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;
typedef long long ll;
const ll INF=1000000010;
const ll MOD=1000000007;
const ll LINF=4000000000000000000;
struct LazySegmentTree{
private:
    int siz;
    vector<ll> node,lazy;
public:
    LazySegmentTree(int n){
        siz=1;
        while(siz<n)siz*=2;
        node.resize(2*siz-1);
        lazy.resize(2*siz-1);
    }
    void eval(int k){
        node[k]+=lazy[k];
        if(k<siz-1){
            lazy[2*k+1]+=lazy[k];
            lazy[2*k+2]+=lazy[k];
        }
        lazy[k]=0;
    }
    void update(int a,int b,ll x,int k,int l,int r){
        eval(k);
        if(b<=l||r<=a)return;
        if(a<=l&&r<=b){
            lazy[k]+=x;
            eval(k);
        }else{
            update(a,b,x,2*k+1,l,(l+r)/2);
            update(a,b,x,2*k+2,(l+r)/2,r);
            node[k]=min(node[2*k+1],node[2*k+2]);
        }
    }
    ll query(int a,int b,int k,int l,int r){
        eval(k);
        if(b<=l||r<=a)return INF;
        if(a<=l&&r<=b)return node[k];
        ll vl=query(a,b,2*k+1,l,(l+r)/2);
        ll vr=query(a,b,2*k+2,(l+r)/2,r);
        return min(vl,vr);
    }
    void add(int a,int b,ll x){
        update(a,b,x,0,0,siz);
    }
    ll getmin(int a,int b){
        return query(a,b,0,0,siz);
    }
};

int main(){
    int n,q;cin>>n>>q;
    LazySegmentTree tree(n);
    while(q--){
        int a;cin>>a;
        int s,t,x;
        if(a==1){
            cin>>s>>t;
            cout<<tree.getmin(s,t+1)<<endl;
        }else{
            cin>>s>>t>>x;
            tree.add(s,t+1,x);
        }
    }
}