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 int long long
using namespace std;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }

class SegmentTree
{
 private:
    int n;
    vector<int> node,lazy;
 public:
    SegmentTree(int sz){
        n=1;
        while(n<sz) n*=2;
        node.assign(2*n-1,0);
        lazy.assign(2*n-1,0);
    }
    void update(int a,int b,int x,int k,int l,int r){
        if(a<=l and r<=b) node[k]+=x,lazy[k]+=x;
        else{
            if(lazy[k]!=0) push(k),lazy[k]=0;
            if(check(a,b,l,(l+r)/2)) update(a,b,x,2*k+1,l,(l+r)/2);
            if(check(a,b,(l+r)/2,r)) update(a,b,x,2*k+2,(l+r)/2,r);
            node[k]=min(node[2*k+1],node[2*k+2]);
        }
    }
    int get(int a,int b,int k,int l,int r){
        if(a<=l and r<=b) return node[k];
        else{
            if(lazy[k]!=0) push(k),lazy[k]=0;
            int res=INT_MAX;
            if(check(a,b,l,(l+r)/2)) res=min(res,get(a,b,2*k+1,l,(l+r)/2));
            if(check(a,b,(l+r)/2,r)) res=min(res,get(a,b,2*k+2,(l+r)/2,r));
            return res;
        }
    }
    void push(int k){
        node[2*k+1]+=lazy[k]; node[2*k+2]+=lazy[k];
        lazy[2*k+1]+=lazy[k]; lazy[2*k+2]+=lazy[k];
    }
    bool check(int a,int b,int l,int r){
        return max(a,l)<min(b,r);
    }
    void update(int a,int b,int x){ update(a,b,x,0,0,n); }
    int get(int a,int b){ return get(a,b,0,0,n); }
};

signed main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N,Q; cin>>N>>Q;
    SegmentTree seg(N);
    while(Q--){
        int q; cin>>q;
        if(q==0){
            int s,t,x; cin>>s>>t>>x;
            seg.update(s,t+1,x);
        }else{
            int s,t; cin>>s>>t;
            cout<<seg.get(s,t+1)<<endl;
        }
        // seg.print();
    }
    return 0;
}