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:
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
#define ll long long
#define rep(i,n) for(ll i=0;i<n;i++)
using namespace std;

const ll INF=1e9;

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

int main(){
    ll n;
    cin >> n;
    vector<ll> a(n,0);
    LazySegmentTree seg(a);
    ll q;
    cin >> q;
    while(q--){
        ll query;
        cin >> query;
        if(query==0){
            ll s,t,x;
            cin >> s >> t >> x;
            t++;
            seg.add(s,t,x);
        }
        if(query==1){
            ll s,t;
            cin >> s >> t;
            t++;
            cout << seg.getmin(s,t) << endl;
            
        }
    }
    return 0;
}