }
    void range(int a, int b, T x) {
        a += n, b += n - 1;
        for(int i = h; i > 0; i--) eval(a >> i), eval(b >> i);
        int ta = a, tb = b++;
        while(a < b){
            if(a & 1) lazy[a++] += x;
            if(b & 1) lazy[--b] += x;
            a >>= 1, b >>= 1;
        }
        while(ta >>= 1, tb >>= 1, ta){
            if(!lazy[ta]){
                eval(2*ta), eval(2*ta+1), node[ta] = min(node[2*ta], node[2*ta+1]);
            }
            if(!lazy[tb]){
                eval(2*tb), eval(2*tb+1), node[tb] = min(node[2*tb], node[2*tb+1]);
            }
        }
    }
    T query(int a, int b) {
        a += n, b += n - 1;
        for(int i = h; i > 0; i--) eval(a >> i), eval(b >> i);
        b++;
        T res1 = numeric_limits<T>::max(), res2 = numeric_limits<T>::max();
        while(a < b) {
            if(a & 1) eval(a), res1 = min(res1, node[a++]);
            if(b & 1) eval(--b), res2 = min(res2, node[b]);
            a >>= 1, b >>= 1;
        }
        return min(res1, res2);
    }
    void print() {
        for(int i = 0; i < sz; i++){
            pair<T,int> p;
            p = query(i,i+1);
            cout << "st[" << i << "]: " << p.fi << " " << p.se << endl;
        }
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n,q;
    cin >> n >> q;
    vl hoge(n, 0);
    segtree<ll> sg(hoge);
    rep(i,q){
        int a;
        cin >> a;
        if(a == 0){
            int s,t,x;
            cin >> s >> t >> x;
            sg.range(s,t+1,x);
        }else{
            int s,t;
            cin >> s >> t;
            cout << sg.query(s,t+1) << "\n";
        }
    }
    return 0;
}